Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(149,350)]
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([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.79476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 249.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.249 |
Dual form | 350.2.j.d.149.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 1.73205 | + | 1.00000i | 1.00000 | + | 0.577350i | 0.908248 | − | 0.418432i | \(-0.137420\pi\) |
0.0917517 | + | 0.995782i | \(0.470753\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | 1.73205 | + | 2.00000i | 0.654654 | + | 0.755929i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 1.73205 | − | 1.00000i | 0.500000 | − | 0.288675i | ||||
\(13\) | − | 1.00000i | − | 0.277350i | −0.990338 | − | 0.138675i | \(-0.955716\pi\) | ||
0.990338 | − | 0.138675i | \(-0.0442844\pi\) | |||||||
\(14\) | 2.50000 | + | 0.866025i | 0.668153 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −5.19615 | − | 3.00000i | −1.26025 | − | 0.727607i | −0.287129 | − | 0.957892i | \(-0.592701\pi\) |
−0.973123 | + | 0.230285i | \(0.926034\pi\) | |||||||
\(18\) | 0.866025 | + | 0.500000i | 0.204124 | + | 0.117851i | ||||
\(19\) | −0.500000 | − | 0.866025i | −0.114708 | − | 0.198680i | 0.802955 | − | 0.596040i | \(-0.203260\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | + | 5.19615i | 0.218218 | + | 1.13389i | ||||
\(22\) | 3.00000i | 0.639602i | ||||||||
\(23\) | 7.79423 | − | 4.50000i | 1.62521 | − | 0.938315i | 0.639713 | − | 0.768613i | \(-0.279053\pi\) |
0.985496 | − | 0.169701i | \(-0.0542803\pi\) | |||||||
\(24\) | 1.00000 | − | 1.73205i | 0.204124 | − | 0.353553i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.500000 | − | 0.866025i | −0.0980581 | − | 0.169842i | ||||
\(27\) | − | 4.00000i | − | 0.769800i | ||||||
\(28\) | 2.59808 | − | 0.500000i | 0.490990 | − | 0.0944911i | ||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | + | 6.92820i | −0.718421 | + | 1.24434i | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −5.19615 | + | 3.00000i | −0.904534 | + | 0.522233i | ||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.06218 | − | 3.50000i | 0.996616 | − | 0.575396i | 0.0893706 | − | 0.995998i | \(-0.471514\pi\) |
0.907245 | + | 0.420602i | \(0.138181\pi\) | |||||||
\(38\) | −0.866025 | − | 0.500000i | −0.140488 | − | 0.0811107i | ||||
\(39\) | 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 | \(0.424733\pi\) | |||||||
\(42\) | 3.46410 | + | 4.00000i | 0.534522 | + | 0.617213i | ||||
\(43\) | 2.00000i | 0.304997i | 0.988304 | + | 0.152499i | \(0.0487319\pi\) | ||||
−0.988304 | + | 0.152499i | \(0.951268\pi\) | |||||||
\(44\) | 1.50000 | + | 2.59808i | 0.226134 | + | 0.391675i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.50000 | − | 7.79423i | 0.663489 | − | 1.14920i | ||||
\(47\) | −7.79423 | + | 4.50000i | −1.13691 | + | 0.656392i | −0.945662 | − | 0.325150i | \(-0.894585\pi\) |
−0.191243 | + | 0.981543i | \(0.561252\pi\) | |||||||
\(48\) | − | 2.00000i | − | 0.288675i | ||||||
\(49\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | − | 10.3923i | −0.840168 | − | 1.45521i | ||||
\(52\) | −0.866025 | − | 0.500000i | −0.120096 | − | 0.0693375i | ||||
\(53\) | −7.79423 | − | 4.50000i | −1.07062 | − | 0.618123i | −0.142269 | − | 0.989828i | \(-0.545440\pi\) |
−0.928351 | + | 0.371706i | \(0.878773\pi\) | |||||||
\(54\) | −2.00000 | − | 3.46410i | −0.272166 | − | 0.471405i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.00000 | − | 1.73205i | 0.267261 | − | 0.231455i | ||||
\(57\) | − | 2.00000i | − | 0.264906i | ||||||
\(58\) | −5.19615 | + | 3.00000i | −0.682288 | + | 0.393919i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | 8.00000i | 1.01600i | ||||||||
\(63\) | −0.866025 | + | 2.50000i | −0.109109 | + | 0.314970i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.00000 | + | 5.19615i | −0.369274 | + | 0.639602i | ||||
\(67\) | 6.92820 | + | 4.00000i | 0.846415 | + | 0.488678i | 0.859440 | − | 0.511237i | \(-0.170813\pi\) |
−0.0130248 | + | 0.999915i | \(0.504146\pi\) | |||||||
\(68\) | −5.19615 | + | 3.00000i | −0.630126 | + | 0.363803i | ||||
\(69\) | 18.0000 | 2.16695 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | 3.46410 | + | 2.00000i | 0.405442 | + | 0.234082i | 0.688830 | − | 0.724923i | \(-0.258125\pi\) |
−0.283387 | + | 0.959006i | \(0.591458\pi\) | |||||||
\(74\) | 3.50000 | − | 6.06218i | 0.406867 | − | 0.704714i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −7.79423 | + | 1.50000i | −0.888235 | + | 0.170941i | ||||
\(78\) | − | 2.00000i | − | 0.226455i | ||||||
\(79\) | −5.00000 | − | 8.66025i | −0.562544 | − | 0.974355i | −0.997274 | − | 0.0737937i | \(-0.976489\pi\) |
0.434730 | − | 0.900561i | \(-0.356844\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | 2.59808 | − | 1.50000i | 0.286910 | − | 0.165647i | ||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 5.00000 | + | 1.73205i | 0.545545 | + | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.00000 | + | 1.73205i | 0.107833 | + | 0.186772i | ||||
\(87\) | −10.3923 | − | 6.00000i | −1.11417 | − | 0.643268i | ||||
\(88\) | 2.59808 | + | 1.50000i | 0.276956 | + | 0.159901i | ||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | − | 1.73205i | 0.209657 | − | 0.181568i | ||||
\(92\) | − | 9.00000i | − | 0.938315i | ||||||
\(93\) | −13.8564 | + | 8.00000i | −1.43684 | + | 0.829561i | ||||
\(94\) | −4.50000 | + | 7.79423i | −0.464140 | + | 0.803913i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | − | 1.73205i | −0.102062 | − | 0.176777i | ||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | 2.59808 | + | 6.50000i | 0.262445 | + | 0.656599i | ||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | + | 10.3923i | −0.597022 | + | 1.03407i | 0.396236 | + | 0.918149i | \(0.370316\pi\) |
−0.993258 | + | 0.115924i | \(0.963017\pi\) | |||||||
\(102\) | −10.3923 | − | 6.00000i | −1.02899 | − | 0.594089i | ||||
\(103\) | −3.46410 | + | 2.00000i | −0.341328 | + | 0.197066i | −0.660859 | − | 0.750510i | \(-0.729808\pi\) |
0.319531 | + | 0.947576i | \(0.396475\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.00000 | −0.874157 | ||||||||
\(107\) | 10.3923 | − | 6.00000i | 1.00466 | − | 0.580042i | 0.0950377 | − | 0.995474i | \(-0.469703\pi\) |
0.909624 | + | 0.415432i | \(0.136370\pi\) | |||||||
\(108\) | −3.46410 | − | 2.00000i | −0.333333 | − | 0.192450i | ||||
\(109\) | −8.00000 | + | 13.8564i | −0.766261 | + | 1.32720i | 0.173316 | + | 0.984866i | \(0.444552\pi\) |
−0.939577 | + | 0.342337i | \(0.888782\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.0000 | 1.32882 | ||||||||
\(112\) | 0.866025 | − | 2.50000i | 0.0818317 | − | 0.236228i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | −1.00000 | − | 1.73205i | −0.0936586 | − | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.00000 | + | 5.19615i | −0.278543 | + | 0.482451i | ||||
\(117\) | 0.866025 | − | 0.500000i | 0.0800641 | − | 0.0462250i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | − | 15.5885i | −0.275010 | − | 1.42899i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | −6.92820 | − | 4.00000i | −0.627250 | − | 0.362143i | ||||
\(123\) | 5.19615 | + | 3.00000i | 0.468521 | + | 0.270501i | ||||
\(124\) | 4.00000 | + | 6.92820i | 0.359211 | + | 0.622171i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.500000 | + | 2.59808i | 0.0445435 | + | 0.231455i | ||||
\(127\) | 1.00000i | 0.0887357i | 0.999015 | + | 0.0443678i | \(0.0141274\pi\) | ||||
−0.999015 | + | 0.0443678i | \(0.985873\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −2.00000 | + | 3.46410i | −0.176090 | + | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.50000 | − | 2.59808i | −0.131056 | − | 0.226995i | 0.793028 | − | 0.609185i | \(-0.208503\pi\) |
−0.924084 | + | 0.382190i | \(0.875170\pi\) | |||||||
\(132\) | 6.00000i | 0.522233i | ||||||||
\(133\) | 0.866025 | − | 2.50000i | 0.0750939 | − | 0.216777i | ||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | + | 5.19615i | −0.257248 | + | 0.445566i | ||||
\(137\) | 10.3923 | + | 6.00000i | 0.887875 | + | 0.512615i | 0.873247 | − | 0.487278i | \(-0.162010\pi\) |
0.0146279 | + | 0.999893i | \(0.495344\pi\) | |||||||
\(138\) | 15.5885 | − | 9.00000i | 1.32698 | − | 0.766131i | ||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.0000 | −1.51587 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.59808 | + | 1.50000i | 0.217262 | + | 0.125436i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.00000 | 0.331042 | ||||||||
\(147\) | −8.66025 | + | 11.0000i | −0.714286 | + | 0.907265i | ||||
\(148\) | − | 7.00000i | − | 0.575396i | ||||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | − | 8.66025i | 0.406894 | − | 0.704761i | −0.587646 | − | 0.809118i | \(-0.699945\pi\) |
0.994540 | + | 0.104357i | \(0.0332784\pi\) | |||||||
\(152\) | −0.866025 | + | 0.500000i | −0.0702439 | + | 0.0405554i | ||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | −6.00000 | + | 5.19615i | −0.483494 | + | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00000 | − | 1.73205i | −0.0800641 | − | 0.138675i | ||||
\(157\) | 19.9186 | + | 11.5000i | 1.58968 | + | 0.917800i | 0.993360 | + | 0.115050i | \(0.0367030\pi\) |
0.596316 | + | 0.802749i | \(0.296630\pi\) | |||||||
\(158\) | −8.66025 | − | 5.00000i | −0.688973 | − | 0.397779i | ||||
\(159\) | −9.00000 | − | 15.5885i | −0.713746 | − | 1.23625i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.5000 | + | 7.79423i | 1.77325 | + | 0.614271i | ||||
\(162\) | − | 11.0000i | − | 0.864242i | ||||||
\(163\) | 17.3205 | − | 10.0000i | 1.35665 | − | 0.783260i | 0.367477 | − | 0.930033i | \(-0.380222\pi\) |
0.989170 | + | 0.146772i | \(0.0468885\pi\) | |||||||
\(164\) | 1.50000 | − | 2.59808i | 0.117130 | − | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.00000i | − | 0.232147i | −0.993241 | − | 0.116073i | \(-0.962969\pi\) | ||
0.993241 | − | 0.116073i | \(-0.0370308\pi\) | |||||||
\(168\) | 5.19615 | − | 1.00000i | 0.400892 | − | 0.0771517i | ||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.500000 | − | 0.866025i | 0.0382360 | − | 0.0662266i | ||||
\(172\) | 1.73205 | + | 1.00000i | 0.132068 | + | 0.0762493i | ||||
\(173\) | 7.79423 | − | 4.50000i | 0.592584 | − | 0.342129i | −0.173534 | − | 0.984828i | \(-0.555519\pi\) |
0.766119 | + | 0.642699i | \(0.222185\pi\) | |||||||
\(174\) | −12.0000 | −0.909718 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.19615 | + | 3.00000i | 0.389468 | + | 0.224860i | ||||
\(179\) | −1.50000 | + | 2.59808i | −0.112115 | + | 0.194189i | −0.916623 | − | 0.399753i | \(-0.869096\pi\) |
0.804508 | + | 0.593942i | \(0.202429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0.866025 | − | 2.50000i | 0.0641941 | − | 0.185312i | ||||
\(183\) | − | 16.0000i | − | 1.18275i | ||||||
\(184\) | −4.50000 | − | 7.79423i | −0.331744 | − | 0.574598i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −8.00000 | + | 13.8564i | −0.586588 | + | 1.01600i | ||||
\(187\) | 15.5885 | − | 9.00000i | 1.13994 | − | 0.658145i | ||||
\(188\) | 9.00000i | 0.656392i | ||||||||
\(189\) | 8.00000 | − | 6.92820i | 0.581914 | − | 0.503953i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | − | 10.3923i | −0.434145 | − | 0.751961i | 0.563081 | − | 0.826402i | \(-0.309616\pi\) |
−0.997225 | + | 0.0744412i | \(0.976283\pi\) | |||||||
\(192\) | −1.73205 | − | 1.00000i | −0.125000 | − | 0.0721688i | ||||
\(193\) | 13.8564 | + | 8.00000i | 0.997406 | + | 0.575853i | 0.907480 | − | 0.420096i | \(-0.138004\pi\) |
0.0899262 | + | 0.995948i | \(0.471337\pi\) | |||||||
\(194\) | 5.00000 | + | 8.66025i | 0.358979 | + | 0.621770i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | + | 4.33013i | 0.392857 | + | 0.309295i | ||||
\(197\) | − | 15.0000i | − | 1.06871i | −0.845262 | − | 0.534353i | \(-0.820555\pi\) | ||
0.845262 | − | 0.534353i | \(-0.179445\pi\) | |||||||
\(198\) | −2.59808 | + | 1.50000i | −0.184637 | + | 0.106600i | ||||
\(199\) | −8.00000 | + | 13.8564i | −0.567105 | + | 0.982255i | 0.429745 | + | 0.902950i | \(0.358603\pi\) |
−0.996850 | + | 0.0793045i | \(0.974730\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | + | 13.8564i | 0.564276 | + | 0.977356i | ||||
\(202\) | 12.0000i | 0.844317i | ||||||||
\(203\) | −10.3923 | − | 12.0000i | −0.729397 | − | 0.842235i | ||||
\(204\) | −12.0000 | −0.840168 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.00000 | + | 3.46410i | −0.139347 | + | 0.241355i | ||||
\(207\) | 7.79423 | + | 4.50000i | 0.541736 | + | 0.312772i | ||||
\(208\) | −0.866025 | + | 0.500000i | −0.0600481 | + | 0.0346688i | ||||
\(209\) | 3.00000 | 0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0000 | 1.58339 | 0.791693 | − | 0.610920i | \(-0.209200\pi\) | ||||
0.791693 | + | 0.610920i | \(0.209200\pi\) | |||||||
\(212\) | −7.79423 | + | 4.50000i | −0.535310 | + | 0.309061i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | − | 10.3923i | 0.410152 | − | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | −20.7846 | + | 4.00000i | −1.41095 | + | 0.271538i | ||||
\(218\) | 16.0000i | 1.08366i | ||||||||
\(219\) | 4.00000 | + | 6.92820i | 0.270295 | + | 0.468165i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | + | 5.19615i | −0.201802 | + | 0.349531i | ||||
\(222\) | 12.1244 | − | 7.00000i | 0.813733 | − | 0.469809i | ||||
\(223\) | 8.00000i | 0.535720i | 0.963458 | + | 0.267860i | \(0.0863164\pi\) | ||||
−0.963458 | + | 0.267860i | \(0.913684\pi\) | |||||||
\(224\) | −0.500000 | − | 2.59808i | −0.0334077 | − | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.3923 | − | 6.00000i | −0.689761 | − | 0.398234i | 0.113761 | − | 0.993508i | \(-0.463710\pi\) |
−0.803523 | + | 0.595274i | \(0.797043\pi\) | |||||||
\(228\) | −1.73205 | − | 1.00000i | −0.114708 | − | 0.0662266i | ||||
\(229\) | −2.00000 | − | 3.46410i | −0.132164 | − | 0.228914i | 0.792347 | − | 0.610071i | \(-0.208859\pi\) |
−0.924510 | + | 0.381157i | \(0.875526\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.0000 | − | 5.19615i | −0.986928 | − | 0.341882i | ||||
\(232\) | 6.00000i | 0.393919i | ||||||||
\(233\) | −5.19615 | + | 3.00000i | −0.340411 | + | 0.196537i | −0.660454 | − | 0.750867i | \(-0.729636\pi\) |
0.320043 | + | 0.947403i | \(0.396303\pi\) | |||||||
\(234\) | 0.500000 | − | 0.866025i | 0.0326860 | − | 0.0566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 20.0000i | − | 1.29914i | ||||||
\(238\) | −10.3923 | − | 12.0000i | −0.673633 | − | 0.777844i | ||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | − | 0.866025i | 0.0322078 | − | 0.0557856i | −0.849472 | − | 0.527633i | \(-0.823079\pi\) |
0.881680 | + | 0.471848i | \(0.156413\pi\) | |||||||
\(242\) | 1.73205 | + | 1.00000i | 0.111340 | + | 0.0642824i | ||||
\(243\) | 8.66025 | − | 5.00000i | 0.555556 | − | 0.320750i | ||||
\(244\) | −8.00000 | −0.512148 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.00000 | 0.382546 | ||||||||
\(247\) | −0.866025 | + | 0.500000i | −0.0551039 | + | 0.0318142i | ||||
\(248\) | 6.92820 | + | 4.00000i | 0.439941 | + | 0.254000i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0000 | −0.946792 | −0.473396 | − | 0.880850i | \(-0.656972\pi\) | ||||
−0.473396 | + | 0.880850i | \(0.656972\pi\) | |||||||
\(252\) | 1.73205 | + | 2.00000i | 0.109109 | + | 0.125988i | ||||
\(253\) | 27.0000i | 1.69748i | ||||||||
\(254\) | 0.500000 | + | 0.866025i | 0.0313728 | + | 0.0543393i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(258\) | 4.00000i | 0.249029i | ||||||||
\(259\) | 17.5000 | + | 6.06218i | 1.08740 | + | 0.376685i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | −2.59808 | − | 1.50000i | −0.160510 | − | 0.0926703i | ||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 3.00000 | + | 5.19615i | 0.184637 | + | 0.319801i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.500000 | − | 2.59808i | −0.0306570 | − | 0.159298i | ||||
\(267\) | 12.0000i | 0.734388i | ||||||||
\(268\) | 6.92820 | − | 4.00000i | 0.423207 | − | 0.244339i | ||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | + | 13.8564i | 0.485965 | + | 0.841717i | 0.999870 | − | 0.0161307i | \(-0.00513477\pi\) |
−0.513905 | + | 0.857847i | \(0.671801\pi\) | |||||||
\(272\) | 6.00000i | 0.363803i | ||||||||
\(273\) | 5.19615 | − | 1.00000i | 0.314485 | − | 0.0605228i | ||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 9.00000 | − | 15.5885i | 0.541736 | − | 0.938315i | ||||
\(277\) | −8.66025 | − | 5.00000i | −0.520344 | − | 0.300421i | 0.216731 | − | 0.976231i | \(-0.430460\pi\) |
−0.737075 | + | 0.675810i | \(0.763794\pi\) | |||||||
\(278\) | 3.46410 | − | 2.00000i | 0.207763 | − | 0.119952i | ||||
\(279\) | −8.00000 | −0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.0000 | −1.61068 | −0.805342 | − | 0.592810i | \(-0.798019\pi\) | ||||
−0.805342 | + | 0.592810i | \(0.798019\pi\) | |||||||
\(282\) | −15.5885 | + | 9.00000i | −0.928279 | + | 0.535942i | ||||
\(283\) | −12.1244 | − | 7.00000i | −0.720718 | − | 0.416107i | 0.0942988 | − | 0.995544i | \(-0.469939\pi\) |
−0.815017 | + | 0.579437i | \(0.803272\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.00000 | 0.177394 | ||||||||
\(287\) | 5.19615 | + | 6.00000i | 0.306719 | + | 0.354169i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 9.50000 | + | 16.4545i | 0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.0000 | + | 17.3205i | −0.586210 | + | 1.01535i | ||||
\(292\) | 3.46410 | − | 2.00000i | 0.202721 | − | 0.117041i | ||||
\(293\) | − | 9.00000i | − | 0.525786i | −0.964825 | − | 0.262893i | \(-0.915323\pi\) | ||
0.964825 | − | 0.262893i | \(-0.0846766\pi\) | |||||||
\(294\) | −2.00000 | + | 13.8564i | −0.116642 | + | 0.808122i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.50000 | − | 6.06218i | −0.203433 | − | 0.352357i | ||||
\(297\) | 10.3923 | + | 6.00000i | 0.603023 | + | 0.348155i | ||||
\(298\) | −5.19615 | − | 3.00000i | −0.301005 | − | 0.173785i | ||||
\(299\) | −4.50000 | − | 7.79423i | −0.260242 | − | 0.450752i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | + | 3.46410i | −0.230556 | + | 0.199667i | ||||
\(302\) | − | 10.0000i | − | 0.575435i | ||||||
\(303\) | −20.7846 | + | 12.0000i | −1.19404 | + | 0.689382i | ||||
\(304\) | −0.500000 | + | 0.866025i | −0.0286770 | + | 0.0496700i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.00000 | − | 5.19615i | −0.171499 | − | 0.297044i | ||||
\(307\) | − | 14.0000i | − | 0.799022i | −0.916728 | − | 0.399511i | \(-0.869180\pi\) | ||
0.916728 | − | 0.399511i | \(-0.130820\pi\) | |||||||
\(308\) | −2.59808 | + | 7.50000i | −0.148039 | + | 0.427352i | ||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | −1.73205 | − | 1.00000i | −0.0980581 | − | 0.0566139i | ||||
\(313\) | −24.2487 | + | 14.0000i | −1.37062 | + | 0.791327i | −0.991006 | − | 0.133819i | \(-0.957276\pi\) |
−0.379612 | + | 0.925146i | \(0.623943\pi\) | |||||||
\(314\) | 23.0000 | 1.29797 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | −5.19615 | + | 3.00000i | −0.291845 | + | 0.168497i | −0.638774 | − | 0.769395i | \(-0.720558\pi\) |
0.346929 | + | 0.937892i | \(0.387225\pi\) | |||||||
\(318\) | −15.5885 | − | 9.00000i | −0.874157 | − | 0.504695i | ||||
\(319\) | 9.00000 | − | 15.5885i | 0.503903 | − | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.0000 | 1.33955 | ||||||||
\(322\) | 23.3827 | − | 4.50000i | 1.30307 | − | 0.250775i | ||||
\(323\) | 6.00000i | 0.333849i | ||||||||
\(324\) | −5.50000 | − | 9.52628i | −0.305556 | − | 0.529238i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.0000 | − | 17.3205i | 0.553849 | − | 0.959294i | ||||
\(327\) | −27.7128 | + | 16.0000i | −1.53252 | + | 0.884802i | ||||
\(328\) | − | 3.00000i | − | 0.165647i | ||||||
\(329\) | −22.5000 | − | 7.79423i | −1.24047 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.50000 | + | 6.06218i | 0.192377 | + | 0.333207i | 0.946038 | − | 0.324057i | \(-0.105047\pi\) |
−0.753660 | + | 0.657264i | \(0.771714\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.06218 | + | 3.50000i | 0.332205 | + | 0.191799i | ||||
\(334\) | −1.50000 | − | 2.59808i | −0.0820763 | − | 0.142160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.00000 | − | 3.46410i | 0.218218 | − | 0.188982i | ||||
\(337\) | 22.0000i | 1.19842i | 0.800593 | + | 0.599208i | \(0.204518\pi\) | ||||
−0.800593 | + | 0.599208i | \(0.795482\pi\) | |||||||
\(338\) | 10.3923 | − | 6.00000i | 0.565267 | − | 0.326357i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | − | 20.7846i | −0.649836 | − | 1.12555i | ||||
\(342\) | − | 1.00000i | − | 0.0540738i | ||||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | 2.00000 | 0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.50000 | − | 7.79423i | 0.241921 | − | 0.419020i | ||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | −10.3923 | + | 6.00000i | −0.557086 | + | 0.321634i | ||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | 2.59808 | − | 1.50000i | 0.138478 | − | 0.0799503i | ||||
\(353\) | −10.3923 | − | 6.00000i | −0.553127 | − | 0.319348i | 0.197256 | − | 0.980352i | \(-0.436797\pi\) |
−0.750382 | + | 0.661004i | \(0.770130\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 10.3923 | − | 30.0000i | 0.550019 | − | 1.58777i | ||||
\(358\) | 3.00000i | 0.158555i | ||||||||
\(359\) | 9.00000 | + | 15.5885i | 0.475002 | + | 0.822727i | 0.999590 | − | 0.0286287i | \(-0.00911406\pi\) |
−0.524588 | + | 0.851356i | \(0.675781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | − | 15.5885i | 0.473684 | − | 0.820445i | ||||
\(362\) | 1.73205 | − | 1.00000i | 0.0910346 | − | 0.0525588i | ||||
\(363\) | 4.00000i | 0.209946i | ||||||||
\(364\) | −0.500000 | − | 2.59808i | −0.0262071 | − | 0.136176i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.00000 | − | 13.8564i | −0.418167 | − | 0.724286i | ||||
\(367\) | −16.4545 | − | 9.50000i | −0.858917 | − | 0.495896i | 0.00473247 | − | 0.999989i | \(-0.498494\pi\) |
−0.863649 | + | 0.504093i | \(0.831827\pi\) | |||||||
\(368\) | −7.79423 | − | 4.50000i | −0.406302 | − | 0.234579i | ||||
\(369\) | 1.50000 | + | 2.59808i | 0.0780869 | + | 0.135250i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.50000 | − | 23.3827i | −0.233628 | − | 1.21397i | ||||
\(372\) | 16.0000i | 0.829561i | ||||||||
\(373\) | 1.73205 | − | 1.00000i | 0.0896822 | − | 0.0517780i | −0.454488 | − | 0.890753i | \(-0.650178\pi\) |
0.544170 | + | 0.838975i | \(0.316844\pi\) | |||||||
\(374\) | 9.00000 | − | 15.5885i | 0.465379 | − | 0.806060i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.50000 | + | 7.79423i | 0.232070 | + | 0.401957i | ||||
\(377\) | 6.00000i | 0.309016i | ||||||||
\(378\) | 3.46410 | − | 10.0000i | 0.178174 | − | 0.514344i | ||||
\(379\) | −23.0000 | −1.18143 | −0.590715 | − | 0.806880i | \(-0.701154\pi\) | ||||
−0.590715 | + | 0.806880i | \(0.701154\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.00000 | + | 1.73205i | −0.0512316 | + | 0.0887357i | ||||
\(382\) | −10.3923 | − | 6.00000i | −0.531717 | − | 0.306987i | ||||
\(383\) | 18.1865 | − | 10.5000i | 0.929288 | − | 0.536525i | 0.0427020 | − | 0.999088i | \(-0.486403\pi\) |
0.886586 | + | 0.462563i | \(0.153070\pi\) | |||||||
\(384\) | −2.00000 | −0.102062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.0000 | 0.814379 | ||||||||
\(387\) | −1.73205 | + | 1.00000i | −0.0880451 | + | 0.0508329i | ||||
\(388\) | 8.66025 | + | 5.00000i | 0.439658 | + | 0.253837i | ||||
\(389\) | −6.00000 | + | 10.3923i | −0.304212 | + | 0.526911i | −0.977086 | − | 0.212847i | \(-0.931726\pi\) |
0.672874 | + | 0.739758i | \(0.265060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −54.0000 | −2.73090 | ||||||||
\(392\) | 6.92820 | + | 1.00000i | 0.349927 | + | 0.0505076i | ||||
\(393\) | − | 6.00000i | − | 0.302660i | ||||||
\(394\) | −7.50000 | − | 12.9904i | −0.377845 | − | 0.654446i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.50000 | + | 2.59808i | −0.0753778 | + | 0.130558i | ||||
\(397\) | −12.1244 | + | 7.00000i | −0.608504 | + | 0.351320i | −0.772380 | − | 0.635161i | \(-0.780934\pi\) |
0.163876 | + | 0.986481i | \(0.447600\pi\) | |||||||
\(398\) | 16.0000i | 0.802008i | ||||||||
\(399\) | 4.00000 | − | 3.46410i | 0.200250 | − | 0.173422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.5000 | + | 23.3827i | 0.674158 | + | 1.16768i | 0.976714 | + | 0.214544i | \(0.0688266\pi\) |
−0.302556 | + | 0.953131i | \(0.597840\pi\) | |||||||
\(402\) | 13.8564 | + | 8.00000i | 0.691095 | + | 0.399004i | ||||
\(403\) | 6.92820 | + | 4.00000i | 0.345118 | + | 0.199254i | ||||
\(404\) | 6.00000 | + | 10.3923i | 0.298511 | + | 0.517036i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.0000 | − | 5.19615i | −0.744438 | − | 0.257881i | ||||
\(407\) | 21.0000i | 1.04093i | ||||||||
\(408\) | −10.3923 | + | 6.00000i | −0.514496 | + | 0.297044i | ||||
\(409\) | 13.0000 | − | 22.5167i | 0.642809 | − | 1.11338i | −0.341994 | − | 0.939702i | \(-0.611102\pi\) |
0.984803 | − | 0.173675i | \(-0.0555643\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000 | + | 20.7846i | 0.591916 | + | 1.02523i | ||||
\(412\) | 4.00000i | 0.197066i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9.00000 | 0.442326 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.500000 | + | 0.866025i | −0.0245145 | + | 0.0424604i | ||||
\(417\) | 6.92820 | + | 4.00000i | 0.339276 | + | 0.195881i | ||||
\(418\) | 2.59808 | − | 1.50000i | 0.127076 | − | 0.0733674i | ||||
\(419\) | 9.00000 | 0.439679 | 0.219839 | − | 0.975536i | \(-0.429447\pi\) | ||||
0.219839 | + | 0.975536i | \(0.429447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | 19.9186 | − | 11.5000i | 0.969622 | − | 0.559811i | ||||
\(423\) | −7.79423 | − | 4.50000i | −0.378968 | − | 0.218797i | ||||
\(424\) | −4.50000 | + | 7.79423i | −0.218539 | + | 0.378521i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.92820 | − | 20.0000i | 0.335279 | − | 0.967868i | ||||
\(428\) | − | 12.0000i | − | 0.580042i | ||||||
\(429\) | 3.00000 | + | 5.19615i | 0.144841 | + | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.00000 | + | 10.3923i | −0.289010 | + | 0.500580i | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | −3.46410 | + | 2.00000i | −0.166667 | + | 0.0962250i | ||||
\(433\) | − | 40.0000i | − | 1.92228i | −0.276066 | − | 0.961139i | \(-0.589031\pi\) | ||
0.276066 | − | 0.961139i | \(-0.410969\pi\) | |||||||
\(434\) | −16.0000 | + | 13.8564i | −0.768025 | + | 0.665129i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.00000 | + | 13.8564i | 0.383131 | + | 0.663602i | ||||
\(437\) | −7.79423 | − | 4.50000i | −0.372849 | − | 0.215264i | ||||
\(438\) | 6.92820 | + | 4.00000i | 0.331042 | + | 0.191127i | ||||
\(439\) | 13.0000 | + | 22.5167i | 0.620456 | + | 1.07466i | 0.989401 | + | 0.145210i | \(0.0463858\pi\) |
−0.368945 | + | 0.929451i | \(0.620281\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50000 | + | 2.59808i | −0.309524 | + | 0.123718i | ||||
\(442\) | 6.00000i | 0.285391i | ||||||||
\(443\) | 10.3923 | − | 6.00000i | 0.493753 | − | 0.285069i | −0.232377 | − | 0.972626i | \(-0.574650\pi\) |
0.726130 | + | 0.687557i | \(0.241317\pi\) | |||||||
\(444\) | 7.00000 | − | 12.1244i | 0.332205 | − | 0.575396i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.00000 | + | 6.92820i | 0.189405 | + | 0.328060i | ||||
\(447\) | − | 12.0000i | − | 0.567581i | ||||||
\(448\) | −1.73205 | − | 2.00000i | −0.0818317 | − | 0.0944911i | ||||
\(449\) | −21.0000 | −0.991051 | −0.495526 | − | 0.868593i | \(-0.665025\pi\) | ||||
−0.495526 | + | 0.868593i | \(0.665025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.50000 | + | 7.79423i | −0.211897 | + | 0.367016i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.3205 | − | 10.0000i | 0.813788 | − | 0.469841i | ||||
\(454\) | −12.0000 | −0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | −12.1244 | + | 7.00000i | −0.567153 | + | 0.327446i | −0.756012 | − | 0.654558i | \(-0.772855\pi\) |
0.188858 | + | 0.982004i | \(0.439521\pi\) | |||||||
\(458\) | −3.46410 | − | 2.00000i | −0.161867 | − | 0.0934539i | ||||
\(459\) | −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 | \(0.746202\pi\) | |||||||
\(462\) | −15.5885 | + | 3.00000i | −0.725241 | + | 0.139573i | ||||
\(463\) | − | 1.00000i | − | 0.0464739i | −0.999730 | − | 0.0232370i | \(-0.992603\pi\) | ||
0.999730 | − | 0.0232370i | \(-0.00739722\pi\) | |||||||
\(464\) | 3.00000 | + | 5.19615i | 0.139272 | + | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | + | 5.19615i | −0.138972 | + | 0.240707i | ||||
\(467\) | 5.19615 | − | 3.00000i | 0.240449 | − | 0.138823i | −0.374934 | − | 0.927052i | \(-0.622335\pi\) |
0.615383 | + | 0.788228i | \(0.289001\pi\) | |||||||
\(468\) | − | 1.00000i | − | 0.0462250i | ||||||
\(469\) | 4.00000 | + | 20.7846i | 0.184703 | + | 0.959744i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.0000 | + | 39.8372i | 1.05978 | + | 1.83560i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.19615 | − | 3.00000i | −0.238919 | − | 0.137940i | ||||
\(474\) | −10.0000 | − | 17.3205i | −0.459315 | − | 0.795557i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −15.0000 | − | 5.19615i | −0.687524 | − | 0.238165i | ||||
\(477\) | − | 9.00000i | − | 0.412082i | ||||||
\(478\) | 5.19615 | − | 3.00000i | 0.237666 | − | 0.137217i | ||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.50000 | − | 6.06218i | −0.159586 | − | 0.276412i | ||||
\(482\) | − | 1.00000i | − | 0.0455488i | ||||||
\(483\) | 31.1769 | + | 36.0000i | 1.41860 | + | 1.63806i | ||||
\(484\) | 2.00000 | 0.0909091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.00000 | − | 8.66025i | 0.226805 | − | 0.392837i | ||||
\(487\) | −13.8564 | − | 8.00000i | −0.627894 | − | 0.362515i | 0.152042 | − | 0.988374i | \(-0.451415\pi\) |
−0.779936 | + | 0.625859i | \(0.784748\pi\) | |||||||
\(488\) | −6.92820 | + | 4.00000i | −0.313625 | + | 0.181071i | ||||
\(489\) | 40.0000 | 1.80886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.0000 | 1.62466 | 0.812329 | − | 0.583200i | \(-0.198200\pi\) | ||||
0.812329 | + | 0.583200i | \(0.198200\pi\) | |||||||
\(492\) | 5.19615 | − | 3.00000i | 0.234261 | − | 0.135250i | ||||
\(493\) | 31.1769 | + | 18.0000i | 1.40414 | + | 0.810679i | ||||
\(494\) | −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 | \(-0.195204\pi\) |
−0.907314 | + | 0.420455i | \(0.861871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.00000 | − | 5.19615i | 0.134030 | − | 0.232147i | ||||
\(502\) | −12.9904 | + | 7.50000i | −0.579789 | + | 0.334741i | ||||
\(503\) | 24.0000i | 1.07011i | 0.844818 | + | 0.535054i | \(0.179709\pi\) | ||||
−0.844818 | + | 0.535054i | \(0.820291\pi\) | |||||||
\(504\) | 2.50000 | + | 0.866025i | 0.111359 | + | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 13.5000 | + | 23.3827i | 0.600148 | + | 1.03949i | ||||
\(507\) | 20.7846 | + | 12.0000i | 0.923077 | + | 0.532939i | ||||
\(508\) | 0.866025 | + | 0.500000i | 0.0384237 | + | 0.0221839i | ||||
\(509\) | −21.0000 | − | 36.3731i | −0.930809 | − | 1.61221i | −0.781943 | − | 0.623350i | \(-0.785771\pi\) |
−0.148866 | − | 0.988857i | \(-0.547562\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | + | 10.3923i | 0.0884748 | + | 0.459728i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −3.46410 | + | 2.00000i | −0.152944 | + | 0.0883022i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.00000 | + | 3.46410i | 0.0880451 | + | 0.152499i | ||||
\(517\) | − | 27.0000i | − | 1.18746i | ||||||
\(518\) | 18.1865 | − | 3.50000i | 0.799070 | − | 0.153781i | ||||
\(519\) | 18.0000 | 0.790112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.50000 | − | 12.9904i | 0.328581 | − | 0.569119i | −0.653650 | − | 0.756797i | \(-0.726763\pi\) |
0.982231 | + | 0.187678i | \(0.0600963\pi\) | |||||||
\(522\) | −5.19615 | − | 3.00000i | −0.227429 | − | 0.131306i | ||||
\(523\) | −24.2487 | + | 14.0000i | −1.06032 | + | 0.612177i | −0.925521 | − | 0.378695i | \(-0.876373\pi\) |
−0.134801 | + | 0.990873i | \(0.543039\pi\) | |||||||
\(524\) | −3.00000 | −0.131056 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 41.5692 | − | 24.0000i | 1.81078 | − | 1.04546i | ||||
\(528\) | 5.19615 | + | 3.00000i | 0.226134 | + | 0.130558i | ||||
\(529\) | 29.0000 | − | 50.2295i | 1.26087 | − | 2.18389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.73205 | − | 2.00000i | −0.0750939 | − | 0.0867110i | ||||
\(533\) | − | 3.00000i | − | 0.129944i | ||||||
\(534\) | 6.00000 | + | 10.3923i | 0.259645 | + | 0.449719i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.00000 | − | 6.92820i | 0.172774 | − | 0.299253i | ||||
\(537\) | −5.19615 | + | 3.00000i | −0.224231 | + | 0.129460i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.5000 | − | 12.9904i | −0.710705 | − | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00000 | − | 6.92820i | −0.171973 | − | 0.297867i | 0.767136 | − | 0.641484i | \(-0.221681\pi\) |
−0.939110 | + | 0.343617i | \(0.888348\pi\) | |||||||
\(542\) | 13.8564 | + | 8.00000i | 0.595184 | + | 0.343629i | ||||
\(543\) | 3.46410 | + | 2.00000i | 0.148659 | + | 0.0858282i | ||||
\(544\) | 3.00000 | + | 5.19615i | 0.128624 | + | 0.222783i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.00000 | − | 3.46410i | 0.171184 | − | 0.148250i | ||||
\(547\) | − | 8.00000i | − | 0.342055i | −0.985266 | − | 0.171028i | \(-0.945291\pi\) | ||
0.985266 | − | 0.171028i | \(-0.0547087\pi\) | |||||||
\(548\) | 10.3923 | − | 6.00000i | 0.443937 | − | 0.256307i | ||||
\(549\) | 4.00000 | − | 6.92820i | 0.170716 | − | 0.295689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.00000 | + | 5.19615i | 0.127804 | + | 0.221364i | ||||
\(552\) | − | 18.0000i | − | 0.766131i | ||||||
\(553\) | 8.66025 | − | 25.0000i | 0.368271 | − | 1.06311i | ||||
\(554\) | −10.0000 | −0.424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | − | 3.46410i | 0.0848189 | − | 0.146911i | ||||
\(557\) | −7.79423 | − | 4.50000i | −0.330252 | − | 0.190671i | 0.325701 | − | 0.945473i | \(-0.394400\pi\) |
−0.655953 | + | 0.754802i | \(0.727733\pi\) | |||||||
\(558\) | −6.92820 | + | 4.00000i | −0.293294 | + | 0.169334i | ||||
\(559\) | 2.00000 | 0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.0000 | 1.51992 | ||||||||
\(562\) | −23.3827 | + | 13.5000i | −0.986339 | + | 0.569463i | ||||
\(563\) | −36.3731 | − | 21.0000i | −1.53294 | − | 0.885044i | −0.999224 | − | 0.0393818i | \(-0.987461\pi\) |
−0.533718 | − | 0.845663i | \(-0.679206\pi\) | |||||||
\(564\) | −9.00000 | + | 15.5885i | −0.378968 | + | 0.656392i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.0000 | −0.588464 | ||||||||
\(567\) | 28.5788 | − | 5.50000i | 1.20020 | − | 0.230978i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.5000 | + | 18.1865i | 0.440183 | + | 0.762419i | 0.997703 | − | 0.0677445i | \(-0.0215803\pi\) |
−0.557520 | + | 0.830164i | \(0.688247\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 2.59808 | − | 1.50000i | 0.108631 | − | 0.0627182i | ||||
\(573\) | − | 24.0000i | − | 1.00261i | ||||||
\(574\) | 7.50000 | + | 2.59808i | 0.313044 | + | 0.108442i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 38.1051 | + | 22.0000i | 1.58634 | + | 0.915872i | 0.993904 | + | 0.110252i | \(0.0351659\pi\) |
0.592433 | + | 0.805620i | \(0.298167\pi\) | |||||||
\(578\) | 16.4545 | + | 9.50000i | 0.684416 | + | 0.395148i | ||||
\(579\) | 16.0000 | + | 27.7128i | 0.664937 | + | 1.15171i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 20.0000i | 0.829027i | ||||||||
\(583\) | 23.3827 | − | 13.5000i | 0.968412 | − | 0.559113i | ||||
\(584\) | 2.00000 | − | 3.46410i | 0.0827606 | − | 0.143346i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.50000 | − | 7.79423i | −0.185893 | − | 0.321977i | ||||
\(587\) | 24.0000i | 0.990586i | 0.868726 | + | 0.495293i | \(0.164939\pi\) | ||||
−0.868726 | + | 0.495293i | \(0.835061\pi\) | |||||||
\(588\) | 5.19615 | + | 13.0000i | 0.214286 | + | 0.536111i | ||||
\(589\) | 8.00000 | 0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.0000 | − | 25.9808i | 0.617018 | − | 1.06871i | ||||
\(592\) | −6.06218 | − | 3.50000i | −0.249154 | − | 0.143849i | ||||
\(593\) | 20.7846 | − | 12.0000i | 0.853522 | − | 0.492781i | −0.00831589 | − | 0.999965i | \(-0.502647\pi\) |
0.861838 | + | 0.507184i | \(0.169314\pi\) | |||||||
\(594\) | 12.0000 | 0.492366 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | −27.7128 | + | 16.0000i | −1.13421 | + | 0.654836i | ||||
\(598\) | −7.79423 | − | 4.50000i | −0.318730 | − | 0.184019i | ||||
\(599\) | −21.0000 | + | 36.3731i | −0.858037 | + | 1.48616i | 0.0157622 | + | 0.999876i | \(0.494983\pi\) |
−0.873799 | + | 0.486287i | \(0.838351\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | −1.73205 | + | 5.00000i | −0.0705931 | + | 0.203785i | ||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | −5.00000 | − | 8.66025i | −0.203447 | − | 0.352381i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.0000 | + | 20.7846i | −0.487467 | + | 0.844317i | ||||
\(607\) | 0.866025 | − | 0.500000i | 0.0351509 | − | 0.0202944i | −0.482322 | − | 0.875994i | \(-0.660206\pi\) |
0.517472 | + | 0.855700i | \(0.326873\pi\) | |||||||
\(608\) | 1.00000i | 0.0405554i | ||||||||
\(609\) | −6.00000 | − | 31.1769i | −0.243132 | − | 1.26335i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.50000 | + | 7.79423i | 0.182051 | + | 0.315321i | ||||
\(612\) | −5.19615 | − | 3.00000i | −0.210042 | − | 0.121268i | ||||
\(613\) | −25.1147 | − | 14.5000i | −1.01437 | − | 0.585649i | −0.101905 | − | 0.994794i | \(-0.532494\pi\) |
−0.912470 | + | 0.409145i | \(0.865827\pi\) | |||||||
\(614\) | −7.00000 | − | 12.1244i | −0.282497 | − | 0.489299i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.50000 | + | 7.79423i | 0.0604367 | + | 0.314038i | ||||
\(617\) | 18.0000i | 0.724653i | 0.932051 | + | 0.362326i | \(0.118017\pi\) | ||||
−0.932051 | + | 0.362326i | \(0.881983\pi\) | |||||||
\(618\) | −6.92820 | + | 4.00000i | −0.278693 | + | 0.160904i | ||||
\(619\) | 11.5000 | − | 19.9186i | 0.462224 | − | 0.800595i | −0.536847 | − | 0.843679i | \(-0.680385\pi\) |
0.999071 | + | 0.0430838i | \(0.0137183\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.0000 | − | 31.1769i | −0.722315 | − | 1.25109i | ||||
\(622\) | − | 24.0000i | − | 0.962312i | ||||||
\(623\) | −5.19615 | + | 15.0000i | −0.208179 | + | 0.600962i | ||||
\(624\) | −2.00000 | −0.0800641 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.0000 | + | 24.2487i | −0.559553 | + | 0.969173i | ||||
\(627\) | 5.19615 | + | 3.00000i | 0.207514 | + | 0.119808i | ||||
\(628\) | 19.9186 | − | 11.5000i | 0.794838 | − | 0.458900i | ||||
\(629\) | −42.0000 | −1.67465 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | −8.66025 | + | 5.00000i | −0.344486 | + | 0.198889i | ||||
\(633\) | 39.8372 | + | 23.0000i | 1.58339 | + | 0.914168i | ||||
\(634\) | −3.00000 | + | 5.19615i | −0.119145 | + | 0.206366i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −18.0000 | −0.713746 | ||||||||
\(637\) | 6.92820 | + | 1.00000i | 0.274505 | + | 0.0396214i | ||||
\(638\) | − | 18.0000i | − | 0.712627i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.5000 | + | 23.3827i | −0.533218 | + | 0.923561i | 0.466029 | + | 0.884769i | \(0.345684\pi\) |
−0.999247 | + | 0.0387913i | \(0.987649\pi\) | |||||||
\(642\) | 20.7846 | − | 12.0000i | 0.820303 | − | 0.473602i | ||||
\(643\) | 2.00000i | 0.0788723i | 0.999222 | + | 0.0394362i | \(0.0125562\pi\) | ||||
−0.999222 | + | 0.0394362i | \(0.987444\pi\) | |||||||
\(644\) | 18.0000 | − | 15.5885i | 0.709299 | − | 0.614271i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.00000 | + | 5.19615i | 0.118033 | + | 0.204440i | ||||
\(647\) | 28.5788 | + | 16.5000i | 1.12355 | + | 0.648682i | 0.942305 | − | 0.334756i | \(-0.108654\pi\) |
0.181245 | + | 0.983438i | \(0.441987\pi\) | |||||||
\(648\) | −9.52628 | − | 5.50000i | −0.374228 | − | 0.216060i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −40.0000 | − | 13.8564i | −1.56772 | − | 0.543075i | ||||
\(652\) | − | 20.0000i | − | 0.783260i | ||||||
\(653\) | −7.79423 | + | 4.50000i | −0.305012 | + | 0.176099i | −0.644692 | − | 0.764442i | \(-0.723014\pi\) |
0.339680 | + | 0.940541i | \(0.389681\pi\) | |||||||
\(654\) | −16.0000 | + | 27.7128i | −0.625650 | + | 1.08366i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.50000 | − | 2.59808i | −0.0585652 | − | 0.101438i | ||||
\(657\) | 4.00000i | 0.156055i | ||||||||
\(658\) | −23.3827 | + | 4.50000i | −0.911552 | + | 0.175428i | ||||
\(659\) | 24.0000 | 0.934907 | 0.467454 | − | 0.884018i | \(-0.345171\pi\) | ||||
0.467454 | + | 0.884018i | \(0.345171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0000 | − | 24.2487i | 0.544537 | − | 0.943166i | −0.454099 | − | 0.890951i | \(-0.650039\pi\) |
0.998636 | − | 0.0522143i | \(-0.0166279\pi\) | |||||||
\(662\) | 6.06218 | + | 3.50000i | 0.235613 | + | 0.136031i | ||||
\(663\) | −10.3923 | + | 6.00000i | −0.403604 | + | 0.233021i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.00000 | 0.271244 | ||||||||
\(667\) | −46.7654 | + | 27.0000i | −1.81076 | + | 1.04544i | ||||
\(668\) | −2.59808 | − | 1.50000i | −0.100523 | − | 0.0580367i | ||||
\(669\) | −8.00000 | + | 13.8564i | −0.309298 | + | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 1.73205 | − | 5.00000i | 0.0668153 | − | 0.192879i | ||||
\(673\) | − | 34.0000i | − | 1.31060i | −0.755367 | − | 0.655302i | \(-0.772541\pi\) | ||
0.755367 | − | 0.655302i | \(-0.227459\pi\) | |||||||
\(674\) | 11.0000 | + | 19.0526i | 0.423704 | + | 0.733877i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.00000 | − | 10.3923i | 0.230769 | − | 0.399704i | ||||
\(677\) | 7.79423 | − | 4.50000i | 0.299557 | − | 0.172949i | −0.342687 | − | 0.939450i | \(-0.611337\pi\) |
0.642244 | + | 0.766501i | \(0.278004\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.0000 | + | 17.3205i | −0.767530 | + | 0.664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | − | 20.7846i | −0.459841 | − | 0.796468i | ||||
\(682\) | −20.7846 | − | 12.0000i | −0.795884 | − | 0.459504i | ||||
\(683\) | −10.3923 | − | 6.00000i | −0.397650 | − | 0.229584i | 0.287819 | − | 0.957685i | \(-0.407070\pi\) |
−0.685470 | + | 0.728101i | \(0.740403\pi\) | |||||||
\(684\) | −0.500000 | − | 0.866025i | −0.0191180 | − | 0.0331133i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | + | 16.4545i | −0.324532 | + | 0.628235i | ||||
\(687\) | − | 8.00000i | − | 0.305219i | ||||||
\(688\) | 1.73205 | − | 1.00000i | 0.0660338 | − | 0.0381246i | ||||
\(689\) | −4.50000 | + | 7.79423i | −0.171436 | + | 0.296936i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.0000 | − | 27.7128i | −0.608669 | − | 1.05425i | −0.991460 | − | 0.130410i | \(-0.958371\pi\) |
0.382791 | − | 0.923835i | \(-0.374963\pi\) | |||||||
\(692\) | − | 9.00000i | − | 0.342129i | ||||||
\(693\) | −5.19615 | − | 6.00000i | −0.197386 | − | 0.227921i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.00000 | + | 10.3923i | −0.227429 | + | 0.393919i | ||||
\(697\) | −15.5885 | − | 9.00000i | −0.590455 | − | 0.340899i | ||||
\(698\) | −22.5167 | + | 13.0000i | −0.852268 | + | 0.492057i | ||||
\(699\) | −12.0000 | −0.453882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | −3.46410 | + | 2.00000i | −0.130744 | + | 0.0754851i | ||||
\(703\) | −6.06218 | − | 3.50000i | −0.228639 | − | 0.132005i | ||||
\(704\) | 1.50000 | − | 2.59808i | 0.0565334 | − | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.0000 | −0.451626 | ||||||||
\(707\) | −31.1769 | + | 6.00000i | −1.17253 | + | 0.225653i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.0000 | − | 39.8372i | −0.863783 | − | 1.49612i | −0.868250 | − | 0.496126i | \(-0.834755\pi\) |
0.00446726 | − | 0.999990i | \(-0.498578\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.00000 | − | 8.66025i | 0.187515 | − | 0.324785i | ||||
\(712\) | 5.19615 | − | 3.00000i | 0.194734 | − | 0.112430i | ||||
\(713\) | 72.0000i | 2.69642i | ||||||||
\(714\) | −6.00000 | − | 31.1769i | −0.224544 | − | 1.16677i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.50000 | + | 2.59808i | 0.0560576 | + | 0.0970947i | ||||
\(717\) | 10.3923 | + | 6.00000i | 0.388108 | + | 0.224074i | ||||
\(718\) | 15.5885 | + | 9.00000i | 0.581756 | + | 0.335877i | ||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0000 | − | 3.46410i | −0.372419 | − | 0.129010i | ||||
\(722\) | − | 18.0000i | − | 0.669891i | ||||||
\(723\) | 1.73205 | − | 1.00000i | 0.0644157 | − | 0.0371904i | ||||
\(724\) | 1.00000 | − | 1.73205i | 0.0371647 | − | 0.0643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.00000 | + | 3.46410i | 0.0742270 | + | 0.128565i | ||||
\(727\) | 1.00000i | 0.0370879i | 0.999828 | + | 0.0185440i | \(0.00590307\pi\) | ||||
−0.999828 | + | 0.0185440i | \(0.994097\pi\) | |||||||
\(728\) | −1.73205 | − | 2.00000i | −0.0641941 | − | 0.0741249i | ||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | − | 10.3923i | 0.221918 | − | 0.384373i | ||||
\(732\) | −13.8564 | − | 8.00000i | −0.512148 | − | 0.295689i | ||||
\(733\) | −37.2391 | + | 21.5000i | −1.37546 | + | 0.794121i | −0.991609 | − | 0.129275i | \(-0.958735\pi\) |
−0.383849 | + | 0.923396i | \(0.625402\pi\) | |||||||
\(734\) | −19.0000 | −0.701303 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.00000 | −0.331744 | ||||||||
\(737\) | −20.7846 | + | 12.0000i | −0.765611 | + | 0.442026i | ||||
\(738\) | 2.59808 | + | 1.50000i | 0.0956365 | + | 0.0552158i | ||||
\(739\) | 17.5000 | − | 30.3109i | 0.643748 | − | 1.11500i | −0.340841 | − | 0.940121i | \(-0.610712\pi\) |
0.984589 | − | 0.174883i | \(-0.0559548\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | −15.5885 | − | 18.0000i | −0.572270 | − | 0.660801i | ||||
\(743\) | − | 45.0000i | − | 1.65089i | −0.564483 | − | 0.825445i | \(-0.690924\pi\) | ||
0.564483 | − | 0.825445i | \(-0.309076\pi\) | |||||||
\(744\) | 8.00000 | + | 13.8564i | 0.293294 | + | 0.508001i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.00000 | − | 1.73205i | 0.0366126 | − | 0.0634149i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 18.0000i | − | 0.658145i | ||||||
\(749\) | 30.0000 | + | 10.3923i | 1.09618 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.00000 | + | 8.66025i | 0.182453 | + | 0.316017i | 0.942715 | − | 0.333599i | \(-0.108263\pi\) |
−0.760263 | + | 0.649616i | \(0.774930\pi\) | |||||||
\(752\) | 7.79423 | + | 4.50000i | 0.284226 | + | 0.164098i | ||||
\(753\) | −25.9808 | − | 15.0000i | −0.946792 | − | 0.546630i | ||||
\(754\) | 3.00000 | + | 5.19615i | 0.109254 | + | 0.189233i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.00000 | − | 10.3923i | −0.0727393 | − | 0.377964i | ||||
\(757\) | − | 38.0000i | − | 1.38113i | −0.723269 | − | 0.690567i | \(-0.757361\pi\) | ||
0.723269 | − | 0.690567i | \(-0.242639\pi\) | |||||||
\(758\) | −19.9186 | + | 11.5000i | −0.723476 | + | 0.417699i | ||||
\(759\) | −27.0000 | + | 46.7654i | −0.980038 | + | 1.69748i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.5000 | + | 23.3827i | 0.489375 | + | 0.847622i | 0.999925 | − | 0.0122260i | \(-0.00389175\pi\) |
−0.510551 | + | 0.859848i | \(0.670558\pi\) | |||||||
\(762\) | 2.00000i | 0.0724524i | ||||||||
\(763\) | −41.5692 | + | 8.00000i | −1.50491 | + | 0.289619i | ||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.5000 | − | 18.1865i | 0.379380 | − | 0.657106i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.73205 | + | 1.00000i | −0.0625000 | + | 0.0360844i | ||||
\(769\) | −23.0000 | −0.829401 | −0.414701 | − | 0.909958i | \(-0.636114\pi\) | ||||
−0.414701 | + | 0.909958i | \(0.636114\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.8564 | − | 8.00000i | 0.498703 | − | 0.287926i | ||||
\(773\) | 44.1673 | + | 25.5000i | 1.58859 | + | 0.917171i | 0.993540 | + | 0.113480i | \(0.0361999\pi\) |
0.595047 | + | 0.803691i | \(0.297133\pi\) | |||||||
\(774\) | −1.00000 | + | 1.73205i | −0.0359443 | + | 0.0622573i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.0000 | 0.358979 | ||||||||
\(777\) | 24.2487 | + | 28.0000i | 0.869918 | + | 1.00449i | ||||
\(778\) | 12.0000i | 0.430221i | ||||||||
\(779\) | −1.50000 | − | 2.59808i | −0.0537431 | − | 0.0930857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −46.7654 | + | 27.0000i | −1.67233 | + | 0.965518i | ||||
\(783\) | 24.0000i | 0.857690i | ||||||||
\(784\) | 6.50000 | − | 2.59808i | 0.232143 | − | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.00000 | − | 5.19615i | −0.107006 | − | 0.185341i | ||||
\(787\) | −19.0526 | − | 11.0000i | −0.679150 | − | 0.392108i | 0.120384 | − | 0.992727i | \(-0.461587\pi\) |
−0.799535 | + | 0.600620i | \(0.794921\pi\) | |||||||
\(788\) | −12.9904 | − | 7.50000i | −0.462763 | − | 0.267176i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.00000i | 0.106600i | ||||||||
\(793\) | −6.92820 | + | 4.00000i | −0.246028 | + | 0.142044i | ||||
\(794\) | −7.00000 | + | 12.1244i | −0.248421 | + | 0.430277i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.00000 | + | 13.8564i | 0.283552 | + | 0.491127i | ||||
\(797\) | − | 6.00000i | − | 0.212531i | −0.994338 | − | 0.106265i | \(-0.966111\pi\) | ||
0.994338 | − | 0.106265i | \(-0.0338893\pi\) | |||||||
\(798\) | 1.73205 | − | 5.00000i | 0.0613139 | − | 0.176998i | ||||
\(799\) | 54.0000 | 1.91038 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00000 | + | 5.19615i | −0.106000 | + | 0.183597i | ||||
\(802\) | 23.3827 | + | 13.5000i | 0.825671 | + | 0.476702i | ||||
\(803\) | −10.3923 | + | 6.00000i | −0.366736 | + | 0.211735i | ||||
\(804\) | 16.0000 | 0.564276 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.00000 | 0.281788 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.3923 | + | 6.00000i | 0.365600 | + | 0.211079i | ||||
\(809\) | −4.50000 | + | 7.79423i | −0.158212 | + | 0.274030i | −0.934224 | − | 0.356687i | \(-0.883906\pi\) |
0.776012 | + | 0.630718i | \(0.217239\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.0000 | −0.877869 | −0.438934 | − | 0.898519i | \(-0.644644\pi\) | ||||
−0.438934 | + | 0.898519i | \(0.644644\pi\) | |||||||
\(812\) | −15.5885 | + | 3.00000i | −0.547048 | + | 0.105279i | ||||
\(813\) | 32.0000i | 1.12229i | ||||||||
\(814\) | 10.5000 | + | 18.1865i | 0.368025 | + | 0.637438i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.00000 | + | 10.3923i | −0.210042 | + | 0.363803i | ||||
\(817\) | 1.73205 | − | 1.00000i | 0.0605968 | − | 0.0349856i | ||||
\(818\) | − | 26.0000i | − | 0.909069i | ||||||
\(819\) | 2.50000 | + | 0.866025i | 0.0873571 | + | 0.0302614i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0000 | − | 25.9808i | −0.523504 | − | 0.906735i | −0.999626 | − | 0.0273557i | \(-0.991291\pi\) |
0.476122 | − | 0.879379i | \(-0.342042\pi\) | |||||||
\(822\) | 20.7846 | + | 12.0000i | 0.724947 | + | 0.418548i | ||||
\(823\) | 3.46410 | + | 2.00000i | 0.120751 | + | 0.0697156i | 0.559159 | − | 0.829060i | \(-0.311124\pi\) |
−0.438408 | + | 0.898776i | \(0.644457\pi\) | |||||||
\(824\) | 2.00000 | + | 3.46410i | 0.0696733 | + | 0.120678i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 6.00000i | − | 0.208640i | −0.994544 | − | 0.104320i | \(-0.966733\pi\) | ||
0.994544 | − | 0.104320i | \(-0.0332667\pi\) | |||||||
\(828\) | 7.79423 | − | 4.50000i | 0.270868 | − | 0.156386i | ||||
\(829\) | 7.00000 | − | 12.1244i | 0.243120 | − | 0.421096i | −0.718481 | − | 0.695546i | \(-0.755162\pi\) |
0.961601 | + | 0.274450i | \(0.0884958\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.0000 | − | 17.3205i | −0.346896 | − | 0.600842i | ||||
\(832\) | 1.00000i | 0.0346688i | ||||||||
\(833\) | 25.9808 | − | 33.0000i | 0.900180 | − | 1.14338i | ||||
\(834\) | 8.00000 | 0.277017 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.50000 | − | 2.59808i | 0.0518786 | − | 0.0898563i | ||||
\(837\) | 27.7128 | + | 16.0000i | 0.957895 | + | 0.553041i | ||||
\(838\) | 7.79423 | − | 4.50000i | 0.269247 | − | 0.155450i | ||||
\(839\) | 30.0000 | 1.03572 | 0.517858 | − | 0.855467i | \(-0.326730\pi\) | ||||
0.517858 | + | 0.855467i | \(0.326730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 1.73205 | − | 1.00000i | 0.0596904 | − | 0.0344623i | ||||
\(843\) | −46.7654 | − | 27.0000i | −1.61068 | − | 0.929929i | ||||
\(844\) | 11.5000 | − | 19.9186i | 0.395846 | − | 0.685626i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.00000 | −0.309426 | ||||||||
\(847\) | −1.73205 | + | 5.00000i | −0.0595140 | + | 0.171802i | ||||
\(848\) | 9.00000i | 0.309061i | ||||||||
\(849\) | −14.0000 | − | 24.2487i | −0.480479 | − | 0.832214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.5000 | − | 54.5596i | 1.07981 | − | 1.87028i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 19.0000i | − | 0.650548i | −0.945620 | − | 0.325274i | \(-0.894544\pi\) | ||
0.945620 | − | 0.325274i | \(-0.105456\pi\) | |||||||
\(854\) | −4.00000 | − | 20.7846i | −0.136877 | − | 0.711235i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | −15.5885 | − | 9.00000i | −0.532492 | − | 0.307434i | 0.209539 | − | 0.977800i | \(-0.432804\pi\) |
−0.742030 | + | 0.670366i | \(0.766137\pi\) | |||||||
\(858\) | 5.19615 | + | 3.00000i | 0.177394 | + | 0.102418i | ||||
\(859\) | 16.0000 | + | 27.7128i | 0.545913 | + | 0.945549i | 0.998549 | + | 0.0538535i | \(0.0171504\pi\) |
−0.452636 | + | 0.891695i | \(0.649516\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.00000 | + | 15.5885i | 0.102240 | + | 0.531253i | ||||
\(862\) | 12.0000i | 0.408722i | ||||||||
\(863\) | −2.59808 | + | 1.50000i | −0.0884395 | + | 0.0510606i | −0.543568 | − | 0.839365i | \(-0.682927\pi\) |
0.455128 | + | 0.890426i | \(0.349593\pi\) | |||||||
\(864\) | −2.00000 | + | 3.46410i | −0.0680414 | + | 0.117851i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −20.0000 | − | 34.6410i | −0.679628 | − | 1.17715i | ||||
\(867\) | 38.0000i | 1.29055i | ||||||||
\(868\) | −6.92820 | + | 20.0000i | −0.235159 | + | 0.678844i | ||||
\(869\) | 30.0000 | 1.01768 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00000 | − | 6.92820i | 0.135535 | − | 0.234753i | ||||
\(872\) | 13.8564 | + | 8.00000i | 0.469237 | + | 0.270914i | ||||
\(873\) | −8.66025 | + | 5.00000i | −0.293105 | + | 0.169224i | ||||
\(874\) | −9.00000 | −0.304430 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.00000 | 0.270295 | ||||||||
\(877\) | 11.2583 | − | 6.50000i | 0.380167 | − | 0.219489i | −0.297724 | − | 0.954652i | \(-0.596228\pi\) |
0.677891 | + | 0.735163i | \(0.262894\pi\) | |||||||
\(878\) | 22.5167 | + | 13.0000i | 0.759900 | + | 0.438729i | ||||
\(879\) | 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 | \(0.312374\pi\) | |||||||
\(882\) | −4.33013 | + | 5.50000i | −0.145803 | + | 0.185195i | ||||
\(883\) | 8.00000i | 0.269221i | 0.990899 | + | 0.134611i | \(0.0429784\pi\) | ||||
−0.990899 | + | 0.134611i | \(0.957022\pi\) | |||||||
\(884\) | 3.00000 | + | 5.19615i | 0.100901 | + | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.00000 | − | 10.3923i | 0.201574 | − | 0.349136i | ||||
\(887\) | 41.5692 | − | 24.0000i | 1.39576 | − | 0.805841i | 0.401813 | − | 0.915722i | \(-0.368380\pi\) |
0.993945 | + | 0.109881i | \(0.0350469\pi\) | |||||||
\(888\) | − | 14.0000i | − | 0.469809i | ||||||
\(889\) | −2.00000 | + | 1.73205i | −0.0670778 | + | 0.0580911i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.5000 | + | 28.5788i | 0.552771 | + | 0.957427i | ||||
\(892\) | 6.92820 | + | 4.00000i | 0.231973 | + | 0.133930i | ||||
\(893\) | 7.79423 | + | 4.50000i | 0.260824 | + | 0.150587i | ||||
\(894\) | −6.00000 | − | 10.3923i | −0.200670 | − | 0.347571i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.50000 | − | 0.866025i | −0.0835191 | − | 0.0289319i | ||||
\(897\) | − | 18.0000i | − | 0.601003i | ||||||
\(898\) | −18.1865 | + | 10.5000i | −0.606892 | + | 0.350390i | ||||
\(899\) | 24.0000 | − | 41.5692i | 0.800445 | − | 1.38641i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.0000 | + | 46.7654i | 0.899500 | + | 1.55798i | ||||
\(902\) | 9.00000i | 0.299667i | ||||||||
\(903\) | −10.3923 | + | 2.00000i | −0.345834 | + | 0.0665558i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.0000 | − | 17.3205i | 0.332228 | − | 0.575435i | ||||
\(907\) | −8.66025 | − | 5.00000i | −0.287559 | − | 0.166022i | 0.349281 | − | 0.937018i | \(-0.386426\pi\) |
−0.636841 | + | 0.770996i | \(0.719759\pi\) | |||||||
\(908\) | −10.3923 | + | 6.00000i | −0.344881 | + | 0.199117i | ||||
\(909\) | −12.0000 | −0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.0000 | −0.993944 | −0.496972 | − | 0.867766i | \(-0.665555\pi\) | ||||
−0.496972 | + | 0.867766i | \(0.665555\pi\) | |||||||
\(912\) | −1.73205 | + | 1.00000i | −0.0573539 | + | 0.0331133i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −7.00000 | + | 12.1244i | −0.231539 | + | 0.401038i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.00000 | −0.132164 | ||||||||
\(917\) | 2.59808 | − | 7.50000i | 0.0857960 | − | 0.247672i | ||||
\(918\) | 24.0000i | 0.792118i | ||||||||
\(919\) | −11.0000 | − | 19.0526i | −0.362857 | − | 0.628486i | 0.625573 | − | 0.780165i | \(-0.284865\pi\) |
−0.988430 | + | 0.151680i | \(0.951532\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | − | 24.2487i | 0.461316 | − | 0.799022i | ||||
\(922\) | −25.9808 | + | 15.0000i | −0.855631 | + | 0.493999i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −12.0000 | + | 10.3923i | −0.394771 | + | 0.341882i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.500000 | − | 0.866025i | −0.0164310 | − | 0.0284594i | ||||
\(927\) | −3.46410 | − | 2.00000i | −0.113776 | − | 0.0656886i | ||||
\(928\) | 5.19615 | + | 3.00000i | 0.170572 | + | 0.0984798i | ||||
\(929\) | 28.5000 | + | 49.3634i | 0.935055 | + | 1.61956i | 0.774536 | + | 0.632529i | \(0.217983\pi\) |
0.160518 | + | 0.987033i | \(0.448683\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.50000 | − | 2.59808i | 0.213029 | − | 0.0851485i | ||||
\(932\) | 6.00000i | 0.196537i | ||||||||
\(933\) | 41.5692 | − | 24.0000i | 1.36092 | − | 0.785725i | ||||
\(934\) | 3.00000 | − | 5.19615i | 0.0981630 | − | 0.170023i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.500000 | − | 0.866025i | −0.0163430 | − | 0.0283069i | ||||
\(937\) | 10.0000i | 0.326686i | 0.986569 | + | 0.163343i | \(0.0522277\pi\) | ||||
−0.986569 | + | 0.163343i | \(0.947772\pi\) | |||||||
\(938\) | 13.8564 | + | 16.0000i | 0.452428 | + | 0.522419i | ||||
\(939\) | −56.0000 | −1.82749 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.0000 | + | 41.5692i | −0.782378 | + | 1.35512i | 0.148176 | + | 0.988961i | \(0.452660\pi\) |
−0.930553 | + | 0.366157i | \(0.880673\pi\) | |||||||
\(942\) | 39.8372 | + | 23.0000i | 1.29797 | + | 0.749380i | ||||
\(943\) | 23.3827 | − | 13.5000i | 0.761445 | − | 0.439620i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.00000 | −0.195077 | ||||||||
\(947\) | −5.19615 | + | 3.00000i | −0.168852 | + | 0.0974869i | −0.582045 | − | 0.813157i | \(-0.697747\pi\) |
0.413192 | + | 0.910644i | \(0.364414\pi\) | |||||||
\(948\) | −17.3205 | − | 10.0000i | −0.562544 | − | 0.324785i | ||||
\(949\) | 2.00000 | − | 3.46410i | 0.0649227 | − | 0.112449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.0000 | −0.389127 | ||||||||
\(952\) | −15.5885 | + | 3.00000i | −0.505225 | + | 0.0972306i | ||||
\(953\) | 36.0000i | 1.16615i | 0.812417 | + | 0.583077i | \(0.198151\pi\) | ||||
−0.812417 | + | 0.583077i | \(0.801849\pi\) | |||||||
\(954\) | −4.50000 | − | 7.79423i | −0.145693 | − | 0.252347i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.00000 | − | 5.19615i | 0.0970269 | − | 0.168056i | ||||
\(957\) | 31.1769 | − | 18.0000i | 1.00781 | − | 0.581857i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.00000 | + | 31.1769i | 0.193750 | + | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | −6.06218 | − | 3.50000i | −0.195452 | − | 0.112845i | ||||
\(963\) | 10.3923 | + | 6.00000i | 0.334887 | + | 0.193347i | ||||
\(964\) | −0.500000 | − | 0.866025i | −0.0161039 | − | 0.0278928i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 45.0000 | + | 15.5885i | 1.44785 | + | 0.501550i | ||||
\(967\) | − | 32.0000i | − | 1.02905i | −0.857475 | − | 0.514525i | \(-0.827968\pi\) | ||
0.857475 | − | 0.514525i | \(-0.172032\pi\) | |||||||
\(968\) | 1.73205 | − | 1.00000i | 0.0556702 | − | 0.0321412i | ||||
\(969\) | −6.00000 | + | 10.3923i | −0.192748 | + | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.5000 | + | 38.9711i | 0.722059 | + | 1.25064i | 0.960173 | + | 0.279406i | \(0.0901376\pi\) |
−0.238114 | + | 0.971237i | \(0.576529\pi\) | |||||||
\(972\) | − | 10.0000i | − | 0.320750i | ||||||
\(973\) | 6.92820 | + | 8.00000i | 0.222108 | + | 0.256468i | ||||
\(974\) | −16.0000 | −0.512673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | + | 6.92820i | −0.128037 | + | 0.221766i | ||||
\(977\) | −36.3731 | − | 21.0000i | −1.16368 | − | 0.671850i | −0.211495 | − | 0.977379i | \(-0.567833\pi\) |
−0.952183 | + | 0.305530i | \(0.901167\pi\) | |||||||
\(978\) | 34.6410 | − | 20.0000i | 1.10770 | − | 0.639529i | ||||
\(979\) | −18.0000 | −0.575282 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.0000 | −0.510841 | ||||||||
\(982\) | 31.1769 | − | 18.0000i | 0.994895 | − | 0.574403i | ||||
\(983\) | −2.59808 | − | 1.50000i | −0.0828658 | − | 0.0478426i | 0.457995 | − | 0.888955i | \(-0.348568\pi\) |
−0.540860 | + | 0.841112i | \(0.681901\pi\) | |||||||
\(984\) | 3.00000 | − | 5.19615i | 0.0956365 | − | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 36.0000 | 1.14647 | ||||||||
\(987\) | −31.1769 | − | 36.0000i | −0.992372 | − | 1.14589i | ||||
\(988\) | 1.00000i | 0.0318142i | ||||||||
\(989\) | 9.00000 | + | 15.5885i | 0.286183 | + | 0.495684i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.0000 | + | 38.1051i | −0.698853 | + | 1.21045i | 0.270011 | + | 0.962857i | \(0.412973\pi\) |
−0.968864 | + | 0.247592i | \(0.920361\pi\) | |||||||
\(992\) | 6.92820 | − | 4.00000i | 0.219971 | − | 0.127000i | ||||
\(993\) | 14.0000i | 0.444277i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.0526 | − | 11.0000i | −0.603401 | − | 0.348373i | 0.166978 | − | 0.985961i | \(-0.446599\pi\) |
−0.770378 | + | 0.637587i | \(0.779933\pi\) | |||||||
\(998\) | −3.46410 | − | 2.00000i | −0.109654 | − | 0.0633089i | ||||
\(999\) | −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.j.d.249.2 | 4 | ||
5.2 | odd | 4 | 70.2.e.d.11.1 | ✓ | 2 | ||
5.3 | odd | 4 | 350.2.e.b.151.1 | 2 | |||
5.4 | even | 2 | inner | 350.2.j.d.249.1 | 4 | ||
7.2 | even | 3 | inner | 350.2.j.d.149.1 | 4 | ||
7.3 | odd | 6 | 2450.2.c.e.99.2 | 2 | |||
7.4 | even | 3 | 2450.2.c.q.99.2 | 2 | |||
15.2 | even | 4 | 630.2.k.d.361.1 | 2 | |||
20.7 | even | 4 | 560.2.q.b.81.1 | 2 | |||
35.2 | odd | 12 | 70.2.e.d.51.1 | yes | 2 | ||
35.3 | even | 12 | 2450.2.a.v.1.1 | 1 | |||
35.4 | even | 6 | 2450.2.c.q.99.1 | 2 | |||
35.9 | even | 6 | inner | 350.2.j.d.149.2 | 4 | ||
35.12 | even | 12 | 490.2.e.g.471.1 | 2 | |||
35.17 | even | 12 | 490.2.a.d.1.1 | 1 | |||
35.18 | odd | 12 | 2450.2.a.bf.1.1 | 1 | |||
35.23 | odd | 12 | 350.2.e.b.51.1 | 2 | |||
35.24 | odd | 6 | 2450.2.c.e.99.1 | 2 | |||
35.27 | even | 4 | 490.2.e.g.361.1 | 2 | |||
35.32 | odd | 12 | 490.2.a.a.1.1 | 1 | |||
105.2 | even | 12 | 630.2.k.d.541.1 | 2 | |||
105.17 | odd | 12 | 4410.2.a.bg.1.1 | 1 | |||
105.32 | even | 12 | 4410.2.a.x.1.1 | 1 | |||
140.67 | even | 12 | 3920.2.a.bh.1.1 | 1 | |||
140.87 | odd | 12 | 3920.2.a.e.1.1 | 1 | |||
140.107 | even | 12 | 560.2.q.b.401.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.e.d.11.1 | ✓ | 2 | 5.2 | odd | 4 | ||
70.2.e.d.51.1 | yes | 2 | 35.2 | odd | 12 | ||
350.2.e.b.51.1 | 2 | 35.23 | odd | 12 | |||
350.2.e.b.151.1 | 2 | 5.3 | odd | 4 | |||
350.2.j.d.149.1 | 4 | 7.2 | even | 3 | inner | ||
350.2.j.d.149.2 | 4 | 35.9 | even | 6 | inner | ||
350.2.j.d.249.1 | 4 | 5.4 | even | 2 | inner | ||
350.2.j.d.249.2 | 4 | 1.1 | even | 1 | trivial | ||
490.2.a.a.1.1 | 1 | 35.32 | odd | 12 | |||
490.2.a.d.1.1 | 1 | 35.17 | even | 12 | |||
490.2.e.g.361.1 | 2 | 35.27 | even | 4 | |||
490.2.e.g.471.1 | 2 | 35.12 | even | 12 | |||
560.2.q.b.81.1 | 2 | 20.7 | even | 4 | |||
560.2.q.b.401.1 | 2 | 140.107 | even | 12 | |||
630.2.k.d.361.1 | 2 | 15.2 | even | 4 | |||
630.2.k.d.541.1 | 2 | 105.2 | even | 12 | |||
2450.2.a.v.1.1 | 1 | 35.3 | even | 12 | |||
2450.2.a.bf.1.1 | 1 | 35.18 | odd | 12 | |||
2450.2.c.e.99.1 | 2 | 35.24 | odd | 6 | |||
2450.2.c.e.99.2 | 2 | 7.3 | odd | 6 | |||
2450.2.c.q.99.1 | 2 | 35.4 | even | 6 | |||
2450.2.c.q.99.2 | 2 | 7.4 | even | 3 | |||
3920.2.a.e.1.1 | 1 | 140.87 | odd | 12 | |||
3920.2.a.bh.1.1 | 1 | 140.67 | even | 12 | |||
4410.2.a.x.1.1 | 1 | 105.32 | even | 12 | |||
4410.2.a.bg.1.1 | 1 | 105.17 | odd | 12 |