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 | 249.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.249 |
Dual form | 350.2.j.d.149.1 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 | −0.0917517 | − | 0.995782i | \(-0.529247\pi\) |
−0.908248 | + | 0.418432i | \(0.862580\pi\) | |||||||
\(4\) | 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 | \(0.0442844\pi\) | ||||
−0.990338 | + | 0.138675i | \(0.955716\pi\) | |||||||
\(14\) | 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 | 0.973123 | − | 0.230285i | \(-0.0739659\pi\) |
0.287129 | + | 0.957892i | \(0.407299\pi\) | |||||||
\(18\) | −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 | \(0.720947\pi\) |
−0.985496 | + | 0.169701i | \(0.945720\pi\) | |||||||
\(24\) | 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 | −0.907245 | − | 0.420602i | \(-0.861819\pi\) |
−0.0893706 | + | 0.995998i | \(0.528486\pi\) | |||||||
\(38\) | 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 | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | 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 | 0.191243 | − | 0.981543i | \(-0.438748\pi\) |
0.945662 | + | 0.325150i | \(0.105415\pi\) | |||||||
\(48\) | 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 | 0.928351 | − | 0.371706i | \(-0.121227\pi\) |
0.142269 | + | 0.989828i | \(0.454560\pi\) | |||||||
\(54\) | −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 | 0.0130248 | − | 0.999915i | \(-0.495854\pi\) |
−0.859440 | + | 0.511237i | \(0.829187\pi\) | |||||||
\(68\) | 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 | 0.283387 | − | 0.959006i | \(-0.408542\pi\) |
−0.688830 | + | 0.724923i | \(0.741875\pi\) | |||||||
\(74\) | 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 | \(-0.830506\pi\) | ||
0.861550 | − | 0.507673i | \(-0.169494\pi\) | |||||||
\(98\) | −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 | −0.319531 | − | 0.947576i | \(-0.603525\pi\) |
0.660859 | + | 0.750510i | \(0.270192\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.00000 | −0.874157 | ||||||||
\(107\) | −10.3923 | + | 6.00000i | −1.00466 | + | 0.580042i | −0.909624 | − | 0.415432i | \(-0.863630\pi\) |
−0.0950377 | + | 0.995474i | \(0.530297\pi\) | |||||||
\(108\) | 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 | \(-0.985873\pi\) | ||
0.999015 | − | 0.0443678i | \(-0.0141274\pi\) | |||||||
\(128\) | 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 | −0.0146279 | − | 0.999893i | \(-0.504656\pi\) |
−0.873247 | + | 0.487278i | \(0.837990\pi\) | |||||||
\(138\) | −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 | \(-0.963297\pi\) |
−0.596316 | − | 0.802749i | \(-0.703370\pi\) | |||||||
\(158\) | 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 | −0.989170 | − | 0.146772i | \(-0.953112\pi\) |
−0.367477 | + | 0.930033i | \(0.619778\pi\) | |||||||
\(164\) | 1.50000 | − | 2.59808i | 0.117130 | − | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.00000i | 0.232147i | 0.993241 | + | 0.116073i | \(0.0370308\pi\) | ||||
−0.993241 | + | 0.116073i | \(0.962969\pi\) | |||||||
\(168\) | −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 | −0.766119 | − | 0.642699i | \(-0.777815\pi\) |
0.173534 | + | 0.984828i | \(0.444481\pi\) | |||||||
\(174\) | −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 | −0.0899262 | − | 0.995948i | \(-0.528663\pi\) |
−0.907480 | + | 0.420096i | \(0.861996\pi\) | |||||||
\(194\) | 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 | \(0.179445\pi\) | ||||
−0.845262 | + | 0.534353i | \(0.820555\pi\) | |||||||
\(198\) | 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 | \(-0.913684\pi\) | ||
0.963458 | − | 0.267860i | \(-0.0863164\pi\) | |||||||
\(224\) | −0.500000 | − | 2.59808i | −0.0334077 | − | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.3923 | + | 6.00000i | 0.689761 | + | 0.398234i | 0.803523 | − | 0.595274i | \(-0.202957\pi\) |
−0.113761 | + | 0.993508i | \(0.536290\pi\) | |||||||
\(228\) | 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 | −0.320043 | − | 0.947403i | \(-0.603697\pi\) |
0.660454 | + | 0.750867i | \(0.270364\pi\) | |||||||
\(234\) | 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 | 0.737075 | − | 0.675810i | \(-0.236206\pi\) |
−0.216731 | + | 0.976231i | \(0.569540\pi\) | |||||||
\(278\) | −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 | 0.815017 | − | 0.579437i | \(-0.196728\pi\) |
−0.0942988 | + | 0.995544i | \(0.530061\pi\) | |||||||
\(284\) | 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 | \(0.0846766\pi\) | ||||
−0.964825 | + | 0.262893i | \(0.915323\pi\) | |||||||
\(294\) | −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 | \(0.130820\pi\) | ||||
−0.916728 | + | 0.399511i | \(0.869180\pi\) | |||||||
\(308\) | 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 | 0.379612 | − | 0.925146i | \(-0.376057\pi\) |
0.991006 | + | 0.133819i | \(0.0427240\pi\) | |||||||
\(314\) | 23.0000 | 1.29797 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | 5.19615 | − | 3.00000i | 0.291845 | − | 0.168497i | −0.346929 | − | 0.937892i | \(-0.612775\pi\) |
0.638774 | + | 0.769395i | \(0.279442\pi\) | |||||||
\(318\) | 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 | \(-0.795482\pi\) | ||
0.800593 | − | 0.599208i | \(-0.204518\pi\) | |||||||
\(338\) | −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 | 0.750382 | − | 0.661004i | \(-0.229870\pi\) |
−0.197256 | + | 0.980352i | \(0.563203\pi\) | |||||||
\(354\) | 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 | 0.863649 | − | 0.504093i | \(-0.168173\pi\) |
−0.00473247 | + | 0.999989i | \(0.501506\pi\) | |||||||
\(368\) | 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 | −0.544170 | − | 0.838975i | \(-0.683156\pi\) |
0.454488 | + | 0.890753i | \(0.349822\pi\) | |||||||
\(374\) | 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 | −0.886586 | − | 0.462563i | \(-0.846930\pi\) |
−0.0427020 | + | 0.999088i | \(0.513597\pi\) | |||||||
\(384\) | −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 | −0.163876 | − | 0.986481i | \(-0.552400\pi\) |
0.772380 | + | 0.635161i | \(0.219066\pi\) | |||||||
\(398\) | − | 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 | \(0.410969\pi\) | ||||
−0.276066 | + | 0.961139i | \(0.589031\pi\) | |||||||
\(434\) | −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 | −0.726130 | − | 0.687557i | \(-0.758683\pi\) |
0.232377 | + | 0.972626i | \(0.425350\pi\) | |||||||
\(444\) | 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 | −0.188858 | − | 0.982004i | \(-0.560479\pi\) |
0.756012 | + | 0.654558i | \(0.227145\pi\) | |||||||
\(458\) | 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 | \(0.00739722\pi\) | ||||
−0.999730 | + | 0.0232370i | \(0.992603\pi\) | |||||||
\(464\) | 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 | −0.615383 | − | 0.788228i | \(-0.710999\pi\) |
0.374934 | + | 0.927052i | \(0.377665\pi\) | |||||||
\(468\) | 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 | 0.779936 | − | 0.625859i | \(-0.215252\pi\) |
−0.152042 | + | 0.988374i | \(0.548585\pi\) | |||||||
\(488\) | 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 | \(-0.820291\pi\) | ||
0.844818 | − | 0.535054i | \(-0.179709\pi\) | |||||||
\(504\) | 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 | 0.134801 | − | 0.990873i | \(-0.456961\pi\) |
0.925521 | + | 0.378695i | \(0.123627\pi\) | |||||||
\(524\) | −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 | \(0.0547087\pi\) | ||||
−0.985266 | + | 0.171028i | \(0.945291\pi\) | |||||||
\(548\) | −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 | 0.655953 | − | 0.754802i | \(-0.272267\pi\) |
−0.325701 | + | 0.945473i | \(0.605600\pi\) | |||||||
\(558\) | 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 | \(0.0125389\pi\) |
0.533718 | + | 0.845663i | \(0.320794\pi\) | |||||||
\(564\) | −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 | \(-0.964834\pi\) |
−0.592433 | − | 0.805620i | \(-0.701833\pi\) | |||||||
\(578\) | −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 | \(-0.835061\pi\) | ||
0.868726 | − | 0.495293i | \(-0.164939\pi\) | |||||||
\(588\) | −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 | −0.861838 | − | 0.507184i | \(-0.830686\pi\) |
0.00831589 | + | 0.999965i | \(0.497353\pi\) | |||||||
\(594\) | 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 | −0.517472 | − | 0.855700i | \(-0.673127\pi\) |
0.482322 | + | 0.875994i | \(0.339794\pi\) | |||||||
\(608\) | − | 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 | 0.912470 | − | 0.409145i | \(-0.134173\pi\) |
0.101905 | + | 0.994794i | \(0.467506\pi\) | |||||||
\(614\) | −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 | \(-0.881983\pi\) | ||
0.932051 | − | 0.362326i | \(-0.118017\pi\) | |||||||
\(618\) | 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 | \(-0.987444\pi\) | ||
0.999222 | − | 0.0394362i | \(-0.0125562\pi\) | |||||||
\(644\) | 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 | −0.181245 | − | 0.983438i | \(-0.558013\pi\) |
−0.942305 | + | 0.334756i | \(0.891346\pi\) | |||||||
\(648\) | 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 | −0.339680 | − | 0.940541i | \(-0.610319\pi\) |
0.644692 | + | 0.764442i | \(0.276986\pi\) | |||||||
\(654\) | −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 | \(0.227459\pi\) | ||||
−0.755367 | + | 0.655302i | \(0.772541\pi\) | |||||||
\(674\) | 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 | −0.642244 | − | 0.766501i | \(-0.721996\pi\) |
0.342687 | + | 0.939450i | \(0.388663\pi\) | |||||||
\(678\) | 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 | 0.685470 | − | 0.728101i | \(-0.259597\pi\) |
−0.287819 | + | 0.957685i | \(0.592930\pi\) | |||||||
\(684\) | −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 | \(-0.994097\pi\) | ||
0.999828 | − | 0.0185440i | \(-0.00590307\pi\) | |||||||
\(728\) | 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 | 0.383849 | − | 0.923396i | \(-0.374598\pi\) |
0.991609 | + | 0.129275i | \(0.0412651\pi\) | |||||||
\(734\) | −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 | \(0.309076\pi\) | ||||
−0.564483 | + | 0.825445i | \(0.690924\pi\) | |||||||
\(744\) | 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 | \(0.242639\pi\) | ||||
−0.723269 | + | 0.690567i | \(0.757361\pi\) | |||||||
\(758\) | 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 | \(-0.963800\pi\) |
−0.595047 | − | 0.803691i | \(-0.702867\pi\) | |||||||
\(774\) | −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 | 0.799535 | − | 0.600620i | \(-0.205079\pi\) |
−0.120384 | + | 0.992727i | \(0.538413\pi\) | |||||||
\(788\) | 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 | \(0.0338893\pi\) | ||||
−0.994338 | + | 0.106265i | \(0.966111\pi\) | |||||||
\(798\) | −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 | 0.438408 | − | 0.898776i | \(-0.355543\pi\) |
−0.559159 | + | 0.829060i | \(0.688876\pi\) | |||||||
\(824\) | 2.00000 | + | 3.46410i | 0.0696733 | + | 0.120678i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.00000i | 0.208640i | 0.994544 | + | 0.104320i | \(0.0332667\pi\) | ||||
−0.994544 | + | 0.104320i | \(0.966733\pi\) | |||||||
\(828\) | −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 | \(0.105456\pi\) | ||||
−0.945620 | + | 0.325274i | \(0.894544\pi\) | |||||||
\(854\) | −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 | 0.742030 | − | 0.670366i | \(-0.233863\pi\) |
−0.209539 | + | 0.977800i | \(0.567196\pi\) | |||||||
\(858\) | −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 | −0.455128 | − | 0.890426i | \(-0.650407\pi\) |
0.543568 | + | 0.839365i | \(0.317073\pi\) | |||||||
\(864\) | −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 | −0.677891 | − | 0.735163i | \(-0.737106\pi\) |
0.297724 | + | 0.954652i | \(0.403772\pi\) | |||||||
\(878\) | −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 | \(-0.957022\pi\) | ||
0.990899 | − | 0.134611i | \(-0.0429784\pi\) | |||||||
\(884\) | 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 | −0.993945 | − | 0.109881i | \(-0.964953\pi\) |
−0.401813 | + | 0.915722i | \(0.631620\pi\) | |||||||
\(888\) | 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 | 0.636841 | − | 0.770996i | \(-0.280241\pi\) |
−0.349281 | + | 0.937018i | \(0.613574\pi\) | |||||||
\(908\) | 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 | \(-0.947772\pi\) | ||
0.986569 | − | 0.163343i | \(-0.0522277\pi\) | |||||||
\(938\) | −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 | −0.413192 | − | 0.910644i | \(-0.635586\pi\) |
0.582045 | + | 0.813157i | \(0.302253\pi\) | |||||||
\(948\) | 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 | \(-0.801849\pi\) | ||
0.812417 | − | 0.583077i | \(-0.198151\pi\) | |||||||
\(954\) | −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 | \(0.172032\pi\) | ||||
−0.857475 | + | 0.514525i | \(0.827968\pi\) | |||||||
\(968\) | −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 | 0.952183 | − | 0.305530i | \(-0.0988335\pi\) |
0.211495 | + | 0.977379i | \(0.432167\pi\) | |||||||
\(978\) | −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 | 0.540860 | − | 0.841112i | \(-0.318099\pi\) |
−0.457995 | + | 0.888955i | \(0.651432\pi\) | |||||||
\(984\) | 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 | 0.770378 | − | 0.637587i | \(-0.220067\pi\) |
−0.166978 | + | 0.985961i | \(0.553401\pi\) | |||||||
\(998\) | 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.249.1 | 4 | ||
5.2 | odd | 4 | 350.2.e.b.151.1 | 2 | |||
5.3 | odd | 4 | 70.2.e.d.11.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 350.2.j.d.249.2 | 4 | ||
7.2 | even | 3 | inner | 350.2.j.d.149.2 | 4 | ||
7.3 | odd | 6 | 2450.2.c.e.99.1 | 2 | |||
7.4 | even | 3 | 2450.2.c.q.99.1 | 2 | |||
15.8 | even | 4 | 630.2.k.d.361.1 | 2 | |||
20.3 | even | 4 | 560.2.q.b.81.1 | 2 | |||
35.2 | odd | 12 | 350.2.e.b.51.1 | 2 | |||
35.3 | even | 12 | 490.2.a.d.1.1 | 1 | |||
35.4 | even | 6 | 2450.2.c.q.99.2 | 2 | |||
35.9 | even | 6 | inner | 350.2.j.d.149.1 | 4 | ||
35.13 | even | 4 | 490.2.e.g.361.1 | 2 | |||
35.17 | even | 12 | 2450.2.a.v.1.1 | 1 | |||
35.18 | odd | 12 | 490.2.a.a.1.1 | 1 | |||
35.23 | odd | 12 | 70.2.e.d.51.1 | yes | 2 | ||
35.24 | odd | 6 | 2450.2.c.e.99.2 | 2 | |||
35.32 | odd | 12 | 2450.2.a.bf.1.1 | 1 | |||
35.33 | even | 12 | 490.2.e.g.471.1 | 2 | |||
105.23 | even | 12 | 630.2.k.d.541.1 | 2 | |||
105.38 | odd | 12 | 4410.2.a.bg.1.1 | 1 | |||
105.53 | even | 12 | 4410.2.a.x.1.1 | 1 | |||
140.3 | odd | 12 | 3920.2.a.e.1.1 | 1 | |||
140.23 | even | 12 | 560.2.q.b.401.1 | 2 | |||
140.123 | even | 12 | 3920.2.a.bh.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.e.d.11.1 | ✓ | 2 | 5.3 | odd | 4 | ||
70.2.e.d.51.1 | yes | 2 | 35.23 | odd | 12 | ||
350.2.e.b.51.1 | 2 | 35.2 | odd | 12 | |||
350.2.e.b.151.1 | 2 | 5.2 | odd | 4 | |||
350.2.j.d.149.1 | 4 | 35.9 | even | 6 | inner | ||
350.2.j.d.149.2 | 4 | 7.2 | even | 3 | inner | ||
350.2.j.d.249.1 | 4 | 1.1 | even | 1 | trivial | ||
350.2.j.d.249.2 | 4 | 5.4 | even | 2 | inner | ||
490.2.a.a.1.1 | 1 | 35.18 | odd | 12 | |||
490.2.a.d.1.1 | 1 | 35.3 | even | 12 | |||
490.2.e.g.361.1 | 2 | 35.13 | even | 4 | |||
490.2.e.g.471.1 | 2 | 35.33 | even | 12 | |||
560.2.q.b.81.1 | 2 | 20.3 | even | 4 | |||
560.2.q.b.401.1 | 2 | 140.23 | even | 12 | |||
630.2.k.d.361.1 | 2 | 15.8 | even | 4 | |||
630.2.k.d.541.1 | 2 | 105.23 | even | 12 | |||
2450.2.a.v.1.1 | 1 | 35.17 | even | 12 | |||
2450.2.a.bf.1.1 | 1 | 35.32 | odd | 12 | |||
2450.2.c.e.99.1 | 2 | 7.3 | odd | 6 | |||
2450.2.c.e.99.2 | 2 | 35.24 | odd | 6 | |||
2450.2.c.q.99.1 | 2 | 7.4 | even | 3 | |||
2450.2.c.q.99.2 | 2 | 35.4 | even | 6 | |||
3920.2.a.e.1.1 | 1 | 140.3 | odd | 12 | |||
3920.2.a.bh.1.1 | 1 | 140.123 | even | 12 | |||
4410.2.a.x.1.1 | 1 | 105.53 | even | 12 | |||
4410.2.a.bg.1.1 | 1 | 105.38 | odd | 12 |