Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [70,2,Mod(11,70)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(70, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("70.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 70 = 2 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 70.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.558952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 70.11 |
Dual form | 70.2.e.d.51.1 |
$q$-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 \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(57\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 1.00000 | − | 1.73205i | 0.577350 | − | 1.00000i | −0.418432 | − | 0.908248i | \(-0.637420\pi\) |
0.995782 | − | 0.0917517i | \(-0.0292466\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | −2.00000 | + | 1.73205i | −0.755929 | + | 0.654654i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 1.00000 | + | 1.73205i | 0.288675 | + | 0.500000i | ||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | −2.50000 | − | 0.866025i | −0.668153 | − | 0.231455i | ||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.00000 | − | 5.19615i | 0.727607 | − | 1.26025i | −0.230285 | − | 0.973123i | \(-0.573966\pi\) |
0.957892 | − | 0.287129i | \(-0.0927008\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | 0.500000 | + | 0.866025i | 0.114708 | + | 0.198680i | 0.917663 | − | 0.397360i | \(-0.130073\pi\) |
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.00000 | + | 5.19615i | 0.218218 | + | 1.13389i | ||||
\(22\) | −3.00000 | −0.639602 | ||||||||
\(23\) | −4.50000 | − | 7.79423i | −0.938315 | − | 1.62521i | −0.768613 | − | 0.639713i | \(-0.779053\pi\) |
−0.169701 | − | 0.985496i | \(-0.554280\pi\) | |||||||
\(24\) | −1.00000 | + | 1.73205i | −0.204124 | + | 0.353553i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −0.500000 | − | 0.866025i | −0.0980581 | − | 0.169842i | ||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | −0.500000 | − | 2.59808i | −0.0944911 | − | 0.490990i | ||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | −1.00000 | − | 1.73205i | −0.182574 | − | 0.316228i | ||||
\(31\) | −4.00000 | + | 6.92820i | −0.718421 | + | 1.24434i | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 3.00000 | + | 5.19615i | 0.522233 | + | 0.904534i | ||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 2.50000 | + | 0.866025i | 0.422577 | + | 0.146385i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.50000 | + | 6.06218i | 0.575396 | + | 0.996616i | 0.995998 | + | 0.0893706i | \(0.0284856\pi\) |
−0.420602 | + | 0.907245i | \(0.638181\pi\) | |||||||
\(38\) | −0.500000 | + | 0.866025i | −0.0811107 | + | 0.140488i | ||||
\(39\) | −1.00000 | + | 1.73205i | −0.160128 | + | 0.277350i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | −4.00000 | + | 3.46410i | −0.617213 | + | 0.534522i | ||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | −1.50000 | − | 2.59808i | −0.226134 | − | 0.391675i | ||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | 4.50000 | − | 7.79423i | 0.663489 | − | 1.14920i | ||||
\(47\) | −4.50000 | − | 7.79423i | −0.656392 | − | 1.13691i | −0.981543 | − | 0.191243i | \(-0.938748\pi\) |
0.325150 | − | 0.945662i | \(-0.394585\pi\) | |||||||
\(48\) | −2.00000 | −0.288675 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −6.00000 | − | 10.3923i | −0.840168 | − | 1.45521i | ||||
\(52\) | 0.500000 | − | 0.866025i | 0.0693375 | − | 0.120096i | ||||
\(53\) | −4.50000 | + | 7.79423i | −0.618123 | + | 1.07062i | 0.371706 | + | 0.928351i | \(0.378773\pi\) |
−0.989828 | + | 0.142269i | \(0.954560\pi\) | |||||||
\(54\) | 2.00000 | + | 3.46410i | 0.272166 | + | 0.471405i | ||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 2.00000 | − | 1.73205i | 0.267261 | − | 0.231455i | ||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 3.00000 | + | 5.19615i | 0.393919 | + | 0.682288i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 1.00000 | − | 1.73205i | 0.129099 | − | 0.223607i | ||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | −8.00000 | −1.01600 | ||||||||
\(63\) | 2.50000 | + | 0.866025i | 0.314970 | + | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.500000 | + | 0.866025i | 0.0620174 | + | 0.107417i | ||||
\(66\) | −3.00000 | + | 5.19615i | −0.369274 | + | 0.639602i | ||||
\(67\) | −4.00000 | + | 6.92820i | −0.488678 | + | 0.846415i | −0.999915 | − | 0.0130248i | \(-0.995854\pi\) |
0.511237 | + | 0.859440i | \(0.329187\pi\) | |||||||
\(68\) | 3.00000 | + | 5.19615i | 0.363803 | + | 0.630126i | ||||
\(69\) | −18.0000 | −2.16695 | ||||||||
\(70\) | 0.500000 | + | 2.59808i | 0.0597614 | + | 0.310530i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 2.00000 | − | 3.46410i | 0.234082 | − | 0.405442i | −0.724923 | − | 0.688830i | \(-0.758125\pi\) |
0.959006 | + | 0.283387i | \(0.0914581\pi\) | |||||||
\(74\) | −3.50000 | + | 6.06218i | −0.406867 | + | 0.704714i | ||||
\(75\) | 1.00000 | + | 1.73205i | 0.115470 | + | 0.200000i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −1.50000 | − | 7.79423i | −0.170941 | − | 0.888235i | ||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | 5.00000 | + | 8.66025i | 0.562544 | + | 0.974355i | 0.997274 | + | 0.0737937i | \(0.0235106\pi\) |
−0.434730 | + | 0.900561i | \(0.643156\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | 1.50000 | + | 2.59808i | 0.165647 | + | 0.286910i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | −5.00000 | − | 1.73205i | −0.545545 | − | 0.188982i | ||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | 1.00000 | + | 1.73205i | 0.107833 | + | 0.186772i | ||||
\(87\) | 6.00000 | − | 10.3923i | 0.643268 | − | 1.11417i | ||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 2.00000 | − | 1.73205i | 0.209657 | − | 0.181568i | ||||
\(92\) | 9.00000 | 0.938315 | ||||||||
\(93\) | 8.00000 | + | 13.8564i | 0.829561 | + | 1.43684i | ||||
\(94\) | 4.50000 | − | 7.79423i | 0.464140 | − | 0.803913i | ||||
\(95\) | 0.500000 | − | 0.866025i | 0.0512989 | − | 0.0888523i | ||||
\(96\) | −1.00000 | − | 1.73205i | −0.102062 | − | 0.176777i | ||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 6.50000 | − | 2.59808i | 0.656599 | − | 0.262445i | ||||
\(99\) | 3.00000 | 0.301511 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −6.00000 | + | 10.3923i | −0.597022 | + | 1.03407i | 0.396236 | + | 0.918149i | \(0.370316\pi\) |
−0.993258 | + | 0.115924i | \(0.963017\pi\) | |||||||
\(102\) | 6.00000 | − | 10.3923i | 0.594089 | − | 1.02899i | ||||
\(103\) | 2.00000 | + | 3.46410i | 0.197066 | + | 0.341328i | 0.947576 | − | 0.319531i | \(-0.103525\pi\) |
−0.750510 | + | 0.660859i | \(0.770192\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 4.00000 | − | 3.46410i | 0.390360 | − | 0.338062i | ||||
\(106\) | −9.00000 | −0.874157 | ||||||||
\(107\) | 6.00000 | + | 10.3923i | 0.580042 | + | 1.00466i | 0.995474 | + | 0.0950377i | \(0.0302972\pi\) |
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(108\) | −2.00000 | + | 3.46410i | −0.192450 | + | 0.333333i | ||||
\(109\) | 8.00000 | − | 13.8564i | 0.766261 | − | 1.32720i | −0.173316 | − | 0.984866i | \(-0.555448\pi\) |
0.939577 | − | 0.342337i | \(-0.111218\pi\) | |||||||
\(110\) | 1.50000 | + | 2.59808i | 0.143019 | + | 0.247717i | ||||
\(111\) | 14.0000 | 1.32882 | ||||||||
\(112\) | 2.50000 | + | 0.866025i | 0.236228 | + | 0.0818317i | ||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 1.00000 | + | 1.73205i | 0.0936586 | + | 0.162221i | ||||
\(115\) | −4.50000 | + | 7.79423i | −0.419627 | + | 0.726816i | ||||
\(116\) | −3.00000 | + | 5.19615i | −0.278543 | + | 0.482451i | ||||
\(117\) | 0.500000 | + | 0.866025i | 0.0462250 | + | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.00000 | + | 15.5885i | 0.275010 | + | 1.42899i | ||||
\(120\) | 2.00000 | 0.182574 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 4.00000 | − | 6.92820i | 0.362143 | − | 0.627250i | ||||
\(123\) | 3.00000 | − | 5.19615i | 0.270501 | − | 0.468521i | ||||
\(124\) | −4.00000 | − | 6.92820i | −0.359211 | − | 0.622171i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.500000 | + | 2.59808i | 0.0445435 | + | 0.231455i | ||||
\(127\) | −1.00000 | −0.0887357 | −0.0443678 | − | 0.999015i | \(-0.514127\pi\) | ||||
−0.0443678 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.00000 | − | 3.46410i | 0.176090 | − | 0.304997i | ||||
\(130\) | −0.500000 | + | 0.866025i | −0.0438529 | + | 0.0759555i | ||||
\(131\) | −1.50000 | − | 2.59808i | −0.131056 | − | 0.226995i | 0.793028 | − | 0.609185i | \(-0.208503\pi\) |
−0.924084 | + | 0.382190i | \(0.875170\pi\) | |||||||
\(132\) | −6.00000 | −0.522233 | ||||||||
\(133\) | −2.50000 | − | 0.866025i | −0.216777 | − | 0.0750939i | ||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | −2.00000 | − | 3.46410i | −0.172133 | − | 0.298142i | ||||
\(136\) | −3.00000 | + | 5.19615i | −0.257248 | + | 0.445566i | ||||
\(137\) | −6.00000 | + | 10.3923i | −0.512615 | + | 0.887875i | 0.487278 | + | 0.873247i | \(0.337990\pi\) |
−0.999893 | + | 0.0146279i | \(0.995344\pi\) | |||||||
\(138\) | −9.00000 | − | 15.5885i | −0.766131 | − | 1.32698i | ||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | −2.00000 | + | 1.73205i | −0.169031 | + | 0.146385i | ||||
\(141\) | −18.0000 | −1.51587 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.50000 | − | 2.59808i | 0.125436 | − | 0.217262i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −3.00000 | − | 5.19615i | −0.249136 | − | 0.431517i | ||||
\(146\) | 4.00000 | 0.331042 | ||||||||
\(147\) | −11.0000 | − | 8.66025i | −0.907265 | − | 0.714286i | ||||
\(148\) | −7.00000 | −0.575396 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | −1.00000 | + | 1.73205i | −0.0816497 | + | 0.141421i | ||||
\(151\) | 5.00000 | − | 8.66025i | 0.406894 | − | 0.704761i | −0.587646 | − | 0.809118i | \(-0.699945\pi\) |
0.994540 | + | 0.104357i | \(0.0332784\pi\) | |||||||
\(152\) | −0.500000 | − | 0.866025i | −0.0405554 | − | 0.0702439i | ||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | 6.00000 | − | 5.19615i | 0.483494 | − | 0.418718i | ||||
\(155\) | 8.00000 | 0.642575 | ||||||||
\(156\) | −1.00000 | − | 1.73205i | −0.0800641 | − | 0.138675i | ||||
\(157\) | −11.5000 | + | 19.9186i | −0.917800 | + | 1.58968i | −0.115050 | + | 0.993360i | \(0.536703\pi\) |
−0.802749 | + | 0.596316i | \(0.796630\pi\) | |||||||
\(158\) | −5.00000 | + | 8.66025i | −0.397779 | + | 0.688973i | ||||
\(159\) | 9.00000 | + | 15.5885i | 0.713746 | + | 1.23625i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 22.5000 | + | 7.79423i | 1.77325 | + | 0.614271i | ||||
\(162\) | 11.0000 | 0.864242 | ||||||||
\(163\) | −10.0000 | − | 17.3205i | −0.783260 | − | 1.35665i | −0.930033 | − | 0.367477i | \(-0.880222\pi\) |
0.146772 | − | 0.989170i | \(-0.453112\pi\) | |||||||
\(164\) | −1.50000 | + | 2.59808i | −0.117130 | + | 0.202876i | ||||
\(165\) | 3.00000 | − | 5.19615i | 0.233550 | − | 0.404520i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.00000 | 0.232147 | 0.116073 | − | 0.993241i | \(-0.462969\pi\) | ||||
0.116073 | + | 0.993241i | \(0.462969\pi\) | |||||||
\(168\) | −1.00000 | − | 5.19615i | −0.0771517 | − | 0.400892i | ||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | −3.00000 | − | 5.19615i | −0.230089 | − | 0.398527i | ||||
\(171\) | 0.500000 | − | 0.866025i | 0.0382360 | − | 0.0662266i | ||||
\(172\) | −1.00000 | + | 1.73205i | −0.0762493 | + | 0.132068i | ||||
\(173\) | −4.50000 | − | 7.79423i | −0.342129 | − | 0.592584i | 0.642699 | − | 0.766119i | \(-0.277815\pi\) |
−0.984828 | + | 0.173534i | \(0.944481\pi\) | |||||||
\(174\) | 12.0000 | 0.909718 | ||||||||
\(175\) | −0.500000 | − | 2.59808i | −0.0377964 | − | 0.196396i | ||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.00000 | − | 5.19615i | 0.224860 | − | 0.389468i | ||||
\(179\) | 1.50000 | − | 2.59808i | 0.112115 | − | 0.194189i | −0.804508 | − | 0.593942i | \(-0.797571\pi\) |
0.916623 | + | 0.399753i | \(0.130904\pi\) | |||||||
\(180\) | −0.500000 | − | 0.866025i | −0.0372678 | − | 0.0645497i | ||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 2.50000 | + | 0.866025i | 0.185312 | + | 0.0641941i | ||||
\(183\) | −16.0000 | −1.18275 | ||||||||
\(184\) | 4.50000 | + | 7.79423i | 0.331744 | + | 0.574598i | ||||
\(185\) | 3.50000 | − | 6.06218i | 0.257325 | − | 0.445700i | ||||
\(186\) | −8.00000 | + | 13.8564i | −0.586588 | + | 1.01600i | ||||
\(187\) | 9.00000 | + | 15.5885i | 0.658145 | + | 1.13994i | ||||
\(188\) | 9.00000 | 0.656392 | ||||||||
\(189\) | −8.00000 | + | 6.92820i | −0.581914 | + | 0.503953i | ||||
\(190\) | 1.00000 | 0.0725476 | ||||||||
\(191\) | −6.00000 | − | 10.3923i | −0.434145 | − | 0.751961i | 0.563081 | − | 0.826402i | \(-0.309616\pi\) |
−0.997225 | + | 0.0744412i | \(0.976283\pi\) | |||||||
\(192\) | 1.00000 | − | 1.73205i | 0.0721688 | − | 0.125000i | ||||
\(193\) | 8.00000 | − | 13.8564i | 0.575853 | − | 0.997406i | −0.420096 | − | 0.907480i | \(-0.638004\pi\) |
0.995948 | − | 0.0899262i | \(-0.0286631\pi\) | |||||||
\(194\) | −5.00000 | − | 8.66025i | −0.358979 | − | 0.621770i | ||||
\(195\) | 2.00000 | 0.143223 | ||||||||
\(196\) | 5.50000 | + | 4.33013i | 0.392857 | + | 0.309295i | ||||
\(197\) | 15.0000 | 1.06871 | 0.534353 | − | 0.845262i | \(-0.320555\pi\) | ||||
0.534353 | + | 0.845262i | \(0.320555\pi\) | |||||||
\(198\) | 1.50000 | + | 2.59808i | 0.106600 | + | 0.184637i | ||||
\(199\) | 8.00000 | − | 13.8564i | 0.567105 | − | 0.982255i | −0.429745 | − | 0.902950i | \(-0.641397\pi\) |
0.996850 | − | 0.0793045i | \(-0.0252700\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | 8.00000 | + | 13.8564i | 0.564276 | + | 0.977356i | ||||
\(202\) | −12.0000 | −0.844317 | ||||||||
\(203\) | −12.0000 | + | 10.3923i | −0.842235 | + | 0.729397i | ||||
\(204\) | 12.0000 | 0.840168 | ||||||||
\(205\) | −1.50000 | − | 2.59808i | −0.104765 | − | 0.181458i | ||||
\(206\) | −2.00000 | + | 3.46410i | −0.139347 | + | 0.241355i | ||||
\(207\) | −4.50000 | + | 7.79423i | −0.312772 | + | 0.541736i | ||||
\(208\) | 0.500000 | + | 0.866025i | 0.0346688 | + | 0.0600481i | ||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 5.00000 | + | 1.73205i | 0.345033 | + | 0.119523i | ||||
\(211\) | 23.0000 | 1.58339 | 0.791693 | − | 0.610920i | \(-0.209200\pi\) | ||||
0.791693 | + | 0.610920i | \(0.209200\pi\) | |||||||
\(212\) | −4.50000 | − | 7.79423i | −0.309061 | − | 0.535310i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | + | 10.3923i | −0.410152 | + | 0.710403i | ||||
\(215\) | −1.00000 | − | 1.73205i | −0.0681994 | − | 0.118125i | ||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | −4.00000 | − | 20.7846i | −0.271538 | − | 1.41095i | ||||
\(218\) | 16.0000 | 1.08366 | ||||||||
\(219\) | −4.00000 | − | 6.92820i | −0.270295 | − | 0.468165i | ||||
\(220\) | −1.50000 | + | 2.59808i | −0.101130 | + | 0.175162i | ||||
\(221\) | −3.00000 | + | 5.19615i | −0.201802 | + | 0.349531i | ||||
\(222\) | 7.00000 | + | 12.1244i | 0.469809 | + | 0.813733i | ||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 0.500000 | + | 2.59808i | 0.0334077 | + | 0.173591i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.00000 | − | 10.3923i | 0.398234 | − | 0.689761i | −0.595274 | − | 0.803523i | \(-0.702957\pi\) |
0.993508 | + | 0.113761i | \(0.0362899\pi\) | |||||||
\(228\) | −1.00000 | + | 1.73205i | −0.0662266 | + | 0.114708i | ||||
\(229\) | 2.00000 | + | 3.46410i | 0.132164 | + | 0.228914i | 0.924510 | − | 0.381157i | \(-0.124474\pi\) |
−0.792347 | + | 0.610071i | \(0.791141\pi\) | |||||||
\(230\) | −9.00000 | −0.593442 | ||||||||
\(231\) | −15.0000 | − | 5.19615i | −0.986928 | − | 0.341882i | ||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | 3.00000 | + | 5.19615i | 0.196537 | + | 0.340411i | 0.947403 | − | 0.320043i | \(-0.103697\pi\) |
−0.750867 | + | 0.660454i | \(0.770364\pi\) | |||||||
\(234\) | −0.500000 | + | 0.866025i | −0.0326860 | + | 0.0566139i | ||||
\(235\) | −4.50000 | + | 7.79423i | −0.293548 | + | 0.508439i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.0000 | 1.29914 | ||||||||
\(238\) | −12.0000 | + | 10.3923i | −0.777844 | + | 0.673633i | ||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 1.00000 | + | 1.73205i | 0.0645497 | + | 0.111803i | ||||
\(241\) | 0.500000 | − | 0.866025i | 0.0322078 | − | 0.0557856i | −0.849472 | − | 0.527633i | \(-0.823079\pi\) |
0.881680 | + | 0.471848i | \(0.156413\pi\) | |||||||
\(242\) | −1.00000 | + | 1.73205i | −0.0642824 | + | 0.111340i | ||||
\(243\) | −5.00000 | − | 8.66025i | −0.320750 | − | 0.555556i | ||||
\(244\) | 8.00000 | 0.512148 | ||||||||
\(245\) | −6.50000 | + | 2.59808i | −0.415270 | + | 0.165985i | ||||
\(246\) | 6.00000 | 0.382546 | ||||||||
\(247\) | −0.500000 | − | 0.866025i | −0.0318142 | − | 0.0551039i | ||||
\(248\) | 4.00000 | − | 6.92820i | 0.254000 | − | 0.439941i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | −15.0000 | −0.946792 | −0.473396 | − | 0.880850i | \(-0.656972\pi\) | ||||
−0.473396 | + | 0.880850i | \(0.656972\pi\) | |||||||
\(252\) | −2.00000 | + | 1.73205i | −0.125988 | + | 0.109109i | ||||
\(253\) | 27.0000 | 1.69748 | ||||||||
\(254\) | −0.500000 | − | 0.866025i | −0.0313728 | − | 0.0543393i | ||||
\(255\) | −6.00000 | + | 10.3923i | −0.375735 | + | 0.650791i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 4.00000 | 0.249029 | ||||||||
\(259\) | −17.5000 | − | 6.06218i | −1.08740 | − | 0.376685i | ||||
\(260\) | −1.00000 | −0.0620174 | ||||||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | 1.50000 | − | 2.59808i | 0.0926703 | − | 0.160510i | ||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | −3.00000 | − | 5.19615i | −0.184637 | − | 0.319801i | ||||
\(265\) | 9.00000 | 0.552866 | ||||||||
\(266\) | −0.500000 | − | 2.59808i | −0.0306570 | − | 0.159298i | ||||
\(267\) | −12.0000 | −0.734388 | ||||||||
\(268\) | −4.00000 | − | 6.92820i | −0.244339 | − | 0.423207i | ||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 2.00000 | − | 3.46410i | 0.121716 | − | 0.210819i | ||||
\(271\) | 8.00000 | + | 13.8564i | 0.485965 | + | 0.841717i | 0.999870 | − | 0.0161307i | \(-0.00513477\pi\) |
−0.513905 | + | 0.857847i | \(0.671801\pi\) | |||||||
\(272\) | −6.00000 | −0.363803 | ||||||||
\(273\) | −1.00000 | − | 5.19615i | −0.0605228 | − | 0.314485i | ||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | 9.00000 | − | 15.5885i | 0.541736 | − | 0.938315i | ||||
\(277\) | 5.00000 | − | 8.66025i | 0.300421 | − | 0.520344i | −0.675810 | − | 0.737075i | \(-0.736206\pi\) |
0.976231 | + | 0.216731i | \(0.0695395\pi\) | |||||||
\(278\) | −2.00000 | − | 3.46410i | −0.119952 | − | 0.207763i | ||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | −2.50000 | − | 0.866025i | −0.149404 | − | 0.0517549i | ||||
\(281\) | −27.0000 | −1.61068 | −0.805342 | − | 0.592810i | \(-0.798019\pi\) | ||||
−0.805342 | + | 0.592810i | \(0.798019\pi\) | |||||||
\(282\) | −9.00000 | − | 15.5885i | −0.535942 | − | 0.928279i | ||||
\(283\) | −7.00000 | + | 12.1244i | −0.416107 | + | 0.720718i | −0.995544 | − | 0.0942988i | \(-0.969939\pi\) |
0.579437 | + | 0.815017i | \(0.303272\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00000 | − | 1.73205i | −0.0592349 | − | 0.102598i | ||||
\(286\) | 3.00000 | 0.177394 | ||||||||
\(287\) | −6.00000 | + | 5.19615i | −0.354169 | + | 0.306719i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 3.00000 | − | 5.19615i | 0.176166 | − | 0.305129i | ||||
\(291\) | −10.0000 | + | 17.3205i | −0.586210 | + | 1.01535i | ||||
\(292\) | 2.00000 | + | 3.46410i | 0.117041 | + | 0.202721i | ||||
\(293\) | −9.00000 | −0.525786 | −0.262893 | − | 0.964825i | \(-0.584677\pi\) | ||||
−0.262893 | + | 0.964825i | \(0.584677\pi\) | |||||||
\(294\) | 2.00000 | − | 13.8564i | 0.116642 | − | 0.808122i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.50000 | − | 6.06218i | −0.203433 | − | 0.352357i | ||||
\(297\) | −6.00000 | + | 10.3923i | −0.348155 | + | 0.603023i | ||||
\(298\) | −3.00000 | + | 5.19615i | −0.173785 | + | 0.301005i | ||||
\(299\) | 4.50000 | + | 7.79423i | 0.260242 | + | 0.450752i | ||||
\(300\) | −2.00000 | −0.115470 | ||||||||
\(301\) | −4.00000 | + | 3.46410i | −0.230556 | + | 0.199667i | ||||
\(302\) | 10.0000 | 0.575435 | ||||||||
\(303\) | 12.0000 | + | 20.7846i | 0.689382 | + | 1.19404i | ||||
\(304\) | 0.500000 | − | 0.866025i | 0.0286770 | − | 0.0496700i | ||||
\(305\) | −4.00000 | + | 6.92820i | −0.229039 | + | 0.396708i | ||||
\(306\) | −3.00000 | − | 5.19615i | −0.171499 | − | 0.297044i | ||||
\(307\) | 14.0000 | 0.799022 | 0.399511 | − | 0.916728i | \(-0.369180\pi\) | ||||
0.399511 | + | 0.916728i | \(0.369180\pi\) | |||||||
\(308\) | 7.50000 | + | 2.59808i | 0.427352 | + | 0.148039i | ||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 4.00000 | + | 6.92820i | 0.227185 | + | 0.393496i | ||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | 1.00000 | − | 1.73205i | 0.0566139 | − | 0.0980581i | ||||
\(313\) | 14.0000 | + | 24.2487i | 0.791327 | + | 1.37062i | 0.925146 | + | 0.379612i | \(0.123943\pi\) |
−0.133819 | + | 0.991006i | \(0.542724\pi\) | |||||||
\(314\) | −23.0000 | −1.29797 | ||||||||
\(315\) | −0.500000 | − | 2.59808i | −0.0281718 | − | 0.146385i | ||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | −3.00000 | − | 5.19615i | −0.168497 | − | 0.291845i | 0.769395 | − | 0.638774i | \(-0.220558\pi\) |
−0.937892 | + | 0.346929i | \(0.887225\pi\) | |||||||
\(318\) | −9.00000 | + | 15.5885i | −0.504695 | + | 0.874157i | ||||
\(319\) | −9.00000 | + | 15.5885i | −0.503903 | + | 0.872786i | ||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | 24.0000 | 1.33955 | ||||||||
\(322\) | 4.50000 | + | 23.3827i | 0.250775 | + | 1.30307i | ||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | 5.50000 | + | 9.52628i | 0.305556 | + | 0.529238i | ||||
\(325\) | 0.500000 | − | 0.866025i | 0.0277350 | − | 0.0480384i | ||||
\(326\) | 10.0000 | − | 17.3205i | 0.553849 | − | 0.959294i | ||||
\(327\) | −16.0000 | − | 27.7128i | −0.884802 | − | 1.53252i | ||||
\(328\) | −3.00000 | −0.165647 | ||||||||
\(329\) | 22.5000 | + | 7.79423i | 1.24047 | + | 0.429710i | ||||
\(330\) | 6.00000 | 0.330289 | ||||||||
\(331\) | 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 | ||||||||
\(333\) | 3.50000 | − | 6.06218i | 0.191799 | − | 0.332205i | ||||
\(334\) | 1.50000 | + | 2.59808i | 0.0820763 | + | 0.142160i | ||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | 4.00000 | − | 3.46410i | 0.218218 | − | 0.188982i | ||||
\(337\) | −22.0000 | −1.19842 | −0.599208 | − | 0.800593i | \(-0.704518\pi\) | ||||
−0.599208 | + | 0.800593i | \(0.704518\pi\) | |||||||
\(338\) | −6.00000 | − | 10.3923i | −0.326357 | − | 0.565267i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.00000 | − | 5.19615i | 0.162698 | − | 0.281801i | ||||
\(341\) | −12.0000 | − | 20.7846i | −0.649836 | − | 1.12555i | ||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | 9.00000 | + | 15.5885i | 0.484544 | + | 0.839254i | ||||
\(346\) | 4.50000 | − | 7.79423i | 0.241921 | − | 0.419020i | ||||
\(347\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(348\) | 6.00000 | + | 10.3923i | 0.321634 | + | 0.557086i | ||||
\(349\) | 26.0000 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | 2.00000 | − | 1.73205i | 0.106904 | − | 0.0925820i | ||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | 1.50000 | + | 2.59808i | 0.0799503 | + | 0.138478i | ||||
\(353\) | −6.00000 | + | 10.3923i | −0.319348 | + | 0.553127i | −0.980352 | − | 0.197256i | \(-0.936797\pi\) |
0.661004 | + | 0.750382i | \(0.270130\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 30.0000 | + | 10.3923i | 1.58777 | + | 0.550019i | ||||
\(358\) | 3.00000 | 0.158555 | ||||||||
\(359\) | −9.00000 | − | 15.5885i | −0.475002 | − | 0.822727i | 0.524588 | − | 0.851356i | \(-0.324219\pi\) |
−0.999590 | + | 0.0286287i | \(0.990886\pi\) | |||||||
\(360\) | 0.500000 | − | 0.866025i | 0.0263523 | − | 0.0456435i | ||||
\(361\) | 9.00000 | − | 15.5885i | 0.473684 | − | 0.820445i | ||||
\(362\) | 1.00000 | + | 1.73205i | 0.0525588 | + | 0.0910346i | ||||
\(363\) | 4.00000 | 0.209946 | ||||||||
\(364\) | 0.500000 | + | 2.59808i | 0.0262071 | + | 0.136176i | ||||
\(365\) | −4.00000 | −0.209370 | ||||||||
\(366\) | −8.00000 | − | 13.8564i | −0.418167 | − | 0.724286i | ||||
\(367\) | 9.50000 | − | 16.4545i | 0.495896 | − | 0.858917i | −0.504093 | − | 0.863649i | \(-0.668173\pi\) |
0.999989 | + | 0.00473247i | \(0.00150640\pi\) | |||||||
\(368\) | −4.50000 | + | 7.79423i | −0.234579 | + | 0.406302i | ||||
\(369\) | −1.50000 | − | 2.59808i | −0.0780869 | − | 0.135250i | ||||
\(370\) | 7.00000 | 0.363913 | ||||||||
\(371\) | −4.50000 | − | 23.3827i | −0.233628 | − | 1.21397i | ||||
\(372\) | −16.0000 | −0.829561 | ||||||||
\(373\) | −1.00000 | − | 1.73205i | −0.0517780 | − | 0.0896822i | 0.838975 | − | 0.544170i | \(-0.183156\pi\) |
−0.890753 | + | 0.454488i | \(0.849822\pi\) | |||||||
\(374\) | −9.00000 | + | 15.5885i | −0.465379 | + | 0.806060i | ||||
\(375\) | 1.00000 | − | 1.73205i | 0.0516398 | − | 0.0894427i | ||||
\(376\) | 4.50000 | + | 7.79423i | 0.232070 | + | 0.401957i | ||||
\(377\) | −6.00000 | −0.309016 | ||||||||
\(378\) | −10.0000 | − | 3.46410i | −0.514344 | − | 0.178174i | ||||
\(379\) | 23.0000 | 1.18143 | 0.590715 | − | 0.806880i | \(-0.298846\pi\) | ||||
0.590715 | + | 0.806880i | \(0.298846\pi\) | |||||||
\(380\) | 0.500000 | + | 0.866025i | 0.0256495 | + | 0.0444262i | ||||
\(381\) | −1.00000 | + | 1.73205i | −0.0512316 | + | 0.0887357i | ||||
\(382\) | 6.00000 | − | 10.3923i | 0.306987 | − | 0.531717i | ||||
\(383\) | −10.5000 | − | 18.1865i | −0.536525 | − | 0.929288i | −0.999088 | − | 0.0427020i | \(-0.986403\pi\) |
0.462563 | − | 0.886586i | \(-0.346930\pi\) | |||||||
\(384\) | 2.00000 | 0.102062 | ||||||||
\(385\) | −6.00000 | + | 5.19615i | −0.305788 | + | 0.264820i | ||||
\(386\) | 16.0000 | 0.814379 | ||||||||
\(387\) | −1.00000 | − | 1.73205i | −0.0508329 | − | 0.0880451i | ||||
\(388\) | 5.00000 | − | 8.66025i | 0.253837 | − | 0.439658i | ||||
\(389\) | 6.00000 | − | 10.3923i | 0.304212 | − | 0.526911i | −0.672874 | − | 0.739758i | \(-0.734940\pi\) |
0.977086 | + | 0.212847i | \(0.0682735\pi\) | |||||||
\(390\) | 1.00000 | + | 1.73205i | 0.0506370 | + | 0.0877058i | ||||
\(391\) | −54.0000 | −2.73090 | ||||||||
\(392\) | −1.00000 | + | 6.92820i | −0.0505076 | + | 0.349927i | ||||
\(393\) | −6.00000 | −0.302660 | ||||||||
\(394\) | 7.50000 | + | 12.9904i | 0.377845 | + | 0.654446i | ||||
\(395\) | 5.00000 | − | 8.66025i | 0.251577 | − | 0.435745i | ||||
\(396\) | −1.50000 | + | 2.59808i | −0.0753778 | + | 0.130558i | ||||
\(397\) | −7.00000 | − | 12.1244i | −0.351320 | − | 0.608504i | 0.635161 | − | 0.772380i | \(-0.280934\pi\) |
−0.986481 | + | 0.163876i | \(0.947600\pi\) | |||||||
\(398\) | 16.0000 | 0.802008 | ||||||||
\(399\) | −4.00000 | + | 3.46410i | −0.200250 | + | 0.173422i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 13.5000 | + | 23.3827i | 0.674158 | + | 1.16768i | 0.976714 | + | 0.214544i | \(0.0688266\pi\) |
−0.302556 | + | 0.953131i | \(0.597840\pi\) | |||||||
\(402\) | −8.00000 | + | 13.8564i | −0.399004 | + | 0.691095i | ||||
\(403\) | 4.00000 | − | 6.92820i | 0.199254 | − | 0.345118i | ||||
\(404\) | −6.00000 | − | 10.3923i | −0.298511 | − | 0.517036i | ||||
\(405\) | −11.0000 | −0.546594 | ||||||||
\(406\) | −15.0000 | − | 5.19615i | −0.744438 | − | 0.257881i | ||||
\(407\) | −21.0000 | −1.04093 | ||||||||
\(408\) | 6.00000 | + | 10.3923i | 0.297044 | + | 0.514496i | ||||
\(409\) | −13.0000 | + | 22.5167i | −0.642809 | + | 1.11338i | 0.341994 | + | 0.939702i | \(0.388898\pi\) |
−0.984803 | + | 0.173675i | \(0.944436\pi\) | |||||||
\(410\) | 1.50000 | − | 2.59808i | 0.0740797 | − | 0.128310i | ||||
\(411\) | 12.0000 | + | 20.7846i | 0.591916 | + | 1.02523i | ||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −9.00000 | −0.442326 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.500000 | + | 0.866025i | −0.0245145 | + | 0.0424604i | ||||
\(417\) | −4.00000 | + | 6.92820i | −0.195881 | + | 0.339276i | ||||
\(418\) | −1.50000 | − | 2.59808i | −0.0733674 | − | 0.127076i | ||||
\(419\) | −9.00000 | −0.439679 | −0.219839 | − | 0.975536i | \(-0.570553\pi\) | ||||
−0.219839 | + | 0.975536i | \(0.570553\pi\) | |||||||
\(420\) | 1.00000 | + | 5.19615i | 0.0487950 | + | 0.253546i | ||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | 11.5000 | + | 19.9186i | 0.559811 | + | 0.969622i | ||||
\(423\) | −4.50000 | + | 7.79423i | −0.218797 | + | 0.378968i | ||||
\(424\) | 4.50000 | − | 7.79423i | 0.218539 | − | 0.378521i | ||||
\(425\) | 3.00000 | + | 5.19615i | 0.145521 | + | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0000 | + | 6.92820i | 0.967868 | + | 0.335279i | ||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | −3.00000 | − | 5.19615i | −0.144841 | − | 0.250873i | ||||
\(430\) | 1.00000 | − | 1.73205i | 0.0482243 | − | 0.0835269i | ||||
\(431\) | −6.00000 | + | 10.3923i | −0.289010 | + | 0.500580i | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | −2.00000 | − | 3.46410i | −0.0962250 | − | 0.166667i | ||||
\(433\) | −40.0000 | −1.92228 | −0.961139 | − | 0.276066i | \(-0.910969\pi\) | ||||
−0.961139 | + | 0.276066i | \(0.910969\pi\) | |||||||
\(434\) | 16.0000 | − | 13.8564i | 0.768025 | − | 0.665129i | ||||
\(435\) | −12.0000 | −0.575356 | ||||||||
\(436\) | 8.00000 | + | 13.8564i | 0.383131 | + | 0.663602i | ||||
\(437\) | 4.50000 | − | 7.79423i | 0.215264 | − | 0.372849i | ||||
\(438\) | 4.00000 | − | 6.92820i | 0.191127 | − | 0.331042i | ||||
\(439\) | −13.0000 | − | 22.5167i | −0.620456 | − | 1.07466i | −0.989401 | − | 0.145210i | \(-0.953614\pi\) |
0.368945 | − | 0.929451i | \(-0.379719\pi\) | |||||||
\(440\) | −3.00000 | −0.143019 | ||||||||
\(441\) | −6.50000 | + | 2.59808i | −0.309524 | + | 0.123718i | ||||
\(442\) | −6.00000 | −0.285391 | ||||||||
\(443\) | −6.00000 | − | 10.3923i | −0.285069 | − | 0.493753i | 0.687557 | − | 0.726130i | \(-0.258683\pi\) |
−0.972626 | + | 0.232377i | \(0.925350\pi\) | |||||||
\(444\) | −7.00000 | + | 12.1244i | −0.332205 | + | 0.575396i | ||||
\(445\) | −3.00000 | + | 5.19615i | −0.142214 | + | 0.246321i | ||||
\(446\) | 4.00000 | + | 6.92820i | 0.189405 | + | 0.328060i | ||||
\(447\) | 12.0000 | 0.567581 | ||||||||
\(448\) | −2.00000 | + | 1.73205i | −0.0944911 | + | 0.0818317i | ||||
\(449\) | 21.0000 | 0.991051 | 0.495526 | − | 0.868593i | \(-0.334975\pi\) | ||||
0.495526 | + | 0.868593i | \(0.334975\pi\) | |||||||
\(450\) | 0.500000 | + | 0.866025i | 0.0235702 | + | 0.0408248i | ||||
\(451\) | −4.50000 | + | 7.79423i | −0.211897 | + | 0.367016i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.0000 | − | 17.3205i | −0.469841 | − | 0.813788i | ||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | −2.50000 | − | 0.866025i | −0.117202 | − | 0.0405999i | ||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | −7.00000 | − | 12.1244i | −0.327446 | − | 0.567153i | 0.654558 | − | 0.756012i | \(-0.272855\pi\) |
−0.982004 | + | 0.188858i | \(0.939521\pi\) | |||||||
\(458\) | −2.00000 | + | 3.46410i | −0.0934539 | + | 0.161867i | ||||
\(459\) | 12.0000 | − | 20.7846i | 0.560112 | − | 0.970143i | ||||
\(460\) | −4.50000 | − | 7.79423i | −0.209814 | − | 0.363408i | ||||
\(461\) | −30.0000 | −1.39724 | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
−0.698620 | + | 0.715493i | \(0.746202\pi\) | |||||||
\(462\) | −3.00000 | − | 15.5885i | −0.139573 | − | 0.725241i | ||||
\(463\) | −1.00000 | −0.0464739 | −0.0232370 | − | 0.999730i | \(-0.507397\pi\) | ||||
−0.0232370 | + | 0.999730i | \(0.507397\pi\) | |||||||
\(464\) | −3.00000 | − | 5.19615i | −0.139272 | − | 0.241225i | ||||
\(465\) | 8.00000 | − | 13.8564i | 0.370991 | − | 0.642575i | ||||
\(466\) | −3.00000 | + | 5.19615i | −0.138972 | + | 0.240707i | ||||
\(467\) | 3.00000 | + | 5.19615i | 0.138823 | + | 0.240449i | 0.927052 | − | 0.374934i | \(-0.122335\pi\) |
−0.788228 | + | 0.615383i | \(0.789001\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −4.00000 | − | 20.7846i | −0.184703 | − | 0.959744i | ||||
\(470\) | −9.00000 | −0.415139 | ||||||||
\(471\) | 23.0000 | + | 39.8372i | 1.05978 | + | 1.83560i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.00000 | + | 5.19615i | −0.137940 | + | 0.238919i | ||||
\(474\) | 10.0000 | + | 17.3205i | 0.459315 | + | 0.795557i | ||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | −15.0000 | − | 5.19615i | −0.687524 | − | 0.238165i | ||||
\(477\) | 9.00000 | 0.412082 | ||||||||
\(478\) | −3.00000 | − | 5.19615i | −0.137217 | − | 0.237666i | ||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | −1.00000 | + | 1.73205i | −0.0456435 | + | 0.0790569i | ||||
\(481\) | −3.50000 | − | 6.06218i | −0.159586 | − | 0.276412i | ||||
\(482\) | 1.00000 | 0.0455488 | ||||||||
\(483\) | 36.0000 | − | 31.1769i | 1.63806 | − | 1.41860i | ||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | 5.00000 | + | 8.66025i | 0.227038 | + | 0.393242i | ||||
\(486\) | 5.00000 | − | 8.66025i | 0.226805 | − | 0.392837i | ||||
\(487\) | 8.00000 | − | 13.8564i | 0.362515 | − | 0.627894i | −0.625859 | − | 0.779936i | \(-0.715252\pi\) |
0.988374 | + | 0.152042i | \(0.0485850\pi\) | |||||||
\(488\) | 4.00000 | + | 6.92820i | 0.181071 | + | 0.313625i | ||||
\(489\) | −40.0000 | −1.80886 | ||||||||
\(490\) | −5.50000 | − | 4.33013i | −0.248465 | − | 0.195615i | ||||
\(491\) | 36.0000 | 1.62466 | 0.812329 | − | 0.583200i | \(-0.198200\pi\) | ||||
0.812329 | + | 0.583200i | \(0.198200\pi\) | |||||||
\(492\) | 3.00000 | + | 5.19615i | 0.135250 | + | 0.234261i | ||||
\(493\) | 18.0000 | − | 31.1769i | 0.810679 | − | 1.40414i | ||||
\(494\) | 0.500000 | − | 0.866025i | 0.0224961 | − | 0.0389643i | ||||
\(495\) | −1.50000 | − | 2.59808i | −0.0674200 | − | 0.116775i | ||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.00000 | + | 3.46410i | 0.0895323 | + | 0.155074i | 0.907314 | − | 0.420455i | \(-0.138129\pi\) |
−0.817781 | + | 0.575529i | \(0.804796\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | 3.00000 | − | 5.19615i | 0.134030 | − | 0.232147i | ||||
\(502\) | −7.50000 | − | 12.9904i | −0.334741 | − | 0.579789i | ||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | −2.50000 | − | 0.866025i | −0.111359 | − | 0.0385758i | ||||
\(505\) | 12.0000 | 0.533993 | ||||||||
\(506\) | 13.5000 | + | 23.3827i | 0.600148 | + | 1.03949i | ||||
\(507\) | −12.0000 | + | 20.7846i | −0.532939 | + | 0.923077i | ||||
\(508\) | 0.500000 | − | 0.866025i | 0.0221839 | − | 0.0384237i | ||||
\(509\) | 21.0000 | + | 36.3731i | 0.930809 | + | 1.61221i | 0.781943 | + | 0.623350i | \(0.214229\pi\) |
0.148866 | + | 0.988857i | \(0.452438\pi\) | |||||||
\(510\) | −12.0000 | −0.531369 | ||||||||
\(511\) | 2.00000 | + | 10.3923i | 0.0884748 | + | 0.459728i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.00000 | + | 3.46410i | 0.0883022 | + | 0.152944i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.00000 | − | 3.46410i | 0.0881305 | − | 0.152647i | ||||
\(516\) | 2.00000 | + | 3.46410i | 0.0880451 | + | 0.152499i | ||||
\(517\) | 27.0000 | 1.18746 | ||||||||
\(518\) | −3.50000 | − | 18.1865i | −0.153781 | − | 0.799070i | ||||
\(519\) | −18.0000 | −0.790112 | ||||||||
\(520\) | −0.500000 | − | 0.866025i | −0.0219265 | − | 0.0379777i | ||||
\(521\) | 7.50000 | − | 12.9904i | 0.328581 | − | 0.569119i | −0.653650 | − | 0.756797i | \(-0.726763\pi\) |
0.982231 | + | 0.187678i | \(0.0600963\pi\) | |||||||
\(522\) | 3.00000 | − | 5.19615i | 0.131306 | − | 0.227429i | ||||
\(523\) | 14.0000 | + | 24.2487i | 0.612177 | + | 1.06032i | 0.990873 | + | 0.134801i | \(0.0430394\pi\) |
−0.378695 | + | 0.925521i | \(0.623627\pi\) | |||||||
\(524\) | 3.00000 | 0.131056 | ||||||||
\(525\) | −5.00000 | − | 1.73205i | −0.218218 | − | 0.0755929i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.0000 | + | 41.5692i | 1.04546 | + | 1.81078i | ||||
\(528\) | 3.00000 | − | 5.19615i | 0.130558 | − | 0.226134i | ||||
\(529\) | −29.0000 | + | 50.2295i | −1.26087 | + | 2.18389i | ||||
\(530\) | 4.50000 | + | 7.79423i | 0.195468 | + | 0.338560i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.00000 | − | 1.73205i | 0.0867110 | − | 0.0750939i | ||||
\(533\) | −3.00000 | −0.129944 | ||||||||
\(534\) | −6.00000 | − | 10.3923i | −0.259645 | − | 0.449719i | ||||
\(535\) | 6.00000 | − | 10.3923i | 0.259403 | − | 0.449299i | ||||
\(536\) | 4.00000 | − | 6.92820i | 0.172774 | − | 0.299253i | ||||
\(537\) | −3.00000 | − | 5.19615i | −0.129460 | − | 0.224231i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.5000 | + | 12.9904i | 0.710705 | + | 0.559535i | ||||
\(540\) | 4.00000 | 0.172133 | ||||||||
\(541\) | −4.00000 | − | 6.92820i | −0.171973 | − | 0.297867i | 0.767136 | − | 0.641484i | \(-0.221681\pi\) |
−0.939110 | + | 0.343617i | \(0.888348\pi\) | |||||||
\(542\) | −8.00000 | + | 13.8564i | −0.343629 | + | 0.595184i | ||||
\(543\) | 2.00000 | − | 3.46410i | 0.0858282 | − | 0.148659i | ||||
\(544\) | −3.00000 | − | 5.19615i | −0.128624 | − | 0.222783i | ||||
\(545\) | −16.0000 | −0.685365 | ||||||||
\(546\) | 4.00000 | − | 3.46410i | 0.171184 | − | 0.148250i | ||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | −6.00000 | − | 10.3923i | −0.256307 | − | 0.443937i | ||||
\(549\) | −4.00000 | + | 6.92820i | −0.170716 | + | 0.295689i | ||||
\(550\) | 1.50000 | − | 2.59808i | 0.0639602 | − | 0.110782i | ||||
\(551\) | 3.00000 | + | 5.19615i | 0.127804 | + | 0.221364i | ||||
\(552\) | 18.0000 | 0.766131 | ||||||||
\(553\) | −25.0000 | − | 8.66025i | −1.06311 | − | 0.368271i | ||||
\(554\) | 10.0000 | 0.424859 | ||||||||
\(555\) | −7.00000 | − | 12.1244i | −0.297133 | − | 0.514650i | ||||
\(556\) | 2.00000 | − | 3.46410i | 0.0848189 | − | 0.146911i | ||||
\(557\) | 4.50000 | − | 7.79423i | 0.190671 | − | 0.330252i | −0.754802 | − | 0.655953i | \(-0.772267\pi\) |
0.945473 | + | 0.325701i | \(0.105600\pi\) | |||||||
\(558\) | 4.00000 | + | 6.92820i | 0.169334 | + | 0.293294i | ||||
\(559\) | −2.00000 | −0.0845910 | ||||||||
\(560\) | −0.500000 | − | 2.59808i | −0.0211289 | − | 0.109789i | ||||
\(561\) | 36.0000 | 1.51992 | ||||||||
\(562\) | −13.5000 | − | 23.3827i | −0.569463 | − | 0.986339i | ||||
\(563\) | −21.0000 | + | 36.3731i | −0.885044 | + | 1.53294i | −0.0393818 | + | 0.999224i | \(0.512539\pi\) |
−0.845663 | + | 0.533718i | \(0.820794\pi\) | |||||||
\(564\) | 9.00000 | − | 15.5885i | 0.378968 | − | 0.656392i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.0000 | −0.588464 | ||||||||
\(567\) | 5.50000 | + | 28.5788i | 0.230978 | + | 1.20020i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.5000 | − | 18.1865i | −0.440183 | − | 0.762419i | 0.557520 | − | 0.830164i | \(-0.311753\pi\) |
−0.997703 | + | 0.0677445i | \(0.978420\pi\) | |||||||
\(570\) | 1.00000 | − | 1.73205i | 0.0418854 | − | 0.0725476i | ||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 1.50000 | + | 2.59808i | 0.0627182 | + | 0.108631i | ||||
\(573\) | −24.0000 | −1.00261 | ||||||||
\(574\) | −7.50000 | − | 2.59808i | −0.313044 | − | 0.108442i | ||||
\(575\) | 9.00000 | 0.375326 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −22.0000 | + | 38.1051i | −0.915872 | + | 1.58634i | −0.110252 | + | 0.993904i | \(0.535166\pi\) |
−0.805620 | + | 0.592433i | \(0.798167\pi\) | |||||||
\(578\) | 9.50000 | − | 16.4545i | 0.395148 | − | 0.684416i | ||||
\(579\) | −16.0000 | − | 27.7128i | −0.664937 | − | 1.15171i | ||||
\(580\) | 6.00000 | 0.249136 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −20.0000 | −0.829027 | ||||||||
\(583\) | −13.5000 | − | 23.3827i | −0.559113 | − | 0.968412i | ||||
\(584\) | −2.00000 | + | 3.46410i | −0.0827606 | + | 0.143346i | ||||
\(585\) | 0.500000 | − | 0.866025i | 0.0206725 | − | 0.0358057i | ||||
\(586\) | −4.50000 | − | 7.79423i | −0.185893 | − | 0.321977i | ||||
\(587\) | −24.0000 | −0.990586 | −0.495293 | − | 0.868726i | \(-0.664939\pi\) | ||||
−0.495293 | + | 0.868726i | \(0.664939\pi\) | |||||||
\(588\) | 13.0000 | − | 5.19615i | 0.536111 | − | 0.214286i | ||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.0000 | − | 25.9808i | 0.617018 | − | 1.06871i | ||||
\(592\) | 3.50000 | − | 6.06218i | 0.143849 | − | 0.249154i | ||||
\(593\) | −12.0000 | − | 20.7846i | −0.492781 | − | 0.853522i | 0.507184 | − | 0.861838i | \(-0.330686\pi\) |
−0.999965 | + | 0.00831589i | \(0.997353\pi\) | |||||||
\(594\) | −12.0000 | −0.492366 | ||||||||
\(595\) | 12.0000 | − | 10.3923i | 0.491952 | − | 0.426043i | ||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | −16.0000 | − | 27.7128i | −0.654836 | − | 1.13421i | ||||
\(598\) | −4.50000 | + | 7.79423i | −0.184019 | + | 0.318730i | ||||
\(599\) | 21.0000 | − | 36.3731i | 0.858037 | − | 1.48616i | −0.0157622 | − | 0.999876i | \(-0.505017\pi\) |
0.873799 | − | 0.486287i | \(-0.161649\pi\) | |||||||
\(600\) | −1.00000 | − | 1.73205i | −0.0408248 | − | 0.0707107i | ||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | −5.00000 | − | 1.73205i | −0.203785 | − | 0.0705931i | ||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 5.00000 | + | 8.66025i | 0.203447 | + | 0.352381i | ||||
\(605\) | 1.00000 | − | 1.73205i | 0.0406558 | − | 0.0704179i | ||||
\(606\) | −12.0000 | + | 20.7846i | −0.487467 | + | 0.844317i | ||||
\(607\) | 0.500000 | + | 0.866025i | 0.0202944 | + | 0.0351509i | 0.875994 | − | 0.482322i | \(-0.160206\pi\) |
−0.855700 | + | 0.517472i | \(0.826873\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 6.00000 | + | 31.1769i | 0.243132 | + | 1.26335i | ||||
\(610\) | −8.00000 | −0.323911 | ||||||||
\(611\) | 4.50000 | + | 7.79423i | 0.182051 | + | 0.315321i | ||||
\(612\) | 3.00000 | − | 5.19615i | 0.121268 | − | 0.210042i | ||||
\(613\) | −14.5000 | + | 25.1147i | −0.585649 | + | 1.01437i | 0.409145 | + | 0.912470i | \(0.365827\pi\) |
−0.994794 | + | 0.101905i | \(0.967506\pi\) | |||||||
\(614\) | 7.00000 | + | 12.1244i | 0.282497 | + | 0.489299i | ||||
\(615\) | −6.00000 | −0.241943 | ||||||||
\(616\) | 1.50000 | + | 7.79423i | 0.0604367 | + | 0.314038i | ||||
\(617\) | −18.0000 | −0.724653 | −0.362326 | − | 0.932051i | \(-0.618017\pi\) | ||||
−0.362326 | + | 0.932051i | \(0.618017\pi\) | |||||||
\(618\) | 4.00000 | + | 6.92820i | 0.160904 | + | 0.278693i | ||||
\(619\) | −11.5000 | + | 19.9186i | −0.462224 | + | 0.800595i | −0.999071 | − | 0.0430838i | \(-0.986282\pi\) |
0.536847 | + | 0.843679i | \(0.319615\pi\) | |||||||
\(620\) | −4.00000 | + | 6.92820i | −0.160644 | + | 0.278243i | ||||
\(621\) | −18.0000 | − | 31.1769i | −0.722315 | − | 1.25109i | ||||
\(622\) | 24.0000 | 0.962312 | ||||||||
\(623\) | 15.0000 | + | 5.19615i | 0.600962 | + | 0.208179i | ||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −14.0000 | + | 24.2487i | −0.559553 | + | 0.969173i | ||||
\(627\) | −3.00000 | + | 5.19615i | −0.119808 | + | 0.207514i | ||||
\(628\) | −11.5000 | − | 19.9186i | −0.458900 | − | 0.794838i | ||||
\(629\) | 42.0000 | 1.67465 | ||||||||
\(630\) | 2.00000 | − | 1.73205i | 0.0796819 | − | 0.0690066i | ||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | −5.00000 | − | 8.66025i | −0.198889 | − | 0.344486i | ||||
\(633\) | 23.0000 | − | 39.8372i | 0.914168 | − | 1.58339i | ||||
\(634\) | 3.00000 | − | 5.19615i | 0.119145 | − | 0.206366i | ||||
\(635\) | 0.500000 | + | 0.866025i | 0.0198419 | + | 0.0343672i | ||||
\(636\) | −18.0000 | −0.713746 | ||||||||
\(637\) | −1.00000 | + | 6.92820i | −0.0396214 | + | 0.274505i | ||||
\(638\) | −18.0000 | −0.712627 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −13.5000 | + | 23.3827i | −0.533218 | + | 0.923561i | 0.466029 | + | 0.884769i | \(0.345684\pi\) |
−0.999247 | + | 0.0387913i | \(0.987649\pi\) | |||||||
\(642\) | 12.0000 | + | 20.7846i | 0.473602 | + | 0.820303i | ||||
\(643\) | 2.00000 | 0.0788723 | 0.0394362 | − | 0.999222i | \(-0.487444\pi\) | ||||
0.0394362 | + | 0.999222i | \(0.487444\pi\) | |||||||
\(644\) | −18.0000 | + | 15.5885i | −0.709299 | + | 0.614271i | ||||
\(645\) | −4.00000 | −0.157500 | ||||||||
\(646\) | 3.00000 | + | 5.19615i | 0.118033 | + | 0.204440i | ||||
\(647\) | −16.5000 | + | 28.5788i | −0.648682 | + | 1.12355i | 0.334756 | + | 0.942305i | \(0.391346\pi\) |
−0.983438 | + | 0.181245i | \(0.941987\pi\) | |||||||
\(648\) | −5.50000 | + | 9.52628i | −0.216060 | + | 0.374228i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.00000 | 0.0392232 | ||||||||
\(651\) | −40.0000 | − | 13.8564i | −1.56772 | − | 0.543075i | ||||
\(652\) | 20.0000 | 0.783260 | ||||||||
\(653\) | 4.50000 | + | 7.79423i | 0.176099 | + | 0.305012i | 0.940541 | − | 0.339680i | \(-0.110319\pi\) |
−0.764442 | + | 0.644692i | \(0.776986\pi\) | |||||||
\(654\) | 16.0000 | − | 27.7128i | 0.625650 | − | 1.08366i | ||||
\(655\) | −1.50000 | + | 2.59808i | −0.0586098 | + | 0.101515i | ||||
\(656\) | −1.50000 | − | 2.59808i | −0.0585652 | − | 0.101438i | ||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 4.50000 | + | 23.3827i | 0.175428 | + | 0.911552i | ||||
\(659\) | −24.0000 | −0.934907 | −0.467454 | − | 0.884018i | \(-0.654829\pi\) | ||||
−0.467454 | + | 0.884018i | \(0.654829\pi\) | |||||||
\(660\) | 3.00000 | + | 5.19615i | 0.116775 | + | 0.202260i | ||||
\(661\) | 14.0000 | − | 24.2487i | 0.544537 | − | 0.943166i | −0.454099 | − | 0.890951i | \(-0.650039\pi\) |
0.998636 | − | 0.0522143i | \(-0.0166279\pi\) | |||||||
\(662\) | −3.50000 | + | 6.06218i | −0.136031 | + | 0.235613i | ||||
\(663\) | 6.00000 | + | 10.3923i | 0.233021 | + | 0.403604i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.500000 | + | 2.59808i | 0.0193892 | + | 0.100749i | ||||
\(666\) | 7.00000 | 0.271244 | ||||||||
\(667\) | −27.0000 | − | 46.7654i | −1.04544 | − | 1.81076i | ||||
\(668\) | −1.50000 | + | 2.59808i | −0.0580367 | + | 0.100523i | ||||
\(669\) | 8.00000 | − | 13.8564i | 0.309298 | − | 0.535720i | ||||
\(670\) | 4.00000 | + | 6.92820i | 0.154533 | + | 0.267660i | ||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 5.00000 | + | 1.73205i | 0.192879 | + | 0.0668153i | ||||
\(673\) | −34.0000 | −1.31060 | −0.655302 | − | 0.755367i | \(-0.727459\pi\) | ||||
−0.655302 | + | 0.755367i | \(0.727459\pi\) | |||||||
\(674\) | −11.0000 | − | 19.0526i | −0.423704 | − | 0.733877i | ||||
\(675\) | −2.00000 | + | 3.46410i | −0.0769800 | + | 0.133333i | ||||
\(676\) | 6.00000 | − | 10.3923i | 0.230769 | − | 0.399704i | ||||
\(677\) | 4.50000 | + | 7.79423i | 0.172949 | + | 0.299557i | 0.939450 | − | 0.342687i | \(-0.111337\pi\) |
−0.766501 | + | 0.642244i | \(0.778004\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.0000 | − | 17.3205i | 0.767530 | − | 0.664700i | ||||
\(680\) | 6.00000 | 0.230089 | ||||||||
\(681\) | −12.0000 | − | 20.7846i | −0.459841 | − | 0.796468i | ||||
\(682\) | 12.0000 | − | 20.7846i | 0.459504 | − | 0.795884i | ||||
\(683\) | −6.00000 | + | 10.3923i | −0.229584 | + | 0.397650i | −0.957685 | − | 0.287819i | \(-0.907070\pi\) |
0.728101 | + | 0.685470i | \(0.240403\pi\) | |||||||
\(684\) | 0.500000 | + | 0.866025i | 0.0191180 | + | 0.0331133i | ||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | −8.50000 | + | 16.4545i | −0.324532 | + | 0.628235i | ||||
\(687\) | 8.00000 | 0.305219 | ||||||||
\(688\) | −1.00000 | − | 1.73205i | −0.0381246 | − | 0.0660338i | ||||
\(689\) | 4.50000 | − | 7.79423i | 0.171436 | − | 0.296936i | ||||
\(690\) | −9.00000 | + | 15.5885i | −0.342624 | + | 0.593442i | ||||
\(691\) | −16.0000 | − | 27.7128i | −0.608669 | − | 1.05425i | −0.991460 | − | 0.130410i | \(-0.958371\pi\) |
0.382791 | − | 0.923835i | \(-0.374963\pi\) | |||||||
\(692\) | 9.00000 | 0.342129 | ||||||||
\(693\) | −6.00000 | + | 5.19615i | −0.227921 | + | 0.197386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.00000 | + | 3.46410i | 0.0758643 | + | 0.131401i | ||||
\(696\) | −6.00000 | + | 10.3923i | −0.227429 | + | 0.393919i | ||||
\(697\) | 9.00000 | − | 15.5885i | 0.340899 | − | 0.590455i | ||||
\(698\) | 13.0000 | + | 22.5167i | 0.492057 | + | 0.852268i | ||||
\(699\) | 12.0000 | 0.453882 | ||||||||
\(700\) | 2.50000 | + | 0.866025i | 0.0944911 | + | 0.0327327i | ||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | −2.00000 | − | 3.46410i | −0.0754851 | − | 0.130744i | ||||
\(703\) | −3.50000 | + | 6.06218i | −0.132005 | + | 0.228639i | ||||
\(704\) | −1.50000 | + | 2.59808i | −0.0565334 | + | 0.0979187i | ||||
\(705\) | 9.00000 | + | 15.5885i | 0.338960 | + | 0.587095i | ||||
\(706\) | −12.0000 | −0.451626 | ||||||||
\(707\) | −6.00000 | − | 31.1769i | −0.225653 | − | 1.17253i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.0000 | + | 39.8372i | 0.863783 | + | 1.49612i | 0.868250 | + | 0.496126i | \(0.165245\pi\) |
−0.00446726 | + | 0.999990i | \(0.501422\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.00000 | − | 8.66025i | 0.187515 | − | 0.324785i | ||||
\(712\) | 3.00000 | + | 5.19615i | 0.112430 | + | 0.194734i | ||||
\(713\) | 72.0000 | 2.69642 | ||||||||
\(714\) | 6.00000 | + | 31.1769i | 0.224544 | + | 1.16677i | ||||
\(715\) | −3.00000 | −0.112194 | ||||||||
\(716\) | 1.50000 | + | 2.59808i | 0.0560576 | + | 0.0970947i | ||||
\(717\) | −6.00000 | + | 10.3923i | −0.224074 | + | 0.388108i | ||||
\(718\) | 9.00000 | − | 15.5885i | 0.335877 | − | 0.581756i | ||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −10.0000 | − | 3.46410i | −0.372419 | − | 0.129010i | ||||
\(722\) | 18.0000 | 0.669891 | ||||||||
\(723\) | −1.00000 | − | 1.73205i | −0.0371904 | − | 0.0644157i | ||||
\(724\) | −1.00000 | + | 1.73205i | −0.0371647 | + | 0.0643712i | ||||
\(725\) | −3.00000 | + | 5.19615i | −0.111417 | + | 0.192980i | ||||
\(726\) | 2.00000 | + | 3.46410i | 0.0742270 | + | 0.128565i | ||||
\(727\) | −1.00000 | −0.0370879 | −0.0185440 | − | 0.999828i | \(-0.505903\pi\) | ||||
−0.0185440 | + | 0.999828i | \(0.505903\pi\) | |||||||
\(728\) | −2.00000 | + | 1.73205i | −0.0741249 | + | 0.0641941i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −2.00000 | − | 3.46410i | −0.0740233 | − | 0.128212i | ||||
\(731\) | 6.00000 | − | 10.3923i | 0.221918 | − | 0.384373i | ||||
\(732\) | 8.00000 | − | 13.8564i | 0.295689 | − | 0.512148i | ||||
\(733\) | 21.5000 | + | 37.2391i | 0.794121 | + | 1.37546i | 0.923396 | + | 0.383849i | \(0.125402\pi\) |
−0.129275 | + | 0.991609i | \(0.541265\pi\) | |||||||
\(734\) | 19.0000 | 0.701303 | ||||||||
\(735\) | −2.00000 | + | 13.8564i | −0.0737711 | + | 0.511101i | ||||
\(736\) | −9.00000 | −0.331744 | ||||||||
\(737\) | −12.0000 | − | 20.7846i | −0.442026 | − | 0.765611i | ||||
\(738\) | 1.50000 | − | 2.59808i | 0.0552158 | − | 0.0956365i | ||||
\(739\) | −17.5000 | + | 30.3109i | −0.643748 | + | 1.11500i | 0.340841 | + | 0.940121i | \(0.389288\pi\) |
−0.984589 | + | 0.174883i | \(0.944045\pi\) | |||||||
\(740\) | 3.50000 | + | 6.06218i | 0.128663 | + | 0.222850i | ||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 18.0000 | − | 15.5885i | 0.660801 | − | 0.572270i | ||||
\(743\) | −45.0000 | −1.65089 | −0.825445 | − | 0.564483i | \(-0.809076\pi\) | ||||
−0.825445 | + | 0.564483i | \(0.809076\pi\) | |||||||
\(744\) | −8.00000 | − | 13.8564i | −0.293294 | − | 0.508001i | ||||
\(745\) | 3.00000 | − | 5.19615i | 0.109911 | − | 0.190372i | ||||
\(746\) | 1.00000 | − | 1.73205i | 0.0366126 | − | 0.0634149i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −18.0000 | −0.658145 | ||||||||
\(749\) | −30.0000 | − | 10.3923i | −1.09618 | − | 0.379727i | ||||
\(750\) | 2.00000 | 0.0730297 | ||||||||
\(751\) | 5.00000 | + | 8.66025i | 0.182453 | + | 0.316017i | 0.942715 | − | 0.333599i | \(-0.108263\pi\) |
−0.760263 | + | 0.649616i | \(0.774930\pi\) | |||||||
\(752\) | −4.50000 | + | 7.79423i | −0.164098 | + | 0.284226i | ||||
\(753\) | −15.0000 | + | 25.9808i | −0.546630 | + | 0.946792i | ||||
\(754\) | −3.00000 | − | 5.19615i | −0.109254 | − | 0.189233i | ||||
\(755\) | −10.0000 | −0.363937 | ||||||||
\(756\) | −2.00000 | − | 10.3923i | −0.0727393 | − | 0.377964i | ||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | 11.5000 | + | 19.9186i | 0.417699 | + | 0.723476i | ||||
\(759\) | 27.0000 | − | 46.7654i | 0.980038 | − | 1.69748i | ||||
\(760\) | −0.500000 | + | 0.866025i | −0.0181369 | + | 0.0314140i | ||||
\(761\) | 13.5000 | + | 23.3827i | 0.489375 | + | 0.847622i | 0.999925 | − | 0.0122260i | \(-0.00389175\pi\) |
−0.510551 | + | 0.859848i | \(0.670558\pi\) | |||||||
\(762\) | −2.00000 | −0.0724524 | ||||||||
\(763\) | 8.00000 | + | 41.5692i | 0.289619 | + | 1.50491i | ||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 3.00000 | + | 5.19615i | 0.108465 | + | 0.187867i | ||||
\(766\) | 10.5000 | − | 18.1865i | 0.379380 | − | 0.657106i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | + | 1.73205i | 0.0360844 | + | 0.0625000i | ||||
\(769\) | 23.0000 | 0.829401 | 0.414701 | − | 0.909958i | \(-0.363886\pi\) | ||||
0.414701 | + | 0.909958i | \(0.363886\pi\) | |||||||
\(770\) | −7.50000 | − | 2.59808i | −0.270281 | − | 0.0936282i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.00000 | + | 13.8564i | 0.287926 | + | 0.498703i | ||||
\(773\) | 25.5000 | − | 44.1673i | 0.917171 | − | 1.58859i | 0.113480 | − | 0.993540i | \(-0.463800\pi\) |
0.803691 | − | 0.595047i | \(-0.202867\pi\) | |||||||
\(774\) | 1.00000 | − | 1.73205i | 0.0359443 | − | 0.0622573i | ||||
\(775\) | −4.00000 | − | 6.92820i | −0.143684 | − | 0.248868i | ||||
\(776\) | 10.0000 | 0.358979 | ||||||||
\(777\) | −28.0000 | + | 24.2487i | −1.00449 | + | 0.869918i | ||||
\(778\) | 12.0000 | 0.430221 | ||||||||
\(779\) | 1.50000 | + | 2.59808i | 0.0537431 | + | 0.0930857i | ||||
\(780\) | −1.00000 | + | 1.73205i | −0.0358057 | + | 0.0620174i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −27.0000 | − | 46.7654i | −0.965518 | − | 1.67233i | ||||
\(783\) | 24.0000 | 0.857690 | ||||||||
\(784\) | −6.50000 | + | 2.59808i | −0.232143 | + | 0.0927884i | ||||
\(785\) | 23.0000 | 0.820905 | ||||||||
\(786\) | −3.00000 | − | 5.19615i | −0.107006 | − | 0.185341i | ||||
\(787\) | 11.0000 | − | 19.0526i | 0.392108 | − | 0.679150i | −0.600620 | − | 0.799535i | \(-0.705079\pi\) |
0.992727 | + | 0.120384i | \(0.0384127\pi\) | |||||||
\(788\) | −7.50000 | + | 12.9904i | −0.267176 | + | 0.462763i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.0000 | 0.355784 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.00000 | −0.106600 | ||||||||
\(793\) | 4.00000 | + | 6.92820i | 0.142044 | + | 0.246028i | ||||
\(794\) | 7.00000 | − | 12.1244i | 0.248421 | − | 0.430277i | ||||
\(795\) | 9.00000 | − | 15.5885i | 0.319197 | − | 0.552866i | ||||
\(796\) | 8.00000 | + | 13.8564i | 0.283552 | + | 0.491127i | ||||
\(797\) | 6.00000 | 0.212531 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(798\) | −5.00000 | − | 1.73205i | −0.176998 | − | 0.0613139i | ||||
\(799\) | −54.0000 | −1.91038 | ||||||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | −3.00000 | + | 5.19615i | −0.106000 | + | 0.183597i | ||||
\(802\) | −13.5000 | + | 23.3827i | −0.476702 | + | 0.825671i | ||||
\(803\) | 6.00000 | + | 10.3923i | 0.211735 | + | 0.366736i | ||||
\(804\) | −16.0000 | −0.564276 | ||||||||
\(805\) | −4.50000 | − | 23.3827i | −0.158604 | − | 0.824131i | ||||
\(806\) | 8.00000 | 0.281788 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.00000 | − | 10.3923i | 0.211079 | − | 0.365600i | ||||
\(809\) | 4.50000 | − | 7.79423i | 0.158212 | − | 0.274030i | −0.776012 | − | 0.630718i | \(-0.782761\pi\) |
0.934224 | + | 0.356687i | \(0.116094\pi\) | |||||||
\(810\) | −5.50000 | − | 9.52628i | −0.193250 | − | 0.334719i | ||||
\(811\) | −25.0000 | −0.877869 | −0.438934 | − | 0.898519i | \(-0.644644\pi\) | ||||
−0.438934 | + | 0.898519i | \(0.644644\pi\) | |||||||
\(812\) | −3.00000 | − | 15.5885i | −0.105279 | − | 0.547048i | ||||
\(813\) | 32.0000 | 1.12229 | ||||||||
\(814\) | −10.5000 | − | 18.1865i | −0.368025 | − | 0.637438i | ||||
\(815\) | −10.0000 | + | 17.3205i | −0.350285 | + | 0.606711i | ||||
\(816\) | −6.00000 | + | 10.3923i | −0.210042 | + | 0.363803i | ||||
\(817\) | 1.00000 | + | 1.73205i | 0.0349856 | + | 0.0605968i | ||||
\(818\) | −26.0000 | −0.909069 | ||||||||
\(819\) | −2.50000 | − | 0.866025i | −0.0873571 | − | 0.0302614i | ||||
\(820\) | 3.00000 | 0.104765 | ||||||||
\(821\) | −15.0000 | − | 25.9808i | −0.523504 | − | 0.906735i | −0.999626 | − | 0.0273557i | \(-0.991291\pi\) |
0.476122 | − | 0.879379i | \(-0.342042\pi\) | |||||||
\(822\) | −12.0000 | + | 20.7846i | −0.418548 | + | 0.724947i | ||||
\(823\) | 2.00000 | − | 3.46410i | 0.0697156 | − | 0.120751i | −0.829060 | − | 0.559159i | \(-0.811124\pi\) |
0.898776 | + | 0.438408i | \(0.144457\pi\) | |||||||
\(824\) | −2.00000 | − | 3.46410i | −0.0696733 | − | 0.120678i | ||||
\(825\) | −6.00000 | −0.208893 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.00000 | 0.208640 | 0.104320 | − | 0.994544i | \(-0.466733\pi\) | ||||
0.104320 | + | 0.994544i | \(0.466733\pi\) | |||||||
\(828\) | −4.50000 | − | 7.79423i | −0.156386 | − | 0.270868i | ||||
\(829\) | −7.00000 | + | 12.1244i | −0.243120 | + | 0.421096i | −0.961601 | − | 0.274450i | \(-0.911504\pi\) |
0.718481 | + | 0.695546i | \(0.244838\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.0000 | − | 17.3205i | −0.346896 | − | 0.600842i | ||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −33.0000 | − | 25.9808i | −1.14338 | − | 0.900180i | ||||
\(834\) | −8.00000 | −0.277017 | ||||||||
\(835\) | −1.50000 | − | 2.59808i | −0.0519096 | − | 0.0899101i | ||||
\(836\) | 1.50000 | − | 2.59808i | 0.0518786 | − | 0.0898563i | ||||
\(837\) | −16.0000 | + | 27.7128i | −0.553041 | + | 0.957895i | ||||
\(838\) | −4.50000 | − | 7.79423i | −0.155450 | − | 0.269247i | ||||
\(839\) | −30.0000 | −1.03572 | −0.517858 | − | 0.855467i | \(-0.673270\pi\) | ||||
−0.517858 | + | 0.855467i | \(0.673270\pi\) | |||||||
\(840\) | −4.00000 | + | 3.46410i | −0.138013 | + | 0.119523i | ||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 1.00000 | + | 1.73205i | 0.0344623 | + | 0.0596904i | ||||
\(843\) | −27.0000 | + | 46.7654i | −0.929929 | + | 1.61068i | ||||
\(844\) | −11.5000 | + | 19.9186i | −0.395846 | + | 0.685626i | ||||
\(845\) | 6.00000 | + | 10.3923i | 0.206406 | + | 0.357506i | ||||
\(846\) | −9.00000 | −0.309426 | ||||||||
\(847\) | −5.00000 | − | 1.73205i | −0.171802 | − | 0.0595140i | ||||
\(848\) | 9.00000 | 0.309061 | ||||||||
\(849\) | 14.0000 | + | 24.2487i | 0.480479 | + | 0.832214i | ||||
\(850\) | −3.00000 | + | 5.19615i | −0.102899 | + | 0.178227i | ||||
\(851\) | 31.5000 | − | 54.5596i | 1.07981 | − | 1.87028i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.0000 | −0.650548 | −0.325274 | − | 0.945620i | \(-0.605456\pi\) | ||||
−0.325274 | + | 0.945620i | \(0.605456\pi\) | |||||||
\(854\) | 4.00000 | + | 20.7846i | 0.136877 | + | 0.711235i | ||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | 9.00000 | − | 15.5885i | 0.307434 | − | 0.532492i | −0.670366 | − | 0.742030i | \(-0.733863\pi\) |
0.977800 | + | 0.209539i | \(0.0671963\pi\) | |||||||
\(858\) | 3.00000 | − | 5.19615i | 0.102418 | − | 0.177394i | ||||
\(859\) | −16.0000 | − | 27.7128i | −0.545913 | − | 0.945549i | −0.998549 | − | 0.0538535i | \(-0.982850\pi\) |
0.452636 | − | 0.891695i | \(-0.350484\pi\) | |||||||
\(860\) | 2.00000 | 0.0681994 | ||||||||
\(861\) | 3.00000 | + | 15.5885i | 0.102240 | + | 0.531253i | ||||
\(862\) | −12.0000 | −0.408722 | ||||||||
\(863\) | 1.50000 | + | 2.59808i | 0.0510606 | + | 0.0884395i | 0.890426 | − | 0.455128i | \(-0.150407\pi\) |
−0.839365 | + | 0.543568i | \(0.817073\pi\) | |||||||
\(864\) | 2.00000 | − | 3.46410i | 0.0680414 | − | 0.117851i | ||||
\(865\) | −4.50000 | + | 7.79423i | −0.153005 | + | 0.265012i | ||||
\(866\) | −20.0000 | − | 34.6410i | −0.679628 | − | 1.17715i | ||||
\(867\) | −38.0000 | −1.29055 | ||||||||
\(868\) | 20.0000 | + | 6.92820i | 0.678844 | + | 0.235159i | ||||
\(869\) | −30.0000 | −1.01768 | ||||||||
\(870\) | −6.00000 | − | 10.3923i | −0.203419 | − | 0.352332i | ||||
\(871\) | 4.00000 | − | 6.92820i | 0.135535 | − | 0.234753i | ||||
\(872\) | −8.00000 | + | 13.8564i | −0.270914 | + | 0.469237i | ||||
\(873\) | 5.00000 | + | 8.66025i | 0.169224 | + | 0.293105i | ||||
\(874\) | 9.00000 | 0.304430 | ||||||||
\(875\) | −2.00000 | + | 1.73205i | −0.0676123 | + | 0.0585540i | ||||
\(876\) | 8.00000 | 0.270295 | ||||||||
\(877\) | 6.50000 | + | 11.2583i | 0.219489 | + | 0.380167i | 0.954652 | − | 0.297724i | \(-0.0962275\pi\) |
−0.735163 | + | 0.677891i | \(0.762894\pi\) | |||||||
\(878\) | 13.0000 | − | 22.5167i | 0.438729 | − | 0.759900i | ||||
\(879\) | −9.00000 | + | 15.5885i | −0.303562 | + | 0.525786i | ||||
\(880\) | −1.50000 | − | 2.59808i | −0.0505650 | − | 0.0875811i | ||||
\(881\) | 33.0000 | 1.11180 | 0.555899 | − | 0.831250i | \(-0.312374\pi\) | ||||
0.555899 | + | 0.831250i | \(0.312374\pi\) | |||||||
\(882\) | −5.50000 | − | 4.33013i | −0.185195 | − | 0.145803i | ||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | −3.00000 | − | 5.19615i | −0.100901 | − | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.00000 | − | 10.3923i | 0.201574 | − | 0.349136i | ||||
\(887\) | 24.0000 | + | 41.5692i | 0.805841 | + | 1.39576i | 0.915722 | + | 0.401813i | \(0.131620\pi\) |
−0.109881 | + | 0.993945i | \(0.535047\pi\) | |||||||
\(888\) | −14.0000 | −0.469809 | ||||||||
\(889\) | 2.00000 | − | 1.73205i | 0.0670778 | − | 0.0580911i | ||||
\(890\) | −6.00000 | −0.201120 | ||||||||
\(891\) | 16.5000 | + | 28.5788i | 0.552771 | + | 0.957427i | ||||
\(892\) | −4.00000 | + | 6.92820i | −0.133930 | + | 0.231973i | ||||
\(893\) | 4.50000 | − | 7.79423i | 0.150587 | − | 0.260824i | ||||
\(894\) | 6.00000 | + | 10.3923i | 0.200670 | + | 0.347571i | ||||
\(895\) | −3.00000 | −0.100279 | ||||||||
\(896\) | −2.50000 | − | 0.866025i | −0.0835191 | − | 0.0289319i | ||||
\(897\) | 18.0000 | 0.601003 | ||||||||
\(898\) | 10.5000 | + | 18.1865i | 0.350390 | + | 0.606892i | ||||
\(899\) | −24.0000 | + | 41.5692i | −0.800445 | + | 1.38641i | ||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | 27.0000 | + | 46.7654i | 0.899500 | + | 1.55798i | ||||
\(902\) | −9.00000 | −0.299667 | ||||||||
\(903\) | 2.00000 | + | 10.3923i | 0.0665558 | + | 0.345834i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.00000 | − | 1.73205i | −0.0332411 | − | 0.0575753i | ||||
\(906\) | 10.0000 | − | 17.3205i | 0.332228 | − | 0.575435i | ||||
\(907\) | 5.00000 | − | 8.66025i | 0.166022 | − | 0.287559i | −0.770996 | − | 0.636841i | \(-0.780241\pi\) |
0.937018 | + | 0.349281i | \(0.113574\pi\) | |||||||
\(908\) | 6.00000 | + | 10.3923i | 0.199117 | + | 0.344881i | ||||
\(909\) | 12.0000 | 0.398015 | ||||||||
\(910\) | −0.500000 | − | 2.59808i | −0.0165748 | − | 0.0861254i | ||||
\(911\) | −30.0000 | −0.993944 | −0.496972 | − | 0.867766i | \(-0.665555\pi\) | ||||
−0.496972 | + | 0.867766i | \(0.665555\pi\) | |||||||
\(912\) | −1.00000 | − | 1.73205i | −0.0331133 | − | 0.0573539i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 7.00000 | − | 12.1244i | 0.231539 | − | 0.401038i | ||||
\(915\) | 8.00000 | + | 13.8564i | 0.264472 | + | 0.458079i | ||||
\(916\) | −4.00000 | −0.132164 | ||||||||
\(917\) | 7.50000 | + | 2.59808i | 0.247672 | + | 0.0857960i | ||||
\(918\) | 24.0000 | 0.792118 | ||||||||
\(919\) | 11.0000 | + | 19.0526i | 0.362857 | + | 0.628486i | 0.988430 | − | 0.151680i | \(-0.0484682\pi\) |
−0.625573 | + | 0.780165i | \(0.715135\pi\) | |||||||
\(920\) | 4.50000 | − | 7.79423i | 0.148361 | − | 0.256968i | ||||
\(921\) | 14.0000 | − | 24.2487i | 0.461316 | − | 0.799022i | ||||
\(922\) | −15.0000 | − | 25.9808i | −0.493999 | − | 0.855631i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 12.0000 | − | 10.3923i | 0.394771 | − | 0.341882i | ||||
\(925\) | −7.00000 | −0.230159 | ||||||||
\(926\) | −0.500000 | − | 0.866025i | −0.0164310 | − | 0.0284594i | ||||
\(927\) | 2.00000 | − | 3.46410i | 0.0656886 | − | 0.113776i | ||||
\(928\) | 3.00000 | − | 5.19615i | 0.0984798 | − | 0.170572i | ||||
\(929\) | −28.5000 | − | 49.3634i | −0.935055 | − | 1.61956i | −0.774536 | − | 0.632529i | \(-0.782017\pi\) |
−0.160518 | − | 0.987033i | \(-0.551317\pi\) | |||||||
\(930\) | 16.0000 | 0.524661 | ||||||||
\(931\) | 6.50000 | − | 2.59808i | 0.213029 | − | 0.0851485i | ||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | −24.0000 | − | 41.5692i | −0.785725 | − | 1.36092i | ||||
\(934\) | −3.00000 | + | 5.19615i | −0.0981630 | + | 0.170023i | ||||
\(935\) | 9.00000 | − | 15.5885i | 0.294331 | − | 0.509797i | ||||
\(936\) | −0.500000 | − | 0.866025i | −0.0163430 | − | 0.0283069i | ||||
\(937\) | −10.0000 | −0.326686 | −0.163343 | − | 0.986569i | \(-0.552228\pi\) | ||||
−0.163343 | + | 0.986569i | \(0.552228\pi\) | |||||||
\(938\) | 16.0000 | − | 13.8564i | 0.522419 | − | 0.452428i | ||||
\(939\) | 56.0000 | 1.82749 | ||||||||
\(940\) | −4.50000 | − | 7.79423i | −0.146774 | − | 0.254220i | ||||
\(941\) | −24.0000 | + | 41.5692i | −0.782378 | + | 1.35512i | 0.148176 | + | 0.988961i | \(0.452660\pi\) |
−0.930553 | + | 0.366157i | \(0.880673\pi\) | |||||||
\(942\) | −23.0000 | + | 39.8372i | −0.749380 | + | 1.29797i | ||||
\(943\) | −13.5000 | − | 23.3827i | −0.439620 | − | 0.761445i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.0000 | + | 3.46410i | 0.325300 | + | 0.112687i | ||||
\(946\) | −6.00000 | −0.195077 | ||||||||
\(947\) | −3.00000 | − | 5.19615i | −0.0974869 | − | 0.168852i | 0.813157 | − | 0.582045i | \(-0.197747\pi\) |
−0.910644 | + | 0.413192i | \(0.864414\pi\) | |||||||
\(948\) | −10.0000 | + | 17.3205i | −0.324785 | + | 0.562544i | ||||
\(949\) | −2.00000 | + | 3.46410i | −0.0649227 | + | 0.112449i | ||||
\(950\) | −0.500000 | − | 0.866025i | −0.0162221 | − | 0.0280976i | ||||
\(951\) | −12.0000 | −0.389127 | ||||||||
\(952\) | −3.00000 | − | 15.5885i | −0.0972306 | − | 0.505225i | ||||
\(953\) | 36.0000 | 1.16615 | 0.583077 | − | 0.812417i | \(-0.301849\pi\) | ||||
0.583077 | + | 0.812417i | \(0.301849\pi\) | |||||||
\(954\) | 4.50000 | + | 7.79423i | 0.145693 | + | 0.252347i | ||||
\(955\) | −6.00000 | + | 10.3923i | −0.194155 | + | 0.336287i | ||||
\(956\) | 3.00000 | − | 5.19615i | 0.0970269 | − | 0.168056i | ||||
\(957\) | 18.0000 | + | 31.1769i | 0.581857 | + | 1.00781i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.00000 | − | 31.1769i | −0.193750 | − | 1.00676i | ||||
\(960\) | −2.00000 | −0.0645497 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | 3.50000 | − | 6.06218i | 0.112845 | − | 0.195452i | ||||
\(963\) | 6.00000 | − | 10.3923i | 0.193347 | − | 0.334887i | ||||
\(964\) | 0.500000 | + | 0.866025i | 0.0161039 | + | 0.0278928i | ||||
\(965\) | −16.0000 | −0.515058 | ||||||||
\(966\) | 45.0000 | + | 15.5885i | 1.44785 | + | 0.501550i | ||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | −1.00000 | − | 1.73205i | −0.0321412 | − | 0.0556702i | ||||
\(969\) | 6.00000 | − | 10.3923i | 0.192748 | − | 0.333849i | ||||
\(970\) | −5.00000 | + | 8.66025i | −0.160540 | + | 0.278064i | ||||
\(971\) | 22.5000 | + | 38.9711i | 0.722059 | + | 1.25064i | 0.960173 | + | 0.279406i | \(0.0901376\pi\) |
−0.238114 | + | 0.971237i | \(0.576529\pi\) | |||||||
\(972\) | 10.0000 | 0.320750 | ||||||||
\(973\) | 8.00000 | − | 6.92820i | 0.256468 | − | 0.222108i | ||||
\(974\) | 16.0000 | 0.512673 | ||||||||
\(975\) | −1.00000 | − | 1.73205i | −0.0320256 | − | 0.0554700i | ||||
\(976\) | −4.00000 | + | 6.92820i | −0.128037 | + | 0.221766i | ||||
\(977\) | 21.0000 | − | 36.3731i | 0.671850 | − | 1.16368i | −0.305530 | − | 0.952183i | \(-0.598833\pi\) |
0.977379 | − | 0.211495i | \(-0.0678332\pi\) | |||||||
\(978\) | −20.0000 | − | 34.6410i | −0.639529 | − | 1.10770i | ||||
\(979\) | 18.0000 | 0.575282 | ||||||||
\(980\) | 1.00000 | − | 6.92820i | 0.0319438 | − | 0.221313i | ||||
\(981\) | −16.0000 | −0.510841 | ||||||||
\(982\) | 18.0000 | + | 31.1769i | 0.574403 | + | 0.994895i | ||||
\(983\) | −1.50000 | + | 2.59808i | −0.0478426 | + | 0.0828658i | −0.888955 | − | 0.457995i | \(-0.848568\pi\) |
0.841112 | + | 0.540860i | \(0.181901\pi\) | |||||||
\(984\) | −3.00000 | + | 5.19615i | −0.0956365 | + | 0.165647i | ||||
\(985\) | −7.50000 | − | 12.9904i | −0.238970 | − | 0.413908i | ||||
\(986\) | 36.0000 | 1.14647 | ||||||||
\(987\) | 36.0000 | − | 31.1769i | 1.14589 | − | 0.992372i | ||||
\(988\) | 1.00000 | 0.0318142 | ||||||||
\(989\) | −9.00000 | − | 15.5885i | −0.286183 | − | 0.495684i | ||||
\(990\) | 1.50000 | − | 2.59808i | 0.0476731 | − | 0.0825723i | ||||
\(991\) | −22.0000 | + | 38.1051i | −0.698853 | + | 1.21045i | 0.270011 | + | 0.962857i | \(0.412973\pi\) |
−0.968864 | + | 0.247592i | \(0.920361\pi\) | |||||||
\(992\) | 4.00000 | + | 6.92820i | 0.127000 | + | 0.219971i | ||||
\(993\) | 14.0000 | 0.444277 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.0000 | −0.507234 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0000 | − | 19.0526i | 0.348373 | − | 0.603401i | −0.637587 | − | 0.770378i | \(-0.720067\pi\) |
0.985961 | + | 0.166978i | \(0.0534008\pi\) | |||||||
\(998\) | −2.00000 | + | 3.46410i | −0.0633089 | + | 0.109654i | ||||
\(999\) | 14.0000 | + | 24.2487i | 0.442940 | + | 0.767195i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 70.2.e.d.11.1 | ✓ | 2 | |
3.2 | odd | 2 | 630.2.k.d.361.1 | 2 | |||
4.3 | odd | 2 | 560.2.q.b.81.1 | 2 | |||
5.2 | odd | 4 | 350.2.j.d.249.1 | 4 | |||
5.3 | odd | 4 | 350.2.j.d.249.2 | 4 | |||
5.4 | even | 2 | 350.2.e.b.151.1 | 2 | |||
7.2 | even | 3 | inner | 70.2.e.d.51.1 | yes | 2 | |
7.3 | odd | 6 | 490.2.a.d.1.1 | 1 | |||
7.4 | even | 3 | 490.2.a.a.1.1 | 1 | |||
7.5 | odd | 6 | 490.2.e.g.471.1 | 2 | |||
7.6 | odd | 2 | 490.2.e.g.361.1 | 2 | |||
21.2 | odd | 6 | 630.2.k.d.541.1 | 2 | |||
21.11 | odd | 6 | 4410.2.a.x.1.1 | 1 | |||
21.17 | even | 6 | 4410.2.a.bg.1.1 | 1 | |||
28.3 | even | 6 | 3920.2.a.e.1.1 | 1 | |||
28.11 | odd | 6 | 3920.2.a.bh.1.1 | 1 | |||
28.23 | odd | 6 | 560.2.q.b.401.1 | 2 | |||
35.2 | odd | 12 | 350.2.j.d.149.2 | 4 | |||
35.3 | even | 12 | 2450.2.c.e.99.2 | 2 | |||
35.4 | even | 6 | 2450.2.a.bf.1.1 | 1 | |||
35.9 | even | 6 | 350.2.e.b.51.1 | 2 | |||
35.17 | even | 12 | 2450.2.c.e.99.1 | 2 | |||
35.18 | odd | 12 | 2450.2.c.q.99.2 | 2 | |||
35.23 | odd | 12 | 350.2.j.d.149.1 | 4 | |||
35.24 | odd | 6 | 2450.2.a.v.1.1 | 1 | |||
35.32 | odd | 12 | 2450.2.c.q.99.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.e.d.11.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
70.2.e.d.51.1 | yes | 2 | 7.2 | even | 3 | inner | |
350.2.e.b.51.1 | 2 | 35.9 | even | 6 | |||
350.2.e.b.151.1 | 2 | 5.4 | even | 2 | |||
350.2.j.d.149.1 | 4 | 35.23 | odd | 12 | |||
350.2.j.d.149.2 | 4 | 35.2 | odd | 12 | |||
350.2.j.d.249.1 | 4 | 5.2 | odd | 4 | |||
350.2.j.d.249.2 | 4 | 5.3 | odd | 4 | |||
490.2.a.a.1.1 | 1 | 7.4 | even | 3 | |||
490.2.a.d.1.1 | 1 | 7.3 | odd | 6 | |||
490.2.e.g.361.1 | 2 | 7.6 | odd | 2 | |||
490.2.e.g.471.1 | 2 | 7.5 | odd | 6 | |||
560.2.q.b.81.1 | 2 | 4.3 | odd | 2 | |||
560.2.q.b.401.1 | 2 | 28.23 | odd | 6 | |||
630.2.k.d.361.1 | 2 | 3.2 | odd | 2 | |||
630.2.k.d.541.1 | 2 | 21.2 | odd | 6 | |||
2450.2.a.v.1.1 | 1 | 35.24 | odd | 6 | |||
2450.2.a.bf.1.1 | 1 | 35.4 | even | 6 | |||
2450.2.c.e.99.1 | 2 | 35.17 | even | 12 | |||
2450.2.c.e.99.2 | 2 | 35.3 | even | 12 | |||
2450.2.c.q.99.1 | 2 | 35.32 | odd | 12 | |||
2450.2.c.q.99.2 | 2 | 35.18 | odd | 12 | |||
3920.2.a.e.1.1 | 1 | 28.3 | even | 6 | |||
3920.2.a.bh.1.1 | 1 | 28.11 | odd | 6 | |||
4410.2.a.x.1.1 | 1 | 21.11 | odd | 6 | |||
4410.2.a.bg.1.1 | 1 | 21.17 | even | 6 |