Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(341,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1890.341");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.bk (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: | \(15.0917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.5 | ||
Character | \(\chi\) | \(=\) | 1890.521 |
Dual form | 1890.2.bk.b.341.5 |
$q$-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 \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(1081\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.55256 | − | 0.696025i | 0.964776 | − | 0.263073i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.866025 | − | 0.500000i | −0.273861 | − | 0.158114i | ||||
\(11\) | −1.26877 | + | 0.732523i | −0.382548 | + | 0.220864i | −0.678926 | − | 0.734206i | \(-0.737554\pi\) |
0.296378 | + | 0.955071i | \(0.404221\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.03529 | + | 3.48448i | −1.67389 | + | 0.966420i | −0.708461 | + | 0.705750i | \(0.750610\pi\) |
−0.965428 | + | 0.260671i | \(0.916056\pi\) | |||||||
\(14\) | −0.696025 | − | 2.55256i | −0.186020 | − | 0.682200i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.30332 | − | 5.72151i | 0.801172 | − | 1.38767i | −0.117673 | − | 0.993052i | \(-0.537544\pi\) |
0.918845 | − | 0.394618i | \(-0.129123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.08388 | + | 1.78048i | −0.707491 | + | 0.408470i | −0.810131 | − | 0.586249i | \(-0.800604\pi\) |
0.102640 | + | 0.994719i | \(0.467271\pi\) | |||||||
\(20\) | −0.500000 | + | 0.866025i | −0.111803 | + | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.732523 | + | 1.26877i | 0.156175 | + | 0.270502i | ||||
\(23\) | −5.51016 | − | 3.18129i | −1.14895 | − | 0.663346i | −0.200318 | − | 0.979731i | \(-0.564197\pi\) |
−0.948631 | + | 0.316385i | \(0.897531\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 3.48448 | + | 6.03529i | 0.683362 | + | 1.18362i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.55256 | + | 0.696025i | −0.482388 | + | 0.131536i | ||||
\(29\) | −1.49409 | − | 0.862614i | −0.277446 | − | 0.160183i | 0.354821 | − | 0.934934i | \(-0.384542\pi\) |
−0.632267 | + | 0.774751i | \(0.717875\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.84985i | − | 1.40987i | −0.709269 | − | 0.704937i | \(-0.750975\pi\) | ||
0.709269 | − | 0.704937i | \(-0.249025\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.72151 | − | 3.30332i | −0.981231 | − | 0.566514i | ||||
\(35\) | 0.673503 | − | 2.55859i | 0.113843 | − | 0.432481i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.75951 | − | 4.77962i | −0.453661 | − | 0.785764i | 0.544949 | − | 0.838469i | \(-0.316549\pi\) |
−0.998610 | + | 0.0527049i | \(0.983216\pi\) | |||||||
\(38\) | 1.78048 | + | 3.08388i | 0.288832 | + | 0.500272i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.866025 | + | 0.500000i | 0.136931 | + | 0.0790569i | ||||
\(41\) | −0.632413 | − | 1.09537i | −0.0987663 | − | 0.171068i | 0.812408 | − | 0.583089i | \(-0.198156\pi\) |
−0.911174 | + | 0.412021i | \(0.864823\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.24581 | + | 5.62191i | −0.494981 | + | 0.857333i | −0.999983 | − | 0.00578540i | \(-0.998158\pi\) |
0.505002 | + | 0.863118i | \(0.331492\pi\) | |||||||
\(44\) | 1.26877 | − | 0.732523i | 0.191274 | − | 0.110432i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.18129 | + | 5.51016i | −0.469056 | + | 0.812429i | ||||
\(47\) | −5.39759 | −0.787320 | −0.393660 | − | 0.919256i | \(-0.628791\pi\) | ||||
−0.393660 | + | 0.919256i | \(0.628791\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.03110 | − | 3.55329i | 0.861586 | − | 0.507612i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.03529 | − | 3.48448i | 0.836945 | − | 0.483210i | ||||
\(53\) | −5.60809 | − | 3.23783i | −0.770331 | − | 0.444751i | 0.0626620 | − | 0.998035i | \(-0.480041\pi\) |
−0.832993 | + | 0.553284i | \(0.813374\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.46505i | 0.197547i | ||||||||
\(56\) | 0.696025 | + | 2.55256i | 0.0930102 | + | 0.341100i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.862614 | + | 1.49409i | −0.113267 | + | 0.196184i | ||||
\(59\) | 1.49328 | 0.194409 | 0.0972045 | − | 0.995264i | \(-0.469010\pi\) | ||||
0.0972045 | + | 0.995264i | \(0.469010\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.73592i | − | 0.478335i | −0.970978 | − | 0.239167i | \(-0.923126\pi\) | ||
0.970978 | − | 0.239167i | \(-0.0768745\pi\) | |||||||
\(62\) | −7.84985 | −0.996932 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.96896i | 0.864393i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.5498 | 1.53320 | 0.766602 | − | 0.642123i | \(-0.221946\pi\) | ||||
0.766602 | + | 0.642123i | \(0.221946\pi\) | |||||||
\(68\) | −3.30332 | + | 5.72151i | −0.400586 | + | 0.693835i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.55859 | − | 0.673503i | −0.305810 | − | 0.0804991i | ||||
\(71\) | − | 14.2133i | − | 1.68681i | −0.537281 | − | 0.843403i | \(-0.680549\pi\) | ||
0.537281 | − | 0.843403i | \(-0.319451\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.11022 | − | 0.640987i | −0.129942 | − | 0.0750218i | 0.433620 | − | 0.901096i | \(-0.357236\pi\) |
−0.563562 | + | 0.826074i | \(0.690569\pi\) | |||||||
\(74\) | −4.77962 | + | 2.75951i | −0.555619 | + | 0.320787i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.08388 | − | 1.78048i | 0.353745 | − | 0.204235i | ||||
\(77\) | −2.72875 | + | 2.75290i | −0.310970 | + | 0.313722i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.994011 | 0.111835 | 0.0559175 | − | 0.998435i | \(-0.482192\pi\) | ||||
0.0559175 | + | 0.998435i | \(0.482192\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.09537 | + | 0.632413i | −0.120964 | + | 0.0698383i | ||||
\(83\) | 5.93463 | − | 10.2791i | 0.651411 | − | 1.12828i | −0.331370 | − | 0.943501i | \(-0.607511\pi\) |
0.982781 | − | 0.184776i | \(-0.0591559\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.30332 | − | 5.72151i | −0.358295 | − | 0.620585i | ||||
\(86\) | 5.62191 | + | 3.24581i | 0.606226 | + | 0.350005i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.732523 | − | 1.26877i | −0.0780873 | − | 0.135251i | ||||
\(89\) | −2.18741 | − | 3.78871i | −0.231865 | − | 0.401602i | 0.726492 | − | 0.687175i | \(-0.241149\pi\) |
−0.958357 | + | 0.285573i | \(0.907816\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.9801 | + | 13.0950i | −1.36069 | + | 1.37273i | ||||
\(92\) | 5.51016 | + | 3.18129i | 0.574474 | + | 0.331673i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.39759i | 0.556719i | ||||||||
\(95\) | 3.56096i | 0.365347i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.04933 | + | 5.22463i | 0.918820 | + | 0.530481i | 0.883259 | − | 0.468886i | \(-0.155345\pi\) |
0.0355618 | + | 0.999367i | \(0.488678\pi\) | |||||||
\(98\) | −3.55329 | − | 6.03110i | −0.358936 | − | 0.609233i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 1.01983 | + | 1.76640i | 0.101477 | + | 0.175763i | 0.912293 | − | 0.409537i | \(-0.134310\pi\) |
−0.810816 | + | 0.585301i | \(0.800977\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.75430 | − | 1.59020i | −0.271389 | − | 0.156687i | 0.358130 | − | 0.933672i | \(-0.383415\pi\) |
−0.629519 | + | 0.776985i | \(0.716748\pi\) | |||||||
\(104\) | −3.48448 | − | 6.03529i | −0.341681 | − | 0.591809i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.23783 | + | 5.60809i | −0.314486 | + | 0.544706i | ||||
\(107\) | −13.7903 | + | 7.96185i | −1.33316 | + | 0.769701i | −0.985783 | − | 0.168024i | \(-0.946261\pi\) |
−0.347379 | + | 0.937725i | \(0.612928\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.60853 | + | 6.25017i | −0.345635 | + | 0.598657i | −0.985469 | − | 0.169856i | \(-0.945670\pi\) |
0.639834 | + | 0.768513i | \(0.279003\pi\) | |||||||
\(110\) | 1.46505 | 0.139687 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.55256 | − | 0.696025i | 0.241194 | − | 0.0657682i | ||||
\(113\) | −5.42707 | + | 3.13332i | −0.510536 | + | 0.294758i | −0.733054 | − | 0.680170i | \(-0.761906\pi\) |
0.222518 | + | 0.974929i | \(0.428572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.51016 | + | 3.18129i | −0.513825 | + | 0.296657i | ||||
\(116\) | 1.49409 | + | 0.862614i | 0.138723 | + | 0.0800917i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.49328i | − | 0.137468i | ||||||
\(119\) | 4.44959 | − | 16.9037i | 0.407893 | − | 1.54956i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.42682 | + | 7.66748i | −0.402438 | + | 0.697043i | ||||
\(122\) | −3.73592 | −0.338234 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.84985i | 0.704937i | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.914380 | −0.0811381 | −0.0405691 | − | 0.999177i | \(-0.512917\pi\) | ||||
−0.0405691 | + | 0.999177i | \(0.512917\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.96896 | 0.611218 | ||||||||
\(131\) | −4.94937 | + | 8.57256i | −0.432429 | + | 0.748988i | −0.997082 | − | 0.0763399i | \(-0.975677\pi\) |
0.564653 | + | 0.825328i | \(0.309010\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.63252 | + | 6.69123i | −0.575113 | + | 0.580204i | ||||
\(134\) | − | 12.5498i | − | 1.08414i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.72151 | + | 3.30332i | 0.490616 | + | 0.283257i | ||||
\(137\) | −10.4341 | + | 6.02412i | −0.891444 | + | 0.514675i | −0.874414 | − | 0.485180i | \(-0.838754\pi\) |
−0.0170294 | + | 0.999855i | \(0.505421\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.6077 | + | 9.01113i | −1.32383 | + | 0.764314i | −0.984338 | − | 0.176294i | \(-0.943589\pi\) |
−0.339494 | + | 0.940608i | \(0.610256\pi\) | |||||||
\(140\) | −0.673503 | + | 2.55859i | −0.0569214 | + | 0.216240i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.2133 | −1.19275 | ||||||||
\(143\) | 5.10492 | − | 8.84199i | 0.426895 | − | 0.739404i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.49409 | + | 0.862614i | −0.124078 | + | 0.0716362i | ||||
\(146\) | −0.640987 | + | 1.11022i | −0.0530484 | + | 0.0918826i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.75951 | + | 4.77962i | 0.226831 | + | 0.392882i | ||||
\(149\) | 7.44381 | + | 4.29769i | 0.609821 | + | 0.352080i | 0.772895 | − | 0.634534i | \(-0.218808\pi\) |
−0.163075 | + | 0.986614i | \(0.552141\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.30386 | + | 2.25835i | 0.106106 | + | 0.183782i | 0.914190 | − | 0.405287i | \(-0.132828\pi\) |
−0.808083 | + | 0.589068i | \(0.799495\pi\) | |||||||
\(152\) | −1.78048 | − | 3.08388i | −0.144416 | − | 0.250136i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.75290 | + | 2.72875i | 0.221835 | + | 0.219889i | ||||
\(155\) | −6.79817 | − | 3.92493i | −0.546042 | − | 0.315258i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.79034i | − | 0.621737i | −0.950453 | − | 0.310868i | \(-0.899380\pi\) | ||
0.950453 | − | 0.310868i | \(-0.100620\pi\) | |||||||
\(158\) | − | 0.994011i | − | 0.0790793i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.866025 | − | 0.500000i | −0.0684653 | − | 0.0395285i | ||||
\(161\) | −16.2793 | − | 4.28523i | −1.28299 | − | 0.337723i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.14705 | − | 7.18290i | −0.324822 | − | 0.562608i | 0.656654 | − | 0.754192i | \(-0.271971\pi\) |
−0.981476 | + | 0.191584i | \(0.938638\pi\) | |||||||
\(164\) | 0.632413 | + | 1.09537i | 0.0493832 | + | 0.0855342i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.2791 | − | 5.93463i | −0.797812 | − | 0.460617i | ||||
\(167\) | −6.88497 | − | 11.9251i | −0.532775 | − | 0.922793i | −0.999268 | − | 0.0382680i | \(-0.987816\pi\) |
0.466493 | − | 0.884525i | \(-0.345517\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.7832 | − | 30.8014i | 1.36794 | − | 2.36934i | ||||
\(170\) | −5.72151 | + | 3.30332i | −0.438820 | + | 0.253353i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.24581 | − | 5.62191i | 0.247491 | − | 0.428666i | ||||
\(173\) | −11.6394 | −0.884929 | −0.442464 | − | 0.896786i | \(-0.645896\pi\) | ||||
−0.442464 | + | 0.896786i | \(0.645896\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.87905 | − | 1.86257i | −0.142043 | − | 0.140797i | ||||
\(176\) | −1.26877 | + | 0.732523i | −0.0956370 | + | 0.0552160i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.78871 | + | 2.18741i | −0.283976 | + | 0.163953i | ||||
\(179\) | −1.21808 | − | 0.703262i | −0.0910439 | − | 0.0525642i | 0.453787 | − | 0.891110i | \(-0.350073\pi\) |
−0.544831 | + | 0.838546i | \(0.683406\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.1582i | 0.755054i | 0.925998 | + | 0.377527i | \(0.123226\pi\) | ||||
−0.925998 | + | 0.377527i | \(0.876774\pi\) | |||||||
\(182\) | 13.0950 | + | 12.9801i | 0.970669 | + | 0.962153i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.18129 | − | 5.51016i | 0.234528 | − | 0.406215i | ||||
\(185\) | −5.51903 | −0.405767 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.67903i | 0.707801i | ||||||||
\(188\) | 5.39759 | 0.393660 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.56096 | 0.258339 | ||||||||
\(191\) | 17.1243i | 1.23907i | 0.784968 | + | 0.619536i | \(0.212679\pi\) | ||||
−0.784968 | + | 0.619536i | \(0.787321\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.93306 | 0.139144 | 0.0695722 | − | 0.997577i | \(-0.477837\pi\) | ||||
0.0695722 | + | 0.997577i | \(0.477837\pi\) | |||||||
\(194\) | 5.22463 | − | 9.04933i | 0.375107 | − | 0.649704i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.03110 | + | 3.55329i | −0.430793 | + | 0.253806i | ||||
\(197\) | − | 22.0136i | − | 1.56840i | −0.620508 | − | 0.784200i | \(-0.713073\pi\) | ||
0.620508 | − | 0.784200i | \(-0.286927\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.0430 | + | 13.3039i | 1.63348 | + | 0.943088i | 0.983010 | + | 0.183554i | \(0.0587604\pi\) |
0.650468 | + | 0.759534i | \(0.274573\pi\) | |||||||
\(200\) | 0.866025 | − | 0.500000i | 0.0612372 | − | 0.0353553i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.76640 | − | 1.01983i | 0.124283 | − | 0.0717550i | ||||
\(203\) | −4.41416 | − | 1.16195i | −0.309813 | − | 0.0815527i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.26483 | −0.0883393 | ||||||||
\(206\) | −1.59020 | + | 2.75430i | −0.110794 | + | 0.191901i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.03529 | + | 3.48448i | −0.418472 | + | 0.241605i | ||||
\(209\) | 2.60849 | − | 4.51803i | 0.180433 | − | 0.312519i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.44298 | − | 5.96341i | −0.237024 | − | 0.410538i | 0.722835 | − | 0.691021i | \(-0.242839\pi\) |
−0.959859 | + | 0.280483i | \(0.909505\pi\) | |||||||
\(212\) | 5.60809 | + | 3.23783i | 0.385165 | + | 0.222375i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.96185 | + | 13.7903i | 0.544261 | + | 0.942688i | ||||
\(215\) | 3.24581 | + | 5.62191i | 0.221362 | + | 0.383411i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.46369 | − | 20.0372i | −0.370900 | − | 1.36021i | ||||
\(218\) | 6.25017 | + | 3.60853i | 0.423315 | + | 0.244401i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 1.46505i | − | 0.0987734i | ||||||
\(221\) | 46.0413i | 3.09708i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.6938 | + | 6.75140i | 0.783072 | + | 0.452107i | 0.837518 | − | 0.546410i | \(-0.184006\pi\) |
−0.0544458 | + | 0.998517i | \(0.517339\pi\) | |||||||
\(224\) | −0.696025 | − | 2.55256i | −0.0465051 | − | 0.170550i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.13332 | + | 5.42707i | 0.208426 | + | 0.361004i | ||||
\(227\) | 10.7490 | + | 18.6179i | 0.713438 | + | 1.23571i | 0.963559 | + | 0.267497i | \(0.0861965\pi\) |
−0.250120 | + | 0.968215i | \(0.580470\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.4936 | + | 11.2546i | 1.28817 | + | 0.743727i | 0.978328 | − | 0.207060i | \(-0.0663896\pi\) |
0.309845 | + | 0.950787i | \(0.399723\pi\) | |||||||
\(230\) | 3.18129 | + | 5.51016i | 0.209768 | + | 0.363329i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.862614 | − | 1.49409i | 0.0566334 | − | 0.0980919i | ||||
\(233\) | 15.4408 | − | 8.91477i | 1.01156 | − | 0.584026i | 0.0999142 | − | 0.994996i | \(-0.468143\pi\) |
0.911649 | + | 0.410970i | \(0.134810\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.69880 | + | 4.67445i | −0.176050 | + | 0.304928i | ||||
\(236\) | −1.49328 | −0.0972045 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −16.9037 | − | 4.44959i | −1.09570 | − | 0.288424i | ||||
\(239\) | −13.7144 | + | 7.91804i | −0.887114 | + | 0.512175i | −0.872997 | − | 0.487725i | \(-0.837827\pi\) |
−0.0141164 | + | 0.999900i | \(0.504494\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.8842 | − | 13.2122i | 1.47410 | − | 0.851073i | 0.474526 | − | 0.880241i | \(-0.342619\pi\) |
0.999575 | + | 0.0291688i | \(0.00928603\pi\) | |||||||
\(242\) | 7.66748 | + | 4.42682i | 0.492884 | + | 0.284567i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.73592i | 0.239167i | ||||||||
\(245\) | −0.0616877 | − | 6.99973i | −0.00394109 | − | 0.447196i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.4081 | − | 21.4914i | 0.789507 | − | 1.36747i | ||||
\(248\) | 7.84985 | 0.498466 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | 27.9912 | 1.76679 | 0.883395 | − | 0.468628i | \(-0.155252\pi\) | ||||
0.883395 | + | 0.468628i | \(0.155252\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.32149 | 0.586037 | ||||||||
\(254\) | 0.914380i | 0.0573733i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.21520 | − | 12.4971i | 0.450072 | − | 0.779547i | −0.548318 | − | 0.836270i | \(-0.684732\pi\) |
0.998390 | + | 0.0567229i | \(0.0180651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.3706 | − | 10.2796i | −0.644395 | − | 0.638741i | ||||
\(260\) | − | 6.96896i | − | 0.432196i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.57256 | + | 4.94937i | 0.529615 | + | 0.305773i | ||||
\(263\) | 1.39555 | − | 0.805722i | 0.0860534 | − | 0.0496830i | −0.456356 | − | 0.889797i | \(-0.650846\pi\) |
0.542409 | + | 0.840114i | \(0.317512\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.60809 | + | 3.23783i | −0.344502 | + | 0.198898i | ||||
\(266\) | 6.69123 | + | 6.63252i | 0.410266 | + | 0.406666i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.5498 | −0.766602 | ||||||||
\(269\) | −2.06266 | + | 3.57264i | −0.125763 | + | 0.217828i | −0.922031 | − | 0.387116i | \(-0.873471\pi\) |
0.796268 | + | 0.604944i | \(0.206804\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.02680 | + | 2.32488i | −0.244611 | + | 0.141226i | −0.617294 | − | 0.786732i | \(-0.711771\pi\) |
0.372683 | + | 0.927959i | \(0.378438\pi\) | |||||||
\(272\) | 3.30332 | − | 5.72151i | 0.200293 | − | 0.346918i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.02412 | + | 10.4341i | 0.363930 | + | 0.630346i | ||||
\(275\) | 1.26877 | + | 0.732523i | 0.0765096 | + | 0.0441728i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.7120 | − | 20.2858i | −0.703705 | − | 1.21885i | −0.967157 | − | 0.254180i | \(-0.918194\pi\) |
0.263452 | − | 0.964673i | \(-0.415139\pi\) | |||||||
\(278\) | 9.01113 | + | 15.6077i | 0.540452 | + | 0.936090i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.55859 | + | 0.673503i | 0.152905 | + | 0.0402495i | ||||
\(281\) | 17.5671 | + | 10.1424i | 1.04797 | + | 0.605043i | 0.922079 | − | 0.387001i | \(-0.126489\pi\) |
0.125887 | + | 0.992045i | \(0.459822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.74367i | 0.341426i | 0.985321 | + | 0.170713i | \(0.0546071\pi\) | ||||
−0.985321 | + | 0.170713i | \(0.945393\pi\) | |||||||
\(284\) | 14.2133i | 0.843403i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.84199 | − | 5.10492i | −0.522838 | − | 0.301860i | ||||
\(287\) | −2.37668 | − | 2.35582i | −0.140291 | − | 0.139060i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.3238 | − | 23.0775i | −0.783753 | − | 1.35750i | ||||
\(290\) | 0.862614 | + | 1.49409i | 0.0506545 | + | 0.0877361i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.11022 | + | 0.640987i | 0.0649708 | + | 0.0375109i | ||||
\(293\) | −10.7874 | − | 18.6844i | −0.630209 | − | 1.09155i | −0.987509 | − | 0.157564i | \(-0.949636\pi\) |
0.357300 | − | 0.933990i | \(-0.383697\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.746642 | − | 1.29322i | 0.0434712 | − | 0.0752943i | ||||
\(296\) | 4.77962 | − | 2.75951i | 0.277810 | − | 0.160393i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.29769 | − | 7.44381i | 0.248958 | − | 0.431208i | ||||
\(299\) | 44.3406 | 2.56428 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.37213 | + | 16.6094i | −0.252005 | + | 0.957350i | ||||
\(302\) | 2.25835 | − | 1.30386i | 0.129953 | − | 0.0750285i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.08388 | + | 1.78048i | −0.176873 | + | 0.102117i | ||||
\(305\) | −3.23540 | − | 1.86796i | −0.185258 | − | 0.106959i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.22295i | 0.298090i | 0.988830 | + | 0.149045i | \(0.0476199\pi\) | ||||
−0.988830 | + | 0.149045i | \(0.952380\pi\) | |||||||
\(308\) | 2.72875 | − | 2.75290i | 0.155485 | − | 0.156861i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.92493 | + | 6.79817i | −0.222921 | + | 0.386110i | ||||
\(311\) | 13.2357 | 0.750526 | 0.375263 | − | 0.926918i | \(-0.377552\pi\) | ||||
0.375263 | + | 0.926918i | \(0.377552\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 30.9549i | − | 1.74968i | −0.484416 | − | 0.874838i | \(-0.660968\pi\) | ||
0.484416 | − | 0.874838i | \(-0.339032\pi\) | |||||||
\(314\) | −7.79034 | −0.439634 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.994011 | −0.0559175 | ||||||||
\(317\) | − | 15.1480i | − | 0.850796i | −0.905006 | − | 0.425398i | \(-0.860134\pi\) | ||
0.905006 | − | 0.425398i | \(-0.139866\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.52754 | 0.141515 | ||||||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.28523 | + | 16.2793i | −0.238806 | + | 0.907208i | ||||
\(323\) | 23.5259i | 1.30902i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.03529 | + | 3.48448i | 0.334778 | + | 0.193284i | ||||
\(326\) | −7.18290 | + | 4.14705i | −0.397824 | + | 0.229684i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.09537 | − | 0.632413i | 0.0604818 | − | 0.0349192i | ||||
\(329\) | −13.7777 | + | 3.75686i | −0.759587 | + | 0.207122i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.30322 | 0.0716313 | 0.0358157 | − | 0.999358i | \(-0.488597\pi\) | ||||
0.0358157 | + | 0.999358i | \(0.488597\pi\) | |||||||
\(332\) | −5.93463 | + | 10.2791i | −0.325705 | + | 0.564138i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.9251 | + | 6.88497i | −0.652513 | + | 0.376729i | ||||
\(335\) | 6.27490 | − | 10.8685i | 0.342835 | − | 0.593807i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.12095 | + | 14.0659i | 0.442377 | + | 0.766219i | 0.997865 | − | 0.0653053i | \(-0.0208021\pi\) |
−0.555489 | + | 0.831524i | \(0.687469\pi\) | |||||||
\(338\) | −30.8014 | − | 17.7832i | −1.67537 | − | 0.967277i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.30332 | + | 5.72151i | 0.179147 | + | 0.310293i | ||||
\(341\) | 5.75020 | + | 9.95964i | 0.311391 | + | 0.539345i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.9215 | − | 13.2678i | 0.697698 | − | 0.716392i | ||||
\(344\) | −5.62191 | − | 3.24581i | −0.303113 | − | 0.175002i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.6394i | 0.625739i | ||||||||
\(347\) | − | 5.07209i | − | 0.272284i | −0.990689 | − | 0.136142i | \(-0.956530\pi\) | ||
0.990689 | − | 0.136142i | \(-0.0434703\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.4996 | − | 11.8354i | −1.09732 | − | 0.633536i | −0.161802 | − | 0.986823i | \(-0.551731\pi\) |
−0.935515 | + | 0.353287i | \(0.885064\pi\) | |||||||
\(350\) | −1.86257 | + | 1.87905i | −0.0995584 | + | 0.100440i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.732523 | + | 1.26877i | 0.0390436 | + | 0.0676255i | ||||
\(353\) | −0.272379 | − | 0.471774i | −0.0144973 | − | 0.0251100i | 0.858686 | − | 0.512502i | \(-0.171281\pi\) |
−0.873183 | + | 0.487392i | \(0.837948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.3091 | − | 7.10664i | −0.653297 | − | 0.377181i | ||||
\(356\) | 2.18741 | + | 3.78871i | 0.115933 | + | 0.200801i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.703262 | + | 1.21808i | −0.0371685 | + | 0.0643778i | ||||
\(359\) | −5.44862 | + | 3.14576i | −0.287567 | + | 0.166027i | −0.636844 | − | 0.770993i | \(-0.719761\pi\) |
0.349277 | + | 0.937019i | \(0.386427\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.15979 | + | 5.47291i | −0.166305 | + | 0.288048i | ||||
\(362\) | 10.1582 | 0.533904 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.9801 | − | 13.0950i | 0.680345 | − | 0.686367i | ||||
\(365\) | −1.11022 | + | 0.640987i | −0.0581117 | + | 0.0335508i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.0875 | − | 12.1749i | 1.10076 | − | 0.635522i | 0.164337 | − | 0.986404i | \(-0.447452\pi\) |
0.936420 | + | 0.350882i | \(0.114118\pi\) | |||||||
\(368\) | −5.51016 | − | 3.18129i | −0.287237 | − | 0.165836i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.51903i | 0.286921i | ||||||||
\(371\) | −16.5686 | − | 4.36138i | −0.860198 | − | 0.226432i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.08878 | + | 1.88581i | −0.0563746 | + | 0.0976437i | −0.892835 | − | 0.450383i | \(-0.851287\pi\) |
0.836461 | + | 0.548027i | \(0.184621\pi\) | |||||||
\(374\) | 9.67903 | 0.500491 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 5.39759i | − | 0.278360i | ||||||
\(377\) | 12.0230 | 0.619218 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.5954 | −1.16065 | −0.580323 | − | 0.814387i | \(-0.697074\pi\) | ||||
−0.580323 | + | 0.814387i | \(0.697074\pi\) | |||||||
\(380\) | − | 3.56096i | − | 0.182673i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17.1243 | 0.876156 | ||||||||
\(383\) | −3.26282 | + | 5.65138i | −0.166723 | + | 0.288772i | −0.937266 | − | 0.348616i | \(-0.886652\pi\) |
0.770543 | + | 0.637388i | \(0.219985\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.01971 | + | 3.73962i | 0.0519692 | + | 0.190588i | ||||
\(386\) | − | 1.93306i | − | 0.0983900i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.04933 | − | 5.22463i | −0.459410 | − | 0.265241i | ||||
\(389\) | 30.0342 | − | 17.3402i | 1.52279 | − | 0.879184i | 0.523155 | − | 0.852238i | \(-0.324755\pi\) |
0.999637 | − | 0.0269467i | \(-0.00857846\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.4036 | + | 21.0176i | −1.84101 | + | 1.06291i | ||||
\(392\) | 3.55329 | + | 6.03110i | 0.179468 | + | 0.304616i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.0136 | −1.10903 | ||||||||
\(395\) | 0.497005 | − | 0.860839i | 0.0250071 | − | 0.0433135i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.8417 | − | 13.7650i | 1.19658 | − | 0.690845i | 0.236788 | − | 0.971561i | \(-0.423905\pi\) |
0.959791 | + | 0.280717i | \(0.0905721\pi\) | |||||||
\(398\) | 13.3039 | − | 23.0430i | 0.666864 | − | 1.15504i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | −12.1926 | − | 7.03938i | −0.608868 | − | 0.351530i | 0.163655 | − | 0.986518i | \(-0.447672\pi\) |
−0.772522 | + | 0.634988i | \(0.781005\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.3526 | + | 47.3762i | 1.36253 | + | 2.35997i | ||||
\(404\) | −1.01983 | − | 1.76640i | −0.0507385 | − | 0.0878816i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.16195 | + | 4.41416i | −0.0576665 | + | 0.219071i | ||||
\(407\) | 7.00236 | + | 4.04282i | 0.347094 | + | 0.200395i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 32.7642i | − | 1.62009i | −0.586371 | − | 0.810043i | \(-0.699444\pi\) | ||
0.586371 | − | 0.810043i | \(-0.300556\pi\) | |||||||
\(410\) | 1.26483i | 0.0624653i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.75430 | + | 1.59020i | 0.135695 | + | 0.0783433i | ||||
\(413\) | 3.81169 | − | 1.03936i | 0.187561 | − | 0.0511437i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.93463 | − | 10.2791i | −0.291320 | − | 0.504581i | ||||
\(416\) | 3.48448 | + | 6.03529i | 0.170841 | + | 0.295905i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.51803 | − | 2.60849i | −0.220984 | − | 0.127585i | ||||
\(419\) | 5.81259 | + | 10.0677i | 0.283964 | + | 0.491839i | 0.972357 | − | 0.233498i | \(-0.0750172\pi\) |
−0.688394 | + | 0.725337i | \(0.741684\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.4508 | − | 19.8333i | 0.558076 | − | 0.966615i | −0.439582 | − | 0.898203i | \(-0.644873\pi\) |
0.997657 | − | 0.0684126i | \(-0.0217934\pi\) | |||||||
\(422\) | −5.96341 | + | 3.44298i | −0.290294 | + | 0.167601i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.23783 | − | 5.60809i | 0.157243 | − | 0.272353i | ||||
\(425\) | −6.60663 | −0.320469 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.60029 | − | 9.53614i | −0.125837 | − | 0.461486i | ||||
\(428\) | 13.7903 | − | 7.96185i | 0.666581 | − | 0.384851i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.62191 | − | 3.24581i | 0.271112 | − | 0.156527i | ||||
\(431\) | 8.34407 | + | 4.81745i | 0.401920 | + | 0.232048i | 0.687312 | − | 0.726362i | \(-0.258791\pi\) |
−0.285392 | + | 0.958411i | \(0.592124\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 37.8458i | − | 1.81875i | −0.415972 | − | 0.909377i | \(-0.636559\pi\) | ||
0.415972 | − | 0.909377i | \(-0.363441\pi\) | |||||||
\(434\) | −20.0372 | + | 5.46369i | −0.961816 | + | 0.262266i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.60853 | − | 6.25017i | 0.172817 | − | 0.299329i | ||||
\(437\) | 22.6569 | 1.08383 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.3974i | 1.54624i | 0.634257 | + | 0.773122i | \(0.281306\pi\) | ||||
−0.634257 | + | 0.773122i | \(0.718694\pi\) | |||||||
\(440\) | −1.46505 | −0.0698434 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 46.0413 | 2.18996 | ||||||||
\(443\) | 21.9018i | 1.04059i | 0.853988 | + | 0.520293i | \(0.174177\pi\) | ||||
−0.853988 | + | 0.520293i | \(0.825823\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.37482 | −0.207387 | ||||||||
\(446\) | 6.75140 | − | 11.6938i | 0.319688 | − | 0.553716i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.55256 | + | 0.696025i | −0.120597 | + | 0.0328841i | ||||
\(449\) | 25.8522i | 1.22004i | 0.792385 | + | 0.610021i | \(0.208839\pi\) | ||||
−0.792385 | + | 0.610021i | \(0.791161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.60477 | + | 0.926515i | 0.0755657 | + | 0.0436279i | ||||
\(452\) | 5.42707 | − | 3.13332i | 0.255268 | − | 0.147379i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.6179 | − | 10.7490i | 0.873780 | − | 0.504477i | ||||
\(455\) | 4.85057 | + | 17.7887i | 0.227398 | + | 0.833945i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.2463 | −1.04064 | −0.520318 | − | 0.853973i | \(-0.674187\pi\) | ||||
−0.520318 | + | 0.853973i | \(0.674187\pi\) | |||||||
\(458\) | 11.2546 | − | 19.4936i | 0.525894 | − | 0.910876i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.51016 | − | 3.18129i | 0.256913 | − | 0.148329i | ||||
\(461\) | −7.05369 | + | 12.2173i | −0.328523 | + | 0.569018i | −0.982219 | − | 0.187739i | \(-0.939884\pi\) |
0.653696 | + | 0.756757i | \(0.273217\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.33243 | + | 5.77194i | 0.154871 | + | 0.268245i | 0.933012 | − | 0.359845i | \(-0.117170\pi\) |
−0.778141 | + | 0.628090i | \(0.783837\pi\) | |||||||
\(464\) | −1.49409 | − | 0.862614i | −0.0693615 | − | 0.0400459i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.91477 | − | 15.4408i | −0.412969 | − | 0.715283i | ||||
\(467\) | 1.75717 | + | 3.04350i | 0.0813119 | + | 0.140836i | 0.903814 | − | 0.427926i | \(-0.140756\pi\) |
−0.822502 | + | 0.568763i | \(0.807422\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.0341 | − | 8.73498i | 1.47920 | − | 0.403344i | ||||
\(470\) | 4.67445 | + | 2.69880i | 0.215616 | + | 0.124486i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.49328i | 0.0687340i | ||||||||
\(473\) | − | 9.51053i | − | 0.437294i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.08388 | + | 1.78048i | 0.141498 | + | 0.0816940i | ||||
\(476\) | −4.44959 | + | 16.9037i | −0.203947 | + | 0.774779i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.91804 | + | 13.7144i | 0.362163 | + | 0.627284i | ||||
\(479\) | 0.500486 | + | 0.866868i | 0.0228678 | + | 0.0396082i | 0.877233 | − | 0.480065i | \(-0.159387\pi\) |
−0.854365 | + | 0.519673i | \(0.826054\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.3089 | + | 19.2309i | 1.51876 | + | 0.876855i | ||||
\(482\) | −13.2122 | − | 22.8842i | −0.601799 | − | 1.04235i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.42682 | − | 7.66748i | 0.201219 | − | 0.348522i | ||||
\(485\) | 9.04933 | − | 5.22463i | 0.410909 | − | 0.237238i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.4755 | + | 25.0723i | −0.655948 | + | 1.13613i | 0.325708 | + | 0.945471i | \(0.394397\pi\) |
−0.981655 | + | 0.190664i | \(0.938936\pi\) | |||||||
\(488\) | 3.73592 | 0.169117 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.99973 | + | 0.0616877i | −0.316215 | + | 0.00278677i | ||||
\(491\) | −30.6555 | + | 17.6990i | −1.38346 | + | 0.798743i | −0.992568 | − | 0.121691i | \(-0.961168\pi\) |
−0.390896 | + | 0.920435i | \(0.627835\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.87092 | + | 5.69898i | −0.444564 | + | 0.256669i | ||||
\(494\) | −21.4914 | − | 12.4081i | −0.966945 | − | 0.558266i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 7.84985i | − | 0.352469i | ||||||
\(497\) | −9.89280 | − | 36.2802i | −0.443753 | − | 1.62739i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.31844 | + | 14.4080i | −0.372384 | + | 0.644989i | −0.989932 | − | 0.141545i | \(-0.954793\pi\) |
0.617547 | + | 0.786534i | \(0.288126\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 27.9912i | − | 1.24931i | ||||||
\(503\) | −12.7352 | −0.567834 | −0.283917 | − | 0.958849i | \(-0.591634\pi\) | ||||
−0.283917 | + | 0.958849i | \(0.591634\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.03966 | 0.0907638 | ||||||||
\(506\) | − | 9.32149i | − | 0.414391i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.914380 | 0.0405691 | ||||||||
\(509\) | 4.73445 | − | 8.20032i | 0.209851 | − | 0.363473i | −0.741816 | − | 0.670603i | \(-0.766035\pi\) |
0.951667 | + | 0.307130i | \(0.0993688\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.28005 | − | 0.863414i | −0.145101 | − | 0.0381952i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.4971 | − | 7.21520i | −0.551223 | − | 0.318249i | ||||
\(515\) | −2.75430 | + | 1.59020i | −0.121369 | + | 0.0700724i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.84829 | − | 3.95386i | 0.301187 | − | 0.173891i | ||||
\(518\) | −10.2796 | + | 10.3706i | −0.451658 | + | 0.455656i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.96896 | −0.305609 | ||||||||
\(521\) | 2.37330 | − | 4.11068i | 0.103976 | − | 0.180092i | −0.809343 | − | 0.587336i | \(-0.800177\pi\) |
0.913320 | + | 0.407244i | \(0.133510\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.1376 | − | 17.3999i | 1.31782 | − | 0.760846i | 0.334446 | − | 0.942415i | \(-0.391451\pi\) |
0.983378 | + | 0.181569i | \(0.0581176\pi\) | |||||||
\(524\) | 4.94937 | − | 8.57256i | 0.216214 | − | 0.374494i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.805722 | − | 1.39555i | −0.0351312 | − | 0.0608490i | ||||
\(527\) | −44.9130 | − | 25.9305i | −1.95644 | − | 1.12955i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.74127 | + | 15.1403i | 0.380055 | + | 0.658275i | ||||
\(530\) | 3.23783 | + | 5.60809i | 0.140642 | + | 0.243600i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.63252 | − | 6.69123i | 0.287556 | − | 0.290102i | ||||
\(533\) | 7.63360 | + | 4.40726i | 0.330648 | + | 0.190900i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.9237i | 0.688442i | ||||||||
\(536\) | 12.5498i | 0.542069i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.57264 | + | 2.06266i | 0.154027 | + | 0.0889277i | ||||
\(539\) | −5.04920 | + | 8.92622i | −0.217484 | + | 0.384479i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.542248 | − | 0.939202i | −0.0233131 | − | 0.0403794i | 0.854133 | − | 0.520054i | \(-0.174088\pi\) |
−0.877447 | + | 0.479674i | \(0.840755\pi\) | |||||||
\(542\) | 2.32488 | + | 4.02680i | 0.0998620 | + | 0.172966i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.72151 | − | 3.30332i | −0.245308 | − | 0.141629i | ||||
\(545\) | 3.60853 | + | 6.25017i | 0.154573 | + | 0.267728i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.77785 | + | 15.2037i | −0.375314 | + | 0.650063i | −0.990374 | − | 0.138417i | \(-0.955798\pi\) |
0.615060 | + | 0.788480i | \(0.289132\pi\) | |||||||
\(548\) | 10.4341 | − | 6.02412i | 0.445722 | − | 0.257338i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.732523 | − | 1.26877i | 0.0312349 | − | 0.0541004i | ||||
\(551\) | 6.14347 | 0.261721 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.53727 | − | 0.691856i | 0.107896 | − | 0.0294207i | ||||
\(554\) | −20.2858 | + | 11.7120i | −0.861859 | + | 0.497595i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.6077 | − | 9.01113i | 0.661916 | − | 0.382157i | ||||
\(557\) | −27.9379 | − | 16.1300i | −1.18377 | − | 0.683449i | −0.226885 | − | 0.973922i | \(-0.572854\pi\) |
−0.956883 | + | 0.290472i | \(0.906188\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 45.2398i | − | 1.91344i | ||||||
\(560\) | 0.673503 | − | 2.55859i | 0.0284607 | − | 0.108120i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.1424 | − | 17.5671i | 0.427830 | − | 0.741024i | ||||
\(563\) | 35.5704 | 1.49911 | 0.749557 | − | 0.661940i | \(-0.230267\pi\) | ||||
0.749557 | + | 0.661940i | \(0.230267\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.26664i | 0.263640i | ||||||||
\(566\) | 5.74367 | 0.241425 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.2133 | 0.596376 | ||||||||
\(569\) | 41.9657i | 1.75929i | 0.475627 | + | 0.879647i | \(0.342221\pi\) | ||||
−0.475627 | + | 0.879647i | \(0.657779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.77247 | 0.283419 | 0.141709 | − | 0.989908i | \(-0.454740\pi\) | ||||
0.141709 | + | 0.989908i | \(0.454740\pi\) | |||||||
\(572\) | −5.10492 | + | 8.84199i | −0.213448 | + | 0.369702i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.35582 | + | 2.37668i | −0.0983302 | + | 0.0992006i | ||||
\(575\) | 6.36259i | 0.265338i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.1675 | − | 17.4172i | −1.25589 | − | 0.725087i | −0.283616 | − | 0.958938i | \(-0.591534\pi\) |
−0.972273 | + | 0.233851i | \(0.924867\pi\) | |||||||
\(578\) | −23.0775 | + | 13.3238i | −0.959897 | + | 0.554197i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.49409 | − | 0.862614i | 0.0620388 | − | 0.0358181i | ||||
\(581\) | 7.99399 | − | 30.3686i | 0.331647 | − | 1.25990i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.48715 | 0.392918 | ||||||||
\(584\) | 0.640987 | − | 1.11022i | 0.0265242 | − | 0.0459413i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.6844 | + | 10.7874i | −0.771845 | + | 0.445625i | ||||
\(587\) | 20.1646 | − | 34.9261i | 0.832281 | − | 1.44155i | −0.0639444 | − | 0.997953i | \(-0.520368\pi\) |
0.896225 | − | 0.443599i | \(-0.146299\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.9765 | + | 24.2080i | 0.575892 | + | 0.997474i | ||||
\(590\) | −1.29322 | − | 0.746642i | −0.0532411 | − | 0.0307388i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.75951 | − | 4.77962i | −0.113415 | − | 0.196441i | ||||
\(593\) | −13.7783 | − | 23.8647i | −0.565806 | − | 0.980005i | −0.996974 | − | 0.0777332i | \(-0.975232\pi\) |
0.431168 | − | 0.902272i | \(-0.358102\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.4142 | − | 12.3053i | −0.508933 | − | 0.504468i | ||||
\(596\) | −7.44381 | − | 4.29769i | −0.304910 | − | 0.176040i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 44.3406i | − | 1.81322i | ||||||
\(599\) | − | 14.1442i | − | 0.577917i | −0.957342 | − | 0.288959i | \(-0.906691\pi\) | ||
0.957342 | − | 0.288959i | \(-0.0933090\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.7893 | + | 6.22920i | 0.440104 | + | 0.254094i | 0.703642 | − | 0.710555i | \(-0.251556\pi\) |
−0.263537 | + | 0.964649i | \(0.584889\pi\) | |||||||
\(602\) | 16.6094 | + | 4.37213i | 0.676949 | + | 0.178195i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.30386 | − | 2.25835i | −0.0530532 | − | 0.0918908i | ||||
\(605\) | 4.42682 | + | 7.66748i | 0.179976 | + | 0.311727i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.89996 | + | 3.98369i | 0.280061 | + | 0.161693i | 0.633451 | − | 0.773783i | \(-0.281638\pi\) |
−0.353390 | + | 0.935476i | \(0.614971\pi\) | |||||||
\(608\) | 1.78048 | + | 3.08388i | 0.0722080 | + | 0.125068i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.86796 | + | 3.23540i | −0.0756314 | + | 0.130997i | ||||
\(611\) | 32.5760 | − | 18.8078i | 1.31789 | − | 0.760882i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.28676 | − | 5.69283i | 0.132751 | − | 0.229931i | −0.791985 | − | 0.610540i | \(-0.790952\pi\) |
0.924736 | + | 0.380609i | \(0.124286\pi\) | |||||||
\(614\) | 5.22295 | 0.210781 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.75290 | − | 2.72875i | −0.110918 | − | 0.109944i | ||||
\(617\) | 6.77484 | − | 3.91146i | 0.272745 | − | 0.157469i | −0.357389 | − | 0.933955i | \(-0.616333\pi\) |
0.630134 | + | 0.776486i | \(0.283000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.8161 | − | 22.9878i | 1.60034 | − | 0.923959i | 0.608926 | − | 0.793227i | \(-0.291601\pi\) |
0.991418 | − | 0.130732i | \(-0.0417327\pi\) | |||||||
\(620\) | 6.79817 | + | 3.92493i | 0.273021 | + | 0.157629i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 13.2357i | − | 0.530702i | ||||||
\(623\) | −8.22053 | − | 8.14840i | −0.329349 | − | 0.326459i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −30.9549 | −1.23721 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.79034i | 0.310868i | ||||||||
\(629\) | −36.4622 | −1.45384 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.0931 | −0.959131 | −0.479566 | − | 0.877506i | \(-0.659206\pi\) | ||||
−0.479566 | + | 0.877506i | \(0.659206\pi\) | |||||||
\(632\) | 0.994011i | 0.0395396i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.1480 | −0.601604 | ||||||||
\(635\) | −0.457190 | + | 0.791877i | −0.0181430 | + | 0.0314247i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.0181 | + | 42.4604i | −0.951632 | + | 1.68234i | ||||
\(638\) | − | 2.52754i | − | 0.100066i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.866025 | + | 0.500000i | 0.0342327 | + | 0.0197642i | ||||
\(641\) | −20.6665 | + | 11.9318i | −0.816279 | + | 0.471279i | −0.849132 | − | 0.528181i | \(-0.822874\pi\) |
0.0328524 | + | 0.999460i | \(0.489541\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.9563 | + | 7.48033i | −0.510947 | + | 0.294996i | −0.733223 | − | 0.679988i | \(-0.761985\pi\) |
0.222276 | + | 0.974984i | \(0.428652\pi\) | |||||||
\(644\) | 16.2793 | + | 4.28523i | 0.641493 | + | 0.168862i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 23.5259 | 0.925616 | ||||||||
\(647\) | 3.99382 | − | 6.91751i | 0.157013 | − | 0.271955i | −0.776777 | − | 0.629776i | \(-0.783147\pi\) |
0.933790 | + | 0.357821i | \(0.116480\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.89463 | + | 1.09387i | −0.0743708 | + | 0.0429380i | ||||
\(650\) | 3.48448 | − | 6.03529i | 0.136672 | − | 0.236724i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.14705 | + | 7.18290i | 0.162411 | + | 0.281304i | ||||
\(653\) | −24.4998 | − | 14.1449i | −0.958750 | − | 0.553535i | −0.0629620 | − | 0.998016i | \(-0.520055\pi\) |
−0.895788 | + | 0.444481i | \(0.853388\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.94937 | + | 8.57256i | 0.193388 | + | 0.334958i | ||||
\(656\) | −0.632413 | − | 1.09537i | −0.0246916 | − | 0.0427671i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.75686 | + | 13.7777i | 0.146458 | + | 0.537109i | ||||
\(659\) | 0.349881 | + | 0.202004i | 0.0136294 | + | 0.00786894i | 0.506799 | − | 0.862064i | \(-0.330829\pi\) |
−0.493170 | + | 0.869933i | \(0.664162\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.41898i | 0.132983i | 0.997787 | + | 0.0664915i | \(0.0211805\pi\) | ||||
−0.997787 | + | 0.0664915i | \(0.978819\pi\) | |||||||
\(662\) | − | 1.30322i | − | 0.0506510i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.2791 | + | 5.93463i | 0.398906 | + | 0.230308i | ||||
\(665\) | 2.47852 | + | 9.08955i | 0.0961127 | + | 0.352478i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.48846 | + | 9.50629i | 0.212514 | + | 0.368085i | ||||
\(668\) | 6.88497 | + | 11.9251i | 0.266387 | + | 0.461397i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.8685 | − | 6.27490i | −0.419885 | − | 0.242421i | ||||
\(671\) | 2.73665 | + | 4.74001i | 0.105647 | + | 0.182986i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.47604 | − | 16.4130i | 0.365274 | − | 0.632674i | −0.623546 | − | 0.781787i | \(-0.714309\pi\) |
0.988820 | + | 0.149113i | \(0.0476418\pi\) | |||||||
\(674\) | 14.0659 | − | 8.12095i | 0.541798 | − | 0.312807i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.7832 | + | 30.8014i | −0.683968 | + | 1.18467i | ||||
\(677\) | 15.3569 | 0.590214 | 0.295107 | − | 0.955464i | \(-0.404645\pi\) | ||||
0.295107 | + | 0.955464i | \(0.404645\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.7354 | + | 7.03762i | 1.02601 | + | 0.270079i | ||||
\(680\) | 5.72151 | − | 3.30332i | 0.219410 | − | 0.126676i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.95964 | − | 5.75020i | 0.381374 | − | 0.220187i | ||||
\(683\) | 26.9763 | + | 15.5748i | 1.03222 | + | 0.595951i | 0.917619 | − | 0.397460i | \(-0.130108\pi\) |
0.114599 | + | 0.993412i | \(0.463442\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0482i | 0.460340i | ||||||||
\(686\) | −13.2678 | − | 12.9215i | −0.506566 | − | 0.493347i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.24581 | + | 5.62191i | −0.123745 | + | 0.214333i | ||||
\(689\) | 45.1286 | 1.71926 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 26.8062i | − | 1.01976i | −0.860247 | − | 0.509878i | \(-0.829691\pi\) | ||
0.860247 | − | 0.509878i | \(-0.170309\pi\) | |||||||
\(692\) | 11.6394 | 0.442464 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.07209 | −0.192534 | ||||||||
\(695\) | 18.0223i | 0.683624i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.35624 | −0.316515 | ||||||||
\(698\) | −11.8354 | + | 20.4996i | −0.447978 | + | 0.775921i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.87905 | + | 1.86257i | 0.0710216 | + | 0.0703984i | ||||
\(701\) | − | 9.39873i | − | 0.354985i | −0.984122 | − | 0.177493i | \(-0.943201\pi\) | ||
0.984122 | − | 0.177493i | \(-0.0567985\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.0200 | + | 9.82652i | 0.641922 | + | 0.370614i | ||||
\(704\) | 1.26877 | − | 0.732523i | 0.0478185 | − | 0.0276080i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.471774 | + | 0.272379i | −0.0177554 | + | 0.0102511i | ||||
\(707\) | 3.83263 | + | 3.79901i | 0.144141 | + | 0.142876i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.2298 | 0.759745 | 0.379873 | − | 0.925039i | \(-0.375968\pi\) | ||||
0.379873 | + | 0.925039i | \(0.375968\pi\) | |||||||
\(710\) | −7.10664 | + | 12.3091i | −0.266707 | + | 0.461951i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.78871 | − | 2.18741i | 0.141988 | − | 0.0819767i | ||||
\(713\) | −24.9727 | + | 43.2540i | −0.935234 | + | 1.61987i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.10492 | − | 8.84199i | −0.190913 | − | 0.330672i | ||||
\(716\) | 1.21808 | + | 0.703262i | 0.0455220 | + | 0.0262821i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.14576 | + | 5.44862i | 0.117399 | + | 0.203341i | ||||
\(719\) | 0.154148 | + | 0.266992i | 0.00574874 | + | 0.00995710i | 0.868885 | − | 0.495013i | \(-0.164837\pi\) |
−0.863137 | + | 0.504970i | \(0.831503\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.13732 | − | 2.14200i | −0.303050 | − | 0.0797724i | ||||
\(722\) | 5.47291 | + | 3.15979i | 0.203681 | + | 0.117595i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 10.1582i | − | 0.377527i | ||||||
\(725\) | 1.72523i | 0.0640734i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.69340 | + | 2.13238i | 0.136980 | + | 0.0790857i | 0.566924 | − | 0.823770i | \(-0.308133\pi\) |
−0.429944 | + | 0.902856i | \(0.641467\pi\) | |||||||
\(728\) | −13.0950 | − | 12.9801i | −0.485335 | − | 0.481076i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.640987 | + | 1.11022i | 0.0237240 | + | 0.0410911i | ||||
\(731\) | 21.4439 | + | 37.1419i | 0.793130 | + | 1.37374i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.60873 | + | 1.50615i | 0.0963558 | + | 0.0556310i | 0.547404 | − | 0.836869i | \(-0.315616\pi\) |
−0.451048 | + | 0.892500i | \(0.648950\pi\) | |||||||
\(734\) | −12.1749 | − | 21.0875i | −0.449382 | − | 0.778353i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.18129 | + | 5.51016i | −0.117264 | + | 0.203107i | ||||
\(737\) | −15.9228 | + | 9.19303i | −0.586524 | + | 0.338630i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.01920 | − | 15.6217i | 0.331776 | − | 0.574654i | −0.651084 | − | 0.759006i | \(-0.725685\pi\) |
0.982860 | + | 0.184352i | \(0.0590187\pi\) | |||||||
\(740\) | 5.51903 | 0.202884 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.36138 | + | 16.5686i | −0.160111 | + | 0.608252i | ||||
\(743\) | −1.82145 | + | 1.05161i | −0.0668225 | + | 0.0385800i | −0.533039 | − | 0.846091i | \(-0.678950\pi\) |
0.466217 | + | 0.884671i | \(0.345617\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.44381 | − | 4.29769i | 0.272720 | − | 0.157455i | ||||
\(746\) | 1.88581 | + | 1.08878i | 0.0690445 | + | 0.0398629i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 9.67903i | − | 0.353900i | ||||||
\(749\) | −29.6590 | + | 29.9215i | −1.08371 | + | 1.09331i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.40069 | − | 5.89017i | 0.124093 | − | 0.214935i | −0.797285 | − | 0.603603i | \(-0.793731\pi\) |
0.921378 | + | 0.388668i | \(0.127065\pi\) | |||||||
\(752\) | −5.39759 | −0.196830 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 12.0230i | − | 0.437853i | ||||||
\(755\) | 2.60771 | 0.0949044 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.9017 | −0.977761 | −0.488880 | − | 0.872351i | \(-0.662595\pi\) | ||||
−0.488880 | + | 0.872351i | \(0.662595\pi\) | |||||||
\(758\) | 22.5954i | 0.820700i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.56096 | −0.129170 | ||||||||
\(761\) | −2.08165 | + | 3.60553i | −0.0754598 | + | 0.130700i | −0.901286 | − | 0.433224i | \(-0.857376\pi\) |
0.825826 | + | 0.563925i | \(0.190709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.86072 | + | 18.4655i | −0.175970 | + | 0.668497i | ||||
\(764\) | − | 17.1243i | − | 0.619536i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.65138 | + | 3.26282i | 0.204193 | + | 0.117891i | ||||
\(767\) | −9.01241 | + | 5.20332i | −0.325419 | + | 0.187881i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.1341 | + | 8.73768i | −0.545750 | + | 0.315089i | −0.747406 | − | 0.664368i | \(-0.768701\pi\) |
0.201656 | + | 0.979456i | \(0.435368\pi\) | |||||||
\(770\) | 3.73962 | − | 1.01971i | 0.134766 | − | 0.0367478i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.93306 | −0.0695722 | ||||||||
\(773\) | −9.80159 | + | 16.9768i | −0.352539 | + | 0.610615i | −0.986694 | − | 0.162591i | \(-0.948015\pi\) |
0.634155 | + | 0.773206i | \(0.281348\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.79817 | + | 3.92493i | −0.244197 | + | 0.140987i | ||||
\(776\) | −5.22463 | + | 9.04933i | −0.187553 | + | 0.324852i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17.3402 | − | 30.0342i | −0.621677 | − | 1.07678i | ||||
\(779\) | 3.90057 | + | 2.25200i | 0.139753 | + | 0.0806862i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.4116 | + | 18.0334i | 0.372555 | + | 0.645284i | ||||
\(782\) | 21.0176 | + | 36.4036i | 0.751589 | + | 1.30179i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.03110 | − | 3.55329i | 0.215396 | − | 0.126903i | ||||
\(785\) | −6.74663 | − | 3.89517i | −0.240798 | − | 0.139025i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.0422i | 1.03524i | 0.855610 | + | 0.517620i | \(0.173182\pi\) | ||||
−0.855610 | + | 0.517620i | \(0.826818\pi\) | |||||||
\(788\) | 22.0136i | 0.784200i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.860839 | − | 0.497005i | −0.0306273 | − | 0.0176827i | ||||
\(791\) | −11.6720 | + | 11.7754i | −0.415010 | + | 0.418684i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.0177 | + | 22.5473i | 0.462273 | + | 0.800680i | ||||
\(794\) | −13.7650 | − | 23.8417i | −0.488501 | − | 0.846109i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −23.0430 | − | 13.3039i | −0.816739 | − | 0.471544i | ||||
\(797\) | 14.0345 | + | 24.3085i | 0.497129 | + | 0.861052i | 0.999995 | − | 0.00331218i | \(-0.00105430\pi\) |
−0.502866 | + | 0.864365i | \(0.667721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.8300 | + | 30.8824i | −0.630778 | + | 1.09254i | ||||
\(800\) | −0.866025 | + | 0.500000i | −0.0306186 | + | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.03938 | + | 12.1926i | −0.248569 | + | 0.430534i | ||||
\(803\) | 1.87815 | 0.0662785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.8507 | + | 11.9556i | −0.417684 | + | 0.421381i | ||||
\(806\) | 47.3762 | − | 27.3526i | 1.66875 | − | 0.963455i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.76640 | + | 1.01983i | −0.0621417 | + | 0.0358775i | ||||
\(809\) | 2.46533 | + | 1.42336i | 0.0866764 | + | 0.0500427i | 0.542712 | − | 0.839919i | \(-0.317398\pi\) |
−0.456035 | + | 0.889962i | \(0.650731\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.05522i | − | 0.177513i | −0.996053 | − | 0.0887564i | \(-0.971711\pi\) | ||
0.996053 | − | 0.0887564i | \(-0.0282893\pi\) | |||||||
\(812\) | 4.41416 | + | 1.16195i | 0.154907 | + | 0.0407764i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.04282 | − | 7.00236i | 0.141701 | − | 0.245433i | ||||
\(815\) | −8.29410 | −0.290530 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 23.1164i | − | 0.808740i | ||||||
\(818\) | −32.7642 | −1.14557 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.26483 | 0.0441696 | ||||||||
\(821\) | − | 39.0748i | − | 1.36372i | −0.731482 | − | 0.681861i | \(-0.761171\pi\) | ||
0.731482 | − | 0.681861i | \(-0.238829\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.7968 | −1.14322 | −0.571612 | − | 0.820524i | \(-0.693682\pi\) | ||||
−0.571612 | + | 0.820524i | \(0.693682\pi\) | |||||||
\(824\) | 1.59020 | − | 2.75430i | 0.0553971 | − | 0.0959506i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.03936 | − | 3.81169i | −0.0361641 | − | 0.132626i | ||||
\(827\) | − | 53.3096i | − | 1.85376i | −0.375361 | − | 0.926879i | \(-0.622481\pi\) | ||
0.375361 | − | 0.926879i | \(-0.377519\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.1781 | + | 22.6195i | 1.36071 | + | 0.785607i | 0.989718 | − | 0.143029i | \(-0.0456844\pi\) |
0.370992 | + | 0.928636i | \(0.379018\pi\) | |||||||
\(830\) | −10.2791 | + | 5.93463i | −0.356792 | + | 0.205994i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.03529 | − | 3.48448i | 0.209236 | − | 0.120803i | ||||
\(833\) | −0.407548 | − | 46.2446i | −0.0141207 | − | 1.60228i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.7699 | −0.476528 | ||||||||
\(836\) | −2.60849 | + | 4.51803i | −0.0902164 | + | 0.156259i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.0677 | − | 5.81259i | 0.347783 | − | 0.200793i | ||||
\(839\) | 19.1888 | − | 33.2360i | 0.662472 | − | 1.14744i | −0.317492 | − | 0.948261i | \(-0.602841\pi\) |
0.979964 | − | 0.199175i | \(-0.0638261\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0118 | − | 22.5371i | −0.448683 | − | 0.777141i | ||||
\(842\) | −19.8333 | − | 11.4508i | −0.683500 | − | 0.394619i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.44298 | + | 5.96341i | 0.118512 | + | 0.205269i | ||||
\(845\) | −17.7832 | − | 30.8014i | −0.611760 | − | 1.05960i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.96296 | + | 22.6528i | −0.204890 | + | 0.778361i | ||||
\(848\) | −5.60809 | − | 3.23783i | −0.192583 | − | 0.111188i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.60663i | 0.226606i | ||||||||
\(851\) | 35.1153i | 1.20374i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.3554 | − | 25.0313i | −1.48446 | − | 0.857054i | −0.484618 | − | 0.874726i | \(-0.661041\pi\) |
−0.999844 | + | 0.0176720i | \(0.994375\pi\) | |||||||
\(854\) | −9.53614 | + | 2.60029i | −0.326320 | + | 0.0889801i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.96185 | − | 13.7903i | −0.272130 | − | 0.471344i | ||||
\(857\) | −15.7216 | − | 27.2305i | −0.537038 | − | 0.930178i | −0.999062 | − | 0.0433100i | \(-0.986210\pi\) |
0.462023 | − | 0.886868i | \(-0.347124\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.1528 | − | 15.0993i | −0.892323 | − | 0.515183i | −0.0176215 | − | 0.999845i | \(-0.505609\pi\) |
−0.874702 | + | 0.484662i | \(0.838943\pi\) | |||||||
\(860\) | −3.24581 | − | 5.62191i | −0.110681 | − | 0.191705i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.81745 | − | 8.34407i | 0.164083 | − | 0.284200i | ||||
\(863\) | −13.8288 | + | 7.98404i | −0.470736 | + | 0.271780i | −0.716548 | − | 0.697538i | \(-0.754279\pi\) |
0.245812 | + | 0.969318i | \(0.420946\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.81971 | + | 10.0800i | −0.197876 | + | 0.342731i | ||||
\(866\) | −37.8458 | −1.28605 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.46369 | + | 20.0372i | 0.185450 | + | 0.680107i | ||||
\(869\) | −1.26117 | + | 0.728136i | −0.0427822 | + | 0.0247003i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −75.7418 | + | 43.7295i | −2.56641 | + | 1.48172i | ||||
\(872\) | −6.25017 | − | 3.60853i | −0.211657 | − | 0.122200i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 22.6569i | − | 0.766382i | ||||||
\(875\) | −2.55256 | + | 0.696025i | −0.0862922 | + | 0.0235299i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.2758 | + | 43.7790i | −0.853503 | + | 1.47831i | 0.0245242 | + | 0.999699i | \(0.492193\pi\) |
−0.878027 | + | 0.478611i | \(0.841140\pi\) | |||||||
\(878\) | 32.3974 | 1.09336 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.46505i | 0.0493867i | ||||||||
\(881\) | 7.58608 | 0.255581 | 0.127791 | − | 0.991801i | \(-0.459211\pi\) | ||||
0.127791 | + | 0.991801i | \(0.459211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.9066 | −0.669910 | −0.334955 | − | 0.942234i | \(-0.608721\pi\) | ||||
−0.334955 | + | 0.942234i | \(0.608721\pi\) | |||||||
\(884\) | − | 46.0413i | − | 1.54854i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.9018 | 0.735806 | ||||||||
\(887\) | 17.5255 | − | 30.3551i | 0.588449 | − | 1.01922i | −0.405987 | − | 0.913879i | \(-0.633072\pi\) |
0.994436 | − | 0.105345i | \(-0.0335947\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.33401 | + | 0.636431i | −0.0782801 | + | 0.0213452i | ||||
\(890\) | 4.37482i | 0.146644i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.6938 | − | 6.75140i | −0.391536 | − | 0.226053i | ||||
\(893\) | 16.6455 | − | 9.61030i | 0.557021 | − | 0.321596i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.21808 | + | 0.703262i | −0.0407161 | + | 0.0235074i | ||||
\(896\) | 0.696025 | + | 2.55256i | 0.0232526 | + | 0.0852750i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.8522 | 0.862700 | ||||||||
\(899\) | −6.77139 | + | 11.7284i | −0.225839 | + | 0.391164i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.0506 | + | 21.3912i | −1.23433 | + | 0.712643i | ||||
\(902\) | 0.926515 | − | 1.60477i | 0.0308496 | − | 0.0534330i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.13332 | − | 5.42707i | −0.104213 | − | 0.180502i | ||||
\(905\) | 8.79728 | + | 5.07911i | 0.292431 | + | 0.168835i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.06535 | − | 3.57729i | −0.0685789 | − | 0.118782i | 0.829697 | − | 0.558214i | \(-0.188513\pi\) |
−0.898276 | + | 0.439432i | \(0.855180\pi\) | |||||||
\(908\) | −10.7490 | − | 18.6179i | −0.356719 | − | 0.617856i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 17.7887 | − | 4.85057i | 0.589688 | − | 0.160795i | ||||
\(911\) | 22.0418 | + | 12.7258i | 0.730276 | + | 0.421625i | 0.818523 | − | 0.574474i | \(-0.194793\pi\) |
−0.0882472 | + | 0.996099i | \(0.528127\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.3890i | 0.575493i | ||||||||
\(914\) | 22.2463i | 0.735841i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.4936 | − | 11.2546i | −0.644086 | − | 0.371863i | ||||
\(917\) | −6.66684 | + | 25.3268i | −0.220158 | + | 0.836366i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.41703 | + | 5.91848i | 0.112718 | + | 0.195232i | 0.916865 | − | 0.399197i | \(-0.130711\pi\) |
−0.804148 | + | 0.594430i | \(0.797378\pi\) | |||||||
\(920\) | −3.18129 | − | 5.51016i | −0.104884 | − | 0.181665i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.2173 | + | 7.05369i | 0.402357 | + | 0.232301i | ||||
\(923\) | 49.5259 | + | 85.7813i | 1.63016 | + | 2.82353i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.75951 | + | 4.77962i | −0.0907323 | + | 0.157153i | ||||
\(926\) | 5.77194 | − | 3.33243i | 0.189678 | − | 0.109510i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.862614 | + | 1.49409i | −0.0283167 | + | 0.0490460i | ||||
\(929\) | −36.1564 | −1.18625 | −0.593126 | − | 0.805110i | \(-0.702106\pi\) | ||||
−0.593126 | + | 0.805110i | \(0.702106\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.2726 | + | 21.6962i | −0.402219 | + | 0.711063i | ||||
\(932\) | −15.4408 | + | 8.91477i | −0.505782 | + | 0.292013i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.04350 | − | 1.75717i | 0.0995864 | − | 0.0574962i | ||||
\(935\) | 8.38228 | + | 4.83951i | 0.274130 | + | 0.158269i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.1125i | 0.820391i | 0.911998 | + | 0.410195i | \(0.134539\pi\) | ||||
−0.911998 | + | 0.410195i | \(0.865461\pi\) | |||||||
\(938\) | −8.73498 | − | 32.0341i | −0.285207 | − | 1.04595i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.69880 | − | 4.67445i | 0.0880250 | − | 0.152464i | ||||
\(941\) | −2.72207 | −0.0887370 | −0.0443685 | − | 0.999015i | \(-0.514128\pi\) | ||||
−0.0443685 | + | 0.999015i | \(0.514128\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.04757i | 0.262065i | ||||||||
\(944\) | 1.49328 | 0.0486023 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.51053 | −0.309214 | ||||||||
\(947\) | − | 4.50181i | − | 0.146289i | −0.997321 | − | 0.0731446i | \(-0.976697\pi\) | ||
0.997321 | − | 0.0731446i | \(-0.0233034\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.93402 | 0.290010 | ||||||||
\(950\) | 1.78048 | − | 3.08388i | 0.0577664 | − | 0.100054i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16.9037 | + | 4.44959i | 0.547851 | + | 0.144212i | ||||
\(953\) | 18.8442i | 0.610423i | 0.952285 | + | 0.305211i | \(0.0987271\pi\) | ||||
−0.952285 | + | 0.305211i | \(0.901273\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.8301 | + | 8.56216i | 0.479890 | + | 0.277065i | ||||
\(956\) | 13.7144 | − | 7.91804i | 0.443557 | − | 0.256088i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.866868 | − | 0.500486i | 0.0280072 | − | 0.0161700i | ||||
\(959\) | −22.4407 | + | 22.6393i | −0.724647 | + | 0.731061i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6202 | −0.987747 | ||||||||
\(962\) | 19.2309 | − | 33.3089i | 0.620030 | − | 1.07392i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.8842 | + | 13.2122i | −0.737050 | + | 0.425536i | ||||
\(965\) | 0.966528 | − | 1.67408i | 0.0311136 | − | 0.0538904i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.7127 | − | 30.6793i | −0.569602 | − | 0.986579i | −0.996605 | − | 0.0823294i | \(-0.973764\pi\) |
0.427003 | − | 0.904250i | \(-0.359569\pi\) | |||||||
\(968\) | −7.66748 | − | 4.42682i | −0.246442 | − | 0.142283i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.22463 | − | 9.04933i | −0.167753 | − | 0.290556i | ||||
\(971\) | 0.536311 | + | 0.928919i | 0.0172111 | + | 0.0298104i | 0.874503 | − | 0.485021i | \(-0.161188\pi\) |
−0.857292 | + | 0.514831i | \(0.827855\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.5677 | + | 33.8648i | −1.07613 | + | 1.08566i | ||||
\(974\) | 25.0723 | + | 14.4755i | 0.803368 | + | 0.463825i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 3.73592i | − | 0.119584i | ||||||
\(977\) | − | 7.75308i | − | 0.248043i | −0.992280 | − | 0.124021i | \(-0.960421\pi\) | ||
0.992280 | − | 0.124021i | \(-0.0395792\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.55063 | + | 3.20466i | 0.177399 | + | 0.102421i | ||||
\(980\) | 0.0616877 | + | 6.99973i | 0.00197054 | + | 0.223598i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.6990 | + | 30.6555i | 0.564797 | + | 0.978257i | ||||
\(983\) | 10.7940 | + | 18.6958i | 0.344275 | + | 0.596302i | 0.985222 | − | 0.171283i | \(-0.0547913\pi\) |
−0.640947 | + | 0.767585i | \(0.721458\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.0643 | − | 11.0068i | −0.607439 | − | 0.350705i | ||||
\(986\) | 5.69898 | + | 9.87092i | 0.181492 | + | 0.314354i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.4081 | + | 21.4914i | −0.394754 | + | 0.683733i | ||||
\(989\) | 35.7699 | − | 20.6518i | 1.13742 | − | 0.656687i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.97525 | + | 6.88534i | −0.126278 | + | 0.218720i | −0.922232 | − | 0.386637i | \(-0.873636\pi\) |
0.795954 | + | 0.605357i | \(0.206970\pi\) | |||||||
\(992\) | −7.84985 | −0.249233 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −36.2802 | + | 9.89280i | −1.15074 | + | 0.313780i | ||||
\(995\) | 23.0430 | − | 13.3039i | 0.730513 | − | 0.421762i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.5700 | − | 28.6192i | 1.56990 | − | 0.906380i | 0.573717 | − | 0.819054i | \(-0.305501\pi\) |
0.996180 | − | 0.0873264i | \(-0.0278323\pi\) | |||||||
\(998\) | 14.4080 | + | 8.31844i | 0.456076 | + | 0.263316i | ||||
\(999\) | 0 | 0 |
(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 | 1890.2.bk.b.521.5 | 28 | ||
3.2 | odd | 2 | 630.2.bk.b.101.11 | yes | 28 | ||
7.5 | odd | 6 | 1890.2.t.b.1601.3 | 28 | |||
9.4 | even | 3 | 630.2.t.b.311.14 | ✓ | 28 | ||
9.5 | odd | 6 | 1890.2.t.b.1151.3 | 28 | |||
21.5 | even | 6 | 630.2.t.b.551.14 | yes | 28 | ||
63.5 | even | 6 | inner | 1890.2.bk.b.341.5 | 28 | ||
63.40 | odd | 6 | 630.2.bk.b.131.4 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.t.b.311.14 | ✓ | 28 | 9.4 | even | 3 | ||
630.2.t.b.551.14 | yes | 28 | 21.5 | even | 6 | ||
630.2.bk.b.101.11 | yes | 28 | 3.2 | odd | 2 | ||
630.2.bk.b.131.4 | yes | 28 | 63.40 | odd | 6 | ||
1890.2.t.b.1151.3 | 28 | 9.5 | odd | 6 | |||
1890.2.t.b.1601.3 | 28 | 7.5 | odd | 6 | |||
1890.2.bk.b.341.5 | 28 | 63.5 | even | 6 | inner | ||
1890.2.bk.b.521.5 | 28 | 1.1 | even | 1 | trivial |