Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,3,Mod(115,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.115");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.j (of order \(4\), 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: | \(3.70573159530\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 115.2 | ||
Character | \(\chi\) | \(=\) | 136.115 |
Dual form | 136.3.j.b.123.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.95592 | + | 0.417606i | −0.977958 | + | 0.208803i | ||||
\(3\) | 0.749243 | + | 0.749243i | 0.249748 | + | 0.249748i | 0.820867 | − | 0.571119i | \(-0.193491\pi\) |
−0.571119 | + | 0.820867i | \(0.693491\pi\) | |||||||
\(4\) | 3.65121 | − | 1.63360i | 0.912803 | − | 0.408401i | ||||
\(5\) | 3.60984 | − | 3.60984i | 0.721968 | − | 0.721968i | −0.247038 | − | 0.969006i | \(-0.579457\pi\) |
0.969006 | + | 0.247038i | \(0.0794571\pi\) | |||||||
\(6\) | −1.77834 | − | 1.15257i | −0.296391 | − | 0.192095i | ||||
\(7\) | −3.85896 | − | 3.85896i | −0.551280 | − | 0.551280i | 0.375530 | − | 0.926810i | \(-0.377461\pi\) |
−0.926810 | + | 0.375530i | \(0.877461\pi\) | |||||||
\(8\) | −6.45926 | + | 4.71996i | −0.807407 | + | 0.589994i | ||||
\(9\) | − | 7.87727i | − | 0.875252i | ||||||
\(10\) | −5.55305 | + | 8.56803i | −0.555305 | + | 0.856803i | ||||
\(11\) | −2.59125 | + | 2.59125i | −0.235568 | + | 0.235568i | −0.815012 | − | 0.579444i | \(-0.803270\pi\) |
0.579444 | + | 0.815012i | \(0.303270\pi\) | |||||||
\(12\) | 3.95961 | + | 1.51168i | 0.329968 | + | 0.125973i | ||||
\(13\) | − | 2.98374i | − | 0.229519i | −0.993393 | − | 0.114759i | \(-0.963390\pi\) | ||
0.993393 | − | 0.114759i | \(-0.0366097\pi\) | |||||||
\(14\) | 9.15932 | + | 5.93627i | 0.654237 | + | 0.424020i | ||||
\(15\) | 5.40930 | 0.360620 | ||||||||
\(16\) | 10.6627 | − | 11.9293i | 0.666418 | − | 0.745579i | ||||
\(17\) | 13.0434 | − | 10.9027i | 0.767261 | − | 0.641335i | ||||
\(18\) | 3.28959 | + | 15.4073i | 0.182755 | + | 0.855960i | ||||
\(19\) | − | 25.8973i | − | 1.36302i | −0.731810 | − | 0.681509i | \(-0.761324\pi\) | ||
0.731810 | − | 0.681509i | \(-0.238676\pi\) | |||||||
\(20\) | 7.28325 | − | 19.0773i | 0.364162 | − | 0.953867i | ||||
\(21\) | − | 5.78260i | − | 0.275362i | ||||||
\(22\) | 3.98614 | − | 6.15038i | 0.181188 | − | 0.279563i | ||||
\(23\) | 20.9457 | + | 20.9457i | 0.910682 | + | 0.910682i | 0.996326 | − | 0.0856440i | \(-0.0272948\pi\) |
−0.0856440 | + | 0.996326i | \(0.527295\pi\) | |||||||
\(24\) | −8.37595 | − | 1.30316i | −0.348998 | − | 0.0542984i | ||||
\(25\) | − | 1.06191i | − | 0.0424764i | ||||||
\(26\) | 1.24603 | + | 5.83595i | 0.0479242 | + | 0.224460i | ||||
\(27\) | 12.6452 | − | 12.6452i | 0.468340 | − | 0.468340i | ||||
\(28\) | −20.3939 | − | 7.78587i | −0.728353 | − | 0.278067i | ||||
\(29\) | 22.7491 | − | 22.7491i | 0.784451 | − | 0.784451i | −0.196128 | − | 0.980578i | \(-0.562837\pi\) |
0.980578 | + | 0.196128i | \(0.0628367\pi\) | |||||||
\(30\) | −10.5801 | + | 2.25895i | −0.352671 | + | 0.0752985i | ||||
\(31\) | −18.3612 | + | 18.3612i | −0.592297 | + | 0.592297i | −0.938251 | − | 0.345954i | \(-0.887555\pi\) |
0.345954 | + | 0.938251i | \(0.387555\pi\) | |||||||
\(32\) | −15.8736 | + | 27.7854i | −0.496049 | + | 0.868294i | ||||
\(33\) | −3.88295 | −0.117665 | ||||||||
\(34\) | −20.9588 | + | 26.7718i | −0.616436 | + | 0.787405i | ||||
\(35\) | −27.8605 | −0.796013 | ||||||||
\(36\) | −12.8683 | − | 28.7616i | −0.357454 | − | 0.798933i | ||||
\(37\) | 0.733830 | − | 0.733830i | 0.0198332 | − | 0.0198332i | −0.697121 | − | 0.716954i | \(-0.745536\pi\) |
0.716954 | + | 0.697121i | \(0.245536\pi\) | |||||||
\(38\) | 10.8149 | + | 50.6530i | 0.284602 | + | 1.33297i | ||||
\(39\) | 2.23555 | − | 2.23555i | 0.0573218 | − | 0.0573218i | ||||
\(40\) | −6.27861 | + | 40.3552i | −0.156965 | + | 1.00888i | ||||
\(41\) | −26.2827 | + | 26.2827i | −0.641042 | + | 0.641042i | −0.950812 | − | 0.309770i | \(-0.899748\pi\) |
0.309770 | + | 0.950812i | \(0.399748\pi\) | |||||||
\(42\) | 2.41485 | + | 11.3103i | 0.0574963 | + | 0.269292i | ||||
\(43\) | − | 10.7209i | − | 0.249323i | −0.992199 | − | 0.124661i | \(-0.960216\pi\) | ||
0.992199 | − | 0.124661i | \(-0.0397845\pi\) | |||||||
\(44\) | −5.22812 | + | 13.6943i | −0.118821 | + | 0.311233i | ||||
\(45\) | −28.4357 | − | 28.4357i | −0.631904 | − | 0.631904i | ||||
\(46\) | −49.7150 | − | 32.2209i | −1.08076 | − | 0.700455i | ||||
\(47\) | 84.3467i | 1.79461i | 0.441411 | + | 0.897305i | \(0.354478\pi\) | ||||
−0.441411 | + | 0.897305i | \(0.645522\pi\) | |||||||
\(48\) | 16.9269 | − | 0.948971i | 0.352643 | − | 0.0197702i | ||||
\(49\) | − | 19.2169i | − | 0.392181i | ||||||
\(50\) | 0.443459 | + | 2.07701i | 0.00886919 | + | 0.0415401i | ||||
\(51\) | 17.9415 | + | 1.60393i | 0.351794 | + | 0.0314496i | ||||
\(52\) | −4.87425 | − | 10.8943i | −0.0937356 | − | 0.209505i | ||||
\(53\) | 33.8459 | 0.638602 | 0.319301 | − | 0.947653i | \(-0.396552\pi\) | ||||
0.319301 | + | 0.947653i | \(0.396552\pi\) | |||||||
\(54\) | −19.4522 | + | 30.0136i | −0.360226 | + | 0.555807i | ||||
\(55\) | 18.7080i | 0.340145i | ||||||||
\(56\) | 43.1401 | + | 6.71190i | 0.770359 | + | 0.119855i | ||||
\(57\) | 19.4034 | − | 19.4034i | 0.340411 | − | 0.340411i | ||||
\(58\) | −34.9951 | + | 53.9954i | −0.603364 | + | 0.930955i | ||||
\(59\) | 69.9591i | 1.18575i | 0.805296 | + | 0.592874i | \(0.202007\pi\) | ||||
−0.805296 | + | 0.592874i | \(0.797993\pi\) | |||||||
\(60\) | 19.7505 | − | 8.83665i | 0.329175 | − | 0.147277i | ||||
\(61\) | −65.8369 | − | 65.8369i | −1.07929 | − | 1.07929i | −0.996573 | − | 0.0827207i | \(-0.973639\pi\) |
−0.0827207 | − | 0.996573i | \(-0.526361\pi\) | |||||||
\(62\) | 28.2452 | − | 43.5807i | 0.455569 | − | 0.702915i | ||||
\(63\) | −30.3981 | + | 30.3981i | −0.482509 | + | 0.482509i | ||||
\(64\) | 19.4440 | − | 60.9748i | 0.303813 | − | 0.952732i | ||||
\(65\) | −10.7708 | − | 10.7708i | −0.165705 | − | 0.165705i | ||||
\(66\) | 7.59472 | − | 1.62154i | 0.115071 | − | 0.0245688i | ||||
\(67\) | −76.0157 | −1.13456 | −0.567282 | − | 0.823524i | \(-0.692005\pi\) | ||||
−0.567282 | + | 0.823524i | \(0.692005\pi\) | |||||||
\(68\) | 29.8137 | − | 61.1158i | 0.438436 | − | 0.898762i | ||||
\(69\) | 31.3868i | 0.454882i | ||||||||
\(70\) | 54.4927 | − | 11.6347i | 0.778467 | − | 0.166210i | ||||
\(71\) | 27.4650 | − | 27.4650i | 0.386831 | − | 0.386831i | −0.486724 | − | 0.873556i | \(-0.661808\pi\) |
0.873556 | + | 0.486724i | \(0.161808\pi\) | |||||||
\(72\) | 37.1804 | + | 50.8813i | 0.516394 | + | 0.706685i | ||||
\(73\) | 48.3347 | + | 48.3347i | 0.662119 | + | 0.662119i | 0.955879 | − | 0.293760i | \(-0.0949067\pi\) |
−0.293760 | + | 0.955879i | \(0.594907\pi\) | |||||||
\(74\) | −1.12886 | + | 1.74176i | −0.0152548 | + | 0.0235373i | ||||
\(75\) | 0.795629 | − | 0.795629i | 0.0106084 | − | 0.0106084i | ||||
\(76\) | −42.3060 | − | 94.5567i | −0.556658 | − | 1.24417i | ||||
\(77\) | 19.9990 | 0.259728 | ||||||||
\(78\) | −3.43897 | + | 5.30613i | −0.0440893 | + | 0.0680273i | ||||
\(79\) | 17.0189 | + | 17.0189i | 0.215429 | + | 0.215429i | 0.806569 | − | 0.591140i | \(-0.201322\pi\) |
−0.591140 | + | 0.806569i | \(0.701322\pi\) | |||||||
\(80\) | −4.57213 | − | 81.5533i | −0.0571516 | − | 1.01942i | ||||
\(81\) | −51.9468 | −0.641318 | ||||||||
\(82\) | 40.4310 | − | 62.3826i | 0.493060 | − | 0.760763i | ||||
\(83\) | 20.9027i | 0.251839i | 0.992040 | + | 0.125920i | \(0.0401882\pi\) | ||||
−0.992040 | + | 0.125920i | \(0.959812\pi\) | |||||||
\(84\) | −9.44647 | − | 21.1135i | −0.112458 | − | 0.251351i | ||||
\(85\) | 7.72772 | − | 86.4417i | 0.0909143 | − | 1.01696i | ||||
\(86\) | 4.47710 | + | 20.9692i | 0.0520593 | + | 0.243827i | ||||
\(87\) | 34.0892 | 0.391830 | ||||||||
\(88\) | 4.50696 | − | 28.9681i | 0.0512155 | − | 0.329183i | ||||
\(89\) | 115.759 | 1.30066 | 0.650329 | − | 0.759652i | \(-0.274631\pi\) | ||||
0.650329 | + | 0.759652i | \(0.274631\pi\) | |||||||
\(90\) | 67.4927 | + | 43.7429i | 0.749919 | + | 0.486032i | ||||
\(91\) | −11.5141 | + | 11.5141i | −0.126529 | + | 0.126529i | ||||
\(92\) | 110.694 | + | 42.2602i | 1.20320 | + | 0.459350i | ||||
\(93\) | −27.5140 | −0.295850 | ||||||||
\(94\) | −35.2237 | − | 164.975i | −0.374720 | − | 1.75505i | ||||
\(95\) | −93.4853 | − | 93.4853i | −0.984056 | − | 0.984056i | ||||
\(96\) | −32.7112 | + | 8.92486i | −0.340742 | + | 0.0929673i | ||||
\(97\) | 66.5506 | + | 66.5506i | 0.686088 | + | 0.686088i | 0.961365 | − | 0.275277i | \(-0.0887694\pi\) |
−0.275277 | + | 0.961365i | \(0.588769\pi\) | |||||||
\(98\) | 8.02507 | + | 37.5866i | 0.0818885 | + | 0.383537i | ||||
\(99\) | 20.4119 | + | 20.4119i | 0.206181 | + | 0.206181i | ||||
\(100\) | −1.73474 | − | 3.87726i | −0.0173474 | − | 0.0387726i | ||||
\(101\) | − | 21.8709i | − | 0.216543i | −0.994121 | − | 0.108272i | \(-0.965468\pi\) | ||
0.994121 | − | 0.108272i | \(-0.0345316\pi\) | |||||||
\(102\) | −35.7618 | + | 4.35531i | −0.350606 | + | 0.0426991i | ||||
\(103\) | − | 26.9524i | − | 0.261673i | −0.991404 | − | 0.130837i | \(-0.958234\pi\) | ||
0.991404 | − | 0.130837i | \(-0.0417664\pi\) | |||||||
\(104\) | 14.0831 | + | 19.2728i | 0.135415 | + | 0.185315i | ||||
\(105\) | −20.8743 | − | 20.8743i | −0.198802 | − | 0.198802i | ||||
\(106\) | −66.1997 | + | 14.1342i | −0.624525 | + | 0.133342i | ||||
\(107\) | 69.9821 | + | 69.9821i | 0.654038 | + | 0.654038i | 0.953963 | − | 0.299925i | \(-0.0969616\pi\) |
−0.299925 | + | 0.953963i | \(0.596962\pi\) | |||||||
\(108\) | 25.5130 | − | 66.8274i | 0.236232 | − | 0.618772i | ||||
\(109\) | 26.7602 | + | 26.7602i | 0.245507 | + | 0.245507i | 0.819124 | − | 0.573617i | \(-0.194460\pi\) |
−0.573617 | + | 0.819124i | \(0.694460\pi\) | |||||||
\(110\) | −7.81256 | − | 36.5912i | −0.0710232 | − | 0.332647i | ||||
\(111\) | 1.09963 | 0.00990661 | ||||||||
\(112\) | −87.1814 | + | 4.88765i | −0.778405 | + | 0.0436398i | ||||
\(113\) | −103.894 | + | 103.894i | −0.919414 | + | 0.919414i | −0.996987 | − | 0.0775723i | \(-0.975283\pi\) |
0.0775723 | + | 0.996987i | \(0.475283\pi\) | |||||||
\(114\) | −29.8485 | + | 46.0544i | −0.261829 | + | 0.403986i | ||||
\(115\) | 151.221 | 1.31497 | ||||||||
\(116\) | 45.8987 | − | 120.225i | 0.395679 | − | 1.03642i | ||||
\(117\) | −23.5038 | −0.200887 | ||||||||
\(118\) | −29.2153 | − | 136.834i | −0.247587 | − | 1.15961i | ||||
\(119\) | −92.4071 | − | 8.26101i | −0.776531 | − | 0.0694203i | ||||
\(120\) | −34.9401 | + | 25.5316i | −0.291167 | + | 0.212764i | ||||
\(121\) | 107.571i | 0.889016i | ||||||||
\(122\) | 156.265 | + | 101.278i | 1.28086 | + | 0.830144i | ||||
\(123\) | −39.3843 | −0.320197 | ||||||||
\(124\) | −37.0458 | + | 97.0356i | −0.298756 | + | 0.782545i | ||||
\(125\) | 86.4127 | + | 86.4127i | 0.691302 | + | 0.691302i | ||||
\(126\) | 46.7616 | − | 72.1504i | 0.371124 | − | 0.572622i | ||||
\(127\) | −17.2092 | −0.135505 | −0.0677527 | − | 0.997702i | \(-0.521583\pi\) | ||||
−0.0677527 | + | 0.997702i | \(0.521583\pi\) | |||||||
\(128\) | −12.5675 | + | 127.382i | −0.0981834 | + | 0.995168i | ||||
\(129\) | 8.03255 | − | 8.03255i | 0.0622679 | − | 0.0622679i | ||||
\(130\) | 25.5648 | + | 16.5689i | 0.196652 | + | 0.127453i | ||||
\(131\) | −112.948 | − | 112.948i | −0.862200 | − | 0.862200i | 0.129393 | − | 0.991593i | \(-0.458697\pi\) |
−0.991593 | + | 0.129393i | \(0.958697\pi\) | |||||||
\(132\) | −14.1775 | + | 6.34319i | −0.107405 | + | 0.0480545i | ||||
\(133\) | −99.9368 | + | 99.9368i | −0.751404 | + | 0.751404i | ||||
\(134\) | 148.680 | − | 31.7446i | 1.10955 | − | 0.236900i | ||||
\(135\) | − | 91.2942i | − | 0.676253i | ||||||
\(136\) | −32.7907 | + | 131.988i | −0.241108 | + | 0.970498i | ||||
\(137\) | −195.481 | −1.42687 | −0.713436 | − | 0.700721i | \(-0.752862\pi\) | ||||
−0.713436 | + | 0.700721i | \(0.752862\pi\) | |||||||
\(138\) | −13.1073 | − | 61.3900i | −0.0949805 | − | 0.444855i | ||||
\(139\) | −4.95033 | − | 4.95033i | −0.0356139 | − | 0.0356139i | 0.689076 | − | 0.724689i | \(-0.258017\pi\) |
−0.724689 | + | 0.689076i | \(0.758017\pi\) | |||||||
\(140\) | −101.724 | + | 45.5129i | −0.726603 | + | 0.325092i | ||||
\(141\) | −63.1962 | + | 63.1962i | −0.448200 | + | 0.448200i | ||||
\(142\) | −42.2497 | + | 65.1888i | −0.297533 | + | 0.459076i | ||||
\(143\) | 7.73162 | + | 7.73162i | 0.0540672 | + | 0.0540672i | ||||
\(144\) | −93.9700 | − | 83.9928i | −0.652569 | − | 0.583284i | ||||
\(145\) | − | 164.241i | − | 1.13270i | ||||||
\(146\) | −114.723 | − | 74.3537i | −0.785777 | − | 0.509272i | ||||
\(147\) | 14.3981 | − | 14.3981i | 0.0979463 | − | 0.0979463i | ||||
\(148\) | 1.48058 | − | 3.87815i | 0.0100039 | − | 0.0262037i | ||||
\(149\) | 34.5639i | 0.231973i | 0.993251 | + | 0.115986i | \(0.0370029\pi\) | ||||
−0.993251 | + | 0.115986i | \(0.962997\pi\) | |||||||
\(150\) | −1.22392 | + | 1.88844i | −0.00815949 | + | 0.0125896i | ||||
\(151\) | 152.346 | 1.00892 | 0.504458 | − | 0.863436i | \(-0.331692\pi\) | ||||
0.504458 | + | 0.863436i | \(0.331692\pi\) | |||||||
\(152\) | 122.234 | + | 167.278i | 0.804173 | + | 1.10051i | ||||
\(153\) | −85.8835 | − | 102.747i | −0.561330 | − | 0.671547i | ||||
\(154\) | −39.1164 | + | 8.35171i | −0.254003 | + | 0.0542319i | ||||
\(155\) | 132.562i | 0.855240i | ||||||||
\(156\) | 4.51046 | − | 11.8145i | 0.0289132 | − | 0.0757338i | ||||
\(157\) | 287.858i | 1.83349i | 0.399473 | + | 0.916745i | \(0.369193\pi\) | ||||
−0.399473 | + | 0.916745i | \(0.630807\pi\) | |||||||
\(158\) | −40.3948 | − | 26.1804i | −0.255663 | − | 0.165699i | ||||
\(159\) | 25.3588 | + | 25.3588i | 0.159489 | + | 0.159489i | ||||
\(160\) | 42.9998 | + | 157.602i | 0.268749 | + | 0.985013i | ||||
\(161\) | − | 161.657i | − | 1.00408i | ||||||
\(162\) | 101.604 | − | 21.6933i | 0.627182 | − | 0.133909i | ||||
\(163\) | 199.813 | − | 199.813i | 1.22584 | − | 1.22584i | 0.260322 | − | 0.965522i | \(-0.416171\pi\) |
0.965522 | − | 0.260322i | \(-0.0838288\pi\) | |||||||
\(164\) | −53.0282 | + | 138.899i | −0.323343 | + | 0.846946i | ||||
\(165\) | −14.0168 | + | 14.0168i | −0.0849505 | + | 0.0849505i | ||||
\(166\) | −8.72907 | − | 40.8839i | −0.0525848 | − | 0.246288i | ||||
\(167\) | 79.1049 | − | 79.1049i | 0.473682 | − | 0.473682i | −0.429422 | − | 0.903104i | \(-0.641283\pi\) |
0.903104 | + | 0.429422i | \(0.141283\pi\) | |||||||
\(168\) | 27.2936 | + | 37.3513i | 0.162462 | + | 0.222329i | ||||
\(169\) | 160.097 | 0.947321 | ||||||||
\(170\) | 20.9838 | + | 172.300i | 0.123434 | + | 1.01353i | ||||
\(171\) | −204.000 | −1.19298 | ||||||||
\(172\) | −17.5137 | − | 39.1442i | −0.101824 | − | 0.227583i | ||||
\(173\) | 232.520 | − | 232.520i | 1.34404 | − | 1.34404i | 0.452052 | − | 0.891991i | \(-0.350692\pi\) |
0.891991 | − | 0.452052i | \(-0.149308\pi\) | |||||||
\(174\) | −66.6755 | + | 14.2358i | −0.383193 | + | 0.0818151i | ||||
\(175\) | −4.09787 | + | 4.09787i | −0.0234164 | + | 0.0234164i | ||||
\(176\) | 3.28200 | + | 58.5413i | 0.0186477 | + | 0.332621i | ||||
\(177\) | −52.4164 | + | 52.4164i | −0.296138 | + | 0.296138i | ||||
\(178\) | −226.414 | + | 48.3415i | −1.27199 | + | 0.271581i | ||||
\(179\) | − | 215.338i | − | 1.20301i | −0.798871 | − | 0.601503i | \(-0.794569\pi\) | ||
0.798871 | − | 0.601503i | \(-0.205431\pi\) | |||||||
\(180\) | −150.277 | − | 57.3721i | −0.834874 | − | 0.318734i | ||||
\(181\) | 85.2707 | + | 85.2707i | 0.471109 | + | 0.471109i | 0.902273 | − | 0.431164i | \(-0.141897\pi\) |
−0.431164 | + | 0.902273i | \(0.641897\pi\) | |||||||
\(182\) | 17.7123 | − | 27.3291i | 0.0973205 | − | 0.150160i | ||||
\(183\) | − | 98.6557i | − | 0.539102i | ||||||
\(184\) | −234.156 | − | 36.4309i | −1.27259 | − | 0.197994i | ||||
\(185\) | − | 5.29802i | − | 0.0286379i | ||||||
\(186\) | 53.8151 | − | 11.4900i | 0.289329 | − | 0.0617743i | ||||
\(187\) | −5.54717 | + | 62.0503i | −0.0296640 | + | 0.331820i | ||||
\(188\) | 137.789 | + | 307.968i | 0.732920 | + | 1.63813i | ||||
\(189\) | −97.5945 | −0.516373 | ||||||||
\(190\) | 221.889 | + | 143.809i | 1.16784 | + | 0.756891i | ||||
\(191\) | − | 213.241i | − | 1.11644i | −0.829692 | − | 0.558221i | \(-0.811484\pi\) | ||
0.829692 | − | 0.558221i | \(-0.188516\pi\) | |||||||
\(192\) | 60.2533 | − | 31.1167i | 0.313819 | − | 0.162066i | ||||
\(193\) | 95.8456 | − | 95.8456i | 0.496610 | − | 0.496610i | −0.413771 | − | 0.910381i | \(-0.635789\pi\) |
0.910381 | + | 0.413771i | \(0.135789\pi\) | |||||||
\(194\) | −157.959 | − | 102.375i | −0.814223 | − | 0.527708i | ||||
\(195\) | − | 16.1400i | − | 0.0827690i | ||||||
\(196\) | −31.3927 | − | 70.1649i | −0.160167 | − | 0.357984i | ||||
\(197\) | 117.420 | + | 117.420i | 0.596041 | + | 0.596041i | 0.939257 | − | 0.343216i | \(-0.111516\pi\) |
−0.343216 | + | 0.939257i | \(0.611516\pi\) | |||||||
\(198\) | −48.4482 | − | 31.3999i | −0.244688 | − | 0.158585i | ||||
\(199\) | −121.225 | + | 121.225i | −0.609173 | + | 0.609173i | −0.942730 | − | 0.333557i | \(-0.891751\pi\) |
0.333557 | + | 0.942730i | \(0.391751\pi\) | |||||||
\(200\) | 5.01217 | + | 6.85915i | 0.0250608 | + | 0.0342957i | ||||
\(201\) | −56.9543 | − | 56.9543i | −0.283355 | − | 0.283355i | ||||
\(202\) | 9.13340 | + | 42.7776i | 0.0452149 | + | 0.211770i | ||||
\(203\) | −175.575 | −0.864904 | ||||||||
\(204\) | 68.1283 | − | 23.4530i | 0.333962 | − | 0.114965i | ||||
\(205\) | 189.753i | 0.925624i | ||||||||
\(206\) | 11.2555 | + | 52.7166i | 0.0546382 | + | 0.255906i | ||||
\(207\) | 164.995 | − | 164.995i | 0.797076 | − | 0.797076i | ||||
\(208\) | −35.5938 | − | 31.8147i | −0.171124 | − | 0.152955i | ||||
\(209\) | 67.1064 | + | 67.1064i | 0.321083 | + | 0.321083i | ||||
\(210\) | 49.5455 | + | 32.1111i | 0.235931 | + | 0.152910i | ||||
\(211\) | −15.7879 | + | 15.7879i | −0.0748241 | + | 0.0748241i | −0.743528 | − | 0.668704i | \(-0.766849\pi\) |
0.668704 | + | 0.743528i | \(0.266849\pi\) | |||||||
\(212\) | 123.578 | − | 55.2907i | 0.582917 | − | 0.260805i | ||||
\(213\) | 41.1560 | 0.193220 | ||||||||
\(214\) | −166.104 | − | 107.654i | −0.776187 | − | 0.503057i | ||||
\(215\) | −38.7007 | − | 38.7007i | −0.180003 | − | 0.180003i | ||||
\(216\) | −21.9938 | + | 141.363i | −0.101823 | + | 0.654459i | ||||
\(217\) | 141.710 | 0.653043 | ||||||||
\(218\) | −63.5160 | − | 41.1655i | −0.291358 | − | 0.188833i | ||||
\(219\) | 72.4289i | 0.330725i | ||||||||
\(220\) | 30.5614 | + | 68.3068i | 0.138915 | + | 0.310485i | ||||
\(221\) | −32.5309 | − | 38.9183i | −0.147198 | − | 0.176101i | ||||
\(222\) | −2.15079 | + | 0.459213i | −0.00968825 | + | 0.00206853i | ||||
\(223\) | 74.7498 | 0.335201 | 0.167600 | − | 0.985855i | \(-0.446398\pi\) | ||||
0.167600 | + | 0.985855i | \(0.446398\pi\) | |||||||
\(224\) | 168.478 | − | 45.9673i | 0.752135 | − | 0.205211i | ||||
\(225\) | −8.36495 | −0.0371775 | ||||||||
\(226\) | 159.821 | − | 246.594i | 0.707172 | − | 1.09112i | ||||
\(227\) | 142.640 | − | 142.640i | 0.628370 | − | 0.628370i | −0.319288 | − | 0.947658i | \(-0.603444\pi\) |
0.947658 | + | 0.319288i | \(0.103444\pi\) | |||||||
\(228\) | 39.1485 | − | 102.543i | 0.171704 | − | 0.449752i | ||||
\(229\) | −262.209 | −1.14502 | −0.572508 | − | 0.819899i | \(-0.694029\pi\) | ||||
−0.572508 | + | 0.819899i | \(0.694029\pi\) | |||||||
\(230\) | −295.776 | + | 63.1508i | −1.28598 | + | 0.274569i | ||||
\(231\) | 14.9841 | + | 14.9841i | 0.0648664 | + | 0.0648664i | ||||
\(232\) | −39.5675 | + | 254.317i | −0.170550 | + | 1.09619i | ||||
\(233\) | −60.8609 | − | 60.8609i | −0.261206 | − | 0.261206i | 0.564338 | − | 0.825544i | \(-0.309131\pi\) |
−0.825544 | + | 0.564338i | \(0.809131\pi\) | |||||||
\(234\) | 45.9714 | − | 9.81530i | 0.196459 | − | 0.0419457i | ||||
\(235\) | 304.478 | + | 304.478i | 1.29565 | + | 1.29565i | ||||
\(236\) | 114.285 | + | 255.435i | 0.484260 | + | 1.08235i | ||||
\(237\) | 25.5026i | 0.107606i | ||||||||
\(238\) | 184.190 | − | 22.4319i | 0.773909 | − | 0.0942517i | ||||
\(239\) | 95.1858i | 0.398267i | 0.979972 | + | 0.199133i | \(0.0638127\pi\) | ||||
−0.979972 | + | 0.199133i | \(0.936187\pi\) | |||||||
\(240\) | 57.6776 | − | 64.5289i | 0.240324 | − | 0.268870i | ||||
\(241\) | −117.983 | − | 117.983i | −0.489557 | − | 0.489557i | 0.418609 | − | 0.908166i | \(-0.362518\pi\) |
−0.908166 | + | 0.418609i | \(0.862518\pi\) | |||||||
\(242\) | −44.9222 | − | 210.400i | −0.185629 | − | 0.869420i | ||||
\(243\) | −152.727 | − | 152.727i | −0.628508 | − | 0.628508i | ||||
\(244\) | −347.936 | − | 132.833i | −1.42597 | − | 0.544398i | ||||
\(245\) | −69.3699 | − | 69.3699i | −0.283142 | − | 0.283142i | ||||
\(246\) | 77.0323 | − | 16.4471i | 0.313140 | − | 0.0668581i | ||||
\(247\) | −77.2710 | −0.312838 | ||||||||
\(248\) | 31.9357 | − | 205.264i | 0.128773 | − | 0.827677i | ||||
\(249\) | −15.6612 | + | 15.6612i | −0.0628963 | + | 0.0628963i | ||||
\(250\) | −205.102 | − | 132.930i | −0.820410 | − | 0.531718i | ||||
\(251\) | 131.822 | 0.525188 | 0.262594 | − | 0.964906i | \(-0.415422\pi\) | ||||
0.262594 | + | 0.964906i | \(0.415422\pi\) | |||||||
\(252\) | −61.3314 | + | 160.648i | −0.243378 | + | 0.637492i | ||||
\(253\) | −108.551 | −0.429055 | ||||||||
\(254\) | 33.6597 | − | 7.18665i | 0.132519 | − | 0.0282939i | ||||
\(255\) | 70.5558 | − | 58.9760i | 0.276690 | − | 0.231278i | ||||
\(256\) | −28.6143 | − | 254.396i | −0.111775 | − | 0.993734i | ||||
\(257\) | 342.708i | 1.33349i | 0.745284 | + | 0.666747i | \(0.232314\pi\) | ||||
−0.745284 | + | 0.666747i | \(0.767686\pi\) | |||||||
\(258\) | −12.3566 | + | 19.0654i | −0.0478936 | + | 0.0738970i | ||||
\(259\) | −5.66364 | −0.0218673 | ||||||||
\(260\) | −56.9219 | − | 21.7313i | −0.218930 | − | 0.0835821i | ||||
\(261\) | −179.201 | − | 179.201i | −0.686592 | − | 0.686592i | ||||
\(262\) | 268.085 | + | 173.749i | 1.02322 | + | 0.663165i | ||||
\(263\) | −494.500 | −1.88023 | −0.940114 | − | 0.340862i | \(-0.889281\pi\) | ||||
−0.940114 | + | 0.340862i | \(0.889281\pi\) | |||||||
\(264\) | 25.0810 | − | 18.3273i | 0.0950037 | − | 0.0694217i | ||||
\(265\) | 122.178 | − | 122.178i | 0.461050 | − | 0.461050i | ||||
\(266\) | 153.734 | − | 237.202i | 0.577946 | − | 0.891737i | ||||
\(267\) | 86.7314 | + | 86.7314i | 0.324837 | + | 0.324837i | ||||
\(268\) | −277.549 | + | 124.180i | −1.03563 | + | 0.463356i | ||||
\(269\) | 116.803 | − | 116.803i | 0.434211 | − | 0.434211i | −0.455847 | − | 0.890058i | \(-0.650664\pi\) |
0.890058 | + | 0.455847i | \(0.150664\pi\) | |||||||
\(270\) | 38.1250 | + | 178.564i | 0.141204 | + | 0.661347i | ||||
\(271\) | − | 241.196i | − | 0.890021i | −0.895525 | − | 0.445011i | \(-0.853200\pi\) | ||
0.895525 | − | 0.445011i | \(-0.146800\pi\) | |||||||
\(272\) | 9.01693 | − | 271.851i | 0.0331505 | − | 0.999450i | ||||
\(273\) | −17.2538 | −0.0632007 | ||||||||
\(274\) | 382.345 | − | 81.6341i | 1.39542 | − | 0.297935i | ||||
\(275\) | 2.75167 | + | 2.75167i | 0.0100061 | + | 0.0100061i | ||||
\(276\) | 51.2736 | + | 114.600i | 0.185774 | + | 0.415217i | ||||
\(277\) | 340.749 | − | 340.749i | 1.23014 | − | 1.23014i | 0.266234 | − | 0.963908i | \(-0.414221\pi\) |
0.963908 | − | 0.266234i | \(-0.0857794\pi\) | |||||||
\(278\) | 11.7497 | + | 7.61514i | 0.0422651 | + | 0.0273926i | ||||
\(279\) | 144.636 | + | 144.636i | 0.518410 | + | 0.518410i | ||||
\(280\) | 179.958 | − | 131.500i | 0.642707 | − | 0.469643i | ||||
\(281\) | 428.504i | 1.52493i | 0.647032 | + | 0.762463i | \(0.276010\pi\) | ||||
−0.647032 | + | 0.762463i | \(0.723990\pi\) | |||||||
\(282\) | 97.2153 | − | 149.997i | 0.344735 | − | 0.531906i | ||||
\(283\) | 55.7718 | − | 55.7718i | 0.197073 | − | 0.197073i | −0.601671 | − | 0.798744i | \(-0.705498\pi\) |
0.798744 | + | 0.601671i | \(0.205498\pi\) | |||||||
\(284\) | 55.4136 | − | 145.148i | 0.195118 | − | 0.511083i | ||||
\(285\) | − | 140.086i | − | 0.491531i | ||||||
\(286\) | −18.3512 | − | 11.8936i | −0.0641649 | − | 0.0415861i | ||||
\(287\) | 202.848 | 0.706787 | ||||||||
\(288\) | 218.873 | + | 125.040i | 0.759976 | + | 0.434168i | ||||
\(289\) | 51.2623 | − | 284.417i | 0.177378 | − | 0.984143i | ||||
\(290\) | 68.5880 | + | 321.242i | 0.236510 | + | 1.10773i | ||||
\(291\) | 99.7252i | 0.342698i | ||||||||
\(292\) | 255.440 | + | 97.5204i | 0.874794 | + | 0.333974i | ||||
\(293\) | 343.598i | 1.17269i | 0.810062 | + | 0.586344i | \(0.199433\pi\) | ||||
−0.810062 | + | 0.586344i | \(0.800567\pi\) | |||||||
\(294\) | −22.1488 | + | 34.1742i | −0.0753359 | + | 0.116239i | ||||
\(295\) | 252.541 | + | 252.541i | 0.856072 | + | 0.856072i | ||||
\(296\) | −1.27635 | + | 8.20364i | −0.00431200 | + | 0.0277150i | ||||
\(297\) | 65.5336i | 0.220652i | ||||||||
\(298\) | −14.4341 | − | 67.6041i | −0.0484366 | − | 0.226860i | ||||
\(299\) | 62.4966 | − | 62.4966i | 0.209019 | − | 0.209019i | ||||
\(300\) | 1.60527 | − | 4.20475i | 0.00535089 | − | 0.0140158i | ||||
\(301\) | −41.3715 | + | 41.3715i | −0.137447 | + | 0.137447i | ||||
\(302\) | −297.976 | + | 63.6207i | −0.986677 | + | 0.210664i | ||||
\(303\) | 16.3866 | − | 16.3866i | 0.0540812 | − | 0.0540812i | ||||
\(304\) | −308.936 | − | 276.135i | −1.01624 | − | 0.908339i | ||||
\(305\) | −475.322 | −1.55843 | ||||||||
\(306\) | 210.888 | + | 165.098i | 0.689178 | + | 0.539537i | ||||
\(307\) | −100.962 | −0.328867 | −0.164433 | − | 0.986388i | \(-0.552580\pi\) | ||||
−0.164433 | + | 0.986388i | \(0.552580\pi\) | |||||||
\(308\) | 73.0207 | − | 32.6705i | 0.237080 | − | 0.106073i | ||||
\(309\) | 20.1939 | − | 20.1939i | 0.0653524 | − | 0.0653524i | ||||
\(310\) | −55.3587 | − | 259.280i | −0.178577 | − | 0.836389i | ||||
\(311\) | −36.0997 | + | 36.0997i | −0.116076 | + | 0.116076i | −0.762759 | − | 0.646683i | \(-0.776156\pi\) |
0.646683 | + | 0.762759i | \(0.276156\pi\) | |||||||
\(312\) | −3.88830 | + | 24.9917i | −0.0124625 | + | 0.0801016i | ||||
\(313\) | −207.384 | + | 207.384i | −0.662568 | + | 0.662568i | −0.955985 | − | 0.293417i | \(-0.905208\pi\) |
0.293417 | + | 0.955985i | \(0.405208\pi\) | |||||||
\(314\) | −120.211 | − | 563.026i | −0.382838 | − | 1.79308i | ||||
\(315\) | 219.464i | 0.696712i | ||||||||
\(316\) | 89.9419 | + | 34.3375i | 0.284626 | + | 0.108663i | ||||
\(317\) | 91.2105 | + | 91.2105i | 0.287730 | + | 0.287730i | 0.836182 | − | 0.548452i | \(-0.184783\pi\) |
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(318\) | −60.1896 | − | 39.0097i | −0.189276 | − | 0.122672i | ||||
\(319\) | 117.897i | 0.369583i | ||||||||
\(320\) | −149.920 | − | 290.299i | −0.468499 | − | 0.907185i | ||||
\(321\) | 104.867i | 0.326689i | ||||||||
\(322\) | 67.5089 | + | 316.188i | 0.209655 | + | 0.981949i | ||||
\(323\) | −282.351 | − | 337.790i | −0.874151 | − | 1.04579i | ||||
\(324\) | −189.669 | + | 84.8604i | −0.585397 | + | 0.261915i | ||||
\(325\) | −3.16847 | −0.00974913 | ||||||||
\(326\) | −307.374 | + | 474.259i | −0.942864 | + | 1.45478i | ||||
\(327\) | 40.0998i | 0.122630i | ||||||||
\(328\) | 45.7136 | − | 293.820i | 0.139371 | − | 0.895793i | ||||
\(329\) | 325.490 | − | 325.490i | 0.989332 | − | 0.989332i | ||||
\(330\) | 21.5622 | − | 33.2692i | 0.0653401 | − | 0.100816i | ||||
\(331\) | 265.861i | 0.803206i | 0.915814 | + | 0.401603i | \(0.131547\pi\) | ||||
−0.915814 | + | 0.401603i | \(0.868453\pi\) | |||||||
\(332\) | 34.1467 | + | 76.3201i | 0.102851 | + | 0.229880i | ||||
\(333\) | −5.78057 | − | 5.78057i | −0.0173591 | − | 0.0173591i | ||||
\(334\) | −121.688 | + | 187.757i | −0.364335 | + | 0.562147i | ||||
\(335\) | −274.405 | + | 274.405i | −0.819119 | + | 0.819119i | ||||
\(336\) | −68.9821 | − | 61.6580i | −0.205304 | − | 0.183506i | ||||
\(337\) | 373.456 | + | 373.456i | 1.10818 | + | 1.10818i | 0.993390 | + | 0.114787i | \(0.0366186\pi\) |
0.114787 | + | 0.993390i | \(0.463381\pi\) | |||||||
\(338\) | −313.137 | + | 66.8575i | −0.926440 | + | 0.197803i | ||||
\(339\) | −155.684 | −0.459243 | ||||||||
\(340\) | −112.996 | − | 328.241i | −0.332341 | − | 0.965415i | ||||
\(341\) | − | 95.1569i | − | 0.279052i | ||||||
\(342\) | 399.007 | − | 85.1917i | 1.16669 | − | 0.249099i | ||||
\(343\) | −263.246 | + | 263.246i | −0.767481 | + | 0.767481i | ||||
\(344\) | 50.6021 | + | 69.2490i | 0.147099 | + | 0.201305i | ||||
\(345\) | 113.301 | + | 113.301i | 0.328410 | + | 0.328410i | ||||
\(346\) | −357.687 | + | 551.890i | −1.03378 | + | 1.59506i | ||||
\(347\) | −455.522 | + | 455.522i | −1.31274 | + | 1.31274i | −0.393359 | + | 0.919385i | \(0.628687\pi\) |
−0.919385 | + | 0.393359i | \(0.871313\pi\) | |||||||
\(348\) | 124.467 | − | 55.6882i | 0.357663 | − | 0.160023i | ||||
\(349\) | −338.237 | −0.969159 | −0.484580 | − | 0.874747i | \(-0.661027\pi\) | ||||
−0.484580 | + | 0.874747i | \(0.661027\pi\) | |||||||
\(350\) | 6.30379 | − | 9.72637i | 0.0180108 | − | 0.0277896i | ||||
\(351\) | −37.7300 | − | 37.7300i | −0.107493 | − | 0.107493i | ||||
\(352\) | −30.8665 | − | 113.131i | −0.0876889 | − | 0.321396i | ||||
\(353\) | 26.2790 | 0.0744448 | 0.0372224 | − | 0.999307i | \(-0.488149\pi\) | ||||
0.0372224 | + | 0.999307i | \(0.488149\pi\) | |||||||
\(354\) | 80.6326 | − | 124.411i | 0.227776 | − | 0.351445i | ||||
\(355\) | − | 198.289i | − | 0.558560i | ||||||
\(356\) | 422.659 | − | 189.104i | 1.18724 | − | 0.531190i | ||||
\(357\) | −63.0459 | − | 75.4249i | −0.176599 | − | 0.211274i | ||||
\(358\) | 89.9264 | + | 421.183i | 0.251191 | + | 1.17649i | ||||
\(359\) | −562.774 | −1.56762 | −0.783808 | − | 0.621004i | \(-0.786725\pi\) | ||||
−0.783808 | + | 0.621004i | \(0.786725\pi\) | |||||||
\(360\) | 317.889 | + | 49.4583i | 0.883024 | + | 0.137384i | ||||
\(361\) | −309.672 | −0.857818 | ||||||||
\(362\) | −202.392 | − | 131.173i | −0.559093 | − | 0.362356i | ||||
\(363\) | −80.5968 | + | 80.5968i | −0.222030 | + | 0.222030i | ||||
\(364\) | −23.2310 | + | 60.8501i | −0.0638215 | + | 0.167171i | ||||
\(365\) | 348.961 | 0.956058 | ||||||||
\(366\) | 41.1992 | + | 192.962i | 0.112566 | + | 0.527219i | ||||
\(367\) | 294.820 | + | 294.820i | 0.803324 | + | 0.803324i | 0.983614 | − | 0.180290i | \(-0.0577035\pi\) |
−0.180290 | + | 0.983614i | \(0.557703\pi\) | |||||||
\(368\) | 473.204 | − | 26.5292i | 1.28588 | − | 0.0720903i | ||||
\(369\) | 207.036 | + | 207.036i | 0.561073 | + | 0.561073i | ||||
\(370\) | 2.21248 | + | 10.3625i | 0.00597968 | + | 0.0280067i | ||||
\(371\) | −130.610 | − | 130.610i | −0.352048 | − | 0.352048i | ||||
\(372\) | −100.460 | + | 44.9470i | −0.270053 | + | 0.120825i | ||||
\(373\) | − | 317.003i | − | 0.849875i | −0.905223 | − | 0.424937i | \(-0.860296\pi\) | ||
0.905223 | − | 0.424937i | \(-0.139704\pi\) | |||||||
\(374\) | −15.0628 | − | 123.682i | −0.0402748 | − | 0.330700i | ||||
\(375\) | 129.488i | 0.345302i | ||||||||
\(376\) | −398.113 | − | 544.817i | −1.05881 | − | 1.44898i | ||||
\(377\) | −67.8774 | − | 67.8774i | −0.180046 | − | 0.180046i | ||||
\(378\) | 190.887 | − | 40.7560i | 0.504991 | − | 0.107820i | ||||
\(379\) | 315.390 | + | 315.390i | 0.832164 | + | 0.832164i | 0.987812 | − | 0.155649i | \(-0.0497468\pi\) |
−0.155649 | + | 0.987812i | \(0.549747\pi\) | |||||||
\(380\) | −494.052 | − | 188.617i | −1.30014 | − | 0.496360i | ||||
\(381\) | −12.8939 | − | 12.8939i | −0.0338422 | − | 0.0338422i | ||||
\(382\) | 89.0505 | + | 417.081i | 0.233116 | + | 1.09183i | ||||
\(383\) | −522.656 | −1.36464 | −0.682319 | − | 0.731055i | \(-0.739028\pi\) | ||||
−0.682319 | + | 0.731055i | \(0.739028\pi\) | |||||||
\(384\) | −104.856 | + | 86.0237i | −0.273062 | + | 0.224020i | ||||
\(385\) | 72.1933 | − | 72.1933i | 0.187515 | − | 0.187515i | ||||
\(386\) | −147.440 | + | 227.492i | −0.381970 | + | 0.589357i | ||||
\(387\) | −84.4513 | −0.218220 | ||||||||
\(388\) | 351.707 | + | 134.273i | 0.906462 | + | 0.346064i | ||||
\(389\) | −256.711 | −0.659926 | −0.329963 | − | 0.943994i | \(-0.607036\pi\) | ||||
−0.329963 | + | 0.943994i | \(0.607036\pi\) | |||||||
\(390\) | 6.74014 | + | 31.5684i | 0.0172824 | + | 0.0809446i | ||||
\(391\) | 501.568 | + | 44.8392i | 1.28278 | + | 0.114678i | ||||
\(392\) | 90.7028 | + | 124.127i | 0.231385 | + | 0.316650i | ||||
\(393\) | − | 169.251i | − | 0.430665i | ||||||
\(394\) | −278.699 | − | 180.628i | −0.707358 | − | 0.458448i | ||||
\(395\) | 122.871 | 0.311066 | ||||||||
\(396\) | 107.873 | + | 41.1833i | 0.272407 | + | 0.103998i | ||||
\(397\) | −366.419 | − | 366.419i | −0.922969 | − | 0.922969i | 0.0742691 | − | 0.997238i | \(-0.476338\pi\) |
−0.997238 | + | 0.0742691i | \(0.976338\pi\) | |||||||
\(398\) | 186.482 | − | 287.731i | 0.468548 | − | 0.722942i | ||||
\(399\) | −149.754 | −0.375323 | ||||||||
\(400\) | −12.6678 | − | 11.3228i | −0.0316695 | − | 0.0283070i | ||||
\(401\) | 385.780 | − | 385.780i | 0.962044 | − | 0.962044i | −0.0372612 | − | 0.999306i | \(-0.511863\pi\) |
0.999306 | + | 0.0372612i | \(0.0118634\pi\) | |||||||
\(402\) | 135.182 | + | 87.6133i | 0.336274 | + | 0.217944i | ||||
\(403\) | 54.7852 | + | 54.7852i | 0.135943 | + | 0.135943i | ||||
\(404\) | −35.7283 | − | 79.8552i | −0.0884364 | − | 0.197661i | ||||
\(405\) | −187.520 | + | 187.520i | −0.463012 | + | 0.463012i | ||||
\(406\) | 343.411 | − | 73.3213i | 0.845839 | − | 0.180594i | ||||
\(407\) | 3.80307i | 0.00934414i | ||||||||
\(408\) | −123.459 | + | 74.3228i | −0.302596 | + | 0.182164i | ||||
\(409\) | −270.337 | −0.660970 | −0.330485 | − | 0.943811i | \(-0.607212\pi\) | ||||
−0.330485 | + | 0.943811i | \(0.607212\pi\) | |||||||
\(410\) | −79.2419 | − | 371.140i | −0.193273 | − | 0.905221i | ||||
\(411\) | −146.463 | − | 146.463i | −0.356358 | − | 0.356358i | ||||
\(412\) | −44.0295 | − | 98.4088i | −0.106868 | − | 0.238856i | ||||
\(413\) | 269.969 | − | 269.969i | 0.653678 | − | 0.653678i | ||||
\(414\) | −253.813 | + | 391.619i | −0.613075 | + | 0.945939i | ||||
\(415\) | 75.4553 | + | 75.4553i | 0.181820 | + | 0.181820i | ||||
\(416\) | 82.9046 | + | 47.3627i | 0.199290 | + | 0.113853i | ||||
\(417\) | − | 7.41800i | − | 0.0177890i | ||||||
\(418\) | −159.278 | − | 103.230i | −0.381049 | − | 0.246963i | ||||
\(419\) | 252.051 | − | 252.051i | 0.601553 | − | 0.601553i | −0.339172 | − | 0.940725i | \(-0.610147\pi\) |
0.940725 | + | 0.339172i | \(0.110147\pi\) | |||||||
\(420\) | −110.317 | − | 42.1161i | −0.262659 | − | 0.100276i | ||||
\(421\) | 179.427i | 0.426193i | 0.977031 | + | 0.213097i | \(0.0683549\pi\) | ||||
−0.977031 | + | 0.213097i | \(0.931645\pi\) | |||||||
\(422\) | 24.2866 | − | 37.4729i | 0.0575513 | − | 0.0887983i | ||||
\(423\) | 664.422 | 1.57074 | ||||||||
\(424\) | −218.619 | + | 159.751i | −0.515612 | + | 0.376771i | ||||
\(425\) | −11.5777 | − | 13.8509i | −0.0272416 | − | 0.0325905i | ||||
\(426\) | −80.4976 | + | 17.1870i | −0.188961 | + | 0.0403450i | ||||
\(427\) | 508.124i | 1.18999i | ||||||||
\(428\) | 369.842 | + | 141.196i | 0.864117 | + | 0.329898i | ||||
\(429\) | 11.5857i | 0.0270063i | ||||||||
\(430\) | 91.8569 | + | 59.5337i | 0.213621 | + | 0.138450i | ||||
\(431\) | 470.235 | + | 470.235i | 1.09103 | + | 1.09103i | 0.995418 | + | 0.0956143i | \(0.0304815\pi\) |
0.0956143 | + | 0.995418i | \(0.469518\pi\) | |||||||
\(432\) | −16.0160 | − | 285.679i | −0.0370742 | − | 0.661294i | ||||
\(433\) | 261.547i | 0.604034i | 0.953303 | + | 0.302017i | \(0.0976600\pi\) | ||||
−0.953303 | + | 0.302017i | \(0.902340\pi\) | |||||||
\(434\) | −277.174 | + | 59.1791i | −0.638649 | + | 0.136357i | ||||
\(435\) | 123.057 | − | 123.057i | 0.282889 | − | 0.282889i | ||||
\(436\) | 141.423 | + | 53.9917i | 0.324364 | + | 0.123834i | ||||
\(437\) | 542.438 | − | 542.438i | 1.24128 | − | 1.24128i | ||||
\(438\) | −30.2467 | − | 141.665i | −0.0690564 | − | 0.323435i | ||||
\(439\) | 126.052 | − | 126.052i | 0.287134 | − | 0.287134i | −0.548812 | − | 0.835946i | \(-0.684920\pi\) |
0.835946 | + | 0.548812i | \(0.184920\pi\) | |||||||
\(440\) | −88.3008 | − | 120.840i | −0.200684 | − | 0.274636i | ||||
\(441\) | −151.376 | −0.343257 | ||||||||
\(442\) | 79.8801 | + | 62.5358i | 0.180724 | + | 0.141484i | ||||
\(443\) | 69.9824 | 0.157974 | 0.0789869 | − | 0.996876i | \(-0.474831\pi\) | ||||
0.0789869 | + | 0.996876i | \(0.474831\pi\) | |||||||
\(444\) | 4.01500 | − | 1.79637i | 0.00904278 | − | 0.00404587i | ||||
\(445\) | 417.870 | − | 417.870i | 0.939034 | − | 0.939034i | ||||
\(446\) | −146.204 | + | 31.2159i | −0.327812 | + | 0.0699909i | ||||
\(447\) | −25.8968 | + | 25.8968i | −0.0579347 | + | 0.0579347i | ||||
\(448\) | −310.333 | + | 160.266i | −0.692708 | + | 0.357736i | ||||
\(449\) | 219.719 | − | 219.719i | 0.489352 | − | 0.489352i | −0.418749 | − | 0.908102i | \(-0.637531\pi\) |
0.908102 | + | 0.418749i | \(0.137531\pi\) | |||||||
\(450\) | 16.3611 | − | 3.49325i | 0.0363581 | − | 0.00776278i | ||||
\(451\) | − | 136.210i | − | 0.302018i | ||||||
\(452\) | −209.617 | + | 549.060i | −0.463755 | + | 1.21473i | ||||
\(453\) | 114.144 | + | 114.144i | 0.251974 | + | 0.251974i | ||||
\(454\) | −219.425 | + | 338.559i | −0.483314 | + | 0.745725i | ||||
\(455\) | 83.1285i | 0.182700i | ||||||||
\(456\) | −33.7484 | + | 216.915i | −0.0740097 | + | 0.475691i | ||||
\(457\) | − | 485.155i | − | 1.06161i | −0.847495 | − | 0.530804i | \(-0.821890\pi\) | ||
0.847495 | − | 0.530804i | \(-0.178110\pi\) | |||||||
\(458\) | 512.858 | − | 109.500i | 1.11978 | − | 0.239082i | ||||
\(459\) | 27.0700 | − | 302.803i | 0.0589760 | − | 0.659702i | ||||
\(460\) | 552.140 | − | 247.035i | 1.20031 | − | 0.537033i | ||||
\(461\) | −803.704 | −1.74339 | −0.871697 | − | 0.490046i | \(-0.836980\pi\) | ||||
−0.871697 | + | 0.490046i | \(0.836980\pi\) | |||||||
\(462\) | −35.5652 | − | 23.0502i | −0.0769809 | − | 0.0498923i | ||||
\(463\) | − | 673.039i | − | 1.45365i | −0.686824 | − | 0.726824i | \(-0.740996\pi\) | ||
0.686824 | − | 0.726824i | \(-0.259004\pi\) | |||||||
\(464\) | −28.8134 | − | 513.946i | −0.0620977 | − | 1.10764i | ||||
\(465\) | −99.3213 | + | 99.3213i | −0.213594 | + | 0.213594i | ||||
\(466\) | 144.455 | + | 93.6229i | 0.309988 | + | 0.200908i | ||||
\(467\) | − | 769.187i | − | 1.64708i | −0.567258 | − | 0.823540i | \(-0.691996\pi\) | ||
0.567258 | − | 0.823540i | \(-0.308004\pi\) | |||||||
\(468\) | −85.8172 | + | 38.3958i | −0.183370 | + | 0.0820423i | ||||
\(469\) | 293.342 | + | 293.342i | 0.625462 | + | 0.625462i | ||||
\(470\) | −722.685 | − | 468.382i | −1.53763 | − | 0.996557i | ||||
\(471\) | −215.676 | + | 215.676i | −0.457910 | + | 0.457910i | ||||
\(472\) | −330.204 | − | 451.884i | −0.699584 | − | 0.957381i | ||||
\(473\) | 27.7805 | + | 27.7805i | 0.0587325 | + | 0.0587325i | ||||
\(474\) | −10.6500 | − | 49.8810i | −0.0224684 | − | 0.105234i | ||||
\(475\) | −27.5006 | −0.0578961 | ||||||||
\(476\) | −350.893 | + | 120.794i | −0.737171 | + | 0.253769i | ||||
\(477\) | − | 266.613i | − | 0.558937i | ||||||
\(478\) | −39.7501 | − | 186.175i | −0.0831592 | − | 0.389488i | ||||
\(479\) | −129.681 | + | 129.681i | −0.270733 | + | 0.270733i | −0.829395 | − | 0.558662i | \(-0.811315\pi\) |
0.558662 | + | 0.829395i | \(0.311315\pi\) | |||||||
\(480\) | −85.8650 | + | 150.300i | −0.178885 | + | 0.313124i | ||||
\(481\) | −2.18956 | − | 2.18956i | −0.00455210 | − | 0.00455210i | ||||
\(482\) | 280.036 | + | 181.495i | 0.580987 | + | 0.376545i | ||||
\(483\) | 121.120 | − | 121.120i | 0.250767 | − | 0.250767i | ||||
\(484\) | 175.728 | + | 392.764i | 0.363075 | + | 0.811496i | ||||
\(485\) | 480.474 | 0.990668 | ||||||||
\(486\) | 362.502 | + | 234.942i | 0.745888 | + | 0.483420i | ||||
\(487\) | −67.2949 | − | 67.2949i | −0.138182 | − | 0.138182i | 0.634632 | − | 0.772814i | \(-0.281152\pi\) |
−0.772814 | + | 0.634632i | \(0.781152\pi\) | |||||||
\(488\) | 736.005 | + | 114.510i | 1.50821 | + | 0.234652i | ||||
\(489\) | 299.416 | 0.612304 | ||||||||
\(490\) | 164.651 | + | 106.712i | 0.336022 | + | 0.217780i | ||||
\(491\) | 95.5137i | 0.194529i | 0.995259 | + | 0.0972644i | \(0.0310093\pi\) | ||||
−0.995259 | + | 0.0972644i | \(0.968991\pi\) | |||||||
\(492\) | −143.800 | + | 64.3383i | −0.292277 | + | 0.130769i | ||||
\(493\) | 48.6997 | − | 544.752i | 0.0987825 | − | 1.10497i | ||||
\(494\) | 151.136 | − | 32.2688i | 0.305943 | − | 0.0653215i | ||||
\(495\) | 147.368 | 0.297713 | ||||||||
\(496\) | 23.2558 | + | 414.816i | 0.0468867 | + | 0.836322i | ||||
\(497\) | −211.973 | −0.426505 | ||||||||
\(498\) | 24.0918 | − | 37.1722i | 0.0483770 | − | 0.0746429i | ||||
\(499\) | 575.936 | − | 575.936i | 1.15418 | − | 1.15418i | 0.168475 | − | 0.985706i | \(-0.446116\pi\) |
0.985706 | − | 0.168475i | \(-0.0538843\pi\) | |||||||
\(500\) | 456.675 | + | 174.347i | 0.913350 | + | 0.348694i | ||||
\(501\) | 118.538 | 0.236602 | ||||||||
\(502\) | −257.833 | + | 55.0497i | −0.513612 | + | 0.109661i | ||||
\(503\) | −401.223 | − | 401.223i | −0.797661 | − | 0.797661i | 0.185065 | − | 0.982726i | \(-0.440750\pi\) |
−0.982726 | + | 0.185065i | \(0.940750\pi\) | |||||||
\(504\) | 52.8714 | − | 339.826i | 0.104904 | − | 0.674259i | ||||
\(505\) | −78.9504 | − | 78.9504i | −0.156337 | − | 0.156337i | ||||
\(506\) | 212.316 | − | 45.3314i | 0.419597 | − | 0.0895878i | ||||
\(507\) | 119.952 | + | 119.952i | 0.236591 | + | 0.236591i | ||||
\(508\) | −62.8344 | + | 28.1130i | −0.123690 | + | 0.0553405i | ||||
\(509\) | 534.020i | 1.04915i | 0.851363 | + | 0.524577i | \(0.175777\pi\) | ||||
−0.851363 | + | 0.524577i | \(0.824223\pi\) | |||||||
\(510\) | −113.373 | + | 144.816i | −0.222299 | + | 0.283954i | ||||
\(511\) | − | 373.043i | − | 0.730026i | ||||||
\(512\) | 162.204 | + | 485.627i | 0.316805 | + | 0.948491i | ||||
\(513\) | −327.477 | − | 327.477i | −0.638356 | − | 0.638356i | ||||
\(514\) | −143.117 | − | 670.308i | −0.278437 | − | 1.30410i | ||||
\(515\) | −97.2938 | − | 97.2938i | −0.188920 | − | 0.188920i | ||||
\(516\) | 16.2065 | − | 42.4505i | 0.0314080 | − | 0.0822685i | ||||
\(517\) | −218.563 | − | 218.563i | −0.422753 | − | 0.422753i | ||||
\(518\) | 11.0776 | − | 2.36517i | 0.0213853 | − | 0.00456596i | ||||
\(519\) | 348.427 | 0.671344 | ||||||||
\(520\) | 120.410 | + | 18.7338i | 0.231557 | + | 0.0360265i | ||||
\(521\) | 182.296 | − | 182.296i | 0.349897 | − | 0.349897i | −0.510174 | − | 0.860071i | \(-0.670419\pi\) |
0.860071 | + | 0.510174i | \(0.170419\pi\) | |||||||
\(522\) | 425.336 | + | 275.666i | 0.814820 | + | 0.528096i | ||||
\(523\) | −864.350 | −1.65268 | −0.826338 | − | 0.563174i | \(-0.809580\pi\) | ||||
−0.826338 | + | 0.563174i | \(0.809580\pi\) | |||||||
\(524\) | −596.910 | − | 227.885i | −1.13914 | − | 0.434895i | ||||
\(525\) | −6.14060 | −0.0116964 | ||||||||
\(526\) | 967.200 | − | 206.506i | 1.83878 | − | 0.392597i | ||||
\(527\) | −39.3065 | + | 439.680i | −0.0745854 | + | 0.834308i | ||||
\(528\) | −41.4026 | + | 46.3207i | −0.0784141 | + | 0.0877286i | ||||
\(529\) | 348.443i | 0.658683i | ||||||||
\(530\) | −187.948 | + | 289.993i | −0.354619 | + | 0.547156i | ||||
\(531\) | 551.086 | 1.03783 | ||||||||
\(532\) | −201.633 | + | 528.147i | −0.379010 | + | 0.992758i | ||||
\(533\) | 78.4209 | + | 78.4209i | 0.147131 | + | 0.147131i | ||||
\(534\) | −205.859 | − | 133.420i | −0.385503 | − | 0.249850i | ||||
\(535\) | 505.248 | 0.944390 | ||||||||
\(536\) | 491.005 | − | 358.791i | 0.916055 | − | 0.669386i | ||||
\(537\) | 161.341 | − | 161.341i | 0.300448 | − | 0.300448i | ||||
\(538\) | −179.679 | + | 277.234i | −0.333975 | + | 0.515304i | ||||
\(539\) | 49.7957 | + | 49.7957i | 0.0923853 | + | 0.0923853i | ||||
\(540\) | −149.138 | − | 333.334i | −0.276182 | − | 0.617286i | ||||
\(541\) | −671.567 | + | 671.567i | −1.24134 | + | 1.24134i | −0.281899 | + | 0.959444i | \(0.590964\pi\) |
−0.959444 | + | 0.281899i | \(0.909036\pi\) | |||||||
\(542\) | 100.725 | + | 471.758i | 0.185839 | + | 0.870403i | ||||
\(543\) | 127.777i | 0.235317i | ||||||||
\(544\) | 95.8900 | + | 535.482i | 0.176268 | + | 0.984342i | ||||
\(545\) | 193.200 | 0.354496 | ||||||||
\(546\) | 33.7470 | − | 7.20528i | 0.0618076 | − | 0.0131965i | ||||
\(547\) | −700.646 | − | 700.646i | −1.28089 | − | 1.28089i | −0.940163 | − | 0.340725i | \(-0.889327\pi\) |
−0.340725 | − | 0.940163i | \(-0.610673\pi\) | |||||||
\(548\) | −713.744 | + | 319.339i | −1.30245 | + | 0.582735i | ||||
\(549\) | −518.615 | + | 518.615i | −0.944654 | + | 0.944654i | ||||
\(550\) | −6.53115 | − | 4.23292i | −0.0118748 | − | 0.00769622i | ||||
\(551\) | −589.140 | − | 589.140i | −1.06922 | − | 1.06922i | ||||
\(552\) | −148.144 | − | 202.736i | −0.268378 | − | 0.367275i | ||||
\(553\) | − | 131.351i | − | 0.237524i | ||||||
\(554\) | −524.178 | + | 808.776i | −0.946170 | + | 1.45988i | ||||
\(555\) | 3.96950 | − | 3.96950i | 0.00715226 | − | 0.00715226i | ||||
\(556\) | −26.1616 | − | 9.98782i | −0.0470532 | − | 0.0179637i | ||||
\(557\) | 94.2272i | 0.169169i | 0.996416 | + | 0.0845845i | \(0.0269563\pi\) | ||||
−0.996416 | + | 0.0845845i | \(0.973044\pi\) | |||||||
\(558\) | −343.297 | − | 222.495i | −0.615228 | − | 0.398737i | ||||
\(559\) | −31.9884 | −0.0572243 | ||||||||
\(560\) | −297.067 | + | 332.355i | −0.530477 | + | 0.593490i | ||||
\(561\) | −50.6470 | + | 42.3346i | −0.0902798 | + | 0.0754628i | ||||
\(562\) | −178.946 | − | 838.118i | −0.318409 | − | 1.49131i | ||||
\(563\) | 930.351i | 1.65249i | 0.563312 | + | 0.826244i | \(0.309527\pi\) | ||||
−0.563312 | + | 0.826244i | \(0.690473\pi\) | |||||||
\(564\) | −127.505 | + | 333.980i | −0.226073 | + | 0.592163i | ||||
\(565\) | 750.081i | 1.32758i | ||||||||
\(566\) | −85.7942 | + | 132.375i | −0.151580 | + | 0.233879i | ||||
\(567\) | 200.461 | + | 200.461i | 0.353546 | + | 0.353546i | ||||
\(568\) | −47.7700 | + | 307.037i | −0.0841021 | + | 0.540559i | ||||
\(569\) | 701.405i | 1.23270i | 0.787473 | + | 0.616349i | \(0.211389\pi\) | ||||
−0.787473 | + | 0.616349i | \(0.788611\pi\) | |||||||
\(570\) | 58.5009 | + | 273.997i | 0.102633 | + | 0.480697i | ||||
\(571\) | −49.4687 | + | 49.4687i | −0.0866352 | + | 0.0866352i | −0.749096 | − | 0.662461i | \(-0.769512\pi\) |
0.662461 | + | 0.749096i | \(0.269512\pi\) | |||||||
\(572\) | 40.8601 | + | 15.5994i | 0.0714338 | + | 0.0272716i | ||||
\(573\) | 159.769 | − | 159.769i | 0.278829 | − | 0.278829i | ||||
\(574\) | −396.753 | + | 84.7104i | −0.691208 | + | 0.147579i | ||||
\(575\) | 22.2424 | − | 22.2424i | 0.0386825 | − | 0.0386825i | ||||
\(576\) | −480.315 | − | 153.166i | −0.833880 | − | 0.265913i | ||||
\(577\) | −719.179 | −1.24641 | −0.623205 | − | 0.782059i | \(-0.714170\pi\) | ||||
−0.623205 | + | 0.782059i | \(0.714170\pi\) | |||||||
\(578\) | 18.5094 | + | 577.704i | 0.0320232 | + | 0.999487i | ||||
\(579\) | 143.623 | 0.248054 | ||||||||
\(580\) | −268.305 | − | 599.679i | −0.462594 | − | 1.03393i | ||||
\(581\) | 80.6626 | − | 80.6626i | 0.138834 | − | 0.138834i | ||||
\(582\) | −41.6458 | − | 195.054i | −0.0715563 | − | 0.335144i | ||||
\(583\) | −87.7030 | + | 87.7030i | −0.150434 | + | 0.150434i | ||||
\(584\) | −540.344 | − | 84.0687i | −0.925246 | − | 0.143953i | ||||
\(585\) | −84.8448 | + | 84.8448i | −0.145034 | + | 0.145034i | ||||
\(586\) | −143.488 | − | 672.048i | −0.244861 | − | 1.14684i | ||||
\(587\) | 404.505i | 0.689105i | 0.938767 | + | 0.344553i | \(0.111969\pi\) | ||||
−0.938767 | + | 0.344553i | \(0.888031\pi\) | |||||||
\(588\) | 29.0498 | − | 76.0913i | 0.0494043 | − | 0.129407i | ||||
\(589\) | 475.507 | + | 475.507i | 0.807312 | + | 0.807312i | ||||
\(590\) | −599.412 | − | 388.487i | −1.01595 | − | 0.658452i | ||||
\(591\) | 175.952i | 0.297720i | ||||||||
\(592\) | −0.929449 | − | 16.5786i | −0.00157001 | − | 0.0280045i | ||||
\(593\) | 70.0150i | 0.118069i | 0.998256 | + | 0.0590345i | \(0.0188022\pi\) | ||||
−0.998256 | + | 0.0590345i | \(0.981198\pi\) | |||||||
\(594\) | −27.3672 | − | 128.178i | −0.0460727 | − | 0.215788i | ||||
\(595\) | −363.396 | + | 303.754i | −0.610750 | + | 0.510511i | ||||
\(596\) | 56.4637 | + | 126.200i | 0.0947378 | + | 0.211745i | ||||
\(597\) | −181.655 | −0.304279 | ||||||||
\(598\) | −96.1391 | + | 148.337i | −0.160768 | + | 0.248055i | ||||
\(599\) | − | 935.940i | − | 1.56250i | −0.624216 | − | 0.781252i | \(-0.714581\pi\) | ||
0.624216 | − | 0.781252i | \(-0.285419\pi\) | |||||||
\(600\) | −1.38384 | + | 8.89450i | −0.00230640 | + | 0.0148242i | ||||
\(601\) | 264.545 | − | 264.545i | 0.440174 | − | 0.440174i | −0.451896 | − | 0.892071i | \(-0.649252\pi\) |
0.892071 | + | 0.451896i | \(0.149252\pi\) | |||||||
\(602\) | 63.6421 | − | 98.1960i | 0.105718 | − | 0.163116i | ||||
\(603\) | 598.796i | 0.993029i | ||||||||
\(604\) | 556.248 | − | 248.873i | 0.920941 | − | 0.412042i | ||||
\(605\) | 388.314 | + | 388.314i | 0.641841 | + | 0.641841i | ||||
\(606\) | −25.2077 | + | 38.8940i | −0.0415968 | + | 0.0641815i | ||||
\(607\) | −66.1875 | + | 66.1875i | −0.109040 | + | 0.109040i | −0.759522 | − | 0.650482i | \(-0.774567\pi\) |
0.650482 | + | 0.759522i | \(0.274567\pi\) | |||||||
\(608\) | 719.568 | + | 411.084i | 1.18350 | + | 0.676124i | ||||
\(609\) | −131.549 | − | 131.549i | −0.216008 | − | 0.216008i | ||||
\(610\) | 929.689 | − | 198.497i | 1.52408 | − | 0.325405i | ||||
\(611\) | 251.669 | 0.411897 | ||||||||
\(612\) | −481.426 | − | 234.850i | −0.786644 | − | 0.383742i | ||||
\(613\) | 125.163i | 0.204181i | 0.994775 | + | 0.102091i | \(0.0325532\pi\) | ||||
−0.994775 | + | 0.102091i | \(0.967447\pi\) | |||||||
\(614\) | 197.473 | − | 42.1623i | 0.321618 | − | 0.0686683i | ||||
\(615\) | −142.171 | + | 142.171i | −0.231172 | + | 0.231172i | ||||
\(616\) | −129.179 | + | 94.3945i | −0.209706 | + | 0.153238i | ||||
\(617\) | −387.365 | − | 387.365i | −0.627819 | − | 0.627819i | 0.319700 | − | 0.947519i | \(-0.396418\pi\) |
−0.947519 | + | 0.319700i | \(0.896418\pi\) | |||||||
\(618\) | −31.0644 | + | 47.9306i | −0.0502661 | + | 0.0775576i | ||||
\(619\) | −83.9355 | + | 83.9355i | −0.135599 | + | 0.135599i | −0.771648 | − | 0.636050i | \(-0.780567\pi\) |
0.636050 | + | 0.771648i | \(0.280567\pi\) | |||||||
\(620\) | 216.554 | + | 484.013i | 0.349281 | + | 0.780665i | ||||
\(621\) | 529.724 | 0.853018 | ||||||||
\(622\) | 55.5325 | − | 85.6834i | 0.0892806 | − | 0.137755i | ||||
\(623\) | −446.708 | − | 446.708i | −0.717027 | − | 0.717027i | ||||
\(624\) | −2.83149 | − | 50.5054i | −0.00453764 | − | 0.0809382i | ||||
\(625\) | 650.420 | 1.04067 | ||||||||
\(626\) | 319.021 | − | 492.230i | 0.509618 | − | 0.786310i | ||||
\(627\) | 100.558i | 0.160380i | ||||||||
\(628\) | 470.245 | + | 1051.03i | 0.748799 | + | 1.67361i | ||||
\(629\) | 1.57094 | − | 17.5724i | 0.00249751 | − | 0.0279370i | ||||
\(630\) | −91.6495 | − | 429.254i | −0.145475 | − | 0.681355i | ||||
\(631\) | 922.673 | 1.46224 | 0.731120 | − | 0.682249i | \(-0.238998\pi\) | ||||
0.731120 | + | 0.682249i | \(0.238998\pi\) | |||||||
\(632\) | −190.258 | − | 29.6011i | −0.301041 | − | 0.0468371i | ||||
\(633\) | −23.6579 | −0.0373743 | ||||||||
\(634\) | −216.490 | − | 140.310i | −0.341467 | − | 0.221309i | ||||
\(635\) | −62.1224 | + | 62.1224i | −0.0978306 | + | 0.0978306i | ||||
\(636\) | 134.017 | + | 51.1641i | 0.210718 | + | 0.0804467i | ||||
\(637\) | −57.3382 | −0.0900129 | ||||||||
\(638\) | −49.2344 | − | 230.596i | −0.0771699 | − | 0.361436i | ||||
\(639\) | −216.349 | − | 216.349i | −0.338575 | − | 0.338575i | ||||
\(640\) | 414.461 | + | 505.194i | 0.647595 | + | 0.789365i | ||||
\(641\) | −15.7419 | − | 15.7419i | −0.0245583 | − | 0.0245583i | 0.694721 | − | 0.719279i | \(-0.255528\pi\) |
−0.719279 | + | 0.694721i | \(0.755528\pi\) | |||||||
\(642\) | −43.7931 | − | 205.111i | −0.0682136 | − | 0.319488i | ||||
\(643\) | −389.434 | − | 389.434i | −0.605651 | − | 0.605651i | 0.336155 | − | 0.941807i | \(-0.390873\pi\) |
−0.941807 | + | 0.336155i | \(0.890873\pi\) | |||||||
\(644\) | −264.083 | − | 590.244i | −0.410067 | − | 0.916528i | ||||
\(645\) | − | 57.9925i | − | 0.0899108i | ||||||
\(646\) | 693.318 | + | 542.778i | 1.07325 | + | 0.840214i | ||||
\(647\) | − | 550.318i | − | 0.850568i | −0.905060 | − | 0.425284i | \(-0.860174\pi\) | ||
0.905060 | − | 0.425284i | \(-0.139826\pi\) | |||||||
\(648\) | 335.538 | − | 245.187i | 0.517805 | − | 0.378374i | ||||
\(649\) | −181.281 | − | 181.281i | −0.279324 | − | 0.279324i | ||||
\(650\) | 6.19725 | − | 1.32317i | 0.00953424 | − | 0.00203565i | ||||
\(651\) | 106.176 | + | 106.176i | 0.163096 | + | 0.163096i | ||||
\(652\) | 403.144 | − | 1055.97i | 0.618318 | − | 1.61959i | ||||
\(653\) | 626.017 | + | 626.017i | 0.958678 | + | 0.958678i | 0.999179 | − | 0.0405016i | \(-0.0128956\pi\) |
−0.0405016 | + | 0.999179i | \(0.512896\pi\) | |||||||
\(654\) | −16.7459 | − | 78.4319i | −0.0256054 | − | 0.119926i | ||||
\(655\) | −815.450 | −1.24496 | ||||||||
\(656\) | 33.2890 | + | 593.777i | 0.0507454 | + | 0.905148i | ||||
\(657\) | 380.745 | − | 380.745i | 0.579521 | − | 0.579521i | ||||
\(658\) | −500.705 | + | 772.558i | −0.760950 | + | 1.17410i | ||||
\(659\) | 1139.03 | 1.72841 | 0.864207 | − | 0.503136i | \(-0.167820\pi\) | ||||
0.864207 | + | 0.503136i | \(0.167820\pi\) | |||||||
\(660\) | −28.2805 | + | 74.0763i | −0.0428492 | + | 0.112237i | ||||
\(661\) | −1263.02 | −1.91077 | −0.955386 | − | 0.295359i | \(-0.904561\pi\) | ||||
−0.955386 | + | 0.295359i | \(0.904561\pi\) | |||||||
\(662\) | −111.025 | − | 520.002i | −0.167712 | − | 0.785502i | ||||
\(663\) | 4.78572 | − | 53.5328i | 0.00721828 | − | 0.0807433i | ||||
\(664\) | −98.6597 | − | 135.016i | −0.148584 | − | 0.203337i | ||||
\(665\) | 721.512i | 1.08498i | ||||||||
\(666\) | 13.7203 | + | 8.89231i | 0.0206011 | + | 0.0133518i | ||||
\(667\) | 952.989 | 1.42877 | ||||||||
\(668\) | 159.603 | − | 418.055i | 0.238926 | − | 0.625830i | ||||
\(669\) | 56.0058 | + | 56.0058i | 0.0837157 | + | 0.0837157i | ||||
\(670\) | 422.120 | − | 651.305i | 0.630029 | − | 0.972098i | ||||
\(671\) | 341.199 | 0.508494 | ||||||||
\(672\) | 160.672 | + | 91.7906i | 0.239095 | + | 0.136593i | ||||
\(673\) | −700.225 | + | 700.225i | −1.04045 | + | 1.04045i | −0.0413059 | + | 0.999147i | \(0.513152\pi\) |
−0.999147 | + | 0.0413059i | \(0.986848\pi\) | |||||||
\(674\) | −886.405 | − | 574.491i | −1.31514 | − | 0.852360i | ||||
\(675\) | −13.4280 | − | 13.4280i | −0.0198934 | − | 0.0198934i | ||||
\(676\) | 584.549 | − | 261.535i | 0.864717 | − | 0.386887i | ||||
\(677\) | −378.421 | + | 378.421i | −0.558967 | + | 0.558967i | −0.929013 | − | 0.370046i | \(-0.879342\pi\) |
0.370046 | + | 0.929013i | \(0.379342\pi\) | |||||||
\(678\) | 304.504 | − | 65.0143i | 0.449121 | − | 0.0958913i | ||||
\(679\) | − | 513.632i | − | 0.756453i | ||||||
\(680\) | 358.086 | + | 594.824i | 0.526597 | + | 0.874741i | ||||
\(681\) | 213.744 | 0.313868 | ||||||||
\(682\) | 39.7381 | + | 186.119i | 0.0582669 | + | 0.272902i | ||||
\(683\) | −400.345 | − | 400.345i | −0.586156 | − | 0.586156i | 0.350432 | − | 0.936588i | \(-0.386035\pi\) |
−0.936588 | + | 0.350432i | \(0.886035\pi\) | |||||||
\(684\) | −744.848 | + | 333.256i | −1.08896 | + | 0.487216i | ||||
\(685\) | −705.657 | + | 705.657i | −1.03016 | + | 1.03016i | ||||
\(686\) | 404.954 | − | 624.820i | 0.590312 | − | 0.910817i | ||||
\(687\) | −196.458 | − | 196.458i | −0.285965 | − | 0.285965i | ||||
\(688\) | −127.892 | − | 114.313i | −0.185890 | − | 0.166153i | ||||
\(689\) | − | 100.987i | − | 0.146571i | ||||||
\(690\) | −268.923 | − | 174.293i | −0.389744 | − | 0.252598i | ||||
\(691\) | −665.780 | + | 665.780i | −0.963502 | + | 0.963502i | −0.999357 | − | 0.0358553i | \(-0.988584\pi\) |
0.0358553 | + | 0.999357i | \(0.488584\pi\) | |||||||
\(692\) | 469.133 | − | 1228.82i | 0.677938 | − | 1.77576i | ||||
\(693\) | − | 157.538i | − | 0.227327i | ||||||
\(694\) | 700.734 | − | 1081.19i | 1.00970 | − | 1.55791i | ||||
\(695\) | −35.7398 | −0.0514242 | ||||||||
\(696\) | −220.191 | + | 160.899i | −0.316366 | + | 0.231177i | ||||
\(697\) | −56.2643 | + | 629.369i | −0.0807236 | + | 0.902969i | ||||
\(698\) | 661.562 | − | 141.250i | 0.947797 | − | 0.202363i | ||||
\(699\) | − | 91.1992i | − | 0.130471i | ||||||
\(700\) | −8.26789 | + | 21.6565i | −0.0118113 | + | 0.0309378i | ||||
\(701\) | 92.7896i | 0.132368i | 0.997807 | + | 0.0661838i | \(0.0210824\pi\) | ||||
−0.997807 | + | 0.0661838i | \(0.978918\pi\) | |||||||
\(702\) | 89.5529 | + | 58.0404i | 0.127568 | + | 0.0826786i | ||||
\(703\) | −19.0042 | − | 19.0042i | −0.0270331 | − | 0.0270331i | ||||
\(704\) | 107.616 | + | 208.385i | 0.152864 | + | 0.296002i | ||||
\(705\) | 456.256i | 0.647172i | ||||||||
\(706\) | −51.3995 | + | 10.9743i | −0.0728038 | + | 0.0155443i | ||||
\(707\) | −84.3988 | + | 84.3988i | −0.119376 | + | 0.119376i | ||||
\(708\) | −105.756 | + | 277.011i | −0.149372 | + | 0.391258i | ||||
\(709\) | 796.746 | − | 796.746i | 1.12376 | − | 1.12376i | 0.132590 | − | 0.991171i | \(-0.457671\pi\) |
0.991171 | − | 0.132590i | \(-0.0423293\pi\) | |||||||
\(710\) | 82.8065 | + | 387.836i | 0.116629 | + | 0.546248i | ||||
\(711\) | 134.063 | − | 134.063i | 0.188555 | − | 0.188555i | ||||
\(712\) | −747.715 | + | 546.375i | −1.05016 | + | 0.767381i | ||||
\(713\) | −769.177 | −1.07879 | ||||||||
\(714\) | 154.810 | + | 121.196i | 0.216821 | + | 0.169743i | ||||
\(715\) | 55.8198 | 0.0780697 | ||||||||
\(716\) | −351.777 | − | 786.245i | −0.491308 | − | 1.09811i | ||||
\(717\) | −71.3173 | + | 71.3173i | −0.0994662 | + | 0.0994662i | ||||
\(718\) | 1100.74 | − | 235.018i | 1.53306 | − | 0.327323i | ||||
\(719\) | −171.227 | + | 171.227i | −0.238146 | + | 0.238146i | −0.816082 | − | 0.577936i | \(-0.803858\pi\) |
0.577936 | + | 0.816082i | \(0.303858\pi\) | |||||||
\(720\) | −642.417 | + | 36.0159i | −0.892246 | + | 0.0500221i | ||||
\(721\) | −104.008 | + | 104.008i | −0.144255 | + | 0.144255i | ||||
\(722\) | 605.693 | − | 129.321i | 0.838910 | − | 0.179115i | ||||
\(723\) | − | 176.796i | − | 0.244532i | ||||||
\(724\) | 450.640 | + | 172.043i | 0.622431 | + | 0.237628i | ||||
\(725\) | −24.1575 | − | 24.1575i | −0.0333206 | − | 0.0333206i | ||||
\(726\) | 123.983 | − | 191.298i | 0.170775 | − | 0.263496i | ||||
\(727\) | − | 263.954i | − | 0.363073i | −0.983384 | − | 0.181536i | \(-0.941893\pi\) | ||
0.983384 | − | 0.181536i | \(-0.0581070\pi\) | |||||||
\(728\) | 20.0266 | − | 128.719i | 0.0275091 | − | 0.176812i | ||||
\(729\) | 238.661i | 0.327382i | ||||||||
\(730\) | −682.538 | + | 145.728i | −0.934984 | + | 0.199628i | ||||
\(731\) | −116.887 | − | 139.837i | −0.159900 | − | 0.191296i | ||||
\(732\) | −161.164 | − | 360.213i | −0.220170 | − | 0.492094i | ||||
\(733\) | −61.0527 | −0.0832915 | −0.0416457 | − | 0.999132i | \(-0.513260\pi\) | ||||
−0.0416457 | + | 0.999132i | \(0.513260\pi\) | |||||||
\(734\) | −699.761 | − | 453.524i | −0.953353 | − | 0.617881i | ||||
\(735\) | − | 103.950i | − | 0.141428i | ||||||
\(736\) | −914.468 | + | 249.501i | −1.24248 | + | 0.338997i | ||||
\(737\) | 196.975 | − | 196.975i | 0.267267 | − | 0.267267i | ||||
\(738\) | −491.404 | − | 318.485i | −0.665859 | − | 0.431552i | ||||
\(739\) | 437.344i | 0.591805i | 0.955218 | + | 0.295903i | \(0.0956204\pi\) | ||||
−0.955218 | + | 0.295903i | \(0.904380\pi\) | |||||||
\(740\) | −8.65486 | − | 19.3442i | −0.0116958 | − | 0.0261408i | ||||
\(741\) | −57.8948 | − | 57.8948i | −0.0781306 | − | 0.0781306i | ||||
\(742\) | 310.005 | + | 200.918i | 0.417797 | + | 0.270780i | ||||
\(743\) | −598.705 | + | 598.705i | −0.805794 | + | 0.805794i | −0.983994 | − | 0.178200i | \(-0.942972\pi\) |
0.178200 | + | 0.983994i | \(0.442972\pi\) | |||||||
\(744\) | 177.720 | − | 129.865i | 0.238871 | − | 0.174550i | ||||
\(745\) | 124.770 | + | 124.770i | 0.167477 | + | 0.167477i | ||||
\(746\) | 132.382 | + | 620.032i | 0.177456 | + | 0.831142i | ||||
\(747\) | 164.656 | 0.220423 | ||||||||
\(748\) | 81.1117 | + | 235.621i | 0.108438 | + | 0.315001i | ||||
\(749\) | − | 540.116i | − | 0.721116i | ||||||
\(750\) | −54.0750 | − | 253.268i | −0.0721001 | − | 0.337691i | ||||
\(751\) | −146.723 | + | 146.723i | −0.195370 | + | 0.195370i | −0.798012 | − | 0.602642i | \(-0.794115\pi\) |
0.602642 | + | 0.798012i | \(0.294115\pi\) | |||||||
\(752\) | 1006.19 | + | 899.362i | 1.33802 | + | 1.19596i | ||||
\(753\) | 98.7670 | + | 98.7670i | 0.131165 | + | 0.131165i | ||||
\(754\) | 161.108 | + | 104.416i | 0.213672 | + | 0.138483i | ||||
\(755\) | 549.946 | − | 549.946i | 0.728405 | − | 0.728405i | ||||
\(756\) | −356.338 | + | 159.431i | −0.471347 | + | 0.210887i | ||||
\(757\) | 96.4029 | 0.127349 | 0.0636743 | − | 0.997971i | \(-0.479718\pi\) | ||||
0.0636743 | + | 0.997971i | \(0.479718\pi\) | |||||||
\(758\) | −748.585 | − | 485.168i | −0.987579 | − | 0.640063i | ||||
\(759\) | −81.3310 | − | 81.3310i | −0.107155 | − | 0.107155i | ||||
\(760\) | 1045.09 | + | 162.599i | 1.37512 | + | 0.213946i | ||||
\(761\) | −256.811 | −0.337466 | −0.168733 | − | 0.985662i | \(-0.553968\pi\) | ||||
−0.168733 | + | 0.985662i | \(0.553968\pi\) | |||||||
\(762\) | 30.6039 | + | 19.8348i | 0.0401626 | + | 0.0260299i | ||||
\(763\) | − | 206.533i | − | 0.270686i | ||||||
\(764\) | −348.350 | − | 778.586i | −0.455956 | − | 1.01909i | ||||
\(765\) | −680.925 | − | 60.8733i | −0.890098 | − | 0.0795730i | ||||
\(766\) | 1022.27 | − | 218.264i | 1.33456 | − | 0.284940i | ||||
\(767\) | 208.740 | 0.272151 | ||||||||
\(768\) | 169.165 | − | 212.043i | 0.220267 | − | 0.276098i | ||||
\(769\) | 439.409 | 0.571403 | 0.285702 | − | 0.958319i | \(-0.407773\pi\) | ||||
0.285702 | + | 0.958319i | \(0.407773\pi\) | |||||||
\(770\) | −111.056 | + | 171.352i | −0.144228 | + | 0.222536i | ||||
\(771\) | −256.772 | + | 256.772i | −0.333037 | + | 0.333037i | ||||
\(772\) | 193.379 | − | 506.526i | 0.250491 | − | 0.656122i | ||||
\(773\) | 961.024 | 1.24324 | 0.621619 | − | 0.783319i | \(-0.286475\pi\) | ||||
0.621619 | + | 0.783319i | \(0.286475\pi\) | |||||||
\(774\) | 165.180 | − | 35.2673i | 0.213410 | − | 0.0455650i | ||||
\(775\) | 19.4980 | + | 19.4980i | 0.0251587 | + | 0.0251587i | ||||
\(776\) | −743.983 | − | 115.752i | −0.958741 | − | 0.149164i | ||||
\(777\) | −4.24344 | − | 4.24344i | −0.00546132 | − | 0.00546132i | ||||
\(778\) | 502.105 | − | 107.204i | 0.645380 | − | 0.137794i | ||||
\(779\) | 680.652 | + | 680.652i | 0.873751 | + | 0.873751i | ||||
\(780\) | −26.3663 | − | 58.9304i | −0.0338029 | − | 0.0755518i | ||||
\(781\) | 142.337i | 0.182250i | ||||||||
\(782\) | −999.750 | + | 121.756i | −1.27845 | + | 0.155698i | ||||
\(783\) | − | 575.332i | − | 0.734779i | ||||||
\(784\) | −229.243 | − | 204.903i | −0.292402 | − | 0.261356i | ||||
\(785\) | 1039.12 | + | 1039.12i | 1.32372 | + | 1.32372i | ||||
\(786\) | 70.6803 | + | 331.041i | 0.0899241 | + | 0.421172i | ||||
\(787\) | −198.734 | − | 198.734i | −0.252521 | − | 0.252521i | 0.569483 | − | 0.822003i | \(-0.307144\pi\) |
−0.822003 | + | 0.569483i | \(0.807144\pi\) | |||||||
\(788\) | 620.543 | + | 236.908i | 0.787491 | + | 0.300644i | ||||
\(789\) | −370.501 | − | 370.501i | −0.469582 | − | 0.469582i | ||||
\(790\) | −240.326 | + | 51.3117i | −0.304210 | + | 0.0649516i | ||||
\(791\) | 801.844 | 1.01371 | ||||||||
\(792\) | −228.189 | − | 35.5026i | −0.288118 | − | 0.0448265i | ||||
\(793\) | −196.440 | + | 196.440i | −0.247718 | + | 0.247718i | ||||
\(794\) | 869.703 | + | 563.666i | 1.09534 | + | 0.709906i | ||||
\(795\) | 183.082 | 0.230292 | ||||||||
\(796\) | −244.585 | + | 640.654i | −0.307268 | + | 0.804841i | ||||
\(797\) | −987.969 | −1.23961 | −0.619805 | − | 0.784756i | \(-0.712788\pi\) | ||||
−0.619805 | + | 0.784756i | \(0.712788\pi\) | |||||||
\(798\) | 292.906 | − | 62.5381i | 0.367050 | − | 0.0783685i | ||||
\(799\) | 919.606 | + | 1100.17i | 1.15095 | + | 1.37693i | ||||
\(800\) | 29.5056 | + | 16.8563i | 0.0368820 | + | 0.0210704i | ||||
\(801\) | − | 911.862i | − | 1.13840i | ||||||
\(802\) | −593.449 | + | 915.657i | −0.739961 | + | 1.14172i | ||||
\(803\) | −250.494 | −0.311948 | ||||||||
\(804\) | −300.993 | − | 114.911i | −0.374369 | − | 0.142925i | ||||
\(805\) | −583.556 | − | 583.556i | −0.724915 | − | 0.724915i | ||||
\(806\) | −130.034 | − | 84.2766i | −0.161332 | − | 0.104562i | ||||
\(807\) | 175.027 | 0.216886 | ||||||||
\(808\) | 103.230 | + | 141.270i | 0.127759 | + | 0.174839i | ||||
\(809\) | 407.336 | − | 407.336i | 0.503506 | − | 0.503506i | −0.409020 | − | 0.912526i | \(-0.634129\pi\) |
0.912526 | + | 0.409020i | \(0.134129\pi\) | |||||||
\(810\) | 288.463 | − | 445.082i | 0.356128 | − | 0.549484i | ||||
\(811\) | −38.6417 | − | 38.6417i | −0.0476469 | − | 0.0476469i | 0.682882 | − | 0.730529i | \(-0.260726\pi\) |
−0.730529 | + | 0.682882i | \(0.760726\pi\) | |||||||
\(812\) | −641.063 | + | 286.821i | −0.789486 | + | 0.353227i | ||||
\(813\) | 180.714 | − | 180.714i | 0.222281 | − | 0.222281i | ||||
\(814\) | −1.58818 | − | 7.43848i | −0.00195108 | − | 0.00913818i | ||||
\(815\) | − | 1442.58i | − | 1.77004i | ||||||
\(816\) | 210.438 | − | 196.926i | 0.257890 | − | 0.241331i | ||||
\(817\) | −277.643 | −0.339832 | ||||||||
\(818\) | 528.755 | − | 112.894i | 0.646400 | − | 0.138012i | ||||
\(819\) | 90.7000 | + | 90.7000i | 0.110745 | + | 0.110745i | ||||
\(820\) | 309.981 | + | 692.828i | 0.378025 | + | 0.844912i | ||||
\(821\) | −39.8813 | + | 39.8813i | −0.0485765 | + | 0.0485765i | −0.730978 | − | 0.682401i | \(-0.760936\pi\) |
0.682401 | + | 0.730978i | \(0.260936\pi\) | |||||||
\(822\) | 347.633 | + | 225.306i | 0.422912 | + | 0.274094i | ||||
\(823\) | −1118.37 | − | 1118.37i | −1.35889 | − | 1.35889i | −0.875287 | − | 0.483604i | \(-0.839327\pi\) |
−0.483604 | − | 0.875287i | \(-0.660673\pi\) | |||||||
\(824\) | 127.214 | + | 174.092i | 0.154386 | + | 0.211277i | ||||
\(825\) | 4.12334i | 0.00499799i | ||||||||
\(826\) | −415.296 | + | 640.778i | −0.502780 | + | 0.775760i | ||||
\(827\) | −350.629 | + | 350.629i | −0.423976 | + | 0.423976i | −0.886570 | − | 0.462594i | \(-0.846919\pi\) |
0.462594 | + | 0.886570i | \(0.346919\pi\) | |||||||
\(828\) | 332.895 | − | 871.967i | 0.402047 | − | 1.05310i | ||||
\(829\) | − | 470.897i | − | 0.568030i | −0.958820 | − | 0.284015i | \(-0.908333\pi\) | ||
0.958820 | − | 0.284015i | \(-0.0916665\pi\) | |||||||
\(830\) | −179.095 | − | 116.074i | −0.215777 | − | 0.139848i | ||||
\(831\) | 510.608 | 0.614451 | ||||||||
\(832\) | −181.933 | − | 58.0160i | −0.218670 | − | 0.0697308i | ||||
\(833\) | −209.516 | − | 250.654i | −0.251520 | − | 0.300905i | ||||
\(834\) | 3.09780 | + | 14.5090i | 0.00371439 | + | 0.0173969i | ||||
\(835\) | − | 571.112i | − | 0.683967i | ||||||
\(836\) | 354.645 | + | 135.394i | 0.424216 | + | 0.161955i | ||||
\(837\) | 464.362i | 0.554793i | ||||||||
\(838\) | −387.732 | + | 598.248i | −0.462687 | + | 0.713899i | ||||
\(839\) | 1145.65 | + | 1145.65i | 1.36549 | + | 1.36549i | 0.866748 | + | 0.498747i | \(0.166206\pi\) |
0.498747 | + | 0.866748i | \(0.333794\pi\) | |||||||
\(840\) | 233.358 | + | 36.3067i | 0.277807 | + | 0.0432222i | ||||
\(841\) | − | 194.040i | − | 0.230726i | ||||||
\(842\) | −74.9299 | − | 350.945i | −0.0889904 | − | 0.416799i | ||||
\(843\) | −321.054 | + | 321.054i | −0.380847 | + | 0.380847i | ||||
\(844\) | −31.8538 | + | 83.4360i | −0.0377414 | + | 0.0988578i | ||||
\(845\) | 577.926 | − | 577.926i | 0.683936 | − | 0.683936i | ||||
\(846\) | −1299.55 | + | 277.466i | −1.53611 | + | 0.327974i | ||||
\(847\) | 415.112 | − | 415.112i | 0.490096 | − | 0.490096i | ||||
\(848\) | 360.888 | − | 403.756i | 0.425575 | − | 0.476128i | ||||
\(849\) | 83.5732 | 0.0984373 | ||||||||
\(850\) | 28.4292 | + | 22.2564i | 0.0334461 | + | 0.0261840i | ||||
\(851\) | 30.7411 | 0.0361235 | ||||||||
\(852\) | 150.269 | − | 67.2325i | 0.176372 | − | 0.0789114i | ||||
\(853\) | 161.359 | − | 161.359i | 0.189167 | − | 0.189167i | −0.606169 | − | 0.795336i | \(-0.707294\pi\) |
0.795336 | + | 0.606169i | \(0.207294\pi\) | |||||||
\(854\) | −212.195 | − | 993.847i | −0.248472 | − | 1.16376i | ||||
\(855\) | −736.409 | + | 736.409i | −0.861297 | + | 0.861297i | ||||
\(856\) | −782.345 | − | 121.720i | −0.913954 | − | 0.142196i | ||||
\(857\) | −248.656 | + | 248.656i | −0.290147 | + | 0.290147i | −0.837138 | − | 0.546991i | \(-0.815773\pi\) |
0.546991 | + | 0.837138i | \(0.315773\pi\) | |||||||
\(858\) | −4.83826 | − | 22.6607i | −0.00563900 | − | 0.0264111i | ||||
\(859\) | − | 369.325i | − | 0.429947i | −0.976620 | − | 0.214974i | \(-0.931033\pi\) | ||
0.976620 | − | 0.214974i | \(-0.0689665\pi\) | |||||||
\(860\) | −204.526 | − | 78.0829i | −0.237821 | − | 0.0907940i | ||||
\(861\) | 151.982 | + | 151.982i | 0.176518 | + | 0.176518i | ||||
\(862\) | −1116.11 | − | 723.367i | −1.29479 | − | 0.839173i | ||||
\(863\) | 1657.91i | 1.92110i | 0.278107 | + | 0.960550i | \(0.410293\pi\) | ||||
−0.278107 | + | 0.960550i | \(0.589707\pi\) | |||||||
\(864\) | 150.627 | + | 552.076i | 0.174337 | + | 0.638977i | ||||
\(865\) | − | 1678.72i | − | 1.94071i | ||||||
\(866\) | −109.223 | − | 511.563i | −0.126124 | − | 0.590720i | ||||
\(867\) | 251.506 | − | 174.690i | 0.290087 | − | 0.201488i | ||||
\(868\) | 517.415 | − | 231.498i | 0.596100 | − | 0.266703i | ||||
\(869\) | −88.2005 | −0.101497 | ||||||||
\(870\) | −189.299 | + | 292.077i | −0.217585 | + | 0.335721i | ||||
\(871\) | 226.811i | 0.260404i | ||||||||
\(872\) | −299.158 | − | 46.5442i | −0.343072 | − | 0.0533763i | ||||
\(873\) | 524.237 | − | 524.237i | 0.600500 | − | 0.600500i | ||||
\(874\) | −834.437 | + | 1287.49i | −0.954733 | + | 1.47310i | ||||
\(875\) | − | 666.926i | − | 0.762201i | ||||||
\(876\) | 118.320 | + | 264.453i | 0.135068 | + | 0.301887i | ||||
\(877\) | 262.995 | + | 262.995i | 0.299881 | + | 0.299881i | 0.840967 | − | 0.541086i | \(-0.181987\pi\) |
−0.541086 | + | 0.840967i | \(0.681987\pi\) | |||||||
\(878\) | −193.907 | + | 299.186i | −0.220850 | + | 0.340759i | ||||
\(879\) | −257.438 | + | 257.438i | −0.292876 | + | 0.292876i | ||||
\(880\) | 223.172 | + | 199.477i | 0.253605 | + | 0.226679i | ||||
\(881\) | −692.939 | − | 692.939i | −0.786537 | − | 0.786537i | 0.194388 | − | 0.980925i | \(-0.437728\pi\) |
−0.980925 | + | 0.194388i | \(0.937728\pi\) | |||||||
\(882\) | 296.080 | − | 63.2157i | 0.335691 | − | 0.0716731i | ||||
\(883\) | −654.812 | −0.741577 | −0.370788 | − | 0.928717i | \(-0.620912\pi\) | ||||
−0.370788 | + | 0.928717i | \(0.620912\pi\) | |||||||
\(884\) | −182.354 | − | 88.9563i | −0.206283 | − | 0.100629i | ||||
\(885\) | 378.430i | 0.427604i | ||||||||
\(886\) | −136.880 | + | 29.2251i | −0.154492 | + | 0.0329854i | ||||
\(887\) | −1025.67 | + | 1025.67i | −1.15634 | + | 1.15634i | −0.171085 | + | 0.985256i | \(0.554727\pi\) |
−0.985256 | + | 0.171085i | \(0.945273\pi\) | |||||||
\(888\) | −7.10282 | + | 5.19022i | −0.00799867 | + | 0.00584485i | ||||
\(889\) | 66.4095 | + | 66.4095i | 0.0747014 | + | 0.0747014i | ||||
\(890\) | −642.814 | + | 991.824i | −0.722263 | + | 1.11441i | ||||
\(891\) | 134.607 | − | 134.607i | 0.151074 | − | 0.151074i | ||||
\(892\) | 272.927 | − | 122.111i | 0.305972 | − | 0.136896i | ||||
\(893\) | 2184.36 | 2.44609 | ||||||||
\(894\) | 39.8373 | − | 61.4666i | 0.0445607 | − | 0.0687546i | ||||
\(895\) | −777.336 | − | 777.336i | −0.868532 | − | 0.868532i | ||||
\(896\) | 540.058 | − | 443.063i | 0.602743 | − | 0.494490i | ||||
\(897\) | 93.6502 | 0.104404 | ||||||||
\(898\) | −337.996 | + | 521.508i | −0.376388 | + | 0.580744i | ||||
\(899\) | 835.401i | 0.929256i | ||||||||
\(900\) | −30.5422 | + | 13.6650i | −0.0339358 | + | 0.0151833i | ||||
\(901\) | 441.467 | − | 369.011i | 0.489974 | − | 0.409558i | ||||
\(902\) | 56.8820 | + | 266.415i | 0.0630621 | + | 0.295360i | ||||
\(903\) | −61.9946 | −0.0686540 | ||||||||
\(904\) | 180.703 | − | 1161.45i | 0.199893 | − | 1.28479i | ||||
\(905\) | 615.627 | 0.680251 | ||||||||
\(906\) | −270.924 | − | 175.590i | −0.299033 | − | 0.193807i | ||||
\(907\) | −63.4688 | + | 63.4688i | −0.0699766 | + | 0.0699766i | −0.741229 | − | 0.671252i | \(-0.765757\pi\) |
0.671252 | + | 0.741229i | \(0.265757\pi\) | |||||||
\(908\) | 287.792 | − | 753.826i | 0.316951 | − | 0.830205i | ||||
\(909\) | −172.283 | −0.189530 | ||||||||
\(910\) | −34.7149 | − | 162.592i | −0.0381483 | − | 0.178673i | ||||
\(911\) | 949.166 | + | 949.166i | 1.04189 | + | 1.04189i | 0.999083 | + | 0.0428112i | \(0.0136314\pi\) |
0.0428112 | + | 0.999083i | \(0.486369\pi\) | |||||||
\(912\) | −24.5758 | − | 438.361i | −0.0269472 | − | 0.480659i | ||||
\(913\) | −54.1640 | − | 54.1640i | −0.0593253 | − | 0.0593253i | ||||
\(914\) | 202.603 | + | 948.922i | 0.221667 | + | 1.03821i | ||||
\(915\) | −356.131 | − | 356.131i | −0.389215 | − | 0.389215i | ||||
\(916\) | −957.379 | + | 428.345i | −1.04517 | + | 0.467625i | ||||
\(917\) | 871.725i | 0.950627i | ||||||||
\(918\) | 73.5057 | + | 603.562i | 0.0800716 | + | 0.657475i | ||||
\(919\) | 1082.82i | 1.17826i | 0.808040 | + | 0.589128i | \(0.200529\pi\) | ||||
−0.808040 | + | 0.589128i | \(0.799471\pi\) | |||||||
\(920\) | −976.777 | + | 713.757i | −1.06171 | + | 0.775823i | ||||
\(921\) | −75.6452 | − | 75.6452i | −0.0821338 | − | 0.0821338i | ||||
\(922\) | 1571.98 | − | 335.631i | 1.70496 | − | 0.364025i | ||||
\(923\) | −81.9486 | − | 81.9486i | −0.0887850 | − | 0.0887850i | ||||
\(924\) | 79.1884 | + | 30.2321i | 0.0857017 | + | 0.0327187i | ||||
\(925\) | −0.779261 | − | 0.779261i | −0.000842444 | − | 0.000842444i | ||||
\(926\) | 281.065 | + | 1316.41i | 0.303526 | + | 1.42161i | ||||
\(927\) | −212.311 | −0.229030 | ||||||||
\(928\) | 270.983 | + | 993.202i | 0.292008 | + | 1.07026i | ||||
\(929\) | −517.649 | + | 517.649i | −0.557211 | + | 0.557211i | −0.928513 | − | 0.371301i | \(-0.878912\pi\) |
0.371301 | + | 0.928513i | \(0.378912\pi\) | |||||||
\(930\) | 152.787 | − | 235.741i | 0.164287 | − | 0.253485i | ||||
\(931\) | −497.666 | −0.534550 | ||||||||
\(932\) | −321.638 | − | 122.793i | −0.345106 | − | 0.131753i | ||||
\(933\) | −54.0949 | −0.0579796 | ||||||||
\(934\) | 321.217 | + | 1504.46i | 0.343915 | + | 1.61078i | ||||
\(935\) | 203.967 | + | 244.016i | 0.218147 | + | 0.260980i | ||||
\(936\) | 151.817 | − | 110.937i | 0.162197 | − | 0.118522i | ||||
\(937\) | − | 1102.17i | − | 1.17627i | −0.808762 | − | 0.588137i | \(-0.799862\pi\) | ||
0.808762 | − | 0.588137i | \(-0.200138\pi\) | |||||||
\(938\) | −696.252 | − | 451.250i | −0.742273 | − | 0.481077i | ||||
\(939\) | −310.762 | −0.330950 | ||||||||
\(940\) | 1609.11 | + | 614.318i | 1.71182 | + | 0.653529i | ||||
\(941\) | −917.863 | − | 917.863i | −0.975412 | − | 0.975412i | 0.0242925 | − | 0.999705i | \(-0.492267\pi\) |
−0.999705 | + | 0.0242925i | \(0.992267\pi\) | |||||||
\(942\) | 331.776 | − | 511.911i | 0.352204 | − | 0.543430i | ||||
\(943\) | −1101.02 | −1.16757 | ||||||||
\(944\) | 834.560 | + | 745.952i | 0.884068 | + | 0.790203i | ||||
\(945\) | −352.301 | + | 352.301i | −0.372805 | + | 0.372805i | ||||
\(946\) | −65.9375 | − | 42.7350i | −0.0697014 | − | 0.0451744i | ||||
\(947\) | −356.250 | − | 356.250i | −0.376188 | − | 0.376188i | 0.493537 | − | 0.869725i | \(-0.335704\pi\) |
−0.869725 | + | 0.493537i | \(0.835704\pi\) | |||||||
\(948\) | 41.6612 | + | 93.1155i | 0.0439464 | + | 0.0982231i | ||||
\(949\) | 144.218 | − | 144.218i | 0.151969 | − | 0.151969i | ||||
\(950\) | 53.7889 | − | 11.4844i | 0.0566199 | − | 0.0120889i | ||||
\(951\) | 136.678i | 0.143720i | ||||||||
\(952\) | 635.873 | − | 382.798i | 0.667934 | − | 0.402098i | ||||
\(953\) | 195.343 | 0.204977 | 0.102489 | − | 0.994734i | \(-0.467319\pi\) | ||||
0.102489 | + | 0.994734i | \(0.467319\pi\) | |||||||
\(954\) | 111.339 | + | 521.473i | 0.116708 | + | 0.546617i | ||||
\(955\) | −769.765 | − | 769.765i | −0.806036 | − | 0.806036i | ||||
\(956\) | 155.496 | + | 347.543i | 0.162652 | + | 0.363539i | ||||
\(957\) | −88.3334 | + | 88.3334i | −0.0923025 | + | 0.0923025i | ||||
\(958\) | 199.490 | − | 307.801i | 0.208236 | − | 0.321296i | ||||
\(959\) | 754.355 | + | 754.355i | 0.786605 | + | 0.786605i | ||||
\(960\) | 105.179 | − | 329.831i | 0.109561 | − | 0.343574i | ||||
\(961\) | 286.731i | 0.298367i | ||||||||
\(962\) | 5.19697 | + | 3.36822i | 0.00540225 | + | 0.00350127i | ||||
\(963\) | 551.268 | − | 551.268i | 0.572448 | − | 0.572448i | ||||
\(964\) | −623.519 | − | 238.044i | −0.646804 | − | 0.246934i | ||||
\(965\) | − | 691.975i | − | 0.717073i | ||||||
\(966\) | −186.321 | + | 287.482i | −0.192879 | + | 0.297600i | ||||
\(967\) | 1170.65 | 1.21060 | 0.605299 | − | 0.795998i | \(-0.293053\pi\) | ||||
0.605299 | + | 0.795998i | \(0.293053\pi\) | |||||||
\(968\) | −507.730 | − | 694.828i | −0.524514 | − | 0.717798i | ||||
\(969\) | 41.5376 | − | 464.637i | 0.0428664 | − | 0.479501i | ||||
\(970\) | −939.767 | + | 200.649i | −0.968832 | + | 0.206854i | ||||
\(971\) | − | 1519.02i | − | 1.56438i | −0.623037 | − | 0.782192i | \(-0.714101\pi\) | ||
0.623037 | − | 0.782192i | \(-0.285899\pi\) | |||||||
\(972\) | −807.136 | − | 308.144i | −0.830387 | − | 0.317021i | ||||
\(973\) | 38.2062i | 0.0392664i | ||||||||
\(974\) | 159.726 | + | 103.520i | 0.163989 | + | 0.106284i | ||||
\(975\) | −2.37395 | − | 2.37395i | −0.00243482 | − | 0.00243482i | ||||
\(976\) | −1487.38 | + | 83.3872i | −1.52396 | + | 0.0854377i | ||||
\(977\) | 109.675i | 0.112257i | 0.998424 | + | 0.0561283i | \(0.0178756\pi\) | ||||
−0.998424 | + | 0.0561283i | \(0.982124\pi\) | |||||||
\(978\) | −585.633 | + | 125.038i | −0.598807 | + | 0.127851i | ||||
\(979\) | −299.959 | + | 299.959i | −0.306393 | + | 0.306393i | ||||
\(980\) | −366.607 | − | 139.961i | −0.374089 | − | 0.142818i | ||||
\(981\) | 210.798 | − | 210.798i | 0.214880 | − | 0.214880i | ||||
\(982\) | −39.8870 | − | 186.817i | −0.0406182 | − | 0.190241i | ||||
\(983\) | 176.945 | − | 176.945i | 0.180005 | − | 0.180005i | −0.611353 | − | 0.791358i | \(-0.709374\pi\) |
0.791358 | + | 0.611353i | \(0.209374\pi\) | |||||||
\(984\) | 254.393 | − | 185.892i | 0.258530 | − | 0.188915i | ||||
\(985\) | 847.736 | 0.860645 | ||||||||
\(986\) | 132.239 | + | 1085.83i | 0.134117 | + | 1.10124i | ||||
\(987\) | 487.743 | 0.494167 | ||||||||
\(988\) | −282.133 | + | 126.230i | −0.285560 | + | 0.127763i | ||||
\(989\) | 224.556 | − | 224.556i | 0.227054 | − | 0.227054i | ||||
\(990\) | −288.239 | + | 61.5416i | −0.291150 | + | 0.0621632i | ||||
\(991\) | 478.714 | − | 478.714i | 0.483062 | − | 0.483062i | −0.423046 | − | 0.906108i | \(-0.639039\pi\) |
0.906108 | + | 0.423046i | \(0.139039\pi\) | |||||||
\(992\) | −218.716 | − | 801.633i | −0.220480 | − | 0.808097i | ||||
\(993\) | −199.195 | + | 199.195i | −0.200599 | + | 0.200599i | ||||
\(994\) | 414.601 | − | 88.5210i | 0.417103 | − | 0.0890553i | ||||
\(995\) | 875.209i | 0.879607i | ||||||||
\(996\) | −31.5981 | + | 82.7665i | −0.0317250 | + | 0.0830989i | ||||
\(997\) | −231.688 | − | 231.688i | −0.232385 | − | 0.232385i | 0.581303 | − | 0.813687i | \(-0.302543\pi\) |
−0.813687 | + | 0.581303i | \(0.802543\pi\) | |||||||
\(998\) | −885.969 | + | 1367.00i | −0.887744 | + | 1.36974i | ||||
\(999\) | − | 18.5588i | − | 0.0185774i |
(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 | 136.3.j.b.115.2 | ✓ | 64 | |
4.3 | odd | 2 | 544.3.n.b.47.13 | 64 | |||
8.3 | odd | 2 | inner | 136.3.j.b.115.31 | yes | 64 | |
8.5 | even | 2 | 544.3.n.b.47.14 | 64 | |||
17.4 | even | 4 | inner | 136.3.j.b.123.31 | yes | 64 | |
68.55 | odd | 4 | 544.3.n.b.463.14 | 64 | |||
136.21 | even | 4 | 544.3.n.b.463.13 | 64 | |||
136.123 | odd | 4 | inner | 136.3.j.b.123.2 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.3.j.b.115.2 | ✓ | 64 | 1.1 | even | 1 | trivial | |
136.3.j.b.115.31 | yes | 64 | 8.3 | odd | 2 | inner | |
136.3.j.b.123.2 | yes | 64 | 136.123 | odd | 4 | inner | |
136.3.j.b.123.31 | yes | 64 | 17.4 | even | 4 | inner | |
544.3.n.b.47.13 | 64 | 4.3 | odd | 2 | |||
544.3.n.b.47.14 | 64 | 8.5 | even | 2 | |||
544.3.n.b.463.13 | 64 | 136.21 | even | 4 | |||
544.3.n.b.463.14 | 64 | 68.55 | odd | 4 |