Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [414,3,Mod(229,414)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(414, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("414.229");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 414 = 2 \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 414.h (of order \(6\), 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: | \(11.2806829445\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 229.18 | ||
Character | \(\chi\) | \(=\) | 414.229 |
Dual form | 414.3.h.a.367.18 |
$q$-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 \(\left(\mathbb{Z}/414\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(235\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 1.22474i | −0.353553 | − | 0.612372i | ||||
\(3\) | 1.61253 | − | 2.52977i | 0.537512 | − | 0.843256i | ||||
\(4\) | −1.00000 | + | 1.73205i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.849237 | + | 0.490307i | 0.169847 | + | 0.0980614i | 0.582514 | − | 0.812821i | \(-0.302069\pi\) |
−0.412666 | + | 0.910882i | \(0.635402\pi\) | |||||||
\(6\) | −4.23856 | − | 0.186126i | −0.706426 | − | 0.0310211i | ||||
\(7\) | −3.58678 | + | 2.07083i | −0.512397 | + | 0.295832i | −0.733818 | − | 0.679346i | \(-0.762264\pi\) |
0.221421 | + | 0.975178i | \(0.428930\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −3.79946 | − | 8.15868i | −0.422163 | − | 0.906520i | ||||
\(10\) | − | 1.38680i | − | 0.138680i | ||||||
\(11\) | −15.3577 | + | 8.86675i | −1.39615 | + | 0.806068i | −0.993987 | − | 0.109499i | \(-0.965075\pi\) |
−0.402164 | + | 0.915568i | \(0.631742\pi\) | |||||||
\(12\) | 2.76915 | + | 5.32276i | 0.230763 | + | 0.443563i | ||||
\(13\) | −3.68522 | + | 6.38299i | −0.283479 | + | 0.491000i | −0.972239 | − | 0.233989i | \(-0.924822\pi\) |
0.688760 | + | 0.724989i | \(0.258155\pi\) | |||||||
\(14\) | 5.07247 | + | 2.92859i | 0.362319 | + | 0.209185i | ||||
\(15\) | 2.60979 | − | 1.35774i | 0.173986 | − | 0.0905158i | ||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.29875i | 0.135221i | 0.997712 | + | 0.0676103i | \(0.0215374\pi\) | ||||
−0.997712 | + | 0.0676103i | \(0.978463\pi\) | |||||||
\(18\) | −7.30567 | + | 10.4224i | −0.405871 | + | 0.579024i | ||||
\(19\) | 18.1720i | 0.956422i | 0.878245 | + | 0.478211i | \(0.158715\pi\) | ||||
−0.878245 | + | 0.478211i | \(0.841285\pi\) | |||||||
\(20\) | −1.69847 | + | 0.980614i | −0.0849237 | + | 0.0490307i | ||||
\(21\) | −0.545088 | + | 12.4130i | −0.0259566 | + | 0.591095i | ||||
\(22\) | 21.7190 | + | 12.5395i | 0.987228 | + | 0.569976i | ||||
\(23\) | −22.9867 | + | 0.782265i | −0.999421 | + | 0.0340115i | ||||
\(24\) | 4.56094 | − | 7.15527i | 0.190039 | − | 0.298136i | ||||
\(25\) | −12.0192 | − | 20.8179i | −0.480768 | − | 0.832714i | ||||
\(26\) | 10.4234 | 0.400899 | ||||||||
\(27\) | −26.7663 | − | 3.54438i | −0.991346 | − | 0.131273i | ||||
\(28\) | − | 8.28331i | − | 0.295832i | ||||||
\(29\) | −15.7758 | − | 27.3245i | −0.543993 | − | 0.942223i | −0.998670 | − | 0.0515664i | \(-0.983579\pi\) |
0.454677 | − | 0.890656i | \(-0.349755\pi\) | |||||||
\(30\) | −3.50828 | − | 2.23626i | −0.116943 | − | 0.0745420i | ||||
\(31\) | −9.77841 | + | 16.9367i | −0.315433 | + | 0.546345i | −0.979529 | − | 0.201301i | \(-0.935483\pi\) |
0.664097 | + | 0.747647i | \(0.268816\pi\) | |||||||
\(32\) | −2.82843 | + | 4.89898i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −2.33393 | + | 53.1493i | −0.0707251 | + | 1.61058i | ||||
\(34\) | 2.81538 | − | 1.62546i | 0.0828053 | − | 0.0478077i | ||||
\(35\) | −4.06137 | −0.116039 | ||||||||
\(36\) | 17.9307 | + | 1.57781i | 0.498075 | + | 0.0438282i | ||||
\(37\) | 38.8585i | 1.05023i | 0.851031 | + | 0.525115i | \(0.175978\pi\) | ||||
−0.851031 | + | 0.525115i | \(0.824022\pi\) | |||||||
\(38\) | 22.2561 | − | 12.8496i | 0.585687 | − | 0.338146i | ||||
\(39\) | 10.2050 | + | 19.6156i | 0.261665 | + | 0.502963i | ||||
\(40\) | 2.40201 | + | 1.38680i | 0.0600501 | + | 0.0346700i | ||||
\(41\) | 7.71546 | − | 13.3636i | 0.188182 | − | 0.325941i | −0.756462 | − | 0.654038i | \(-0.773074\pi\) |
0.944644 | + | 0.328097i | \(0.106407\pi\) | |||||||
\(42\) | 15.5882 | − | 8.10972i | 0.371147 | − | 0.193089i | ||||
\(43\) | 11.3402 | − | 6.54727i | 0.263726 | − | 0.152262i | −0.362307 | − | 0.932059i | \(-0.618011\pi\) |
0.626033 | + | 0.779797i | \(0.284678\pi\) | |||||||
\(44\) | − | 35.4670i | − | 0.806068i | ||||||
\(45\) | 0.773614 | − | 8.79156i | 0.0171914 | − | 0.195368i | ||||
\(46\) | 17.2121 | + | 27.5997i | 0.374177 | + | 0.599993i | ||||
\(47\) | 13.0659 | + | 22.6307i | 0.277997 | + | 0.481505i | 0.970887 | − | 0.239538i | \(-0.0769961\pi\) |
−0.692890 | + | 0.721044i | \(0.743663\pi\) | |||||||
\(48\) | −11.9884 | − | 0.526445i | −0.249759 | − | 0.0109676i | ||||
\(49\) | −15.9233 | + | 27.5800i | −0.324966 | + | 0.562858i | ||||
\(50\) | −16.9977 | + | 29.4409i | −0.339954 | + | 0.588818i | ||||
\(51\) | 5.81530 | + | 3.70681i | 0.114026 | + | 0.0726826i | ||||
\(52\) | −7.37045 | − | 12.7660i | −0.141739 | − | 0.245500i | ||||
\(53\) | − | 58.2363i | − | 1.09880i | −0.835560 | − | 0.549399i | \(-0.814857\pi\) | ||
0.835560 | − | 0.549399i | \(-0.185143\pi\) | |||||||
\(54\) | 14.5857 | + | 35.2882i | 0.270106 | + | 0.653485i | ||||
\(55\) | −17.3897 | −0.316177 | ||||||||
\(56\) | −10.1449 | + | 5.85718i | −0.181160 | + | 0.104593i | ||||
\(57\) | 45.9710 | + | 29.3030i | 0.806509 | + | 0.514088i | ||||
\(58\) | −22.3103 | + | 38.6426i | −0.384661 | + | 0.666252i | ||||
\(59\) | 15.8527 | − | 27.4577i | 0.268690 | − | 0.465384i | −0.699834 | − | 0.714306i | \(-0.746743\pi\) |
0.968524 | + | 0.248921i | \(0.0800760\pi\) | |||||||
\(60\) | −0.258120 | + | 5.87802i | −0.00430200 | + | 0.0979670i | ||||
\(61\) | 27.3550 | − | 15.7934i | 0.448442 | − | 0.258908i | −0.258730 | − | 0.965950i | \(-0.583304\pi\) |
0.707172 | + | 0.707042i | \(0.249971\pi\) | |||||||
\(62\) | 27.6575 | 0.446089 | ||||||||
\(63\) | 30.5231 | + | 21.3953i | 0.484493 | + | 0.339609i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −6.25926 | + | 3.61378i | −0.0962963 | + | 0.0555967i | ||||
\(66\) | 66.7446 | − | 34.7238i | 1.01128 | − | 0.526117i | ||||
\(67\) | 92.3125 | + | 53.2966i | 1.37780 | + | 0.795472i | 0.991894 | − | 0.127067i | \(-0.0405563\pi\) |
0.385904 | + | 0.922539i | \(0.373890\pi\) | |||||||
\(68\) | −3.98155 | − | 2.29875i | −0.0585522 | − | 0.0338051i | ||||
\(69\) | −35.0879 | + | 59.4125i | −0.508520 | + | 0.861050i | ||||
\(70\) | 2.87182 | + | 4.97414i | 0.0410260 | + | 0.0710591i | ||||
\(71\) | 113.316 | 1.59599 | 0.797997 | − | 0.602661i | \(-0.205893\pi\) | ||||
0.797997 | + | 0.602661i | \(0.205893\pi\) | |||||||
\(72\) | −10.7465 | − | 23.0762i | −0.149257 | − | 0.320503i | ||||
\(73\) | −80.0956 | −1.09720 | −0.548600 | − | 0.836085i | \(-0.684839\pi\) | ||||
−0.548600 | + | 0.836085i | \(0.684839\pi\) | |||||||
\(74\) | 47.5918 | − | 27.4771i | 0.643132 | − | 0.371312i | ||||
\(75\) | −72.0458 | − | 3.16372i | −0.960610 | − | 0.0421830i | ||||
\(76\) | −31.4749 | − | 18.1720i | −0.414143 | − | 0.239106i | ||||
\(77\) | 36.7230 | − | 63.6061i | 0.476922 | − | 0.826054i | ||||
\(78\) | 16.8081 | − | 26.3688i | 0.215488 | − | 0.338061i | ||||
\(79\) | −70.5310 | + | 40.7211i | −0.892798 | + | 0.515457i | −0.874857 | − | 0.484382i | \(-0.839044\pi\) |
−0.0179411 | + | 0.999839i | \(0.505711\pi\) | |||||||
\(80\) | − | 3.92246i | − | 0.0490307i | ||||||
\(81\) | −52.1281 | + | 61.9972i | −0.643557 | + | 0.765398i | ||||
\(82\) | −21.8226 | −0.266130 | ||||||||
\(83\) | −64.1087 | + | 37.0132i | −0.772394 | + | 0.445942i | −0.833728 | − | 0.552176i | \(-0.813798\pi\) |
0.0613341 | + | 0.998117i | \(0.480464\pi\) | |||||||
\(84\) | −20.9549 | − | 13.3571i | −0.249463 | − | 0.159013i | ||||
\(85\) | −1.12709 | + | 1.95218i | −0.0132599 | + | 0.0229669i | ||||
\(86\) | −16.0375 | − | 9.25924i | −0.186482 | − | 0.107666i | ||||
\(87\) | −94.5636 | − | 4.15254i | −1.08694 | − | 0.0477304i | ||||
\(88\) | −43.4380 | + | 25.0790i | −0.493614 | + | 0.284988i | ||||
\(89\) | − | 27.9881i | − | 0.314473i | −0.987561 | − | 0.157237i | \(-0.949741\pi\) | ||
0.987561 | − | 0.157237i | \(-0.0502585\pi\) | |||||||
\(90\) | −11.3144 | + | 5.26909i | −0.125716 | + | 0.0585455i | ||||
\(91\) | − | 30.5258i | − | 0.335449i | ||||||
\(92\) | 21.6318 | − | 40.5964i | 0.235128 | − | 0.441265i | ||||
\(93\) | 27.0779 | + | 52.0481i | 0.291160 | + | 0.559657i | ||||
\(94\) | 18.4779 | − | 32.0047i | 0.196574 | − | 0.340476i | ||||
\(95\) | −8.90988 | + | 15.4324i | −0.0937882 | + | 0.162446i | ||||
\(96\) | 7.83235 | + | 15.0550i | 0.0815870 | + | 0.156823i | ||||
\(97\) | −144.732 | + | 83.5609i | −1.49208 | + | 0.861453i | −0.999959 | − | 0.00907394i | \(-0.997112\pi\) |
−0.492121 | + | 0.870527i | \(0.663778\pi\) | |||||||
\(98\) | 45.0380 | 0.459572 | ||||||||
\(99\) | 130.692 | + | 91.6094i | 1.32012 | + | 0.925347i | ||||
\(100\) | 48.0768 | 0.480768 | ||||||||
\(101\) | −41.1198 | − | 71.2217i | −0.407127 | − | 0.705165i | 0.587439 | − | 0.809268i | \(-0.300136\pi\) |
−0.994566 | + | 0.104103i | \(0.966803\pi\) | |||||||
\(102\) | 0.427858 | − | 9.74338i | 0.00419468 | − | 0.0955233i | ||||
\(103\) | −17.8847 | − | 10.3257i | −0.173637 | − | 0.100250i | 0.410662 | − | 0.911787i | \(-0.365297\pi\) |
−0.584300 | + | 0.811538i | \(0.698631\pi\) | |||||||
\(104\) | −10.4234 | + | 18.0538i | −0.100225 | + | 0.173595i | ||||
\(105\) | −6.54909 | + | 10.2743i | −0.0623723 | + | 0.0978507i | ||||
\(106\) | −71.3246 | + | 41.1793i | −0.672874 | + | 0.388484i | ||||
\(107\) | − | 194.165i | − | 1.81462i | −0.420457 | − | 0.907312i | \(-0.638130\pi\) | ||
0.420457 | − | 0.907312i | \(-0.361870\pi\) | |||||||
\(108\) | 32.9054 | − | 42.8163i | 0.304680 | − | 0.396447i | ||||
\(109\) | − | 19.9275i | − | 0.182821i | −0.995813 | − | 0.0914105i | \(-0.970862\pi\) | ||
0.995813 | − | 0.0914105i | \(-0.0291376\pi\) | |||||||
\(110\) | 12.2964 | + | 21.2980i | 0.111785 | + | 0.193618i | ||||
\(111\) | 98.3031 | + | 62.6607i | 0.885613 | + | 0.564511i | ||||
\(112\) | 14.3471 | + | 8.28331i | 0.128099 | + | 0.0739581i | ||||
\(113\) | −71.5034 | − | 41.2825i | −0.632773 | − | 0.365332i | 0.149052 | − | 0.988829i | \(-0.452378\pi\) |
−0.781825 | + | 0.623498i | \(0.785711\pi\) | |||||||
\(114\) | 3.38229 | − | 77.0232i | 0.0296692 | − | 0.675642i | ||||
\(115\) | −19.9047 | − | 10.6062i | −0.173084 | − | 0.0922279i | ||||
\(116\) | 63.1031 | 0.543993 | ||||||||
\(117\) | 66.0787 | + | 5.81460i | 0.564775 | + | 0.0496974i | ||||
\(118\) | −44.8382 | −0.379985 | ||||||||
\(119\) | −4.76031 | − | 8.24510i | −0.0400026 | − | 0.0692866i | ||||
\(120\) | 7.38160 | − | 3.84026i | 0.0615133 | − | 0.0320022i | ||||
\(121\) | 96.7385 | − | 167.556i | 0.799492 | − | 1.38476i | ||||
\(122\) | −38.6858 | − | 22.3352i | −0.317096 | − | 0.183076i | ||||
\(123\) | −21.3653 | − | 41.0676i | −0.173702 | − | 0.333883i | ||||
\(124\) | −19.5568 | − | 33.8734i | −0.157716 | − | 0.273173i | ||||
\(125\) | − | 48.0878i | − | 0.384702i | ||||||
\(126\) | 4.62077 | − | 52.5117i | 0.0366728 | − | 0.416760i | ||||
\(127\) | 86.6391 | 0.682197 | 0.341099 | − | 0.940027i | \(-0.389201\pi\) | ||||
0.341099 | + | 0.940027i | \(0.389201\pi\) | |||||||
\(128\) | −5.65685 | − | 9.79796i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.72339 | − | 39.2458i | 0.0133596 | − | 0.304231i | ||||
\(130\) | 8.85193 | + | 5.11066i | 0.0680917 | + | 0.0393128i | ||||
\(131\) | −9.69998 | + | 16.8009i | −0.0740457 | + | 0.128251i | −0.900671 | − | 0.434502i | \(-0.856924\pi\) |
0.826625 | + | 0.562753i | \(0.190258\pi\) | |||||||
\(132\) | −89.7233 | − | 57.1918i | −0.679722 | − | 0.433271i | ||||
\(133\) | −37.6311 | − | 65.1790i | −0.282941 | − | 0.490068i | ||||
\(134\) | − | 150.746i | − | 1.12497i | ||||||
\(135\) | −20.9931 | − | 16.1338i | −0.155505 | − | 0.119509i | ||||
\(136\) | 6.50184i | 0.0478077i | ||||||||
\(137\) | −196.324 | + | 113.348i | −1.43302 | + | 0.827355i | −0.997350 | − | 0.0727503i | \(-0.976822\pi\) |
−0.435671 | + | 0.900106i | \(0.643489\pi\) | |||||||
\(138\) | 97.5760 | + | 0.962755i | 0.707072 | + | 0.00697648i | ||||
\(139\) | 33.2641 | − | 57.6151i | 0.239310 | − | 0.414497i | −0.721207 | − | 0.692720i | \(-0.756412\pi\) |
0.960516 | + | 0.278223i | \(0.0897455\pi\) | |||||||
\(140\) | 4.06137 | − | 7.03449i | 0.0290098 | − | 0.0502464i | ||||
\(141\) | 78.3197 | + | 3.43923i | 0.555459 | + | 0.0243917i | ||||
\(142\) | −80.1262 | − | 138.783i | −0.564269 | − | 0.977343i | ||||
\(143\) | − | 130.704i | − | 0.914013i | ||||||
\(144\) | −20.6636 | + | 29.4791i | −0.143497 | + | 0.204716i | ||||
\(145\) | − | 30.9399i | − | 0.213379i | ||||||
\(146\) | 56.6361 | + | 98.0967i | 0.387919 | + | 0.671895i | ||||
\(147\) | 44.0942 | + | 84.7562i | 0.299961 | + | 0.576573i | ||||
\(148\) | −67.3049 | − | 38.8585i | −0.454763 | − | 0.262557i | ||||
\(149\) | −136.558 | − | 78.8416i | −0.916494 | − | 0.529138i | −0.0339791 | − | 0.999423i | \(-0.510818\pi\) |
−0.882515 | + | 0.470285i | \(0.844151\pi\) | |||||||
\(150\) | 47.0693 | + | 90.4748i | 0.313795 | + | 0.603165i | ||||
\(151\) | 30.3612 | + | 52.5871i | 0.201068 | + | 0.348259i | 0.948873 | − | 0.315659i | \(-0.102226\pi\) |
−0.747805 | + | 0.663918i | \(0.768892\pi\) | |||||||
\(152\) | 51.3983i | 0.338146i | ||||||||
\(153\) | 18.7548 | − | 8.73402i | 0.122580 | − | 0.0570851i | ||||
\(154\) | −103.868 | −0.674470 | ||||||||
\(155\) | −16.6084 | + | 9.58885i | −0.107151 | + | 0.0618635i | ||||
\(156\) | −44.1801 | − | 1.94007i | −0.283206 | − | 0.0124363i | ||||
\(157\) | −234.557 | − | 135.422i | −1.49399 | − | 0.862558i | −0.494018 | − | 0.869451i | \(-0.664472\pi\) |
−0.999976 | + | 0.00689326i | \(0.997806\pi\) | |||||||
\(158\) | 99.7459 | + | 57.5883i | 0.631303 | + | 0.364483i | ||||
\(159\) | −147.324 | − | 93.9080i | −0.926568 | − | 0.590617i | ||||
\(160\) | −4.80401 | + | 2.77360i | −0.0300251 | + | 0.0173350i | ||||
\(161\) | 80.8282 | − | 50.4073i | 0.502039 | − | 0.313089i | ||||
\(162\) | 112.791 | + | 20.0050i | 0.696240 | + | 0.123488i | ||||
\(163\) | 43.0670 | 0.264215 | 0.132107 | − | 0.991235i | \(-0.457826\pi\) | ||||
0.132107 | + | 0.991235i | \(0.457826\pi\) | |||||||
\(164\) | 15.4309 | + | 26.7272i | 0.0940910 | + | 0.162970i | ||||
\(165\) | −28.0415 | + | 43.9920i | −0.169949 | + | 0.266618i | ||||
\(166\) | 90.6634 | + | 52.3445i | 0.546165 | + | 0.315328i | ||||
\(167\) | 78.2517 | − | 135.536i | 0.468573 | − | 0.811592i | −0.530782 | − | 0.847508i | \(-0.678102\pi\) |
0.999355 | + | 0.0359164i | \(0.0114350\pi\) | |||||||
\(168\) | −1.54174 | + | 35.1093i | −0.00917704 | + | 0.208984i | ||||
\(169\) | 57.3383 | + | 99.3128i | 0.339280 | + | 0.587650i | ||||
\(170\) | 3.18790 | 0.0187524 | ||||||||
\(171\) | 148.260 | − | 69.0440i | 0.867016 | − | 0.403766i | ||||
\(172\) | 26.1891i | 0.152262i | ||||||||
\(173\) | 32.3244 | + | 55.9874i | 0.186846 | + | 0.323627i | 0.944197 | − | 0.329381i | \(-0.106840\pi\) |
−0.757351 | + | 0.653008i | \(0.773507\pi\) | |||||||
\(174\) | 61.7807 | + | 118.753i | 0.355062 | + | 0.682486i | ||||
\(175\) | 86.2204 | + | 49.7794i | 0.492688 | + | 0.284454i | ||||
\(176\) | 61.4306 | + | 35.4670i | 0.349038 | + | 0.201517i | ||||
\(177\) | −43.8986 | − | 84.3801i | −0.248015 | − | 0.476724i | ||||
\(178\) | −34.2783 | + | 19.7906i | −0.192575 | + | 0.111183i | ||||
\(179\) | −107.309 | −0.599493 | −0.299746 | − | 0.954019i | \(-0.596902\pi\) | ||||
−0.299746 | + | 0.954019i | \(0.596902\pi\) | |||||||
\(180\) | 14.4538 | + | 10.1315i | 0.0802990 | + | 0.0562861i | ||||
\(181\) | − | 126.115i | − | 0.696765i | −0.937352 | − | 0.348383i | \(-0.886731\pi\) | ||
0.937352 | − | 0.348383i | \(-0.113269\pi\) | |||||||
\(182\) | −37.3864 | + | 21.5850i | −0.205420 | + | 0.118599i | ||||
\(183\) | 4.15718 | − | 94.6691i | 0.0227168 | − | 0.517318i | ||||
\(184\) | −65.0162 | + | 2.21258i | −0.353349 | + | 0.0120249i | ||||
\(185\) | −19.0526 | + | 33.0001i | −0.102987 | + | 0.178379i | ||||
\(186\) | 44.5987 | − | 69.9671i | 0.239778 | − | 0.376167i | ||||
\(187\) | −20.3824 | − | 35.3034i | −0.108997 | − | 0.188788i | ||||
\(188\) | −52.2635 | −0.277997 | ||||||||
\(189\) | 103.345 | − | 42.7156i | 0.546798 | − | 0.226008i | ||||
\(190\) | 25.2009 | 0.132636 | ||||||||
\(191\) | 125.126 | − | 72.2414i | 0.655109 | − | 0.378227i | −0.135302 | − | 0.990804i | \(-0.543200\pi\) |
0.790411 | + | 0.612577i | \(0.209867\pi\) | |||||||
\(192\) | 12.9003 | − | 20.2382i | 0.0671889 | − | 0.105407i | ||||
\(193\) | −3.28182 | + | 5.68428i | −0.0170043 | + | 0.0294522i | −0.874402 | − | 0.485202i | \(-0.838746\pi\) |
0.857398 | + | 0.514654i | \(0.172080\pi\) | |||||||
\(194\) | 204.682 | + | 118.173i | 1.05506 | + | 0.609139i | ||||
\(195\) | −0.951229 | + | 21.6618i | −0.00487810 | + | 0.111086i | ||||
\(196\) | −31.8467 | − | 55.1601i | −0.162483 | − | 0.281429i | ||||
\(197\) | 88.3951 | 0.448706 | 0.224353 | − | 0.974508i | \(-0.427973\pi\) | ||||
0.224353 | + | 0.974508i | \(0.427973\pi\) | |||||||
\(198\) | 19.7850 | − | 224.842i | 0.0999241 | − | 1.13556i | ||||
\(199\) | 151.628i | 0.761952i | 0.924585 | + | 0.380976i | \(0.124412\pi\) | ||||
−0.924585 | + | 0.380976i | \(0.875588\pi\) | |||||||
\(200\) | −33.9954 | − | 58.8818i | −0.169977 | − | 0.294409i | ||||
\(201\) | 283.685 | − | 147.587i | 1.41137 | − | 0.734262i | ||||
\(202\) | −58.1522 | + | 100.723i | −0.287882 | + | 0.498627i | ||||
\(203\) | 113.168 | + | 65.3379i | 0.557480 | + | 0.321861i | ||||
\(204\) | −12.2357 | + | 6.36559i | −0.0599789 | + | 0.0312039i | ||||
\(205\) | 13.1045 | − | 7.56590i | 0.0639245 | − | 0.0369068i | ||||
\(206\) | 29.2055i | 0.141774i | ||||||||
\(207\) | 93.7194 | + | 184.569i | 0.452751 | + | 0.891637i | ||||
\(208\) | 29.4818 | 0.141739 | ||||||||
\(209\) | −161.127 | − | 279.080i | −0.770942 | − | 1.33531i | ||||
\(210\) | 17.2143 | + | 0.755927i | 0.0819730 | + | 0.00359965i | ||||
\(211\) | −186.998 | + | 323.890i | −0.886247 | + | 1.53502i | −0.0419689 | + | 0.999119i | \(0.513363\pi\) |
−0.844278 | + | 0.535906i | \(0.819970\pi\) | |||||||
\(212\) | 100.868 | + | 58.2363i | 0.475793 | + | 0.274699i | ||||
\(213\) | 182.725 | − | 286.662i | 0.857865 | − | 1.34583i | ||||
\(214\) | −237.802 | + | 137.295i | −1.11123 | + | 0.641567i | ||||
\(215\) | 12.8407 | 0.0597242 | ||||||||
\(216\) | −75.7067 | − | 10.0250i | −0.350494 | − | 0.0464122i | ||||
\(217\) | − | 80.9976i | − | 0.373261i | ||||||
\(218\) | −24.4061 | + | 14.0909i | −0.111955 | + | 0.0646370i | ||||
\(219\) | −129.157 | + | 202.623i | −0.589757 | + | 0.925221i | ||||
\(220\) | 17.3897 | − | 30.1199i | 0.0790442 | − | 0.136909i | ||||
\(221\) | −14.6729 | − | 8.47140i | −0.0663932 | − | 0.0383321i | ||||
\(222\) | 7.23259 | − | 164.704i | 0.0325793 | − | 0.741910i | ||||
\(223\) | −55.3259 | − | 95.8273i | −0.248098 | − | 0.429719i | 0.714900 | − | 0.699227i | \(-0.246472\pi\) |
−0.962998 | + | 0.269508i | \(0.913139\pi\) | |||||||
\(224\) | − | 23.4287i | − | 0.104593i | ||||||
\(225\) | −124.180 | + | 177.158i | −0.551910 | + | 0.787367i | ||||
\(226\) | 116.765i | 0.516657i | ||||||||
\(227\) | −375.033 | + | 216.525i | −1.65213 | + | 0.953856i | −0.675930 | + | 0.736966i | \(0.736258\pi\) |
−0.976196 | + | 0.216890i | \(0.930409\pi\) | |||||||
\(228\) | −96.7254 | + | 50.3211i | −0.424234 | + | 0.220707i | ||||
\(229\) | 123.494 | + | 71.2993i | 0.539275 | + | 0.311351i | 0.744785 | − | 0.667304i | \(-0.232552\pi\) |
−0.205510 | + | 0.978655i | \(0.565885\pi\) | |||||||
\(230\) | 1.08484 | + | 31.8779i | 0.00471671 | + | 0.138600i | ||||
\(231\) | −101.692 | − | 195.468i | −0.440224 | − | 0.846181i | ||||
\(232\) | −44.6207 | − | 77.2853i | −0.192330 | − | 0.333126i | ||||
\(233\) | 378.978 | 1.62651 | 0.813257 | − | 0.581905i | \(-0.197692\pi\) | ||||
0.813257 | + | 0.581905i | \(0.197692\pi\) | |||||||
\(234\) | −39.6033 | − | 85.0411i | −0.169245 | − | 0.363423i | ||||
\(235\) | 25.6252i | 0.109043i | ||||||||
\(236\) | 31.7054 | + | 54.9154i | 0.134345 | + | 0.232692i | ||||
\(237\) | −10.7187 | + | 244.091i | −0.0452266 | + | 1.02992i | ||||
\(238\) | −6.73210 | + | 11.6603i | −0.0282861 | + | 0.0489930i | ||||
\(239\) | −25.0651 | + | 43.4140i | −0.104875 | + | 0.181649i | −0.913687 | − | 0.406418i | \(-0.866778\pi\) |
0.808812 | + | 0.588067i | \(0.200111\pi\) | |||||||
\(240\) | −9.92291 | − | 6.32510i | −0.0413455 | − | 0.0263546i | ||||
\(241\) | 311.784 | − | 180.009i | 1.29371 | − | 0.746924i | 0.314400 | − | 0.949290i | \(-0.398197\pi\) |
0.979310 | + | 0.202367i | \(0.0648632\pi\) | |||||||
\(242\) | −273.618 | −1.13065 | ||||||||
\(243\) | 72.7803 | + | 231.845i | 0.299507 | + | 0.954094i | ||||
\(244\) | 63.1736i | 0.258908i | ||||||||
\(245\) | −27.0454 | + | 15.6147i | −0.110389 | + | 0.0637333i | ||||
\(246\) | −35.1897 | + | 55.2062i | −0.143048 | + | 0.224416i | ||||
\(247\) | −115.992 | − | 66.9680i | −0.469603 | − | 0.271125i | ||||
\(248\) | −27.6575 | + | 47.9042i | −0.111522 | + | 0.193162i | ||||
\(249\) | −9.74270 | + | 221.865i | −0.0391273 | + | 0.891025i | ||||
\(250\) | −58.8952 | + | 34.0032i | −0.235581 | + | 0.136013i | ||||
\(251\) | 370.371i | 1.47558i | 0.675029 | + | 0.737791i | \(0.264131\pi\) | ||||
−0.675029 | + | 0.737791i | \(0.735869\pi\) | |||||||
\(252\) | −67.5809 | + | 31.4721i | −0.268178 | + | 0.124889i | ||||
\(253\) | 346.086 | − | 215.831i | 1.36793 | − | 0.853087i | ||||
\(254\) | −61.2631 | − | 106.111i | −0.241193 | − | 0.417759i | ||||
\(255\) | 3.12109 | + | 5.99925i | 0.0122396 | + | 0.0235265i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −189.843 | + | 328.817i | −0.738688 | + | 1.27944i | 0.214399 | + | 0.976746i | \(0.431221\pi\) |
−0.953086 | + | 0.302699i | \(0.902112\pi\) | |||||||
\(258\) | −49.2847 | + | 25.6403i | −0.191026 | + | 0.0993809i | ||||
\(259\) | −80.4693 | − | 139.377i | −0.310692 | − | 0.538135i | ||||
\(260\) | − | 14.4551i | − | 0.0555967i | ||||||
\(261\) | −162.992 | + | 232.528i | −0.624490 | + | 0.890912i | ||||
\(262\) | 27.4357 | 0.104716 | ||||||||
\(263\) | 77.2629 | − | 44.6078i | 0.293775 | − | 0.169611i | −0.345868 | − | 0.938283i | \(-0.612415\pi\) |
0.639643 | + | 0.768672i | \(0.279082\pi\) | |||||||
\(264\) | −6.60134 | + | 150.329i | −0.0250051 | + | 0.569428i | ||||
\(265\) | 28.5537 | − | 49.4564i | 0.107750 | − | 0.186628i | ||||
\(266\) | −53.2185 | + | 92.1771i | −0.200069 | + | 0.346530i | ||||
\(267\) | −70.8034 | − | 45.1318i | −0.265181 | − | 0.169033i | ||||
\(268\) | −184.625 | + | 106.593i | −0.688899 | + | 0.397736i | ||||
\(269\) | −273.415 | −1.01641 | −0.508207 | − | 0.861235i | \(-0.669691\pi\) | ||||
−0.508207 | + | 0.861235i | \(0.669691\pi\) | |||||||
\(270\) | −4.91535 | + | 37.1195i | −0.0182050 | + | 0.137480i | ||||
\(271\) | −394.390 | −1.45532 | −0.727658 | − | 0.685940i | \(-0.759391\pi\) | ||||
−0.727658 | + | 0.685940i | \(0.759391\pi\) | |||||||
\(272\) | 7.96310 | − | 4.59750i | 0.0292761 | − | 0.0169026i | ||||
\(273\) | −77.2233 | − | 49.2240i | −0.282869 | − | 0.180308i | ||||
\(274\) | 277.644 | + | 160.298i | 1.01330 | + | 0.585029i | ||||
\(275\) | 369.174 | + | 213.142i | 1.34245 | + | 0.775063i | ||||
\(276\) | −67.8175 | − | 120.186i | −0.245716 | − | 0.435458i | ||||
\(277\) | 42.6847 | + | 73.9321i | 0.154097 | + | 0.266903i | 0.932730 | − | 0.360576i | \(-0.117420\pi\) |
−0.778633 | + | 0.627479i | \(0.784087\pi\) | |||||||
\(278\) | −94.0850 | −0.338435 | ||||||||
\(279\) | 175.334 | + | 15.4285i | 0.628437 | + | 0.0552993i | ||||
\(280\) | −11.4873 | −0.0410260 | ||||||||
\(281\) | −71.5619 | + | 41.3163i | −0.254669 | + | 0.147033i | −0.621900 | − | 0.783097i | \(-0.713639\pi\) |
0.367231 | + | 0.930130i | \(0.380306\pi\) | |||||||
\(282\) | −51.1682 | − | 98.3536i | −0.181448 | − | 0.348772i | ||||
\(283\) | 43.5925 | + | 25.1681i | 0.154037 | + | 0.0889333i | 0.575037 | − | 0.818127i | \(-0.304988\pi\) |
−0.421000 | + | 0.907061i | \(0.638321\pi\) | |||||||
\(284\) | −113.316 | + | 196.268i | −0.398999 | + | 0.691086i | ||||
\(285\) | 24.6728 | + | 47.4251i | 0.0865713 | + | 0.166404i | ||||
\(286\) | −160.079 | + | 92.4216i | −0.559716 | + | 0.323152i | ||||
\(287\) | 63.9096i | 0.222681i | ||||||||
\(288\) | 50.7157 | + | 4.46273i | 0.176096 | + | 0.0154956i | ||||
\(289\) | 283.716 | 0.981715 | ||||||||
\(290\) | −37.8935 | + | 21.8778i | −0.130667 | + | 0.0754408i | ||||
\(291\) | −21.9951 | + | 500.883i | −0.0755846 | + | 1.72125i | ||||
\(292\) | 80.0956 | − | 138.730i | 0.274300 | − | 0.475101i | ||||
\(293\) | 151.799 | + | 87.6415i | 0.518087 | + | 0.299118i | 0.736152 | − | 0.676817i | \(-0.236641\pi\) |
−0.218065 | + | 0.975934i | \(0.569974\pi\) | |||||||
\(294\) | 72.6254 | − | 113.936i | 0.247025 | − | 0.387537i | ||||
\(295\) | 26.9254 | − | 15.5454i | 0.0912725 | − | 0.0526962i | ||||
\(296\) | 109.908i | 0.371312i | ||||||||
\(297\) | 442.496 | − | 182.897i | 1.48988 | − | 0.615815i | ||||
\(298\) | 222.998i | 0.748314i | ||||||||
\(299\) | 79.7179 | − | 149.607i | 0.266615 | − | 0.500357i | ||||
\(300\) | 77.5255 | − | 121.623i | 0.258418 | − | 0.405411i | ||||
\(301\) | −27.1165 | + | 46.9672i | −0.0900882 | + | 0.156037i | ||||
\(302\) | 42.9372 | − | 74.3694i | 0.142176 | − | 0.246256i | ||||
\(303\) | −246.482 | − | 10.8237i | −0.813470 | − | 0.0357217i | ||||
\(304\) | 62.9497 | − | 36.3441i | 0.207072 | − | 0.119553i | ||||
\(305\) | 30.9745 | 0.101556 | ||||||||
\(306\) | −23.9586 | − | 16.7939i | −0.0782959 | − | 0.0548821i | ||||
\(307\) | −149.595 | −0.487281 | −0.243640 | − | 0.969866i | \(-0.578342\pi\) | ||||
−0.243640 | + | 0.969866i | \(0.578342\pi\) | |||||||
\(308\) | 73.4460 | + | 127.212i | 0.238461 | + | 0.413027i | ||||
\(309\) | −54.9613 | + | 28.5935i | −0.177868 | + | 0.0925356i | ||||
\(310\) | 23.4878 | + | 13.5607i | 0.0757670 | + | 0.0437441i | ||||
\(311\) | −151.212 | + | 261.908i | −0.486213 | + | 0.842146i | −0.999874 | − | 0.0158469i | \(-0.994956\pi\) |
0.513661 | + | 0.857993i | \(0.328289\pi\) | |||||||
\(312\) | 28.8640 | + | 55.4812i | 0.0925127 | + | 0.177824i | ||||
\(313\) | 463.721 | − | 267.730i | 1.48154 | − | 0.855366i | 0.481757 | − | 0.876305i | \(-0.339999\pi\) |
0.999781 | + | 0.0209386i | \(0.00666546\pi\) | |||||||
\(314\) | 383.030i | 1.21984i | ||||||||
\(315\) | 15.4310 | + | 33.1354i | 0.0489874 | + | 0.105192i | ||||
\(316\) | − | 162.884i | − | 0.515457i | ||||||
\(317\) | −266.086 | − | 460.875i | −0.839389 | − | 1.45386i | −0.890406 | − | 0.455166i | \(-0.849580\pi\) |
0.0510175 | − | 0.998698i | \(-0.483754\pi\) | |||||||
\(318\) | −10.8393 | + | 246.838i | −0.0340859 | + | 0.776219i | ||||
\(319\) | 484.558 | + | 279.760i | 1.51899 | + | 0.876990i | ||||
\(320\) | 6.79390 | + | 3.92246i | 0.0212309 | + | 0.0122577i | ||||
\(321\) | −491.192 | − | 313.097i | −1.53019 | − | 0.975382i | ||||
\(322\) | −118.890 | − | 63.3506i | −0.369224 | − | 0.196741i | ||||
\(323\) | −41.7729 | −0.129328 | ||||||||
\(324\) | −55.2542 | − | 152.286i | −0.170538 | − | 0.470018i | ||||
\(325\) | 177.174 | 0.545150 | ||||||||
\(326\) | −30.4529 | − | 52.7460i | −0.0934139 | − | 0.161798i | ||||
\(327\) | −50.4120 | − | 32.1338i | −0.154165 | − | 0.0982684i | ||||
\(328\) | 21.8226 | − | 37.7979i | 0.0665324 | − | 0.115238i | ||||
\(329\) | −93.7287 | − | 54.1143i | −0.284890 | − | 0.164481i | ||||
\(330\) | 73.7073 | + | 3.23669i | 0.223356 | + | 0.00980814i | ||||
\(331\) | 270.145 | + | 467.904i | 0.816147 | + | 1.41361i | 0.908501 | + | 0.417882i | \(0.137228\pi\) |
−0.0923540 | + | 0.995726i | \(0.529439\pi\) | |||||||
\(332\) | − | 148.053i | − | 0.445942i | ||||||
\(333\) | 317.034 | − | 147.642i | 0.952055 | − | 0.443368i | ||||
\(334\) | −221.329 | −0.662662 | ||||||||
\(335\) | 52.2634 | + | 90.5229i | 0.156010 | + | 0.270218i | ||||
\(336\) | 44.0901 | − | 22.9378i | 0.131220 | − | 0.0682671i | ||||
\(337\) | −196.536 | − | 113.470i | −0.583193 | − | 0.336707i | 0.179208 | − | 0.983811i | \(-0.442646\pi\) |
−0.762401 | + | 0.647105i | \(0.775980\pi\) | |||||||
\(338\) | 81.0885 | − | 140.449i | 0.239907 | − | 0.415531i | ||||
\(339\) | −219.737 | + | 114.318i | −0.648191 | + | 0.337220i | ||||
\(340\) | −2.25419 | − | 3.90437i | −0.00662996 | − | 0.0114834i | ||||
\(341\) | − | 346.811i | − | 1.01704i | ||||||
\(342\) | −189.397 | − | 132.759i | −0.553792 | − | 0.388184i | ||||
\(343\) | − | 334.839i | − | 0.976207i | ||||||
\(344\) | 32.0750 | − | 18.5185i | 0.0932411 | − | 0.0538328i | ||||
\(345\) | −58.9283 | + | 33.2514i | −0.170807 | + | 0.0963809i | ||||
\(346\) | 45.7135 | − | 79.1782i | 0.132120 | − | 0.228839i | ||||
\(347\) | 93.2581 | − | 161.528i | 0.268755 | − | 0.465498i | −0.699785 | − | 0.714353i | \(-0.746721\pi\) |
0.968541 | + | 0.248855i | \(0.0800544\pi\) | |||||||
\(348\) | 101.756 | − | 159.636i | 0.292402 | − | 0.458725i | ||||
\(349\) | 240.154 | + | 415.958i | 0.688119 | + | 1.19186i | 0.972446 | + | 0.233130i | \(0.0748967\pi\) |
−0.284327 | + | 0.958727i | \(0.591770\pi\) | |||||||
\(350\) | − | 140.797i | − | 0.402278i | ||||||
\(351\) | 121.264 | − | 157.788i | 0.345481 | − | 0.449537i | ||||
\(352\) | − | 100.316i | − | 0.284988i | ||||||
\(353\) | 302.768 | + | 524.409i | 0.857699 | + | 1.48558i | 0.874119 | + | 0.485713i | \(0.161440\pi\) |
−0.0164197 | + | 0.999865i | \(0.505227\pi\) | |||||||
\(354\) | −72.3031 | + | 113.430i | −0.204246 | + | 0.320425i | ||||
\(355\) | 96.2318 | + | 55.5595i | 0.271076 | + | 0.156506i | ||||
\(356\) | 48.4768 | + | 27.9881i | 0.136171 | + | 0.0786183i | ||||
\(357\) | −28.5344 | − | 1.25302i | −0.0799282 | − | 0.00350986i | ||||
\(358\) | 75.8790 | + | 131.426i | 0.211953 | + | 0.367113i | ||||
\(359\) | − | 118.476i | − | 0.330018i | −0.986292 | − | 0.165009i | \(-0.947235\pi\) | ||
0.986292 | − | 0.165009i | \(-0.0527653\pi\) | |||||||
\(360\) | 2.18811 | − | 24.8663i | 0.00607808 | − | 0.0690730i | ||||
\(361\) | 30.7775 | 0.0852561 | ||||||||
\(362\) | −154.458 | + | 89.1764i | −0.426680 | + | 0.246344i | ||||
\(363\) | −267.884 | − | 514.916i | −0.737972 | − | 1.41850i | ||||
\(364\) | 52.8723 | + | 30.5258i | 0.145254 | + | 0.0838622i | ||||
\(365\) | −68.0201 | − | 39.2714i | −0.186357 | − | 0.107593i | ||||
\(366\) | −118.885 | + | 61.8497i | −0.324823 | + | 0.168988i | ||||
\(367\) | 256.526 | − | 148.105i | 0.698981 | − | 0.403557i | −0.107987 | − | 0.994152i | \(-0.534440\pi\) |
0.806968 | + | 0.590595i | \(0.201107\pi\) | |||||||
\(368\) | 48.6832 | + | 78.0637i | 0.132291 | + | 0.212130i | ||||
\(369\) | −138.344 | − | 12.1736i | −0.374915 | − | 0.0329907i | ||||
\(370\) | 53.8889 | 0.145646 | ||||||||
\(371\) | 120.597 | + | 208.881i | 0.325060 | + | 0.563021i | ||||
\(372\) | −117.228 | − | 5.14779i | −0.315129 | − | 0.0138382i | ||||
\(373\) | −418.651 | − | 241.708i | −1.12239 | − | 0.648011i | −0.180379 | − | 0.983597i | \(-0.557732\pi\) |
−0.942010 | + | 0.335586i | \(0.891066\pi\) | |||||||
\(374\) | −28.8251 | + | 49.9266i | −0.0770725 | + | 0.133493i | ||||
\(375\) | −121.651 | − | 77.5432i | −0.324402 | − | 0.206782i | ||||
\(376\) | 36.9559 | + | 64.0094i | 0.0982869 | + | 0.170238i | ||||
\(377\) | 232.549 | 0.616841 | ||||||||
\(378\) | −125.391 | − | 96.3665i | −0.331723 | − | 0.254938i | ||||
\(379\) | 190.541i | 0.502748i | 0.967890 | + | 0.251374i | \(0.0808824\pi\) | ||||
−0.967890 | + | 0.251374i | \(0.919118\pi\) | |||||||
\(380\) | −17.8198 | − | 30.8647i | −0.0468941 | − | 0.0812229i | ||||
\(381\) | 139.709 | − | 219.177i | 0.366689 | − | 0.575267i | ||||
\(382\) | −176.955 | − | 102.165i | −0.463232 | − | 0.267447i | ||||
\(383\) | −70.3194 | − | 40.5989i | −0.183602 | − | 0.106002i | 0.405382 | − | 0.914147i | \(-0.367138\pi\) |
−0.588984 | + | 0.808145i | \(0.700472\pi\) | |||||||
\(384\) | −33.9084 | − | 1.48901i | −0.0883033 | − | 0.00387763i | ||||
\(385\) | 62.3731 | − | 36.0111i | 0.162008 | − | 0.0935354i | ||||
\(386\) | 9.28240 | 0.0240477 | ||||||||
\(387\) | −96.5038 | − | 67.6450i | −0.249364 | − | 0.174793i | ||||
\(388\) | − | 334.244i | − | 0.861453i | ||||||
\(389\) | −259.619 | + | 149.891i | −0.667400 | + | 0.385324i | −0.795091 | − | 0.606490i | \(-0.792577\pi\) |
0.127691 | + | 0.991814i | \(0.459244\pi\) | |||||||
\(390\) | 27.2028 | − | 14.1522i | 0.0697508 | − | 0.0362877i | ||||
\(391\) | −1.79823 | − | 52.8406i | −0.00459906 | − | 0.135142i | ||||
\(392\) | −45.0380 | + | 78.0082i | −0.114893 | + | 0.199000i | ||||
\(393\) | 26.8608 | + | 51.6307i | 0.0683480 | + | 0.131376i | ||||
\(394\) | −62.5048 | − | 108.261i | −0.158642 | − | 0.274775i | ||||
\(395\) | −79.8634 | −0.202186 | ||||||||
\(396\) | −289.364 | + | 134.756i | −0.730717 | + | 0.340292i | ||||
\(397\) | 268.949 | 0.677455 | 0.338727 | − | 0.940885i | \(-0.390004\pi\) | ||||
0.338727 | + | 0.940885i | \(0.390004\pi\) | |||||||
\(398\) | 185.706 | − | 107.217i | 0.466598 | − | 0.269391i | ||||
\(399\) | −225.569 | − | 9.90536i | −0.565337 | − | 0.0248255i | ||||
\(400\) | −48.0768 | + | 83.2714i | −0.120192 | + | 0.208179i | ||||
\(401\) | 220.867 | + | 127.518i | 0.550791 | + | 0.317999i | 0.749441 | − | 0.662071i | \(-0.230322\pi\) |
−0.198650 | + | 0.980070i | \(0.563656\pi\) | |||||||
\(402\) | −381.352 | − | 243.083i | −0.948636 | − | 0.604683i | ||||
\(403\) | −72.0712 | − | 124.831i | −0.178837 | − | 0.309754i | ||||
\(404\) | 164.479 | 0.407127 | ||||||||
\(405\) | −74.6668 | + | 27.0916i | −0.184363 | + | 0.0668927i | ||||
\(406\) | − | 184.803i | − | 0.455181i | ||||||
\(407\) | −344.549 | − | 596.776i | −0.846557 | − | 1.46628i | ||||
\(408\) | 16.4482 | + | 10.4844i | 0.0403141 | + | 0.0256972i | ||||
\(409\) | 187.187 | − | 324.217i | 0.457669 | − | 0.792706i | −0.541168 | − | 0.840914i | \(-0.682018\pi\) |
0.998837 | + | 0.0482084i | \(0.0153511\pi\) | |||||||
\(410\) | −18.5326 | − | 10.6998i | −0.0452014 | − | 0.0260971i | ||||
\(411\) | −29.8357 | + | 679.431i | −0.0725928 | + | 1.65312i | ||||
\(412\) | 35.7693 | − | 20.6514i | 0.0868187 | − | 0.0501248i | ||||
\(413\) | 131.313i | 0.317949i | ||||||||
\(414\) | 159.780 | − | 245.292i | 0.385942 | − | 0.592493i | ||||
\(415\) | −72.5913 | −0.174919 | ||||||||
\(416\) | −20.8468 | − | 36.1077i | −0.0501124 | − | 0.0867973i | ||||
\(417\) | −92.1134 | − | 177.057i | −0.220895 | − | 0.424596i | ||||
\(418\) | −227.868 | + | 394.679i | −0.545138 | + | 0.944207i | ||||
\(419\) | 485.038 | + | 280.037i | 1.15761 | + | 0.668346i | 0.950730 | − | 0.310021i | \(-0.100336\pi\) |
0.206879 | + | 0.978367i | \(0.433669\pi\) | |||||||
\(420\) | −11.2466 | − | 21.6177i | −0.0267775 | − | 0.0514707i | ||||
\(421\) | −112.171 | + | 64.7620i | −0.266440 | + | 0.153829i | −0.627269 | − | 0.778803i | \(-0.715827\pi\) |
0.360829 | + | 0.932632i | \(0.382494\pi\) | |||||||
\(422\) | 528.910 | 1.25334 | ||||||||
\(423\) | 134.994 | − | 192.585i | 0.319134 | − | 0.455284i | ||||
\(424\) | − | 164.717i | − | 0.388484i | ||||||
\(425\) | 47.8550 | − | 27.6291i | 0.112600 | − | 0.0650097i | ||||
\(426\) | −480.295 | − | 21.0910i | −1.12745 | − | 0.0495095i | ||||
\(427\) | −65.4108 | + | 113.295i | −0.153187 | + | 0.265327i | ||||
\(428\) | 336.303 | + | 194.165i | 0.785755 | + | 0.453656i | ||||
\(429\) | −330.651 | − | 210.764i | −0.770747 | − | 0.491292i | ||||
\(430\) | −9.07975 | − | 15.7266i | −0.0211157 | − | 0.0365734i | ||||
\(431\) | − | 229.692i | − | 0.532929i | −0.963845 | − | 0.266464i | \(-0.914145\pi\) | ||
0.963845 | − | 0.266464i | \(-0.0858555\pi\) | |||||||
\(432\) | 41.2546 | + | 99.8101i | 0.0954967 | + | 0.231042i | ||||
\(433\) | − | 359.678i | − | 0.830666i | −0.909670 | − | 0.415333i | \(-0.863665\pi\) | ||
0.909670 | − | 0.415333i | \(-0.136335\pi\) | |||||||
\(434\) | −99.2014 | + | 57.2739i | −0.228575 | + | 0.131968i | ||||
\(435\) | −78.2709 | − | 49.8917i | −0.179933 | − | 0.114694i | ||||
\(436\) | 34.5154 | + | 19.9275i | 0.0791638 | + | 0.0457053i | ||||
\(437\) | −14.2153 | − | 417.715i | −0.0325294 | − | 0.955869i | ||||
\(438\) | 339.490 | + | 14.9079i | 0.775090 | + | 0.0340363i | ||||
\(439\) | 260.175 | + | 450.636i | 0.592654 | + | 1.02651i | 0.993873 | + | 0.110525i | \(0.0352531\pi\) |
−0.401220 | + | 0.915982i | \(0.631414\pi\) | |||||||
\(440\) | −49.1856 | −0.111785 | ||||||||
\(441\) | 285.517 | + | 25.1241i | 0.647431 | + | 0.0569707i | ||||
\(442\) | 23.9607i | 0.0542098i | ||||||||
\(443\) | 178.302 | + | 308.828i | 0.402487 | + | 0.697129i | 0.994025 | − | 0.109148i | \(-0.0348124\pi\) |
−0.591538 | + | 0.806277i | \(0.701479\pi\) | |||||||
\(444\) | −206.835 | + | 107.605i | −0.465844 | + | 0.242354i | ||||
\(445\) | 13.7228 | − | 23.7685i | 0.0308377 | − | 0.0534124i | ||||
\(446\) | −78.2426 | + | 135.520i | −0.175432 | + | 0.303857i | ||||
\(447\) | −419.655 | + | 218.324i | −0.938825 | + | 0.488422i | ||||
\(448\) | −28.6942 | + | 16.5666i | −0.0640496 | + | 0.0369791i | ||||
\(449\) | −241.898 | −0.538749 | −0.269375 | − | 0.963035i | \(-0.586817\pi\) | ||||
−0.269375 | + | 0.963035i | \(0.586817\pi\) | |||||||
\(450\) | 304.781 | + | 26.8192i | 0.677291 | + | 0.0595983i | ||||
\(451\) | 273.644i | 0.606750i | ||||||||
\(452\) | 143.007 | − | 82.5650i | 0.316387 | − | 0.182666i | ||||
\(453\) | 181.992 | + | 7.99175i | 0.401748 | + | 0.0176418i | ||||
\(454\) | 530.376 | + | 306.213i | 1.16823 | + | 0.674478i | ||||
\(455\) | 14.9670 | − | 25.9237i | 0.0328946 | − | 0.0569751i | ||||
\(456\) | 130.026 | + | 82.8815i | 0.285144 | + | 0.181758i | ||||
\(457\) | 332.381 | − | 191.900i | 0.727310 | − | 0.419913i | −0.0901273 | − | 0.995930i | \(-0.528727\pi\) |
0.817437 | + | 0.576018i | \(0.195394\pi\) | |||||||
\(458\) | − | 201.665i | − | 0.440316i | ||||||
\(459\) | 8.14765 | − | 61.5291i | 0.0177509 | − | 0.134050i | ||||
\(460\) | 38.2752 | − | 23.8697i | 0.0832070 | − | 0.0518907i | ||||
\(461\) | −347.415 | − | 601.741i | −0.753612 | − | 1.30529i | −0.946061 | − | 0.323987i | \(-0.894976\pi\) |
0.192449 | − | 0.981307i | \(-0.438357\pi\) | |||||||
\(462\) | −167.491 | + | 262.763i | −0.362535 | + | 0.568751i | ||||
\(463\) | 39.2651 | − | 68.0092i | 0.0848059 | − | 0.146888i | −0.820503 | − | 0.571643i | \(-0.806306\pi\) |
0.905308 | + | 0.424755i | \(0.139640\pi\) | |||||||
\(464\) | −63.1031 | + | 109.298i | −0.135998 | + | 0.235556i | ||||
\(465\) | −2.52400 | + | 57.4777i | −0.00542796 | + | 0.123608i | ||||
\(466\) | −267.978 | − | 464.151i | −0.575060 | − | 0.996032i | ||||
\(467\) | 35.7597i | 0.0765733i | 0.999267 | + | 0.0382866i | \(0.0121900\pi\) | ||||
−0.999267 | + | 0.0382866i | \(0.987810\pi\) | |||||||
\(468\) | −76.1499 | + | 108.637i | −0.162713 | + | 0.232130i | ||||
\(469\) | −441.472 | −0.941306 | ||||||||
\(470\) | 31.3843 | − | 18.1197i | 0.0667751 | − | 0.0385526i | ||||
\(471\) | −720.817 | + | 375.003i | −1.53040 | + | 0.796186i | ||||
\(472\) | 44.8382 | − | 77.6620i | 0.0949962 | − | 0.164538i | ||||
\(473\) | −116.106 | + | 201.102i | −0.245467 | + | 0.425162i | ||||
\(474\) | 306.529 | − | 159.471i | 0.646685 | − | 0.336437i | ||||
\(475\) | 378.303 | − | 218.413i | 0.796427 | − | 0.459817i | ||||
\(476\) | 19.0412 | 0.0400026 | ||||||||
\(477\) | −475.131 | + | 221.267i | −0.996082 | + | 0.463872i | ||||
\(478\) | 70.8948 | 0.148316 | ||||||||
\(479\) | −595.405 | + | 343.757i | −1.24302 | + | 0.717656i | −0.969707 | − | 0.244270i | \(-0.921452\pi\) |
−0.273310 | + | 0.961926i | \(0.588118\pi\) | |||||||
\(480\) | −0.730073 | + | 16.6256i | −0.00152099 | + | 0.0346366i | ||||
\(481\) | −248.034 | − | 143.202i | −0.515662 | − | 0.297718i | ||||
\(482\) | −440.929 | − | 254.571i | −0.914791 | − | 0.528155i | ||||
\(483\) | 2.81952 | − | 285.760i | 0.00583751 | − | 0.591636i | ||||
\(484\) | 193.477 | + | 335.112i | 0.399746 | + | 0.692380i | ||||
\(485\) | −163.882 | −0.337901 | ||||||||
\(486\) | 232.487 | − | 253.076i | 0.478369 | − | 0.520733i | ||||
\(487\) | −242.594 | −0.498139 | −0.249069 | − | 0.968486i | \(-0.580125\pi\) | ||||
−0.249069 | + | 0.968486i | \(0.580125\pi\) | |||||||
\(488\) | 77.3715 | − | 44.6705i | 0.158548 | − | 0.0915378i | ||||
\(489\) | 69.4470 | − | 108.949i | 0.142018 | − | 0.222801i | ||||
\(490\) | 38.2480 | + | 22.0825i | 0.0780571 | + | 0.0450663i | ||||
\(491\) | −266.956 | + | 462.381i | −0.543698 | + | 0.941713i | 0.454989 | + | 0.890497i | \(0.349643\pi\) |
−0.998688 | + | 0.0512163i | \(0.983690\pi\) | |||||||
\(492\) | 92.4964 | + | 4.06177i | 0.188001 | + | 0.00825562i | ||||
\(493\) | 62.8121 | − | 36.2646i | 0.127408 | − | 0.0735590i | ||||
\(494\) | 189.414i | 0.383429i | ||||||||
\(495\) | 66.0717 | + | 141.877i | 0.133478 | + | 0.286621i | ||||
\(496\) | 78.2273 | 0.157716 | ||||||||
\(497\) | −406.438 | + | 234.657i | −0.817783 | + | 0.472147i | ||||
\(498\) | 278.617 | − | 144.950i | 0.559473 | − | 0.291064i | ||||
\(499\) | 91.0694 | − | 157.737i | 0.182504 | − | 0.316106i | −0.760229 | − | 0.649655i | \(-0.774913\pi\) |
0.942733 | + | 0.333550i | \(0.108247\pi\) | |||||||
\(500\) | 83.2904 | + | 48.0878i | 0.166581 | + | 0.0961755i | ||||
\(501\) | −216.691 | − | 416.515i | −0.432517 | − | 0.831367i | ||||
\(502\) | 453.610 | − | 261.892i | 0.903606 | − | 0.521697i | ||||
\(503\) | − | 679.118i | − | 1.35014i | −0.737756 | − | 0.675068i | \(-0.764114\pi\) | ||
0.737756 | − | 0.675068i | \(-0.235886\pi\) | |||||||
\(504\) | 86.3322 | + | 60.5152i | 0.171294 | + | 0.120070i | ||||
\(505\) | − | 80.6454i | − | 0.159694i | ||||||
\(506\) | −509.058 | − | 271.251i | −1.00604 | − | 0.536069i | ||||
\(507\) | 343.698 | + | 15.0927i | 0.677906 | + | 0.0297687i | ||||
\(508\) | −86.6391 | + | 150.063i | −0.170549 | + | 0.295400i | ||||
\(509\) | 13.7527 | − | 23.8204i | 0.0270191 | − | 0.0467985i | −0.852200 | − | 0.523217i | \(-0.824732\pi\) |
0.879219 | + | 0.476418i | \(0.158065\pi\) | |||||||
\(510\) | 5.14060 | − | 8.06465i | 0.0100796 | − | 0.0158130i | ||||
\(511\) | 287.285 | − | 165.864i | 0.562202 | − | 0.324587i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 64.4086 | − | 486.399i | 0.125553 | − | 0.948146i | ||||
\(514\) | 536.956 | 1.04466 | ||||||||
\(515\) | −10.1255 | − | 17.5380i | −0.0196612 | − | 0.0340543i | ||||
\(516\) | 66.2523 | + | 42.2308i | 0.128396 | + | 0.0818427i | ||||
\(517\) | −401.322 | − | 231.704i | −0.776252 | − | 0.448169i | ||||
\(518\) | −113.801 | + | 197.109i | −0.219693 | + | 0.380519i | ||||
\(519\) | 193.759 | + | 8.50850i | 0.373332 | + | 0.0163940i | ||||
\(520\) | −17.7039 | + | 10.2213i | −0.0340459 | + | 0.0196564i | ||||
\(521\) | 113.084i | 0.217051i | 0.994094 | + | 0.108526i | \(0.0346130\pi\) | ||||
−0.994094 | + | 0.108526i | \(0.965387\pi\) | |||||||
\(522\) | 400.040 | + | 35.2016i | 0.766360 | + | 0.0674359i | ||||
\(523\) | 572.847i | 1.09531i | 0.836704 | + | 0.547655i | \(0.184479\pi\) | ||||
−0.836704 | + | 0.547655i | \(0.815521\pi\) | |||||||
\(524\) | −19.4000 | − | 33.6017i | −0.0370228 | − | 0.0641254i | ||||
\(525\) | 264.964 | − | 137.847i | 0.504693 | − | 0.262565i | ||||
\(526\) | −109.266 | − | 63.0849i | −0.207731 | − | 0.119933i | ||||
\(527\) | −38.9332 | − | 22.4781i | −0.0738771 | − | 0.0426529i | ||||
\(528\) | 188.782 | − | 98.2136i | 0.357542 | − | 0.186011i | ||||
\(529\) | 527.776 | − | 35.9634i | 0.997686 | − | 0.0679837i | ||||
\(530\) | −80.7620 | −0.152381 | ||||||||
\(531\) | −284.250 | − | 25.0126i | −0.535311 | − | 0.0471047i | ||||
\(532\) | 150.525 | 0.282941 | ||||||||
\(533\) | 56.8664 | + | 98.4955i | 0.106691 | + | 0.184795i | ||||
\(534\) | −5.20932 | + | 118.629i | −0.00975529 | + | 0.222152i | ||||
\(535\) | 95.2004 | − | 164.892i | 0.177945 | − | 0.308209i | ||||
\(536\) | 261.099 | + | 150.746i | 0.487125 | + | 0.281242i | ||||
\(537\) | −173.040 | + | 271.467i | −0.322234 | + | 0.505526i | ||||
\(538\) | 193.334 | + | 334.864i | 0.359356 | + | 0.622423i | ||||
\(539\) | − | 564.753i | − | 1.04778i | ||||||
\(540\) | 48.9376 | − | 20.2274i | 0.0906252 | − | 0.0374582i | ||||
\(541\) | 432.206 | 0.798902 | 0.399451 | − | 0.916755i | \(-0.369201\pi\) | ||||
0.399451 | + | 0.916755i | \(0.369201\pi\) | |||||||
\(542\) | 278.876 | + | 483.028i | 0.514532 | + | 0.891195i | ||||
\(543\) | −319.041 | − | 203.364i | −0.587552 | − | 0.374519i | ||||
\(544\) | −11.2615 | − | 6.50184i | −0.0207013 | − | 0.0119519i | ||||
\(545\) | 9.77060 | − | 16.9232i | 0.0179277 | − | 0.0310517i | ||||
\(546\) | −5.68167 | + | 129.386i | −0.0104060 | + | 0.236970i | ||||
\(547\) | −359.375 | − | 622.455i | −0.656992 | − | 1.13794i | −0.981390 | − | 0.192023i | \(-0.938495\pi\) |
0.324398 | − | 0.945921i | \(-0.394838\pi\) | |||||||
\(548\) | − | 453.391i | − | 0.827355i | ||||||
\(549\) | −232.787 | − | 163.174i | −0.424021 | − | 0.297220i | ||||
\(550\) | − | 602.858i | − | 1.09611i | ||||||
\(551\) | 496.541 | − | 286.678i | 0.901163 | − | 0.520287i | ||||
\(552\) | −99.2435 | + | 168.044i | −0.179789 | + | 0.304427i | ||||
\(553\) | 168.653 | − | 292.115i | 0.304978 | − | 0.528237i | ||||
\(554\) | 60.3653 | − | 104.556i | 0.108963 | − | 0.188729i | ||||
\(555\) | 52.7596 | + | 101.412i | 0.0950624 | + | 0.182725i | ||||
\(556\) | 66.5282 | + | 115.230i | 0.119655 | + | 0.207248i | ||||
\(557\) | 856.179i | 1.53713i | 0.639775 | + | 0.768563i | \(0.279028\pi\) | ||||
−0.639775 | + | 0.768563i | \(0.720972\pi\) | |||||||
\(558\) | −105.084 | − | 225.649i | −0.188322 | − | 0.404389i | ||||
\(559\) | 96.5126i | 0.172652i | ||||||||
\(560\) | 8.12273 | + | 14.0690i | 0.0145049 | + | 0.0251232i | ||||
\(561\) | −122.177 | − | 5.36511i | −0.217784 | − | 0.00956348i | ||||
\(562\) | 101.204 | + | 58.4301i | 0.180078 | + | 0.103968i | ||||
\(563\) | 63.4352 | + | 36.6243i | 0.112673 | + | 0.0650521i | 0.555278 | − | 0.831665i | \(-0.312612\pi\) |
−0.442604 | + | 0.896717i | \(0.645945\pi\) | |||||||
\(564\) | −84.2767 | + | 132.215i | −0.149427 | + | 0.234423i | ||||
\(565\) | −40.4822 | − | 70.1172i | −0.0716499 | − | 0.124101i | ||||
\(566\) | − | 71.1862i | − | 0.125771i | ||||||
\(567\) | 58.5865 | − | 330.319i | 0.103327 | − | 0.582573i | ||||
\(568\) | 320.505 | 0.564269 | ||||||||
\(569\) | −397.300 | + | 229.381i | −0.698242 | + | 0.403130i | −0.806692 | − | 0.590972i | \(-0.798745\pi\) |
0.108450 | + | 0.994102i | \(0.465411\pi\) | |||||||
\(570\) | 40.6374 | − | 63.7525i | 0.0712936 | − | 0.111847i | ||||
\(571\) | 173.760 | + | 100.320i | 0.304308 | + | 0.175692i | 0.644377 | − | 0.764708i | \(-0.277117\pi\) |
−0.340068 | + | 0.940401i | \(0.610450\pi\) | |||||||
\(572\) | 226.386 | + | 130.704i | 0.395779 | + | 0.228503i | ||||
\(573\) | 19.0156 | − | 433.031i | 0.0331860 | − | 0.755726i | ||||
\(574\) | 78.2729 | − | 45.1909i | 0.136364 | − | 0.0787298i | ||||
\(575\) | 292.567 | + | 469.132i | 0.508812 | + | 0.815881i | ||||
\(576\) | −30.3957 | − | 65.2694i | −0.0527703 | − | 0.113315i | ||||
\(577\) | −633.369 | −1.09769 | −0.548847 | − | 0.835923i | \(-0.684933\pi\) | ||||
−0.548847 | + | 0.835923i | \(0.684933\pi\) | |||||||
\(578\) | −200.617 | − | 347.479i | −0.347089 | − | 0.601175i | ||||
\(579\) | 9.08787 | + | 17.4684i | 0.0156958 | + | 0.0301699i | ||||
\(580\) | 53.5895 | + | 30.9399i | 0.0923957 | + | 0.0533447i | ||||
\(581\) | 153.296 | − | 265.516i | 0.263848 | − | 0.456998i | ||||
\(582\) | 629.007 | − | 327.239i | 1.08077 | − | 0.562267i | ||||
\(583\) | 516.367 | + | 894.373i | 0.885706 | + | 1.53409i | ||||
\(584\) | −226.545 | −0.387919 | ||||||||
\(585\) | 53.2655 | + | 37.3368i | 0.0910522 | + | 0.0638236i | ||||
\(586\) | − | 247.888i | − | 0.423016i | ||||||
\(587\) | 93.3024 | + | 161.604i | 0.158948 | + | 0.275306i | 0.934490 | − | 0.355991i | \(-0.115856\pi\) |
−0.775542 | + | 0.631296i | \(0.782523\pi\) | |||||||
\(588\) | −190.896 | − | 8.38277i | −0.324653 | − | 0.0142564i | ||||
\(589\) | −307.774 | − | 177.693i | −0.522537 | − | 0.301687i | ||||
\(590\) | −38.0783 | − | 21.9845i | −0.0645394 | − | 0.0372619i | ||||
\(591\) | 142.540 | − | 223.619i | 0.241185 | − | 0.378374i | ||||
\(592\) | 134.610 | − | 77.7170i | 0.227381 | − | 0.131279i | ||||
\(593\) | 575.370 | 0.970270 | 0.485135 | − | 0.874439i | \(-0.338771\pi\) | ||||
0.485135 | + | 0.874439i | \(0.338771\pi\) | |||||||
\(594\) | −536.894 | − | 412.617i | −0.903862 | − | 0.694641i | ||||
\(595\) | − | 9.33606i | − | 0.0156909i | ||||||
\(596\) | 273.115 | − | 157.683i | 0.458247 | − | 0.264569i | ||||
\(597\) | 383.585 | + | 244.506i | 0.642521 | + | 0.409558i | ||||
\(598\) | −239.599 | + | 8.15385i | −0.400668 | + | 0.0136352i | ||||
\(599\) | −109.208 | + | 189.154i | −0.182318 | + | 0.315783i | −0.942669 | − | 0.333728i | \(-0.891693\pi\) |
0.760352 | + | 0.649511i | \(0.225027\pi\) | |||||||
\(600\) | −203.776 | − | 8.94836i | −0.339627 | − | 0.0149139i | ||||
\(601\) | 55.2942 | + | 95.7724i | 0.0920037 | + | 0.159355i | 0.908354 | − | 0.418202i | \(-0.137340\pi\) |
−0.816350 | + | 0.577557i | \(0.804006\pi\) | |||||||
\(602\) | 76.6972 | 0.127404 | ||||||||
\(603\) | 84.0922 | − | 955.647i | 0.139456 | − | 1.58482i | ||||
\(604\) | −121.445 | −0.201068 | ||||||||
\(605\) | 164.308 | − | 94.8632i | 0.271583 | − | 0.156799i | ||||
\(606\) | 161.033 | + | 309.531i | 0.265730 | + | 0.510776i | ||||
\(607\) | −129.011 | + | 223.454i | −0.212539 | + | 0.368128i | −0.952508 | − | 0.304512i | \(-0.901507\pi\) |
0.739970 | + | 0.672640i | \(0.234840\pi\) | |||||||
\(608\) | −89.0244 | − | 51.3983i | −0.146422 | − | 0.0845366i | ||||
\(609\) | 347.778 | − | 180.931i | 0.571064 | − | 0.297095i | ||||
\(610\) | −21.9022 | − | 37.9358i | −0.0359053 | − | 0.0621899i | ||||
\(611\) | −192.603 | −0.315225 | ||||||||
\(612\) | −3.62700 | + | 41.2182i | −0.00592647 | + | 0.0673500i | ||||
\(613\) | 224.415i | 0.366093i | 0.983104 | + | 0.183047i | \(0.0585959\pi\) | ||||
−0.983104 | + | 0.183047i | \(0.941404\pi\) | |||||||
\(614\) | 105.780 | + | 183.216i | 0.172280 | + | 0.298397i | ||||
\(615\) | 1.99151 | − | 45.3517i | 0.00323823 | − | 0.0737426i | ||||
\(616\) | 103.868 | − | 179.905i | 0.168617 | − | 0.292054i | ||||
\(617\) | 937.839 | + | 541.462i | 1.52000 | + | 0.877572i | 0.999722 | + | 0.0235744i | \(0.00750466\pi\) |
0.520277 | + | 0.853998i | \(0.325829\pi\) | |||||||
\(618\) | 73.8832 | + | 47.0949i | 0.119552 | + | 0.0762054i | ||||
\(619\) | −767.323 | + | 443.014i | −1.23962 | + | 0.715693i | −0.969016 | − | 0.246998i | \(-0.920556\pi\) |
−0.270601 | + | 0.962692i | \(0.587222\pi\) | |||||||
\(620\) | − | 38.3554i | − | 0.0618635i | ||||||
\(621\) | 618.042 | + | 60.5353i | 0.995237 | + | 0.0974803i | ||||
\(622\) | 427.693 | 0.687610 | ||||||||
\(623\) | 57.9585 | + | 100.387i | 0.0930313 | + | 0.161135i | ||||
\(624\) | 47.5404 | − | 74.5821i | 0.0761865 | − | 0.119523i | ||||
\(625\) | −276.902 | + | 479.609i | −0.443043 | + | 0.767374i | ||||
\(626\) | −655.801 | − | 378.627i | −1.04761 | − | 0.604835i | ||||
\(627\) | −965.830 | − | 42.4122i | −1.54040 | − | 0.0676431i | ||||
\(628\) | 469.114 | − | 270.843i | 0.746997 | − | 0.431279i | ||||
\(629\) | −89.3260 | −0.142013 | ||||||||
\(630\) | 29.6710 | − | 42.3293i | 0.0470969 | − | 0.0671894i | ||||
\(631\) | 885.523i | 1.40336i | 0.712490 | + | 0.701682i | \(0.247567\pi\) | ||||
−0.712490 | + | 0.701682i | \(0.752433\pi\) | |||||||
\(632\) | −199.492 | + | 115.177i | −0.315652 | + | 0.182242i | ||||
\(633\) | 517.827 | + | 995.346i | 0.818051 | + | 1.57243i | ||||
\(634\) | −376.303 | + | 651.776i | −0.593538 | + | 1.02804i | ||||
\(635\) | 73.5771 | + | 42.4798i | 0.115869 | + | 0.0668973i | ||||
\(636\) | 309.978 | − | 161.265i | 0.487387 | − | 0.253562i | ||||
\(637\) | −117.362 | − | 203.277i | −0.184242 | − | 0.319117i | ||||
\(638\) | − | 791.281i | − | 1.24025i | ||||||
\(639\) | −430.539 | − | 924.506i | −0.673770 | − | 1.44680i | ||||
\(640\) | − | 11.0944i | − | 0.0173350i | ||||||
\(641\) | 197.585 | − | 114.076i | 0.308245 | − | 0.177965i | −0.337896 | − | 0.941184i | \(-0.609715\pi\) |
0.646141 | + | 0.763218i | \(0.276382\pi\) | |||||||
\(642\) | −36.1392 | + | 822.978i | −0.0562916 | + | 1.28190i | ||||
\(643\) | −272.088 | − | 157.090i | −0.423154 | − | 0.244308i | 0.273272 | − | 0.961937i | \(-0.411894\pi\) |
−0.696426 | + | 0.717629i | \(0.745227\pi\) | |||||||
\(644\) | 6.47975 | + | 190.406i | 0.0100617 | + | 0.295661i | ||||
\(645\) | 20.7061 | − | 32.4840i | 0.0321024 | − | 0.0503628i | ||||
\(646\) | 29.5379 | + | 51.1612i | 0.0457243 | + | 0.0791969i | ||||
\(647\) | 477.050 | 0.737326 | 0.368663 | − | 0.929563i | \(-0.379816\pi\) | ||||
0.368663 | + | 0.929563i | \(0.379816\pi\) | |||||||
\(648\) | −147.441 | + | 175.355i | −0.227532 | + | 0.270609i | ||||
\(649\) | 562.248i | 0.866329i | ||||||||
\(650\) | −125.281 | − | 216.993i | −0.192740 | − | 0.333835i | ||||
\(651\) | −204.905 | − | 130.611i | −0.314754 | − | 0.200632i | ||||
\(652\) | −43.0670 | + | 74.5942i | −0.0660536 | + | 0.114408i | ||||
\(653\) | 176.505 | − | 305.716i | 0.270299 | − | 0.468171i | −0.698639 | − | 0.715474i | \(-0.746211\pi\) |
0.968938 | + | 0.247302i | \(0.0795441\pi\) | |||||||
\(654\) | −3.70903 | + | 84.4638i | −0.00567130 | + | 0.129150i | ||||
\(655\) | −16.4752 | + | 9.51194i | −0.0251529 | + | 0.0145221i | ||||
\(656\) | −61.7237 | −0.0940910 | ||||||||
\(657\) | 304.320 | + | 653.474i | 0.463197 | + | 0.994634i | ||||
\(658\) | 153.058i | 0.232612i | ||||||||
\(659\) | 237.660 | − | 137.213i | 0.360638 | − | 0.208214i | −0.308723 | − | 0.951152i | \(-0.599901\pi\) |
0.669361 | + | 0.742938i | \(0.266568\pi\) | |||||||
\(660\) | −48.1548 | − | 92.5614i | −0.0729619 | − | 0.140244i | ||||
\(661\) | −821.884 | − | 474.515i | −1.24339 | − | 0.717874i | −0.273611 | − | 0.961840i | \(-0.588218\pi\) |
−0.969784 | + | 0.243966i | \(0.921551\pi\) | |||||||
\(662\) | 382.042 | − | 661.717i | 0.577103 | − | 0.999572i | ||||
\(663\) | −45.0913 | + | 23.4586i | −0.0680109 | + | 0.0353825i | ||||
\(664\) | −181.327 | + | 104.689i | −0.273082 | + | 0.157664i | ||||
\(665\) | − | 73.8033i | − | 0.110982i | ||||||
\(666\) | −405.000 | − | 283.888i | −0.608108 | − | 0.426258i | ||||
\(667\) | 384.008 | + | 615.758i | 0.575724 | + | 0.923176i | ||||
\(668\) | 156.503 | + | 271.072i | 0.234286 | + | 0.405796i | ||||
\(669\) | −331.636 | − | 14.5630i | −0.495719 | − | 0.0217683i | ||||
\(670\) | 73.9117 | − | 128.019i | 0.110316 | − | 0.191073i | ||||
\(671\) | −280.072 | + | 485.099i | −0.417395 | + | 0.722950i | ||||
\(672\) | −59.2693 | − | 37.7796i | −0.0881984 | − | 0.0562197i | ||||
\(673\) | −522.394 | − | 904.812i | −0.776216 | − | 1.34445i | −0.934108 | − | 0.356990i | \(-0.883803\pi\) |
0.157892 | − | 0.987456i | \(-0.449530\pi\) | |||||||
\(674\) | 320.942i | 0.476175i | ||||||||
\(675\) | 247.924 | + | 599.819i | 0.367294 | + | 0.888620i | ||||
\(676\) | −229.353 | −0.339280 | ||||||||
\(677\) | −846.999 | + | 489.015i | −1.25111 | + | 0.722327i | −0.971329 | − | 0.237738i | \(-0.923594\pi\) |
−0.279777 | + | 0.960065i | \(0.590261\pi\) | |||||||
\(678\) | 295.387 | + | 188.287i | 0.435674 | + | 0.277709i | ||||
\(679\) | 346.080 | − | 599.429i | 0.509691 | − | 0.882811i | ||||
\(680\) | −3.18790 | + | 5.52161i | −0.00468809 | + | 0.00812001i | ||||
\(681\) | −56.9943 | + | 1297.90i | −0.0836921 | + | 1.90587i | ||||
\(682\) | −424.755 | + | 245.232i | −0.622808 | + | 0.359578i | ||||
\(683\) | −659.173 | −0.965114 | −0.482557 | − | 0.875865i | \(-0.660292\pi\) | ||||
−0.482557 | + | 0.875865i | \(0.660292\pi\) | |||||||
\(684\) | −28.6721 | + | 325.837i | −0.0419182 | + | 0.476370i | ||||
\(685\) | −222.301 | −0.324527 | ||||||||
\(686\) | −410.092 | + | 236.767i | −0.597802 | + | 0.345141i | ||||
\(687\) | 379.509 | − | 197.439i | 0.552415 | − | 0.287393i | ||||
\(688\) | −45.3608 | − | 26.1891i | −0.0659314 | − | 0.0380655i | ||||
\(689\) | 371.722 | + | 214.614i | 0.539509 | + | 0.311486i | ||||
\(690\) | 82.3931 | + | 48.6598i | 0.119410 | + | 0.0705215i | ||||
\(691\) | −418.142 | − | 724.243i | −0.605126 | − | 1.04811i | −0.992032 | − | 0.125989i | \(-0.959790\pi\) |
0.386906 | − | 0.922119i | \(-0.373544\pi\) | |||||||
\(692\) | −129.297 | −0.186846 | ||||||||
\(693\) | −658.470 | − | 57.9421i | −0.950173 | − | 0.0836105i | ||||
\(694\) | −263.774 | −0.380077 | ||||||||
\(695\) | 56.4982 | − | 32.6192i | 0.0812923 | − | 0.0469342i | ||||
\(696\) | −267.466 | − | 11.7452i | −0.384291 | − | 0.0168752i | ||||
\(697\) | 30.7195 | + | 17.7359i | 0.0440739 | + | 0.0254461i | ||||
\(698\) | 339.628 | − | 588.254i | 0.486574 | − | 0.842770i | ||||
\(699\) | 611.115 | − | 958.726i | 0.874270 | − | 1.37157i | ||||
\(700\) | −172.441 | + | 99.5587i | −0.246344 | + | 0.142227i | ||||
\(701\) | 790.817i | 1.12813i | 0.825732 | + | 0.564063i | \(0.190763\pi\) | ||||
−0.825732 | + | 0.564063i | \(0.809237\pi\) | |||||||
\(702\) | −278.996 | − | 36.9445i | −0.397430 | − | 0.0526275i | ||||
\(703\) | −706.138 | −1.00446 | ||||||||
\(704\) | −122.861 | + | 70.9340i | −0.174519 | + | 0.100759i | ||||
\(705\) | 64.8257 | + | 41.3215i | 0.0919514 | + | 0.0586120i | ||||
\(706\) | 428.178 | − | 741.626i | 0.606485 | − | 1.05046i | ||||
\(707\) | 294.976 | + | 170.304i | 0.417221 | + | 0.240883i | ||||
\(708\) | 190.049 | + | 8.34557i | 0.268431 | + | 0.0117875i | ||||
\(709\) | 29.7784 | − | 17.1926i | 0.0420006 | − | 0.0242491i | −0.478853 | − | 0.877895i | \(-0.658947\pi\) |
0.520853 | + | 0.853646i | \(0.325614\pi\) | |||||||
\(710\) | − | 157.146i | − | 0.221332i | ||||||
\(711\) | 600.211 | + | 420.722i | 0.844178 | + | 0.591732i | ||||
\(712\) | − | 79.1623i | − | 0.111183i | ||||||
\(713\) | 211.524 | − | 396.968i | 0.296668 | − | 0.556757i | ||||
\(714\) | 18.6422 | + | 35.8333i | 0.0261095 | + | 0.0501868i | ||||
\(715\) | 64.0850 | − | 110.999i | 0.0896294 | − | 0.155243i | ||||
\(716\) | 107.309 | − | 185.865i | 0.149873 | − | 0.259588i | ||||
\(717\) | 69.4092 | + | 133.416i | 0.0968050 | + | 0.186075i | ||||
\(718\) | −145.103 | + | 83.7755i | −0.202094 | + | 0.116679i | ||||
\(719\) | 519.100 | 0.721975 | 0.360988 | − | 0.932571i | \(-0.382440\pi\) | ||||
0.360988 | + | 0.932571i | \(0.382440\pi\) | |||||||
\(720\) | −32.0021 | + | 14.9032i | −0.0444473 | + | 0.0206989i | ||||
\(721\) | 85.5311 | 0.118628 | ||||||||
\(722\) | −21.7629 | − | 37.6945i | −0.0301426 | − | 0.0522085i | ||||
\(723\) | 47.3823 | − | 1079.01i | 0.0655357 | − | 1.49241i | ||||
\(724\) | 218.437 | + | 126.115i | 0.301708 | + | 0.174191i | ||||
\(725\) | −379.225 | + | 656.836i | −0.523068 | + | 0.905981i | ||||
\(726\) | −441.218 | + | 692.190i | −0.607739 | + | 0.953430i | ||||
\(727\) | −556.190 | + | 321.116i | −0.765048 | + | 0.441701i | −0.831105 | − | 0.556115i | \(-0.812291\pi\) |
0.0660573 | + | 0.997816i | \(0.478958\pi\) | |||||||
\(728\) | − | 86.3401i | − | 0.118599i | ||||||
\(729\) | 703.875 | + | 189.740i | 0.965535 | + | 0.260275i | ||||
\(730\) | 111.076i | 0.152159i | ||||||||
\(731\) | 15.0505 | + | 26.0683i | 0.0205890 | + | 0.0356611i | ||||
\(732\) | 159.815 | + | 101.870i | 0.218326 | + | 0.139166i | ||||
\(733\) | −423.779 | − | 244.669i | −0.578143 | − | 0.333791i | 0.182252 | − | 0.983252i | \(-0.441661\pi\) |
−0.760395 | + | 0.649461i | \(0.774995\pi\) | |||||||
\(734\) | −362.783 | − | 209.453i | −0.494254 | − | 0.285358i | ||||
\(735\) | −4.11013 | + | 93.5978i | −0.00559201 | + | 0.127344i | ||||
\(736\) | 61.1839 | − | 114.824i | 0.0831303 | − | 0.156011i | ||||
\(737\) | −1890.27 | −2.56482 | ||||||||
\(738\) | 82.9143 | + | 178.044i | 0.112350 | + | 0.241252i | ||||
\(739\) | −1308.76 | −1.77099 | −0.885493 | − | 0.464653i | \(-0.846179\pi\) | ||||
−0.885493 | + | 0.464653i | \(0.846179\pi\) | |||||||
\(740\) | −38.1052 | − | 66.0002i | −0.0514935 | − | 0.0891894i | ||||
\(741\) | −356.455 | + | 185.445i | −0.481045 | + | 0.250263i | ||||
\(742\) | 170.550 | − | 295.402i | 0.229852 | − | 0.398116i | ||||
\(743\) | −912.093 | − | 526.597i | −1.22758 | − | 0.708745i | −0.261058 | − | 0.965323i | \(-0.584071\pi\) |
−0.966523 | + | 0.256579i | \(0.917405\pi\) | |||||||
\(744\) | 76.5879 | + | 147.214i | 0.102941 | + | 0.197869i | ||||
\(745\) | −77.3132 | − | 133.910i | −0.103776 | − | 0.179745i | ||||
\(746\) | 683.654i | 0.916426i | ||||||||
\(747\) | 545.557 | + | 382.412i | 0.730331 | + | 0.511930i | ||||
\(748\) | 81.5297 | 0.108997 | ||||||||
\(749\) | 402.082 | + | 696.426i | 0.536825 | + | 0.929808i | ||||
\(750\) | −8.95040 | + | 203.823i | −0.0119339 | + | 0.271764i | ||||
\(751\) | 311.585 | + | 179.894i | 0.414894 | + | 0.239539i | 0.692890 | − | 0.721043i | \(-0.256337\pi\) |
−0.277996 | + | 0.960582i | \(0.589670\pi\) | |||||||
\(752\) | 52.2635 | − | 90.5230i | 0.0694993 | − | 0.120376i | ||||
\(753\) | 936.954 | + | 597.236i | 1.24429 | + | 0.793143i | ||||
\(754\) | −164.437 | − | 284.813i | −0.218086 | − | 0.377737i | ||||
\(755\) | 59.5453i | 0.0788679i | ||||||||
\(756\) | −29.3592 | + | 221.714i | −0.0388350 | + | 0.293272i | ||||
\(757\) | 959.578i | 1.26761i | 0.773494 | + | 0.633803i | \(0.218507\pi\) | ||||
−0.773494 | + | 0.633803i | \(0.781493\pi\) | |||||||
\(758\) | 233.365 | − | 134.733i | 0.307869 | − | 0.177748i | ||||
\(759\) | 12.0724 | − | 1223.55i | 0.0159057 | − | 1.61206i | ||||
\(760\) | −25.2009 | + | 43.6493i | −0.0331591 | + | 0.0574333i | ||||
\(761\) | −168.738 | + | 292.263i | −0.221732 | + | 0.384051i | −0.955334 | − | 0.295528i | \(-0.904504\pi\) |
0.733602 | + | 0.679580i | \(0.237838\pi\) | |||||||
\(762\) | −367.225 | − | 16.1258i | −0.481922 | − | 0.0211625i | ||||
\(763\) | 41.2664 | + | 71.4755i | 0.0540844 | + | 0.0936769i | ||||
\(764\) | 288.966i | 0.378227i | ||||||||
\(765\) | 20.2096 | + | 1.77834i | 0.0264178 | + | 0.00232463i | ||||
\(766\) | 114.831i | 0.149910i | ||||||||
\(767\) | 116.841 | + | 202.375i | 0.152336 | + | 0.263853i | ||||
\(768\) | 22.1532 | + | 42.5821i | 0.0288454 | + | 0.0554454i | ||||
\(769\) | 139.064 | + | 80.2884i | 0.180837 | + | 0.104406i | 0.587686 | − | 0.809089i | \(-0.300039\pi\) |
−0.406849 | + | 0.913495i | \(0.633372\pi\) | |||||||
\(770\) | −88.2089 | − | 50.9274i | −0.114557 | − | 0.0661395i | ||||
\(771\) | 525.704 | + | 1010.49i | 0.681847 | + | 1.31062i | ||||
\(772\) | −6.56364 | − | 11.3686i | −0.00850213 | − | 0.0147261i | ||||
\(773\) | − | 1183.13i | − | 1.53057i | −0.643693 | − | 0.765284i | \(-0.722598\pi\) | ||
0.643693 | − | 0.765284i | \(-0.277402\pi\) | |||||||
\(774\) | −14.6094 | + | 166.025i | −0.0188751 | + | 0.214502i | ||||
\(775\) | 470.114 | 0.606599 | ||||||||
\(776\) | −409.363 | + | 236.346i | −0.527530 | + | 0.304570i | ||||
\(777\) | −482.351 | − | 21.1813i | −0.620786 | − | 0.0272604i | ||||
\(778\) | 367.156 | + | 211.978i | 0.471923 | + | 0.272465i | ||||
\(779\) | 242.843 | + | 140.206i | 0.311737 | + | 0.179982i | ||||
\(780\) | −36.5682 | − | 23.3094i | −0.0468822 | − | 0.0298839i | ||||
\(781\) | −1740.26 | + | 1004.74i | −2.22825 | + | 1.28648i | ||||
\(782\) | −63.4448 | + | 39.5663i | −0.0811314 | + | 0.0505963i | ||||
\(783\) | 325.412 | + | 787.292i | 0.415596 | + | 1.00548i | ||||
\(784\) | 127.387 | 0.162483 | ||||||||
\(785\) | −132.796 | − | 230.010i | −0.169167 | − | 0.293007i | ||||
\(786\) | 44.2410 | − | 69.4060i | 0.0562863 | − | 0.0883028i | ||||
\(787\) | 102.736 | + | 59.3144i | 0.130541 | + | 0.0753677i | 0.563848 | − | 0.825878i | \(-0.309320\pi\) |
−0.433308 | + | 0.901246i | \(0.642654\pi\) | |||||||
\(788\) | −88.3951 | + | 153.105i | −0.112177 | + | 0.194295i | ||||
\(789\) | 11.7418 | − | 267.389i | 0.0148818 | − | 0.338896i | ||||
\(790\) | 56.4719 | + | 97.8123i | 0.0714835 | + | 0.123813i | ||||
\(791\) | 341.956 | 0.432308 | ||||||||
\(792\) | 369.652 | + | 259.110i | 0.466733 | + | 0.327160i | ||||
\(793\) | 232.809i | 0.293580i | ||||||||
\(794\) | −190.176 | − | 329.395i | −0.239516 | − | 0.414855i | ||||
\(795\) | −79.0695 | − | 151.984i | −0.0994585 | − | 0.191175i | ||||
\(796\) | −262.628 | − | 151.628i | −0.329935 | − | 0.190488i | ||||
\(797\) | −55.9196 | − | 32.2852i | −0.0701626 | − | 0.0405084i | 0.464508 | − | 0.885569i | \(-0.346231\pi\) |
−0.534671 | + | 0.845060i | \(0.679564\pi\) | |||||||
\(798\) | 147.370 | + | 283.269i | 0.184674 | + | 0.354974i | ||||
\(799\) | −52.0224 | + | 30.0351i | −0.0651094 | + | 0.0375909i | ||||
\(800\) | 135.982 | 0.169977 | ||||||||
\(801\) | −228.346 | + | 106.340i | −0.285076 | + | 0.132759i | ||||
\(802\) | − | 360.674i | − | 0.449719i | ||||||
\(803\) | 1230.08 | − | 710.188i | 1.53186 | − | 0.884418i | ||||
\(804\) | −28.0577 | + | 638.944i | −0.0348977 | + | 0.794706i | ||||
\(805\) | 93.3574 | − | 3.17707i | 0.115972 | − | 0.00394667i | ||||
\(806\) | −101.924 | + | 176.538i | −0.126457 | + | 0.219029i | ||||
\(807\) | −440.891 | + | 691.677i | −0.546334 | + | 0.857097i | ||||
\(808\) | −116.304 | − | 201.445i | −0.143941 | − | 0.249313i | ||||
\(809\) | −51.5548 | −0.0637266 | −0.0318633 | − | 0.999492i | \(-0.510144\pi\) | ||||
−0.0318633 | + | 0.999492i | \(0.510144\pi\) | |||||||
\(810\) | 85.9777 | + | 72.2912i | 0.106145 | + | 0.0892484i | ||||
\(811\) | −426.794 | −0.526257 | −0.263128 | − | 0.964761i | \(-0.584754\pi\) | ||||
−0.263128 | + | 0.964761i | \(0.584754\pi\) | |||||||
\(812\) | −226.337 | + | 130.676i | −0.278740 | + | 0.160931i | ||||
\(813\) | −635.968 | + | 997.717i | −0.782249 | + | 1.22720i | ||||
\(814\) | −487.265 | + | 843.969i | −0.598606 | + | 1.03682i | ||||
\(815\) | 36.5741 | + | 21.1160i | 0.0448761 | + | 0.0259093i | ||||
\(816\) | 1.21016 | − | 27.5584i | 0.00148304 | − | 0.0337726i | ||||
\(817\) | 118.977 | + | 206.075i | 0.145627 | + | 0.252233i | ||||
\(818\) | −529.444 | −0.647242 | ||||||||
\(819\) | −249.051 | + | 115.982i | −0.304091 | + | 0.141614i | ||||
\(820\) | 30.2636i | 0.0369068i | ||||||||
\(821\) | −343.710 | − | 595.324i | −0.418649 | − | 0.725121i | 0.577155 | − | 0.816634i | \(-0.304163\pi\) |
−0.995804 | + | 0.0915139i | \(0.970829\pi\) | |||||||
\(822\) | 853.227 | − | 443.889i | 1.03799 | − | 0.540012i | ||||
\(823\) | 551.081 | − | 954.500i | 0.669600 | − | 1.15978i | −0.308416 | − | 0.951252i | \(-0.599799\pi\) |
0.978016 | − | 0.208530i | \(-0.0668679\pi\) | |||||||
\(824\) | −50.5855 | − | 29.2055i | −0.0613901 | − | 0.0354436i | ||||
\(825\) | 1134.51 | − | 590.224i | 1.37516 | − | 0.715423i | ||||
\(826\) | 160.825 | − | 92.8522i | 0.194703 | − | 0.112412i | ||||
\(827\) | − | 553.746i | − | 0.669584i | −0.942292 | − | 0.334792i | \(-0.891334\pi\) | ||
0.942292 | − | 0.334792i | \(-0.108666\pi\) | |||||||
\(828\) | −413.402 | − | 22.2422i | −0.499278 | − | 0.0268625i | ||||
\(829\) | −1423.73 | −1.71740 | −0.858701 | − | 0.512477i | \(-0.828728\pi\) | ||||
−0.858701 | + | 0.512477i | \(0.828728\pi\) | |||||||
\(830\) | 51.3298 | + | 88.9058i | 0.0618431 | + | 0.107115i | ||||
\(831\) | 255.862 | + | 11.2356i | 0.307896 | + | 0.0135206i | ||||
\(832\) | −29.4818 | + | 51.0640i | −0.0354348 | + | 0.0613749i | ||||
\(833\) | −63.3996 | − | 36.6038i | −0.0761100 | − | 0.0439421i | ||||
\(834\) | −151.715 | + | 238.013i | −0.181913 | + | 0.285388i | ||||
\(835\) | 132.908 | − | 76.7347i | 0.159172 | − | 0.0918979i | ||||
\(836\) | 644.507 | 0.770942 | ||||||||
\(837\) | 321.762 | − | 418.675i | 0.384423 | − | 0.500209i | ||||
\(838\) | − | 792.064i | − | 0.945183i | ||||||
\(839\) | 895.440 | − | 516.983i | 1.06727 | − | 0.616189i | 0.139836 | − | 0.990175i | \(-0.455342\pi\) |
0.927435 | + | 0.373985i | \(0.122009\pi\) | |||||||
\(840\) | −18.5236 | + | 29.0602i | −0.0220519 | + | 0.0345954i | ||||
\(841\) | −77.2509 | + | 133.802i | −0.0918560 | + | 0.159099i | ||||
\(842\) | 158.634 | + | 91.5873i | 0.188401 | + | 0.108773i | ||||
\(843\) | −10.8754 | + | 247.659i | −0.0129008 | + | 0.293783i | ||||
\(844\) | −373.996 | − | 647.780i | −0.443123 | − | 0.767512i | ||||
\(845\) | 112.453i | 0.133081i | ||||||||
\(846\) | −331.322 | − | 29.1547i | −0.391634 | − | 0.0344619i | ||||
\(847\) | 801.315i | 0.946063i | ||||||||
\(848\) | −201.736 | + | 116.473i | −0.237897 | + | 0.137350i | ||||
\(849\) | 133.964 | − | 69.6945i | 0.157790 | − | 0.0820901i | ||||
\(850\) | −67.6772 | − | 39.0735i | −0.0796203 | − | 0.0459688i | ||||
\(851\) | −30.3977 | − | 893.229i | −0.0357199 | − | 1.04962i | ||||
\(852\) | 313.788 | + | 603.152i | 0.368296 | + | 0.707925i | ||||
\(853\) | 419.879 | + | 727.252i | 0.492238 | + | 0.852581i | 0.999960 | − | 0.00893960i | \(-0.00284560\pi\) |
−0.507722 | + | 0.861521i | \(0.669512\pi\) | |||||||
\(854\) | 185.010 | 0.216639 | ||||||||
\(855\) | 159.760 | + | 14.0581i | 0.186854 | + | 0.0164423i | ||||
\(856\) | − | 549.181i | − | 0.641567i | ||||||
\(857\) | 73.7020 | + | 127.656i | 0.0860000 | + | 0.148956i | 0.905817 | − | 0.423669i | \(-0.139258\pi\) |
−0.819817 | + | 0.572626i | \(0.805925\pi\) | |||||||
\(858\) | −24.3274 | + | 553.996i | −0.0283537 | + | 0.645682i | ||||
\(859\) | −403.363 | + | 698.644i | −0.469572 | + | 0.813323i | −0.999395 | − | 0.0347856i | \(-0.988925\pi\) |
0.529823 | + | 0.848108i | \(0.322259\pi\) | |||||||
\(860\) | −12.8407 | + | 22.2407i | −0.0149310 | + | 0.0258613i | ||||
\(861\) | 161.676 | + | 103.056i | 0.187778 | + | 0.119694i | ||||
\(862\) | −281.315 | + | 162.417i | −0.326351 | + | 0.188419i | ||||
\(863\) | 1670.72 | 1.93595 | 0.967974 | − | 0.251051i | \(-0.0807761\pi\) | ||||
0.967974 | + | 0.251051i | \(0.0807761\pi\) | |||||||
\(864\) | 93.0705 | − | 121.103i | 0.107721 | − | 0.140165i | ||||
\(865\) | 63.3955i | 0.0732896i | ||||||||
\(866\) | −440.514 | + | 254.331i | −0.508677 | + | 0.293685i | ||||
\(867\) | 457.501 | − | 717.735i | 0.527683 | − | 0.827838i | ||||
\(868\) | 140.292 | + | 80.9976i | 0.161627 | + | 0.0933152i | ||||
\(869\) | 722.128 | − | 1250.76i | 0.830987 | − | 1.43931i | ||||
\(870\) | −5.75874 | + | 131.141i | −0.00661924 | + | 0.150736i | ||||
\(871\) | −680.384 | + | 392.820i | −0.781153 | + | 0.450999i | ||||
\(872\) | − | 56.3635i | − | 0.0646370i | ||||||
\(873\) | 1231.65 | + | 863.333i | 1.41082 | + | 0.988927i | ||||
\(874\) | −501.542 | + | 312.779i | −0.573847 | + | 0.357871i | ||||
\(875\) | 99.5814 | + | 172.480i | 0.113807 | + | 0.197120i | ||||
\(876\) | −221.797 | − | 426.330i | −0.253193 | − | 0.486678i | ||||
\(877\) | 534.311 | − | 925.454i | 0.609248 | − | 1.05525i | −0.382116 | − | 0.924114i | \(-0.624805\pi\) |
0.991365 | − | 0.131135i | \(-0.0418621\pi\) | |||||||
\(878\) | 367.943 | − | 637.296i | 0.419069 | − | 0.725850i | ||||
\(879\) | 466.495 | − | 242.693i | 0.530711 | − | 0.276101i | ||||
\(880\) | 34.7795 | + | 60.2398i | 0.0395221 | + | 0.0684543i | ||||
\(881\) | 1168.27i | 1.32608i | 0.748585 | + | 0.663038i | \(0.230733\pi\) | ||||
−0.748585 | + | 0.663038i | \(0.769267\pi\) | |||||||
\(882\) | −171.120 | − | 367.451i | −0.194014 | − | 0.416611i | ||||
\(883\) | −49.0517 | −0.0555512 | −0.0277756 | − | 0.999614i | \(-0.508842\pi\) | ||||
−0.0277756 | + | 0.999614i | \(0.508842\pi\) | |||||||
\(884\) | 29.3458 | − | 16.9428i | 0.0331966 | − | 0.0191661i | ||||
\(885\) | 4.09189 | − | 93.1825i | 0.00462361 | − | 0.105291i | ||||
\(886\) | 252.157 | − | 436.749i | 0.284602 | − | 0.492944i | ||||
\(887\) | −646.784 | + | 1120.26i | −0.729182 | + | 1.26298i | 0.228048 | + | 0.973650i | \(0.426766\pi\) |
−0.957229 | + | 0.289330i | \(0.906568\pi\) | |||||||
\(888\) | 278.043 | + | 177.231i | 0.313112 | + | 0.199585i | ||||
\(889\) | −310.755 | + | 179.415i | −0.349556 | + | 0.201816i | ||||
\(890\) | −38.8139 | −0.0436111 | ||||||||
\(891\) | 250.852 | − | 1414.34i | 0.281540 | − | 1.58736i | ||||
\(892\) | 221.304 | 0.248098 | ||||||||
\(893\) | −411.247 | + | 237.433i | −0.460522 | + | 0.265883i | ||||
\(894\) | 564.133 | + | 359.591i | 0.631021 | + | 0.402227i | ||||
\(895\) | −91.1309 | − | 52.6145i | −0.101822 | − | 0.0587871i | ||||
\(896\) | 40.5798 | + | 23.4287i | 0.0452899 | + | 0.0261481i | ||||
\(897\) | −249.923 | − | 442.914i | −0.278621 | − | 0.493773i | ||||
\(898\) | 171.048 | + | 296.264i | 0.190477 | + | 0.329915i | ||||
\(899\) | 617.048 | 0.686372 | ||||||||
\(900\) | −182.666 | − | 392.243i | −0.202962 | − | 0.435826i | ||||
\(901\) | 133.871 | 0.148580 | ||||||||
\(902\) | 335.145 | − | 193.496i | 0.371557 | − | 0.214519i | ||||
\(903\) | 75.0899 | + | 144.335i | 0.0831560 | + | 0.159839i | ||||
\(904\) | −202.242 | − | 116.765i | −0.223719 | − | 0.129164i | ||||
\(905\) | 61.8349 | − | 107.101i | 0.0683258 | − | 0.118344i | ||||
\(906\) | −118.900 | − | 228.545i | −0.131236 | − | 0.252257i | ||||
\(907\) | 300.597 | − | 173.550i | 0.331419 | − | 0.191345i | −0.325052 | − | 0.945696i | \(-0.605382\pi\) |
0.656471 | + | 0.754351i | \(0.272048\pi\) | |||||||
\(908\) | − | 866.101i | − | 0.953856i | ||||||
\(909\) | −424.841 | + | 606.088i | −0.467372 | + | 0.666763i | ||||
\(910\) | −42.3332 | −0.0465200 | ||||||||
\(911\) | 1457.94 | − | 841.744i | 1.60038 | − | 0.923978i | 0.608966 | − | 0.793196i | \(-0.291584\pi\) |
0.991411 | − | 0.130782i | \(-0.0417489\pi\) | |||||||
\(912\) | 9.56657 | − | 217.854i | 0.0104897 | − | 0.238875i | ||||
\(913\) | 656.373 | − | 1136.87i | 0.718919 | − | 1.24520i | ||||
\(914\) | −470.057 | − | 271.388i | −0.514286 | − | 0.296923i | ||||
\(915\) | 49.9474 | − | 78.3582i | 0.0545873 | − | 0.0856374i | ||||
\(916\) | −246.988 | + | 142.599i | −0.269637 | + | 0.155675i | ||||
\(917\) | − | 80.3480i | − | 0.0876205i | ||||||
\(918\) | −81.1187 | + | 33.5289i | −0.0883646 | + | 0.0365238i | ||||
\(919\) | − | 953.686i | − | 1.03774i | −0.854852 | − | 0.518872i | \(-0.826352\pi\) | ||
0.854852 | − | 0.518872i | \(-0.173648\pi\) | |||||||
\(920\) | −56.2990 | − | 29.9989i | −0.0611946 | − | 0.0326075i | ||||
\(921\) | −241.227 | + | 378.441i | −0.261919 | + | 0.410903i | ||||
\(922\) | −491.319 | + | 850.990i | −0.532884 | + | 0.922982i | ||||
\(923\) | −417.593 | + | 723.293i | −0.452431 | + | 0.783633i | ||||
\(924\) | 440.252 | + | 19.3326i | 0.476463 | + | 0.0209228i | ||||
\(925\) | 808.951 | − | 467.048i | 0.874542 | − | 0.504917i | ||||
\(926\) | −111.059 | −0.119934 | ||||||||
\(927\) | −16.2921 | + | 185.147i | −0.0175750 | + | 0.199728i | ||||
\(928\) | 178.483 | 0.192330 | ||||||||
\(929\) | 257.648 | + | 446.259i | 0.277339 | + | 0.480365i | 0.970722 | − | 0.240204i | \(-0.0772143\pi\) |
−0.693384 | + | 0.720568i | \(0.743881\pi\) | |||||||
\(930\) | 72.1803 | − | 37.5516i | 0.0776132 | − | 0.0403781i | ||||
\(931\) | −501.185 | − | 289.360i | −0.538330 | − | 0.310805i | ||||
\(932\) | −378.978 | + | 656.409i | −0.406628 | + | 0.704301i | ||||
\(933\) | 418.730 | + | 804.867i | 0.448800 | + | 0.862666i | ||||
\(934\) | 43.7965 | − | 25.2859i | 0.0468914 | − | 0.0270727i | ||||
\(935\) | − | 39.9746i | − | 0.0427536i | ||||||
\(936\) | 186.899 | + | 16.4462i | 0.199678 | + | 0.0175707i | ||||
\(937\) | − | 137.513i | − | 0.146759i | −0.997304 | − | 0.0733796i | \(-0.976622\pi\) | ||
0.997304 | − | 0.0733796i | \(-0.0233785\pi\) | |||||||
\(938\) | 312.168 | + | 540.691i | 0.332802 | + | 0.576430i | ||||
\(939\) | 70.4725 | − | 1604.83i | 0.0750505 | − | 1.70909i | ||||
\(940\) | −44.3841 | − | 25.6252i | −0.0472171 | − | 0.0272608i | ||||
\(941\) | −332.363 | − | 191.890i | −0.353202 | − | 0.203921i | 0.312893 | − | 0.949789i | \(-0.398702\pi\) |
−0.666095 | + | 0.745867i | \(0.732035\pi\) | |||||||
\(942\) | 968.978 | + | 617.649i | 1.02864 | + | 0.655679i | ||||
\(943\) | −166.899 | + | 313.220i | −0.176987 | + | 0.332153i | ||||
\(944\) | −126.822 | −0.134345 | ||||||||
\(945\) | 108.708 | + | 14.3950i | 0.115035 | + | 0.0152328i | ||||
\(946\) | 328.398 | 0.347143 | ||||||||
\(947\) | 299.242 | + | 518.303i | 0.315990 | + | 0.547310i | 0.979647 | − | 0.200726i | \(-0.0643301\pi\) |
−0.663658 | + | 0.748036i | \(0.730997\pi\) | |||||||
\(948\) | −412.060 | − | 262.657i | −0.434662 | − | 0.277064i | ||||
\(949\) | 295.170 | − | 511.250i | 0.311033 | − | 0.538725i | ||||
\(950\) | −535.001 | − | 308.883i | −0.563159 | − | 0.325140i | ||||
\(951\) | −1594.98 | − | 70.0399i | −1.67716 | − | 0.0736487i | ||||
\(952\) | −13.4642 | − | 23.3207i | −0.0141431 | − | 0.0244965i | ||||
\(953\) | 136.062i | 0.142772i | 0.997449 | + | 0.0713860i | \(0.0227422\pi\) | ||||
−0.997449 | + | 0.0713860i | \(0.977258\pi\) | |||||||
\(954\) | 606.964 | + | 425.455i | 0.636230 | + | 0.445970i | ||||
\(955\) | 141.682 | 0.148358 | ||||||||
\(956\) | −50.1302 | − | 86.8281i | −0.0524375 | − | 0.0908244i | ||||
\(957\) | 1489.10 | − | 774.698i | 1.55600 | − | 0.809507i | ||||
\(958\) | 842.030 | + | 486.146i | 0.878946 | + | 0.507460i | ||||
\(959\) | 469.447 | − | 813.106i | 0.489517 | − | 0.847869i | ||||
\(960\) | 20.8783 | − | 10.8619i | 0.0217482 | − | 0.0113145i | ||||
\(961\) | 289.265 | + | 501.022i | 0.301005 | + | 0.521355i | ||||
\(962\) | 405.037i | 0.421037i | ||||||||
\(963\) | −1584.13 | + | 737.722i | −1.64499 | + | 0.766067i | ||||
\(964\) | 720.035i | 0.746924i | ||||||||
\(965\) | −5.57409 | + | 3.21820i | −0.00577626 | + | 0.00333492i | ||||
\(966\) | −351.977 | + | 198.610i | −0.364366 | + | 0.205600i | ||||
\(967\) | −915.469 | + | 1585.64i | −0.946710 | + | 1.63975i | −0.194421 | + | 0.980918i | \(0.562283\pi\) |
−0.752290 | + | 0.658832i | \(0.771051\pi\) | |||||||
\(968\) | 273.618 | − | 473.920i | 0.282663 | − | 0.489587i | ||||
\(969\) | −67.3603 | + | 105.676i | −0.0695153 | + | 0.109057i | ||||
\(970\) | 115.882 | + | 200.714i | 0.119466 | + | 0.206921i | ||||
\(971\) | − | 1391.02i | − | 1.43256i | −0.697811 | − | 0.716282i | \(-0.745842\pi\) | ||
0.697811 | − | 0.716282i | \(-0.254158\pi\) | |||||||
\(972\) | −474.347 | − | 105.786i | −0.488012 | − | 0.108833i | ||||
\(973\) | 275.537i | 0.283183i | ||||||||
\(974\) | 171.540 | + | 297.115i | 0.176119 | + | 0.305046i | ||||
\(975\) | 285.699 | − | 448.209i | 0.293024 | − | 0.459701i | ||||
\(976\) | −109.420 | − | 63.1736i | −0.112110 | − | 0.0647270i | ||||
\(977\) | −1411.18 | − | 814.747i | −1.44441 | − | 0.833928i | −0.446266 | − | 0.894901i | \(-0.647246\pi\) |
−0.998139 | + | 0.0609728i | \(0.980580\pi\) | |||||||
\(978\) | −182.542 | − | 8.01590i | −0.186648 | − | 0.00819622i | ||||
\(979\) | 248.164 | + | 429.832i | 0.253487 | + | 0.439052i | ||||
\(980\) | − | 62.4587i | − | 0.0637333i | ||||||
\(981\) | −162.582 | + | 75.7138i | −0.165731 | + | 0.0771803i | ||||
\(982\) | 755.065 | 0.768906 | ||||||||
\(983\) | 1260.08 | − | 727.510i | 1.28188 | − | 0.740091i | 0.304685 | − | 0.952453i | \(-0.401449\pi\) |
0.977191 | + | 0.212362i | \(0.0681156\pi\) | |||||||
\(984\) | −60.4302 | − | 116.157i | −0.0614128 | − | 0.118045i | ||||
\(985\) | 75.0684 | + | 43.3408i | 0.0762116 | + | 0.0440008i | ||||
\(986\) | −88.8297 | − | 51.2858i | −0.0900910 | − | 0.0520140i | ||||
\(987\) | −288.038 | + | 149.851i | −0.291831 | + | 0.151825i | ||||
\(988\) | 231.984 | − | 133.936i | 0.234802 | − | 0.135563i | ||||
\(989\) | −255.552 | + | 159.371i | −0.258395 | + | 0.161144i | ||||
\(990\) | 127.044 | − | 181.243i | 0.128327 | − | 0.183074i | ||||
\(991\) | 33.3671 | 0.0336702 | 0.0168351 | − | 0.999858i | \(-0.494641\pi\) | ||||
0.0168351 | + | 0.999858i | \(0.494641\pi\) | |||||||
\(992\) | −55.3150 | − | 95.8084i | −0.0557611 | − | 0.0965811i | ||||
\(993\) | 1619.31 | + | 71.1082i | 1.63072 | + | 0.0716094i | ||||
\(994\) | 574.790 | + | 331.855i | 0.578260 | + | 0.333858i | ||||
\(995\) | −74.3445 | + | 128.768i | −0.0747181 | + | 0.129416i | ||||
\(996\) | −374.539 | − | 238.740i | −0.376043 | − | 0.239699i | ||||
\(997\) | −573.352 | − | 993.074i | −0.575077 | − | 0.996062i | −0.996033 | − | 0.0889814i | \(-0.971639\pi\) |
0.420957 | − | 0.907081i | \(-0.361694\pi\) | |||||||
\(998\) | −257.583 | −0.258099 | ||||||||
\(999\) | 137.729 | − | 1040.10i | 0.137867 | − | 1.04114i |
(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 | 414.3.h.a.229.18 | yes | 96 | |
3.2 | odd | 2 | 1242.3.h.a.91.45 | 96 | |||
9.2 | odd | 6 | 1242.3.h.a.505.46 | 96 | |||
9.7 | even | 3 | inner | 414.3.h.a.367.17 | yes | 96 | |
23.22 | odd | 2 | inner | 414.3.h.a.229.17 | ✓ | 96 | |
69.68 | even | 2 | 1242.3.h.a.91.46 | 96 | |||
207.137 | even | 6 | 1242.3.h.a.505.45 | 96 | |||
207.160 | odd | 6 | inner | 414.3.h.a.367.18 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
414.3.h.a.229.17 | ✓ | 96 | 23.22 | odd | 2 | inner | |
414.3.h.a.229.18 | yes | 96 | 1.1 | even | 1 | trivial | |
414.3.h.a.367.17 | yes | 96 | 9.7 | even | 3 | inner | |
414.3.h.a.367.18 | yes | 96 | 207.160 | odd | 6 | inner | |
1242.3.h.a.91.45 | 96 | 3.2 | odd | 2 | |||
1242.3.h.a.91.46 | 96 | 69.68 | even | 2 | |||
1242.3.h.a.505.45 | 96 | 207.137 | even | 6 | |||
1242.3.h.a.505.46 | 96 | 9.2 | odd | 6 |