Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(196,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.196");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 196.6 | ||
Character | \(\chi\) | \(=\) | 585.196 |
Dual form | 585.2.i.h.391.6 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.332241 | + | 0.575458i | −0.234930 | + | 0.406910i | −0.959252 | − | 0.282551i | \(-0.908819\pi\) |
0.724323 | + | 0.689461i | \(0.242153\pi\) | |||||||
\(3\) | −0.727463 | + | 1.57188i | −0.420001 | + | 0.907524i | ||||
\(4\) | 0.779232 | + | 1.34967i | 0.389616 | + | 0.674835i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | −0.662856 | − | 0.940866i | −0.270610 | − | 0.384107i | ||||
\(7\) | −1.40460 | + | 2.43283i | −0.530888 | + | 0.919525i | 0.468462 | + | 0.883484i | \(0.344808\pi\) |
−0.999350 | + | 0.0360416i | \(0.988525\pi\) | |||||||
\(8\) | −2.36453 | −0.835989 | ||||||||
\(9\) | −1.94159 | − | 2.28697i | −0.647198 | − | 0.762322i | ||||
\(10\) | −0.664482 | −0.210128 | ||||||||
\(11\) | −0.115146 | + | 0.199439i | −0.0347178 | + | 0.0601330i | −0.882862 | − | 0.469632i | \(-0.844387\pi\) |
0.848144 | + | 0.529765i | \(0.177720\pi\) | |||||||
\(12\) | −2.68838 | + | 0.243022i | −0.776068 | + | 0.0701543i | ||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | ||||
\(14\) | −0.933329 | − | 1.61657i | −0.249443 | − | 0.432048i | ||||
\(15\) | −1.72502 | + | 0.155937i | −0.445397 | + | 0.0402626i | ||||
\(16\) | −0.772870 | + | 1.33865i | −0.193217 | + | 0.334662i | ||||
\(17\) | −3.24172 | −0.786232 | −0.393116 | − | 0.919489i | \(-0.628603\pi\) | ||||
−0.393116 | + | 0.919489i | \(0.628603\pi\) | |||||||
\(18\) | 1.96113 | − | 0.357482i | 0.462243 | − | 0.0842593i | ||||
\(19\) | 3.80076 | 0.871954 | 0.435977 | − | 0.899958i | \(-0.356403\pi\) | ||||
0.435977 | + | 0.899958i | \(0.356403\pi\) | |||||||
\(20\) | −0.779232 | + | 1.34967i | −0.174242 | + | 0.301795i | ||||
\(21\) | −2.80232 | − | 3.97765i | −0.611517 | − | 0.867995i | ||||
\(22\) | −0.0765124 | − | 0.132523i | −0.0163125 | − | 0.0282541i | ||||
\(23\) | 1.25026 | + | 2.16552i | 0.260698 | + | 0.451542i | 0.966428 | − | 0.256939i | \(-0.0827141\pi\) |
−0.705730 | + | 0.708481i | \(0.749381\pi\) | |||||||
\(24\) | 1.72011 | − | 3.71676i | 0.351116 | − | 0.758680i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0.664482 | 0.130316 | ||||||||
\(27\) | 5.00727 | − | 1.38826i | 0.963649 | − | 0.267171i | ||||
\(28\) | −4.37803 | −0.827370 | ||||||||
\(29\) | 2.64853 | − | 4.58739i | 0.491820 | − | 0.851857i | −0.508136 | − | 0.861277i | \(-0.669665\pi\) |
0.999956 | + | 0.00942032i | \(0.00299862\pi\) | |||||||
\(30\) | 0.483386 | − | 1.04448i | 0.0882538 | − | 0.190696i | ||||
\(31\) | 2.05661 | + | 3.56215i | 0.369378 | + | 0.639782i | 0.989468 | − | 0.144749i | \(-0.0462374\pi\) |
−0.620090 | + | 0.784530i | \(0.712904\pi\) | |||||||
\(32\) | −2.87809 | − | 4.98500i | −0.508780 | − | 0.881232i | ||||
\(33\) | −0.229728 | − | 0.326080i | −0.0399906 | − | 0.0567632i | ||||
\(34\) | 1.07703 | − | 1.86547i | 0.184709 | − | 0.319926i | ||||
\(35\) | −2.80920 | −0.474841 | ||||||||
\(36\) | 1.57370 | − | 4.40259i | 0.262283 | − | 0.733765i | ||||
\(37\) | 2.95700 | 0.486128 | 0.243064 | − | 0.970010i | \(-0.421848\pi\) | ||||
0.243064 | + | 0.970010i | \(0.421848\pi\) | |||||||
\(38\) | −1.26277 | + | 2.18718i | −0.204848 | + | 0.354807i | ||||
\(39\) | 1.72502 | − | 0.155937i | 0.276224 | − | 0.0249698i | ||||
\(40\) | −1.18227 | − | 2.04775i | −0.186933 | − | 0.323777i | ||||
\(41\) | −1.74574 | − | 3.02371i | −0.272639 | − | 0.472224i | 0.696898 | − | 0.717170i | \(-0.254563\pi\) |
−0.969537 | + | 0.244946i | \(0.921230\pi\) | |||||||
\(42\) | 3.22002 | − | 0.291080i | 0.496860 | − | 0.0449147i | ||||
\(43\) | −5.66677 | + | 9.81514i | −0.864175 | + | 1.49679i | 0.00368958 | + | 0.999993i | \(0.498826\pi\) |
−0.867864 | + | 0.496801i | \(0.834508\pi\) | |||||||
\(44\) | −0.358902 | −0.0541065 | ||||||||
\(45\) | 1.00977 | − | 2.82495i | 0.150528 | − | 0.421119i | ||||
\(46\) | −1.66155 | −0.244983 | ||||||||
\(47\) | 0.720625 | − | 1.24816i | 0.105114 | − | 0.182063i | −0.808671 | − | 0.588261i | \(-0.799813\pi\) |
0.913785 | + | 0.406199i | \(0.133146\pi\) | |||||||
\(48\) | −1.54196 | − | 2.18867i | −0.222562 | − | 0.315908i | ||||
\(49\) | −0.445790 | − | 0.772130i | −0.0636842 | − | 0.110304i | ||||
\(50\) | −0.332241 | − | 0.575458i | −0.0469859 | − | 0.0813820i | ||||
\(51\) | 2.35823 | − | 5.09558i | 0.330218 | − | 0.713524i | ||||
\(52\) | 0.779232 | − | 1.34967i | 0.108060 | − | 0.187165i | ||||
\(53\) | −3.34833 | −0.459929 | −0.229964 | − | 0.973199i | \(-0.573861\pi\) | ||||
−0.229964 | + | 0.973199i | \(0.573861\pi\) | |||||||
\(54\) | −0.864732 | + | 3.34271i | −0.117675 | + | 0.454885i | ||||
\(55\) | −0.230292 | −0.0310526 | ||||||||
\(56\) | 3.32122 | − | 5.75252i | 0.443817 | − | 0.768713i | ||||
\(57\) | −2.76491 | + | 5.97432i | −0.366222 | + | 0.791318i | ||||
\(58\) | 1.75990 | + | 3.04823i | 0.231086 | + | 0.400253i | ||||
\(59\) | −3.89632 | − | 6.74863i | −0.507258 | − | 0.878596i | −0.999965 | − | 0.00840088i | \(-0.997326\pi\) |
0.492707 | − | 0.870195i | \(-0.336007\pi\) | |||||||
\(60\) | −1.55465 | − | 2.20669i | −0.200705 | − | 0.284883i | ||||
\(61\) | −5.04095 | + | 8.73119i | −0.645428 | + | 1.11791i | 0.338775 | + | 0.940868i | \(0.389988\pi\) |
−0.984203 | + | 0.177046i | \(0.943346\pi\) | |||||||
\(62\) | −2.73316 | −0.347112 | ||||||||
\(63\) | 8.29097 | − | 1.51131i | 1.04456 | − | 0.190407i | ||||
\(64\) | 0.733399 | 0.0916749 | ||||||||
\(65\) | 0.500000 | − | 0.866025i | 0.0620174 | − | 0.107417i | ||||
\(66\) | 0.263970 | − | 0.0238621i | 0.0324925 | − | 0.00293723i | ||||
\(67\) | −1.00966 | − | 1.74879i | −0.123350 | − | 0.213649i | 0.797737 | − | 0.603006i | \(-0.206030\pi\) |
−0.921087 | + | 0.389357i | \(0.872697\pi\) | |||||||
\(68\) | −2.52605 | − | 4.37525i | −0.306328 | − | 0.530576i | ||||
\(69\) | −4.31345 | + | 0.389923i | −0.519278 | + | 0.0469412i | ||||
\(70\) | 0.933329 | − | 1.61657i | 0.111554 | − | 0.193218i | ||||
\(71\) | −3.51686 | −0.417375 | −0.208687 | − | 0.977982i | \(-0.566919\pi\) | ||||
−0.208687 | + | 0.977982i | \(0.566919\pi\) | |||||||
\(72\) | 4.59096 | + | 5.40761i | 0.541050 | + | 0.637293i | ||||
\(73\) | −5.30003 | −0.620322 | −0.310161 | − | 0.950684i | \(-0.600383\pi\) | ||||
−0.310161 | + | 0.950684i | \(0.600383\pi\) | |||||||
\(74\) | −0.982436 | + | 1.70163i | −0.114206 | + | 0.197810i | ||||
\(75\) | −0.997554 | − | 1.41594i | −0.115188 | − | 0.163499i | ||||
\(76\) | 2.96167 | + | 5.12977i | 0.339727 | + | 0.588425i | ||||
\(77\) | −0.323467 | − | 0.560262i | −0.0368625 | − | 0.0638478i | ||||
\(78\) | −0.483386 | + | 1.04448i | −0.0547327 | + | 0.118264i | ||||
\(79\) | 2.69870 | − | 4.67428i | 0.303627 | − | 0.525898i | −0.673327 | − | 0.739344i | \(-0.735136\pi\) |
0.976955 | + | 0.213446i | \(0.0684689\pi\) | |||||||
\(80\) | −1.54574 | −0.172819 | ||||||||
\(81\) | −1.46043 | + | 8.88072i | −0.162270 | + | 0.986746i | ||||
\(82\) | 2.32003 | 0.256204 | ||||||||
\(83\) | −0.0501921 | + | 0.0869352i | −0.00550930 | + | 0.00954238i | −0.868767 | − | 0.495221i | \(-0.835087\pi\) |
0.863258 | + | 0.504764i | \(0.168420\pi\) | |||||||
\(84\) | 3.18486 | − | 6.88173i | 0.347496 | − | 0.750858i | ||||
\(85\) | −1.62086 | − | 2.80741i | −0.175807 | − | 0.304506i | ||||
\(86\) | −3.76547 | − | 6.52198i | −0.406041 | − | 0.703283i | ||||
\(87\) | 5.28410 | + | 7.50032i | 0.566515 | + | 0.804119i | ||||
\(88\) | 0.272266 | − | 0.471579i | 0.0290237 | − | 0.0502705i | ||||
\(89\) | 7.04620 | 0.746896 | 0.373448 | − | 0.927651i | \(-0.378175\pi\) | ||||
0.373448 | + | 0.927651i | \(0.378175\pi\) | |||||||
\(90\) | 1.29015 | + | 1.51965i | 0.135994 | + | 0.160185i | ||||
\(91\) | 2.80920 | 0.294484 | ||||||||
\(92\) | −1.94849 | + | 3.37488i | −0.203144 | + | 0.351856i | ||||
\(93\) | −7.09538 | + | 0.641401i | −0.735756 | + | 0.0665102i | ||||
\(94\) | 0.478842 | + | 0.829379i | 0.0493888 | + | 0.0855439i | ||||
\(95\) | 1.90038 | + | 3.29155i | 0.194975 | + | 0.337706i | ||||
\(96\) | 9.92951 | − | 0.897599i | 1.01343 | − | 0.0916109i | ||||
\(97\) | −1.63221 | + | 2.82707i | −0.165726 | + | 0.287046i | −0.936913 | − | 0.349563i | \(-0.886330\pi\) |
0.771187 | + | 0.636609i | \(0.219663\pi\) | |||||||
\(98\) | 0.592438 | 0.0598453 | ||||||||
\(99\) | 0.679676 | − | 0.123894i | 0.0683100 | − | 0.0124518i | ||||
\(100\) | −1.55846 | −0.155846 | ||||||||
\(101\) | −5.57900 | + | 9.66312i | −0.555132 | + | 0.961516i | 0.442762 | + | 0.896639i | \(0.353999\pi\) |
−0.997893 | + | 0.0648769i | \(0.979335\pi\) | |||||||
\(102\) | 2.14879 | + | 3.05002i | 0.212762 | + | 0.301997i | ||||
\(103\) | 6.33925 | + | 10.9799i | 0.624625 | + | 1.08188i | 0.988613 | + | 0.150479i | \(0.0480815\pi\) |
−0.363988 | + | 0.931404i | \(0.618585\pi\) | |||||||
\(104\) | 1.18227 | + | 2.04775i | 0.115931 | + | 0.200798i | ||||
\(105\) | 2.04359 | − | 4.41571i | 0.199434 | − | 0.430929i | ||||
\(106\) | 1.11245 | − | 1.92682i | 0.108051 | − | 0.187150i | ||||
\(107\) | 4.15748 | 0.401919 | 0.200959 | − | 0.979600i | \(-0.435594\pi\) | ||||
0.200959 | + | 0.979600i | \(0.435594\pi\) | |||||||
\(108\) | 5.77552 | + | 5.67638i | 0.555750 | + | 0.546210i | ||||
\(109\) | −4.90157 | −0.469485 | −0.234742 | − | 0.972058i | \(-0.575425\pi\) | ||||
−0.234742 | + | 0.972058i | \(0.575425\pi\) | |||||||
\(110\) | 0.0765124 | − | 0.132523i | 0.00729517 | − | 0.0126356i | ||||
\(111\) | −2.15111 | + | 4.64804i | −0.204174 | + | 0.441172i | ||||
\(112\) | −2.17114 | − | 3.76053i | −0.205154 | − | 0.355336i | ||||
\(113\) | 8.07368 | + | 13.9840i | 0.759508 | + | 1.31551i | 0.943102 | + | 0.332504i | \(0.107894\pi\) |
−0.183594 | + | 0.983002i | \(0.558773\pi\) | |||||||
\(114\) | −2.51935 | − | 3.57600i | −0.235959 | − | 0.334924i | ||||
\(115\) | −1.25026 | + | 2.16552i | −0.116588 | + | 0.201936i | ||||
\(116\) | 8.25528 | 0.766483 | ||||||||
\(117\) | −1.00977 | + | 2.82495i | −0.0933536 | + | 0.261167i | ||||
\(118\) | 5.17807 | 0.476680 | ||||||||
\(119\) | 4.55331 | − | 7.88656i | 0.417401 | − | 0.722960i | ||||
\(120\) | 4.07886 | − | 0.368717i | 0.372347 | − | 0.0336591i | ||||
\(121\) | 5.47348 | + | 9.48035i | 0.497589 | + | 0.861850i | ||||
\(122\) | −3.34962 | − | 5.80171i | −0.303260 | − | 0.525262i | ||||
\(123\) | 6.02286 | − | 0.544450i | 0.543063 | − | 0.0490914i | ||||
\(124\) | −3.20515 | + | 5.55149i | −0.287831 | + | 0.498538i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.88490 | + | 5.27322i | −0.167921 | + | 0.469776i | ||||
\(127\) | 17.7472 | 1.57481 | 0.787404 | − | 0.616438i | \(-0.211425\pi\) | ||||
0.787404 | + | 0.616438i | \(0.211425\pi\) | |||||||
\(128\) | 5.51252 | − | 9.54796i | 0.487242 | − | 0.843929i | ||||
\(129\) | −11.3058 | − | 16.0476i | −0.995422 | − | 1.41291i | ||||
\(130\) | 0.332241 | + | 0.575458i | 0.0291394 | + | 0.0504710i | ||||
\(131\) | 7.57097 | + | 13.1133i | 0.661479 | + | 1.14571i | 0.980227 | + | 0.197876i | \(0.0634042\pi\) |
−0.318748 | + | 0.947839i | \(0.603262\pi\) | |||||||
\(132\) | 0.261088 | − | 0.564149i | 0.0227248 | − | 0.0491029i | ||||
\(133\) | −5.33854 | + | 9.24661i | −0.462910 | + | 0.801783i | ||||
\(134\) | 1.34181 | 0.115914 | ||||||||
\(135\) | 3.70590 | + | 3.64229i | 0.318953 | + | 0.313478i | ||||
\(136\) | 7.66515 | 0.657281 | ||||||||
\(137\) | −10.4043 | + | 18.0207i | −0.888896 | + | 1.53961i | −0.0477139 | + | 0.998861i | \(0.515194\pi\) |
−0.841182 | + | 0.540752i | \(0.818140\pi\) | |||||||
\(138\) | 1.20872 | − | 2.61176i | 0.102893 | − | 0.222327i | ||||
\(139\) | 3.36287 | + | 5.82466i | 0.285235 | + | 0.494041i | 0.972666 | − | 0.232208i | \(-0.0745951\pi\) |
−0.687431 | + | 0.726249i | \(0.741262\pi\) | |||||||
\(140\) | −2.18902 | − | 3.79149i | −0.185006 | − | 0.320439i | ||||
\(141\) | 1.43772 | + | 2.04072i | 0.121078 | + | 0.171860i | ||||
\(142\) | 1.16844 | − | 2.02381i | 0.0980537 | − | 0.169834i | ||||
\(143\) | 0.230292 | 0.0192580 | ||||||||
\(144\) | 4.56204 | − | 0.831587i | 0.380170 | − | 0.0692989i | ||||
\(145\) | 5.29706 | 0.439897 | ||||||||
\(146\) | 1.76089 | − | 3.04995i | 0.145732 | − | 0.252415i | ||||
\(147\) | 1.53799 | − | 0.139030i | 0.126851 | − | 0.0114670i | ||||
\(148\) | 2.30419 | + | 3.99097i | 0.189403 | + | 0.328056i | ||||
\(149\) | −11.0995 | − | 19.2249i | −0.909306 | − | 1.57496i | −0.815031 | − | 0.579418i | \(-0.803280\pi\) |
−0.0942751 | − | 0.995546i | \(-0.530053\pi\) | |||||||
\(150\) | 1.14624 | − | 0.103617i | 0.0935903 | − | 0.00846029i | ||||
\(151\) | −2.01163 | + | 3.48424i | −0.163704 | + | 0.283544i | −0.936194 | − | 0.351483i | \(-0.885678\pi\) |
0.772490 | + | 0.635027i | \(0.219011\pi\) | |||||||
\(152\) | −8.98702 | −0.728944 | ||||||||
\(153\) | 6.29410 | + | 7.41369i | 0.508847 | + | 0.599362i | ||||
\(154\) | 0.429876 | 0.0346404 | ||||||||
\(155\) | −2.05661 | + | 3.56215i | −0.165191 | + | 0.286119i | ||||
\(156\) | 1.55465 | + | 2.20669i | 0.124472 | + | 0.176677i | ||||
\(157\) | −10.9161 | − | 18.9073i | −0.871201 | − | 1.50896i | −0.860756 | − | 0.509019i | \(-0.830008\pi\) |
−0.0104452 | − | 0.999945i | \(-0.503325\pi\) | |||||||
\(158\) | 1.79324 | + | 3.10598i | 0.142662 | + | 0.247098i | ||||
\(159\) | 2.43579 | − | 5.26317i | 0.193171 | − | 0.417396i | ||||
\(160\) | 2.87809 | − | 4.98500i | 0.227533 | − | 0.394099i | ||||
\(161\) | −7.02446 | −0.553605 | ||||||||
\(162\) | −4.62527 | − | 3.79095i | −0.363395 | − | 0.297845i | ||||
\(163\) | 10.4867 | 0.821381 | 0.410690 | − | 0.911775i | \(-0.365288\pi\) | ||||
0.410690 | + | 0.911775i | \(0.365288\pi\) | |||||||
\(164\) | 2.72067 | − | 4.71235i | 0.212449 | − | 0.367972i | ||||
\(165\) | 0.167529 | − | 0.361990i | 0.0130421 | − | 0.0281809i | ||||
\(166\) | −0.0333517 | − | 0.0577669i | −0.00258859 | − | 0.00448358i | ||||
\(167\) | −3.30617 | − | 5.72645i | −0.255839 | − | 0.443126i | 0.709284 | − | 0.704923i | \(-0.249018\pi\) |
−0.965123 | + | 0.261797i | \(0.915685\pi\) | |||||||
\(168\) | 6.62619 | + | 9.40530i | 0.511221 | + | 0.725634i | ||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | 2.15406 | 0.165209 | ||||||||
\(171\) | −7.37953 | − | 8.69220i | −0.564327 | − | 0.664709i | ||||
\(172\) | −17.6629 | −1.34679 | ||||||||
\(173\) | −8.64411 | + | 14.9720i | −0.657200 | + | 1.13830i | 0.324138 | + | 0.946010i | \(0.394926\pi\) |
−0.981338 | + | 0.192293i | \(0.938408\pi\) | |||||||
\(174\) | −6.07171 | + | 0.548865i | −0.460295 | + | 0.0416094i | ||||
\(175\) | −1.40460 | − | 2.43283i | −0.106178 | − | 0.183905i | ||||
\(176\) | −0.177986 | − | 0.308280i | −0.0134162 | − | 0.0232375i | ||||
\(177\) | 13.4424 | − | 1.21516i | 1.01040 | − | 0.0913368i | ||||
\(178\) | −2.34104 | + | 4.05479i | −0.175468 | + | 0.303920i | ||||
\(179\) | 15.1868 | 1.13512 | 0.567558 | − | 0.823333i | \(-0.307888\pi\) | ||||
0.567558 | + | 0.823333i | \(0.307888\pi\) | |||||||
\(180\) | 4.59960 | − | 0.838433i | 0.342834 | − | 0.0624931i | ||||
\(181\) | 24.3392 | 1.80912 | 0.904559 | − | 0.426348i | \(-0.140200\pi\) | ||||
0.904559 | + | 0.426348i | \(0.140200\pi\) | |||||||
\(182\) | −0.933329 | + | 1.61657i | −0.0691830 | + | 0.119828i | ||||
\(183\) | −10.0572 | − | 14.2754i | −0.743453 | − | 1.05527i | ||||
\(184\) | −2.95629 | − | 5.12044i | −0.217940 | − | 0.377484i | ||||
\(185\) | 1.47850 | + | 2.56084i | 0.108701 | + | 0.188276i | ||||
\(186\) | 1.98827 | − | 4.29619i | 0.145787 | − | 0.315012i | ||||
\(187\) | 0.373270 | − | 0.646523i | 0.0272962 | − | 0.0472785i | ||||
\(188\) | 2.24614 | 0.163816 | ||||||||
\(189\) | −3.65579 | + | 14.1318i | −0.265919 | + | 1.02794i | ||||
\(190\) | −2.52553 | −0.183221 | ||||||||
\(191\) | −7.13201 | + | 12.3530i | −0.516054 | + | 0.893832i | 0.483772 | + | 0.875194i | \(0.339266\pi\) |
−0.999826 | + | 0.0186379i | \(0.994067\pi\) | |||||||
\(192\) | −0.533521 | + | 1.15281i | −0.0385036 | + | 0.0831971i | ||||
\(193\) | −12.7915 | − | 22.1556i | −0.920756 | − | 1.59480i | −0.798249 | − | 0.602328i | \(-0.794240\pi\) |
−0.122507 | − | 0.992468i | \(-0.539093\pi\) | |||||||
\(194\) | −1.08457 | − | 1.87854i | −0.0778679 | − | 0.134871i | ||||
\(195\) | 0.997554 | + | 1.41594i | 0.0714363 | + | 0.101398i | ||||
\(196\) | 0.694747 | − | 1.20334i | 0.0496248 | − | 0.0859527i | ||||
\(197\) | 10.2976 | 0.733675 | 0.366838 | − | 0.930285i | \(-0.380440\pi\) | ||||
0.366838 | + | 0.930285i | \(0.380440\pi\) | |||||||
\(198\) | −0.154520 | + | 0.432288i | −0.0109813 | + | 0.0307213i | ||||
\(199\) | 3.31578 | 0.235049 | 0.117525 | − | 0.993070i | \(-0.462504\pi\) | ||||
0.117525 | + | 0.993070i | \(0.462504\pi\) | |||||||
\(200\) | 1.18227 | − | 2.04775i | 0.0835989 | − | 0.144798i | ||||
\(201\) | 3.48337 | − | 0.314887i | 0.245698 | − | 0.0222104i | ||||
\(202\) | −3.70715 | − | 6.42096i | −0.260834 | − | 0.451777i | ||||
\(203\) | 7.44024 | + | 12.8869i | 0.522202 | + | 0.904481i | ||||
\(204\) | 8.71496 | − | 0.787807i | 0.610169 | − | 0.0551575i | ||||
\(205\) | 1.74574 | − | 3.02371i | 0.121928 | − | 0.211185i | ||||
\(206\) | −8.42463 | −0.586972 | ||||||||
\(207\) | 2.52496 | − | 7.06386i | 0.175497 | − | 0.490972i | ||||
\(208\) | 1.54574 | 0.107178 | ||||||||
\(209\) | −0.437642 | + | 0.758018i | −0.0302723 | + | 0.0524332i | ||||
\(210\) | 1.86209 | + | 2.64308i | 0.128497 | + | 0.182390i | ||||
\(211\) | −5.85961 | − | 10.1491i | −0.403392 | − | 0.698695i | 0.590741 | − | 0.806861i | \(-0.298836\pi\) |
−0.994133 | + | 0.108166i | \(0.965502\pi\) | |||||||
\(212\) | −2.60913 | − | 4.51914i | −0.179196 | − | 0.310376i | ||||
\(213\) | 2.55839 | − | 5.52807i | 0.175298 | − | 0.378777i | ||||
\(214\) | −1.38128 | + | 2.39245i | −0.0944226 | + | 0.163545i | ||||
\(215\) | −11.3335 | −0.772941 | ||||||||
\(216\) | −11.8399 | + | 3.28259i | −0.805600 | + | 0.223352i | ||||
\(217\) | −11.5548 | −0.784394 | ||||||||
\(218\) | 1.62850 | − | 2.82065i | 0.110296 | − | 0.191038i | ||||
\(219\) | 3.85558 | − | 8.33100i | 0.260536 | − | 0.562957i | ||||
\(220\) | −0.179451 | − | 0.310818i | −0.0120986 | − | 0.0209553i | ||||
\(221\) | 1.62086 | + | 2.80741i | 0.109031 | + | 0.188847i | ||||
\(222\) | −1.96006 | − | 2.78214i | −0.131551 | − | 0.186725i | ||||
\(223\) | 0.489654 | − | 0.848106i | 0.0327897 | − | 0.0567934i | −0.849165 | − | 0.528128i | \(-0.822894\pi\) |
0.881955 | + | 0.471334i | \(0.156228\pi\) | |||||||
\(224\) | 16.1702 | 1.08042 | ||||||||
\(225\) | 2.95137 | − | 0.537986i | 0.196758 | − | 0.0358658i | ||||
\(226\) | −10.7296 | −0.713724 | ||||||||
\(227\) | −7.98509 | + | 13.8306i | −0.529989 | + | 0.917967i | 0.469399 | + | 0.882986i | \(0.344471\pi\) |
−0.999388 | + | 0.0349814i | \(0.988863\pi\) | |||||||
\(228\) | −10.2179 | + | 0.923666i | −0.676695 | + | 0.0611713i | ||||
\(229\) | 5.14710 | + | 8.91505i | 0.340130 | + | 0.589123i | 0.984457 | − | 0.175628i | \(-0.0561955\pi\) |
−0.644326 | + | 0.764751i | \(0.722862\pi\) | |||||||
\(230\) | −0.830776 | − | 1.43895i | −0.0547798 | − | 0.0948813i | ||||
\(231\) | 1.11597 | − | 0.100881i | 0.0734257 | − | 0.00663747i | ||||
\(232\) | −6.26254 | + | 10.8470i | −0.411156 | + | 0.712143i | ||||
\(233\) | 7.73176 | 0.506524 | 0.253262 | − | 0.967398i | \(-0.418496\pi\) | ||||
0.253262 | + | 0.967398i | \(0.418496\pi\) | |||||||
\(234\) | −1.29015 | − | 1.51965i | −0.0843400 | − | 0.0993424i | ||||
\(235\) | 1.44125 | 0.0940168 | ||||||||
\(236\) | 6.07228 | − | 10.5175i | 0.395272 | − | 0.684630i | ||||
\(237\) | 5.38419 | + | 7.64240i | 0.349741 | + | 0.496427i | ||||
\(238\) | 3.02559 | + | 5.24047i | 0.196120 | + | 0.339689i | ||||
\(239\) | −7.30932 | − | 12.6601i | −0.472801 | − | 0.818915i | 0.526715 | − | 0.850042i | \(-0.323424\pi\) |
−0.999515 | + | 0.0311272i | \(0.990090\pi\) | |||||||
\(240\) | 1.12447 | − | 2.42971i | 0.0725842 | − | 0.156837i | ||||
\(241\) | −7.15642 | + | 12.3953i | −0.460985 | + | 0.798450i | −0.999010 | − | 0.0444789i | \(-0.985837\pi\) |
0.538025 | + | 0.842929i | \(0.319171\pi\) | |||||||
\(242\) | −7.27406 | −0.467594 | ||||||||
\(243\) | −12.8970 | − | 8.75601i | −0.827342 | − | 0.561698i | ||||
\(244\) | −15.7123 | −1.00588 | ||||||||
\(245\) | 0.445790 | − | 0.772130i | 0.0284805 | − | 0.0493296i | ||||
\(246\) | −1.68773 | + | 3.64679i | −0.107606 | + | 0.232511i | ||||
\(247\) | −1.90038 | − | 3.29155i | −0.120918 | − | 0.209436i | ||||
\(248\) | −4.86292 | − | 8.42283i | −0.308796 | − | 0.534850i | ||||
\(249\) | −0.100139 | − | 0.142138i | −0.00634602 | − | 0.00900763i | ||||
\(250\) | 0.332241 | − | 0.575458i | 0.0210128 | − | 0.0363952i | ||||
\(251\) | −19.0291 | −1.20110 | −0.600552 | − | 0.799586i | \(-0.705052\pi\) | ||||
−0.600552 | + | 0.799586i | \(0.705052\pi\) | |||||||
\(252\) | 8.50036 | + | 10.0124i | 0.535472 | + | 0.630722i | ||||
\(253\) | −0.575851 | −0.0362034 | ||||||||
\(254\) | −5.89634 | + | 10.2128i | −0.369969 | + | 0.640805i | ||||
\(255\) | 5.59202 | − | 0.505502i | 0.350186 | − | 0.0316558i | ||||
\(256\) | 4.39637 | + | 7.61473i | 0.274773 | + | 0.475921i | ||||
\(257\) | 6.97060 | + | 12.0734i | 0.434814 | + | 0.753120i | 0.997280 | − | 0.0737002i | \(-0.0234808\pi\) |
−0.562467 | + | 0.826820i | \(0.690147\pi\) | |||||||
\(258\) | 12.9910 | − | 1.17435i | 0.808783 | − | 0.0731117i | ||||
\(259\) | −4.15339 | + | 7.19389i | −0.258079 | + | 0.447007i | ||||
\(260\) | 1.55846 | 0.0966518 | ||||||||
\(261\) | −15.6336 | + | 2.84975i | −0.967694 | + | 0.176395i | ||||
\(262\) | −10.0615 | −0.621604 | ||||||||
\(263\) | 5.97895 | − | 10.3558i | 0.368678 | − | 0.638569i | −0.620681 | − | 0.784063i | \(-0.713144\pi\) |
0.989359 | + | 0.145494i | \(0.0464772\pi\) | |||||||
\(264\) | 0.543201 | + | 0.771026i | 0.0334317 | + | 0.0474534i | ||||
\(265\) | −1.67417 | − | 2.89974i | −0.102843 | − | 0.178130i | ||||
\(266\) | −3.54736 | − | 6.14421i | −0.217503 | − | 0.376725i | ||||
\(267\) | −5.12585 | + | 11.0758i | −0.313697 | + | 0.677826i | ||||
\(268\) | 1.57352 | − | 2.72543i | 0.0961183 | − | 0.166482i | ||||
\(269\) | 2.54602 | 0.155234 | 0.0776168 | − | 0.996983i | \(-0.475269\pi\) | ||||
0.0776168 | + | 0.996983i | \(0.475269\pi\) | |||||||
\(270\) | −3.32724 | + | 0.922474i | −0.202489 | + | 0.0561400i | ||||
\(271\) | 16.6012 | 1.00845 | 0.504225 | − | 0.863572i | \(-0.331778\pi\) | ||||
0.504225 | + | 0.863572i | \(0.331778\pi\) | |||||||
\(272\) | 2.50542 | − | 4.33952i | 0.151914 | − | 0.263122i | ||||
\(273\) | −2.04359 | + | 4.41571i | −0.123684 | + | 0.267251i | ||||
\(274\) | −6.91344 | − | 11.9744i | −0.417656 | − | 0.723402i | ||||
\(275\) | −0.115146 | − | 0.199439i | −0.00694356 | − | 0.0120266i | ||||
\(276\) | −3.88744 | − | 5.51789i | −0.233997 | − | 0.332138i | ||||
\(277\) | 8.95287 | − | 15.5068i | 0.537926 | − | 0.931714i | −0.461090 | − | 0.887353i | \(-0.652541\pi\) |
0.999016 | − | 0.0443610i | \(-0.0141252\pi\) | |||||||
\(278\) | −4.46913 | −0.268041 | ||||||||
\(279\) | 4.15342 | − | 11.6197i | 0.248659 | − | 0.695650i | ||||
\(280\) | 6.64244 | 0.396962 | ||||||||
\(281\) | −2.36433 | + | 4.09514i | −0.141044 | + | 0.244296i | −0.927890 | − | 0.372854i | \(-0.878379\pi\) |
0.786846 | + | 0.617149i | \(0.211713\pi\) | |||||||
\(282\) | −1.65202 | + | 0.149338i | −0.0983765 | + | 0.00889295i | ||||
\(283\) | 2.98943 | + | 5.17785i | 0.177703 | + | 0.307791i | 0.941094 | − | 0.338146i | \(-0.109800\pi\) |
−0.763390 | + | 0.645938i | \(0.776467\pi\) | |||||||
\(284\) | −2.74045 | − | 4.74660i | −0.162616 | − | 0.281659i | ||||
\(285\) | −6.55637 | + | 0.592677i | −0.388366 | + | 0.0351072i | ||||
\(286\) | −0.0765124 | + | 0.132523i | −0.00452427 | + | 0.00783627i | ||||
\(287\) | 9.80825 | 0.578963 | ||||||||
\(288\) | −5.81244 | + | 16.2609i | −0.342502 | + | 0.958185i | ||||
\(289\) | −6.49128 | −0.381840 | ||||||||
\(290\) | −1.75990 | + | 3.04823i | −0.103345 | + | 0.178998i | ||||
\(291\) | −3.25644 | − | 4.62223i | −0.190896 | − | 0.270960i | ||||
\(292\) | −4.12996 | − | 7.15330i | −0.241687 | − | 0.418615i | ||||
\(293\) | 7.80549 | + | 13.5195i | 0.456002 | + | 0.789818i | 0.998745 | − | 0.0500805i | \(-0.0159478\pi\) |
−0.542744 | + | 0.839898i | \(0.682614\pi\) | |||||||
\(294\) | −0.430977 | + | 0.931240i | −0.0251351 | + | 0.0543110i | ||||
\(295\) | 3.89632 | − | 6.74863i | 0.226853 | − | 0.392920i | ||||
\(296\) | −6.99193 | −0.406397 | ||||||||
\(297\) | −0.299694 | + | 1.15850i | −0.0173900 | + | 0.0672227i | ||||
\(298\) | 14.7508 | 0.854492 | ||||||||
\(299\) | 1.25026 | − | 2.16552i | 0.0723045 | − | 0.125235i | ||||
\(300\) | 1.13373 | − | 2.44971i | 0.0654557 | − | 0.141434i | ||||
\(301\) | −15.9191 | − | 27.5726i | −0.917560 | − | 1.58926i | ||||
\(302\) | −1.33669 | − | 2.31522i | −0.0769179 | − | 0.133226i | ||||
\(303\) | −11.1307 | − | 15.7991i | −0.639443 | − | 0.907633i | ||||
\(304\) | −2.93749 | + | 5.08788i | −0.168477 | + | 0.291810i | ||||
\(305\) | −10.0819 | −0.577288 | ||||||||
\(306\) | −6.35742 | + | 1.15886i | −0.363430 | + | 0.0662474i | ||||
\(307\) | 23.7975 | 1.35819 | 0.679097 | − | 0.734048i | \(-0.262371\pi\) | ||||
0.679097 | + | 0.734048i | \(0.262371\pi\) | |||||||
\(308\) | 0.504112 | − | 0.873148i | 0.0287245 | − | 0.0497523i | ||||
\(309\) | −21.8706 | + | 1.97704i | −1.24418 | + | 0.112470i | ||||
\(310\) | −1.36658 | − | 2.36699i | −0.0776165 | − | 0.134436i | ||||
\(311\) | −0.779514 | − | 1.35016i | −0.0442022 | − | 0.0765604i | 0.843078 | − | 0.537791i | \(-0.180741\pi\) |
−0.887280 | + | 0.461231i | \(0.847408\pi\) | |||||||
\(312\) | −4.07886 | + | 0.368717i | −0.230920 | + | 0.0208745i | ||||
\(313\) | 13.7455 | − | 23.8079i | 0.776941 | − | 1.34570i | −0.156756 | − | 0.987637i | \(-0.550104\pi\) |
0.933697 | − | 0.358064i | \(-0.116563\pi\) | |||||||
\(314\) | 14.5071 | 0.818684 | ||||||||
\(315\) | 5.45432 | + | 6.42453i | 0.307316 | + | 0.361982i | ||||
\(316\) | 8.41165 | 0.473192 | ||||||||
\(317\) | 7.65181 | − | 13.2533i | 0.429768 | − | 0.744381i | −0.567084 | − | 0.823660i | \(-0.691929\pi\) |
0.996852 | + | 0.0792791i | \(0.0252618\pi\) | |||||||
\(318\) | 2.21946 | + | 3.15033i | 0.124461 | + | 0.176662i | ||||
\(319\) | 0.609935 | + | 1.05644i | 0.0341498 | + | 0.0591492i | ||||
\(320\) | 0.366700 | + | 0.635142i | 0.0204991 | + | 0.0355055i | ||||
\(321\) | −3.02441 | + | 6.53504i | −0.168806 | + | 0.364751i | ||||
\(322\) | 2.33381 | − | 4.04228i | 0.130058 | − | 0.225268i | ||||
\(323\) | −12.3210 | −0.685557 | ||||||||
\(324\) | −13.1240 | + | 4.94905i | −0.729114 | + | 0.274947i | ||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | −3.48411 | + | 6.03465i | −0.192967 | + | 0.334228i | ||||
\(327\) | 3.56571 | − | 7.70466i | 0.197184 | − | 0.426069i | ||||
\(328\) | 4.12786 | + | 7.14967i | 0.227923 | + | 0.394774i | ||||
\(329\) | 2.02438 | + | 3.50632i | 0.111608 | + | 0.193310i | ||||
\(330\) | 0.152650 | + | 0.216674i | 0.00840313 | + | 0.0119275i | ||||
\(331\) | 6.68506 | − | 11.5789i | 0.367444 | − | 0.636432i | −0.621721 | − | 0.783239i | \(-0.713566\pi\) |
0.989165 | + | 0.146807i | \(0.0468995\pi\) | |||||||
\(332\) | −0.156445 | −0.00858604 | ||||||||
\(333\) | −5.74129 | − | 6.76256i | −0.314621 | − | 0.370586i | ||||
\(334\) | 4.39377 | 0.240417 | ||||||||
\(335\) | 1.00966 | − | 1.74879i | 0.0551638 | − | 0.0955466i | ||||
\(336\) | 7.49051 | − | 0.677121i | 0.408641 | − | 0.0369400i | ||||
\(337\) | −17.4801 | − | 30.2764i | −0.952200 | − | 1.64926i | −0.740648 | − | 0.671893i | \(-0.765481\pi\) |
−0.211552 | − | 0.977367i | \(-0.567852\pi\) | |||||||
\(338\) | −0.332241 | − | 0.575458i | −0.0180715 | − | 0.0313008i | ||||
\(339\) | −27.8545 | + | 2.51796i | −1.51285 | + | 0.136757i | ||||
\(340\) | 2.52605 | − | 4.37525i | 0.136994 | − | 0.237281i | ||||
\(341\) | −0.947241 | −0.0512960 | ||||||||
\(342\) | 7.45378 | − | 1.35870i | 0.403054 | − | 0.0734702i | ||||
\(343\) | −17.1597 | −0.926539 | ||||||||
\(344\) | 13.3993 | − | 23.2082i | 0.722441 | − | 1.25130i | ||||
\(345\) | −2.49441 | − | 3.54059i | −0.134294 | − | 0.190619i | ||||
\(346\) | −5.74385 | − | 9.94864i | −0.308791 | − | 0.534842i | ||||
\(347\) | 12.1455 | + | 21.0367i | 0.652007 | + | 1.12931i | 0.982635 | + | 0.185548i | \(0.0594059\pi\) |
−0.330629 | + | 0.943761i | \(0.607261\pi\) | |||||||
\(348\) | −6.00541 | + | 12.9763i | −0.321924 | + | 0.695602i | ||||
\(349\) | −16.1586 | + | 27.9875i | −0.864951 | + | 1.49814i | 0.00214531 | + | 0.999998i | \(0.499317\pi\) |
−0.867096 | + | 0.498141i | \(0.834016\pi\) | |||||||
\(350\) | 1.86666 | 0.0997771 | ||||||||
\(351\) | −3.70590 | − | 3.64229i | −0.197807 | − | 0.194411i | ||||
\(352\) | 1.32560 | 0.0706548 | ||||||||
\(353\) | 17.0661 | − | 29.5593i | 0.908334 | − | 1.57328i | 0.0919565 | − | 0.995763i | \(-0.470688\pi\) |
0.816378 | − | 0.577518i | \(-0.195979\pi\) | |||||||
\(354\) | −3.76685 | + | 8.13928i | −0.200206 | + | 0.432598i | ||||
\(355\) | −1.75843 | − | 3.04569i | −0.0933278 | − | 0.161649i | ||||
\(356\) | 5.49063 | + | 9.51004i | 0.291003 | + | 0.504031i | ||||
\(357\) | 9.08433 | + | 12.8944i | 0.480794 | + | 0.682445i | ||||
\(358\) | −5.04568 | + | 8.73938i | −0.266673 | + | 0.461890i | ||||
\(359\) | 25.3297 | 1.33685 | 0.668426 | − | 0.743779i | \(-0.266968\pi\) | ||||
0.668426 | + | 0.743779i | \(0.266968\pi\) | |||||||
\(360\) | −2.38764 | + | 6.67970i | −0.125840 | + | 0.352051i | ||||
\(361\) | −4.55424 | −0.239697 | ||||||||
\(362\) | −8.08647 | + | 14.0062i | −0.425016 | + | 0.736149i | ||||
\(363\) | −18.8837 | + | 1.70703i | −0.991137 | + | 0.0895960i | ||||
\(364\) | 2.18902 | + | 3.79149i | 0.114736 | + | 0.198728i | ||||
\(365\) | −2.65002 | − | 4.58996i | −0.138708 | − | 0.240250i | ||||
\(366\) | 11.5563 | − | 1.04466i | 0.604058 | − | 0.0546051i | ||||
\(367\) | −1.79298 | + | 3.10554i | −0.0935930 | + | 0.162108i | −0.909021 | − | 0.416751i | \(-0.863169\pi\) |
0.815428 | + | 0.578859i | \(0.196502\pi\) | |||||||
\(368\) | −3.86516 | −0.201485 | ||||||||
\(369\) | −3.52561 | + | 9.86327i | −0.183536 | + | 0.513461i | ||||
\(370\) | −1.96487 | −0.102149 | ||||||||
\(371\) | 4.70306 | − | 8.14594i | 0.244171 | − | 0.422916i | ||||
\(372\) | −6.39462 | − | 9.07661i | −0.331546 | − | 0.470600i | ||||
\(373\) | −0.717545 | − | 1.24282i | −0.0371531 | − | 0.0643510i | 0.846851 | − | 0.531830i | \(-0.178496\pi\) |
−0.884004 | + | 0.467479i | \(0.845162\pi\) | |||||||
\(374\) | 0.248031 | + | 0.429603i | 0.0128254 | + | 0.0222142i | ||||
\(375\) | 0.727463 | − | 1.57188i | 0.0375661 | − | 0.0811714i | ||||
\(376\) | −1.70394 | + | 2.95132i | −0.0878741 | + | 0.152202i | ||||
\(377\) | −5.29706 | −0.272812 | ||||||||
\(378\) | −6.91766 | − | 6.79891i | −0.355806 | − | 0.349698i | ||||
\(379\) | 34.5139 | 1.77286 | 0.886429 | − | 0.462864i | \(-0.153178\pi\) | ||||
0.886429 | + | 0.462864i | \(0.153178\pi\) | |||||||
\(380\) | −2.96167 | + | 5.12977i | −0.151931 | + | 0.263151i | ||||
\(381\) | −12.9104 | + | 27.8964i | −0.661421 | + | 1.42917i | ||||
\(382\) | −4.73909 | − | 8.20834i | −0.242473 | − | 0.419975i | ||||
\(383\) | −3.32127 | − | 5.75260i | −0.169709 | − | 0.293944i | 0.768609 | − | 0.639719i | \(-0.220949\pi\) |
−0.938317 | + | 0.345775i | \(0.887616\pi\) | |||||||
\(384\) | 10.9981 | + | 15.6108i | 0.561243 | + | 0.796635i | ||||
\(385\) | 0.323467 | − | 0.560262i | 0.0164854 | − | 0.0285536i | ||||
\(386\) | 16.9995 | 0.865251 | ||||||||
\(387\) | 33.4495 | − | 6.09729i | 1.70033 | − | 0.309943i | ||||
\(388\) | −5.08748 | −0.258278 | ||||||||
\(389\) | −15.0663 | + | 26.0956i | −0.763893 | + | 1.32310i | 0.176937 | + | 0.984222i | \(0.443381\pi\) |
−0.940830 | + | 0.338879i | \(0.889952\pi\) | |||||||
\(390\) | −1.14624 | + | 0.103617i | −0.0580422 | + | 0.00524685i | ||||
\(391\) | −4.05300 | − | 7.01999i | −0.204969 | − | 0.355016i | ||||
\(392\) | 1.05408 | + | 1.82573i | 0.0532393 | + | 0.0922132i | ||||
\(393\) | −26.1201 | + | 2.36118i | −1.31759 | + | 0.119106i | ||||
\(394\) | −3.42129 | + | 5.92585i | −0.172362 | + | 0.298540i | ||||
\(395\) | 5.39740 | 0.271573 | ||||||||
\(396\) | 0.696841 | + | 0.820796i | 0.0350176 | + | 0.0412465i | ||||
\(397\) | 25.4593 | 1.27777 | 0.638883 | − | 0.769304i | \(-0.279397\pi\) | ||||
0.638883 | + | 0.769304i | \(0.279397\pi\) | |||||||
\(398\) | −1.10164 | + | 1.90809i | −0.0552201 | + | 0.0956440i | ||||
\(399\) | −10.6510 | − | 15.1181i | −0.533214 | − | 0.756851i | ||||
\(400\) | −0.772870 | − | 1.33865i | −0.0386435 | − | 0.0669325i | ||||
\(401\) | 5.17727 | + | 8.96730i | 0.258541 | + | 0.447805i | 0.965851 | − | 0.259097i | \(-0.0834251\pi\) |
−0.707311 | + | 0.706903i | \(0.750092\pi\) | |||||||
\(402\) | −0.976115 | + | 2.10915i | −0.0486842 | + | 0.105195i | ||||
\(403\) | 2.05661 | − | 3.56215i | 0.102447 | − | 0.177444i | ||||
\(404\) | −17.3894 | −0.865153 | ||||||||
\(405\) | −8.42114 | + | 3.17559i | −0.418450 | + | 0.157796i | ||||
\(406\) | −9.88780 | −0.490723 | ||||||||
\(407\) | −0.340486 | + | 0.589740i | −0.0168773 | + | 0.0292323i | ||||
\(408\) | −5.57611 | + | 12.0487i | −0.276059 | + | 0.596498i | ||||
\(409\) | −14.1797 | − | 24.5600i | −0.701142 | − | 1.21441i | −0.968066 | − | 0.250696i | \(-0.919340\pi\) |
0.266923 | − | 0.963718i | \(-0.413993\pi\) | |||||||
\(410\) | 1.16001 | + | 2.00920i | 0.0572889 | + | 0.0992273i | ||||
\(411\) | −20.7576 | − | 29.4636i | −1.02390 | − | 1.45333i | ||||
\(412\) | −9.87950 | + | 17.1118i | −0.486728 | + | 0.843037i | ||||
\(413\) | 21.8911 | 1.07719 | ||||||||
\(414\) | 3.22606 | + | 3.79991i | 0.158552 | + | 0.186756i | ||||
\(415\) | −0.100384 | −0.00492766 | ||||||||
\(416\) | −2.87809 | + | 4.98500i | −0.141110 | + | 0.244410i | ||||
\(417\) | −11.6020 | + | 1.04879i | −0.568153 | + | 0.0513594i | ||||
\(418\) | −0.290805 | − | 0.503689i | −0.0142237 | − | 0.0246362i | ||||
\(419\) | 5.32788 | + | 9.22817i | 0.260284 | + | 0.450825i | 0.966317 | − | 0.257353i | \(-0.0828504\pi\) |
−0.706033 | + | 0.708179i | \(0.749517\pi\) | |||||||
\(420\) | 7.55218 | − | 0.682695i | 0.368509 | − | 0.0333121i | ||||
\(421\) | −2.97812 | + | 5.15826i | −0.145145 | + | 0.251398i | −0.929427 | − | 0.369006i | \(-0.879698\pi\) |
0.784282 | + | 0.620404i | \(0.213031\pi\) | |||||||
\(422\) | 7.78720 | 0.379075 | ||||||||
\(423\) | −4.25366 | + | 0.775373i | −0.206820 | + | 0.0376999i | ||||
\(424\) | 7.91724 | 0.384495 | ||||||||
\(425\) | 1.62086 | − | 2.80741i | 0.0786232 | − | 0.136179i | ||||
\(426\) | 2.33117 | + | 3.30890i | 0.112946 | + | 0.160317i | ||||
\(427\) | −14.1610 | − | 24.5276i | −0.685300 | − | 1.18697i | ||||
\(428\) | 3.23964 | + | 5.61122i | 0.156594 | + | 0.271229i | ||||
\(429\) | −0.167529 | + | 0.361990i | −0.00808837 | + | 0.0174771i | ||||
\(430\) | 3.76547 | − | 6.52198i | 0.181587 | − | 0.314518i | ||||
\(431\) | −29.7924 | −1.43505 | −0.717524 | − | 0.696534i | \(-0.754725\pi\) | ||||
−0.717524 | + | 0.696534i | \(0.754725\pi\) | |||||||
\(432\) | −2.01157 | + | 7.77592i | −0.0967817 | + | 0.374119i | ||||
\(433\) | −18.3601 | −0.882332 | −0.441166 | − | 0.897426i | \(-0.645435\pi\) | ||||
−0.441166 | + | 0.897426i | \(0.645435\pi\) | |||||||
\(434\) | 3.83899 | − | 6.64932i | 0.184277 | − | 0.319178i | ||||
\(435\) | −3.85342 | + | 8.32632i | −0.184757 | + | 0.399217i | ||||
\(436\) | −3.81946 | − | 6.61550i | −0.182919 | − | 0.316825i | ||||
\(437\) | 4.75194 | + | 8.23061i | 0.227316 | + | 0.393723i | ||||
\(438\) | 3.51316 | + | 4.98662i | 0.167865 | + | 0.238270i | ||||
\(439\) | −7.50668 | + | 13.0020i | −0.358274 | + | 0.620549i | −0.987673 | − | 0.156534i | \(-0.949968\pi\) |
0.629398 | + | 0.777083i | \(0.283301\pi\) | |||||||
\(440\) | 0.544533 | 0.0259596 | ||||||||
\(441\) | −0.900294 | + | 2.51867i | −0.0428711 | + | 0.119937i | ||||
\(442\) | −2.15406 | −0.102458 | ||||||||
\(443\) | 9.83816 | − | 17.0402i | 0.467425 | − | 0.809604i | −0.531882 | − | 0.846818i | \(-0.678515\pi\) |
0.999307 | + | 0.0372145i | \(0.0118485\pi\) | |||||||
\(444\) | −7.94953 | + | 0.718615i | −0.377268 | + | 0.0341039i | ||||
\(445\) | 3.52310 | + | 6.10219i | 0.167011 | + | 0.289272i | ||||
\(446\) | 0.325366 | + | 0.563551i | 0.0154065 | + | 0.0266849i | ||||
\(447\) | 38.2936 | − | 3.46163i | 1.81123 | − | 0.163730i | ||||
\(448\) | −1.03013 | + | 1.78424i | −0.0486691 | + | 0.0842974i | ||||
\(449\) | 22.3106 | 1.05290 | 0.526452 | − | 0.850205i | \(-0.323522\pi\) | ||||
0.526452 | + | 0.850205i | \(0.323522\pi\) | |||||||
\(450\) | −0.670976 | + | 1.87713i | −0.0316301 | + | 0.0884887i | ||||
\(451\) | 0.804060 | 0.0378617 | ||||||||
\(452\) | −12.5825 | + | 21.7936i | −0.591833 | + | 1.02508i | ||||
\(453\) | −4.01342 | − | 5.69669i | −0.188567 | − | 0.267654i | ||||
\(454\) | −5.30594 | − | 9.19016i | −0.249020 | − | 0.431316i | ||||
\(455\) | 1.40460 | + | 2.43283i | 0.0658486 | + | 0.114053i | ||||
\(456\) | 6.53773 | − | 14.1265i | 0.306157 | − | 0.661533i | ||||
\(457\) | 17.5884 | − | 30.4640i | 0.822751 | − | 1.42505i | −0.0808747 | − | 0.996724i | \(-0.525771\pi\) |
0.903626 | − | 0.428323i | \(-0.140895\pi\) | |||||||
\(458\) | −6.84031 | −0.319627 | ||||||||
\(459\) | −16.2321 | + | 4.50035i | −0.757651 | + | 0.210058i | ||||
\(460\) | −3.89698 | −0.181698 | ||||||||
\(461\) | 19.8328 | − | 34.3514i | 0.923706 | − | 1.59991i | 0.130077 | − | 0.991504i | \(-0.458478\pi\) |
0.793629 | − | 0.608402i | \(-0.208189\pi\) | |||||||
\(462\) | −0.312719 | + | 0.675713i | −0.0145490 | + | 0.0314370i | ||||
\(463\) | −2.66388 | − | 4.61398i | −0.123801 | − | 0.214430i | 0.797463 | − | 0.603369i | \(-0.206175\pi\) |
−0.921264 | + | 0.388939i | \(0.872842\pi\) | |||||||
\(464\) | 4.09394 | + | 7.09090i | 0.190056 | + | 0.329187i | ||||
\(465\) | −4.10316 | − | 5.82407i | −0.190279 | − | 0.270085i | ||||
\(466\) | −2.56880 | + | 4.44930i | −0.118998 | + | 0.206110i | ||||
\(467\) | 6.02093 | 0.278615 | 0.139308 | − | 0.990249i | \(-0.455512\pi\) | ||||
0.139308 | + | 0.990249i | \(0.455512\pi\) | |||||||
\(468\) | −4.59960 | + | 0.838433i | −0.212617 | + | 0.0387566i | ||||
\(469\) | 5.67269 | 0.261940 | ||||||||
\(470\) | −0.478842 | + | 0.829379i | −0.0220873 | + | 0.0382564i | ||||
\(471\) | 37.6610 | − | 3.40444i | 1.73533 | − | 0.156868i | ||||
\(472\) | 9.21298 | + | 15.9574i | 0.424062 | + | 0.734497i | ||||
\(473\) | −1.30501 | − | 2.26035i | −0.0600045 | − | 0.103931i | ||||
\(474\) | −6.18673 | + | 0.559262i | −0.284166 | + | 0.0256878i | ||||
\(475\) | −1.90038 | + | 3.29155i | −0.0871954 | + | 0.151027i | ||||
\(476\) | 14.1923 | 0.650504 | ||||||||
\(477\) | 6.50110 | + | 7.65752i | 0.297665 | + | 0.350614i | ||||
\(478\) | 9.71382 | 0.444300 | ||||||||
\(479\) | 10.2229 | − | 17.7066i | 0.467098 | − | 0.809037i | −0.532196 | − | 0.846621i | \(-0.678633\pi\) |
0.999293 | + | 0.0375843i | \(0.0119663\pi\) | |||||||
\(480\) | 5.74210 | + | 8.15041i | 0.262090 | + | 0.372014i | ||||
\(481\) | −1.47850 | − | 2.56084i | −0.0674138 | − | 0.116764i | ||||
\(482\) | −4.75531 | − | 8.23643i | −0.216598 | − | 0.375159i | ||||
\(483\) | 5.11004 | − | 11.0416i | 0.232515 | − | 0.502410i | ||||
\(484\) | −8.53023 | + | 14.7748i | −0.387738 | + | 0.671581i | ||||
\(485\) | −3.26442 | −0.148230 | ||||||||
\(486\) | 9.32362 | − | 4.51257i | 0.422928 | − | 0.204694i | ||||
\(487\) | −11.8179 | −0.535518 | −0.267759 | − | 0.963486i | \(-0.586283\pi\) | ||||
−0.267759 | + | 0.963486i | \(0.586283\pi\) | |||||||
\(488\) | 11.9195 | − | 20.6452i | 0.539571 | − | 0.934564i | ||||
\(489\) | −7.62868 | + | 16.4838i | −0.344981 | + | 0.745422i | ||||
\(490\) | 0.296219 | + | 0.513066i | 0.0133818 | + | 0.0231780i | ||||
\(491\) | 21.0956 | + | 36.5387i | 0.952031 | + | 1.64897i | 0.741020 | + | 0.671483i | \(0.234342\pi\) |
0.211011 | + | 0.977484i | \(0.432324\pi\) | |||||||
\(492\) | 5.42804 | + | 7.70463i | 0.244715 | + | 0.347351i | ||||
\(493\) | −8.58578 | + | 14.8710i | −0.386684 | + | 0.669756i | ||||
\(494\) | 2.52553 | 0.113629 | ||||||||
\(495\) | 0.447133 | + | 0.526670i | 0.0200971 | + | 0.0236720i | ||||
\(496\) | −6.35797 | −0.285481 | ||||||||
\(497\) | 4.93978 | − | 8.55594i | 0.221579 | − | 0.383787i | ||||
\(498\) | 0.115065 | − | 0.0104015i | 0.00515617 | − | 0.000466102i | ||||
\(499\) | 18.8086 | + | 32.5775i | 0.841989 | + | 1.45837i | 0.888211 | + | 0.459437i | \(0.151949\pi\) |
−0.0462216 | + | 0.998931i | \(0.514718\pi\) | |||||||
\(500\) | −0.779232 | − | 1.34967i | −0.0348483 | − | 0.0603591i | ||||
\(501\) | 11.4064 | − | 1.03110i | 0.509600 | − | 0.0460663i | ||||
\(502\) | 6.32223 | − | 10.9504i | 0.282175 | − | 0.488741i | ||||
\(503\) | 29.4702 | 1.31401 | 0.657005 | − | 0.753886i | \(-0.271823\pi\) | ||||
0.657005 | + | 0.753886i | \(0.271823\pi\) | |||||||
\(504\) | −19.6043 | + | 3.57354i | −0.873244 | + | 0.159178i | ||||
\(505\) | −11.1580 | −0.496525 | ||||||||
\(506\) | 0.191321 | − | 0.331378i | 0.00850526 | − | 0.0147315i | ||||
\(507\) | −0.997554 | − | 1.41594i | −0.0443029 | − | 0.0628841i | ||||
\(508\) | 13.8292 | + | 23.9528i | 0.613570 | + | 1.06273i | ||||
\(509\) | 10.5176 | + | 18.2170i | 0.466185 | + | 0.807456i | 0.999254 | − | 0.0386160i | \(-0.0122949\pi\) |
−0.533069 | + | 0.846071i | \(0.678962\pi\) | |||||||
\(510\) | −1.56700 | + | 3.38592i | −0.0693879 | + | 0.149931i | ||||
\(511\) | 7.44442 | − | 12.8941i | 0.329322 | − | 0.570402i | ||||
\(512\) | 16.2075 | 0.716275 | ||||||||
\(513\) | 19.0314 | − | 5.27645i | 0.840257 | − | 0.232961i | ||||
\(514\) | −9.26367 | −0.408603 | ||||||||
\(515\) | −6.33925 | + | 10.9799i | −0.279341 | + | 0.483833i | ||||
\(516\) | 12.8491 | − | 27.7639i | 0.565652 | − | 1.22224i | ||||
\(517\) | 0.165954 | + | 0.287441i | 0.00729865 | + | 0.0126416i | ||||
\(518\) | −2.75985 | − | 4.78021i | −0.121261 | − | 0.210030i | ||||
\(519\) | −17.2459 | − | 24.4791i | −0.757012 | − | 1.07451i | ||||
\(520\) | −1.18227 | + | 2.04775i | −0.0518458 | + | 0.0897996i | ||||
\(521\) | 30.7616 | 1.34769 | 0.673845 | − | 0.738873i | \(-0.264642\pi\) | ||||
0.673845 | + | 0.738873i | \(0.264642\pi\) | |||||||
\(522\) | 3.55420 | − | 9.94326i | 0.155563 | − | 0.435205i | ||||
\(523\) | −14.0570 | −0.614672 | −0.307336 | − | 0.951601i | \(-0.599438\pi\) | ||||
−0.307336 | + | 0.951601i | \(0.599438\pi\) | |||||||
\(524\) | −11.7991 | + | 20.4366i | −0.515446 | + | 0.892778i | ||||
\(525\) | 4.84591 | − | 0.438056i | 0.211493 | − | 0.0191183i | ||||
\(526\) | 3.97290 | + | 6.88127i | 0.173227 | + | 0.300038i | ||||
\(527\) | −6.66695 | − | 11.5475i | −0.290417 | − | 0.503017i | ||||
\(528\) | 0.614056 | − | 0.0555089i | 0.0267234 | − | 0.00241572i | ||||
\(529\) | 8.37369 | − | 14.5037i | 0.364073 | − | 0.630594i | ||||
\(530\) | 2.22491 | 0.0966437 | ||||||||
\(531\) | −7.86881 | + | 22.0138i | −0.341477 | + | 0.955319i | ||||
\(532\) | −16.6398 | −0.721428 | ||||||||
\(533\) | −1.74574 | + | 3.02371i | −0.0756164 | + | 0.130971i | ||||
\(534\) | −4.67062 | − | 6.62953i | −0.202117 | − | 0.286888i | ||||
\(535\) | 2.07874 | + | 3.60048i | 0.0898717 | + | 0.155662i | ||||
\(536\) | 2.38738 | + | 4.13507i | 0.103119 | + | 0.178608i | ||||
\(537\) | −11.0479 | + | 23.8718i | −0.476750 | + | 1.03014i | ||||
\(538\) | −0.845892 | + | 1.46513i | −0.0364690 | + | 0.0631661i | ||||
\(539\) | 0.205324 | 0.00884391 | ||||||||
\(540\) | −2.02813 | + | 7.83994i | −0.0872768 | + | 0.337377i | ||||
\(541\) | 16.4764 | 0.708374 | 0.354187 | − | 0.935175i | \(-0.384758\pi\) | ||||
0.354187 | + | 0.935175i | \(0.384758\pi\) | |||||||
\(542\) | −5.51559 | + | 9.55328i | −0.236915 | + | 0.410349i | ||||
\(543\) | −17.7059 | + | 38.2582i | −0.759832 | + | 1.64182i | ||||
\(544\) | 9.32996 | + | 16.1600i | 0.400019 | + | 0.692852i | ||||
\(545\) | −2.45078 | − | 4.24488i | −0.104980 | − | 0.181831i | ||||
\(546\) | −1.86209 | − | 2.64308i | −0.0796902 | − | 0.113113i | ||||
\(547\) | 23.0919 | − | 39.9964i | 0.987339 | − | 1.71012i | 0.356295 | − | 0.934374i | \(-0.384040\pi\) |
0.631044 | − | 0.775747i | \(-0.282627\pi\) | |||||||
\(548\) | −32.4293 | −1.38531 | ||||||||
\(549\) | 29.7554 | − | 5.42393i | 1.26993 | − | 0.231488i | ||||
\(550\) | 0.153025 | 0.00652500 | ||||||||
\(551\) | 10.0664 | − | 17.4355i | 0.428844 | − | 0.742779i | ||||
\(552\) | 10.1993 | − | 0.921987i | 0.434111 | − | 0.0392424i | ||||
\(553\) | 7.58117 | + | 13.1310i | 0.322384 | + | 0.558386i | ||||
\(554\) | 5.94901 | + | 10.3040i | 0.252749 | + | 0.437775i | ||||
\(555\) | −5.10087 | + | 0.461104i | −0.216520 | + | 0.0195728i | ||||
\(556\) | −5.24091 | + | 9.07752i | −0.222264 | + | 0.384973i | ||||
\(557\) | −38.2914 | −1.62246 | −0.811229 | − | 0.584728i | \(-0.801201\pi\) | ||||
−0.811229 | + | 0.584728i | \(0.801201\pi\) | |||||||
\(558\) | 5.30668 | + | 6.25064i | 0.224650 | + | 0.264611i | ||||
\(559\) | 11.3335 | 0.479358 | ||||||||
\(560\) | 2.17114 | − | 3.76053i | 0.0917475 | − | 0.158911i | ||||
\(561\) | 0.744715 | + | 1.05706i | 0.0314419 | + | 0.0446290i | ||||
\(562\) | −1.57105 | − | 2.72115i | −0.0662709 | − | 0.114785i | ||||
\(563\) | 5.14550 | + | 8.91227i | 0.216857 | + | 0.375607i | 0.953845 | − | 0.300298i | \(-0.0970861\pi\) |
−0.736988 | + | 0.675905i | \(0.763753\pi\) | |||||||
\(564\) | −1.63398 | + | 3.53065i | −0.0688031 | + | 0.148667i | ||||
\(565\) | −8.07368 | + | 13.9840i | −0.339662 | + | 0.588312i | ||||
\(566\) | −3.97285 | −0.166991 | ||||||||
\(567\) | −19.5540 | − | 16.0268i | −0.821191 | − | 0.673063i | ||||
\(568\) | 8.31574 | 0.348921 | ||||||||
\(569\) | 6.01983 | − | 10.4266i | 0.252364 | − | 0.437108i | −0.711812 | − | 0.702370i | \(-0.752125\pi\) |
0.964176 | + | 0.265262i | \(0.0854586\pi\) | |||||||
\(570\) | 1.83723 | − | 3.96983i | 0.0769532 | − | 0.166278i | ||||
\(571\) | −10.2247 | − | 17.7097i | −0.427890 | − | 0.741127i | 0.568796 | − | 0.822479i | \(-0.307410\pi\) |
−0.996685 | + | 0.0813519i | \(0.974076\pi\) | |||||||
\(572\) | 0.179451 | + | 0.310818i | 0.00750322 | + | 0.0129960i | ||||
\(573\) | −14.2291 | − | 20.1970i | −0.594430 | − | 0.843742i | ||||
\(574\) | −3.25870 | + | 5.64424i | −0.136016 | + | 0.235586i | ||||
\(575\) | −2.50052 | −0.104279 | ||||||||
\(576\) | −1.42396 | − | 1.67726i | −0.0593318 | − | 0.0698858i | ||||
\(577\) | 8.66059 | 0.360545 | 0.180273 | − | 0.983617i | \(-0.442302\pi\) | ||||
0.180273 | + | 0.983617i | \(0.442302\pi\) | |||||||
\(578\) | 2.15667 | − | 3.73546i | 0.0897055 | − | 0.155375i | ||||
\(579\) | 44.1313 | − | 3.98934i | 1.83403 | − | 0.165791i | ||||
\(580\) | 4.12764 | + | 7.14928i | 0.171391 | + | 0.296858i | ||||
\(581\) | −0.140999 | − | 0.244218i | −0.00584964 | − | 0.0101319i | ||||
\(582\) | 3.74182 | − | 0.338250i | 0.155103 | − | 0.0140209i | ||||
\(583\) | 0.385547 | − | 0.667787i | 0.0159677 | − | 0.0276569i | ||||
\(584\) | 12.5321 | 0.518582 | ||||||||
\(585\) | −2.95137 | + | 0.537986i | −0.122024 | + | 0.0222430i | ||||
\(586\) | −10.3732 | −0.428513 | ||||||||
\(587\) | −19.6997 | + | 34.1208i | −0.813092 | + | 1.40832i | 0.0975972 | + | 0.995226i | \(0.468884\pi\) |
−0.910690 | + | 0.413091i | \(0.864449\pi\) | |||||||
\(588\) | 1.38610 | + | 1.96744i | 0.0571616 | + | 0.0811359i | ||||
\(589\) | 7.81668 | + | 13.5389i | 0.322081 | + | 0.557860i | ||||
\(590\) | 2.58903 | + | 4.48434i | 0.106589 | + | 0.184617i | ||||
\(591\) | −7.49114 | + | 16.1866i | −0.308145 | + | 0.665828i | ||||
\(592\) | −2.28537 | + | 3.95839i | −0.0939283 | + | 0.162689i | ||||
\(593\) | 4.26159 | 0.175002 | 0.0875012 | − | 0.996164i | \(-0.472112\pi\) | ||||
0.0875012 | + | 0.996164i | \(0.472112\pi\) | |||||||
\(594\) | −0.567095 | − | 0.557360i | −0.0232682 | − | 0.0228688i | ||||
\(595\) | 9.10661 | 0.373335 | ||||||||
\(596\) | 17.2982 | − | 29.9613i | 0.708560 | − | 1.22726i | ||||
\(597\) | −2.41211 | + | 5.21200i | −0.0987211 | + | 0.213313i | ||||
\(598\) | 0.830776 | + | 1.43895i | 0.0339730 | + | 0.0588429i | ||||
\(599\) | 13.3206 | + | 23.0720i | 0.544266 | + | 0.942696i | 0.998653 | + | 0.0518919i | \(0.0165251\pi\) |
−0.454387 | + | 0.890805i | \(0.650142\pi\) | |||||||
\(600\) | 2.35875 | + | 3.34804i | 0.0962955 | + | 0.136683i | ||||
\(601\) | −21.2732 | + | 36.8462i | −0.867751 | + | 1.50299i | −0.00346220 | + | 0.999994i | \(0.501102\pi\) |
−0.864289 | + | 0.502995i | \(0.832231\pi\) | |||||||
\(602\) | 21.1559 | 0.862249 | ||||||||
\(603\) | −2.03906 | + | 5.70450i | −0.0830371 | + | 0.232305i | ||||
\(604\) | −6.27010 | −0.255127 | ||||||||
\(605\) | −5.47348 | + | 9.48035i | −0.222529 | + | 0.385431i | ||||
\(606\) | 12.7898 | − | 1.15616i | 0.519549 | − | 0.0469657i | ||||
\(607\) | −5.14131 | − | 8.90502i | −0.208679 | − | 0.361443i | 0.742619 | − | 0.669714i | \(-0.233583\pi\) |
−0.951299 | + | 0.308270i | \(0.900250\pi\) | |||||||
\(608\) | −10.9389 | − | 18.9468i | −0.443632 | − | 0.768393i | ||||
\(609\) | −25.6691 | + | 2.32041i | −1.04016 | + | 0.0940278i | ||||
\(610\) | 3.34962 | − | 5.80171i | 0.135622 | − | 0.234904i | ||||
\(611\) | −1.44125 | −0.0583067 | ||||||||
\(612\) | −5.10148 | + | 14.2719i | −0.206215 | + | 0.576909i | ||||
\(613\) | 2.78688 | 0.112561 | 0.0562804 | − | 0.998415i | \(-0.482076\pi\) | ||||
0.0562804 | + | 0.998415i | \(0.482076\pi\) | |||||||
\(614\) | −7.90650 | + | 13.6945i | −0.319080 | + | 0.552663i | ||||
\(615\) | 3.48294 | + | 4.94373i | 0.140446 | + | 0.199350i | ||||
\(616\) | 0.764850 | + | 1.32476i | 0.0308167 | + | 0.0533761i | ||||
\(617\) | −21.4024 | − | 37.0700i | −0.861627 | − | 1.49238i | −0.870358 | − | 0.492420i | \(-0.836113\pi\) |
0.00873099 | − | 0.999962i | \(-0.497221\pi\) | |||||||
\(618\) | 6.12861 | − | 13.2425i | 0.246529 | − | 0.532691i | ||||
\(619\) | −3.74849 | + | 6.49257i | −0.150664 | + | 0.260958i | −0.931472 | − | 0.363813i | \(-0.881475\pi\) |
0.780807 | + | 0.624772i | \(0.214808\pi\) | |||||||
\(620\) | −6.41031 | −0.257444 | ||||||||
\(621\) | 9.26670 | + | 9.10764i | 0.371860 | + | 0.365477i | ||||
\(622\) | 1.03594 | 0.0415376 | ||||||||
\(623\) | −9.89708 | + | 17.1422i | −0.396518 | + | 0.686790i | ||||
\(624\) | −1.12447 | + | 2.42971i | −0.0450148 | + | 0.0972663i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 9.13363 | + | 15.8199i | 0.365053 | + | 0.632291i | ||||
\(627\) | −0.873142 | − | 1.23935i | −0.0348699 | − | 0.0494948i | ||||
\(628\) | 17.0124 | − | 29.4663i | 0.678868 | − | 1.17583i | ||||
\(629\) | −9.58575 | −0.382209 | ||||||||
\(630\) | −5.50920 | + | 1.00424i | −0.219492 | + | 0.0400098i | ||||
\(631\) | 2.02620 | 0.0806619 | 0.0403310 | − | 0.999186i | \(-0.487159\pi\) | ||||
0.0403310 | + | 0.999186i | \(0.487159\pi\) | |||||||
\(632\) | −6.38117 | + | 11.0525i | −0.253829 | + | 0.439645i | ||||
\(633\) | 20.2158 | − | 1.82745i | 0.803507 | − | 0.0726348i | ||||
\(634\) | 5.08449 | + | 8.80659i | 0.201931 | + | 0.349754i | ||||
\(635\) | 8.87359 | + | 15.3695i | 0.352138 | + | 0.609920i | ||||
\(636\) | 9.00158 | − | 0.813717i | 0.356936 | − | 0.0322660i | ||||
\(637\) | −0.445790 | + | 0.772130i | −0.0176628 | + | 0.0305929i | ||||
\(638\) | −0.810581 | −0.0320912 | ||||||||
\(639\) | 6.82832 | + | 8.04294i | 0.270124 | + | 0.318174i | ||||
\(640\) | 11.0250 | 0.435803 | ||||||||
\(641\) | −2.06080 | + | 3.56940i | −0.0813965 | + | 0.140983i | −0.903850 | − | 0.427849i | \(-0.859271\pi\) |
0.822453 | + | 0.568832i | \(0.192605\pi\) | |||||||
\(642\) | −2.75581 | − | 3.91163i | −0.108763 | − | 0.154380i | ||||
\(643\) | 10.1784 | + | 17.6295i | 0.401396 | + | 0.695239i | 0.993895 | − | 0.110333i | \(-0.0351917\pi\) |
−0.592499 | + | 0.805572i | \(0.701858\pi\) | |||||||
\(644\) | −5.47369 | − | 9.48070i | −0.215693 | − | 0.373592i | ||||
\(645\) | 8.24474 | − | 17.8149i | 0.324636 | − | 0.701462i | ||||
\(646\) | 4.09353 | − | 7.09020i | 0.161058 | − | 0.278960i | ||||
\(647\) | −9.76640 | −0.383957 | −0.191978 | − | 0.981399i | \(-0.561490\pi\) | ||||
−0.191978 | + | 0.981399i | \(0.561490\pi\) | |||||||
\(648\) | 3.45323 | − | 20.9988i | 0.135656 | − | 0.824909i | ||||
\(649\) | 1.79458 | 0.0704435 | ||||||||
\(650\) | −0.332241 | + | 0.575458i | −0.0130316 | + | 0.0225713i | ||||
\(651\) | 8.40572 | − | 18.1628i | 0.329446 | − | 0.711856i | ||||
\(652\) | 8.17156 | + | 14.1536i | 0.320023 | + | 0.554296i | ||||
\(653\) | −24.6834 | − | 42.7529i | −0.965937 | − | 1.67305i | −0.707076 | − | 0.707137i | \(-0.749986\pi\) |
−0.258861 | − | 0.965915i | \(-0.583347\pi\) | |||||||
\(654\) | 3.24903 | + | 4.61172i | 0.127047 | + | 0.180332i | ||||
\(655\) | −7.57097 | + | 13.1133i | −0.295822 | + | 0.512379i | ||||
\(656\) | 5.39692 | 0.210714 | ||||||||
\(657\) | 10.2905 | + | 12.1210i | 0.401471 | + | 0.472885i | ||||
\(658\) | −2.69032 | −0.104880 | ||||||||
\(659\) | 3.52180 | − | 6.09994i | 0.137190 | − | 0.237620i | −0.789242 | − | 0.614082i | \(-0.789526\pi\) |
0.926432 | + | 0.376462i | \(0.122860\pi\) | |||||||
\(660\) | 0.619112 | − | 0.0559659i | 0.0240989 | − | 0.00217847i | ||||
\(661\) | 11.1100 | + | 19.2430i | 0.432128 | + | 0.748467i | 0.997056 | − | 0.0766727i | \(-0.0244296\pi\) |
−0.564929 | + | 0.825140i | \(0.691096\pi\) | |||||||
\(662\) | 4.44210 | + | 7.69394i | 0.172647 | + | 0.299034i | ||||
\(663\) | −5.59202 | + | 0.505502i | −0.217176 | + | 0.0196321i | ||||
\(664\) | 0.118681 | − | 0.205561i | 0.00460571 | − | 0.00797733i | ||||
\(665\) | −10.6771 | −0.414039 | ||||||||
\(666\) | 5.79906 | − | 1.05707i | 0.224709 | − | 0.0409608i | ||||
\(667\) | 13.2454 | 0.512865 | ||||||||
\(668\) | 5.15254 | − | 8.92446i | 0.199358 | − | 0.345298i | ||||
\(669\) | 0.976913 | + | 1.38664i | 0.0377696 | + | 0.0536107i | ||||
\(670\) | 0.670903 | + | 1.16204i | 0.0259192 | + | 0.0448934i | ||||
\(671\) | −1.16089 | − | 2.01072i | −0.0448157 | − | 0.0776230i | ||||
\(672\) | −11.7633 | + | 25.4176i | −0.453778 | + | 0.980506i | ||||
\(673\) | 5.46905 | − | 9.47267i | 0.210816 | − | 0.365145i | −0.741154 | − | 0.671335i | \(-0.765721\pi\) |
0.951970 | + | 0.306191i | \(0.0990545\pi\) | |||||||
\(674\) | 23.2304 | 0.894801 | ||||||||
\(675\) | −1.30136 | + | 5.03055i | −0.0500895 | + | 0.193626i | ||||
\(676\) | −1.55846 | −0.0599409 | ||||||||
\(677\) | −4.35062 | + | 7.53550i | −0.167208 | + | 0.289613i | −0.937437 | − | 0.348154i | \(-0.886808\pi\) |
0.770229 | + | 0.637767i | \(0.220142\pi\) | |||||||
\(678\) | 7.80541 | − | 16.8656i | 0.299765 | − | 0.647721i | ||||
\(679\) | −4.58520 | − | 7.94180i | −0.175964 | − | 0.304778i | ||||
\(680\) | 3.83257 | + | 6.63821i | 0.146972 | + | 0.254564i | ||||
\(681\) | −15.9311 | − | 22.6128i | −0.610481 | − | 0.866525i | ||||
\(682\) | 0.314712 | − | 0.545098i | 0.0120510 | − | 0.0208729i | ||||
\(683\) | 7.83468 | 0.299786 | 0.149893 | − | 0.988702i | \(-0.452107\pi\) | ||||
0.149893 | + | 0.988702i | \(0.452107\pi\) | |||||||
\(684\) | 5.98124 | − | 16.7332i | 0.228698 | − | 0.639809i | ||||
\(685\) | −20.8085 | −0.795053 | ||||||||
\(686\) | 5.70117 | − | 9.87471i | 0.217672 | − | 0.377018i | ||||
\(687\) | −17.7577 | + | 1.60524i | −0.677498 | + | 0.0612439i | ||||
\(688\) | −8.75935 | − | 15.1716i | −0.333947 | − | 0.578413i | ||||
\(689\) | 1.67417 | + | 2.89974i | 0.0637806 | + | 0.110471i | ||||
\(690\) | 2.86621 | − | 0.259097i | 0.109115 | − | 0.00986365i | ||||
\(691\) | 18.7536 | − | 32.4822i | 0.713420 | − | 1.23568i | −0.250145 | − | 0.968208i | \(-0.580478\pi\) |
0.963566 | − | 0.267472i | \(-0.0861882\pi\) | |||||||
\(692\) | −26.9431 | −1.02422 | ||||||||
\(693\) | −0.653258 | + | 1.82756i | −0.0248152 | + | 0.0694233i | ||||
\(694\) | −16.1410 | −0.612703 | ||||||||
\(695\) | −3.36287 | + | 5.82466i | −0.127561 | + | 0.220942i | ||||
\(696\) | −12.4944 | − | 17.7348i | −0.473600 | − | 0.672234i | ||||
\(697\) | 5.65920 | + | 9.80201i | 0.214357 | + | 0.371278i | ||||
\(698\) | −10.7371 | − | 18.5972i | −0.406405 | − | 0.703915i | ||||
\(699\) | −5.62457 | + | 12.1534i | −0.212741 | + | 0.459683i | ||||
\(700\) | 2.18902 | − | 3.79149i | 0.0827370 | − | 0.143305i | ||||
\(701\) | −34.0001 | −1.28416 | −0.642082 | − | 0.766636i | \(-0.721929\pi\) | ||||
−0.642082 | + | 0.766636i | \(0.721929\pi\) | |||||||
\(702\) | 3.32724 | − | 0.922474i | 0.125578 | − | 0.0348166i | ||||
\(703\) | 11.2388 | 0.423881 | ||||||||
\(704\) | −0.0844479 | + | 0.146268i | −0.00318275 | + | 0.00551269i | ||||
\(705\) | −1.04846 | + | 2.26547i | −0.0394872 | + | 0.0853225i | ||||
\(706\) | 11.3401 | + | 19.6416i | 0.426789 | + | 0.739221i | ||||
\(707\) | −15.6725 | − | 27.1456i | −0.589426 | − | 1.02091i | ||||
\(708\) | 12.1148 | + | 17.1960i | 0.455304 | + | 0.646264i | ||||
\(709\) | 20.4335 | − | 35.3919i | 0.767397 | − | 1.32917i | −0.171573 | − | 0.985171i | \(-0.554885\pi\) |
0.938970 | − | 0.343999i | \(-0.111782\pi\) | |||||||
\(710\) | 2.33689 | 0.0877019 | ||||||||
\(711\) | −15.9297 | + | 2.90373i | −0.597411 | + | 0.108898i | ||||
\(712\) | −16.6610 | −0.624397 | ||||||||
\(713\) | −5.14260 | + | 8.90725i | −0.192592 | + | 0.333579i | ||||
\(714\) | −10.4384 | + | 0.943600i | −0.390647 | + | 0.0353133i | ||||
\(715\) | 0.115146 | + | 0.199439i | 0.00430621 | + | 0.00745858i | ||||
\(716\) | 11.8341 | + | 20.4972i | 0.442260 | + | 0.766016i | ||||
\(717\) | 25.2174 | − | 2.27958i | 0.941761 | − | 0.0851325i | ||||
\(718\) | −8.41556 | + | 14.5762i | −0.314066 | + | 0.543978i | ||||
\(719\) | −33.2593 | −1.24036 | −0.620181 | − | 0.784459i | \(-0.712941\pi\) | ||||
−0.620181 | + | 0.784459i | \(0.712941\pi\) | |||||||
\(720\) | 3.00120 | + | 3.53505i | 0.111848 | + | 0.131744i | ||||
\(721\) | −35.6164 | −1.32642 | ||||||||
\(722\) | 1.51310 | − | 2.62077i | 0.0563119 | − | 0.0975351i | ||||
\(723\) | −14.2778 | − | 20.2661i | −0.530998 | − | 0.753705i | ||||
\(724\) | 18.9659 | + | 32.8499i | 0.704862 | + | 1.22086i | ||||
\(725\) | 2.64853 | + | 4.58739i | 0.0983639 | + | 0.170371i | ||||
\(726\) | 5.29161 | − | 11.4339i | 0.196390 | − | 0.424353i | ||||
\(727\) | −7.54471 | + | 13.0678i | −0.279818 | + | 0.484659i | −0.971339 | − | 0.237697i | \(-0.923607\pi\) |
0.691521 | + | 0.722356i | \(0.256941\pi\) | |||||||
\(728\) | −6.64244 | −0.246185 | ||||||||
\(729\) | 23.1455 | − | 13.9028i | 0.857239 | − | 0.514918i | ||||
\(730\) | 3.52178 | 0.130347 | ||||||||
\(731\) | 18.3701 | − | 31.8179i | 0.679441 | − | 1.17683i | ||||
\(732\) | 11.4301 | − | 24.6978i | 0.422469 | − | 0.912856i | ||||
\(733\) | 3.43481 | + | 5.94926i | 0.126867 | + | 0.219741i | 0.922461 | − | 0.386089i | \(-0.126174\pi\) |
−0.795594 | + | 0.605830i | \(0.792841\pi\) | |||||||
\(734\) | −1.19140 | − | 2.06357i | −0.0439756 | − | 0.0761679i | ||||
\(735\) | 0.889398 | + | 1.26242i | 0.0328059 | + | 0.0465652i | ||||
\(736\) | 7.19674 | − | 12.4651i | 0.265275 | − | 0.459470i | ||||
\(737\) | 0.465035 | 0.0171298 | ||||||||
\(738\) | −4.50455 | − | 5.30582i | −0.165815 | − | 0.195310i | ||||
\(739\) | 53.1537 | 1.95529 | 0.977645 | − | 0.210265i | \(-0.0674326\pi\) | ||||
0.977645 | + | 0.210265i | \(0.0674326\pi\) | |||||||
\(740\) | −2.30419 | + | 3.99097i | −0.0847037 | + | 0.146711i | ||||
\(741\) | 6.55637 | − | 0.592677i | 0.240854 | − | 0.0217725i | ||||
\(742\) | 3.12510 | + | 5.41283i | 0.114726 | + | 0.198711i | ||||
\(743\) | −21.3602 | − | 36.9969i | −0.783629 | − | 1.35729i | −0.929815 | − | 0.368028i | \(-0.880033\pi\) |
0.146185 | − | 0.989257i | \(-0.453300\pi\) | |||||||
\(744\) | 16.7773 | − | 1.51662i | 0.615084 | − | 0.0556018i | ||||
\(745\) | 11.0995 | − | 19.2249i | 0.406654 | − | 0.704345i | ||||
\(746\) | 0.953590 | 0.0349134 | ||||||||
\(747\) | 0.296271 | − | 0.0540053i | 0.0108400 | − | 0.00197595i | ||||
\(748\) | 1.16346 | 0.0425402 | ||||||||
\(749\) | −5.83959 | + | 10.1145i | −0.213374 | + | 0.369574i | ||||
\(750\) | 0.662856 | + | 0.940866i | 0.0242041 | + | 0.0343556i | ||||
\(751\) | −8.29029 | − | 14.3592i | −0.302517 | − | 0.523975i | 0.674188 | − | 0.738559i | \(-0.264494\pi\) |
−0.976705 | + | 0.214585i | \(0.931160\pi\) | |||||||
\(752\) | 1.11390 | + | 1.92933i | 0.0406197 | + | 0.0703554i | ||||
\(753\) | 13.8429 | − | 29.9113i | 0.504465 | − | 1.09003i | ||||
\(754\) | 1.75990 | − | 3.04823i | 0.0640917 | − | 0.111010i | ||||
\(755\) | −4.02326 | −0.146421 | ||||||||
\(756\) | −21.9220 | + | 6.07785i | −0.797294 | + | 0.221049i | ||||
\(757\) | −28.7091 | −1.04345 | −0.521725 | − | 0.853114i | \(-0.674711\pi\) | ||||
−0.521725 | + | 0.853114i | \(0.674711\pi\) | |||||||
\(758\) | −11.4669 | + | 19.8613i | −0.416497 | + | 0.721394i | ||||
\(759\) | 0.418910 | − | 0.905166i | 0.0152055 | − | 0.0328555i | ||||
\(760\) | −4.49351 | − | 7.78299i | −0.162997 | − | 0.282319i | ||||
\(761\) | 3.37843 | + | 5.85160i | 0.122468 | + | 0.212121i | 0.920740 | − | 0.390176i | \(-0.127586\pi\) |
−0.798272 | + | 0.602296i | \(0.794253\pi\) | |||||||
\(762\) | −11.7638 | − | 16.6977i | −0.426158 | − | 0.604895i | ||||
\(763\) | 6.88473 | − | 11.9247i | 0.249244 | − | 0.431703i | ||||
\(764\) | −22.2300 | −0.804252 | ||||||||
\(765\) | −3.27340 | + | 9.15769i | −0.118350 | + | 0.331097i | ||||
\(766\) | 4.41384 | 0.159479 | ||||||||
\(767\) | −3.89632 | + | 6.74863i | −0.140688 | + | 0.243679i | ||||
\(768\) | −15.1676 | + | 1.37111i | −0.547314 | + | 0.0494756i | ||||
\(769\) | 14.3441 | + | 24.8447i | 0.517262 | + | 0.895923i | 0.999799 | + | 0.0200481i | \(0.00638193\pi\) |
−0.482537 | + | 0.875875i | \(0.660285\pi\) | |||||||
\(770\) | 0.214938 | + | 0.372284i | 0.00774583 | + | 0.0134162i | ||||
\(771\) | −24.0488 | + | 2.17394i | −0.866096 | + | 0.0782926i | ||||
\(772\) | 19.9352 | − | 34.5287i | 0.717482 | − | 1.24272i | ||||
\(773\) | 33.4431 | 1.20286 | 0.601432 | − | 0.798924i | \(-0.294597\pi\) | ||||
0.601432 | + | 0.798924i | \(0.294597\pi\) | |||||||
\(774\) | −7.60454 | + | 21.2745i | −0.273339 | + | 0.764697i | ||||
\(775\) | −4.11322 | −0.147751 | ||||||||
\(776\) | 3.85942 | − | 6.68471i | 0.138545 | − | 0.239967i | ||||
\(777\) | −8.28647 | − | 11.7619i | −0.297275 | − | 0.421956i | ||||
\(778\) | −10.0113 | − | 17.3401i | −0.358922 | − | 0.621672i | ||||
\(779\) | −6.63514 | − | 11.4924i | −0.237728 | − | 0.411758i | ||||
\(780\) | −1.13373 | + | 2.44971i | −0.0405939 | + | 0.0877138i | ||||
\(781\) | 0.404952 | − | 0.701398i | 0.0144903 | − | 0.0250980i | ||||
\(782\) | 5.38628 | 0.192613 | ||||||||
\(783\) | 6.89340 | − | 26.6471i | 0.246350 | − | 0.952291i | ||||
\(784\) | 1.37815 | 0.0492196 | ||||||||
\(785\) | 10.9161 | − | 18.9073i | 0.389613 | − | 0.674829i | ||||
\(786\) | 7.31940 | − | 15.8155i | 0.261074 | − | 0.564120i | ||||
\(787\) | 16.1311 | + | 27.9399i | 0.575012 | + | 0.995950i | 0.996040 | + | 0.0889024i | \(0.0283359\pi\) |
−0.421028 | + | 0.907047i | \(0.638331\pi\) | |||||||
\(788\) | 8.02424 | + | 13.8984i | 0.285852 | + | 0.495110i | ||||
\(789\) | 11.9286 | + | 16.9317i | 0.424671 | + | 0.602784i | ||||
\(790\) | −1.79324 | + | 3.10598i | −0.0638005 | + | 0.110506i | ||||
\(791\) | −45.3611 | −1.61286 | ||||||||
\(792\) | −1.60712 | + | 0.292951i | −0.0571064 | + | 0.0104096i | ||||
\(793\) | 10.0819 | 0.358019 | ||||||||
\(794\) | −8.45862 | + | 14.6508i | −0.300185 | + | 0.519936i | ||||
\(795\) | 5.77593 | − | 0.522127i | 0.204851 | − | 0.0185180i | ||||
\(796\) | 2.58376 | + | 4.47521i | 0.0915790 | + | 0.158620i | ||||
\(797\) | 1.82900 | + | 3.16792i | 0.0647865 | + | 0.112214i | 0.896599 | − | 0.442843i | \(-0.146030\pi\) |
−0.831813 | + | 0.555056i | \(0.812697\pi\) | |||||||
\(798\) | 12.2385 | − | 1.10633i | 0.433238 | − | 0.0391635i | ||||
\(799\) | −2.33606 | + | 4.04618i | −0.0826439 | + | 0.143143i | ||||
\(800\) | 5.75618 | 0.203512 | ||||||||
\(801\) | −13.6809 | − | 16.1144i | −0.483389 | − | 0.569375i | ||||
\(802\) | −6.88040 | −0.242955 | ||||||||
\(803\) | 0.610277 | − | 1.05703i | 0.0215362 | − | 0.0373018i | ||||
\(804\) | 3.13935 | + | 4.45603i | 0.110716 | + | 0.157152i | ||||
\(805\) | −3.51223 | − | 6.08336i | −0.123790 | − | 0.214410i | ||||
\(806\) | 1.36658 | + | 2.36699i | 0.0481357 | + | 0.0833735i | ||||
\(807\) | −1.85214 | + | 4.00203i | −0.0651983 | + | 0.140878i | ||||
\(808\) | 13.1917 | − | 22.8488i | 0.464084 | − | 0.803817i | ||||
\(809\) | −32.1556 | −1.13053 | −0.565266 | − | 0.824909i | \(-0.691226\pi\) | ||||
−0.565266 | + | 0.824909i | \(0.691226\pi\) | |||||||
\(810\) | 0.970427 | − | 5.90107i | 0.0340973 | − | 0.207343i | ||||
\(811\) | −34.8894 | −1.22513 | −0.612566 | − | 0.790420i | \(-0.709862\pi\) | ||||
−0.612566 | + | 0.790420i | \(0.709862\pi\) | |||||||
\(812\) | −11.5953 | + | 20.0837i | −0.406917 | + | 0.704801i | ||||
\(813\) | −12.0768 | + | 26.0950i | −0.423550 | + | 0.915192i | ||||
\(814\) | −0.226247 | − | 0.391871i | −0.00792995 | − | 0.0137351i | ||||
\(815\) | 5.24334 | + | 9.08174i | 0.183666 | + | 0.318119i | ||||
\(816\) | 4.99859 | + | 7.09506i | 0.174986 | + | 0.248377i | ||||
\(817\) | −21.5380 | + | 37.3050i | −0.753520 | + | 1.30514i | ||||
\(818\) | 18.8443 | 0.658877 | ||||||||
\(819\) | −5.45432 | − | 6.42453i | −0.190589 | − | 0.224491i | ||||
\(820\) | 5.44135 | 0.190020 | ||||||||
\(821\) | −13.4332 | + | 23.2670i | −0.468823 | + | 0.812025i | −0.999365 | − | 0.0356337i | \(-0.988655\pi\) |
0.530542 | + | 0.847659i | \(0.321988\pi\) | |||||||
\(822\) | 23.8516 | − | 2.15612i | 0.831920 | − | 0.0752032i | ||||
\(823\) | −12.6858 | − | 21.9724i | −0.442198 | − | 0.765909i | 0.555654 | − | 0.831413i | \(-0.312468\pi\) |
−0.997852 | + | 0.0655040i | \(0.979134\pi\) | |||||||
\(824\) | −14.9894 | − | 25.9624i | −0.522180 | − | 0.904442i | ||||
\(825\) | 0.397257 | − | 0.0359109i | 0.0138307 | − | 0.00125026i | ||||
\(826\) | −7.27310 | + | 12.5974i | −0.253064 | + | 0.438319i | ||||
\(827\) | −40.2364 | −1.39916 | −0.699578 | − | 0.714556i | \(-0.746629\pi\) | ||||
−0.699578 | + | 0.714556i | \(0.746629\pi\) | |||||||
\(828\) | 11.5014 | − | 2.09652i | 0.399702 | − | 0.0728592i | ||||
\(829\) | −52.0737 | −1.80859 | −0.904297 | − | 0.426905i | \(-0.859604\pi\) | ||||
−0.904297 | + | 0.426905i | \(0.859604\pi\) | |||||||
\(830\) | 0.0333517 | − | 0.0577669i | 0.00115765 | − | 0.00200512i | ||||
\(831\) | 17.8619 | + | 25.3534i | 0.619623 | + | 0.879501i | ||||
\(832\) | −0.366700 | − | 0.635142i | −0.0127130 | − | 0.0220196i | ||||
\(833\) | 1.44512 | + | 2.50303i | 0.0500706 | + | 0.0867248i | ||||
\(834\) | 3.25113 | − | 7.02492i | 0.112577 | − | 0.243253i | ||||
\(835\) | 3.30617 | − | 5.72645i | 0.114415 | − | 0.198172i | ||||
\(836\) | −1.36410 | −0.0471783 | ||||||||
\(837\) | 15.2432 | + | 14.9815i | 0.526882 | + | 0.517838i | ||||
\(838\) | −7.08056 | −0.244594 | ||||||||
\(839\) | −4.30416 | + | 7.45503i | −0.148596 | + | 0.257376i | −0.930709 | − | 0.365761i | \(-0.880809\pi\) |
0.782113 | + | 0.623137i | \(0.214142\pi\) | |||||||
\(840\) | −4.83213 | + | 10.4411i | −0.166724 | + | 0.360252i | ||||
\(841\) | 0.470583 | + | 0.815074i | 0.0162270 | + | 0.0281060i | ||||
\(842\) | −1.97891 | − | 3.42757i | −0.0681976 | − | 0.118122i | ||||
\(843\) | −4.71709 | − | 6.69550i | −0.162465 | − | 0.230605i | ||||
\(844\) | 9.13199 | − | 15.8171i | 0.314336 | − | 0.544446i | ||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0.967045 | − | 2.70541i | 0.0332477 | − | 0.0930140i | ||||
\(847\) | −30.7522 | −1.05666 | ||||||||
\(848\) | 2.58782 | − | 4.48224i | 0.0888662 | − | 0.153921i | ||||
\(849\) | −10.3137 | + | 0.932324i | −0.353964 | + | 0.0319973i | ||||
\(850\) | 1.07703 | + | 1.86547i | 0.0369418 | + | 0.0639851i | ||||
\(851\) | 3.69702 | + | 6.40344i | 0.126732 | + | 0.219507i | ||||
\(852\) | 9.45465 | − | 0.854673i | 0.323911 | − | 0.0292806i | ||||
\(853\) | −9.79268 | + | 16.9614i | −0.335295 | + | 0.580748i | −0.983541 | − | 0.180683i | \(-0.942169\pi\) |
0.648246 | + | 0.761431i | \(0.275503\pi\) | |||||||
\(854\) | 18.8195 | 0.643989 | ||||||||
\(855\) | 3.83791 | − | 10.7370i | 0.131254 | − | 0.367196i | ||||
\(856\) | −9.83050 | −0.336000 | ||||||||
\(857\) | −8.20070 | + | 14.2040i | −0.280130 | + | 0.485200i | −0.971417 | − | 0.237381i | \(-0.923711\pi\) |
0.691286 | + | 0.722581i | \(0.257044\pi\) | |||||||
\(858\) | −0.152650 | − | 0.216674i | −0.00521140 | − | 0.00739712i | ||||
\(859\) | 10.5276 | + | 18.2343i | 0.359196 | + | 0.622145i | 0.987827 | − | 0.155559i | \(-0.0497177\pi\) |
−0.628631 | + | 0.777704i | \(0.716384\pi\) | |||||||
\(860\) | −8.83146 | − | 15.2965i | −0.301150 | − | 0.521608i | ||||
\(861\) | −7.13515 | + | 15.4174i | −0.243165 | + | 0.525422i | ||||
\(862\) | 9.89824 | − | 17.1443i | 0.337135 | − | 0.583936i | ||||
\(863\) | −26.1830 | −0.891278 | −0.445639 | − | 0.895213i | \(-0.647023\pi\) | ||||
−0.445639 | + | 0.895213i | \(0.647023\pi\) | |||||||
\(864\) | −21.3319 | − | 20.9657i | −0.725725 | − | 0.713267i | ||||
\(865\) | −17.2882 | −0.587817 | ||||||||
\(866\) | 6.09999 | − | 10.5655i | 0.207286 | − | 0.359030i | ||||
\(867\) | 4.72217 | − | 10.2035i | 0.160373 | − | 0.346529i | ||||
\(868\) | −9.00390 | − | 15.5952i | −0.305612 | − | 0.529336i | ||||
\(869\) | 0.621489 | + | 1.07645i | 0.0210826 | + | 0.0365161i | ||||
\(870\) | −3.51119 | − | 4.98382i | −0.119040 | − | 0.168967i | ||||
\(871\) | −1.00966 | + | 1.74879i | −0.0342112 | + | 0.0592555i | ||||
\(872\) | 11.5899 | 0.392484 | ||||||||
\(873\) | 9.63451 | − | 1.75621i | 0.326079 | − | 0.0594389i | ||||
\(874\) | −6.31516 | −0.213613 | ||||||||
\(875\) | 1.40460 | − | 2.43283i | 0.0474841 | − | 0.0822448i | ||||
\(876\) | 14.2485 | − | 1.28802i | 0.481412 | − | 0.0435182i | ||||
\(877\) | −7.97663 | − | 13.8159i | −0.269352 | − | 0.466531i | 0.699343 | − | 0.714786i | \(-0.253476\pi\) |
−0.968695 | + | 0.248255i | \(0.920143\pi\) | |||||||
\(878\) | −4.98805 | − | 8.63956i | −0.168339 | − | 0.291571i | ||||
\(879\) | −26.9292 | + | 2.43432i | −0.908300 | + | 0.0821077i | ||||
\(880\) | 0.177986 | − | 0.308280i | 0.00599989 | − | 0.0103921i | ||||
\(881\) | −9.63841 | −0.324726 | −0.162363 | − | 0.986731i | \(-0.551912\pi\) | ||||
−0.162363 | + | 0.986731i | \(0.551912\pi\) | |||||||
\(882\) | −1.15027 | − | 1.35489i | −0.0387317 | − | 0.0456214i | ||||
\(883\) | 23.9138 | 0.804765 | 0.402382 | − | 0.915472i | \(-0.368182\pi\) | ||||
0.402382 | + | 0.915472i | \(0.368182\pi\) | |||||||
\(884\) | −2.52605 | + | 4.37525i | −0.0849602 | + | 0.147155i | ||||
\(885\) | 7.77358 | + | 11.0339i | 0.261306 | + | 0.370901i | ||||
\(886\) | 6.53727 | + | 11.3229i | 0.219624 | + | 0.380400i | ||||
\(887\) | −13.8055 | − | 23.9119i | −0.463545 | − | 0.802883i | 0.535590 | − | 0.844478i | \(-0.320089\pi\) |
−0.999135 | + | 0.0415953i | \(0.986756\pi\) | |||||||
\(888\) | 5.08637 | − | 10.9904i | 0.170687 | − | 0.368815i | ||||
\(889\) | −24.9276 | + | 43.1759i | −0.836046 | + | 1.44807i | ||||
\(890\) | −4.68207 | −0.156943 | ||||||||
\(891\) | −1.60300 | − | 1.31384i | −0.0537024 | − | 0.0440154i | ||||
\(892\) | 1.52622 | 0.0511015 | ||||||||
\(893\) | 2.73892 | − | 4.74395i | 0.0916545 | − | 0.158750i | ||||
\(894\) | −10.7307 | + | 23.1865i | −0.358888 | + | 0.775471i | ||||
\(895\) | 7.59341 | + | 13.1522i | 0.253820 | + | 0.439629i | ||||
\(896\) | 15.4857 | + | 26.8221i | 0.517342 | + | 0.896063i | ||||
\(897\) | 2.49441 | + | 3.54059i | 0.0832858 | + | 0.118217i | ||||
\(898\) | −7.41250 | + | 12.8388i | −0.247358 | + | 0.428437i | ||||
\(899\) | 21.7880 | 0.726670 | ||||||||
\(900\) | 3.02590 | + | 3.56415i | 0.100863 | + | 0.118805i | ||||
\(901\) | 10.8543 | 0.361611 | ||||||||
\(902\) | −0.267141 | + | 0.462703i | −0.00889484 | + | 0.0154063i | ||||
\(903\) | 54.9213 | − | 4.96473i | 1.82767 | − | 0.165216i | ||||
\(904\) | −19.0905 | − | 33.0657i | −0.634940 | − | 1.09975i | ||||
\(905\) | 12.1696 | + | 21.0784i | 0.404531 | + | 0.700669i | ||||
\(906\) | 4.61163 | − | 0.416878i | 0.153211 | − | 0.0138498i | ||||
\(907\) | 8.81299 | − | 15.2645i | 0.292630 | − | 0.506851i | −0.681800 | − | 0.731538i | \(-0.738803\pi\) |
0.974431 | + | 0.224687i | \(0.0721361\pi\) | |||||||
\(908\) | −24.8889 | −0.825969 | ||||||||
\(909\) | 32.9314 | − | 6.00286i | 1.09227 | − | 0.199102i | ||||
\(910\) | −1.86666 | −0.0618791 | ||||||||
\(911\) | −1.78012 | + | 3.08326i | −0.0589781 | + | 0.102153i | −0.894007 | − | 0.448053i | \(-0.852118\pi\) |
0.835029 | + | 0.550206i | \(0.185451\pi\) | |||||||
\(912\) | −5.86061 | − | 8.31862i | −0.194064 | − | 0.275457i | ||||
\(913\) | −0.0115588 | − | 0.0200205i | −0.000382541 | − | 0.000662581i | ||||
\(914\) | 11.6872 | + | 20.2428i | 0.386577 | + | 0.669572i | ||||
\(915\) | 7.33422 | − | 15.8475i | 0.242462 | − | 0.523903i | ||||
\(916\) | −8.02158 | + | 13.8938i | −0.265040 | + | 0.459063i | ||||
\(917\) | −42.5367 | −1.40468 | ||||||||
\(918\) | 2.80322 | − | 10.8361i | 0.0925199 | − | 0.357645i | ||||
\(919\) | −17.5135 | −0.577718 | −0.288859 | − | 0.957372i | \(-0.593276\pi\) | ||||
−0.288859 | + | 0.957372i | \(0.593276\pi\) | |||||||
\(920\) | 2.95629 | − | 5.12044i | 0.0974659 | − | 0.168816i | ||||
\(921\) | −17.3118 | + | 37.4067i | −0.570443 | + | 1.23259i | ||||
\(922\) | 13.1785 | + | 22.8259i | 0.434012 | + | 0.751731i | ||||
\(923\) | 1.75843 | + | 3.04569i | 0.0578795 | + | 0.100250i | ||||
\(924\) | 1.00576 | + | 1.42759i | 0.0330870 | + | 0.0469641i | ||||
\(925\) | −1.47850 | + | 2.56084i | −0.0486128 | + | 0.0841998i | ||||
\(926\) | 3.54020 | 0.116338 | ||||||||
\(927\) | 12.8024 | − | 35.8162i | 0.420487 | − | 1.17636i | ||||
\(928\) | −30.4908 | −1.00091 | ||||||||
\(929\) | 12.3192 | − | 21.3374i | 0.404178 | − | 0.700058i | −0.590047 | − | 0.807369i | \(-0.700891\pi\) |
0.994225 | + | 0.107311i | \(0.0342242\pi\) | |||||||
\(930\) | 4.71475 | − | 0.426199i | 0.154603 | − | 0.0139756i | ||||
\(931\) | −1.69434 | − | 2.93468i | −0.0555297 | − | 0.0961803i | ||||
\(932\) | 6.02483 | + | 10.4353i | 0.197350 | + | 0.341820i | ||||
\(933\) | 2.68935 | − | 0.243109i | 0.0880453 | − | 0.00795904i | ||||
\(934\) | −2.00040 | + | 3.46479i | −0.0654550 | + | 0.113371i | ||||
\(935\) | 0.746541 | 0.0244145 | ||||||||
\(936\) | 2.38764 | − | 6.67970i | 0.0780426 | − | 0.218333i | ||||
\(937\) | 53.1274 | 1.73560 | 0.867798 | − | 0.496917i | \(-0.165535\pi\) | ||||
0.867798 | + | 0.496917i | \(0.165535\pi\) | |||||||
\(938\) | −1.88470 | + | 3.26439i | −0.0615376 | + | 0.106586i | ||||
\(939\) | 27.4237 | + | 38.9256i | 0.894940 | + | 1.27029i | ||||
\(940\) | 1.12307 | + | 1.94521i | 0.0366305 | + | 0.0634458i | ||||
\(941\) | −17.2372 | − | 29.8558i | −0.561918 | − | 0.973271i | −0.997329 | − | 0.0730389i | \(-0.976730\pi\) |
0.435411 | − | 0.900232i | \(-0.356603\pi\) | |||||||
\(942\) | −10.5534 | + | 22.8034i | −0.343848 | + | 0.742975i | ||||
\(943\) | 4.36527 | − | 7.56087i | 0.142153 | − | 0.246216i | ||||
\(944\) | 12.0454 | 0.392044 | ||||||||
\(945\) | −14.0664 | + | 3.89990i | −0.457580 | + | 0.126864i | ||||
\(946\) | 1.73431 | 0.0563874 | ||||||||
\(947\) | 9.22116 | − | 15.9715i | 0.299647 | − | 0.519004i | −0.676408 | − | 0.736527i | \(-0.736464\pi\) |
0.976055 | + | 0.217523i | \(0.0697976\pi\) | |||||||
\(948\) | −6.11917 | + | 13.2221i | −0.198741 | + | 0.429433i | ||||
\(949\) | 2.65002 | + | 4.58996i | 0.0860232 | + | 0.148997i | ||||
\(950\) | −1.26277 | − | 2.18718i | −0.0409696 | − | 0.0709614i | ||||
\(951\) | 15.2662 | + | 21.6690i | 0.495040 | + | 0.702666i | ||||
\(952\) | −10.7664 | + | 18.6480i | −0.348943 | + | 0.604386i | ||||
\(953\) | 51.7298 | 1.67569 | 0.837846 | − | 0.545907i | \(-0.183815\pi\) | ||||
0.837846 | + | 0.545907i | \(0.183815\pi\) | |||||||
\(954\) | −6.56651 | + | 1.19697i | −0.212599 | + | 0.0387533i | ||||
\(955\) | −14.2640 | −0.461573 | ||||||||
\(956\) | 11.3913 | − | 19.7303i | 0.368422 | − | 0.638125i | ||||
\(957\) | −2.10430 | + | 0.190222i | −0.0680222 | + | 0.00614901i | ||||
\(958\) | 6.79295 | + | 11.7657i | 0.219470 | + | 0.380134i | ||||
\(959\) | −29.2276 | − | 50.6237i | −0.943809 | − | 1.63472i | ||||
\(960\) | −1.26513 | + | 0.114364i | −0.0408318 | + | 0.00369107i | ||||
\(961\) | 7.04071 | − | 12.1949i | 0.227120 | − | 0.393383i | ||||
\(962\) | 1.96487 | 0.0633500 | ||||||||
\(963\) | −8.07214 | − | 9.50801i | −0.260121 | − | 0.306391i | ||||
\(964\) | −22.3060 | −0.718429 | ||||||||
\(965\) | 12.7915 | − | 22.1556i | 0.411774 | − | 0.713214i | ||||
\(966\) | 4.65621 | + | 6.60908i | 0.149811 | + | 0.212644i | ||||
\(967\) | 7.72784 | + | 13.3850i | 0.248511 | + | 0.430433i | 0.963113 | − | 0.269098i | \(-0.0867256\pi\) |
−0.714602 | + | 0.699531i | \(0.753392\pi\) | |||||||
\(968\) | −12.9422 | − | 22.4166i | −0.415979 | − | 0.720497i | ||||
\(969\) | 8.96306 | − | 19.3671i | 0.287935 | − | 0.622160i | ||||
\(970\) | 1.08457 | − | 1.87854i | 0.0348236 | − | 0.0603162i | ||||
\(971\) | −49.9641 | −1.60343 | −0.801713 | − | 0.597709i | \(-0.796078\pi\) | ||||
−0.801713 | + | 0.597709i | \(0.796078\pi\) | |||||||
\(972\) | 1.76797 | − | 24.2296i | 0.0567078 | − | 0.777166i | ||||
\(973\) | −18.8939 | −0.605711 | ||||||||
\(974\) | 3.92637 | − | 6.80068i | 0.125809 | − | 0.217908i | ||||
\(975\) | −0.727463 | + | 1.57188i | −0.0232975 | + | 0.0503403i | ||||
\(976\) | −7.79200 | − | 13.4961i | −0.249416 | − | 0.432001i | ||||
\(977\) | 2.99281 | + | 5.18369i | 0.0957484 | + | 0.165841i | 0.909921 | − | 0.414782i | \(-0.136142\pi\) |
−0.814172 | + | 0.580623i | \(0.802809\pi\) | |||||||
\(978\) | −6.95116 | − | 9.86657i | −0.222274 | − | 0.315498i | ||||
\(979\) | −0.811342 | + | 1.40528i | −0.0259306 | + | 0.0449131i | ||||
\(980\) | 1.38949 | 0.0443858 | ||||||||
\(981\) | 9.51685 | + | 11.2097i | 0.303850 | + | 0.357899i | ||||
\(982\) | −28.0353 | −0.894642 | ||||||||
\(983\) | −23.9827 | + | 41.5392i | −0.764929 | + | 1.32490i | 0.175355 | + | 0.984505i | \(0.443893\pi\) |
−0.940284 | + | 0.340390i | \(0.889441\pi\) | |||||||
\(984\) | −14.2413 | + | 1.28737i | −0.453995 | + | 0.0410398i | ||||
\(985\) | 5.14881 | + | 8.91800i | 0.164055 | + | 0.284151i | ||||
\(986\) | −5.70509 | − | 9.88151i | −0.181687 | − | 0.314691i | ||||
\(987\) | −6.98417 | + | 0.631349i | −0.222309 | + | 0.0200961i | ||||
\(988\) | 2.96167 | − | 5.12977i | 0.0942234 | − | 0.163200i | ||||
\(989\) | −28.3398 | −0.901154 | ||||||||
\(990\) | −0.451632 | + | 0.0823252i | −0.0143538 | + | 0.00261647i | ||||
\(991\) | 17.4478 | 0.554247 | 0.277124 | − | 0.960834i | \(-0.410619\pi\) | ||||
0.277124 | + | 0.960834i | \(0.410619\pi\) | |||||||
\(992\) | 11.8382 | − | 20.5044i | 0.375864 | − | 0.651016i | ||||
\(993\) | 13.3374 | + | 18.9313i | 0.423250 | + | 0.600767i | ||||
\(994\) | 3.28239 | + | 5.68527i | 0.104111 | + | 0.180326i | ||||
\(995\) | 1.65789 | + | 2.87155i | 0.0525587 | + | 0.0910343i | ||||
\(996\) | 0.113808 | − | 0.245912i | 0.00360615 | − | 0.00779203i | ||||
\(997\) | −5.18935 | + | 8.98822i | −0.164348 | + | 0.284660i | −0.936424 | − | 0.350871i | \(-0.885885\pi\) |
0.772075 | + | 0.635531i | \(0.219219\pi\) | |||||||
\(998\) | −24.9959 | −0.791233 | ||||||||
\(999\) | 14.8065 | − | 4.10509i | 0.468457 | − | 0.129879i |
(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 | 585.2.i.h.196.6 | ✓ | 30 | |
3.2 | odd | 2 | 1755.2.i.h.586.10 | 30 | |||
9.2 | odd | 6 | 5265.2.a.bl.1.6 | 15 | |||
9.4 | even | 3 | inner | 585.2.i.h.391.6 | yes | 30 | |
9.5 | odd | 6 | 1755.2.i.h.1171.10 | 30 | |||
9.7 | even | 3 | 5265.2.a.bk.1.10 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.i.h.196.6 | ✓ | 30 | 1.1 | even | 1 | trivial | |
585.2.i.h.391.6 | yes | 30 | 9.4 | even | 3 | inner | |
1755.2.i.h.586.10 | 30 | 3.2 | odd | 2 | |||
1755.2.i.h.1171.10 | 30 | 9.5 | odd | 6 | |||
5265.2.a.bk.1.10 | 15 | 9.7 | even | 3 | |||
5265.2.a.bl.1.6 | 15 | 9.2 | odd | 6 |