Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(269,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.269");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.cm (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: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 341.22 | ||
Character | \(\chi\) | \(=\) | 1638.341 |
Dual form | 1638.2.cm.a.269.22 |
$q$-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 \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.377027 | − | 0.653029i | 0.168611 | − | 0.292044i | −0.769320 | − | 0.638863i | \(-0.779405\pi\) |
0.937932 | + | 0.346820i | \(0.112738\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.31742 | − | 1.27655i | −0.875901 | − | 0.482491i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.653029 | − | 0.377027i | −0.206506 | − | 0.119226i | ||||
\(11\) | 4.23768 | + | 2.44663i | 1.27771 | + | 0.737686i | 0.976427 | − | 0.215849i | \(-0.0692519\pi\) |
0.301283 | + | 0.953535i | \(0.402585\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.743889 | + | 3.52798i | −0.206318 | + | 0.978485i | ||||
\(14\) | −1.27655 | + | 2.31742i | −0.341173 | + | 0.619355i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.42925 | −0.831715 | −0.415858 | − | 0.909430i | \(-0.636519\pi\) | ||||
−0.415858 | + | 0.909430i | \(0.636519\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.15853 | − | 1.82358i | 0.724616 | − | 0.418357i | −0.0918334 | − | 0.995774i | \(-0.529273\pi\) |
0.816449 | + | 0.577417i | \(0.195939\pi\) | |||||||
\(20\) | −0.377027 | + | 0.653029i | −0.0843057 | + | 0.146022i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.44663 | − | 4.23768i | 0.521623 | − | 0.903477i | ||||
\(23\) | 2.97706i | 0.620759i | 0.950613 | + | 0.310380i | \(0.100456\pi\) | ||||
−0.950613 | + | 0.310380i | \(0.899544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.21570 | + | 3.83771i | 0.443140 | + | 0.767542i | ||||
\(26\) | 3.52798 | + | 0.743889i | 0.691893 | + | 0.145889i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.31742 | + | 1.27655i | 0.437950 | + | 0.241246i | ||||
\(29\) | 2.55786 | − | 1.47678i | 0.474982 | − | 0.274231i | −0.243341 | − | 0.969941i | \(-0.578243\pi\) |
0.718323 | + | 0.695710i | \(0.244910\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.86618 | − | 3.38684i | 1.05360 | − | 0.608294i | 0.129943 | − | 0.991521i | \(-0.458521\pi\) |
0.923654 | + | 0.383227i | \(0.125187\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.42925i | 0.588112i | ||||||||
\(35\) | −1.70735 | + | 1.03205i | −0.288595 | + | 0.174448i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.60752 | 1.41507 | 0.707534 | − | 0.706679i | \(-0.249808\pi\) | ||||
0.707534 | + | 0.706679i | \(0.249808\pi\) | |||||||
\(38\) | −1.82358 | − | 3.15853i | −0.295823 | − | 0.512381i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.653029 | + | 0.377027i | 0.103253 | + | 0.0596131i | ||||
\(41\) | −1.57286 | − | 2.72428i | −0.245640 | − | 0.425461i | 0.716671 | − | 0.697411i | \(-0.245665\pi\) |
−0.962311 | + | 0.271950i | \(0.912331\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.02223 | + | 1.77055i | −0.155889 | + | 0.270007i | −0.933382 | − | 0.358884i | \(-0.883157\pi\) |
0.777494 | + | 0.628891i | \(0.216491\pi\) | |||||||
\(44\) | −4.23768 | − | 2.44663i | −0.638855 | − | 0.368843i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.97706 | 0.438943 | ||||||||
\(47\) | 0.0925217 | − | 0.160252i | 0.0134957 | − | 0.0233752i | −0.859199 | − | 0.511642i | \(-0.829037\pi\) |
0.872694 | + | 0.488267i | \(0.162371\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.74083 | + | 5.91660i | 0.534404 | + | 0.845229i | ||||
\(50\) | 3.83771 | − | 2.21570i | 0.542734 | − | 0.313348i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.743889 | − | 3.52798i | 0.103159 | − | 0.489243i | ||||
\(53\) | −5.09102 | + | 2.93930i | −0.699306 | + | 0.403744i | −0.807089 | − | 0.590430i | \(-0.798958\pi\) |
0.107783 | + | 0.994174i | \(0.465625\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.19544 | − | 1.84489i | 0.430873 | − | 0.248765i | ||||
\(56\) | 1.27655 | − | 2.31742i | 0.170586 | − | 0.309678i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.47678 | − | 2.55786i | −0.193911 | − | 0.335863i | ||||
\(59\) | −9.86178 | −1.28389 | −0.641947 | − | 0.766749i | \(-0.721873\pi\) | ||||
−0.641947 | + | 0.766749i | \(0.721873\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.49997 | − | 4.33011i | 0.960273 | − | 0.554414i | 0.0640159 | − | 0.997949i | \(-0.479609\pi\) |
0.896257 | + | 0.443535i | \(0.146276\pi\) | |||||||
\(62\) | −3.38684 | − | 5.86618i | −0.430129 | − | 0.745006i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.02341 | + | 1.81592i | 0.250973 | + | 0.225238i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.34769 | − | 4.06632i | 0.286816 | − | 0.496780i | −0.686232 | − | 0.727383i | \(-0.740737\pi\) |
0.973048 | + | 0.230603i | \(0.0740699\pi\) | |||||||
\(68\) | 3.42925 | 0.415858 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.03205 | + | 1.70735i | 0.123353 | + | 0.204068i | ||||
\(71\) | 7.33372 | + | 4.23413i | 0.870353 | + | 0.502498i | 0.867465 | − | 0.497497i | \(-0.165748\pi\) |
0.00288731 | + | 0.999996i | \(0.499081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00551 | − | 2.31258i | 0.468809 | − | 0.270667i | −0.246932 | − | 0.969033i | \(-0.579422\pi\) |
0.715741 | + | 0.698366i | \(0.246089\pi\) | |||||||
\(74\) | − | 8.60752i | − | 1.00060i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.15853 | + | 1.82358i | −0.362308 | + | 0.209179i | ||||
\(77\) | −6.69723 | − | 11.0795i | −0.763220 | − | 1.26262i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.83243 | − | 8.37001i | 0.543691 | − | 0.941700i | −0.454998 | − | 0.890493i | \(-0.650360\pi\) |
0.998688 | − | 0.0512070i | \(-0.0163068\pi\) | |||||||
\(80\) | 0.377027 | − | 0.653029i | 0.0421529 | − | 0.0730109i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.72428 | + | 1.57286i | −0.300846 | + | 0.173694i | ||||
\(83\) | 2.66655 | 0.292692 | 0.146346 | − | 0.989233i | \(-0.453249\pi\) | ||||
0.146346 | + | 0.989233i | \(0.453249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.29292 | + | 2.23940i | −0.140237 | + | 0.242897i | ||||
\(86\) | 1.77055 | + | 1.02223i | 0.190924 | + | 0.110230i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.44663 | + | 4.23768i | −0.260811 | + | 0.451739i | ||||
\(89\) | 12.9287 | 1.37044 | 0.685221 | − | 0.728335i | \(-0.259705\pi\) | ||||
0.685221 | + | 0.728335i | \(0.259705\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.22755 | − | 7.22618i | 0.652824 | − | 0.757509i | ||||
\(92\) | − | 2.97706i | − | 0.310380i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.160252 | − | 0.0925217i | −0.0165288 | − | 0.00954289i | ||||
\(95\) | − | 2.75015i | − | 0.282159i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.57654 | − | 3.21961i | −0.566211 | − | 0.326902i | 0.189423 | − | 0.981896i | \(-0.439338\pi\) |
−0.755635 | + | 0.654993i | \(0.772671\pi\) | |||||||
\(98\) | 5.91660 | − | 3.74083i | 0.597667 | − | 0.377881i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.21570 | − | 3.83771i | −0.221570 | − | 0.383771i | ||||
\(101\) | 1.53036 | − | 2.65067i | 0.152277 | − | 0.263751i | −0.779787 | − | 0.626044i | \(-0.784673\pi\) |
0.932064 | + | 0.362293i | \(0.118006\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.42602 | + | 3.13272i | 0.534642 | + | 0.308676i | 0.742905 | − | 0.669397i | \(-0.233448\pi\) |
−0.208263 | + | 0.978073i | \(0.566781\pi\) | |||||||
\(104\) | −3.52798 | − | 0.743889i | −0.345947 | − | 0.0729443i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.93930 | + | 5.09102i | 0.285490 | + | 0.494484i | ||||
\(107\) | 5.83707i | 0.564291i | 0.959372 | + | 0.282145i | \(0.0910461\pi\) | ||||
−0.959372 | + | 0.282145i | \(0.908954\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00167 | − | 3.46699i | −0.191725 | − | 0.332077i | 0.754097 | − | 0.656763i | \(-0.228075\pi\) |
−0.945822 | + | 0.324686i | \(0.894741\pi\) | |||||||
\(110\) | −1.84489 | − | 3.19544i | −0.175903 | − | 0.304673i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.31742 | − | 1.27655i | −0.218975 | − | 0.120623i | ||||
\(113\) | −4.32172 | − | 2.49515i | −0.406554 | − | 0.234724i | 0.282754 | − | 0.959192i | \(-0.408752\pi\) |
−0.689308 | + | 0.724469i | \(0.742085\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.94411 | + | 1.12243i | 0.181289 | + | 0.104667i | ||||
\(116\) | −2.55786 | + | 1.47678i | −0.237491 | + | 0.137115i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.86178i | 0.907850i | ||||||||
\(119\) | 7.94700 | + | 4.37762i | 0.728500 | + | 0.401295i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.47197 | + | 11.2098i | 0.588361 | + | 1.01907i | ||||
\(122\) | −4.33011 | − | 7.49997i | −0.392030 | − | 0.679016i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.86618 | + | 3.38684i | −0.526798 | + | 0.304147i | ||||
\(125\) | 7.11178 | 0.636097 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3407 | + | 17.9106i | 0.917590 | + | 1.58931i | 0.803065 | + | 0.595892i | \(0.203201\pi\) |
0.114525 | + | 0.993420i | \(0.463465\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.81592 | − | 2.02341i | 0.159267 | − | 0.177465i | ||||
\(131\) | −3.65280 | + | 6.32683i | −0.319146 | + | 0.552778i | −0.980310 | − | 0.197464i | \(-0.936730\pi\) |
0.661164 | + | 0.750242i | \(0.270063\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.64751 | + | 0.193960i | −0.836545 | + | 0.0168185i | ||||
\(134\) | −4.06632 | − | 2.34769i | −0.351276 | − | 0.202809i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 3.42925i | − | 0.294056i | ||||||
\(137\) | − | 14.7307i | − | 1.25853i | −0.777192 | − | 0.629263i | \(-0.783357\pi\) | ||
0.777192 | − | 0.629263i | \(-0.216643\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.99518 | + | 4.03867i | 0.593323 | + | 0.342555i | 0.766410 | − | 0.642351i | \(-0.222041\pi\) |
−0.173087 | + | 0.984906i | \(0.555374\pi\) | |||||||
\(140\) | 1.70735 | − | 1.03205i | 0.144298 | − | 0.0872238i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.23413 | − | 7.33372i | 0.355320 | − | 0.615432i | ||||
\(143\) | −11.7840 | + | 13.1304i | −0.985429 | + | 1.09802i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.22714i | − | 0.184954i | ||||||
\(146\) | −2.31258 | − | 4.00551i | −0.191390 | − | 0.331498i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.60752 | −0.707534 | ||||||||
\(149\) | −8.07815 | + | 4.66392i | −0.661788 | + | 0.382083i | −0.792958 | − | 0.609277i | \(-0.791460\pi\) |
0.131170 | + | 0.991360i | \(0.458127\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.63758 | + | 11.4966i | 0.540159 | + | 0.935583i | 0.998894 | + | 0.0470097i | \(0.0149692\pi\) |
−0.458736 | + | 0.888573i | \(0.651697\pi\) | |||||||
\(152\) | 1.82358 | + | 3.15853i | 0.147912 | + | 0.256190i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.0795 | + | 6.69723i | −0.892810 | + | 0.539678i | ||||
\(155\) | − | 5.10772i | − | 0.410262i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.74046 | − | 4.46895i | 0.617756 | − | 0.356661i | −0.158239 | − | 0.987401i | \(-0.550582\pi\) |
0.775995 | + | 0.630739i | \(0.217248\pi\) | |||||||
\(158\) | −8.37001 | − | 4.83243i | −0.665882 | − | 0.384447i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.653029 | − | 0.377027i | −0.0516265 | − | 0.0298066i | ||||
\(161\) | 3.80037 | − | 6.89908i | 0.299511 | − | 0.543724i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.41328 | + | 2.44787i | 0.110696 | + | 0.191732i | 0.916051 | − | 0.401061i | \(-0.131359\pi\) |
−0.805355 | + | 0.592793i | \(0.798025\pi\) | |||||||
\(164\) | 1.57286 | + | 2.72428i | 0.122820 | + | 0.212731i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 2.66655i | − | 0.206965i | ||||||
\(167\) | 7.61244 | + | 13.1851i | 0.589068 | + | 1.02030i | 0.994355 | + | 0.106106i | \(0.0338383\pi\) |
−0.405287 | + | 0.914190i | \(0.632828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8933 | − | 5.24885i | −0.914866 | − | 0.403757i | ||||
\(170\) | 2.23940 | + | 1.29292i | 0.171754 | + | 0.0991623i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.02223 | − | 1.77055i | 0.0779443 | − | 0.135004i | ||||
\(173\) | 0.569456 | + | 0.986326i | 0.0432949 | + | 0.0749890i | 0.886861 | − | 0.462037i | \(-0.152881\pi\) |
−0.843566 | + | 0.537026i | \(0.819548\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.235668 | − | 11.7220i | −0.0178148 | − | 0.886102i | ||||
\(176\) | 4.23768 | + | 2.44663i | 0.319427 | + | 0.184421i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 12.9287i | − | 0.969049i | ||||||
\(179\) | −5.18256 | − | 2.99215i | −0.387363 | − | 0.223644i | 0.293654 | − | 0.955912i | \(-0.405129\pi\) |
−0.681017 | + | 0.732268i | \(0.738462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.8486i | − | 1.40101i | −0.713648 | − | 0.700505i | \(-0.752958\pi\) | ||
0.713648 | − | 0.700505i | \(-0.247042\pi\) | |||||||
\(182\) | −7.22618 | − | 6.22755i | −0.535640 | − | 0.461616i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.97706 | −0.219472 | ||||||||
\(185\) | 3.24526 | − | 5.62096i | 0.238597 | − | 0.413261i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.5321 | − | 8.39010i | −1.06269 | − | 0.613545i | ||||
\(188\) | −0.0925217 | + | 0.160252i | −0.00674784 | + | 0.0116876i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.75015 | −0.199517 | ||||||||
\(191\) | 20.3390 | − | 11.7427i | 1.47168 | − | 0.849673i | 0.472184 | − | 0.881500i | \(-0.343466\pi\) |
0.999493 | + | 0.0318268i | \(0.0101325\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.78214 | + | 3.08676i | −0.128281 | + | 0.222190i | −0.923011 | − | 0.384774i | \(-0.874279\pi\) |
0.794729 | + | 0.606964i | \(0.207613\pi\) | |||||||
\(194\) | −3.21961 | + | 5.57654i | −0.231155 | + | 0.400372i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.74083 | − | 5.91660i | −0.267202 | − | 0.422615i | ||||
\(197\) | −21.8018 | + | 12.5873i | −1.55331 | + | 0.896806i | −0.555444 | + | 0.831554i | \(0.687452\pi\) |
−0.997869 | + | 0.0652521i | \(0.979215\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.4959i | 0.885808i | 0.896569 | + | 0.442904i | \(0.146052\pi\) | ||||
−0.896569 | + | 0.442904i | \(0.853948\pi\) | |||||||
\(200\) | −3.83771 | + | 2.21570i | −0.271367 | + | 0.156674i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.65067 | − | 1.53036i | −0.186500 | − | 0.107676i | ||||
\(203\) | −7.81280 | + | 0.157074i | −0.548351 | + | 0.0110244i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.37205 | −0.165671 | ||||||||
\(206\) | 3.13272 | − | 5.42602i | 0.218267 | − | 0.378049i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.743889 | + | 3.52798i | −0.0515794 | + | 0.244621i | ||||
\(209\) | 17.8465 | 1.23446 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.63458 | + | 4.56323i | 0.181372 | + | 0.314145i | 0.942348 | − | 0.334635i | \(-0.108613\pi\) |
−0.760976 | + | 0.648780i | \(0.775280\pi\) | |||||||
\(212\) | 5.09102 | − | 2.93930i | 0.349653 | − | 0.201872i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.83707 | 0.399014 | ||||||||
\(215\) | 0.770816 | + | 1.33509i | 0.0525692 | + | 0.0910526i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.9179 | + | 0.360233i | −1.21634 | + | 0.0244542i | ||||
\(218\) | −3.46699 | + | 2.00167i | −0.234814 | + | 0.135570i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.19544 | + | 1.84489i | −0.215436 | + | 0.124382i | ||||
\(221\) | 2.55098 | − | 12.0983i | 0.171598 | − | 0.813821i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.40211 | − | 4.85096i | 0.562647 | − | 0.324844i | −0.191560 | − | 0.981481i | \(-0.561355\pi\) |
0.754207 | + | 0.656636i | \(0.228021\pi\) | |||||||
\(224\) | −1.27655 | + | 2.31742i | −0.0852932 | + | 0.154839i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.49515 | + | 4.32172i | −0.165975 | + | 0.287477i | ||||
\(227\) | 5.62699 | 0.373477 | 0.186738 | − | 0.982410i | \(-0.440208\pi\) | ||||
0.186738 | + | 0.982410i | \(0.440208\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.13664 | − | 4.12034i | −0.471603 | − | 0.272280i | 0.245308 | − | 0.969445i | \(-0.421111\pi\) |
−0.716910 | + | 0.697165i | \(0.754444\pi\) | |||||||
\(230\) | 1.12243 | − | 1.94411i | 0.0740109 | − | 0.128191i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.47678 | + | 2.55786i | 0.0969553 | + | 0.167931i | ||||
\(233\) | −16.7363 | − | 9.66269i | −1.09643 | − | 0.633024i | −0.161149 | − | 0.986930i | \(-0.551520\pi\) |
−0.935281 | + | 0.353906i | \(0.884853\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0697663 | − | 0.120839i | −0.00455105 | − | 0.00788265i | ||||
\(236\) | 9.86178 | 0.641947 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.37762 | − | 7.94700i | 0.283759 | − | 0.515127i | ||||
\(239\) | 26.1899i | 1.69408i | 0.531526 | + | 0.847042i | \(0.321619\pi\) | ||||
−0.531526 | + | 0.847042i | \(0.678381\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 16.3956i | − | 1.05614i | −0.849202 | − | 0.528068i | \(-0.822917\pi\) | ||
0.849202 | − | 0.528068i | \(-0.177083\pi\) | |||||||
\(242\) | 11.2098 | − | 6.47197i | 0.720592 | − | 0.416034i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.49997 | + | 4.33011i | −0.480136 | + | 0.277207i | ||||
\(245\) | 5.27411 | − | 0.212154i | 0.336950 | − | 0.0135541i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.08395 | + | 12.4998i | 0.259855 | + | 0.795340i | ||||
\(248\) | 3.38684 | + | 5.86618i | 0.215065 | + | 0.372503i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 7.11178i | − | 0.449789i | ||||||
\(251\) | 5.92653 | − | 10.2650i | 0.374079 | − | 0.647924i | −0.616110 | − | 0.787660i | \(-0.711292\pi\) |
0.990189 | + | 0.139736i | \(0.0446255\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.28375 | + | 12.6158i | −0.457926 | + | 0.793150i | ||||
\(254\) | 17.9106 | − | 10.3407i | 1.12381 | − | 0.648834i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.78334 | 0.423133 | 0.211567 | − | 0.977364i | \(-0.432143\pi\) | ||||
0.211567 | + | 0.977364i | \(0.432143\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.9472 | − | 10.9879i | −1.23946 | − | 0.682758i | ||||
\(260\) | −2.02341 | − | 1.81592i | −0.125486 | − | 0.112619i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.32683 | + | 3.65280i | 0.390873 | + | 0.225671i | ||||
\(263\) | −11.7706 | − | 6.79576i | −0.725806 | − | 0.419044i | 0.0910797 | − | 0.995844i | \(-0.470968\pi\) |
−0.816886 | + | 0.576799i | \(0.804302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.43278i | 0.272304i | ||||||||
\(266\) | 0.193960 | + | 9.64751i | 0.0118925 | + | 0.591527i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.34769 | + | 4.06632i | −0.143408 | + | 0.248390i | ||||
\(269\) | −16.7602 | −1.02189 | −0.510944 | − | 0.859614i | \(-0.670704\pi\) | ||||
−0.510944 | + | 0.859614i | \(0.670704\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.2139i | 1.59238i | 0.605048 | + | 0.796189i | \(0.293154\pi\) | ||||
−0.605048 | + | 0.796189i | \(0.706846\pi\) | |||||||
\(272\) | −3.42925 | −0.207929 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.7307 | −0.889912 | ||||||||
\(275\) | 21.6840i | 1.30759i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.5686 | 1.71652 | 0.858261 | − | 0.513213i | \(-0.171545\pi\) | ||||
0.858261 | + | 0.513213i | \(0.171545\pi\) | |||||||
\(278\) | 4.03867 | − | 6.99518i | 0.242223 | − | 0.419543i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.03205 | − | 1.70735i | −0.0616766 | − | 0.102034i | ||||
\(281\) | 19.1103i | 1.14002i | 0.821637 | + | 0.570012i | \(0.193061\pi\) | ||||
−0.821637 | + | 0.570012i | \(0.806939\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.1452 | − | 13.9403i | −1.43529 | − | 0.828662i | −0.437768 | − | 0.899088i | \(-0.644231\pi\) |
−0.997517 | + | 0.0704252i | \(0.977564\pi\) | |||||||
\(284\) | −7.33372 | − | 4.23413i | −0.435176 | − | 0.251249i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.1304 | + | 11.7840i | 0.776419 | + | 0.696803i | ||||
\(287\) | 0.167294 | + | 8.32113i | 0.00987505 | + | 0.491181i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.24024 | −0.308250 | ||||||||
\(290\) | −2.22714 | −0.130782 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.00551 | + | 2.31258i | −0.234405 | + | 0.135334i | ||||
\(293\) | −16.8908 | + | 29.2557i | −0.986771 | + | 1.70914i | −0.352988 | + | 0.935628i | \(0.614834\pi\) |
−0.633784 | + | 0.773510i | \(0.718499\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.71815 | + | 6.44003i | −0.216479 | + | 0.374953i | ||||
\(296\) | 8.60752i | 0.500302i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.66392 | + | 8.07815i | 0.270174 | + | 0.467954i | ||||
\(299\) | −10.5030 | − | 2.21460i | −0.607404 | − | 0.128074i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.62914 | − | 2.79818i | 0.266819 | − | 0.161284i | ||||
\(302\) | 11.4966 | − | 6.63758i | 0.661557 | − | 0.381950i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.15853 | − | 1.82358i | 0.181154 | − | 0.104589i | ||||
\(305\) | − | 6.53027i | − | 0.373922i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.4632i | 0.711312i | 0.934617 | + | 0.355656i | \(0.115742\pi\) | ||||
−0.934617 | + | 0.355656i | \(0.884258\pi\) | |||||||
\(308\) | 6.69723 | + | 11.0795i | 0.381610 | + | 0.631312i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.10772 | −0.290099 | ||||||||
\(311\) | 0.922899 | + | 1.59851i | 0.0523328 | + | 0.0906430i | 0.891005 | − | 0.453993i | \(-0.150001\pi\) |
−0.838672 | + | 0.544636i | \(0.816668\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.7492 | − | 15.4436i | −1.51195 | − | 0.872926i | −0.999902 | − | 0.0139696i | \(-0.995553\pi\) |
−0.512049 | − | 0.858956i | \(-0.671113\pi\) | |||||||
\(314\) | −4.46895 | − | 7.74046i | −0.252198 | − | 0.436819i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.83243 | + | 8.37001i | −0.271845 | + | 0.470850i | ||||
\(317\) | −6.78164 | − | 3.91538i | −0.380895 | − | 0.219910i | 0.297313 | − | 0.954780i | \(-0.403910\pi\) |
−0.678207 | + | 0.734871i | \(0.737243\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.4525 | 0.809185 | ||||||||
\(320\) | −0.377027 | + | 0.653029i | −0.0210764 | + | 0.0365054i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.89908 | − | 3.80037i | −0.384471 | − | 0.211786i | ||||
\(323\) | −10.8314 | + | 6.25350i | −0.602674 | + | 0.347954i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.1876 | + | 4.96212i | −0.842456 | + | 0.275249i | ||||
\(326\) | 2.44787 | − | 1.41328i | 0.135575 | − | 0.0782741i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.72428 | − | 1.57286i | 0.150423 | − | 0.0868469i | ||||
\(329\) | −0.418982 | + | 0.253262i | −0.0230992 | + | 0.0139628i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.06308 | − | 3.57337i | −0.113397 | − | 0.196410i | 0.803741 | − | 0.594980i | \(-0.202840\pi\) |
−0.917138 | + | 0.398570i | \(0.869507\pi\) | |||||||
\(332\) | −2.66655 | −0.146346 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.1851 | − | 7.61244i | 0.721458 | − | 0.416534i | ||||
\(335\) | −1.77028 | − | 3.06622i | −0.0967209 | − | 0.167525i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.0546 | −1.80060 | −0.900300 | − | 0.435270i | \(-0.856653\pi\) | ||||
−0.900300 | + | 0.435270i | \(0.856653\pi\) | |||||||
\(338\) | −5.24885 | + | 11.8933i | −0.285500 | + | 0.646908i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.29292 | − | 2.23940i | 0.0701184 | − | 0.121449i | ||||
\(341\) | 33.1453 | 1.79492 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.11621 | − | 18.4866i | −0.0602694 | − | 0.998182i | ||||
\(344\) | −1.77055 | − | 1.02223i | −0.0954619 | − | 0.0551150i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.986326 | − | 0.569456i | 0.0530252 | − | 0.0306141i | ||||
\(347\) | 5.94972i | 0.319398i | 0.987166 | + | 0.159699i | \(0.0510523\pi\) | ||||
−0.987166 | + | 0.159699i | \(0.948948\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.95079 | + | 5.74509i | −0.532654 | + | 0.307528i | −0.742096 | − | 0.670293i | \(-0.766168\pi\) |
0.209443 | + | 0.977821i | \(0.432835\pi\) | |||||||
\(350\) | −11.7220 | + | 0.235668i | −0.626568 | + | 0.0125970i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.44663 | − | 4.23768i | 0.130406 | − | 0.225869i | ||||
\(353\) | 1.43456 | − | 2.48472i | 0.0763537 | − | 0.132249i | −0.825320 | − | 0.564665i | \(-0.809006\pi\) |
0.901674 | + | 0.432416i | \(0.142339\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.53002 | − | 3.19276i | 0.293503 | − | 0.169454i | ||||
\(356\) | −12.9287 | −0.685221 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.99215 | + | 5.18256i | −0.158140 | + | 0.273907i | ||||
\(359\) | −7.07807 | − | 4.08652i | −0.373566 | − | 0.215678i | 0.301449 | − | 0.953482i | \(-0.402530\pi\) |
−0.675015 | + | 0.737804i | \(0.735863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.84914 | + | 4.93485i | −0.149955 | + | 0.259729i | ||||
\(362\) | −18.8486 | −0.990663 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.22755 | + | 7.22618i | −0.326412 | + | 0.378755i | ||||
\(365\) | − | 3.48762i | − | 0.182550i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.44645 | − | 4.29921i | −0.388702 | − | 0.224417i | 0.292896 | − | 0.956144i | \(-0.405381\pi\) |
−0.681597 | + | 0.731727i | \(0.738714\pi\) | |||||||
\(368\) | 2.97706i | 0.155190i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.62096 | − | 3.24526i | −0.292220 | − | 0.168713i | ||||
\(371\) | 15.5502 | − | 0.312632i | 0.807326 | − | 0.0162310i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.5491 | + | 28.6639i | 0.856882 | + | 1.48416i | 0.874888 | + | 0.484325i | \(0.160935\pi\) |
−0.0180066 | + | 0.999838i | \(0.505732\pi\) | |||||||
\(374\) | −8.39010 | + | 14.5321i | −0.433842 | + | 0.751436i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.160252 | + | 0.0925217i | 0.00826438 | + | 0.00477144i | ||||
\(377\) | 3.30728 | + | 10.1226i | 0.170334 | + | 0.521341i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.55693 | + | 13.0890i | 0.388173 | + | 0.672336i | 0.992204 | − | 0.124625i | \(-0.0397728\pi\) |
−0.604030 | + | 0.796961i | \(0.706439\pi\) | |||||||
\(380\) | 2.75015i | 0.141080i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.7427 | − | 20.3390i | −0.600810 | − | 1.04063i | ||||
\(383\) | 15.2962 | + | 26.4938i | 0.781599 | + | 1.35377i | 0.931010 | + | 0.364994i | \(0.118929\pi\) |
−0.149410 | + | 0.988775i | \(0.547738\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.76026 | + | 0.196227i | −0.497429 | + | 0.0100007i | ||||
\(386\) | 3.08676 | + | 1.78214i | 0.157112 | + | 0.0907087i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.57654 | + | 3.21961i | 0.283106 | + | 0.163451i | ||||
\(389\) | −4.27808 | + | 2.46995i | −0.216907 | + | 0.125231i | −0.604517 | − | 0.796592i | \(-0.706634\pi\) |
0.387610 | + | 0.921823i | \(0.373301\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.2091i | − | 0.516295i | ||||||
\(392\) | −5.91660 | + | 3.74083i | −0.298834 | + | 0.188940i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.5873 | + | 21.8018i | 0.634137 | + | 1.09836i | ||||
\(395\) | −3.64391 | − | 6.31143i | −0.183345 | − | 0.317563i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.01277 | + | 1.73942i | −0.151207 | + | 0.0872992i | −0.573694 | − | 0.819069i | \(-0.694490\pi\) |
0.422488 | + | 0.906369i | \(0.361157\pi\) | |||||||
\(398\) | 12.4959 | 0.626361 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.21570 | + | 3.83771i | 0.110785 | + | 0.191885i | ||||
\(401\) | 11.4337i | 0.570972i | 0.958383 | + | 0.285486i | \(0.0921550\pi\) | ||||
−0.958383 | + | 0.285486i | \(0.907845\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.58491 | + | 23.2152i | 0.377831 | + | 1.15643i | ||||
\(404\) | −1.53036 | + | 2.65067i | −0.0761384 | + | 0.131876i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.157074 | + | 7.81280i | 0.00779545 | + | 0.387743i | ||||
\(407\) | 36.4759 | + | 21.0594i | 1.80805 | + | 1.04388i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 37.3528i | − | 1.84698i | −0.383623 | − | 0.923490i | \(-0.625324\pi\) | ||
0.383623 | − | 0.923490i | \(-0.374676\pi\) | |||||||
\(410\) | 2.37205i | 0.117147i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.42602 | − | 3.13272i | −0.267321 | − | 0.154338i | ||||
\(413\) | 22.8538 | + | 12.5891i | 1.12456 | + | 0.619468i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.00536 | − | 1.74134i | 0.0493512 | − | 0.0854788i | ||||
\(416\) | 3.52798 | + | 0.743889i | 0.172973 | + | 0.0364721i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 17.8465i | − | 0.872898i | ||||||
\(419\) | −19.1641 | − | 33.1933i | −0.936230 | − | 1.62160i | −0.772426 | − | 0.635105i | \(-0.780957\pi\) |
−0.163804 | − | 0.986493i | \(-0.552376\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.61871 | 0.0788909 | 0.0394454 | − | 0.999222i | \(-0.487441\pi\) | ||||
0.0394454 | + | 0.999222i | \(0.487441\pi\) | |||||||
\(422\) | 4.56323 | − | 2.63458i | 0.222134 | − | 0.128249i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.93930 | − | 5.09102i | −0.142745 | − | 0.247242i | ||||
\(425\) | −7.59820 | − | 13.1605i | −0.368567 | − | 0.638376i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.9082 | + | 0.460562i | −1.10860 | + | 0.0222881i | ||||
\(428\) | − | 5.83707i | − | 0.282145i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.33509 | − | 0.770816i | 0.0643839 | − | 0.0371720i | ||||
\(431\) | −16.4937 | − | 9.52265i | −0.794474 | − | 0.458690i | 0.0470613 | − | 0.998892i | \(-0.485014\pi\) |
−0.841535 | + | 0.540202i | \(0.818348\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.2102 | + | 12.2457i | 1.01930 | + | 0.588490i | 0.913900 | − | 0.405940i | \(-0.133056\pi\) |
0.105395 | + | 0.994430i | \(0.466389\pi\) | |||||||
\(434\) | 0.360233 | + | 17.9179i | 0.0172917 | + | 0.860085i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00167 | + | 3.46699i | 0.0958625 | + | 0.166039i | ||||
\(437\) | 5.42889 | + | 9.40312i | 0.259699 | + | 0.449812i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 34.3635i | − | 1.64008i | −0.572306 | − | 0.820040i | \(-0.693951\pi\) | ||
0.572306 | − | 0.820040i | \(-0.306049\pi\) | |||||||
\(440\) | 1.84489 | + | 3.19544i | 0.0879516 | + | 0.152337i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.0983 | − | 2.55098i | −0.575458 | − | 0.121338i | ||||
\(443\) | 23.4324 | + | 13.5287i | 1.11331 | + | 0.642768i | 0.939684 | − | 0.342044i | \(-0.111119\pi\) |
0.173623 | + | 0.984812i | \(0.444453\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.87448 | − | 8.44284i | 0.231072 | − | 0.400229i | ||||
\(446\) | −4.85096 | − | 8.40211i | −0.229700 | − | 0.397852i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.31742 | + | 1.27655i | 0.109488 | + | 0.0603114i | ||||
\(449\) | 29.5863 | + | 17.0817i | 1.39626 | + | 0.806133i | 0.993999 | − | 0.109390i | \(-0.0348897\pi\) |
0.402265 | + | 0.915523i | \(0.368223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 15.3929i | − | 0.724821i | ||||||
\(452\) | 4.32172 | + | 2.49515i | 0.203277 | + | 0.117362i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 5.62699i | − | 0.264088i | ||||||
\(455\) | −2.37096 | − | 6.79123i | −0.111152 | − | 0.318378i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.2315 | 0.852833 | 0.426417 | − | 0.904527i | \(-0.359776\pi\) | ||||
0.426417 | + | 0.904527i | \(0.359776\pi\) | |||||||
\(458\) | −4.12034 | + | 7.13664i | −0.192531 | + | 0.333473i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.94411 | − | 1.12243i | −0.0906444 | − | 0.0523336i | ||||
\(461\) | 13.8708 | − | 24.0250i | 0.646029 | − | 1.11896i | −0.338033 | − | 0.941134i | \(-0.609762\pi\) |
0.984063 | − | 0.177822i | \(-0.0569050\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.9055 | 1.71514 | 0.857572 | − | 0.514363i | \(-0.171972\pi\) | ||||
0.857572 | + | 0.514363i | \(0.171972\pi\) | |||||||
\(464\) | 2.55786 | − | 1.47678i | 0.118745 | − | 0.0685577i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.66269 | + | 16.7363i | −0.447616 | + | 0.775293i | ||||
\(467\) | −16.7749 | + | 29.0550i | −0.776252 | + | 1.34451i | 0.157837 | + | 0.987465i | \(0.449548\pi\) |
−0.934088 | + | 0.357042i | \(0.883785\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.6314 | + | 6.42640i | −0.490914 | + | 0.296744i | ||||
\(470\) | −0.120839 | + | 0.0697663i | −0.00557388 | + | 0.00321808i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 9.86178i | − | 0.453925i | ||||||
\(473\) | −8.66378 | + | 5.00203i | −0.398361 | + | 0.229994i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.9967 | + | 8.08100i | 0.642213 | + | 0.370782i | ||||
\(476\) | −7.94700 | − | 4.37762i | −0.364250 | − | 0.200648i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 26.1899 | 1.19790 | ||||||||
\(479\) | −19.0433 | + | 32.9840i | −0.870110 | + | 1.50708i | −0.00822834 | + | 0.999966i | \(0.502619\pi\) |
−0.861882 | + | 0.507109i | \(0.830714\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.40304 | + | 30.3671i | −0.291953 | + | 1.38462i | ||||
\(482\) | −16.3956 | −0.746801 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.47197 | − | 11.2098i | −0.294181 | − | 0.509536i | ||||
\(485\) | −4.20500 | + | 2.42776i | −0.190939 | + | 0.110239i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.531844 | 0.0241001 | 0.0120501 | − | 0.999927i | \(-0.496164\pi\) | ||||
0.0120501 | + | 0.999927i | \(0.496164\pi\) | |||||||
\(488\) | 4.33011 | + | 7.49997i | 0.196015 | + | 0.339508i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.212154 | − | 5.27411i | −0.00958416 | − | 0.238260i | ||||
\(491\) | 4.26515 | − | 2.46249i | 0.192484 | − | 0.111130i | −0.400661 | − | 0.916226i | \(-0.631220\pi\) |
0.593145 | + | 0.805096i | \(0.297886\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.77153 | + | 5.06424i | −0.395050 | + | 0.228082i | ||||
\(494\) | 12.4998 | − | 4.08395i | 0.562390 | − | 0.183745i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.86618 | − | 3.38684i | 0.263399 | − | 0.152074i | ||||
\(497\) | −11.5902 | − | 19.1741i | −0.519892 | − | 0.860076i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.27332 | − | 5.66956i | 0.146534 | − | 0.253804i | −0.783410 | − | 0.621505i | \(-0.786522\pi\) |
0.929944 | + | 0.367701i | \(0.119855\pi\) | |||||||
\(500\) | −7.11178 | −0.318049 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.2650 | − | 5.92653i | −0.458152 | − | 0.264514i | ||||
\(503\) | 15.4926 | − | 26.8339i | 0.690780 | − | 1.19647i | −0.280803 | − | 0.959765i | \(-0.590601\pi\) |
0.971583 | − | 0.236700i | \(-0.0760659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.15397 | − | 1.99874i | −0.0513512 | − | 0.0889429i | ||||
\(506\) | 12.6158 | + | 7.28375i | 0.560842 | + | 0.323802i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.3407 | − | 17.9106i | −0.458795 | − | 0.794656i | ||||
\(509\) | −7.42736 | −0.329212 | −0.164606 | − | 0.986359i | \(-0.552635\pi\) | ||||
−0.164606 | + | 0.986359i | \(0.552635\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.2346 | + | 0.245972i | −0.541225 | + | 0.0108812i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 6.78334i | − | 0.299200i | ||||||
\(515\) | 4.09151 | − | 2.36224i | 0.180294 | − | 0.104093i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.784156 | − | 0.452732i | 0.0344871 | − | 0.0199112i | ||||
\(518\) | −10.9879 | + | 19.9472i | −0.482783 | + | 0.876430i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.81592 | + | 2.02341i | −0.0796335 | + | 0.0887323i | ||||
\(521\) | −17.4165 | − | 30.1662i | −0.763029 | − | 1.32161i | −0.941282 | − | 0.337621i | \(-0.890378\pi\) |
0.178253 | − | 0.983985i | \(-0.442955\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 8.07534i | − | 0.353110i | −0.984291 | − | 0.176555i | \(-0.943505\pi\) | ||
0.984291 | − | 0.176555i | \(-0.0564953\pi\) | |||||||
\(524\) | 3.65280 | − | 6.32683i | 0.159573 | − | 0.276389i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.79576 | + | 11.7706i | −0.296309 | + | 0.513223i | ||||
\(527\) | −20.1166 | + | 11.6143i | −0.876293 | + | 0.505928i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.1371 | 0.614658 | ||||||||
\(530\) | 4.43278 | 0.192548 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.64751 | − | 0.193960i | 0.418273 | − | 0.00840925i | ||||
\(533\) | 10.7812 | − | 3.52247i | 0.466987 | − | 0.152575i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.81178 | + | 2.20073i | 0.164798 | + | 0.0951459i | ||||
\(536\) | 4.06632 | + | 2.34769i | 0.175638 | + | 0.101405i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.7602i | 0.722584i | ||||||||
\(539\) | 1.37673 | + | 34.2251i | 0.0592999 | + | 1.47418i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.7730 | + | 30.7838i | −0.764121 | + | 1.32350i | 0.176589 | + | 0.984285i | \(0.443494\pi\) |
−0.940710 | + | 0.339212i | \(0.889840\pi\) | |||||||
\(542\) | 26.2139 | 1.12598 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.42925i | 0.147028i | ||||||||
\(545\) | −3.01873 | −0.129308 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.78283 | −0.290013 | −0.145006 | − | 0.989431i | \(-0.546320\pi\) | ||||
−0.145006 | + | 0.989431i | \(0.546320\pi\) | |||||||
\(548\) | 14.7307i | 0.629263i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 21.6840 | 0.924608 | ||||||||
\(551\) | 5.38604 | − | 9.32889i | 0.229453 | − | 0.397424i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.8835 | + | 13.2279i | −0.930581 | + | 0.562509i | ||||
\(554\) | − | 28.5686i | − | 1.21376i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.99518 | − | 4.03867i | −0.296662 | − | 0.171278i | ||||
\(557\) | 13.3165 | + | 7.68831i | 0.564240 | + | 0.325764i | 0.754845 | − | 0.655903i | \(-0.227712\pi\) |
−0.190606 | + | 0.981667i | \(0.561045\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.48605 | − | 4.92350i | −0.232035 | − | 0.208242i | ||||
\(560\) | −1.70735 | + | 1.03205i | −0.0721488 | + | 0.0436119i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19.1103 | 0.806118 | ||||||||
\(563\) | −32.6174 | −1.37466 | −0.687329 | − | 0.726346i | \(-0.741217\pi\) | ||||
−0.687329 | + | 0.726346i | \(0.741217\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.25881 | + | 1.88147i | −0.137099 | + | 0.0791542i | ||||
\(566\) | −13.9403 | + | 24.1452i | −0.585953 | + | 1.01490i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.23413 | + | 7.33372i | −0.177660 | + | 0.307716i | ||||
\(569\) | − | 17.3290i | − | 0.726467i | −0.931698 | − | 0.363234i | \(-0.881673\pi\) | ||
0.931698 | − | 0.363234i | \(-0.118327\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.55505 | + | 11.3537i | 0.274320 | + | 0.475137i | 0.969963 | − | 0.243251i | \(-0.0782138\pi\) |
−0.695643 | + | 0.718388i | \(0.744880\pi\) | |||||||
\(572\) | 11.7840 | − | 13.1304i | 0.492714 | − | 0.549011i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.32113 | − | 0.167294i | 0.347317 | − | 0.00698271i | ||||
\(575\) | −11.4251 | + | 6.59627i | −0.476459 | + | 0.275084i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.169426 | + | 0.0978179i | −0.00705328 | + | 0.00407221i | −0.503522 | − | 0.863982i | \(-0.667963\pi\) |
0.496469 | + | 0.868054i | \(0.334630\pi\) | |||||||
\(578\) | 5.24024i | 0.217965i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.22714i | 0.0924770i | ||||||||
\(581\) | −6.17951 | − | 3.40399i | −0.256369 | − | 0.141221i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.7655 | −1.19135 | ||||||||
\(584\) | 2.31258 | + | 4.00551i | 0.0956952 | + | 0.165749i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 29.2557 | + | 16.8908i | 1.20854 | + | 0.697753i | ||||
\(587\) | −6.25620 | − | 10.8361i | −0.258221 | − | 0.447252i | 0.707544 | − | 0.706669i | \(-0.249803\pi\) |
−0.965765 | + | 0.259417i | \(0.916470\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.3523 | − | 21.3949i | 0.508969 | − | 0.881560i | ||||
\(590\) | 6.44003 | + | 3.71815i | 0.265132 | + | 0.153074i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.60752 | 0.353767 | ||||||||
\(593\) | 4.26760 | − | 7.39170i | 0.175249 | − | 0.303541i | −0.764998 | − | 0.644032i | \(-0.777260\pi\) |
0.940248 | + | 0.340492i | \(0.110594\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.85494 | − | 3.53914i | 0.240029 | − | 0.145091i | ||||
\(596\) | 8.07815 | − | 4.66392i | 0.330894 | − | 0.191042i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.21460 | + | 10.5030i | −0.0905617 | + | 0.429499i | ||||
\(599\) | −3.65068 | + | 2.10772i | −0.149163 | + | 0.0861192i | −0.572724 | − | 0.819748i | \(-0.694113\pi\) |
0.423561 | + | 0.905868i | \(0.360780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.89940 | + | 1.09662i | −0.0774783 | + | 0.0447321i | −0.538239 | − | 0.842792i | \(-0.680910\pi\) |
0.460760 | + | 0.887525i | \(0.347577\pi\) | |||||||
\(602\) | −2.79818 | − | 4.62914i | −0.114045 | − | 0.188670i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.63758 | − | 11.4966i | −0.270079 | − | 0.467791i | ||||
\(605\) | 9.76042 | 0.396818 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.27710 | + | 4.20144i | −0.295369 | + | 0.170531i | −0.640360 | − | 0.768075i | \(-0.721215\pi\) |
0.344992 | + | 0.938606i | \(0.387882\pi\) | |||||||
\(608\) | −1.82358 | − | 3.15853i | −0.0739558 | − | 0.128095i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.53027 | −0.264403 | ||||||||
\(611\) | 0.496541 | + | 0.445625i | 0.0200879 | + | 0.0180280i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.9839 | − | 39.8092i | 0.928309 | − | 1.60788i | 0.142159 | − | 0.989844i | \(-0.454596\pi\) |
0.786150 | − | 0.618035i | \(-0.212071\pi\) | |||||||
\(614\) | 12.4632 | 0.502973 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.0795 | − | 6.69723i | 0.446405 | − | 0.269839i | ||||
\(617\) | −9.53772 | − | 5.50660i | −0.383974 | − | 0.221688i | 0.295572 | − | 0.955321i | \(-0.404490\pi\) |
−0.679546 | + | 0.733633i | \(0.737823\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.1787 | − | 22.6198i | 1.57473 | − | 0.909168i | 0.579148 | − | 0.815222i | \(-0.303385\pi\) |
0.995577 | − | 0.0939460i | \(-0.0299481\pi\) | |||||||
\(620\) | 5.10772i | 0.205131i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.59851 | − | 0.922899i | 0.0640943 | − | 0.0370049i | ||||
\(623\) | −29.9612 | − | 16.5042i | −1.20037 | − | 0.661227i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.39718 | + | 14.5443i | −0.335887 | + | 0.581774i | ||||
\(626\) | −15.4436 | + | 26.7492i | −0.617252 | + | 1.06911i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.74046 | + | 4.46895i | −0.308878 | + | 0.178331i | ||||
\(629\) | −29.5173 | −1.17693 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.81894 | + | 3.15050i | −0.0724109 | + | 0.125419i | −0.899957 | − | 0.435978i | \(-0.856403\pi\) |
0.827547 | + | 0.561397i | \(0.189736\pi\) | |||||||
\(632\) | 8.37001 | + | 4.83243i | 0.332941 | + | 0.192224i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.91538 | + | 6.78164i | −0.155500 | + | 0.269333i | ||||
\(635\) | 15.5949 | 0.618865 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.6564 | + | 8.79627i | −0.937301 | + | 0.348521i | ||||
\(638\) | − | 14.4525i | − | 0.572180i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.653029 | + | 0.377027i | 0.0258133 | + | 0.0149033i | ||||
\(641\) | − | 44.0507i | − | 1.73990i | −0.493142 | − | 0.869949i | \(-0.664152\pi\) | ||
0.493142 | − | 0.869949i | \(-0.335848\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.9439 | − | 23.6390i | −1.61467 | − | 0.932231i | −0.988268 | − | 0.152733i | \(-0.951193\pi\) |
−0.626404 | − | 0.779499i | \(-0.715474\pi\) | |||||||
\(644\) | −3.80037 | + | 6.89908i | −0.149756 | + | 0.271862i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.25350 | + | 10.8314i | 0.246041 | + | 0.426155i | ||||
\(647\) | 5.78761 | − | 10.0244i | 0.227535 | − | 0.394101i | −0.729542 | − | 0.683936i | \(-0.760267\pi\) |
0.957077 | + | 0.289834i | \(0.0936002\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.7911 | − | 24.1281i | −1.64044 | − | 0.947111i | ||||
\(650\) | 4.96212 | + | 15.1876i | 0.194630 | + | 0.595706i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.41328 | − | 2.44787i | −0.0553482 | − | 0.0958658i | ||||
\(653\) | − | 28.9682i | − | 1.13361i | −0.823851 | − | 0.566806i | \(-0.808179\pi\) | ||
0.823851 | − | 0.566806i | \(-0.191821\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.75440 | + | 4.77077i | 0.107623 | + | 0.186409i | ||||
\(656\) | −1.57286 | − | 2.72428i | −0.0614100 | − | 0.106365i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.253262 | + | 0.418982i | 0.00987320 | + | 0.0163336i | ||||
\(659\) | 10.7730 | + | 6.21981i | 0.419658 | + | 0.242289i | 0.694931 | − | 0.719077i | \(-0.255435\pi\) |
−0.275273 | + | 0.961366i | \(0.588768\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.7002 | − | 16.5700i | −1.11631 | − | 0.644500i | −0.175851 | − | 0.984417i | \(-0.556268\pi\) |
−0.940456 | + | 0.339917i | \(0.889601\pi\) | |||||||
\(662\) | −3.57337 | + | 2.06308i | −0.138883 | + | 0.0801840i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.66655i | 0.103482i | ||||||||
\(665\) | −3.51071 | + | 6.37324i | −0.136139 | + | 0.247143i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.39646 | + | 7.61489i | 0.170231 | + | 0.294850i | ||||
\(668\) | −7.61244 | − | 13.1851i | −0.294534 | − | 0.510148i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.06622 | + | 1.77028i | −0.118458 | + | 0.0683920i | ||||
\(671\) | 42.3767 | 1.63593 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.10484 | + | 15.7701i | 0.350966 | + | 0.607891i | 0.986419 | − | 0.164249i | \(-0.0525200\pi\) |
−0.635453 | + | 0.772140i | \(0.719187\pi\) | |||||||
\(674\) | 33.0546i | 1.27322i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.8933 | + | 5.24885i | 0.457433 | + | 0.201879i | ||||
\(677\) | −18.2468 | + | 31.6044i | −0.701282 | + | 1.21466i | 0.266735 | + | 0.963770i | \(0.414055\pi\) |
−0.968017 | + | 0.250886i | \(0.919278\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.81314 | + | 14.5799i | 0.338217 | + | 0.559526i | ||||
\(680\) | −2.23940 | − | 1.29292i | −0.0858771 | − | 0.0495812i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 33.1453i | − | 1.26920i | ||||||
\(683\) | − | 40.0572i | − | 1.53274i | −0.642397 | − | 0.766372i | \(-0.722060\pi\) | ||
0.642397 | − | 0.766372i | \(-0.277940\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.61956 | − | 5.55386i | −0.367544 | − | 0.212202i | ||||
\(686\) | −18.4866 | + | 1.11621i | −0.705821 | + | 0.0426169i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.02223 | + | 1.77055i | −0.0389722 | + | 0.0675018i | ||||
\(689\) | −6.58264 | − | 20.1475i | −0.250779 | − | 0.767560i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.1396i | 1.37481i | 0.726273 | + | 0.687407i | \(0.241251\pi\) | ||||
−0.726273 | + | 0.687407i | \(0.758749\pi\) | |||||||
\(692\) | −0.569456 | − | 0.986326i | −0.0216475 | − | 0.0374945i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.94972 | 0.225848 | ||||||||
\(695\) | 5.27474 | − | 3.04537i | 0.200082 | − | 0.115517i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.39375 | + | 9.34224i | 0.204303 | + | 0.353863i | ||||
\(698\) | 5.74509 | + | 9.95079i | 0.217455 | + | 0.376643i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.235668 | + | 11.7220i | 0.00890740 | + | 0.443051i | ||||
\(701\) | − | 43.7394i | − | 1.65201i | −0.563659 | − | 0.826007i | \(-0.690607\pi\) | ||
0.563659 | − | 0.826007i | \(-0.309393\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.1871 | − | 15.6965i | 1.02538 | − | 0.592004i | ||||
\(704\) | −4.23768 | − | 2.44663i | −0.159714 | − | 0.0922107i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.48472 | − | 1.43456i | −0.0935138 | − | 0.0539902i | ||||
\(707\) | −6.93020 | + | 4.18911i | −0.260637 | + | 0.157548i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.2922 | − | 23.0228i | −0.499199 | − | 0.864638i | 0.500800 | − | 0.865563i | \(-0.333039\pi\) |
−1.00000 | 0.000924526i | \(0.999706\pi\) | ||||||||
\(710\) | −3.19276 | − | 5.53002i | −0.119822 | − | 0.207538i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.9287i | 0.484525i | ||||||||
\(713\) | 10.0828 | + | 17.4640i | 0.377605 | + | 0.654030i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.13167 | + | 12.6458i | 0.154516 | + | 0.472927i | ||||
\(716\) | 5.18256 | + | 2.99215i | 0.193681 | + | 0.111822i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.08652 | + | 7.07807i | −0.152508 | + | 0.264151i | ||||
\(719\) | −6.00910 | − | 10.4081i | −0.224102 | − | 0.388155i | 0.731948 | − | 0.681361i | \(-0.238611\pi\) |
−0.956050 | + | 0.293205i | \(0.905278\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.57528 | − | 14.1864i | −0.319360 | − | 0.528329i | ||||
\(722\) | 4.93485 | + | 2.84914i | 0.183656 | + | 0.106034i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.8486i | 0.700505i | ||||||||
\(725\) | 11.3349 | + | 6.54420i | 0.420967 | + | 0.243046i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 47.0077i | − | 1.74342i | −0.490024 | − | 0.871709i | \(-0.663012\pi\) | ||
0.490024 | − | 0.871709i | \(-0.336988\pi\) | |||||||
\(728\) | 7.22618 | + | 6.22755i | 0.267820 | + | 0.230808i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.48762 | −0.129083 | ||||||||
\(731\) | 3.50548 | − | 6.07167i | 0.129655 | − | 0.224569i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.2548 | + | 18.6223i | 1.19136 | + | 0.687831i | 0.958615 | − | 0.284707i | \(-0.0918964\pi\) |
0.232744 | + | 0.972538i | \(0.425230\pi\) | |||||||
\(734\) | −4.29921 | + | 7.44645i | −0.158687 | + | 0.274854i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.97706 | 0.109736 | ||||||||
\(737\) | 19.8975 | − | 11.4878i | 0.732935 | − | 0.423160i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.58593 | + | 9.67512i | −0.205482 | + | 0.355905i | −0.950286 | − | 0.311378i | \(-0.899209\pi\) |
0.744804 | + | 0.667283i | \(0.232543\pi\) | |||||||
\(740\) | −3.24526 | + | 5.62096i | −0.119298 | + | 0.206631i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.312632 | − | 15.5502i | −0.0114771 | − | 0.570865i | ||||
\(743\) | 12.6809 | − | 7.32130i | 0.465216 | − | 0.268592i | −0.249019 | − | 0.968499i | \(-0.580108\pi\) |
0.714235 | + | 0.699906i | \(0.246775\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.03369i | 0.257694i | ||||||||
\(746\) | 28.6639 | − | 16.5491i | 1.04946 | − | 0.605907i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14.5321 | + | 8.39010i | 0.531345 | + | 0.306772i | ||||
\(749\) | 7.45132 | − | 13.5269i | 0.272265 | − | 0.494263i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.2981 | −1.65295 | −0.826475 | − | 0.562973i | \(-0.809658\pi\) | ||||
−0.826475 | + | 0.562973i | \(0.809658\pi\) | |||||||
\(752\) | 0.0925217 | − | 0.160252i | 0.00337392 | − | 0.00584380i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.1226 | − | 3.30728i | 0.368644 | − | 0.120444i | ||||
\(755\) | 10.0102 | 0.364308 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.217479 | − | 0.376684i | −0.00790440 | − | 0.0136908i | 0.862046 | − | 0.506830i | \(-0.169183\pi\) |
−0.869951 | + | 0.493139i | \(0.835849\pi\) | |||||||
\(758\) | 13.0890 | − | 7.55693i | 0.475413 | − | 0.274480i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.75015 | 0.0997583 | ||||||||
\(761\) | −26.2848 | − | 45.5265i | −0.952822 | − | 1.65034i | −0.739275 | − | 0.673403i | \(-0.764832\pi\) |
−0.213547 | − | 0.976933i | \(-0.568502\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.212902 | + | 10.5897i | 0.00770759 | + | 0.383372i | ||||
\(764\) | −20.3390 | + | 11.7427i | −0.735839 | + | 0.424837i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.4938 | − | 15.2962i | 0.957260 | − | 0.552674i | ||||
\(767\) | 7.33607 | − | 34.7921i | 0.264890 | − | 1.25627i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.8078 | + | 7.97196i | −0.497924 | + | 0.287476i | −0.727856 | − | 0.685730i | \(-0.759483\pi\) |
0.229932 | + | 0.973207i | \(0.426150\pi\) | |||||||
\(770\) | 0.196227 | + | 9.76026i | 0.00707153 | + | 0.351735i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.78214 | − | 3.08676i | 0.0641407 | − | 0.111095i | ||||
\(773\) | 0.442280 | 0.0159077 | 0.00795385 | − | 0.999968i | \(-0.497468\pi\) | ||||
0.00795385 | + | 0.999968i | \(0.497468\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.9954 | + | 15.0085i | 0.933783 | + | 0.539120i | ||||
\(776\) | 3.21961 | − | 5.57654i | 0.115577 | − | 0.200186i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.46995 | + | 4.27808i | 0.0885520 | + | 0.153377i | ||||
\(779\) | −9.93587 | − | 5.73648i | −0.355989 | − | 0.205531i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.7187 | + | 35.8858i | 0.741372 | + | 1.28409i | ||||
\(782\) | −10.2091 | −0.365076 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.74083 | + | 5.91660i | 0.133601 | + | 0.211307i | ||||
\(785\) | − | 6.73966i | − | 0.240549i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.1465i | 0.397330i | 0.980067 | + | 0.198665i | \(0.0636606\pi\) | ||||
−0.980067 | + | 0.198665i | \(0.936339\pi\) | |||||||
\(788\) | 21.8018 | − | 12.5873i | 0.776657 | − | 0.448403i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.31143 | + | 3.64391i | −0.224551 | + | 0.129644i | ||||
\(791\) | 6.83004 | + | 11.2992i | 0.242848 | + | 0.401753i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.69739 | + | 29.6809i | 0.344364 | + | 1.05400i | ||||
\(794\) | 1.73942 | + | 3.01277i | 0.0617299 | + | 0.106919i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 12.4959i | − | 0.442904i | ||||||
\(797\) | 14.5054 | − | 25.1240i | 0.513806 | − | 0.889939i | −0.486065 | − | 0.873922i | \(-0.661568\pi\) |
0.999872 | − | 0.0160163i | \(-0.00509838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.317280 | + | 0.549545i | −0.0112246 | + | 0.0194415i | ||||
\(800\) | 3.83771 | − | 2.21570i | 0.135683 | − | 0.0783369i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.4337 | 0.403738 | ||||||||
\(803\) | 22.6321 | 0.798669 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.07246 | − | 5.08289i | −0.108290 | − | 0.179148i | ||||
\(806\) | 23.2152 | − | 7.58491i | 0.817720 | − | 0.267167i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.65067 | + | 1.53036i | 0.0932501 | + | 0.0538380i | ||||
\(809\) | −15.0227 | − | 8.67337i | −0.528170 | − | 0.304939i | 0.212101 | − | 0.977248i | \(-0.431970\pi\) |
−0.740271 | + | 0.672309i | \(0.765303\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 29.7180i | − | 1.04354i | −0.853086 | − | 0.521770i | \(-0.825272\pi\) | ||
0.853086 | − | 0.521770i | \(-0.174728\pi\) | |||||||
\(812\) | 7.81280 | − | 0.157074i | 0.274176 | − | 0.00551222i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 21.0594 | − | 36.4759i | 0.738131 | − | 1.27848i | ||||
\(815\) | 2.13137 | 0.0746587 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.45646i | 0.260869i | ||||||||
\(818\) | −37.3528 | −1.30601 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.37205 | 0.0828355 | ||||||||
\(821\) | − | 41.5883i | − | 1.45144i | −0.687988 | − | 0.725722i | \(-0.741506\pi\) | ||
0.687988 | − | 0.725722i | \(-0.258494\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.4928 | 0.923482 | 0.461741 | − | 0.887015i | \(-0.347225\pi\) | ||||
0.461741 | + | 0.887015i | \(0.347225\pi\) | |||||||
\(824\) | −3.13272 | + | 5.42602i | −0.109133 | + | 0.189025i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.5891 | − | 22.8538i | 0.438030 | − | 0.795187i | ||||
\(827\) | 43.5660i | 1.51494i | 0.652872 | + | 0.757468i | \(0.273564\pi\) | ||||
−0.652872 | + | 0.757468i | \(0.726436\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.951475 | − | 0.549334i | −0.0330461 | − | 0.0190792i | 0.483386 | − | 0.875407i | \(-0.339407\pi\) |
−0.516432 | + | 0.856328i | \(0.672740\pi\) | |||||||
\(830\) | −1.74134 | − | 1.00536i | −0.0604427 | − | 0.0348966i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.743889 | − | 3.52798i | 0.0257897 | − | 0.122311i | ||||
\(833\) | −12.8282 | − | 20.2895i | −0.444472 | − | 0.702990i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.4804 | 0.397294 | ||||||||
\(836\) | −17.8465 | −0.617232 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −33.1933 | + | 19.1641i | −1.14664 | + | 0.662015i | ||||
\(839\) | 8.15758 | − | 14.1293i | 0.281631 | − | 0.487799i | −0.690156 | − | 0.723661i | \(-0.742458\pi\) |
0.971787 | + | 0.235862i | \(0.0757913\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.1382 | + | 17.5600i | −0.349595 | + | 0.605516i | ||||
\(842\) | − | 1.61871i | − | 0.0557843i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.63458 | − | 4.56323i | −0.0906860 | − | 0.157073i | ||||
\(845\) | −7.91173 | + | 5.78769i | −0.272172 | + | 0.199103i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.688376 | − | 34.2395i | −0.0236529 | − | 1.17648i | ||||
\(848\) | −5.09102 | + | 2.93930i | −0.174826 | + | 0.100936i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.1605 | + | 7.59820i | −0.451400 | + | 0.260616i | ||||
\(851\) | 25.6251i | 0.878417i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.34078i | 0.182865i | 0.995811 | + | 0.0914324i | \(0.0291445\pi\) | ||||
−0.995811 | + | 0.0914324i | \(0.970855\pi\) | |||||||
\(854\) | 0.460562 | + | 22.9082i | 0.0157601 | + | 0.783901i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.83707 | −0.199507 | ||||||||
\(857\) | −16.1046 | − | 27.8940i | −0.550122 | − | 0.952840i | −0.998265 | − | 0.0588780i | \(-0.981248\pi\) |
0.448143 | − | 0.893962i | \(-0.352086\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.4379 | + | 15.2639i | 0.902050 | + | 0.520799i | 0.877865 | − | 0.478909i | \(-0.158967\pi\) |
0.0241854 | + | 0.999707i | \(0.492301\pi\) | |||||||
\(860\) | −0.770816 | − | 1.33509i | −0.0262846 | − | 0.0455263i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.52265 | + | 16.4937i | −0.324343 | + | 0.561778i | ||||
\(863\) | −42.8644 | − | 24.7478i | −1.45912 | − | 0.842424i | −0.460154 | − | 0.887839i | \(-0.652206\pi\) |
−0.998968 | + | 0.0454148i | \(0.985539\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.858800 | 0.0292001 | ||||||||
\(866\) | 12.2457 | − | 21.2102i | 0.416126 | − | 0.720751i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 17.9179 | − | 0.360233i | 0.608172 | − | 0.0122271i | ||||
\(869\) | 40.9566 | − | 23.6463i | 1.38936 | − | 0.802146i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.5995 | + | 11.3075i | 0.426916 | + | 0.383139i | ||||
\(872\) | 3.46699 | − | 2.00167i | 0.117407 | − | 0.0677850i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.40312 | − | 5.42889i | 0.318065 | − | 0.183635i | ||||
\(875\) | −16.4810 | − | 9.07856i | −0.557158 | − | 0.306911i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.19794 | + | 2.07489i | 0.0404514 | + | 0.0700640i | 0.885542 | − | 0.464559i | \(-0.153787\pi\) |
−0.845091 | + | 0.534623i | \(0.820454\pi\) | |||||||
\(878\) | −34.3635 | −1.15971 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.19544 | − | 1.84489i | 0.107718 | − | 0.0621911i | ||||
\(881\) | 19.5418 | + | 33.8473i | 0.658379 | + | 1.14035i | 0.981035 | + | 0.193830i | \(0.0620909\pi\) |
−0.322656 | + | 0.946516i | \(0.604576\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.4689 | 0.756140 | 0.378070 | − | 0.925777i | \(-0.376588\pi\) | ||||
0.378070 | + | 0.925777i | \(0.376588\pi\) | |||||||
\(884\) | −2.55098 | + | 12.0983i | −0.0857988 | + | 0.406911i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.5287 | − | 23.4324i | 0.454506 | − | 0.787227i | ||||
\(887\) | −11.8745 | −0.398706 | −0.199353 | − | 0.979928i | \(-0.563884\pi\) | ||||
−0.199353 | + | 0.979928i | \(0.563884\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.09987 | − | 54.7069i | −0.0368883 | − | 1.83481i | ||||
\(890\) | −8.44284 | − | 4.87448i | −0.283005 | − | 0.163393i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.40211 | + | 4.85096i | −0.281324 | + | 0.162422i | ||||
\(893\) | − | 0.674882i | − | 0.0225841i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.90793 | + | 2.25624i | −0.130628 | + | 0.0754179i | ||||
\(896\) | 1.27655 | − | 2.31742i | 0.0426466 | − | 0.0774194i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.0817 | − | 29.5863i | 0.570022 | − | 0.987308i | ||||
\(899\) | 10.0032 | − | 17.3261i | 0.333626 | − | 0.577858i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.4584 | − | 10.0796i | 0.581623 | − | 0.335800i | ||||
\(902\) | −15.3929 | −0.512526 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.49515 | − | 4.32172i | 0.0829874 | − | 0.143738i | ||||
\(905\) | −12.3087 | − | 7.10644i | −0.409156 | − | 0.236226i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.00952 | − | 8.67674i | 0.166338 | − | 0.288106i | −0.770791 | − | 0.637088i | \(-0.780139\pi\) |
0.937130 | + | 0.348981i | \(0.113472\pi\) | |||||||
\(908\) | −5.62699 | −0.186738 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.79123 | + | 2.37096i | −0.225127 | + | 0.0785964i | ||||
\(911\) | 29.3842i | 0.973541i | 0.873530 | + | 0.486771i | \(0.161825\pi\) | ||||
−0.873530 | + | 0.486771i | \(0.838175\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.3000 | + | 6.52406i | 0.373975 | + | 0.215915i | ||||
\(914\) | − | 18.2315i | − | 0.603044i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.13664 | + | 4.12034i | 0.235801 | + | 0.136140i | ||||
\(917\) | 16.5416 | − | 9.99891i | 0.546251 | − | 0.330193i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.72015 | − | 16.8358i | −0.320638 | − | 0.555362i | 0.659982 | − | 0.751282i | \(-0.270564\pi\) |
−0.980620 | + | 0.195920i | \(0.937231\pi\) | |||||||
\(920\) | −1.12243 | + | 1.94411i | −0.0370054 | + | 0.0640953i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −24.0250 | − | 13.8708i | −0.791221 | − | 0.456812i | ||||
\(923\) | −20.3934 | + | 22.7235i | −0.671256 | + | 0.747953i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.0717 | + | 33.0332i | 0.627074 | + | 1.08612i | ||||
\(926\) | − | 36.9055i | − | 1.21279i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.47678 | − | 2.55786i | −0.0484776 | − | 0.0839657i | ||||
\(929\) | −9.71746 | − | 16.8311i | −0.318819 | − | 0.552211i | 0.661423 | − | 0.750013i | \(-0.269953\pi\) |
−0.980242 | + | 0.197802i | \(0.936620\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.6049 | + | 11.8661i | 0.740845 | + | 0.388894i | ||||
\(932\) | 16.7363 | + | 9.66269i | 0.548215 | + | 0.316512i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 29.0550 | + | 16.7749i | 0.950710 | + | 0.548893i | ||||
\(935\) | −10.9580 | + | 6.32658i | −0.358364 | + | 0.206901i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 22.6784i | − | 0.740871i | −0.928858 | − | 0.370435i | \(-0.879208\pi\) | ||
0.928858 | − | 0.370435i | \(-0.120792\pi\) | |||||||
\(938\) | 6.42640 | + | 10.6314i | 0.209829 | + | 0.347129i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.0697663 | + | 0.120839i | 0.00227553 | + | 0.00394133i | ||||
\(941\) | −10.1312 | − | 17.5478i | −0.330268 | − | 0.572040i | 0.652297 | − | 0.757964i | \(-0.273806\pi\) |
−0.982564 | + | 0.185923i | \(0.940472\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.11034 | − | 4.68251i | 0.264109 | − | 0.152483i | ||||
\(944\) | −9.86178 | −0.320974 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.00203 | + | 8.66378i | 0.162630 | + | 0.281684i | ||||
\(947\) | − | 30.5079i | − | 0.991372i | −0.868502 | − | 0.495686i | \(-0.834917\pi\) | ||
0.868502 | − | 0.495686i | \(-0.165083\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.17908 | + | 15.8516i | 0.168120 | + | 0.514566i | ||||
\(950\) | 8.08100 | − | 13.9967i | 0.262182 | − | 0.454113i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.37762 | + | 7.94700i | −0.141879 | + | 0.257564i | ||||
\(953\) | −33.3289 | − | 19.2424i | −1.07963 | − | 0.623323i | −0.148832 | − | 0.988863i | \(-0.547551\pi\) |
−0.930796 | + | 0.365539i | \(0.880885\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 17.7093i | − | 0.573059i | ||||||
\(956\) | − | 26.1899i | − | 0.847042i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 32.9840 | + | 19.0433i | 1.06566 | + | 0.615261i | ||||
\(959\) | −18.8045 | + | 34.1371i | −0.607228 | + | 1.10234i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.44137 | − | 12.8888i | 0.240044 | − | 0.415769i | ||||
\(962\) | 30.3671 | + | 6.40304i | 0.979076 | + | 0.206442i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.3956i | 0.528068i | ||||||||
\(965\) | 1.34383 | + | 2.32758i | 0.0432595 | + | 0.0749276i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.5090 | 0.563051 | 0.281525 | − | 0.959554i | \(-0.409160\pi\) | ||||
0.281525 | + | 0.959554i | \(0.409160\pi\) | |||||||
\(968\) | −11.2098 | + | 6.47197i | −0.360296 | + | 0.208017i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.42776 | + | 4.20500i | 0.0779507 | + | 0.135015i | ||||
\(971\) | −6.82401 | − | 11.8195i | −0.218993 | − | 0.379307i | 0.735507 | − | 0.677517i | \(-0.236944\pi\) |
−0.954500 | + | 0.298210i | \(0.903610\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.0552 | − | 18.2890i | −0.354412 | − | 0.586318i | ||||
\(974\) | − | 0.531844i | − | 0.0170414i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.49997 | − | 4.33011i | 0.240068 | − | 0.138603i | ||||
\(977\) | 18.5757 | + | 10.7247i | 0.594290 | + | 0.343113i | 0.766792 | − | 0.641896i | \(-0.221852\pi\) |
−0.172502 | + | 0.985009i | \(0.555185\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.7879 | + | 31.6318i | 1.75103 | + | 1.01096i | ||||
\(980\) | −5.27411 | + | 0.212154i | −0.168475 | + | 0.00677703i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.46249 | − | 4.26515i | −0.0785811 | − | 0.136107i | ||||
\(983\) | 7.53173 | + | 13.0453i | 0.240225 | + | 0.416081i | 0.960778 | − | 0.277318i | \(-0.0894455\pi\) |
−0.720553 | + | 0.693399i | \(0.756112\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.9829i | 0.604847i | ||||||||
\(986\) | 5.06424 | + | 8.77153i | 0.161278 | + | 0.279342i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.08395 | − | 12.4998i | −0.129928 | − | 0.397670i | ||||
\(989\) | −5.27104 | − | 3.04324i | −0.167609 | − | 0.0967694i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.97010 | + | 12.0726i | −0.221412 | + | 0.383498i | −0.955237 | − | 0.295841i | \(-0.904400\pi\) |
0.733825 | + | 0.679339i | \(0.237733\pi\) | |||||||
\(992\) | −3.38684 | − | 5.86618i | −0.107532 | − | 0.186251i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −19.1741 | + | 11.5902i | −0.608166 | + | 0.367619i | ||||
\(995\) | 8.16017 | + | 4.71127i | 0.258695 | + | 0.149357i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 58.7468i | − | 1.86053i | −0.366888 | − | 0.930265i | \(-0.619577\pi\) | ||
0.366888 | − | 0.930265i | \(-0.380423\pi\) | |||||||
\(998\) | −5.66956 | − | 3.27332i | −0.179467 | − | 0.103615i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1638.2.cm.a.341.22 | yes | 72 | |
3.2 | odd | 2 | inner | 1638.2.cm.a.341.15 | yes | 72 | |
7.3 | odd | 6 | 1638.2.bq.a.1277.28 | yes | 72 | ||
13.9 | even | 3 | 1638.2.bq.a.971.9 | ✓ | 72 | ||
21.17 | even | 6 | 1638.2.bq.a.1277.9 | yes | 72 | ||
39.35 | odd | 6 | 1638.2.bq.a.971.28 | yes | 72 | ||
91.87 | odd | 6 | inner | 1638.2.cm.a.269.15 | yes | 72 | |
273.269 | even | 6 | inner | 1638.2.cm.a.269.22 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1638.2.bq.a.971.9 | ✓ | 72 | 13.9 | even | 3 | ||
1638.2.bq.a.971.28 | yes | 72 | 39.35 | odd | 6 | ||
1638.2.bq.a.1277.9 | yes | 72 | 21.17 | even | 6 | ||
1638.2.bq.a.1277.28 | yes | 72 | 7.3 | odd | 6 | ||
1638.2.cm.a.269.15 | yes | 72 | 91.87 | odd | 6 | inner | |
1638.2.cm.a.269.22 | yes | 72 | 273.269 | even | 6 | inner | |
1638.2.cm.a.341.15 | yes | 72 | 3.2 | odd | 2 | inner | |
1638.2.cm.a.341.22 | yes | 72 | 1.1 | even | 1 | trivial |