Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,2,Mod(13,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.i (of order \(9\), degree \(6\), 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: | \(0.862384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(0.381933 + 1.68942i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.13 |
Dual form | 108.2.i.a.25.1 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.73007 | + | 0.0827666i | −0.998858 | + | 0.0477853i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.26400 | + | 1.89972i | 1.01249 | + | 0.849580i | 0.988665 | − | 0.150136i | \(-0.0479713\pi\) |
0.0238244 | + | 0.999716i | \(0.492416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50885 | + | 0.913148i | 0.948257 | + | 0.345137i | 0.769421 | − | 0.638741i | \(-0.220545\pi\) |
0.178836 | + | 0.983879i | \(0.442767\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.98630 | − | 0.286384i | 0.995433 | − | 0.0954615i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.22454 | + | 1.86661i | −0.670724 | + | 0.562804i | −0.913280 | − | 0.407333i | \(-0.866459\pi\) |
0.242556 | + | 0.970138i | \(0.422014\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.588684 | − | 3.33859i | 0.163272 | − | 0.925959i | −0.787557 | − | 0.616242i | \(-0.788654\pi\) |
0.950829 | − | 0.309717i | \(-0.100234\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.07411 | − | 3.09927i | −1.05193 | − | 0.800227i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.40583 | + | 4.16701i | −0.583499 | + | 1.01065i | 0.411562 | + | 0.911382i | \(0.364983\pi\) |
−0.995061 | + | 0.0992678i | \(0.968350\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.13789 | − | 5.43498i | −0.719881 | − | 1.24687i | −0.961047 | − | 0.276386i | \(-0.910863\pi\) |
0.241166 | − | 0.970484i | \(-0.422470\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.41608 | − | 1.37216i | −0.963667 | − | 0.299430i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.841669 | − | 0.306343i | 0.175500 | − | 0.0638769i | −0.252776 | − | 0.967525i | \(-0.581343\pi\) |
0.428276 | + | 0.903648i | \(0.359121\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.648507 | + | 3.67787i | 0.129701 | + | 0.735574i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.14281 | + | 0.742631i | −0.989734 | + | 0.142919i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.06019 | − | 6.01265i | −0.196873 | − | 1.11652i | −0.909726 | − | 0.415208i | \(-0.863709\pi\) |
0.712854 | − | 0.701313i | \(-0.247402\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.86152 | − | 2.86136i | 1.41197 | − | 0.513916i | 0.480263 | − | 0.877124i | \(-0.340541\pi\) |
0.931708 | + | 0.363209i | \(0.118319\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.69412 | − | 3.41349i | 0.643064 | − | 0.594212i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.94531 | + | 6.83348i | 0.666879 | + | 1.15507i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.71058 | + | 8.15896i | −0.774414 | + | 1.34132i | 0.160709 | + | 0.987002i | \(0.448622\pi\) |
−0.935123 | + | 0.354323i | \(0.884711\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.742142 | + | 5.82473i | −0.118838 | + | 0.932703i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.77855 | − | 10.0866i | 0.277762 | − | 1.57527i | −0.452286 | − | 0.891873i | \(-0.649391\pi\) |
0.730048 | − | 0.683396i | \(-0.239498\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.13098 | + | 0.949006i | −0.172473 | + | 0.144722i | −0.724938 | − | 0.688814i | \(-0.758132\pi\) |
0.552465 | + | 0.833536i | \(0.313687\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.30502 | + | 5.02475i | 1.08897 | + | 0.749046i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.41276 | − | 1.97008i | −0.789532 | − | 0.287366i | −0.0843906 | − | 0.996433i | \(-0.526894\pi\) |
−0.705142 | + | 0.709067i | \(0.749117\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0981944 | + | 0.0823949i | 0.0140278 | + | 0.0117707i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.81737 | − | 7.40836i | 0.534538 | − | 1.03738i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.51324 | −0.619942 | −0.309971 | − | 0.950746i | \(-0.600319\pi\) | ||||
−0.309971 | + | 0.950746i | \(0.600319\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.58238 | −1.15725 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.87861 | + | 9.14320i | 0.778641 | + | 1.21105i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.89034 | + | 7.45989i | 1.15742 | + | 0.971194i | 0.999867 | − | 0.0163155i | \(-0.00519361\pi\) |
0.157557 | + | 0.987510i | \(0.449638\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.667734 | − | 0.243035i | −0.0854946 | − | 0.0311175i | 0.298919 | − | 0.954279i | \(-0.403374\pi\) |
−0.384413 | + | 0.923161i | \(0.625596\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.75370 | + | 2.00844i | 0.976874 | + | 0.253039i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.67516 | − | 6.44023i | 0.951987 | − | 0.798812i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.472021 | − | 2.67696i | 0.0576665 | − | 0.327043i | −0.942304 | − | 0.334759i | \(-0.891345\pi\) |
0.999970 | + | 0.00771610i | \(0.00245614\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.43079 | + | 0.599657i | −0.172247 | + | 0.0721902i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.000646382 | − | 0.00111957i | 7.67115e−5 | − | 0.000132868i | −0.865987 | − | 0.500066i | \(-0.833309\pi\) |
0.866064 | + | 0.499934i | \(0.166642\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.878080 | + | 1.52088i | 0.102772 | + | 0.178005i | 0.912826 | − | 0.408350i | \(-0.133896\pi\) |
−0.810054 | + | 0.586355i | \(0.800562\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.42637 | − | 6.30930i | −0.164703 | − | 0.728535i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.28554 | + | 2.65172i | −0.830264 | + | 0.302191i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.73545 | + | 9.84220i | 0.195253 | + | 1.10733i | 0.912058 | + | 0.410061i | \(0.134493\pi\) |
−0.716805 | + | 0.697273i | \(0.754396\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.83597 | − | 1.71046i | 0.981774 | − | 0.190051i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.296685 | − | 1.68259i | −0.0325654 | − | 0.184688i | 0.964186 | − | 0.265227i | \(-0.0854469\pi\) |
−0.996751 | + | 0.0805392i | \(0.974336\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.3629 | + | 4.86371i | −1.44941 | + | 0.527544i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.33186 | + | 10.3146i | 0.250001 | + | 1.10584i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.52283 | − | 11.2979i | −0.691418 | − | 1.19757i | −0.971373 | − | 0.237558i | \(-0.923653\pi\) |
0.279955 | − | 0.960013i | \(-0.409680\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.52555 | − | 7.83848i | 0.474407 | − | 0.821696i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.3642 | + | 5.60103i | −1.38580 | + | 0.580800i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.22077 | − | 18.2659i | 0.330444 | − | 1.87404i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.43956 | + | 2.04703i | −0.247699 | + | 0.207845i | −0.758181 | − | 0.652044i | \(-0.773912\pi\) |
0.510481 | + | 0.859889i | \(0.329467\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.10857 | + | 6.21133i | −0.613935 | + | 0.624262i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.3176 | − | 3.75529i | −1.02664 | − | 0.373666i | −0.226838 | − | 0.973932i | \(-0.572839\pi\) |
−0.799800 | + | 0.600267i | \(0.795061\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.45382 | − | 2.89810i | −0.340315 | − | 0.285558i | 0.456572 | − | 0.889686i | \(-0.349077\pi\) |
−0.796887 | + | 0.604128i | \(0.793521\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.39125 | − | 11.4959i | −0.721313 | − | 1.12188i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.98188 | 0.578290 | 0.289145 | − | 0.957285i | \(-0.406629\pi\) | ||||
0.289145 | + | 0.957285i | \(0.406629\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.37994 | −0.419522 | −0.209761 | − | 0.977753i | \(-0.567269\pi\) | ||||
−0.209761 | + | 0.977753i | \(0.567269\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.47435 | − | 14.5055i | 0.709434 | − | 1.37680i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.7510 | + | 9.02115i | 1.01137 | + | 0.848638i | 0.988518 | − | 0.151101i | \(-0.0482818\pi\) |
0.0228490 | + | 0.999739i | \(0.492726\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.48750 | + | 0.905376i | 0.231961 | + | 0.0844268i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.801866 | − | 10.1386i | 0.0741325 | − | 0.937317i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.84097 | + | 8.25755i | −0.902120 | + | 0.756969i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.445787 | + | 2.52818i | −0.0405261 | + | 0.229835i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.24218 | + | 17.5978i | −0.202170 | + | 1.58674i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.86990 | − | 3.23876i | 0.167249 | − | 0.289683i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.24395 | + | 7.35074i | 0.376590 | + | 0.652273i | 0.990564 | − | 0.137054i | \(-0.0437633\pi\) |
−0.613974 | + | 0.789326i | \(0.710430\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.87813 | − | 1.73546i | 0.165360 | − | 0.152798i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.2866 | + | 4.47197i | −1.07349 | + | 0.390718i | −0.817480 | − | 0.575956i | \(-0.804630\pi\) |
−0.256009 | + | 0.966675i | \(0.582408\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.90956 | − | 16.5009i | −0.252291 | − | 1.43081i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.0541 | − | 8.08858i | −1.12352 | − | 0.696154i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.21248 | + | 18.2189i | 0.274461 | + | 1.55654i | 0.740670 | + | 0.671869i | \(0.234508\pi\) |
−0.466209 | + | 0.884675i | \(0.654381\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.5758 | − | 5.66914i | 1.32112 | − | 0.480850i | 0.417306 | − | 0.908766i | \(-0.362974\pi\) |
0.903818 | + | 0.427916i | \(0.140752\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.52752 | + | 2.96039i | 0.802362 | + | 0.249310i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.92230 | + | 8.52568i | 0.411624 | + | 0.712953i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.02207 | − | 15.6267i | 0.749242 | − | 1.29772i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.176703 | − | 0.134422i | −0.0145742 | − | 0.0110869i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.39504 | + | 13.5830i | −0.196209 | + | 1.11276i | 0.714477 | + | 0.699659i | \(0.246665\pi\) |
−0.910686 | + | 0.413099i | \(0.864446\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.312333 | + | 0.262078i | −0.0254173 | + | 0.0213276i | −0.655408 | − | 0.755275i | \(-0.727503\pi\) |
0.629991 | + | 0.776603i | \(0.283059\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.99115 | + | 13.1329i | −0.484356 | + | 1.06174i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.2342 | + | 8.45657i | 1.86622 | + | 0.679248i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.54870 | + | 5.49501i | 0.522643 | + | 0.438550i | 0.865552 | − | 0.500819i | \(-0.166968\pi\) |
−0.342909 | + | 0.939369i | \(0.611412\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.80824 | − | 0.373546i | 0.619234 | − | 0.0296241i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.39136 | 0.188466 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.49244 | 0.665179 | 0.332590 | − | 0.943072i | \(-0.392078\pi\) | ||||
0.332590 | + | 0.943072i | \(0.392078\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.8481 | − | 0.710335i | 1.15593 | − | 0.0552995i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.42577 | − | 5.39186i | −0.497241 | − | 0.417235i | 0.359372 | − | 0.933194i | \(-0.382991\pi\) |
−0.856613 | + | 0.515960i | \(0.827435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.41635 | + | 0.515509i | 0.108950 | + | 0.0396545i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.9272 | − | 15.3318i | −0.835621 | − | 1.17245i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9442 | − | 9.18331i | 0.832075 | − | 0.698194i | −0.123691 | − | 0.992321i | \(-0.539473\pi\) |
0.955766 | + | 0.294127i | \(0.0950287\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.73143 | + | 9.81941i | −0.130884 | + | 0.742278i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.9984 | − | 12.1703i | −1.20251 | − | 0.914777i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.850987 | + | 1.47395i | −0.0636058 | + | 0.110168i | −0.896075 | − | 0.443903i | \(-0.853593\pi\) |
0.832469 | + | 0.554072i | \(0.186927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.85598 | + | 17.0710i | 0.732589 | + | 1.26888i | 0.955773 | + | 0.294105i | \(0.0950215\pi\) |
−0.223184 | + | 0.974776i | \(0.571645\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.17534 | + | 0.365202i | 0.0868838 | + | 0.0269965i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −26.1644 | + | 9.52308i | −1.92365 | + | 0.700151i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.42634 | − | 13.7604i | −0.177431 | − | 1.00626i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.5807 | − | 2.83299i | −0.987850 | − | 0.206070i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.676006 | − | 3.83382i | −0.0489141 | − | 0.277405i | 0.950534 | − | 0.310620i | \(-0.100537\pi\) |
−0.999448 | + | 0.0332146i | \(0.989426\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.7186 | + | 3.90124i | −0.771540 | + | 0.280818i | −0.697640 | − | 0.716448i | \(-0.745767\pi\) |
−0.0738996 | + | 0.997266i | \(0.523544\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.7456 | + | 11.7773i | −0.912728 | + | 0.843390i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.538764 | − | 0.933167i | −0.0383854 | − | 0.0664854i | 0.846194 | − | 0.532874i | \(-0.178888\pi\) |
−0.884580 | + | 0.466389i | \(0.845555\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.39347 | + | 7.60971i | −0.311445 | + | 0.539438i | −0.978675 | − | 0.205413i | \(-0.934146\pi\) |
0.667231 | + | 0.744851i | \(0.267480\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.595067 | + | 4.67041i | −0.0419728 | + | 0.329425i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.83057 | − | 16.0530i | 0.198667 | − | 1.12670i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.1884 | − | 19.4574i | 1.61955 | − | 1.35896i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.42575 | − | 1.15587i | 0.168601 | − | 0.0803386i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.1254 | + | 6.23312i | 1.18459 | + | 0.431154i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.49136 | + | 1.25140i | 0.102669 | + | 0.0861498i | 0.692677 | − | 0.721248i | \(-0.256431\pi\) |
−0.590008 | + | 0.807397i | \(0.700875\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.00102563 | + | 0.00199043i | −7.02747e−5 | + | 0.000136382i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.36338 | −0.297580 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.3363 | 1.51628 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.64502 | − | 2.55856i | −0.111160 | − | 0.172891i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.4957 | + | 10.4851i | 0.840551 | + | 0.705306i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.8671 | − | 9.77881i | −1.79915 | − | 0.654838i | −0.998443 | − | 0.0557835i | \(-0.982234\pi\) |
−0.800709 | − | 0.599054i | \(-0.795543\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.98992 | + | 10.7975i | 0.199328 | + | 0.719833i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.8265 | + | 12.4409i | −0.984068 | + | 0.825731i | −0.984698 | − | 0.174269i | \(-0.944244\pi\) |
0.000630367 | 1.00000i | \(0.499799\pi\) | ||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.27846 | + | 7.25052i | −0.0844832 | + | 0.479128i | 0.912984 | + | 0.407996i | \(0.133772\pi\) |
−0.997467 | + | 0.0711320i | \(0.977339\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.3850 | − | 5.19066i | 0.814875 | − | 0.341521i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.53698 | − | 14.7865i | 0.559276 | − | 0.968695i | −0.438281 | − | 0.898838i | \(-0.644412\pi\) |
0.997557 | − | 0.0698569i | \(-0.0222543\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.51186 | − | 14.7430i | −0.555253 | − | 0.961726i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.81705 | − | 16.8841i | −0.247944 | − | 1.09674i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.4262 | + | 7.43452i | −1.32126 | + | 0.480899i | −0.903862 | − | 0.427825i | \(-0.859280\pi\) |
−0.417398 | + | 0.908724i | \(0.637058\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.59919 | − | 9.06945i | −0.103013 | − | 0.584214i | −0.991995 | − | 0.126274i | \(-0.959698\pi\) |
0.888983 | − | 0.457941i | \(-0.151413\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.1453 | + | 3.69054i | −0.971571 | + | 0.236748i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.0657847 | + | 0.373084i | 0.00420283 | + | 0.0238354i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.9924 | + | 7.27664i | −1.27209 | + | 0.463002i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.652549 | + | 2.88644i | 0.0413536 | + | 0.182921i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.1762 | − | 17.6257i | −0.642315 | − | 1.11252i | −0.984915 | − | 0.173041i | \(-0.944641\pi\) |
0.342600 | − | 0.939482i | \(-0.388693\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.30051 | + | 2.25254i | −0.0817621 | + | 0.141616i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 22.7163 | − | 9.52058i | 1.42255 | − | 0.596202i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.478088 | + | 2.71137i | −0.0298223 | + | 0.169131i | −0.996081 | − | 0.0884415i | \(-0.971811\pi\) |
0.966259 | + | 0.257572i | \(0.0829225\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.2685 | + | 16.1682i | −1.19729 | + | 1.00464i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.88798 | − | 17.6519i | −0.302558 | − | 1.09263i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.03027 | − | 1.46690i | −0.248517 | − | 0.0904528i | 0.214758 | − | 0.976667i | \(-0.431104\pi\) |
−0.463275 | + | 0.886214i | \(0.653326\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.2180 | − | 8.57389i | −0.627685 | − | 0.526690i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.2200 | + | 19.0063i | 0.747855 | + | 1.16316i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.91806 | −0.299859 | −0.149930 | − | 0.988697i | \(-0.547905\pi\) | ||||
−0.149930 | + | 0.988697i | \(0.547905\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.18471 | 0.132712 | 0.0663558 | − | 0.997796i | \(-0.478863\pi\) | ||||
0.0663558 | + | 0.997796i | \(0.478863\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.18077 | + | 13.9357i | −0.434600 | + | 0.843427i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.30778 | − | 6.97105i | −0.500978 | − | 0.420370i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.57230 | + | 0.572270i | 0.0944703 | + | 0.0343844i | 0.388823 | − | 0.921313i | \(-0.372882\pi\) |
−0.294353 | + | 0.955697i | \(0.595104\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.6574 | − | 10.7963i | 1.35646 | − | 0.646357i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.411839 | − | 0.345574i | 0.0245683 | − | 0.0206152i | −0.630421 | − | 0.776254i | \(-0.717118\pi\) |
0.654989 | + | 0.755638i | \(0.272673\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.0692086 | − | 0.392502i | 0.00411403 | − | 0.0233318i | −0.982682 | − | 0.185302i | \(-0.940674\pi\) |
0.986796 | + | 0.161970i | \(0.0517848\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.06035 | + | 31.8679i | −0.240515 | + | 1.88769i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.6727 | − | 23.6818i | 0.807074 | − | 1.39789i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.07601 | − | 5.32780i | −0.180942 | − | 0.313400i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.05118 | − | 3.74343i | 0.237485 | − | 0.219443i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.0188 | − | 9.83404i | 1.57845 | − | 0.574511i | 0.603588 | − | 0.797297i | \(-0.293737\pi\) |
0.974867 | + | 0.222786i | \(0.0715151\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.95603 | + | 33.7783i | 0.346773 | + | 1.96665i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.0542 | − | 11.2516i | 0.583403 | − | 0.652886i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.527276 | − | 2.99033i | −0.0304932 | − | 0.172935i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.70405 | + | 1.34816i | −0.213498 | + | 0.0777068i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.1610 | + | 5.64298i | 1.04332 | + | 0.324181i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.05005 | − | 1.81874i | −0.0601256 | − | 0.104141i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.22386 | + | 9.04800i | −0.298142 | + | 0.516397i | −0.975711 | − | 0.219063i | \(-0.929700\pi\) |
0.677569 | + | 0.735459i | \(0.263033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.21522 | + | 4.72805i | 0.353571 | + | 0.268970i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.545372 | − | 3.09296i | 0.0309252 | − | 0.175386i | −0.965433 | − | 0.260651i | \(-0.916063\pi\) |
0.996358 | + | 0.0852656i | \(0.0271739\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.77097 | + | 4.00332i | −0.269671 | + | 0.226281i | −0.767588 | − | 0.640944i | \(-0.778543\pi\) |
0.497916 | + | 0.867225i | \(0.334099\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.7389 | + | 19.2769i | 0.774098 | + | 1.08613i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.2045 | − | 3.71413i | −0.573141 | − | 0.208606i | 0.0391571 | − | 0.999233i | \(-0.487533\pi\) |
−0.612299 | + | 0.790627i | \(0.709755\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.5817 | + | 11.3964i | 0.760430 | + | 0.638077i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.3491 | + | 0.495099i | −0.577629 | + | 0.0276338i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.1969 | 1.68020 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.6607 | 0.702288 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.57761 | − | 0.362513i | 0.419043 | − | 0.0200470i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.7808 | − | 9.88530i | −0.649499 | − | 0.544994i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.7943 | + | 8.29643i | 1.25289 | + | 0.456013i | 0.881376 | − | 0.472416i | \(-0.156618\pi\) |
0.371510 | + | 0.928429i | \(0.378840\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.7306 | + | 25.7141i | −0.642833 | + | 1.40913i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.15413 | − | 5.16393i | 0.336236 | − | 0.282135i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.27520 | + | 7.23200i | −0.0694644 | + | 0.393952i | 0.930175 | + | 0.367115i | \(0.119655\pi\) |
−0.999640 | + | 0.0268369i | \(0.991457\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.3466 | − | 14.7174i | −1.05076 | − | 0.799340i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.1472 | + | 21.0396i | −0.657809 | + | 1.13936i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.17341 | − | 15.8888i | −0.495318 | − | 0.857916i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.37849 | − | 1.36048i | −0.235730 | − | 0.0732460i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.4447 | − | 7.80524i | 1.15121 | − | 0.419007i | 0.305262 | − | 0.952268i | \(-0.401256\pi\) |
0.845951 | + | 0.533261i | \(0.179034\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.69320 | − | 9.60262i | −0.0906349 | − | 0.514016i | −0.995998 | − | 0.0893775i | \(-0.971512\pi\) |
0.905363 | − | 0.424639i | \(-0.139599\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.548146 | + | 17.6069i | −0.0292579 | + | 0.939788i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.81438 | + | 15.9611i | 0.149794 | + | 0.849526i | 0.963392 | + | 0.268098i | \(0.0863950\pi\) |
−0.813597 | + | 0.581429i | \(0.802494\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.00359027 | − | 0.00130675i | 0.000190552 | − | 6.93551e-5i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.3421 | − | 15.1007i | 0.864918 | − | 0.799212i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.06212 | − | 10.4999i | −0.319947 | − | 0.554164i | 0.660530 | − | 0.750800i | \(-0.270332\pi\) |
−0.980477 | + | 0.196636i | \(0.936998\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.1927 | + | 17.6542i | −0.536457 | + | 0.929170i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.561995 | − | 4.41084i | 0.0294971 | − | 0.231509i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.901272 | + | 5.11137i | −0.0471748 | + | 0.267541i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.30095 | − | 1.93072i | 0.120109 | − | 0.100783i | −0.580755 | − | 0.814078i | \(-0.697243\pi\) |
0.700864 | + | 0.713295i | \(0.252798\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.42262 | − | 30.6311i | 0.126116 | − | 1.59459i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.3231 | − | 4.12126i | −0.587864 | − | 0.213965i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.6639 | − | 14.8217i | −0.914601 | − | 0.767441i | 0.0583881 | − | 0.998294i | \(-0.481404\pi\) |
−0.972989 | + | 0.230853i | \(0.925848\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.96700 | + | 5.75805i | −0.153215 | + | 0.297344i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.6979 | −1.06600 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.61297 | −0.493785 | −0.246893 | − | 0.969043i | \(-0.579410\pi\) | ||||
−0.246893 | + | 0.969043i | \(0.579410\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.95074 | − | 12.3661i | −0.407329 | − | 0.633532i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.551178 | + | 0.462493i | 0.0281639 | + | 0.0236323i | 0.656761 | − | 0.754099i | \(-0.271926\pi\) |
−0.628597 | + | 0.777731i | \(0.716371\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.5319 | − | 7.83699i | −1.09737 | − | 0.399410i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.10567 | + | 3.15791i | −0.157870 | + | 0.160526i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.1482 | − | 20.2627i | 1.22436 | − | 1.02736i | 0.225775 | − | 0.974179i | \(-0.427509\pi\) |
0.998585 | − | 0.0531804i | \(-0.0169358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.748377 | + | 4.24426i | −0.0378471 | + | 0.214641i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.8866 | − | 8.75376i | 1.05359 | − | 0.441569i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.7684 | + | 25.5796i | −0.743077 | + | 1.28705i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.11075 | + | 1.92388i | 0.0557472 | + | 0.0965569i | 0.892552 | − | 0.450944i | \(-0.148913\pi\) |
−0.836805 | + | 0.547501i | \(0.815579\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.39947 | + | 28.3070i | 0.320374 | + | 1.41712i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.3280 | + | 5.57893i | −0.765443 | + | 0.278598i | −0.695089 | − | 0.718924i | \(-0.744635\pi\) |
−0.0703539 | + | 0.997522i | \(0.522413\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.92496 | − | 27.9309i | −0.245330 | − | 1.39134i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 23.2540 | + | 12.9134i | 1.15550 | + | 0.641671i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.75073 | − | 26.9427i | −0.235485 | − | 1.33550i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.3919 | − | 12.8816i | 1.75002 | − | 0.636954i | 0.750307 | − | 0.661089i | \(-0.229906\pi\) |
0.999709 | + | 0.0241357i | \(0.00768337\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.06574 | − | 31.2541i | −0.348527 | − | 1.54165i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.4926 | + | 26.8340i | 0.762341 | + | 1.32041i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.52474 | − | 4.37299i | 0.123935 | − | 0.214661i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.4781 | + | 11.0972i | −1.29664 | + | 0.543431i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.41940 | + | 19.3924i | −0.167048 | + | 0.947379i | 0.779879 | + | 0.625931i | \(0.215281\pi\) |
−0.946927 | + | 0.321448i | \(0.895830\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.06082 | + | 4.24653i | −0.246649 | + | 0.206963i | −0.757728 | − | 0.652571i | \(-0.773691\pi\) |
0.511079 | + | 0.859534i | \(0.329246\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.7283 | − | 4.33313i | −0.813359 | − | 0.210684i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.8859 | − | 6.14598i | −0.819088 | − | 0.298124i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.45332 | − | 1.21948i | −0.0703310 | − | 0.0590147i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.22158 | − | 14.3426i | −0.445222 | − | 0.692469i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6625 | −0.561765 | −0.280882 | − | 0.959742i | \(-0.590627\pi\) | ||||
−0.280882 | + | 0.959742i | \(0.590627\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.1187 | −1.59158 | −0.795791 | − | 0.605571i | \(-0.792945\pi\) | ||||
−0.795791 | + | 0.605571i | \(0.792945\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.3155 | + | 27.7820i | −0.686374 | + | 1.33205i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.30603 | − | 3.61319i | −0.205985 | − | 0.172842i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.7149 | + | 6.81168i | 0.893215 | + | 0.325104i | 0.747531 | − | 0.664227i | \(-0.231239\pi\) |
0.145684 | + | 0.989331i | \(0.453462\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.316835 | + | 0.217935i | 0.0150874 | + | 0.0103778i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.6039 | + | 10.5759i | −0.598830 | + | 0.502478i | −0.891069 | − | 0.453867i | \(-0.850044\pi\) |
0.292240 | + | 0.956345i | \(0.405600\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.69511 | − | 37.9699i | 0.317379 | − | 1.79994i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.01938 | − | 23.6977i | 0.142812 | − | 1.12086i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.40137 | − | 2.42724i | 0.0661347 | − | 0.114549i | −0.831062 | − | 0.556180i | \(-0.812267\pi\) |
0.897197 | + | 0.441631i | \(0.145600\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.8714 | + | 25.7580i | 0.700266 | + | 1.21290i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.518667 | − | 0.479265i | 0.0243691 | − | 0.0225178i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.1367 | − | 9.14902i | 1.17843 | − | 0.428913i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.54631 | + | 31.4547i | 0.259445 | + | 1.47139i | 0.784399 | + | 0.620256i | \(0.212971\pi\) |
−0.524954 | + | 0.851131i | \(0.675917\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.27816 | − | 23.2168i | 0.433067 | − | 1.08367i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.08832 | + | 11.8434i | 0.0972627 | + | 0.551604i | 0.994030 | + | 0.109103i | \(0.0347977\pi\) |
−0.896768 | + | 0.442501i | \(0.854091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6165 | − | 3.86410i | 0.493392 | − | 0.179580i | −0.0833274 | − | 0.996522i | \(-0.526555\pi\) |
0.576720 | + | 0.816942i | \(0.304333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −40.8968 | − | 12.7075i | −1.89654 | − | 0.589294i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.1810 | + | 22.8301i | 0.609942 | + | 1.05645i | 0.991249 | + | 0.132002i | \(0.0421405\pi\) |
−0.381308 | + | 0.924448i | \(0.624526\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.62869 | − | 6.28508i | 0.167558 | − | 0.290218i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.7845 | − | 8.96476i | −0.543002 | − | 0.413074i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.744488 | − | 4.22220i | 0.0342316 | − | 0.194137i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.9542 | − | 15.0654i | 0.823795 | − | 0.691246i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.4779 | + | 1.29252i | −0.617111 | + | 0.0591805i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.4224 | + | 5.61331i | 0.704669 | + | 0.256479i | 0.669403 | − | 0.742899i | \(-0.266550\pi\) |
0.0352661 | + | 0.999378i | \(0.488772\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.4664 | + | 20.5297i | 1.11557 | + | 0.936076i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.13723 | + | 0.197925i | −0.188250 | + | 0.00900589i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.41193 | −0.427374 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.5466 | −0.613853 | −0.306926 | − | 0.951733i | \(-0.599301\pi\) | ||||
−0.306926 | + | 0.951733i | \(0.599301\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.6925 | + | 0.702890i | −0.664419 | + | 0.0317858i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.54691 | + | 6.33261i | 0.340587 | + | 0.285787i | 0.796997 | − | 0.603983i | \(-0.206421\pi\) |
−0.456410 | + | 0.889770i | \(0.650865\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.6054 | + | 10.0476i | 1.24329 | + | 0.452519i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −25.6296 | + | 2.45786i | −1.15196 | + | 0.110473i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.00264401 | − | 0.00221859i | 0.000118600 | − | 9.95172e-5i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.09489 | − | 34.5659i | 0.272845 | − | 1.54738i | −0.472880 | − | 0.881127i | \(-0.656786\pi\) |
0.745725 | − | 0.666254i | \(-0.232103\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.5633 | + | 8.79646i | 0.516610 | + | 0.392997i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.77729 | + | 11.7386i | −0.302185 | + | 0.523399i | −0.976631 | − | 0.214925i | \(-0.931049\pi\) |
0.674446 | + | 0.738324i | \(0.264383\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.2250 | − | 28.1025i | −0.722002 | − | 1.25054i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.49305 | − | 0.774641i | −0.110720 | − | 0.0344030i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.5176 | − | 13.6553i | 1.66294 | − | 0.605260i | 0.672117 | − | 0.740445i | \(-0.265385\pi\) |
0.990820 | + | 0.135185i | \(0.0431629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.814186 | + | 4.61748i | 0.0360175 | + | 0.204265i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.1737 | + | 25.6208i | 0.890693 | + | 1.13119i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.31386 | − | 13.1226i | −0.101961 | − | 0.578249i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.7183 | − | 5.72099i | 0.691289 | − | 0.251609i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.1743 | + | 16.7936i | −0.797761 | + | 0.737158i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.26497 | + | 16.0474i | 0.405906 | + | 0.703049i | 0.994426 | − | 0.105433i | \(-0.0336228\pi\) |
−0.588521 | + | 0.808482i | \(0.700289\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.47946 | − | 16.4189i | 0.414508 | − | 0.717948i | −0.580869 | − | 0.813997i | \(-0.697287\pi\) |
0.995377 | + | 0.0960487i | \(0.0306205\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.18278 | − | 17.1316i | 0.0952641 | − | 0.747684i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.99013 | + | 39.6430i | −0.304495 | + | 1.72688i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.0045 | + | 14.2684i | −0.739324 | + | 0.620367i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.6856 | + | 19.7314i | 1.24485 | + | 0.856270i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.6282 | − | 11.8757i | −1.41328 | − | 0.514393i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.5429 | + | 11.3639i | 0.585512 | + | 0.491303i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.35028 | − | 2.62048i | 0.0582687 | − | 0.113082i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.372237 | −0.0160334 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.63965 | 0.328454 | 0.164227 | − | 0.986423i | \(-0.447487\pi\) | ||||
0.164227 | + | 0.986423i | \(0.447487\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.4645 | − | 28.7184i | −0.792386 | − | 1.23242i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.91617 | − | 8.32065i | −0.424762 | − | 0.356418i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.67732 | + | 2.79431i | 0.328258 | + | 0.119476i | 0.500892 | − | 0.865510i | \(-0.333005\pi\) |
−0.172634 | + | 0.984986i | \(0.555228\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.06365 | − | 0.534547i | −0.0880746 | − | 0.0228139i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.3519 | + | 24.6291i | −1.25043 | + | 1.04924i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.63341 | + | 26.2774i | −0.197033 | + | 1.11743i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 44.4782 | − | 18.6412i | 1.88799 | − | 0.791273i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.87975 | + | 10.1840i | −0.249133 | + | 0.431511i | −0.963286 | − | 0.268479i | \(-0.913479\pi\) |
0.714152 | + | 0.699990i | \(0.246812\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.50255 | + | 4.33455i | 0.105847 | + | 0.183332i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.33664 | + | 23.6057i | 0.225313 | + | 0.996635i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.6341 | − | 15.1536i | 1.75467 | − | 0.638647i | 0.754818 | − | 0.655935i | \(-0.227725\pi\) |
0.999851 | + | 0.0172875i | \(0.00550305\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.20255 | + | 40.8477i | 0.303013 | + | 1.71847i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.7300 | + | 3.77726i | 0.996568 | + | 0.158630i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.86387 | + | 10.5705i | 0.0781374 | + | 0.443139i | 0.998628 | + | 0.0523735i | \(0.0166786\pi\) |
−0.920490 | + | 0.390766i | \(0.872210\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.0041 | + | 10.5566i | −1.21378 | + | 0.441781i | −0.868014 | − | 0.496539i | \(-0.834604\pi\) |
−0.345769 | + | 0.938320i | \(0.612382\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.48685 | + | 6.57683i | 0.0621141 | + | 0.274751i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.67252 | + | 2.89688i | 0.0697488 | + | 0.120808i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.6690 | − | 30.6037i | 0.735572 | − | 1.27405i | −0.218900 | − | 0.975747i | \(-0.570247\pi\) |
0.954472 | − | 0.298301i | \(-0.0964198\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.2210 | − | 7.63657i | 0.757240 | − | 0.317365i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.792110 | − | 4.49228i | 0.0328623 | − | 0.186371i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0399 | − | 8.42447i | 0.415810 | − | 0.348906i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 21.0760 | − | 21.4305i | 0.871384 | − | 0.886042i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.9028 | + | 7.24403i | 0.821477 | + | 0.298993i | 0.718356 | − | 0.695676i | \(-0.244895\pi\) |
0.103121 | + | 0.994669i | \(0.467117\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.2200 | − | 33.7486i | −1.65724 | − | 1.39059i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.00934 | + | 1.56985i | 0.0415185 | + | 0.0645752i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.4642 | 1.62060 | 0.810299 | − | 0.586016i | \(-0.199305\pi\) | ||||
0.810299 | + | 0.586016i | \(0.199305\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −37.9669 | −1.55649 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.97119 | − | 13.5290i | 0.285312 | − | 0.553704i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.7478 | − | 10.6967i | −0.520862 | − | 0.437055i | 0.344070 | − | 0.938944i | \(-0.388194\pi\) |
−0.864932 | + | 0.501889i | \(0.832639\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.95551 | − | 1.80366i | −0.202140 | − | 0.0735728i | 0.238966 | − | 0.971028i | \(-0.423191\pi\) |
−0.441106 | + | 0.897455i | \(0.645414\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.642955 | − | 8.12939i | 0.0261832 | − | 0.331054i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.81210 | + | 4.87693i | −0.236295 | + | 0.198275i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.07754 | − | 34.4675i | 0.246680 | − | 1.39899i | −0.569879 | − | 0.821729i | \(-0.693010\pi\) |
0.816559 | − | 0.577263i | \(-0.195879\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.56844 | + | 28.0071i | −0.144601 | + | 1.13490i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.76371 | + | 16.9112i | −0.394998 | + | 0.684156i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.4980 | + | 23.3791i | 0.545177 | + | 0.944275i | 0.998596 | + | 0.0529768i | \(0.0168709\pi\) |
−0.453419 | + | 0.891298i | \(0.649796\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −38.5072 | + | 35.5819i | −1.55276 | + | 1.43480i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.8274 | − | 6.12466i | 0.677444 | − | 0.246569i | 0.0196943 | − | 0.999806i | \(-0.493731\pi\) |
0.657750 | + | 0.753237i | \(0.271508\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.11001 | + | 28.9803i | 0.205388 | + | 1.16482i | 0.896827 | + | 0.442381i | \(0.145866\pi\) |
−0.691439 | + | 0.722435i | \(0.743023\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.10105 | + | 2.20051i | −0.164569 | + | 0.0883035i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.04819 | − | 34.3010i | −0.242316 | − | 1.37424i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 27.9331 | − | 10.1668i | 1.11732 | − | 0.406672i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −30.1440 | − | 9.36634i | −1.20383 | − | 0.374055i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.6657 | − | 39.2581i | −0.903739 | − | 1.56532i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.524861 | + | 0.909086i | −0.0208944 | + | 0.0361902i | −0.876284 | − | 0.481796i | \(-0.839985\pi\) |
0.855389 | + | 0.517986i | \(0.173318\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.68373 | − | 2.04157i | −0.106669 | − | 0.0811453i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.35605 | + | 24.7044i | −0.172864 | + | 0.980363i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.332889 | − | 0.279327i | 0.0131895 | − | 0.0110673i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.00160966 | − | 0.00352848i | 6.36774e−5 | − | 0.000139584i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.4725 | − | 11.4550i | −1.24309 | − | 0.452447i | −0.365028 | − | 0.930997i | \(-0.618940\pi\) |
−0.878061 | + | 0.478550i | \(0.841163\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.0926 | − | 15.1815i | −0.713504 | − | 0.598701i | 0.212076 | − | 0.977253i | \(-0.431978\pi\) |
−0.925580 | + | 0.378552i | \(0.876422\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.54896 | − | 0.361142i | 0.297240 | − | 0.0142200i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.5704 | −1.71293 | −0.856465 | − | 0.516205i | \(-0.827344\pi\) | ||||
−0.856465 | + | 0.516205i | \(0.827344\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.7016 | −1.32290 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38.6433 | + | 1.84870i | −1.51455 | + | 0.0724561i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.8475 | − | 13.2976i | −0.620160 | − | 0.520376i | 0.277694 | − | 0.960670i | \(-0.410430\pi\) |
−0.897854 | + | 0.440294i | \(0.854874\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.3124 | − | 13.2166i | −1.41884 | − | 0.516416i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.05777 | + | 4.29033i | 0.119295 | + | 0.167382i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.4931 | − | 9.64387i | 0.447708 | − | 0.375672i | −0.390876 | − | 0.920443i | \(-0.627828\pi\) |
0.838585 | + | 0.544771i | \(0.183384\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.43517 | + | 42.1670i | −0.289195 | + | 1.64010i | 0.400710 | + | 0.916205i | \(0.368763\pi\) |
−0.689905 | + | 0.723900i | \(0.742348\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.4863 | − | 17.1058i | −0.873294 | − | 0.664335i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.7599 | − | 42.8854i | 0.960147 | − | 1.66302i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.73426 | − | 4.73588i | −0.105871 | − | 0.183374i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 47.2913 | + | 14.6944i | 1.82839 | + | 0.568117i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.93905 | − | 0.705758i | 0.0748563 | − | 0.0272455i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.50198 | − | 36.8746i | −0.250633 | − | 1.42141i | −0.807039 | − | 0.590499i | \(-0.798931\pi\) |
0.556406 | − | 0.830911i | \(-0.312180\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.06645 | − | 18.4330i | −0.233498 | − | 0.709486i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.63351 | − | 26.2780i | −0.178080 | − | 1.00994i | −0.934528 | − | 0.355890i | \(-0.884178\pi\) |
0.756448 | − | 0.654054i | \(-0.226933\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.98973 | + | 2.90802i | −0.306618 | + | 0.111600i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.6212 | − | 22.7508i | 0.943486 | − | 0.871812i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.7673 | − | 22.1136i | −0.488526 | − | 0.846152i | 0.511387 | − | 0.859351i | \(-0.329132\pi\) |
−0.999913 | + | 0.0131986i | \(0.995799\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.3377 | + | 47.3503i | −1.04452 | + | 1.80916i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.61173 | − | 12.6497i | 0.0614914 | − | 0.482618i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.65688 | + | 15.0679i | −0.101219 | + | 0.574041i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.52481 | + | 5.47497i | −0.248215 | + | 0.208278i | −0.758403 | − | 0.651785i | \(-0.774020\pi\) |
0.510188 | + | 0.860063i | \(0.329576\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −20.9974 | + | 10.0053i | −0.797625 | + | 0.380069i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 46.0334 | + | 16.7548i | 1.74615 | + | 0.635545i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.7523 | + | 31.6779i | 1.42997 | + | 1.19989i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.5458 | + | 26.2883i | −0.512348 | + | 0.994314i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.06432 | 0.304585 | 0.152293 | − | 0.988335i | \(-0.451334\pi\) | ||||
0.152293 | + | 0.988335i | \(0.451334\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 59.1251 | 2.22994 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.9464 | + | 24.8019i | 0.600575 | + | 0.934094i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.4562 | − | 18.8430i | −0.844551 | − | 0.708663i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5612 | + | 4.93586i | 0.509300 | + | 0.185370i | 0.583872 | − | 0.811846i | \(-0.301537\pi\) |
−0.0745721 | + | 0.997216i | \(0.523759\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00121 | + | 28.8948i | 0.300069 | + | 1.08364i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.74025 | − | 4.81664i | 0.214974 | − | 0.180385i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.05231 | + | 28.6531i | −0.188946 | + | 1.07156i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 34.7234 | − | 14.5529i | 1.29677 | − | 0.543487i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.04046 | − | 8.73033i | 0.187977 | − | 0.325586i | −0.756598 | − | 0.653880i | \(-0.773140\pi\) |
0.944576 | + | 0.328293i | \(0.106473\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.01873 | − | 10.4247i | −0.224149 | − | 0.388238i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.51736 | + | 15.5584i | 0.130812 | + | 0.578625i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.4262 | − | 7.79849i | 0.795749 | − | 0.289629i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.33623 | − | 47.2771i | −0.309174 | − | 1.75341i | −0.603178 | − | 0.797607i | \(-0.706099\pi\) |
0.294004 | − | 0.955804i | \(-0.405012\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.8970 | − | 7.63843i | 0.959148 | − | 0.282905i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.23358 | − | 6.99596i | −0.0456255 | − | 0.258755i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.3735 | + | 15.7867i | −1.60204 | + | 0.583094i | −0.979843 | − | 0.199768i | \(-0.935981\pi\) |
−0.622195 | + | 0.782862i | \(0.713759\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.144691 | − | 0.640017i | −0.00533701 | − | 0.0236074i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.94682 | + | 6.83609i | 0.145383 | + | 0.251811i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.41647 | + | 9.38160i | −0.199248 | + | 0.345108i | −0.948285 | − | 0.317421i | \(-0.897183\pi\) |
0.749037 | + | 0.662528i | \(0.230517\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 33.9861 | − | 14.2438i | 1.24851 | − | 0.523260i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.12864 | − | 6.40081i | 0.0414056 | − | 0.234823i | −0.957081 | − | 0.289821i | \(-0.906404\pi\) |
0.998486 | + | 0.0549982i | \(0.0175153\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31.2261 | + | 26.2018i | −1.14404 | + | 0.959961i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.36786 | − | 4.93974i | −0.0500473 | − | 0.180736i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.0076 | + | 5.46234i | 0.548367 | + | 0.199589i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.9250 | − | 13.3627i | −0.581112 | − | 0.487610i | 0.304200 | − | 0.952608i | \(-0.401611\pi\) |
−0.885312 | + | 0.464998i | \(0.846055\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.0643 | + | 29.6514i | 0.694744 | + | 1.08056i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.20499 | −0.0438543 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.9259 | −0.978639 | −0.489319 | − | 0.872105i | \(-0.662755\pi\) | ||||
−0.489319 | + | 0.872105i | \(0.662755\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.06353 | − | 4.00470i | 0.0749015 | − | 0.145361i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.4256 | − | 27.2083i | −1.17543 | − | 0.986302i | −0.999998 | − | 0.00180962i | \(-0.999424\pi\) |
−0.175430 | − | 0.984492i | \(-0.556132\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.9886 | − | 3.99953i | −0.397815 | − | 0.144793i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −38.5128 | + | 18.3514i | −1.39243 | + | 0.663497i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30.1391 | − | 25.2897i | 1.08826 | − | 0.913159i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.53460 | − | 25.7170i | 0.163522 | − | 0.927378i | −0.787054 | − | 0.616885i | \(-0.788394\pi\) |
0.950575 | − | 0.310494i | \(-0.100494\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.602715 | − | 4.73043i | 0.0217063 | − | 0.170362i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.7533 | + | 42.8740i | −0.890316 | + | 1.54207i | −0.0508186 | + | 0.998708i | \(0.516183\pi\) |
−0.839497 | + | 0.543364i | \(0.817150\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.6220 | + | 27.0580i | 0.561157 | + | 0.971953i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 31.9977 | − | 29.5669i | 1.14791 | − | 1.06071i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −60.4016 | + | 21.9844i | −2.16411 | + | 0.787672i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.000651892 | 0.00369707i | 2.33265e−5 | 0.000132291i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.91755 | + | 30.1346i | 0.354424 | + | 1.07692i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.38726 | + | 24.8814i | 0.156588 | + | 0.888054i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.9602 | − | 5.44506i | 0.533272 | − | 0.194095i | −0.0613265 | − | 0.998118i | \(-0.519533\pi\) |
0.594599 | + | 0.804022i | \(0.297311\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.09407 | + | 2.20427i | 0.252555 | + | 0.0784740i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.7350 | + | 32.4500i | 0.666140 | + | 1.15379i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.20448 | + | 2.08622i | −0.0427723 | + | 0.0740839i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.3875 | + | 13.9877i | 0.652136 | + | 0.496094i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.69068 | − | 15.2596i | 0.0953089 | − | 0.540524i | −0.899343 | − | 0.437243i | \(-0.855955\pi\) |
0.994652 | − | 0.103281i | \(-0.0329339\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.2315 | − | 17.8154i | 0.751118 | − | 0.630263i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.7146 | − | 31.8708i | −0.802583 | − | 1.12610i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.79222 | − | 1.74422i | −0.169114 | − | 0.0615523i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.41403 | + | 4.54291i | 0.190820 | + | 0.160117i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.50860 | − | 0.407051i | 0.299517 | − | 0.0143289i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.9909 | 1.30053 | 0.650265 | − | 0.759708i | \(-0.274658\pi\) | ||||
0.650265 | + | 0.759708i | \(0.274658\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.5190 | 1.80908 | 0.904539 | − | 0.426391i | \(-0.140215\pi\) | ||||
0.904539 | + | 0.426391i | \(0.140215\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.77970 | + | 0.180821i | −0.132560 | + | 0.00634167i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.2268 | + | 16.1332i | 0.673487 | + | 0.565123i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.70672 | + | 3.16899i | 0.304610 | + | 0.110869i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.2698 | − | 24.7041i | 0.393800 | − | 0.863231i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.5504 | + | 12.2092i | −0.507813 | + | 0.426105i | −0.860359 | − | 0.509689i | \(-0.829760\pi\) |
0.352546 | + | 0.935794i | \(0.385316\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.85066 | + | 21.8382i | −0.134226 | + | 0.761231i | 0.841170 | + | 0.540770i | \(0.181867\pi\) |
−0.975396 | + | 0.220461i | \(0.929244\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.9500 | + | 11.3728i | 0.520493 | + | 0.395951i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.3971 | − | 33.5968i | 0.674505 | − | 1.16828i | −0.302109 | − | 0.953273i | \(-0.597691\pi\) |
0.976613 | − | 0.215003i | \(-0.0689761\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.4452 | − | 49.2685i | −0.987942 | − | 1.71117i | −0.628054 | − | 0.778170i | \(-0.716148\pi\) |
−0.359888 | − | 0.932996i | \(-0.617185\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.76756 | − | 0.859934i | −0.0960054 | − | 0.0298308i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.579580 | + | 0.210950i | −0.0200812 | + | 0.00730898i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.30490 | − | 24.4143i | −0.148977 | − | 0.844891i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −38.3054 | + | 20.5536i | −1.32403 | + | 0.710438i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.73704 | + | 55.2215i | 0.336160 | + | 1.90646i | 0.415469 | + | 0.909607i | \(0.363617\pi\) |
−0.0793095 | + | 0.996850i | \(0.525272\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.77685 | + | 2.83054i | −0.268167 | + | 0.0976049i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.683910 | + | 0.631955i | −0.0235551 | + | 0.0217657i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.22729 | + | 3.85778i | 0.0766210 | + | 0.132711i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.42702 | + | 5.93577i | −0.117754 | + | 0.203956i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.0872499 | + | 0.684785i | −0.00299441 | + | 0.0235017i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.46531 | + | 8.31020i | −0.0502303 | + | 0.284870i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.1372 | − | 15.2189i | 0.621006 | − | 0.521086i | −0.277114 | − | 0.960837i | \(-0.589378\pi\) |
0.898119 | + | 0.439751i | \(0.144933\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.38711 | − | 55.4697i | 0.150036 | − | 1.89703i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.2321 | − | 4.81609i | −0.452000 | − | 0.164514i | 0.105981 | − | 0.994368i | \(-0.466202\pi\) |
−0.557981 | + | 0.829854i | \(0.688424\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.5014 | + | 25.5937i | 1.04069 | + | 0.873245i | 0.992084 | − | 0.125573i | \(-0.0400769\pi\) |
0.0486084 | + | 0.998818i | \(0.484521\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.6947 | + | 42.1029i | −0.739354 | + | 1.43486i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.52665 | 0.222170 | 0.111085 | − | 0.993811i | \(-0.464567\pi\) | ||||
0.111085 | + | 0.993811i | \(0.464567\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 42.2234 | 1.43564 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.76268 | + | 8.96289i | 0.195711 | + | 0.304396i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.2321 | − | 18.6550i | −0.754173 | − | 0.632827i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.65942 | − | 3.15177i | −0.293413 | − | 0.106794i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.69901 | + | 6.81170i | −0.226727 | + | 0.230541i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.64876 | − | 6.41807i | 0.258575 | − | 0.216970i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.03569 | + | 5.87369i | −0.0349728 | + | 0.198340i | −0.997288 | − | 0.0735953i | \(-0.976553\pi\) |
0.962315 | + | 0.271936i | \(0.0876638\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −45.9305 | + | 19.2498i | −1.54920 | + | 0.649281i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.6866 | − | 30.6340i | 0.595876 | − | 1.03209i | −0.397547 | − | 0.917582i | \(-0.630138\pi\) |
0.993423 | − | 0.114505i | \(-0.0365283\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.3274 | + | 21.3517i | 0.414851 | + | 0.718542i | 0.995413 | − | 0.0956737i | \(-0.0305005\pi\) |
−0.580562 | + | 0.814216i | \(0.697167\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.1001 | − | 57.9459i | −0.440354 | − | 1.94783i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.9576 | − | 8.35590i | 0.770842 | − | 0.280564i | 0.0734936 | − | 0.997296i | \(-0.476585\pi\) |
0.697349 | + | 0.716732i | \(0.254363\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.93514 | + | 22.3173i | 0.131980 | + | 0.748498i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.4632 | + | 20.2983i | −0.551538 | + | 0.680019i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.27727 | + | 35.6001i | 0.210061 | + | 1.19131i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.72673 | + | 1.72039i | −0.157997 | + | 0.0575062i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.15973 | + | 5.12985i | 0.0387221 | + | 0.171281i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.5391 | − | 44.2350i | −0.851776 | − | 1.47532i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.8581 | − | 18.8068i | 0.361735 | − | 0.626544i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.29669 | − | 2.63899i | 0.209541 | − | 0.0878201i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.1163 | + | 57.3724i | −0.336277 | + | 1.90712i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.7668 | + | 19.9427i | −0.789165 | + | 0.662188i | −0.945539 | − | 0.325510i | \(-0.894464\pi\) |
0.156374 | + | 0.987698i | \(0.450020\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31.8869 | − | 8.25964i | −1.05762 | − | 0.273955i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.6832 | + | 9.34792i | 0.850922 | + | 0.309710i | 0.730416 | − | 0.683002i | \(-0.239326\pi\) |
0.120506 | + | 0.992713i | \(0.461548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.80072 | + | 3.18918i | 0.125786 | + | 0.105547i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.96719 | + | 3.05964i | 0.0650333 | + | 0.101148i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −34.9090 | −1.15280 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.7346 | 0.453064 | 0.226532 | − | 0.974004i | \(-0.427261\pi\) | ||||
0.226532 | + | 0.974004i | \(0.427261\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.28879 | − | 16.0861i | 0.273125 | − | 0.530053i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.00335726 | − | 0.00281708i | −0.000110506 | − | 9.27253e-5i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −33.0624 | − | 12.0337i | −1.08709 | − | 0.395667i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.1441 | − | 7.66546i | −0.366020 | − | 0.251767i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.68827 | − | 2.25572i | 0.0881992 | − | 0.0740079i | −0.597622 | − | 0.801778i | \(-0.703888\pi\) |
0.685821 | + | 0.727770i | \(0.259443\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.139692 | − | 0.792231i | 0.00457821 | − | 0.0259643i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.687539 | + | 5.39618i | −0.0225090 | + | 0.176663i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.6477 | − | 35.7629i | 0.675253 | − | 1.16957i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.63152 | − | 2.82588i | −0.0532996 | − | 0.0923176i | 0.838145 | − | 0.545448i | \(-0.183640\pi\) |
−0.891444 | + | 0.453131i | \(0.850307\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.92279 | − | 7.32091i | 0.258550 | − | 0.238909i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.94129 | + | 0.706570i | −0.0632841 | + | 0.0230335i | −0.373468 | − | 0.927643i | \(-0.621832\pi\) |
0.310184 | + | 0.950677i | \(0.399609\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.59302 | − | 9.03446i | −0.0518759 | − | 0.294203i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −25.3647 | − | 32.2134i | −0.825115 | − | 1.04790i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.42672 | + | 8.09132i | 0.0463621 | + | 0.262933i | 0.999174 | − | 0.0406276i | \(-0.0129357\pi\) |
−0.952812 | + | 0.303560i | \(0.901825\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.59451 | − | 2.03624i | 0.181605 | − | 0.0660990i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.9619 | + | 5.58113i | 0.582455 | + | 0.180980i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.6318 | − | 21.8790i | −0.409185 | − | 0.708729i | 0.585614 | − | 0.810590i | \(-0.300854\pi\) |
−0.994799 | + | 0.101861i | \(0.967520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.75270 | − | 9.96397i | 0.186153 | − | 0.322426i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −24.4406 | − | 18.5925i | −0.790052 | − | 0.601010i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.57689 | + | 48.6420i | −0.276962 | + | 1.57073i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.8688 | − | 25.0629i | 0.963509 | − | 0.808480i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.8637 | − | 1.71312i | 0.575649 | − | 0.0552044i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −31.6781 | − | 11.5299i | −1.01975 | − | 0.371160i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.2579 | − | 33.7804i | −1.29461 | − | 1.08630i | −0.991050 | − | 0.133492i | \(-0.957381\pi\) |
−0.303558 | − | 0.952813i | \(-0.598174\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −52.2428 | + | 2.49929i | −1.67828 | + | 0.0802888i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.8321 | −0.668535 | −0.334267 | − | 0.942478i | \(-0.608489\pi\) | ||||
−0.334267 | + | 0.942478i | \(0.608489\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 44.2542 | 1.41873 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −21.9039 | + | 1.04788i | −0.701485 | + | 0.0335590i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.37625 | − | 1.15481i | −0.0440301 | − | 0.0369457i | 0.620507 | − | 0.784201i | \(-0.286927\pi\) |
−0.664537 | + | 0.747255i | \(0.731371\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.5990 | + | 12.9570i | 1.13775 | + | 0.414107i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.0798 | + | 1.25435i | −0.417606 | + | 0.0400482i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.0605 | + | 31.0974i | −1.18205 | + | 0.991854i | −0.182083 | + | 0.983283i | \(0.558284\pi\) |
−0.999963 | + | 0.00857126i | \(0.997272\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.552994 | − | 3.13619i | 0.0176199 | − | 0.0999272i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.1999 | + | 16.1272i | 0.674800 | + | 0.513335i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.661191 | + | 1.14522i | −0.0210247 | + | 0.0364158i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.8440 | − | 37.8349i | −0.693898 | − | 1.20187i | −0.970551 | − | 0.240897i | \(-0.922559\pi\) |
0.276653 | − | 0.960970i | \(-0.410775\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −40.1224 | − | 12.4668i | −1.27325 | − | 0.395623i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.4031 | + | 8.88200i | −0.773630 | + | 0.281578i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.22483 | − | 23.9602i | −0.133802 | − | 0.758828i | −0.975687 | − | 0.219170i | \(-0.929665\pi\) |
0.841885 | − | 0.539657i | \(-0.181446\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.1665 | − | 45.4582i | 0.574763 | − | 1.43823i |
(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 | 108.2.i.a.13.1 | ✓ | 18 | |
3.2 | odd | 2 | 324.2.i.a.253.1 | 18 | |||
4.3 | odd | 2 | 432.2.u.d.337.3 | 18 | |||
9.2 | odd | 6 | 972.2.i.d.109.3 | 18 | |||
9.4 | even | 3 | 972.2.i.c.433.3 | 18 | |||
9.5 | odd | 6 | 972.2.i.b.433.1 | 18 | |||
9.7 | even | 3 | 972.2.i.a.109.1 | 18 | |||
27.2 | odd | 18 | 324.2.i.a.73.1 | 18 | |||
27.4 | even | 9 | 2916.2.e.c.1945.3 | 18 | |||
27.5 | odd | 18 | 2916.2.a.c.1.3 | 9 | |||
27.7 | even | 9 | 972.2.i.a.865.1 | 18 | |||
27.11 | odd | 18 | 972.2.i.b.541.1 | 18 | |||
27.13 | even | 9 | 2916.2.e.c.973.3 | 18 | |||
27.14 | odd | 18 | 2916.2.e.d.973.7 | 18 | |||
27.16 | even | 9 | 972.2.i.c.541.3 | 18 | |||
27.20 | odd | 18 | 972.2.i.d.865.3 | 18 | |||
27.22 | even | 9 | 2916.2.a.d.1.7 | 9 | |||
27.23 | odd | 18 | 2916.2.e.d.1945.7 | 18 | |||
27.25 | even | 9 | inner | 108.2.i.a.25.1 | yes | 18 | |
108.79 | odd | 18 | 432.2.u.d.241.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.i.a.13.1 | ✓ | 18 | 1.1 | even | 1 | trivial | |
108.2.i.a.25.1 | yes | 18 | 27.25 | even | 9 | inner | |
324.2.i.a.73.1 | 18 | 27.2 | odd | 18 | |||
324.2.i.a.253.1 | 18 | 3.2 | odd | 2 | |||
432.2.u.d.241.3 | 18 | 108.79 | odd | 18 | |||
432.2.u.d.337.3 | 18 | 4.3 | odd | 2 | |||
972.2.i.a.109.1 | 18 | 9.7 | even | 3 | |||
972.2.i.a.865.1 | 18 | 27.7 | even | 9 | |||
972.2.i.b.433.1 | 18 | 9.5 | odd | 6 | |||
972.2.i.b.541.1 | 18 | 27.11 | odd | 18 | |||
972.2.i.c.433.3 | 18 | 9.4 | even | 3 | |||
972.2.i.c.541.3 | 18 | 27.16 | even | 9 | |||
972.2.i.d.109.3 | 18 | 9.2 | odd | 6 | |||
972.2.i.d.865.3 | 18 | 27.20 | odd | 18 | |||
2916.2.a.c.1.3 | 9 | 27.5 | odd | 18 | |||
2916.2.a.d.1.7 | 9 | 27.22 | even | 9 | |||
2916.2.e.c.973.3 | 18 | 27.13 | even | 9 | |||
2916.2.e.c.1945.3 | 18 | 27.4 | even | 9 | |||
2916.2.e.d.973.7 | 18 | 27.14 | odd | 18 | |||
2916.2.e.d.1945.7 | 18 | 27.23 | odd | 18 |