Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(55,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.55");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.f (of order \(6\), degree \(2\), not 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: | \(8.82836056527\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.207360000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 271.2 | ||
Root | \(0.437016 - 0.756934i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.271 |
Dual form | 324.3.f.p.55.1 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.58114 | + | 1.22474i | −0.790569 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | − | 3.87298i | 0.250000 | − | 0.968246i | ||||
\(5\) | 3.70246 | − | 6.41285i | 0.740492 | − | 1.28257i | −0.211780 | − | 0.977317i | \(-0.567926\pi\) |
0.952272 | − | 0.305252i | \(-0.0987407\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.20820 | − | 4.73901i | 1.17260 | − | 0.677001i | 0.218309 | − | 0.975880i | \(-0.429946\pi\) |
0.954291 | + | 0.298878i | \(0.0966125\pi\) | |||||||
\(8\) | 3.16228 | + | 7.34847i | 0.395285 | + | 0.918559i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | + | 14.6742i | 0.200000 | + | 1.46742i | ||||
\(11\) | −5.86319 | + | 3.38511i | −0.533017 | + | 0.307737i | −0.742244 | − | 0.670130i | \(-0.766238\pi\) |
0.209227 | + | 0.977867i | \(0.432905\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.20820 | − | 12.4850i | 0.554477 | − | 0.960383i | −0.443467 | − | 0.896291i | \(-0.646252\pi\) |
0.997944 | − | 0.0640919i | \(-0.0204151\pi\) | |||||||
\(14\) | −7.17423 | + | 17.5460i | −0.512445 | + | 1.25328i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −14.0000 | − | 7.74597i | −0.875000 | − | 0.484123i | ||||
\(17\) | −17.8933 | −1.05255 | −0.526274 | − | 0.850315i | \(-0.676411\pi\) | ||||
−0.526274 | + | 0.850315i | \(0.676411\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.19615i | − | 0.273482i | −0.990607 | − | 0.136741i | \(-0.956337\pi\) | ||
0.990607 | − | 0.136741i | \(-0.0436628\pi\) | |||||||
\(20\) | −21.1344 | − | 20.7524i | −1.05672 | − | 1.03762i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.12461 | − | 12.5332i | 0.232937 | − | 0.569693i | ||||
\(23\) | −21.5958 | − | 12.4683i | −0.938946 | − | 0.542101i | −0.0493164 | − | 0.998783i | \(-0.515704\pi\) |
−0.889630 | + | 0.456682i | \(0.849038\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.9164 | − | 25.8360i | −0.596656 | − | 1.03344i | ||||
\(26\) | 3.89374 | + | 28.5687i | 0.149759 | + | 1.09880i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10.1459 | − | 36.5292i | −0.362354 | − | 1.30462i | ||||
\(29\) | 14.8098 | + | 25.6514i | 0.510684 | + | 0.884531i | 0.999923 | + | 0.0123811i | \(0.00394113\pi\) |
−0.489239 | + | 0.872150i | \(0.662726\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 14.8328 | + | 8.56373i | 0.478478 | + | 0.276249i | 0.719782 | − | 0.694200i | \(-0.244242\pi\) |
−0.241304 | + | 0.970450i | \(0.577575\pi\) | |||||||
\(32\) | 31.6228 | − | 4.89898i | 0.988212 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 28.2918 | − | 21.9147i | 0.832112 | − | 0.644551i | ||||
\(35\) | − | 70.1839i | − | 2.00526i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.41641 | 0.173416 | 0.0867082 | − | 0.996234i | \(-0.472365\pi\) | ||||
0.0867082 | + | 0.996234i | \(0.472365\pi\) | |||||||
\(38\) | 6.36396 | + | 8.21584i | 0.167473 | + | 0.216206i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 58.8328 | + | 6.92820i | 1.47082 | + | 0.173205i | ||||
\(41\) | 4.32145 | − | 7.48497i | 0.105401 | − | 0.182560i | −0.808501 | − | 0.588495i | \(-0.799721\pi\) |
0.913902 | + | 0.405935i | \(0.133054\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −43.4164 | + | 25.0665i | −1.00968 | + | 0.582941i | −0.911099 | − | 0.412187i | \(-0.864765\pi\) |
−0.0985848 | + | 0.995129i | \(0.531432\pi\) | |||||||
\(44\) | 7.24730 | + | 26.0931i | 0.164711 | + | 0.593026i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 49.4164 | − | 6.73516i | 1.07427 | − | 0.146416i | ||||
\(47\) | 45.0485 | − | 26.0088i | 0.958479 | − | 0.553378i | 0.0627743 | − | 0.998028i | \(-0.480005\pi\) |
0.895705 | + | 0.444650i | \(0.146672\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20.4164 | − | 35.3623i | 0.416661 | − | 0.721679i | ||||
\(50\) | 55.2274 | + | 22.5815i | 1.10455 | + | 0.451629i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −41.1459 | − | 40.4022i | −0.791267 | − | 0.776966i | ||||
\(53\) | 82.6921 | 1.56023 | 0.780114 | − | 0.625637i | \(-0.215161\pi\) | ||||
0.780114 | + | 0.625637i | \(0.215161\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 50.1329i | 0.911508i | ||||||||
\(56\) | 60.7811 | + | 45.3317i | 1.08538 | + | 0.809494i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −54.8328 | − | 22.4201i | −0.945393 | − | 0.386554i | ||||
\(59\) | −72.5075 | − | 41.8622i | −1.22894 | − | 0.709529i | −0.262132 | − | 0.965032i | \(-0.584425\pi\) |
−0.966808 | + | 0.255503i | \(0.917759\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.20820 | + | 7.28882i | 0.0689869 | + | 0.119489i | 0.898456 | − | 0.439064i | \(-0.144690\pi\) |
−0.829469 | + | 0.558553i | \(0.811357\pi\) | |||||||
\(62\) | −33.9411 | + | 4.62597i | −0.547438 | + | 0.0746124i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −44.0000 | + | 46.4758i | −0.687500 | + | 0.726184i | ||||
\(65\) | −53.3762 | − | 92.4502i | −0.821172 | − | 1.42231i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −25.1656 | − | 14.5294i | −0.375606 | − | 0.216856i | 0.300299 | − | 0.953845i | \(-0.402914\pi\) |
−0.675905 | + | 0.736989i | \(0.736247\pi\) | |||||||
\(68\) | −17.8933 | + | 69.3005i | −0.263137 | + | 1.01912i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 85.9574 | + | 110.971i | 1.22796 | + | 1.58529i | ||||
\(71\) | − | 113.287i | − | 1.59559i | −0.602928 | − | 0.797796i | \(-0.705999\pi\) | ||
0.602928 | − | 0.797796i | \(-0.294001\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.16718 | 0.0296875 | 0.0148437 | − | 0.999890i | \(-0.495275\pi\) | ||||
0.0148437 | + | 0.999890i | \(0.495275\pi\) | |||||||
\(74\) | −10.1452 | + | 7.85846i | −0.137098 | + | 0.106195i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20.1246 | − | 5.19615i | −0.264798 | − | 0.0683704i | ||||
\(77\) | −32.0841 | + | 55.5714i | −0.416677 | + | 0.721706i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 129.457 | − | 74.7423i | 1.63870 | − | 0.946105i | 0.657421 | − | 0.753524i | \(-0.271648\pi\) |
0.981281 | − | 0.192581i | \(-0.0616858\pi\) | |||||||
\(80\) | −101.508 | + | 61.1007i | −1.26885 | + | 0.763759i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.33437 | + | 17.1275i | 0.0284679 | + | 0.208871i | ||||
\(83\) | 11.7264 | − | 6.77022i | 0.141282 | − | 0.0815690i | −0.427693 | − | 0.903924i | \(-0.640674\pi\) |
0.568975 | + | 0.822355i | \(0.307340\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −66.2492 | + | 114.747i | −0.779403 | + | 1.34996i | ||||
\(86\) | 37.9473 | − | 92.8076i | 0.441248 | − | 1.07916i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −43.4164 | − | 32.3808i | −0.493368 | − | 0.367963i | ||||
\(89\) | −17.8933 | −0.201048 | −0.100524 | − | 0.994935i | \(-0.532052\pi\) | ||||
−0.100524 | + | 0.994935i | \(0.532052\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 136.639i | − | 1.50153i | ||||||
\(92\) | −69.8854 | + | 71.1717i | −0.759623 | + | 0.773606i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −39.3738 | + | 96.2964i | −0.418871 | + | 1.02443i | ||||
\(95\) | −33.3221 | − | 19.2385i | −0.350759 | − | 0.202511i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 69.1656 | + | 119.798i | 0.713048 | + | 1.23503i | 0.963708 | + | 0.266960i | \(0.0860191\pi\) |
−0.250660 | + | 0.968075i | \(0.580648\pi\) | |||||||
\(98\) | 11.0286 | + | 80.9175i | 0.112536 | + | 0.825689i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −114.979 | + | 31.9350i | −1.14979 | + | 0.319350i | ||||
\(101\) | 48.7510 | + | 84.4391i | 0.482683 | + | 0.836031i | 0.999802 | − | 0.0198821i | \(-0.00632907\pi\) |
−0.517120 | + | 0.855913i | \(0.672996\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −36.7918 | − | 21.2418i | −0.357202 | − | 0.206231i | 0.310651 | − | 0.950524i | \(-0.399453\pi\) |
−0.667853 | + | 0.744294i | \(0.732786\pi\) | |||||||
\(104\) | 114.540 | + | 13.4883i | 1.10134 | + | 0.129695i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −130.748 | + | 101.277i | −1.23347 | + | 0.955441i | ||||
\(107\) | 97.2648i | 0.909017i | 0.890742 | + | 0.454509i | \(0.150185\pi\) | ||||
−0.890742 | + | 0.454509i | \(0.849815\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −96.8328 | −0.888374 | −0.444187 | − | 0.895934i | \(-0.646507\pi\) | ||||
−0.444187 | + | 0.895934i | \(0.646507\pi\) | |||||||
\(110\) | −61.4001 | − | 79.2672i | −0.558182 | − | 0.720610i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −151.623 | + | 2.76565i | −1.35378 | + | 0.0246933i | ||||
\(113\) | 19.4350 | − | 33.6625i | 0.171991 | − | 0.297898i | −0.767125 | − | 0.641498i | \(-0.778313\pi\) |
0.939116 | + | 0.343600i | \(0.111647\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −159.915 | + | 92.3269i | −1.39056 | + | 0.802842i | ||||
\(116\) | 114.157 | − | 31.7069i | 0.984114 | − | 0.273335i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 165.915 | − | 22.6132i | 1.40606 | − | 0.191637i | ||||
\(119\) | −146.872 | + | 84.7965i | −1.23422 | + | 0.712576i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −37.5820 | + | 65.0940i | −0.310595 | + | 0.537967i | ||||
\(122\) | −15.5807 | − | 6.37066i | −0.127711 | − | 0.0522186i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 48.0000 | − | 48.8835i | 0.387097 | − | 0.394222i | ||||
\(125\) | −35.7866 | −0.286293 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 99.0165i | 0.779657i | 0.920887 | + | 0.389829i | \(0.127466\pi\) | ||||
−0.920887 | + | 0.389829i | \(0.872534\pi\) | |||||||
\(128\) | 12.6491 | − | 127.373i | 0.0988212 | − | 0.995105i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 197.623 | + | 80.8045i | 1.52018 | + | 0.621573i | ||||
\(131\) | 46.9055 | + | 27.0809i | 0.358057 | + | 0.206724i | 0.668228 | − | 0.743956i | \(-0.267053\pi\) |
−0.310171 | + | 0.950681i | \(0.600386\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.6246 | − | 42.6511i | −0.185147 | − | 0.320685i | ||||
\(134\) | 57.5851 | − | 7.84850i | 0.429740 | − | 0.0585709i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −56.5836 | − | 131.488i | −0.416056 | − | 0.966826i | ||||
\(137\) | −2.77972 | − | 4.81461i | −0.0202899 | − | 0.0351432i | 0.855702 | − | 0.517469i | \(-0.173126\pi\) |
−0.875992 | + | 0.482325i | \(0.839792\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 132.084 | + | 76.2585i | 0.950242 | + | 0.548622i | 0.893156 | − | 0.449747i | \(-0.148486\pi\) |
0.0570857 | + | 0.998369i | \(0.481819\pi\) | |||||||
\(140\) | −271.821 | − | 70.1839i | −1.94158 | − | 0.501314i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 138.748 | + | 179.122i | 0.977096 | + | 1.26143i | ||||
\(143\) | 97.6023i | 0.682534i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 219.331 | 1.51263 | ||||||||
\(146\) | −3.42662 | + | 2.65425i | −0.0234700 | + | 0.0181798i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.41641 | − | 24.8506i | 0.0433541 | − | 0.167910i | ||||
\(149\) | 68.4897 | − | 118.628i | 0.459663 | − | 0.796159i | −0.539280 | − | 0.842126i | \(-0.681304\pi\) |
0.998943 | + | 0.0459672i | \(0.0146370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −67.5395 | + | 38.9939i | −0.447281 | + | 0.258238i | −0.706681 | − | 0.707532i | \(-0.749809\pi\) |
0.259400 | + | 0.965770i | \(0.416475\pi\) | |||||||
\(152\) | 38.1838 | − | 16.4317i | 0.251209 | − | 0.108103i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −17.3313 | − | 127.161i | −0.112541 | − | 0.825720i | ||||
\(155\) | 109.836 | − | 63.4137i | 0.708618 | − | 0.409121i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 36.0820 | − | 62.4959i | 0.229822 | − | 0.398063i | −0.727933 | − | 0.685648i | \(-0.759519\pi\) |
0.957755 | + | 0.287585i | \(0.0928523\pi\) | |||||||
\(158\) | −113.150 | + | 276.730i | −0.716139 | + | 1.75146i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 85.6656 | − | 220.930i | 0.535410 | − | 1.38081i | ||||
\(161\) | −236.350 | −1.46801 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 56.5785i | 0.347108i | 0.984824 | + | 0.173554i | \(0.0555250\pi\) | ||||
−0.984824 | + | 0.173554i | \(0.944475\pi\) | |||||||
\(164\) | −24.6677 | − | 24.2219i | −0.150413 | − | 0.147694i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.2492 | + | 25.0665i | −0.0617423 | + | 0.151003i | ||||
\(167\) | 174.623 | + | 100.819i | 1.04565 | + | 0.603705i | 0.921428 | − | 0.388550i | \(-0.127024\pi\) |
0.124220 | + | 0.992255i | \(0.460357\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19.4164 | − | 33.6302i | −0.114890 | − | 0.198995i | ||||
\(170\) | −35.7866 | − | 262.569i | −0.210509 | − | 1.54453i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 53.6656 | + | 193.217i | 0.312009 | + | 1.12336i | ||||
\(173\) | 46.2750 | + | 80.1506i | 0.267485 | + | 0.463298i | 0.968212 | − | 0.250132i | \(-0.0804739\pi\) |
−0.700726 | + | 0.713430i | \(0.747141\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −244.874 | − | 141.378i | −1.39928 | − | 0.807874i | ||||
\(176\) | 108.306 | − | 1.97552i | 0.615372 | − | 0.0112246i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 28.2918 | − | 21.9147i | 0.158943 | − | 0.123116i | ||||
\(179\) | − | 4.28851i | − | 0.0239581i | −0.999928 | − | 0.0119791i | \(-0.996187\pi\) | ||
0.999928 | − | 0.0119791i | \(-0.00381315\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −289.748 | −1.60082 | −0.800408 | − | 0.599456i | \(-0.795384\pi\) | ||||
−0.800408 | + | 0.599456i | \(0.795384\pi\) | |||||||
\(182\) | 167.348 | + | 216.045i | 0.919494 | + | 1.18706i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 23.3313 | − | 198.124i | 0.126800 | − | 1.07676i | ||||
\(185\) | 23.7565 | − | 41.1474i | 0.128413 | − | 0.222419i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 104.912 | − | 60.5708i | 0.561025 | − | 0.323908i | ||||
\(188\) | −55.6830 | − | 200.481i | −0.296186 | − | 1.06639i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 76.2492 | − | 10.3923i | 0.401312 | − | 0.0546963i | ||||
\(191\) | 80.2276 | − | 46.3194i | 0.420040 | − | 0.242510i | −0.275055 | − | 0.961429i | \(-0.588696\pi\) |
0.695094 | + | 0.718919i | \(0.255363\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 121.582 | − | 210.586i | 0.629959 | − | 1.09112i | −0.357601 | − | 0.933875i | \(-0.616405\pi\) |
0.987559 | − | 0.157246i | \(-0.0502616\pi\) | |||||||
\(194\) | −256.083 | − | 104.708i | −1.32002 | − | 0.539730i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −116.541 | − | 114.435i | −0.594597 | − | 0.583850i | ||||
\(197\) | 139.432 | 0.707779 | 0.353890 | − | 0.935287i | \(-0.384859\pi\) | ||||
0.353890 | + | 0.935287i | \(0.384859\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 110.993i | 0.557756i | 0.960327 | + | 0.278878i | \(0.0899624\pi\) | ||||
−0.960327 | + | 0.278878i | \(0.910038\pi\) | |||||||
\(200\) | 142.685 | − | 191.313i | 0.713425 | − | 0.956566i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −180.498 | − | 73.8025i | −0.893557 | − | 0.365359i | ||||
\(203\) | 243.124 | + | 140.368i | 1.19766 | + | 0.691467i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −32.0000 | − | 55.4256i | −0.156098 | − | 0.270369i | ||||
\(206\) | 84.1887 | − | 11.4744i | 0.408683 | − | 0.0557010i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −197.623 | + | 118.955i | −0.950111 | + | 0.571900i | ||||
\(209\) | 17.5896 | + | 30.4660i | 0.0841606 | + | 0.145770i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 229.579 | + | 132.547i | 1.08805 | + | 0.628187i | 0.933057 | − | 0.359728i | \(-0.117131\pi\) |
0.154995 | + | 0.987915i | \(0.450464\pi\) | |||||||
\(212\) | 82.6921 | − | 320.265i | 0.390057 | − | 1.51068i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −119.125 | − | 153.789i | −0.556657 | − | 0.718641i | ||||
\(215\) | 371.230i | 1.72665i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 162.334 | 0.748085 | ||||||||
\(218\) | 153.106 | − | 118.595i | 0.702322 | − | 0.544016i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 194.164 | + | 50.1329i | 0.882564 | + | 0.227877i | ||||
\(221\) | −128.979 | + | 223.397i | −0.583613 | + | 1.01085i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 275.331 | − | 158.963i | 1.23467 | − | 0.712837i | 0.266670 | − | 0.963788i | \(-0.414077\pi\) |
0.968000 | + | 0.250951i | \(0.0807434\pi\) | |||||||
\(224\) | 236.350 | − | 190.072i | 1.05513 | − | 0.848538i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.4984 | + | 77.0280i | 0.0464533 | + | 0.340832i | ||||
\(227\) | −215.958 | + | 124.683i | −0.951355 | + | 0.549265i | −0.893502 | − | 0.449060i | \(-0.851759\pi\) |
−0.0578535 | + | 0.998325i | \(0.518426\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −76.1672 | + | 131.925i | −0.332608 | + | 0.576094i | −0.983022 | − | 0.183486i | \(-0.941262\pi\) |
0.650415 | + | 0.759579i | \(0.274595\pi\) | |||||||
\(230\) | 139.771 | − | 341.837i | 0.607699 | − | 1.48625i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −141.666 | + | 189.946i | −0.610628 | + | 0.818735i | ||||
\(233\) | 346.793 | 1.48838 | 0.744191 | − | 0.667966i | \(-0.232835\pi\) | ||||
0.744191 | + | 0.667966i | \(0.232835\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 385.186i | − | 1.63909i | ||||||
\(236\) | −234.639 | + | 238.958i | −0.994233 | + | 1.01253i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 128.371 | − | 313.956i | 0.539373 | − | 1.31914i | ||||
\(239\) | −90.0970 | − | 52.0175i | −0.376975 | − | 0.217647i | 0.299526 | − | 0.954088i | \(-0.403171\pi\) |
−0.676501 | + | 0.736441i | \(0.736505\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −140.913 | − | 244.069i | −0.584702 | − | 1.01273i | −0.994912 | − | 0.100743i | \(-0.967878\pi\) |
0.410210 | − | 0.911991i | \(-0.365455\pi\) | |||||||
\(242\) | −20.3011 | − | 148.951i | −0.0838889 | − | 0.615500i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 32.4377 | − | 9.00948i | 0.132941 | − | 0.0369241i | ||||
\(245\) | −151.182 | − | 261.855i | −0.617069 | − | 1.06879i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −64.8738 | − | 37.4549i | −0.262647 | − | 0.151639i | ||||
\(248\) | −16.0248 | + | 136.079i | −0.0646162 | + | 0.548707i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 56.5836 | − | 43.8295i | 0.226334 | − | 0.175318i | ||||
\(251\) | 271.484i | 1.08161i | 0.841148 | + | 0.540804i | \(0.181880\pi\) | ||||
−0.841148 | + | 0.540804i | \(0.818120\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 168.827 | 0.667299 | ||||||||
\(254\) | −121.270 | − | 156.559i | −0.477441 | − | 0.616373i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 136.000 | + | 216.887i | 0.531250 | + | 0.847215i | ||||
\(257\) | −229.552 | + | 397.597i | −0.893200 | + | 1.54707i | −0.0571840 | + | 0.998364i | \(0.518212\pi\) |
−0.836016 | + | 0.548705i | \(0.815121\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 52.6672 | − | 30.4074i | 0.203348 | − | 0.117403i | ||||
\(260\) | −411.434 | + | 114.275i | −1.58244 | + | 0.439518i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −107.331 | + | 14.6286i | −0.409661 | + | 0.0558343i | ||||
\(263\) | 176.480 | − | 101.891i | 0.671027 | − | 0.387418i | −0.125439 | − | 0.992101i | \(-0.540034\pi\) |
0.796466 | + | 0.604684i | \(0.206701\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 306.164 | − | 530.292i | 1.15534 | − | 2.00110i | ||||
\(266\) | 91.1716 | + | 37.2784i | 0.342750 | + | 0.140144i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −81.4377 | + | 82.9367i | −0.303872 | + | 0.309465i | ||||
\(269\) | −323.363 | −1.20209 | −0.601047 | − | 0.799213i | \(-0.705250\pi\) | ||||
−0.601047 | + | 0.799213i | \(0.705250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 104.928i | − | 0.387190i | −0.981082 | − | 0.193595i | \(-0.937985\pi\) | ||
0.981082 | − | 0.193595i | \(-0.0620148\pi\) | |||||||
\(272\) | 250.506 | + | 138.601i | 0.920979 | + | 0.509562i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.2918 | + | 4.20813i | 0.0375613 | + | 0.0153581i | ||||
\(275\) | 174.915 | + | 100.987i | 0.636056 | + | 0.367227i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.4164 | + | 42.2905i | 0.0881459 | + | 0.152673i | 0.906727 | − | 0.421717i | \(-0.138573\pi\) |
−0.818582 | + | 0.574390i | \(0.805239\pi\) | |||||||
\(278\) | −302.240 | + | 41.1934i | −1.08719 | + | 0.148178i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 515.745 | − | 221.941i | 1.84194 | − | 0.792647i | ||||
\(281\) | 14.8098 | + | 25.6514i | 0.0527040 | + | 0.0912861i | 0.891174 | − | 0.453662i | \(-0.149883\pi\) |
−0.838470 | + | 0.544948i | \(0.816549\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 333.580 | + | 192.593i | 1.17873 | + | 0.680540i | 0.955720 | − | 0.294276i | \(-0.0950786\pi\) |
0.223009 | + | 0.974816i | \(0.428412\pi\) | |||||||
\(284\) | −438.759 | − | 113.287i | −1.54492 | − | 0.398898i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −119.538 | − | 154.323i | −0.417965 | − | 0.539590i | ||||
\(287\) | − | 81.9176i | − | 0.285427i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.1703 | 0.107856 | ||||||||
\(290\) | −346.793 | + | 268.625i | −1.19584 | + | 0.926293i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.16718 | − | 8.39347i | 0.00742186 | − | 0.0287448i | ||||
\(293\) | 140.705 | − | 243.708i | 0.480222 | − | 0.831768i | −0.519521 | − | 0.854458i | \(-0.673890\pi\) |
0.999743 | + | 0.0226894i | \(0.00722289\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −536.912 | + | 309.986i | −1.82004 | + | 1.05080i | ||||
\(296\) | 20.2905 | + | 47.1508i | 0.0685489 | + | 0.159293i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 36.9969 | + | 271.449i | 0.124151 | + | 0.910904i | ||||
\(299\) | −311.333 | + | 179.748i | −1.04125 | + | 0.601165i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −237.580 | + | 411.501i | −0.789304 | + | 1.36711i | ||||
\(302\) | 59.0317 | − | 144.373i | 0.195469 | − | 0.478058i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −40.2492 | + | 72.7461i | −0.132399 | + | 0.239296i | ||||
\(305\) | 62.3228 | 0.204337 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 553.961i | 1.80443i | 0.431282 | + | 0.902217i | \(0.358061\pi\) | ||||
−0.431282 | + | 0.902217i | \(0.641939\pi\) | |||||||
\(308\) | 183.143 | + | 179.833i | 0.594620 | + | 0.583873i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −96.0000 | + | 234.787i | −0.309677 | + | 0.757377i | ||||
\(311\) | 13.5833 | + | 7.84235i | 0.0436764 | + | 0.0252166i | 0.521679 | − | 0.853142i | \(-0.325306\pi\) |
−0.478003 | + | 0.878358i | \(0.658639\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 154.080 | + | 266.875i | 0.492270 | + | 0.852637i | 0.999960 | − | 0.00890304i | \(-0.00283396\pi\) |
−0.507690 | + | 0.861540i | \(0.669501\pi\) | |||||||
\(314\) | 19.4909 | + | 143.006i | 0.0620728 | + | 0.455433i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −160.018 | − | 576.129i | −0.506387 | − | 1.82319i | ||||
\(317\) | −248.053 | − | 429.641i | −0.782502 | − | 1.35533i | −0.930480 | − | 0.366343i | \(-0.880610\pi\) |
0.147977 | − | 0.988991i | \(-0.452724\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −173.666 | − | 100.266i | −0.544406 | − | 0.314313i | ||||
\(320\) | 135.134 | + | 454.240i | 0.422294 | + | 1.41950i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 373.702 | − | 289.468i | 1.16057 | − | 0.898970i | ||||
\(323\) | 92.9763i | 0.287852i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −430.082 | −1.32333 | ||||||||
\(326\) | −69.2943 | − | 89.4585i | −0.212559 | − | 0.274413i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 68.6687 | + | 8.08649i | 0.209356 | + | 0.0246539i | ||||
\(329\) | 246.512 | − | 426.970i | 0.749275 | − | 1.29778i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −74.9164 | + | 43.2530i | −0.226334 | + | 0.130674i | −0.608879 | − | 0.793263i | \(-0.708381\pi\) |
0.382546 | + | 0.923936i | \(0.375047\pi\) | |||||||
\(332\) | −14.4946 | − | 52.1863i | −0.0436584 | − | 0.157188i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −399.580 | + | 54.4604i | −1.19635 | + | 0.163055i | ||||
\(335\) | −186.349 | + | 107.589i | −0.556267 | + | 0.321161i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −160.330 | + | 277.699i | −0.475756 | + | 0.824033i | −0.999614 | − | 0.0277721i | \(-0.991159\pi\) |
0.523858 | + | 0.851805i | \(0.324492\pi\) | |||||||
\(338\) | 71.8885 | + | 29.3939i | 0.212688 | + | 0.0869641i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 378.164 | + | 371.329i | 1.11225 | + | 1.09214i | ||||
\(341\) | −115.957 | −0.340049 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 77.4087i | 0.225681i | ||||||||
\(344\) | −321.495 | − | 239.777i | −0.934578 | − | 0.697026i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −171.331 | − | 70.0542i | −0.495177 | − | 0.202469i | ||||
\(347\) | −584.358 | − | 337.379i | −1.68403 | − | 0.972275i | −0.958936 | − | 0.283624i | \(-0.908463\pi\) |
−0.725093 | − | 0.688650i | \(-0.758203\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −76.9590 | − | 133.297i | −0.220513 | − | 0.381939i | 0.734451 | − | 0.678662i | \(-0.237440\pi\) |
−0.954964 | + | 0.296722i | \(0.904106\pi\) | |||||||
\(350\) | 560.331 | − | 76.3698i | 1.60095 | − | 0.218199i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −168.827 | + | 135.770i | −0.479621 | + | 0.385711i | ||||
\(353\) | 311.614 | + | 539.731i | 0.882759 | + | 1.52898i | 0.848260 | + | 0.529579i | \(0.177650\pi\) |
0.0344990 | + | 0.999405i | \(0.489016\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −726.492 | − | 419.440i | −2.04646 | − | 1.18152i | ||||
\(356\) | −17.8933 | + | 69.3005i | −0.0502621 | + | 0.194664i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.25233 | + | 6.78073i | 0.0146713 | + | 0.0189406i | ||||
\(359\) | − | 160.341i | − | 0.446633i | −0.974746 | − | 0.223316i | \(-0.928312\pi\) | ||
0.974746 | − | 0.223316i | \(-0.0716883\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 334.000 | 0.925208 | ||||||||
\(362\) | 458.131 | − | 354.867i | 1.26556 | − | 0.980296i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −529.200 | − | 136.639i | −1.45385 | − | 0.375382i | ||||
\(365\) | 8.02391 | − | 13.8978i | 0.0219833 | − | 0.0380762i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 246.457 | − | 142.292i | 0.671546 | − | 0.387717i | −0.125116 | − | 0.992142i | \(-0.539930\pi\) |
0.796662 | + | 0.604425i | \(0.206597\pi\) | |||||||
\(368\) | 205.761 | + | 341.837i | 0.559134 | + | 0.928904i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.8328 | + | 94.1555i | 0.0346833 | + | 0.254474i | ||||
\(371\) | 678.754 | − | 391.879i | 1.82952 | − | 1.05628i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −150.710 | + | 261.037i | −0.404048 | + | 0.699831i | −0.994210 | − | 0.107453i | \(-0.965730\pi\) |
0.590163 | + | 0.807284i | \(0.299064\pi\) | |||||||
\(374\) | −91.6962 | + | 224.261i | −0.245177 | + | 0.599628i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 333.580 | + | 248.791i | 0.887182 | + | 0.661677i | ||||
\(377\) | 427.009 | 1.13265 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 248.547i | − | 0.655796i | −0.944713 | − | 0.327898i | \(-0.893660\pi\) | ||
0.944713 | − | 0.327898i | \(-0.106340\pi\) | |||||||
\(380\) | −107.833 | + | 109.818i | −0.283770 | + | 0.288993i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −70.1215 | + | 171.496i | −0.183564 | + | 0.448942i | ||||
\(383\) | 422.734 | + | 244.065i | 1.10374 | + | 0.637247i | 0.937202 | − | 0.348788i | \(-0.113407\pi\) |
0.166542 | + | 0.986034i | \(0.446740\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 237.580 | + | 411.501i | 0.617092 | + | 1.06883i | ||||
\(386\) | 65.6764 | + | 481.873i | 0.170146 | + | 1.24838i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 533.143 | − | 148.079i | 1.37408 | − | 0.381647i | ||||
\(389\) | 207.934 | + | 360.152i | 0.534534 | + | 0.925840i | 0.999186 | + | 0.0403465i | \(0.0128462\pi\) |
−0.464652 | + | 0.885493i | \(0.653820\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 386.420 | + | 223.099i | 0.988285 | + | 0.570587i | ||||
\(392\) | 324.421 | + | 38.2041i | 0.827604 | + | 0.0974594i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −220.462 | + | 170.769i | −0.559548 | + | 0.433424i | ||||
\(395\) | − | 1106.92i | − | 2.80233i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −670.827 | −1.68974 | −0.844870 | − | 0.534972i | \(-0.820322\pi\) | ||||
−0.844870 | + | 0.534972i | \(0.820322\pi\) | |||||||
\(398\) | −135.939 | − | 175.496i | −0.341554 | − | 0.440944i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.70510 | + | 477.246i | 0.0217627 | + | 1.19311i | ||||
\(401\) | −57.3709 | + | 99.3693i | −0.143070 | + | 0.247804i | −0.928651 | − | 0.370955i | \(-0.879031\pi\) |
0.785582 | + | 0.618758i | \(0.212364\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 213.836 | − | 123.458i | 0.530610 | − | 0.306348i | ||||
\(404\) | 375.782 | − | 104.373i | 0.930154 | − | 0.258348i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −556.328 | + | 75.8241i | −1.37027 | + | 0.186759i | ||||
\(407\) | −37.6206 | + | 21.7203i | −0.0924339 | + | 0.0533667i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 73.3359 | − | 127.022i | 0.179305 | − | 0.310566i | −0.762337 | − | 0.647180i | \(-0.775948\pi\) |
0.941643 | + | 0.336614i | \(0.109282\pi\) | |||||||
\(410\) | 118.479 | + | 48.4438i | 0.288972 | + | 0.118156i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −119.061 | + | 121.252i | −0.288982 | + | 0.294302i | ||||
\(413\) | −793.541 | −1.92141 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 100.266i | − | 0.241605i | ||||||
\(416\) | 166.780 | − | 430.122i | 0.400913 | − | 1.03395i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −65.1246 | − | 26.6283i | −0.155801 | − | 0.0637040i | ||||
\(419\) | −464.945 | − | 268.436i | −1.10965 | − | 0.640659i | −0.170914 | − | 0.985286i | \(-0.554672\pi\) |
−0.938740 | + | 0.344627i | \(0.888005\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 183.707 | + | 318.189i | 0.436358 | + | 0.755794i | 0.997405 | − | 0.0719896i | \(-0.0229349\pi\) |
−0.561048 | + | 0.827784i | \(0.689602\pi\) | |||||||
\(422\) | −525.333 | + | 71.5997i | −1.24486 | + | 0.169668i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 261.495 | + | 607.660i | 0.616734 | + | 1.43316i | ||||
\(425\) | 266.904 | + | 462.291i | 0.628009 | + | 1.08774i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 69.0836 | + | 39.8854i | 0.161788 | + | 0.0934085i | ||||
\(428\) | 376.705 | + | 97.2648i | 0.880152 | + | 0.227254i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −454.663 | − | 586.967i | −1.05735 | − | 1.36504i | ||||
\(431\) | − | 735.353i | − | 1.70616i | −0.521784 | − | 0.853078i | \(-0.674733\pi\) | ||
0.521784 | − | 0.853078i | \(-0.325267\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 765.161 | 1.76712 | 0.883558 | − | 0.468322i | \(-0.155141\pi\) | ||||
0.883558 | + | 0.468322i | \(0.155141\pi\) | |||||||
\(434\) | −256.673 | + | 198.818i | −0.591413 | + | 0.458106i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −96.8328 | + | 375.032i | −0.222094 | + | 0.860165i | ||||
\(437\) | −64.7873 | + | 112.215i | −0.148255 | + | 0.256785i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.1703 | + | 23.1923i | −0.0915041 | + | 0.0528299i | −0.545054 | − | 0.838401i | \(-0.683491\pi\) |
0.453550 | + | 0.891231i | \(0.350157\pi\) | |||||||
\(440\) | −368.400 | + | 158.534i | −0.837274 | + | 0.360305i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −69.6718 | − | 511.188i | −0.157629 | − | 1.15653i | ||||
\(443\) | 120.978 | − | 69.8465i | 0.273087 | − | 0.157667i | −0.357203 | − | 0.934027i | \(-0.616269\pi\) |
0.630290 | + | 0.776360i | \(0.282936\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −66.2492 | + | 114.747i | −0.148875 | + | 0.257858i | ||||
\(446\) | −240.648 | + | 588.552i | −0.539570 | + | 1.31962i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −140.912 | + | 589.999i | −0.314535 | + | 1.31696i | ||||
\(449\) | −267.139 | −0.594963 | −0.297482 | − | 0.954728i | \(-0.596147\pi\) | ||||
−0.297482 | + | 0.954728i | \(0.596147\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 58.5144i | 0.129744i | ||||||||
\(452\) | −110.939 | − | 108.934i | −0.245441 | − | 0.241005i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 188.754 | − | 461.634i | 0.415757 | − | 1.01682i | ||||
\(455\) | −876.245 | − | 505.900i | −1.92581 | − | 1.11187i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −118.915 | − | 205.967i | −0.260208 | − | 0.450693i | 0.706089 | − | 0.708123i | \(-0.250458\pi\) |
−0.966297 | + | 0.257430i | \(0.917124\pi\) | |||||||
\(458\) | −41.1441 | − | 301.878i | −0.0898343 | − | 0.659122i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 197.666 | + | 711.674i | 0.429708 | + | 1.54712i | ||||
\(461\) | −149.325 | − | 258.638i | −0.323915 | − | 0.561037i | 0.657377 | − | 0.753562i | \(-0.271666\pi\) |
−0.981292 | + | 0.192524i | \(0.938333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 423.950 | + | 244.767i | 0.915658 | + | 0.528655i | 0.882247 | − | 0.470786i | \(-0.156030\pi\) |
0.0334107 | + | 0.999442i | \(0.489363\pi\) | |||||||
\(464\) | −8.64290 | − | 473.836i | −0.0186269 | − | 1.02120i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −548.328 | + | 424.733i | −1.17667 | + | 0.911445i | ||||
\(467\) | 454.280i | 0.972762i | 0.873747 | + | 0.486381i | \(0.161683\pi\) | ||||
−0.873747 | + | 0.486381i | \(0.838317\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −275.420 | −0.587248 | ||||||||
\(470\) | 471.754 | + | 609.032i | 1.00373 | + | 1.29581i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 78.3344 | − | 665.199i | 0.165963 | − | 1.40932i | ||||
\(473\) | 169.706 | − | 293.939i | 0.358786 | − | 0.621435i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −134.248 | + | 77.5079i | −0.282627 | + | 0.163175i | ||||
\(476\) | 181.544 | + | 653.629i | 0.381394 | + | 1.37317i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 206.164 | − | 28.0989i | 0.431306 | − | 0.0587843i | ||||
\(479\) | −3.12946 | + | 1.80679i | −0.00653332 | + | 0.00377201i | −0.503263 | − | 0.864133i | \(-0.667867\pi\) |
0.496730 | + | 0.867905i | \(0.334534\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 46.2508 | − | 80.1087i | 0.0961555 | − | 0.166546i | ||||
\(482\) | 521.726 | + | 213.324i | 1.08242 | + | 0.442581i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 214.526 | + | 210.649i | 0.443235 | + | 0.435224i | ||||
\(485\) | 1024.33 | 2.11202 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 874.538i | − | 1.79577i | −0.440234 | − | 0.897883i | \(-0.645104\pi\) | ||
0.440234 | − | 0.897883i | \(-0.354896\pi\) | |||||||
\(488\) | −40.2542 | + | 53.9731i | −0.0824881 | + | 0.110601i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 559.745 | + | 228.869i | 1.14234 | + | 0.467080i | ||||
\(491\) | 558.756 | + | 322.598i | 1.13800 | + | 0.657022i | 0.945934 | − | 0.324360i | \(-0.105149\pi\) |
0.192063 | + | 0.981383i | \(0.438482\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −264.997 | − | 458.988i | −0.537519 | − | 0.931010i | ||||
\(494\) | 148.447 | − | 20.2325i | 0.300501 | − | 0.0409564i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −141.325 | − | 234.787i | −0.284930 | − | 0.473360i | ||||
\(497\) | −536.868 | − | 929.883i | −1.08022 | − | 1.87099i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −489.167 | − | 282.421i | −0.980295 | − | 0.565974i | −0.0779358 | − | 0.996958i | \(-0.524833\pi\) |
−0.902359 | + | 0.430985i | \(0.858166\pi\) | |||||||
\(500\) | −35.7866 | + | 138.601i | −0.0715732 | + | 0.277202i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −332.498 | − | 429.254i | −0.662348 | − | 0.855087i | ||||
\(503\) | − | 483.048i | − | 0.960334i | −0.877177 | − | 0.480167i | \(-0.840576\pi\) | ||
0.877177 | − | 0.480167i | \(-0.159424\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 721.994 | 1.42969 | ||||||||
\(506\) | −266.938 | + | 206.770i | −0.527546 | + | 0.408635i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 383.489 | + | 99.0165i | 0.754900 | + | 0.194914i | ||||
\(509\) | 108.002 | − | 187.065i | 0.212184 | − | 0.367514i | −0.740214 | − | 0.672372i | \(-0.765276\pi\) |
0.952398 | + | 0.304858i | \(0.0986090\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.7887 | − | 10.2703i | 0.0348115 | − | 0.0200984i | ||||
\(512\) | −480.666 | − | 176.363i | −0.938801 | − | 0.344459i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −124.000 | − | 909.799i | −0.241245 | − | 1.77004i | ||||
\(515\) | −272.440 | + | 157.293i | −0.529010 | + | 0.305424i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −176.085 | + | 304.988i | −0.340590 | + | 0.589920i | ||||
\(518\) | −46.0328 | + | 112.582i | −0.0888664 | + | 0.217340i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 510.577 | − | 684.586i | 0.981880 | − | 1.31651i | ||||
\(521\) | 454.806 | 0.872949 | 0.436475 | − | 0.899717i | \(-0.356227\pi\) | ||||
0.436475 | + | 0.899717i | \(0.356227\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 325.041i | 0.621493i | 0.950493 | + | 0.310747i | \(0.100579\pi\) | ||||
−0.950493 | + | 0.310747i | \(0.899421\pi\) | |||||||
\(524\) | 151.789 | − | 154.583i | 0.289674 | − | 0.295006i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −154.249 | + | 377.247i | −0.293249 | + | 0.717199i | ||||
\(527\) | −265.408 | − | 153.233i | −0.503621 | − | 0.290765i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 46.4180 | + | 80.3983i | 0.0877466 | + | 0.151982i | ||||
\(530\) | 165.384 | + | 1213.44i | 0.312046 | + | 2.28951i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −189.812 | + | 52.7196i | −0.356789 | + | 0.0990971i | ||||
\(533\) | −62.2998 | − | 107.906i | −0.116885 | − | 0.202451i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 623.745 | + | 360.119i | 1.16588 | + | 0.673120i | ||||
\(536\) | 27.1880 | − | 230.875i | 0.0507239 | − | 0.430737i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 511.282 | − | 396.038i | 0.950339 | − | 0.736130i | ||||
\(539\) | 276.447i | 0.512889i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −962.574 | −1.77925 | −0.889625 | − | 0.456692i | \(-0.849034\pi\) | ||||
−0.889625 | + | 0.456692i | \(0.849034\pi\) | |||||||
\(542\) | 128.511 | + | 165.906i | 0.237104 | + | 0.306101i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −565.836 | + | 87.6589i | −1.04014 | + | 0.161138i | ||||
\(545\) | −358.520 | + | 620.974i | −0.657834 | + | 1.13940i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 115.588 | − | 66.7349i | 0.211313 | − | 0.122002i | −0.390608 | − | 0.920557i | \(-0.627735\pi\) |
0.601921 | + | 0.798555i | \(0.294402\pi\) | |||||||
\(548\) | −21.4266 | + | 5.95119i | −0.0390997 | + | 0.0108598i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −400.249 | + | 54.5515i | −0.727726 | + | 0.0991846i | ||||
\(551\) | 133.289 | − | 76.9542i | 0.241903 | − | 0.139663i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 708.409 | − | 1227.00i | 1.28103 | − | 2.21881i | ||||
\(554\) | −90.4008 | − | 36.9632i | −0.163178 | − | 0.0667206i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 427.431 | − | 435.299i | 0.768762 | − | 0.782912i | ||||
\(557\) | 413.437 | 0.742258 | 0.371129 | − | 0.928581i | \(-0.378971\pi\) | ||||
0.371129 | + | 0.928581i | \(0.378971\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 722.737i | 1.29291i | ||||||||
\(560\) | −543.643 | + | 982.575i | −0.970790 | + | 1.75460i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −54.8328 | − | 22.4201i | −0.0975673 | − | 0.0398935i | ||||
\(563\) | −447.356 | − | 258.281i | −0.794592 | − | 0.458758i | 0.0469843 | − | 0.998896i | \(-0.485039\pi\) |
−0.841577 | + | 0.540137i | \(0.818372\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −143.915 | − | 249.268i | −0.254717 | − | 0.441182i | ||||
\(566\) | −763.314 | + | 104.035i | −1.34861 | + | 0.183808i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 832.486 | − | 358.245i | 1.46564 | − | 0.630713i | ||||
\(569\) | −234.178 | − | 405.608i | −0.411560 | − | 0.712843i | 0.583500 | − | 0.812113i | \(-0.301683\pi\) |
−0.995061 | + | 0.0992699i | \(0.968349\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −585.409 | − | 337.986i | −1.02523 | − | 0.591919i | −0.109618 | − | 0.993974i | \(-0.534963\pi\) |
−0.915616 | + | 0.402055i | \(0.868296\pi\) | |||||||
\(572\) | 378.012 | + | 97.6023i | 0.660860 | + | 0.170633i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 100.328 | + | 129.523i | 0.174788 | + | 0.225650i | ||||
\(575\) | 743.930i | 1.29379i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −354.823 | −0.614945 | −0.307473 | − | 0.951557i | \(-0.599483\pi\) | ||||
−0.307473 | + | 0.951557i | \(0.599483\pi\) | |||||||
\(578\) | −49.2846 | + | 38.1757i | −0.0852674 | + | 0.0660478i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 219.331 | − | 849.466i | 0.378157 | − | 1.46460i | ||||
\(581\) | 64.1683 | − | 111.143i | 0.110445 | − | 0.191296i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −484.839 | + | 279.922i | −0.831628 | + | 0.480141i | ||||
\(584\) | 6.85324 | + | 15.9255i | 0.0117350 | + | 0.0272697i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 76.0062 | + | 557.664i | 0.129703 | + | 0.951645i | ||||
\(587\) | −190.940 | + | 110.239i | −0.325281 | + | 0.187801i | −0.653744 | − | 0.756716i | \(-0.726803\pi\) |
0.328463 | + | 0.944517i | \(0.393469\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.4984 | − | 77.0736i | 0.0755491 | − | 0.130855i | ||||
\(590\) | 469.278 | − | 1147.71i | 0.795387 | − | 1.94527i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −89.8297 | − | 49.7013i | −0.151739 | − | 0.0839549i | ||||
\(593\) | −993.520 | −1.67541 | −0.837707 | − | 0.546121i | \(-0.816104\pi\) | ||||
−0.837707 | + | 0.546121i | \(0.816104\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1255.82i | 2.11063i | ||||||||
\(596\) | −390.953 | − | 383.887i | −0.655962 | − | 0.644106i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 272.115 | − | 665.511i | 0.455042 | − | 1.11289i | ||||
\(599\) | 243.124 | + | 140.368i | 0.405884 | + | 0.234337i | 0.689020 | − | 0.724743i | \(-0.258041\pi\) |
−0.283136 | + | 0.959080i | \(0.591375\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −280.915 | − | 486.559i | −0.467412 | − | 0.809582i | 0.531894 | − | 0.846811i | \(-0.321480\pi\) |
−0.999307 | + | 0.0372287i | \(0.988147\pi\) | |||||||
\(602\) | −128.337 | − | 941.616i | −0.213184 | − | 1.56415i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 83.4834 | + | 300.573i | 0.138218 | + | 0.497638i | ||||
\(605\) | 278.292 | + | 482.016i | 0.459987 | + | 0.796720i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −72.7918 | − | 42.0264i | −0.119921 | − | 0.0692362i | 0.438840 | − | 0.898565i | \(-0.355390\pi\) |
−0.558760 | + | 0.829329i | \(0.688723\pi\) | |||||||
\(608\) | −25.4558 | − | 164.317i | −0.0418682 | − | 0.270258i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −98.5410 | + | 76.3295i | −0.161543 | + | 0.125130i | ||||
\(611\) | − | 749.906i | − | 1.22734i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 730.234 | 1.19125 | 0.595623 | − | 0.803264i | \(-0.296905\pi\) | ||||
0.595623 | + | 0.803264i | \(0.296905\pi\) | |||||||
\(614\) | −678.461 | − | 875.890i | −1.10499 | − | 1.42653i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −509.823 | − | 60.0373i | −0.827636 | − | 0.0974631i | ||||
\(617\) | −274.893 | + | 476.129i | −0.445532 | + | 0.771684i | −0.998089 | − | 0.0617910i | \(-0.980319\pi\) |
0.552557 | + | 0.833475i | \(0.313652\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 63.3297 | − | 36.5634i | 0.102310 | − | 0.0590685i | −0.447972 | − | 0.894048i | \(-0.647854\pi\) |
0.550282 | + | 0.834979i | \(0.314520\pi\) | |||||||
\(620\) | −135.765 | − | 488.806i | −0.218975 | − | 0.788397i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −31.0820 | + | 4.23629i | −0.0499711 | + | 0.00681076i | ||||
\(623\) | −146.872 | + | 84.7965i | −0.235749 | + | 0.136110i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 240.412 | − | 416.405i | 0.384659 | − | 0.666249i | ||||
\(626\) | −570.477 | − | 233.258i | −0.911305 | − | 0.372616i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −205.964 | − | 202.241i | −0.327968 | − | 0.322040i | ||||
\(629\) | −114.811 | −0.182529 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 779.849i | − | 1.23589i | −0.786220 | − | 0.617947i | \(-0.787965\pi\) | ||
0.786220 | − | 0.617947i | \(-0.212035\pi\) | |||||||
\(632\) | 958.622 | + | 714.958i | 1.51681 | + | 1.13126i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 918.407 | + | 375.520i | 1.44859 | + | 0.592303i | ||||
\(635\) | 634.977 | + | 366.604i | 0.999965 | + | 0.577330i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −294.331 | − | 509.797i | −0.462058 | − | 0.800309i | ||||
\(638\) | 397.390 | − | 54.1618i | 0.622868 | − | 0.0848931i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −769.994 | − | 552.712i | −1.20312 | − | 0.863612i | ||||
\(641\) | 222.171 | + | 384.811i | 0.346600 | + | 0.600329i | 0.985643 | − | 0.168842i | \(-0.0540028\pi\) |
−0.639043 | + | 0.769171i | \(0.720669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −386.420 | − | 223.099i | −0.600963 | − | 0.346966i | 0.168457 | − | 0.985709i | \(-0.446122\pi\) |
−0.769421 | + | 0.638743i | \(0.779455\pi\) | |||||||
\(644\) | −236.350 | + | 915.379i | −0.367003 | + | 1.42140i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −113.872 | − | 147.008i | −0.176273 | − | 0.227567i | ||||
\(647\) | 861.386i | 1.33135i | 0.746240 | + | 0.665677i | \(0.231857\pi\) | ||||
−0.746240 | + | 0.665677i | \(0.768143\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 566.833 | 0.873394 | ||||||||
\(650\) | 680.019 | − | 526.741i | 1.04618 | − | 0.810370i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 219.128 | + | 56.5785i | 0.336085 | + | 0.0867769i | ||||
\(653\) | −438.151 | + | 758.900i | −0.670982 | + | 1.16217i | 0.306644 | + | 0.951824i | \(0.400794\pi\) |
−0.977626 | + | 0.210350i | \(0.932539\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 347.331 | − | 200.532i | 0.530277 | − | 0.306155i | ||||
\(656\) | −118.479 | + | 71.3158i | −0.180608 | + | 0.108713i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 133.161 | + | 977.013i | 0.202372 | + | 1.48482i | ||||
\(659\) | −489.963 | + | 282.880i | −0.743494 | + | 0.429257i | −0.823338 | − | 0.567551i | \(-0.807891\pi\) |
0.0798443 | + | 0.996807i | \(0.474558\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −316.290 | + | 547.831i | −0.478503 | + | 0.828791i | −0.999696 | − | 0.0246476i | \(-0.992154\pi\) |
0.521194 | + | 0.853438i | \(0.325487\pi\) | |||||||
\(662\) | 65.4793 | − | 160.142i | 0.0989114 | − | 0.241907i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 86.8328 | + | 64.7615i | 0.130772 | + | 0.0975325i | ||||
\(665\) | −364.686 | −0.548401 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 738.615i | − | 1.10737i | ||||||
\(668\) | 565.092 | − | 575.494i | 0.845946 | − | 0.861517i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 162.875 | − | 398.344i | 0.243098 | − | 0.594543i | ||||
\(671\) | −49.3470 | − | 28.4905i | −0.0735424 | − | 0.0424597i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 536.330 | + | 928.950i | 0.796924 | + | 1.38031i | 0.921610 | + | 0.388116i | \(0.126874\pi\) |
−0.124687 | + | 0.992196i | \(0.539793\pi\) | |||||||
\(674\) | −86.6071 | − | 635.444i | −0.128497 | − | 0.942795i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −149.666 | + | 41.5692i | −0.221399 | + | 0.0614929i | ||||
\(677\) | 239.399 | + | 414.651i | 0.353617 | + | 0.612483i | 0.986880 | − | 0.161454i | \(-0.0516182\pi\) |
−0.633263 | + | 0.773937i | \(0.718285\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1135.45 | + | 655.553i | 1.67224 | + | 0.965468i | ||||
\(680\) | −1052.71 | − | 123.968i | −1.54811 | − | 0.182307i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 183.344 | − | 142.017i | 0.268832 | − | 0.208237i | ||||
\(683\) | 318.418i | 0.466206i | 0.972452 | + | 0.233103i | \(0.0748879\pi\) | ||||
−0.972452 | + | 0.233103i | \(0.925112\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −41.1672 | −0.0600981 | ||||||||
\(686\) | −94.8059 | − | 122.394i | −0.138201 | − | 0.178417i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 801.994 | − | 14.6286i | 1.16569 | − | 0.0212625i | ||||
\(689\) | 596.061 | − | 1032.41i | 0.865111 | − | 1.49842i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 971.076 | − | 560.651i | 1.40532 | − | 0.811362i | 0.410388 | − | 0.911911i | \(-0.365393\pi\) |
0.994932 | + | 0.100550i | \(0.0320601\pi\) | |||||||
\(692\) | 356.697 | − | 99.0716i | 0.515458 | − | 0.143167i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1337.15 | − | 182.246i | 1.92674 | − | 0.262602i | ||||
\(695\) | 978.068 | − | 564.688i | 1.40729 | − | 0.812501i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −77.3251 | + | 133.931i | −0.110940 | + | 0.192153i | ||||
\(698\) | 284.937 | + | 116.506i | 0.408220 | + | 0.166914i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −792.428 | + | 807.014i | −1.13204 | + | 1.15288i | ||||
\(701\) | 413.437 | 0.589782 | 0.294891 | − | 0.955531i | \(-0.404717\pi\) | ||||
0.294891 | + | 0.955531i | \(0.404717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 33.3406i | − | 0.0474262i | ||||||
\(704\) | 100.654 | − | 421.441i | 0.142975 | − | 0.598638i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1153.74 | − | 471.743i | −1.63419 | − | 0.668191i | ||||
\(707\) | 800.316 | + | 462.062i | 1.13199 | + | 0.653554i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 341.457 | + | 591.422i | 0.481604 | + | 0.834163i | 0.999777 | − | 0.0211129i | \(-0.00672093\pi\) |
−0.518173 | + | 0.855276i | \(0.673388\pi\) | |||||||
\(710\) | 1662.39 | − | 226.574i | 2.34140 | − | 0.319118i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −56.5836 | − | 131.488i | −0.0794713 | − | 0.184675i | ||||
\(713\) | −213.551 | − | 369.881i | −0.299510 | − | 0.518767i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 625.909 | + | 361.369i | 0.875397 | + | 0.505411i | ||||
\(716\) | −16.6093 | − | 4.28851i | −0.0231974 | − | 0.00598954i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 196.377 | + | 253.522i | 0.273505 | + | 0.353094i | ||||
\(719\) | 286.374i | 0.398295i | 0.979970 | + | 0.199148i | \(0.0638173\pi\) | ||||
−0.979970 | + | 0.199148i | \(0.936183\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −402.659 | −0.558474 | ||||||||
\(722\) | −528.100 | + | 409.065i | −0.731441 | + | 0.566572i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −289.748 | + | 1122.19i | −0.400204 | + | 1.54998i | ||||
\(725\) | 441.819 | − | 765.253i | 0.609406 | − | 1.05552i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −279.659 | + | 161.461i | −0.384676 | + | 0.222093i | −0.679851 | − | 0.733351i | \(-0.737955\pi\) |
0.295175 | + | 0.955443i | \(0.404622\pi\) | |||||||
\(728\) | 1004.09 | − | 432.090i | 1.37924 | − | 0.593531i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.33437 | + | 31.8016i | 0.00593749 | + | 0.0435639i | ||||
\(731\) | 776.863 | − | 448.522i | 1.06274 | − | 0.613573i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 260.915 | − | 451.918i | 0.355955 | − | 0.616532i | −0.631326 | − | 0.775517i | \(-0.717489\pi\) |
0.987281 | + | 0.158986i | \(0.0508224\pi\) | |||||||
\(734\) | −215.412 | + | 526.831i | −0.293476 | + | 0.717754i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −744.000 | − | 288.486i | −1.01087 | − | 0.391964i | ||||
\(737\) | 196.734 | 0.266939 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 965.020i | − | 1.30585i | −0.757424 | − | 0.652923i | \(-0.773542\pi\) | ||
0.757424 | − | 0.652923i | \(-0.226458\pi\) | |||||||
\(740\) | −135.607 | − | 133.156i | −0.183253 | − | 0.179940i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −593.252 | + | 1450.91i | −0.799531 | + | 1.95541i | ||||
\(743\) | 950.317 | + | 548.666i | 1.27903 | + | 0.738447i | 0.976669 | − | 0.214748i | \(-0.0688930\pi\) |
0.302357 | + | 0.953195i | \(0.402226\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −507.161 | − | 878.429i | −0.680753 | − | 1.17910i | ||||
\(746\) | −81.4106 | − | 597.317i | −0.109130 | − | 0.800693i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −129.678 | − | 466.892i | −0.173366 | − | 0.624188i | ||||
\(749\) | 460.939 | + | 798.370i | 0.615406 | + | 1.06591i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1196.02 | − | 690.524i | −1.59257 | − | 0.919472i | −0.992864 | − | 0.119255i | \(-0.961950\pi\) |
−0.599709 | − | 0.800218i | \(-0.704717\pi\) | |||||||
\(752\) | −832.142 | + | 15.1785i | −1.10657 | + | 0.0201842i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −675.161 | + | 522.977i | −0.895439 | + | 0.693604i | ||||
\(755\) | 577.494i | 0.764892i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −516.252 | −0.681971 | −0.340986 | − | 0.940068i | \(-0.610761\pi\) | ||||
−0.340986 | + | 0.940068i | \(0.610761\pi\) | |||||||
\(758\) | 304.406 | + | 392.987i | 0.401591 | + | 0.518452i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 36.0000 | − | 305.704i | 0.0473684 | − | 0.402242i | ||||
\(761\) | 608.092 | − | 1053.25i | 0.799069 | − | 1.38403i | −0.121154 | − | 0.992634i | \(-0.538659\pi\) |
0.920223 | − | 0.391394i | \(-0.128007\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −794.823 | + | 458.892i | −1.04171 | + | 0.601431i | ||||
\(764\) | −99.1668 | − | 357.040i | −0.129799 | − | 0.467329i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −967.319 | + | 131.840i | −1.26282 | + | 0.172114i | ||||
\(767\) | −1045.30 | + | 603.502i | −1.36284 | + | 0.786835i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −502.163 | + | 869.771i | −0.653007 | + | 1.13104i | 0.329382 | + | 0.944197i | \(0.393160\pi\) |
−0.982389 | + | 0.186845i | \(0.940174\pi\) | |||||||
\(770\) | −879.632 | − | 359.665i | −1.14238 | − | 0.467098i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −694.015 | − | 681.471i | −0.898983 | − | 0.882735i | ||||
\(773\) | −382.580 | −0.494929 | −0.247464 | − | 0.968897i | \(-0.579597\pi\) | ||||
−0.247464 | + | 0.968897i | \(0.579597\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 510.960i | − | 0.659304i | ||||||
\(776\) | −661.614 | + | 887.097i | −0.852595 | + | 1.14317i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −769.866 | − | 314.784i | −0.989545 | − | 0.404607i | ||||
\(779\) | −38.8931 | − | 22.4549i | −0.0499269 | − | 0.0288253i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 383.489 | + | 664.223i | 0.491023 | + | 0.850477i | ||||
\(782\) | −884.223 | + | 120.514i | −1.13072 | + | 0.154110i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −559.745 | + | 336.927i | −0.713960 | + | 0.429754i | ||||
\(785\) | −267.185 | − | 462.777i | −0.340362 | − | 0.589525i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 413.327 | + | 238.634i | 0.525193 | + | 0.303220i | 0.739057 | − | 0.673643i | \(-0.235272\pi\) |
−0.213864 | + | 0.976863i | \(0.568605\pi\) | |||||||
\(788\) | 139.432 | − | 540.020i | 0.176945 | − | 0.685304i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1355.70 | + | 1750.20i | 1.71607 | + | 2.21544i | ||||
\(791\) | − | 368.411i | − | 0.465754i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 121.334 | 0.153007 | ||||||||
\(794\) | 1060.67 | − | 821.591i | 1.33586 | − | 1.03475i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 429.875 | + | 110.993i | 0.540044 | + | 0.139439i | ||||
\(797\) | −257.304 | + | 445.663i | −0.322840 | + | 0.559176i | −0.981073 | − | 0.193639i | \(-0.937971\pi\) |
0.658233 | + | 0.752815i | \(0.271304\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −806.067 | + | 465.383i | −1.00884 | + | 0.582456i | ||||
\(800\) | −598.268 | − | 743.930i | −0.747835 | − | 0.929913i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −30.9907 | − | 227.381i | −0.0386417 | − | 0.283518i | ||||
\(803\) | −12.7066 | + | 7.33616i | −0.0158239 | + | 0.00913594i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −875.076 | + | 1515.68i | −1.08705 | + | 1.88283i | ||||
\(806\) | −186.899 | + | 457.099i | −0.231885 | + | 0.567120i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −466.334 | + | 625.265i | −0.577146 | + | 0.773843i | ||||
\(809\) | −1463.74 | −1.80932 | −0.904662 | − | 0.426129i | \(-0.859877\pi\) | ||||
−0.904662 | + | 0.426129i | \(0.859877\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1163.05i | 1.43410i | 0.697023 | + | 0.717049i | \(0.254508\pi\) | ||||
−0.697023 | + | 0.717049i | \(0.745492\pi\) | |||||||
\(812\) | 786.767 | − | 801.249i | 0.968925 | − | 0.986759i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 32.8816 | − | 80.4184i | 0.0403951 | − | 0.0987941i | ||||
\(815\) | 362.830 | + | 209.480i | 0.445190 | + | 0.257030i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 130.249 | + | 225.598i | 0.159424 | + | 0.276130i | ||||
\(818\) | 39.6147 | + | 290.656i | 0.0484287 | + | 0.355326i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −246.663 | + | 68.5098i | −0.300808 | + | 0.0835486i | ||||
\(821\) | 196.276 | + | 339.961i | 0.239070 | + | 0.414081i | 0.960448 | − | 0.278461i | \(-0.0898242\pi\) |
−0.721378 | + | 0.692542i | \(0.756491\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1081.53 | − | 624.422i | −1.31413 | − | 0.758714i | −0.331354 | − | 0.943507i | \(-0.607505\pi\) |
−0.982778 | + | 0.184792i | \(0.940839\pi\) | |||||||
\(824\) | 39.7485 | − | 337.536i | 0.0482385 | − | 0.409631i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1254.70 | − | 971.886i | 1.51901 | − | 1.17662i | ||||
\(827\) | 1369.15i | 1.65557i | 0.561049 | + | 0.827783i | \(0.310398\pi\) | ||||
−0.561049 | + | 0.827783i | \(0.689602\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −73.7477 | −0.0889598 | −0.0444799 | − | 0.999010i | \(-0.514163\pi\) | ||||
−0.0444799 | + | 0.999010i | \(0.514163\pi\) | |||||||
\(830\) | 122.800 | + | 158.534i | 0.147952 | + | 0.191005i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 263.088 | + | 884.346i | 0.316212 | + | 1.06292i | ||||
\(833\) | −365.317 | + | 632.748i | −0.438556 | + | 0.759601i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1293.07 | − | 746.554i | 1.54859 | − | 0.894077i | ||||
\(836\) | 135.584 | − | 37.6581i | 0.162182 | − | 0.0450455i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1063.91 | − | 145.004i | 1.26958 | − | 0.173036i | ||||
\(839\) | −1039.73 | + | 600.286i | −1.23924 | + | 0.715478i | −0.968940 | − | 0.247297i | \(-0.920458\pi\) |
−0.270305 | + | 0.962775i | \(0.587124\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.1625 | + | 31.4584i | −0.0215963 | + | 0.0374060i | ||||
\(842\) | −680.166 | − | 278.108i | −0.807799 | − | 0.330294i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 742.933 | − | 756.608i | 0.880252 | − | 0.896455i | ||||
\(845\) | −287.554 | −0.340300 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 712.406i | 0.841094i | ||||||||
\(848\) | −1157.69 | − | 640.530i | −1.36520 | − | 0.755342i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −988.200 | − | 404.057i | −1.16259 | − | 0.475361i | ||||
\(851\) | −138.567 | − | 80.0018i | −0.162829 | − | 0.0940092i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 219.539 | + | 380.254i | 0.257373 | + | 0.445784i | 0.965537 | − | 0.260264i | \(-0.0838097\pi\) |
−0.708164 | + | 0.706048i | \(0.750476\pi\) | |||||||
\(854\) | −158.080 | + | 21.5454i | −0.185106 | + | 0.0252288i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −714.748 | + | 307.578i | −0.834986 | + | 0.359321i | ||||
\(857\) | −255.481 | − | 442.506i | −0.298111 | − | 0.516344i | 0.677593 | − | 0.735437i | \(-0.263023\pi\) |
−0.975704 | + | 0.219094i | \(0.929690\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 153.093 | + | 88.3882i | 0.178222 | + | 0.102897i | 0.586457 | − | 0.809980i | \(-0.300522\pi\) |
−0.408235 | + | 0.912877i | \(0.633856\pi\) | |||||||
\(860\) | 1437.77 | + | 371.230i | 1.67182 | + | 0.431663i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 900.620 | + | 1162.70i | 1.04480 | + | 1.34883i | ||||
\(863\) | 1028.28i | 1.19152i | 0.803163 | + | 0.595759i | \(0.203149\pi\) | ||||
−0.803163 | + | 0.595759i | \(0.796851\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 685.325 | 0.792283 | ||||||||
\(866\) | −1209.83 | + | 937.127i | −1.39703 | + | 1.08213i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 162.334 | − | 628.718i | 0.187021 | − | 0.724330i | ||||
\(869\) | −506.022 | + | 876.456i | −0.582304 | + | 1.00858i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −362.798 | + | 209.462i | −0.416530 | + | 0.240484i | ||||
\(872\) | −306.212 | − | 711.573i | −0.351161 | − | 0.816024i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −34.9969 | − | 256.775i | −0.0400422 | − | 0.293793i | ||||
\(875\) | −293.744 | + | 169.593i | −0.335707 | + | 0.193821i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 470.457 | − | 814.856i | 0.536439 | − | 0.929140i | −0.462653 | − | 0.886540i | \(-0.653102\pi\) |
0.999092 | − | 0.0426008i | \(-0.0135644\pi\) | |||||||
\(878\) | 35.1101 | − | 85.8686i | 0.0399887 | − | 0.0978003i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 388.328 | − | 701.861i | 0.441282 | − | 0.797570i | ||||
\(881\) | 1065.75 | 1.20970 | 0.604851 | − | 0.796339i | \(-0.293233\pi\) | ||||
0.604851 | + | 0.796339i | \(0.293233\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1001.97i | 1.13474i | 0.823464 | + | 0.567368i | \(0.192038\pi\) | ||||
−0.823464 | + | 0.567368i | \(0.807962\pi\) | |||||||
\(884\) | 736.236 | + | 722.929i | 0.832846 | + | 0.817793i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −105.738 | + | 258.604i | −0.119344 | + | 0.291878i | ||||
\(887\) | 583.774 | + | 337.042i | 0.658144 | + | 0.379980i | 0.791569 | − | 0.611079i | \(-0.209264\pi\) |
−0.133426 | + | 0.991059i | \(0.542598\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 469.240 | + | 812.747i | 0.527829 | + | 0.914227i | ||||
\(890\) | −35.7866 | − | 262.569i | −0.0402097 | − | 0.295022i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −340.328 | − | 1225.32i | −0.381534 | − | 1.37367i | ||||
\(893\) | −135.146 | − | 234.079i | −0.151339 | − | 0.262126i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.5016 | − | 15.8780i | −0.0307280 | − | 0.0177408i | ||||
\(896\) | −499.797 | − | 1105.45i | −0.557810 | − | 1.23376i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 422.383 | − | 327.177i | 0.470360 | − | 0.364339i | ||||
\(899\) | 507.310i | 0.564305i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1479.63 | −1.64221 | ||||||||
\(902\) | −71.6652 | − | 92.5194i | −0.0794514 | − | 0.102571i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 308.827 | + | 36.3677i | 0.341622 | + | 0.0402297i | ||||
\(905\) | −1072.78 | + | 1858.11i | −1.18539 | + | 2.05316i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1023.16 | + | 590.723i | −1.12807 | + | 0.651293i | −0.943450 | − | 0.331516i | \(-0.892440\pi\) |
−0.184624 | + | 0.982809i | \(0.559107\pi\) | |||||||
\(908\) | 266.938 | + | 961.083i | 0.293985 | + | 1.05846i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2005.06 | − | 273.278i | 2.20337 | − | 0.300305i | ||||
\(911\) | 1207.61 | − | 697.213i | 1.32559 | − | 0.765328i | 0.340973 | − | 0.940073i | \(-0.389244\pi\) |
0.984614 | + | 0.174746i | \(0.0559103\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.8359 | + | 79.3901i | −0.0502036 | + | 0.0869553i | ||||
\(914\) | 440.277 | + | 180.021i | 0.481704 | + | 0.196960i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 434.778 | + | 426.920i | 0.474648 | + | 0.466070i | ||||
\(917\) | 513.346 | 0.559811 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 210.163i | 0.228686i | 0.993441 | + | 0.114343i | \(0.0364763\pi\) | ||||
−0.993441 | + | 0.114343i | \(0.963524\pi\) | |||||||
\(920\) | −1184.16 | − | 883.166i | −1.28713 | − | 0.959963i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 552.869 | + | 226.058i | 0.599641 | + | 0.245182i | ||||
\(923\) | −1414.39 | − | 816.596i | −1.53238 | − | 0.884719i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −95.7098 | − | 165.774i | −0.103470 | − | 0.179215i | ||||
\(926\) | −970.101 | + | 132.219i | −1.04763 | + | 0.142785i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 593.994 | + | 738.615i | 0.640080 | + | 0.795921i | ||||
\(929\) | −83.2996 | − | 144.279i | −0.0896659 | − | 0.155306i | 0.817704 | − | 0.575639i | \(-0.195247\pi\) |
−0.907370 | + | 0.420333i | \(0.861913\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −183.748 | − | 106.087i | −0.197366 | − | 0.113949i | ||||
\(932\) | 346.793 | − | 1343.12i | 0.372096 | − | 1.44112i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −556.377 | − | 718.280i | −0.595693 | − | 0.769036i | ||||
\(935\) | − | 897.044i | − | 0.959405i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 251.158 | 0.268045 | 0.134022 | − | 0.990978i | \(-0.457211\pi\) | ||||
0.134022 | + | 0.990978i | \(0.457211\pi\) | |||||||
\(938\) | 435.476 | − | 337.319i | 0.464261 | − | 0.359615i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1491.82 | − | 385.186i | −1.58704 | − | 0.409772i | ||||
\(941\) | 407.282 | − | 705.433i | 0.432818 | − | 0.749663i | −0.564296 | − | 0.825572i | \(-0.690853\pi\) |
0.997115 | + | 0.0759090i | \(0.0241858\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −186.650 | + | 107.762i | −0.197932 | + | 0.114276i | ||||
\(944\) | 690.841 | + | 1147.71i | 0.731823 | + | 1.21580i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 91.6718 | + | 672.604i | 0.0969047 | + | 0.710998i | ||||
\(947\) | −513.020 | + | 296.192i | −0.541731 | + | 0.312769i | −0.745780 | − | 0.666192i | \(-0.767923\pi\) |
0.204049 | + | 0.978961i | \(0.434590\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.6215 | − | 27.0572i | 0.0164610 | − | 0.0285113i | ||||
\(950\) | 117.337 | − | 286.970i | 0.123512 | − | 0.302074i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1087.57 | − | 811.133i | −1.14241 | − | 0.852031i | ||||
\(953\) | 844.768 | 0.886430 | 0.443215 | − | 0.896415i | \(-0.353838\pi\) | ||||
0.443215 | + | 0.896415i | \(0.353838\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 685.983i | − | 0.718307i | ||||||
\(956\) | −291.560 | + | 296.927i | −0.304979 | + | 0.310593i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.73525 | − | 6.68958i | 0.00285517 | − | 0.00698286i | ||||
\(959\) | −45.6330 | − | 26.3462i | −0.0475839 | − | 0.0274726i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −333.825 | − | 578.202i | −0.347373 | − | 0.601667i | ||||
\(962\) | 24.9838 | + | 183.308i | 0.0259707 | + | 0.190549i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1086.19 | + | 301.686i | −1.12675 | + | 0.312952i | ||||
\(965\) | −900.305 | − | 1559.37i | −0.932959 | − | 1.61593i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −156.035 | − | 90.0867i | −0.161360 | − | 0.0931611i | 0.417146 | − | 0.908840i | \(-0.363030\pi\) |
−0.578505 | + | 0.815679i | \(0.696364\pi\) | |||||||
\(968\) | −597.186 | − | 70.3252i | −0.616928 | − | 0.0726500i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1619.61 | + | 1254.55i | −1.66970 | + | 1.29335i | ||||
\(971\) | − | 411.395i | − | 0.423682i | −0.977304 | − | 0.211841i | \(-0.932054\pi\) | ||
0.977304 | − | 0.211841i | \(-0.0679458\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1445.56 | 1.48567 | ||||||||
\(974\) | 1071.09 | + | 1382.77i | 1.09968 | + | 1.41968i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.45587 | − | 134.640i | −0.00251627 | − | 0.137951i | ||||
\(977\) | 878.125 | − | 1520.96i | 0.898797 | − | 1.55676i | 0.0697635 | − | 0.997564i | \(-0.477776\pi\) |
0.829034 | − | 0.559199i | \(-0.188891\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 104.912 | − | 60.5708i | 0.107162 | − | 0.0618701i | ||||
\(980\) | −1165.34 | + | 323.670i | −1.18912 | + | 0.330276i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1278.57 | + | 174.261i | −1.30201 | + | 0.177456i | ||||
\(983\) | −695.466 | + | 401.528i | −0.707494 | + | 0.408472i | −0.810132 | − | 0.586247i | \(-0.800605\pi\) |
0.102639 | + | 0.994719i | \(0.467271\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 516.243 | − | 894.159i | 0.524105 | − | 0.907776i | ||||
\(986\) | 981.140 | + | 401.170i | 0.995071 | + | 0.406866i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −209.936 | + | 213.800i | −0.212486 | + | 0.216397i | ||||
\(989\) | 1250.15 | 1.26405 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 338.466i | 0.341540i | 0.985311 | + | 0.170770i | \(0.0546254\pi\) | ||||
−0.985311 | + | 0.170770i | \(0.945375\pi\) | |||||||
\(992\) | 511.008 | + | 198.143i | 0.515129 | + | 0.199741i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1987.73 | + | 812.747i | 1.99973 | + | 0.817653i | ||||
\(995\) | 711.783 | + | 410.948i | 0.715360 | + | 0.413013i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −295.906 | − | 512.523i | −0.296796 | − | 0.514066i | 0.678605 | − | 0.734503i | \(-0.262585\pi\) |
−0.975401 | + | 0.220438i | \(0.929251\pi\) | |||||||
\(998\) | 1119.33 | − | 152.558i | 1.12158 | − | 0.152864i | ||||
\(999\) | 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 | 324.3.f.p.271.2 | 8 | ||
3.2 | odd | 2 | inner | 324.3.f.p.271.3 | 8 | ||
4.3 | odd | 2 | 324.3.f.o.271.4 | 8 | |||
9.2 | odd | 6 | 324.3.f.o.55.1 | 8 | |||
9.4 | even | 3 | 108.3.d.d.55.3 | ✓ | 8 | ||
9.5 | odd | 6 | 108.3.d.d.55.6 | yes | 8 | ||
9.7 | even | 3 | 324.3.f.o.55.4 | 8 | |||
12.11 | even | 2 | 324.3.f.o.271.1 | 8 | |||
36.7 | odd | 6 | inner | 324.3.f.p.55.1 | 8 | ||
36.11 | even | 6 | inner | 324.3.f.p.55.4 | 8 | ||
36.23 | even | 6 | 108.3.d.d.55.5 | yes | 8 | ||
36.31 | odd | 6 | 108.3.d.d.55.4 | yes | 8 | ||
72.5 | odd | 6 | 1728.3.g.l.703.2 | 8 | |||
72.13 | even | 6 | 1728.3.g.l.703.8 | 8 | |||
72.59 | even | 6 | 1728.3.g.l.703.1 | 8 | |||
72.67 | odd | 6 | 1728.3.g.l.703.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.d.d.55.3 | ✓ | 8 | 9.4 | even | 3 | ||
108.3.d.d.55.4 | yes | 8 | 36.31 | odd | 6 | ||
108.3.d.d.55.5 | yes | 8 | 36.23 | even | 6 | ||
108.3.d.d.55.6 | yes | 8 | 9.5 | odd | 6 | ||
324.3.f.o.55.1 | 8 | 9.2 | odd | 6 | |||
324.3.f.o.55.4 | 8 | 9.7 | even | 3 | |||
324.3.f.o.271.1 | 8 | 12.11 | even | 2 | |||
324.3.f.o.271.4 | 8 | 4.3 | odd | 2 | |||
324.3.f.p.55.1 | 8 | 36.7 | odd | 6 | inner | ||
324.3.f.p.55.4 | 8 | 36.11 | even | 6 | inner | ||
324.3.f.p.271.2 | 8 | 1.1 | even | 1 | trivial | ||
324.3.f.p.271.3 | 8 | 3.2 | odd | 2 | inner | ||
1728.3.g.l.703.1 | 8 | 72.59 | even | 6 | |||
1728.3.g.l.703.2 | 8 | 72.5 | odd | 6 | |||
1728.3.g.l.703.7 | 8 | 72.67 | odd | 6 | |||
1728.3.g.l.703.8 | 8 | 72.13 | even | 6 |