Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,3,Mod(19,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 7, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.u (of order \(8\), degree \(4\), 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: | \(7.84743161358\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 91.4 | ||
Character | \(\chi\) | \(=\) | 288.91 |
Dual form | 288.3.u.a.19.4 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.108191 | − | 1.99707i | 0.0540954 | − | 0.998536i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.97659 | − | 0.432130i | −0.994147 | − | 0.108032i | ||||
\(5\) | 2.81639 | + | 1.16659i | 0.563278 | + | 0.233318i | 0.646108 | − | 0.763246i | \(-0.276396\pi\) |
−0.0828294 | + | 0.996564i | \(0.526396\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.23443 | + | 6.23443i | −0.890633 | + | 0.890633i | −0.994583 | − | 0.103950i | \(-0.966852\pi\) |
0.103950 | + | 0.994583i | \(0.466852\pi\) | |||||||
\(8\) | −1.29322 | + | 7.89478i | −0.161653 | + | 0.986848i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.63447 | − | 5.49832i | 0.263447 | − | 0.549832i | ||||
\(11\) | 8.06262 | + | 3.33965i | 0.732965 | + | 0.303604i | 0.717770 | − | 0.696280i | \(-0.245163\pi\) |
0.0151955 | + | 0.999885i | \(0.495163\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.3208 | − | 5.51766i | 1.02468 | − | 0.424436i | 0.193889 | − | 0.981023i | \(-0.437890\pi\) |
0.830789 | + | 0.556588i | \(0.187890\pi\) | |||||||
\(14\) | 11.7761 | + | 13.1251i | 0.841150 | + | 0.937508i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.6265 | + | 3.43680i | 0.976658 | + | 0.214800i | ||||
\(17\) | 4.56488i | 0.268522i | 0.990946 | + | 0.134261i | \(0.0428661\pi\) | ||||
−0.990946 | + | 0.134261i | \(0.957134\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13.4421 | + | 32.4522i | 0.707481 | + | 1.70801i | 0.706201 | + | 0.708011i | \(0.250407\pi\) |
0.00128016 | + | 0.999999i | \(0.499593\pi\) | |||||||
\(20\) | −10.6955 | − | 5.85609i | −0.534776 | − | 0.292804i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.54181 | − | 15.7403i | 0.342810 | − | 0.715469i | ||||
\(23\) | 6.75277 | + | 6.75277i | 0.293599 | + | 0.293599i | 0.838500 | − | 0.544901i | \(-0.183433\pi\) |
−0.544901 | + | 0.838500i | \(0.683433\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.1065 | − | 11.1065i | −0.444261 | − | 0.444261i | ||||
\(26\) | −9.57798 | − | 27.1996i | −0.368384 | − | 1.04614i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 27.4859 | − | 22.0977i | 0.981638 | − | 0.789203i | ||||
\(29\) | 0.266504 | + | 0.643399i | 0.00918981 | + | 0.0221862i | 0.928408 | − | 0.371563i | \(-0.121178\pi\) |
−0.919218 | + | 0.393749i | \(0.871178\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.326715i | − | 0.0105392i | −0.999986 | − | 0.00526959i | \(-0.998323\pi\) | ||
0.999986 | − | 0.00526959i | \(-0.00167737\pi\) | |||||||
\(32\) | 8.55419 | − | 30.8355i | 0.267318 | − | 0.963608i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.11639 | + | 0.493878i | 0.268129 | + | 0.0145258i | ||||
\(35\) | −24.8316 | + | 10.2856i | −0.709475 | + | 0.293874i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 31.5133 | + | 13.0532i | 0.851710 | + | 0.352790i | 0.765460 | − | 0.643484i | \(-0.222512\pi\) |
0.0862502 | + | 0.996274i | \(0.472512\pi\) | |||||||
\(38\) | 66.2637 | − | 23.3339i | 1.74378 | − | 0.614050i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.8522 | + | 20.7261i | −0.321305 | + | 0.518153i | ||||
\(41\) | −15.7509 | + | 15.7509i | −0.384169 | + | 0.384169i | −0.872601 | − | 0.488433i | \(-0.837569\pi\) |
0.488433 | + | 0.872601i | \(0.337569\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.83274 | + | 2.00179i | 0.112389 | + | 0.0465531i | 0.438170 | − | 0.898892i | \(-0.355627\pi\) |
−0.325780 | + | 0.945446i | \(0.605627\pi\) | |||||||
\(44\) | −30.6186 | − | 16.7645i | −0.695877 | − | 0.381011i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.2164 | − | 12.7552i | 0.309051 | − | 0.277287i | ||||
\(47\) | 49.7096 | 1.05765 | 0.528825 | − | 0.848731i | \(-0.322633\pi\) | ||||
0.528825 | + | 0.848731i | \(0.322633\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 28.7362i | − | 0.586454i | ||||||
\(50\) | −23.3822 | + | 20.9789i | −0.467643 | + | 0.419578i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −55.3558 | + | 16.1852i | −1.06453 | + | 0.311253i | ||||
\(53\) | −4.45882 | + | 10.7645i | −0.0841286 | + | 0.203105i | −0.960346 | − | 0.278812i | \(-0.910059\pi\) |
0.876217 | + | 0.481917i | \(0.160059\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18.8115 | + | 18.8115i | 0.342027 | + | 0.342027i | ||||
\(56\) | −41.1569 | − | 57.2820i | −0.734946 | − | 1.02289i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.31375 | − | 0.462619i | 0.0226508 | − | 0.00797618i | ||||
\(59\) | −13.1268 | + | 31.6909i | −0.222488 | + | 0.537134i | −0.995227 | − | 0.0975907i | \(-0.968886\pi\) |
0.772739 | + | 0.634724i | \(0.218886\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −35.4023 | − | 85.4687i | −0.580366 | − | 1.40113i | −0.892482 | − | 0.451083i | \(-0.851038\pi\) |
0.312116 | − | 0.950044i | \(-0.398962\pi\) | |||||||
\(62\) | −0.652473 | − | 0.0353475i | −0.0105238 | − | 0.000570122i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −60.6551 | − | 20.4194i | −0.947737 | − | 0.319054i | ||||
\(65\) | 43.9535 | 0.676207 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −41.3348 | + | 17.1214i | −0.616938 | + | 0.255544i | −0.669192 | − | 0.743090i | \(-0.733359\pi\) |
0.0522539 | + | 0.998634i | \(0.483359\pi\) | |||||||
\(68\) | 1.97262 | − | 18.1527i | 0.0290091 | − | 0.266951i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 17.8545 | + | 50.7033i | 0.255064 | + | 0.724333i | ||||
\(71\) | −37.6381 | + | 37.6381i | −0.530114 | + | 0.530114i | −0.920606 | − | 0.390492i | \(-0.872305\pi\) |
0.390492 | + | 0.920606i | \(0.372305\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −52.2302 | + | 52.2302i | −0.715482 | + | 0.715482i | −0.967677 | − | 0.252195i | \(-0.918848\pi\) |
0.252195 | + | 0.967677i | \(0.418848\pi\) | |||||||
\(74\) | 29.4777 | − | 61.5220i | 0.398347 | − | 0.831379i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −39.4303 | − | 134.858i | −0.518820 | − | 1.77445i | ||||
\(77\) | −71.0866 | + | 29.4450i | −0.923203 | + | 0.382403i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 26.9061 | 0.340583 | 0.170292 | − | 0.985394i | \(-0.445529\pi\) | ||||
0.170292 | + | 0.985394i | \(0.445529\pi\) | |||||||
\(80\) | 40.0011 | + | 27.9091i | 0.500014 | + | 0.348864i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 29.7516 | + | 33.1598i | 0.362824 | + | 0.404388i | ||||
\(83\) | −10.6315 | − | 25.6667i | −0.128090 | − | 0.309237i | 0.846804 | − | 0.531905i | \(-0.178524\pi\) |
−0.974894 | + | 0.222667i | \(0.928524\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.32533 | + | 12.8565i | −0.0626510 | + | 0.151253i | ||||
\(86\) | 4.52057 | − | 9.43475i | 0.0525647 | − | 0.109706i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −36.7926 | + | 59.3337i | −0.418097 | + | 0.674247i | ||||
\(89\) | 103.292 | + | 103.292i | 1.16058 | + | 1.16058i | 0.984348 | + | 0.176234i | \(0.0563914\pi\) |
0.176234 | + | 0.984348i | \(0.443609\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −48.6482 | + | 117.447i | −0.534596 | + | 1.29063i | ||||
\(92\) | −23.9349 | − | 29.7711i | −0.260162 | − | 0.323599i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.37812 | − | 99.2736i | 0.0572140 | − | 1.05610i | ||||
\(95\) | 107.080i | 1.12715i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 77.9778 | 0.803895 | 0.401948 | − | 0.915663i | \(-0.368333\pi\) | ||||
0.401948 | + | 0.915663i | \(0.368333\pi\) | |||||||
\(98\) | −57.3883 | − | 3.10900i | −0.585595 | − | 0.0317245i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 39.3667 | + | 48.9656i | 0.393667 | + | 0.489656i | ||||
\(101\) | −104.064 | − | 43.1046i | −1.03033 | − | 0.426778i | −0.197500 | − | 0.980303i | \(-0.563282\pi\) |
−0.832833 | + | 0.553525i | \(0.813282\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −76.6571 | + | 76.6571i | −0.744243 | + | 0.744243i | −0.973392 | − | 0.229148i | \(-0.926406\pi\) |
0.229148 | + | 0.973392i | \(0.426406\pi\) | |||||||
\(104\) | 26.3339 | + | 112.301i | 0.253211 | + | 1.07981i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.0152 | + | 10.0692i | 0.198256 | + | 0.0949925i | ||||
\(107\) | 40.9728 | + | 16.9715i | 0.382923 | + | 0.158612i | 0.565837 | − | 0.824517i | \(-0.308553\pi\) |
−0.182914 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 102.183 | − | 42.3255i | 0.937456 | − | 0.388307i | 0.138954 | − | 0.990299i | \(-0.455626\pi\) |
0.798502 | + | 0.601992i | \(0.205626\pi\) | |||||||
\(110\) | 39.6032 | − | 35.5327i | 0.360029 | − | 0.323024i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −118.849 | + | 75.9960i | −1.06115 | + | 0.678536i | ||||
\(113\) | − | 123.602i | − | 1.09383i | −0.837190 | − | 0.546913i | \(-0.815803\pi\) | ||
0.837190 | − | 0.546913i | \(-0.184197\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.1408 | + | 26.8962i | 0.0968761 | + | 0.233880i | ||||
\(116\) | −0.781747 | − | 2.67370i | −0.00673920 | − | 0.0230491i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 61.8688 | + | 29.6438i | 0.524312 | + | 0.251219i | ||||
\(119\) | −28.4594 | − | 28.4594i | −0.239155 | − | 0.239155i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −31.7073 | − | 31.7073i | −0.262044 | − | 0.262044i | ||||
\(122\) | −174.517 | + | 61.4540i | −1.43047 | + | 0.503721i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.141183 | + | 1.29921i | −0.00113857 | + | 0.0104775i | ||||
\(125\) | −47.4883 | − | 114.647i | −0.379906 | − | 0.917175i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 133.213i | − | 1.04892i | −0.851434 | − | 0.524462i | \(-0.824266\pi\) | ||
0.851434 | − | 0.524462i | \(-0.175734\pi\) | |||||||
\(128\) | −47.3414 | + | 118.923i | −0.369855 | + | 0.929090i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.75536 | − | 87.7782i | 0.0365797 | − | 0.675217i | ||||
\(131\) | −228.056 | + | 94.4640i | −1.74089 | + | 0.721100i | −0.742185 | + | 0.670195i | \(0.766210\pi\) |
−0.998704 | + | 0.0509041i | \(0.983790\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −286.125 | − | 118.517i | −2.15132 | − | 0.891104i | ||||
\(134\) | 29.7207 | + | 84.4010i | 0.221796 | + | 0.629858i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −36.0387 | − | 5.90341i | −0.264991 | − | 0.0434075i | ||||
\(137\) | 111.817 | − | 111.817i | 0.816180 | − | 0.816180i | −0.169372 | − | 0.985552i | \(-0.554174\pi\) |
0.985552 | + | 0.169372i | \(0.0541739\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 31.7750 | + | 13.1616i | 0.228597 | + | 0.0946880i | 0.494042 | − | 0.869438i | \(-0.335519\pi\) |
−0.265445 | + | 0.964126i | \(0.585519\pi\) | |||||||
\(140\) | 103.190 | − | 30.1711i | 0.737070 | − | 0.215508i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 71.0939 | + | 79.2381i | 0.500661 | + | 0.558015i | ||||
\(143\) | 125.828 | 0.879914 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.12296i | 0.0146411i | ||||||||
\(146\) | 98.6566 | + | 109.958i | 0.675730 | + | 0.753138i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −119.675 | − | 65.5251i | −0.808613 | − | 0.442737i | ||||
\(149\) | 108.344 | − | 261.565i | 0.727140 | − | 1.75547i | 0.0752422 | − | 0.997165i | \(-0.476027\pi\) |
0.651898 | − | 0.758307i | \(-0.273973\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 51.5292 | + | 51.5292i | 0.341253 | + | 0.341253i | 0.856838 | − | 0.515585i | \(-0.172425\pi\) |
−0.515585 | + | 0.856838i | \(0.672425\pi\) | |||||||
\(152\) | −273.587 | + | 64.1548i | −1.79991 | + | 0.422071i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 51.1129 | + | 145.151i | 0.331902 | + | 0.942538i | ||||
\(155\) | 0.381142 | − | 0.920157i | 0.00245898 | − | 0.00593650i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 39.3450 | + | 94.9872i | 0.250605 | + | 0.605014i | 0.998253 | − | 0.0590811i | \(-0.0188171\pi\) |
−0.747648 | + | 0.664095i | \(0.768817\pi\) | |||||||
\(158\) | 2.91099 | − | 53.7334i | 0.0184240 | − | 0.340085i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 60.0642 | − | 76.8655i | 0.375401 | − | 0.480410i | ||||
\(161\) | −84.1994 | −0.522978 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.97467 | + | 2.06057i | −0.0305194 | + | 0.0126416i | −0.397891 | − | 0.917433i | \(-0.630258\pi\) |
0.367372 | + | 0.930074i | \(0.380258\pi\) | |||||||
\(164\) | 69.4413 | − | 55.8285i | 0.423423 | − | 0.340417i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −52.4085 | + | 18.4550i | −0.315714 | + | 0.111174i | ||||
\(167\) | 165.012 | − | 165.012i | 0.988097 | − | 0.988097i | −0.0118333 | − | 0.999930i | \(-0.503767\pi\) |
0.999930 | + | 0.0118333i | \(0.00376674\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.4985 | − | 27.4985i | 0.162713 | − | 0.162713i | ||||
\(170\) | 25.0992 | + | 12.0260i | 0.147642 | + | 0.0707413i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −18.3528 | − | 10.0486i | −0.106702 | − | 0.0584224i | ||||
\(173\) | 115.760 | − | 47.9493i | 0.669132 | − | 0.277163i | −0.0221438 | − | 0.999755i | \(-0.507049\pi\) |
0.691275 | + | 0.722591i | \(0.257049\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 138.486 | 0.791348 | ||||||||
\(176\) | 114.513 | + | 79.8967i | 0.650642 | + | 0.453959i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 217.456 | − | 195.106i | 1.22166 | − | 1.09610i | ||||
\(179\) | 44.8368 | + | 108.246i | 0.250485 | + | 0.604724i | 0.998243 | − | 0.0592467i | \(-0.0188699\pi\) |
−0.747758 | + | 0.663971i | \(0.768870\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 80.3652 | − | 194.019i | 0.444007 | − | 1.07193i | −0.530524 | − | 0.847670i | \(-0.678005\pi\) |
0.974530 | − | 0.224256i | \(-0.0719953\pi\) | |||||||
\(182\) | 229.287 | + | 109.861i | 1.25982 | + | 0.603630i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −62.0445 | + | 44.5788i | −0.337198 | + | 0.242276i | ||||
\(185\) | 73.5260 | + | 73.5260i | 0.397438 | + | 0.397438i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.2451 | + | 36.8049i | −0.0815245 | + | 0.196818i | ||||
\(188\) | −197.675 | − | 21.4810i | −1.05146 | − | 0.114261i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 213.846 | + | 11.5850i | 1.12550 | + | 0.0609738i | ||||
\(191\) | − | 338.117i | − | 1.77025i | −0.465357 | − | 0.885123i | \(-0.654074\pi\) | ||
0.465357 | − | 0.885123i | \(-0.345926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 234.508 | 1.21507 | 0.607533 | − | 0.794295i | \(-0.292159\pi\) | ||||
0.607533 | + | 0.794295i | \(0.292159\pi\) | |||||||
\(194\) | 8.43648 | − | 155.727i | 0.0434870 | − | 0.802718i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.4178 | + | 114.272i | −0.0633560 | + | 0.583022i | ||||
\(197\) | −237.007 | − | 98.1713i | −1.20308 | − | 0.498332i | −0.311086 | − | 0.950382i | \(-0.600693\pi\) |
−0.891993 | + | 0.452050i | \(0.850693\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 39.2172 | − | 39.2172i | 0.197071 | − | 0.197071i | −0.601672 | − | 0.798743i | \(-0.705499\pi\) |
0.798743 | + | 0.601672i | \(0.205499\pi\) | |||||||
\(200\) | 102.047 | − | 73.3204i | 0.510234 | − | 0.366602i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −97.3416 | + | 203.159i | −0.481889 | + | 1.00574i | ||||
\(203\) | −5.67273 | − | 2.34972i | −0.0279445 | − | 0.0115750i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −62.7356 | + | 25.9859i | −0.306027 | + | 0.126761i | ||||
\(206\) | 144.796 | + | 161.383i | 0.702894 | + | 0.783414i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 227.121 | − | 40.4409i | 1.09193 | − | 0.194427i | ||||
\(209\) | 306.542i | 1.46671i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −79.9026 | − | 192.902i | −0.378685 | − | 0.914227i | −0.992213 | − | 0.124554i | \(-0.960250\pi\) |
0.613528 | − | 0.789673i | \(-0.289750\pi\) | |||||||
\(212\) | 22.3826 | − | 40.8794i | 0.105578 | − | 0.192827i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 38.3261 | − | 79.9894i | 0.179094 | − | 0.373782i | ||||
\(215\) | 11.2756 | + | 11.2756i | 0.0524448 | + | 0.0524448i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.03688 | + | 2.03688i | 0.00938655 | + | 0.00938655i | ||||
\(218\) | −73.4718 | − | 208.645i | −0.337026 | − | 0.957089i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −66.6766 | − | 82.9346i | −0.303076 | − | 0.376976i | ||||
\(221\) | 25.1875 | + | 60.8079i | 0.113970 | + | 0.275149i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 344.421i | − | 1.54449i | −0.635326 | − | 0.772244i | \(-0.719134\pi\) | ||
0.635326 | − | 0.772244i | \(-0.280866\pi\) | |||||||
\(224\) | 138.911 | + | 245.572i | 0.620139 | + | 1.09630i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −246.843 | − | 13.3726i | −1.09222 | − | 0.0591709i | ||||
\(227\) | −68.2639 | + | 28.2758i | −0.300722 | + | 0.124563i | −0.527942 | − | 0.849280i | \(-0.677036\pi\) |
0.227220 | + | 0.973843i | \(0.427036\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −41.8202 | − | 17.3225i | −0.182621 | − | 0.0756440i | 0.289499 | − | 0.957178i | \(-0.406511\pi\) |
−0.472120 | + | 0.881534i | \(0.656511\pi\) | |||||||
\(230\) | 54.9189 | − | 19.3390i | 0.238778 | − | 0.0840824i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.42414 | + | 1.27194i | −0.0233799 | + | 0.00548248i | ||||
\(233\) | −203.044 | + | 203.044i | −0.871432 | + | 0.871432i | −0.992629 | − | 0.121197i | \(-0.961327\pi\) |
0.121197 | + | 0.992629i | \(0.461327\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 140.002 | + | 57.9906i | 0.595752 | + | 0.246768i | ||||
\(236\) | 65.8944 | − | 120.349i | 0.279214 | − | 0.509954i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −59.9146 | + | 53.7565i | −0.251742 | + | 0.225868i | ||||
\(239\) | −87.6710 | −0.366824 | −0.183412 | − | 0.983036i | \(-0.558714\pi\) | ||||
−0.183412 | + | 0.983036i | \(0.558714\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 15.4754i | − | 0.0642135i | −0.999484 | − | 0.0321067i | \(-0.989778\pi\) | ||
0.999484 | − | 0.0321067i | \(-0.0102216\pi\) | |||||||
\(242\) | −66.7522 | + | 59.8913i | −0.275836 | + | 0.247485i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 103.847 | + | 355.172i | 0.425602 | + | 1.45562i | ||||
\(245\) | 33.5233 | − | 80.9325i | 0.136830 | − | 0.330337i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 358.121 | + | 358.121i | 1.44988 | + | 1.44988i | ||||
\(248\) | 2.57934 | + | 0.422516i | 0.0104006 | + | 0.00170369i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −234.096 | + | 82.4338i | −0.936383 | + | 0.329735i | ||||
\(251\) | −95.9530 | + | 231.651i | −0.382283 | + | 0.922913i | 0.609241 | + | 0.792985i | \(0.291474\pi\) |
−0.991524 | + | 0.129927i | \(0.958526\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.8932 | + | 76.9969i | 0.126060 | + | 0.304336i | ||||
\(254\) | −266.037 | − | 14.4125i | −1.04739 | − | 0.0567420i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 232.377 | + | 107.411i | 0.907722 | + | 0.419573i | ||||
\(257\) | 131.142 | 0.510282 | 0.255141 | − | 0.966904i | \(-0.417878\pi\) | ||||
0.255141 | + | 0.966904i | \(0.417878\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −277.847 | + | 115.088i | −1.07277 | + | 0.444355i | ||||
\(260\) | −174.785 | − | 18.9936i | −0.672250 | − | 0.0730523i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 163.978 | + | 465.665i | 0.625870 | + | 1.77735i | ||||
\(263\) | 281.350 | − | 281.350i | 1.06977 | − | 1.06977i | 0.0723955 | − | 0.997376i | \(-0.476936\pi\) |
0.997376 | − | 0.0723955i | \(-0.0230644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.1156 | + | 25.1156i | −0.0947757 | + | 0.0947757i | ||||
\(266\) | −267.643 | + | 558.590i | −1.00618 | + | 2.09996i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 171.770 | − | 50.2230i | 0.640934 | − | 0.187399i | ||||
\(269\) | −133.290 | + | 55.2107i | −0.495503 | + | 0.205244i | −0.616419 | − | 0.787419i | \(-0.711417\pi\) |
0.120915 | + | 0.992663i | \(0.461417\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −368.673 | −1.36042 | −0.680208 | − | 0.733019i | \(-0.738111\pi\) | ||||
−0.680208 | + | 0.733019i | \(0.738111\pi\) | |||||||
\(272\) | −15.6886 | + | 71.3332i | −0.0576787 | + | 0.262255i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −211.208 | − | 235.404i | −0.770834 | − | 0.859137i | ||||
\(275\) | −52.4559 | − | 126.640i | −0.190749 | − | 0.460508i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.6001 | − | 52.1472i | 0.0779786 | − | 0.188257i | −0.880083 | − | 0.474821i | \(-0.842513\pi\) |
0.958061 | + | 0.286564i | \(0.0925130\pi\) | |||||||
\(278\) | 29.7225 | − | 62.0329i | 0.106915 | − | 0.223140i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −49.0896 | − | 209.342i | −0.175320 | − | 0.747649i | ||||
\(281\) | −85.0605 | − | 85.0605i | −0.302706 | − | 0.302706i | 0.539365 | − | 0.842072i | \(-0.318664\pi\) |
−0.842072 | + | 0.539365i | \(0.818664\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.0948 | − | 65.4127i | 0.0957414 | − | 0.231140i | −0.868752 | − | 0.495248i | \(-0.835077\pi\) |
0.964493 | + | 0.264107i | \(0.0850773\pi\) | |||||||
\(284\) | 165.936 | − | 133.407i | 0.584281 | − | 0.469742i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.6134 | − | 251.287i | 0.0475993 | − | 0.878626i | ||||
\(287\) | − | 196.396i | − | 0.684306i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 268.162 | 0.927896 | ||||||||
\(290\) | 4.23971 | + | 0.229685i | 0.0146197 | + | 0.000792018i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 230.268 | − | 185.128i | 0.788590 | − | 0.633999i | ||||
\(293\) | 321.033 | + | 132.976i | 1.09568 | + | 0.453844i | 0.855983 | − | 0.517005i | \(-0.172953\pi\) |
0.239694 | + | 0.970849i | \(0.422953\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −73.9404 | + | 73.9404i | −0.250645 | + | 0.250645i | ||||
\(296\) | −143.806 | + | 231.910i | −0.485831 | + | 0.783479i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −510.643 | − | 244.669i | −1.71357 | − | 0.821039i | ||||
\(299\) | 127.212 | + | 52.6929i | 0.425458 | + | 0.176231i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42.6094 | + | 17.6494i | −0.141559 | + | 0.0586358i | ||||
\(302\) | 108.483 | − | 97.3326i | 0.359214 | − | 0.322293i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 98.5222 | + | 553.313i | 0.324086 | + | 1.82011i | ||||
\(305\) | − | 282.013i | − | 0.924634i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −92.6973 | − | 223.791i | −0.301946 | − | 0.728961i | −0.999918 | − | 0.0128360i | \(-0.995914\pi\) |
0.697972 | − | 0.716125i | \(-0.254086\pi\) | |||||||
\(308\) | 295.406 | − | 86.3722i | 0.959112 | − | 0.280429i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.79638 | − | 0.860719i | −0.00579479 | − | 0.00277651i | ||||
\(311\) | 44.5768 | + | 44.5768i | 0.143334 | + | 0.143334i | 0.775133 | − | 0.631799i | \(-0.217683\pi\) |
−0.631799 | + | 0.775133i | \(0.717683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.9303 | − | 27.9303i | −0.0892343 | − | 0.0892343i | 0.661081 | − | 0.750315i | \(-0.270098\pi\) |
−0.750315 | + | 0.661081i | \(0.770098\pi\) | |||||||
\(314\) | 193.953 | − | 68.2980i | 0.617685 | − | 0.217510i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −106.994 | − | 11.6269i | −0.338590 | − | 0.0367940i | ||||
\(317\) | 125.850 | + | 303.829i | 0.397003 | + | 0.958450i | 0.988373 | + | 0.152049i | \(0.0485873\pi\) |
−0.591370 | + | 0.806400i | \(0.701413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.07751i | 0.0190518i | ||||||||
\(320\) | −147.008 | − | 128.269i | −0.459399 | − | 0.400840i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.10960 | + | 168.152i | −0.0282907 | + | 0.522212i | ||||
\(323\) | −148.140 | + | 61.3618i | −0.458639 | + | 0.189975i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −209.230 | − | 86.6660i | −0.643785 | − | 0.266665i | ||||
\(326\) | 3.57690 | + | 10.1577i | 0.0109721 | + | 0.0311586i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −103.981 | − | 144.719i | −0.317014 | − | 0.441218i | ||||
\(329\) | −309.911 | + | 309.911i | −0.941978 | + | 0.941978i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −169.515 | − | 70.2155i | −0.512131 | − | 0.212131i | 0.111626 | − | 0.993750i | \(-0.464394\pi\) |
−0.623756 | + | 0.781619i | \(0.714394\pi\) | |||||||
\(332\) | 31.1858 | + | 106.660i | 0.0939330 | + | 0.321265i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −311.688 | − | 347.394i | −0.933198 | − | 1.04010i | ||||
\(335\) | −136.389 | −0.407131 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 67.3116i | 0.199738i | 0.995001 | + | 0.0998689i | \(0.0318423\pi\) | ||||
−0.995001 | + | 0.0998689i | \(0.968158\pi\) | |||||||
\(338\) | −51.9414 | − | 57.8916i | −0.153673 | − | 0.171277i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 26.7323 | − | 48.8238i | 0.0786245 | − | 0.143599i | ||||
\(341\) | 1.09111 | − | 2.63418i | 0.00319974 | − | 0.00772486i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −126.333 | − | 126.333i | −0.368318 | − | 0.368318i | ||||
\(344\) | −22.0535 | + | 35.5646i | −0.0641089 | + | 0.103386i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −83.2340 | − | 236.368i | −0.240561 | − | 0.683145i | ||||
\(347\) | 107.157 | − | 258.699i | 0.308809 | − | 0.745530i | −0.690935 | − | 0.722916i | \(-0.742801\pi\) |
0.999744 | − | 0.0226140i | \(-0.00719886\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 165.558 | + | 399.692i | 0.474378 | + | 1.14525i | 0.962209 | + | 0.272311i | \(0.0877881\pi\) |
−0.487831 | + | 0.872938i | \(0.662212\pi\) | |||||||
\(350\) | 14.9829 | − | 276.566i | 0.0428083 | − | 0.790189i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 171.949 | − | 220.047i | 0.488491 | − | 0.625133i | ||||
\(353\) | 574.524 | 1.62755 | 0.813773 | − | 0.581183i | \(-0.197410\pi\) | ||||
0.813773 | + | 0.581183i | \(0.197410\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −149.912 | + | 62.0955i | −0.422287 | + | 0.174917i | ||||
\(356\) | −366.114 | − | 455.385i | −1.02841 | − | 1.27917i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 221.025 | − | 77.8311i | 0.617389 | − | 0.217405i | ||||
\(359\) | −499.243 | + | 499.243i | −1.39065 | + | 1.39065i | −0.566782 | + | 0.823868i | \(0.691812\pi\) |
−0.823868 | + | 0.566782i | \(0.808188\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −617.189 | + | 617.189i | −1.70966 | + | 1.70966i | ||||
\(362\) | −378.774 | − | 181.486i | −1.04634 | − | 0.501343i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 244.206 | − | 446.017i | 0.670897 | − | 1.22532i | ||||
\(365\) | −208.032 | + | 86.1696i | −0.569950 | + | 0.236081i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 295.566 | 0.805357 | 0.402679 | − | 0.915341i | \(-0.368079\pi\) | ||||
0.402679 | + | 0.915341i | \(0.368079\pi\) | |||||||
\(368\) | 82.3144 | + | 128.730i | 0.223681 | + | 0.349811i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 154.792 | − | 138.882i | 0.418355 | − | 0.375356i | ||||
\(371\) | −39.3126 | − | 94.9090i | −0.105964 | − | 0.255819i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −133.878 | + | 323.209i | −0.358921 | + | 0.866512i | 0.636531 | + | 0.771251i | \(0.280369\pi\) |
−0.995452 | + | 0.0952612i | \(0.969631\pi\) | |||||||
\(374\) | 71.8526 | + | 34.4275i | 0.192119 | + | 0.0920521i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −64.2856 | + | 392.446i | −0.170972 | + | 1.04374i | ||||
\(377\) | 7.10011 | + | 7.10011i | 0.0188332 | + | 0.0188332i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 170.642 | − | 411.967i | 0.450244 | − | 1.08698i | −0.521986 | − | 0.852954i | \(-0.674809\pi\) |
0.972229 | − | 0.234030i | \(-0.0751915\pi\) | |||||||
\(380\) | 46.2722 | − | 425.811i | 0.121769 | − | 1.12056i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −675.244 | − | 36.5812i | −1.76765 | − | 0.0957622i | ||||
\(383\) | − | 254.902i | − | 0.665540i | −0.943008 | − | 0.332770i | \(-0.892017\pi\) | ||
0.943008 | − | 0.332770i | \(-0.107983\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −234.558 | −0.609242 | ||||||||
\(386\) | 25.3716 | − | 468.328i | 0.0657294 | − | 1.21329i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −310.086 | − | 33.6965i | −0.799190 | − | 0.0868467i | ||||
\(389\) | −687.246 | − | 284.667i | −1.76670 | − | 0.731791i | −0.995453 | − | 0.0952550i | \(-0.969633\pi\) |
−0.771247 | − | 0.636536i | \(-0.780367\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.8256 | + | 30.8256i | −0.0788379 | + | 0.0788379i | ||||
\(392\) | 226.866 | + | 37.1624i | 0.578741 | + | 0.0948020i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −221.697 | + | 462.698i | −0.562683 | + | 1.17436i | ||||
\(395\) | 75.7781 | + | 31.3883i | 0.191843 | + | 0.0794640i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −56.8981 | + | 23.5679i | −0.143320 | + | 0.0593651i | −0.453191 | − | 0.891414i | \(-0.649714\pi\) |
0.309871 | + | 0.950779i | \(0.399714\pi\) | |||||||
\(398\) | −74.0766 | − | 82.5625i | −0.186122 | − | 0.207443i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −135.386 | − | 211.728i | −0.338464 | − | 0.529319i | ||||
\(401\) | 704.010i | 1.75564i | 0.478994 | + | 0.877818i | \(0.341001\pi\) | ||||
−0.478994 | + | 0.877818i | \(0.658999\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.80270 | − | 4.35211i | −0.00447321 | − | 0.0107993i | ||||
\(404\) | 395.192 | + | 216.378i | 0.978197 | + | 0.535589i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.30630 | + | 11.0746i | −0.0130697 | + | 0.0272774i | ||||
\(407\) | 210.486 | + | 210.486i | 0.517166 | + | 0.517166i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 528.488 | + | 528.488i | 1.29215 | + | 1.29215i | 0.933457 | + | 0.358690i | \(0.116776\pi\) |
0.358690 | + | 0.933457i | \(0.383224\pi\) | |||||||
\(410\) | 45.1083 | + | 128.099i | 0.110020 | + | 0.312436i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 337.959 | − | 271.708i | 0.820290 | − | 0.659485i | ||||
\(413\) | −115.737 | − | 279.413i | −0.280234 | − | 0.676544i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 84.6901i | − | 0.204072i | ||||||
\(416\) | −56.1909 | − | 457.953i | −0.135074 | − | 1.10085i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 612.186 | + | 33.1650i | 1.46456 | + | 0.0793421i | ||||
\(419\) | 153.485 | − | 63.5754i | 0.366312 | − | 0.151731i | −0.191932 | − | 0.981408i | \(-0.561475\pi\) |
0.558244 | + | 0.829677i | \(0.311475\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −240.175 | − | 99.4838i | −0.570487 | − | 0.236304i | 0.0787437 | − | 0.996895i | \(-0.474909\pi\) |
−0.649231 | + | 0.760591i | \(0.724909\pi\) | |||||||
\(422\) | −393.884 | + | 138.701i | −0.933373 | + | 0.328675i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −79.2174 | − | 49.1224i | −0.186834 | − | 0.115855i | ||||
\(425\) | 50.7000 | − | 50.7000i | 0.119294 | − | 0.119294i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 753.562 | + | 312.136i | 1.76478 | + | 0.730997i | ||||
\(428\) | −155.598 | − | 85.1941i | −0.363547 | − | 0.199052i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 23.7381 | − | 21.2983i | 0.0552050 | − | 0.0495310i | ||||
\(431\) | 607.318 | 1.40909 | 0.704546 | − | 0.709659i | \(-0.251151\pi\) | ||||
0.704546 | + | 0.709659i | \(0.251151\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 233.380i | − | 0.538984i | −0.963003 | − | 0.269492i | \(-0.913144\pi\) | ||
0.963003 | − | 0.269492i | \(-0.0868557\pi\) | |||||||
\(434\) | 4.28817 | − | 3.84743i | 0.00988057 | − | 0.00886504i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −424.629 | + | 124.155i | −0.973919 | + | 0.284759i | ||||
\(437\) | −128.371 | + | 309.914i | −0.293754 | + | 0.709185i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −496.850 | − | 496.850i | −1.13178 | − | 1.13178i | −0.989882 | − | 0.141896i | \(-0.954680\pi\) |
−0.141896 | − | 0.989882i | \(-0.545320\pi\) | |||||||
\(440\) | −172.840 | + | 124.185i | −0.392819 | + | 0.282239i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 124.163 | − | 43.7223i | 0.280911 | − | 0.0989193i | ||||
\(443\) | −59.8483 | + | 144.487i | −0.135098 | + | 0.326155i | −0.976922 | − | 0.213597i | \(-0.931482\pi\) |
0.841824 | + | 0.539752i | \(0.181482\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 170.411 | + | 411.409i | 0.382947 | + | 0.924515i | ||||
\(446\) | −687.833 | − | 37.2632i | −1.54223 | − | 0.0835497i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 505.454 | − | 250.847i | 1.12825 | − | 0.559926i | ||||
\(449\) | 15.4530 | 0.0344165 | 0.0172082 | − | 0.999852i | \(-0.494522\pi\) | ||||
0.0172082 | + | 0.999852i | \(0.494522\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −179.596 | + | 74.3911i | −0.398217 | + | 0.164947i | ||||
\(452\) | −53.4122 | + | 491.516i | −0.118169 | + | 1.08742i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 49.0833 | + | 139.387i | 0.108113 | + | 0.307020i | ||||
\(455\) | −274.025 | + | 274.025i | −0.602253 | + | 0.602253i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −93.8365 | + | 93.8365i | −0.205332 | + | 0.205332i | −0.802280 | − | 0.596948i | \(-0.796380\pi\) |
0.596948 | + | 0.802280i | \(0.296380\pi\) | |||||||
\(458\) | −39.1188 | + | 81.6438i | −0.0854122 | + | 0.178261i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −32.6796 | − | 111.769i | −0.0710426 | − | 0.242977i | ||||
\(461\) | 574.348 | − | 237.903i | 1.24588 | − | 0.516058i | 0.340329 | − | 0.940306i | \(-0.389462\pi\) |
0.905546 | + | 0.424248i | \(0.139462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 568.089 | 1.22697 | 0.613487 | − | 0.789705i | \(-0.289766\pi\) | ||||
0.613487 | + | 0.789705i | \(0.289766\pi\) | |||||||
\(464\) | 1.95330 | + | 10.9700i | 0.00420971 | + | 0.0236423i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 383.525 | + | 427.460i | 0.823016 | + | 0.917296i | ||||
\(467\) | 156.459 | + | 377.726i | 0.335030 | + | 0.808835i | 0.998178 | + | 0.0603459i | \(0.0192204\pi\) |
−0.663147 | + | 0.748489i | \(0.730780\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 150.957 | − | 364.442i | 0.321869 | − | 0.777061i | ||||
\(470\) | 130.958 | − | 273.319i | 0.278635 | − | 0.581530i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −233.217 | − | 144.617i | −0.494103 | − | 0.306391i | ||||
\(473\) | 32.2793 | + | 32.2793i | 0.0682437 | + | 0.0682437i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 211.136 | − | 509.727i | 0.444497 | − | 1.07311i | ||||
\(476\) | 100.873 | + | 125.470i | 0.211919 | + | 0.263592i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.48520 | + | 175.085i | −0.0198435 | + | 0.366287i | ||||
\(479\) | 327.880i | 0.684509i | 0.939607 | + | 0.342254i | \(0.111190\pi\) | ||||
−0.939607 | + | 0.342254i | \(0.888810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 491.806 | 1.02247 | ||||||||
\(482\) | −30.9056 | − | 1.67430i | −0.0641194 | − | 0.00347365i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 112.385 | + | 139.789i | 0.232201 | + | 0.288820i | ||||
\(485\) | 219.616 | + | 90.9680i | 0.452817 | + | 0.187563i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −147.493 | + | 147.493i | −0.302861 | + | 0.302861i | −0.842132 | − | 0.539271i | \(-0.818700\pi\) |
0.539271 | + | 0.842132i | \(0.318700\pi\) | |||||||
\(488\) | 720.540 | − | 168.963i | 1.47652 | − | 0.346236i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −158.001 | − | 75.7047i | −0.322451 | − | 0.154499i | ||||
\(491\) | −598.802 | − | 248.032i | −1.21956 | − | 0.505157i | −0.322288 | − | 0.946642i | \(-0.604452\pi\) |
−0.897269 | + | 0.441485i | \(0.854452\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.93704 | + | 1.21656i | −0.00595748 | + | 0.00246767i | ||||
\(494\) | 753.938 | − | 676.447i | 1.52619 | − | 1.36933i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.12285 | − | 5.10542i | 0.00226382 | − | 0.0102932i | ||||
\(497\) | − | 469.304i | − | 0.944274i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 58.1446 | + | 140.373i | 0.116522 | + | 0.281309i | 0.971371 | − | 0.237568i | \(-0.0763502\pi\) |
−0.854849 | + | 0.518877i | \(0.826350\pi\) | |||||||
\(500\) | 139.299 | + | 476.425i | 0.278598 | + | 0.952849i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 452.242 | + | 216.688i | 0.900881 | + | 0.431648i | ||||
\(503\) | 256.204 | + | 256.204i | 0.509351 | + | 0.509351i | 0.914327 | − | 0.404976i | \(-0.132720\pi\) |
−0.404976 | + | 0.914327i | \(0.632720\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −242.799 | − | 242.799i | −0.480789 | − | 0.480789i | ||||
\(506\) | 157.219 | − | 55.3626i | 0.310709 | − | 0.109412i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −57.5655 | + | 529.735i | −0.113318 | + | 1.04279i | ||||
\(509\) | 229.271 | + | 553.510i | 0.450435 | + | 1.08745i | 0.972157 | + | 0.234331i | \(0.0752898\pi\) |
−0.521722 | + | 0.853115i | \(0.674710\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 651.251i | − | 1.27446i | ||||||
\(512\) | 239.648 | − | 452.452i | 0.468062 | − | 0.883696i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.1884 | − | 261.901i | 0.0276039 | − | 0.509534i | ||||
\(515\) | −305.324 | + | 126.469i | −0.592861 | + | 0.245571i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 400.789 | + | 166.012i | 0.775221 | + | 0.321107i | ||||
\(518\) | 199.778 | + | 567.331i | 0.385672 | + | 1.09523i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −56.8417 | + | 347.003i | −0.109311 | + | 0.667314i | ||||
\(521\) | −80.7376 | + | 80.7376i | −0.154967 | + | 0.154967i | −0.780332 | − | 0.625365i | \(-0.784950\pi\) |
0.625365 | + | 0.780332i | \(0.284950\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 123.197 | + | 51.0300i | 0.235559 | + | 0.0975717i | 0.497341 | − | 0.867555i | \(-0.334310\pi\) |
−0.261781 | + | 0.965127i | \(0.584310\pi\) | |||||||
\(524\) | 947.707 | − | 277.095i | 1.80860 | − | 0.528807i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −531.436 | − | 592.315i | −1.01034 | − | 1.12607i | ||||
\(527\) | 1.49141 | 0.00283001 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 437.800i | − | 0.827599i | ||||||
\(530\) | 47.4403 | + | 52.8748i | 0.0895100 | + | 0.0997639i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1086.59 | + | 594.936i | 2.04246 | + | 1.11830i | ||||
\(533\) | −122.907 | + | 296.723i | −0.230594 | + | 0.556704i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 95.5966 | + | 95.5966i | 0.178685 | + | 0.178685i | ||||
\(536\) | −81.7149 | − | 348.471i | −0.152453 | − | 0.650133i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 95.8389 | + | 272.164i | 0.178139 | + | 0.505881i | ||||
\(539\) | 95.9689 | − | 231.689i | 0.178050 | − | 0.429850i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 184.993 | + | 446.613i | 0.341947 | + | 0.825532i | 0.997519 | + | 0.0703996i | \(0.0224275\pi\) |
−0.655572 | + | 0.755132i | \(0.727573\pi\) | |||||||
\(542\) | −39.8870 | + | 736.266i | −0.0735923 | + | 1.35842i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 140.760 | + | 39.0489i | 0.258750 | + | 0.0717810i | ||||
\(545\) | 337.163 | 0.618648 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −570.529 | + | 236.321i | −1.04302 | + | 0.432031i | −0.837394 | − | 0.546600i | \(-0.815922\pi\) |
−0.205622 | + | 0.978632i | \(0.565922\pi\) | |||||||
\(548\) | −492.968 | + | 396.330i | −0.899577 | + | 0.723230i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −258.584 | + | 91.0569i | −0.470152 | + | 0.165558i | ||||
\(551\) | −17.2973 | + | 17.2973i | −0.0313926 | + | 0.0313926i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −167.744 | + | 167.744i | −0.303335 | + | 0.303335i | ||||
\(554\) | −101.805 | − | 48.7787i | −0.183763 | − | 0.0880482i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −120.669 | − | 66.0693i | −0.217030 | − | 0.118830i | ||||
\(557\) | −340.362 | + | 140.983i | −0.611063 | + | 0.253111i | −0.666683 | − | 0.745341i | \(-0.732286\pi\) |
0.0556199 | + | 0.998452i | \(0.482286\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 75.4212 | 0.134922 | ||||||||
\(560\) | −423.381 | + | 75.3867i | −0.756038 | + | 0.134619i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −179.075 | + | 160.669i | −0.318638 | + | 0.285888i | ||||
\(563\) | −241.885 | − | 583.963i | −0.429637 | − | 1.03723i | −0.979403 | − | 0.201916i | \(-0.935283\pi\) |
0.549766 | − | 0.835319i | \(-0.314717\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 144.193 | − | 348.113i | 0.255209 | − | 0.616128i | ||||
\(566\) | −127.702 | − | 61.1873i | −0.225623 | − | 0.108105i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −248.470 | − | 345.819i | −0.437447 | − | 0.608836i | ||||
\(569\) | −88.6373 | − | 88.6373i | −0.155777 | − | 0.155777i | 0.624915 | − | 0.780693i | \(-0.285134\pi\) |
−0.780693 | + | 0.624915i | \(0.785134\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −160.453 | + | 387.367i | −0.281003 | + | 0.678401i | −0.999860 | − | 0.0167573i | \(-0.994666\pi\) |
0.718857 | + | 0.695158i | \(0.244666\pi\) | |||||||
\(572\) | −500.365 | − | 54.3739i | −0.874764 | − | 0.0950592i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −392.217 | − | 21.2482i | −0.683304 | − | 0.0370178i | ||||
\(575\) | − | 150.000i | − | 0.260869i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −501.285 | −0.868778 | −0.434389 | − | 0.900725i | \(-0.643036\pi\) | ||||
−0.434389 | + | 0.900725i | \(0.643036\pi\) | |||||||
\(578\) | 29.0126 | − | 535.538i | 0.0501949 | − | 0.926537i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.917395 | − | 8.44215i | 0.00158172 | − | 0.0145554i | ||||
\(581\) | 226.299 | + | 93.7360i | 0.389498 | + | 0.161336i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −71.8995 | + | 71.8995i | −0.123327 | + | 0.123327i | ||||
\(584\) | −344.800 | − | 479.891i | −0.590412 | − | 0.821731i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 300.296 | − | 626.739i | 0.512451 | − | 1.06952i | ||||
\(587\) | 805.600 | + | 333.691i | 1.37240 | + | 0.568468i | 0.942439 | − | 0.334378i | \(-0.108526\pi\) |
0.429964 | + | 0.902846i | \(0.358526\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.6026 | − | 4.39175i | 0.0180010 | − | 0.00745628i | ||||
\(590\) | 139.665 | + | 155.664i | 0.236720 | + | 0.263837i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 447.582 | + | 312.282i | 0.756050 | + | 0.527503i | ||||
\(593\) | − | 1035.33i | − | 1.74591i | −0.487798 | − | 0.872957i | \(-0.662200\pi\) | ||
0.487798 | − | 0.872957i | \(-0.337800\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −46.9525 | − | 113.353i | −0.0789117 | − | 0.190510i | ||||
\(596\) | −543.869 | + | 993.319i | −0.912532 | + | 1.66664i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 118.995 | − | 248.351i | 0.198988 | − | 0.415302i | ||||
\(599\) | −361.938 | − | 361.938i | −0.604237 | − | 0.604237i | 0.337197 | − | 0.941434i | \(-0.390521\pi\) |
−0.941434 | + | 0.337197i | \(0.890521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −221.839 | − | 221.839i | −0.369116 | − | 0.369116i | 0.498039 | − | 0.867155i | \(-0.334054\pi\) |
−0.867155 | + | 0.498039i | \(0.834054\pi\) | |||||||
\(602\) | 30.6371 | + | 87.0034i | 0.0508922 | + | 0.144524i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −182.643 | − | 227.178i | −0.302390 | − | 0.376122i | ||||
\(605\) | −52.3109 | − | 126.290i | −0.0864642 | − | 0.208743i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 465.834i | − | 0.767437i | −0.923450 | − | 0.383719i | \(-0.874643\pi\) | ||
0.923450 | − | 0.383719i | \(-0.125357\pi\) | |||||||
\(608\) | 1115.67 | − | 136.892i | 1.83498 | − | 0.225152i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −563.201 | − | 30.5113i | −0.923280 | − | 0.0500185i | ||||
\(611\) | 662.172 | − | 274.281i | 1.08375 | − | 0.448905i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 292.579 | + | 121.190i | 0.477290 | + | 0.197700i | 0.608341 | − | 0.793676i | \(-0.291835\pi\) |
−0.131051 | + | 0.991376i | \(0.541835\pi\) | |||||||
\(614\) | −456.956 | + | 160.911i | −0.744227 | + | 0.262070i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −140.531 | − | 599.292i | −0.228135 | − | 0.972877i | ||||
\(617\) | 226.657 | − | 226.657i | 0.367354 | − | 0.367354i | −0.499158 | − | 0.866511i | \(-0.666357\pi\) |
0.866511 | + | 0.499158i | \(0.166357\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 756.530 | + | 313.365i | 1.22218 | + | 0.506244i | 0.898102 | − | 0.439787i | \(-0.144946\pi\) |
0.324078 | + | 0.946030i | \(0.394946\pi\) | |||||||
\(620\) | −1.91327 | + | 3.49438i | −0.00308592 | + | 0.00563610i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 93.8459 | − | 84.2003i | 0.150878 | − | 0.135370i | ||||
\(623\) | −1287.93 | −2.06730 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.3854i | 0.0230167i | ||||||||
\(626\) | −58.8007 | + | 52.7570i | −0.0939308 | + | 0.0842764i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −115.412 | − | 394.727i | −0.183777 | − | 0.628546i | ||||
\(629\) | −59.5864 | + | 143.854i | −0.0947320 | + | 0.228703i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 338.810 | + | 338.810i | 0.536941 | + | 0.536941i | 0.922629 | − | 0.385688i | \(-0.126036\pi\) |
−0.385688 | + | 0.922629i | \(0.626036\pi\) | |||||||
\(632\) | −34.7956 | + | 212.418i | −0.0550563 | + | 0.336104i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 620.383 | − | 218.460i | 0.978522 | − | 0.344574i | ||||
\(635\) | 155.405 | − | 375.181i | 0.244733 | − | 0.590837i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −158.557 | − | 382.790i | −0.248912 | − | 0.600927i | ||||
\(638\) | 12.1372 | + | 0.657531i | 0.0190239 | + | 0.00103061i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −272.067 | + | 279.707i | −0.425104 | + | 0.437042i | ||||
\(641\) | −729.839 | −1.13859 | −0.569297 | − | 0.822132i | \(-0.692785\pi\) | ||||
−0.569297 | + | 0.822132i | \(0.692785\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −370.578 | + | 153.498i | −0.576327 | + | 0.238722i | −0.651756 | − | 0.758429i | \(-0.725967\pi\) |
0.0754293 | + | 0.997151i | \(0.475967\pi\) | |||||||
\(644\) | 334.826 | + | 36.3850i | 0.519917 | + | 0.0564985i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 106.516 | + | 302.486i | 0.164886 | + | 0.468244i | ||||
\(647\) | 179.567 | − | 179.567i | 0.277538 | − | 0.277538i | −0.554587 | − | 0.832126i | \(-0.687124\pi\) |
0.832126 | + | 0.554587i | \(0.187124\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −211.673 | + | 211.673i | −0.326152 | + | 0.326152i | ||||
\(650\) | −195.715 | + | 408.471i | −0.301100 | + | 0.628417i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.6726 | − | 6.04436i | 0.0317065 | − | 0.00927049i | ||||
\(653\) | 964.894 | − | 399.672i | 1.47763 | − | 0.612056i | 0.509048 | − | 0.860738i | \(-0.329998\pi\) |
0.968585 | + | 0.248683i | \(0.0799976\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −752.497 | −1.14885 | ||||||||
\(656\) | −300.265 | + | 191.999i | −0.457721 | + | 0.292682i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 585.385 | + | 652.444i | 0.889642 | + | 0.991556i | ||||
\(659\) | −233.939 | − | 564.778i | −0.354990 | − | 0.857023i | −0.995989 | − | 0.0894804i | \(-0.971479\pi\) |
0.640998 | − | 0.767542i | \(-0.278521\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 281.181 | − | 678.831i | 0.425387 | − | 1.02698i | −0.555345 | − | 0.831620i | \(-0.687414\pi\) |
0.980732 | − | 0.195356i | \(-0.0625862\pi\) | |||||||
\(662\) | −158.565 | + | 330.937i | −0.239525 | + | 0.499905i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 216.382 | − | 50.7405i | 0.325876 | − | 0.0764165i | ||||
\(665\) | −667.580 | − | 667.580i | −1.00388 | − | 1.00388i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.54508 | + | 6.14437i | −0.00381571 | + | 0.00921195i | ||||
\(668\) | −727.492 | + | 584.879i | −1.08906 | + | 0.875567i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.7560 | + | 272.378i | −0.0220239 | + | 0.406534i | ||||
\(671\) | − | 807.333i | − | 1.20318i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 705.345 | 1.04806 | 0.524031 | − | 0.851699i | \(-0.324428\pi\) | ||||
0.524031 | + | 0.851699i | \(0.324428\pi\) | |||||||
\(674\) | 134.426 | + | 7.28250i | 0.199445 | + | 0.0108049i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −121.233 | + | 97.4673i | −0.179339 | + | 0.144182i | ||||
\(677\) | 10.4550 | + | 4.33061i | 0.0154432 | + | 0.00639676i | 0.390392 | − | 0.920649i | \(-0.372340\pi\) |
−0.374948 | + | 0.927046i | \(0.622340\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −486.147 | + | 486.147i | −0.715976 | + | 0.715976i | ||||
\(680\) | −94.6123 | − | 58.6687i | −0.139136 | − | 0.0862775i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.14259 | − | 2.46402i | −0.00754046 | − | 0.00361294i | ||||
\(683\) | 307.101 | + | 127.205i | 0.449635 | + | 0.186245i | 0.595998 | − | 0.802986i | \(-0.296757\pi\) |
−0.146363 | + | 0.989231i | \(0.546757\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 445.364 | − | 184.476i | 0.650166 | − | 0.269308i | ||||
\(686\) | −265.964 | + | 238.628i | −0.387703 | + | 0.347854i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 68.6392 | + | 47.8901i | 0.0997662 | + | 0.0696077i | ||||
\(689\) | 167.995i | 0.243824i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −243.176 | − | 587.078i | −0.351919 | − | 0.849607i | −0.996383 | − | 0.0849727i | \(-0.972920\pi\) |
0.644465 | − | 0.764634i | \(-0.277080\pi\) | |||||||
\(692\) | −481.049 | + | 140.651i | −0.695158 | + | 0.203253i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −505.047 | − | 241.988i | −0.727734 | − | 0.348686i | ||||
\(695\) | 74.1366 | + | 74.1366i | 0.106671 | + | 0.106671i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −71.9010 | − | 71.9010i | −0.103158 | − | 0.103158i | ||||
\(698\) | 816.125 | − | 287.388i | 1.16923 | − | 0.411730i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −550.701 | − | 59.8438i | −0.786716 | − | 0.0854912i | ||||
\(701\) | −65.7383 | − | 158.706i | −0.0937779 | − | 0.226400i | 0.870029 | − | 0.493000i | \(-0.164100\pi\) |
−0.963807 | + | 0.266600i | \(0.914100\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1198.14i | 1.70432i | ||||||||
\(704\) | −420.846 | − | 367.201i | −0.597792 | − | 0.521592i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 62.1582 | − | 1147.37i | 0.0880428 | − | 1.62516i | ||||
\(707\) | 917.510 | − | 380.045i | 1.29775 | − | 0.537546i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1029.00 | − | 426.228i | −1.45135 | − | 0.601167i | −0.488827 | − | 0.872381i | \(-0.662575\pi\) |
−0.962519 | + | 0.271214i | \(0.912575\pi\) | |||||||
\(710\) | 107.790 | + | 306.103i | 0.151817 | + | 0.431131i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −949.046 | + | 681.887i | −1.33293 | + | 0.957706i | ||||
\(713\) | 2.20623 | − | 2.20623i | 0.00309429 | − | 0.00309429i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 354.380 | + | 146.789i | 0.495637 | + | 0.205299i | ||||
\(716\) | −131.521 | − | 449.824i | −0.183689 | − | 0.628245i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 943.011 | + | 1051.04i | 1.31339 | + | 1.46384i | ||||
\(719\) | 439.735 | 0.611592 | 0.305796 | − | 0.952097i | \(-0.401077\pi\) | ||||
0.305796 | + | 0.952097i | \(0.401077\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 955.826i | − | 1.32570i | ||||||
\(722\) | 1165.80 | + | 1299.34i | 1.61468 | + | 1.79965i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −403.421 | + | 736.805i | −0.557211 | + | 1.01769i | ||||
\(725\) | 4.18599 | − | 10.1059i | 0.00577378 | − | 0.0139391i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 137.308 | + | 137.308i | 0.188869 | + | 0.188869i | 0.795207 | − | 0.606338i | \(-0.207362\pi\) |
−0.606338 | + | 0.795207i | \(0.707362\pi\) | |||||||
\(728\) | −864.307 | − | 535.953i | −1.18723 | − | 0.736199i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 149.580 | + | 424.777i | 0.204904 | + | 0.581886i | ||||
\(731\) | −9.13791 | + | 22.0609i | −0.0125006 | + | 0.0301790i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 57.7693 | + | 139.467i | 0.0788121 | + | 0.190269i | 0.958374 | − | 0.285514i | \(-0.0921645\pi\) |
−0.879562 | + | 0.475784i | \(0.842164\pi\) | |||||||
\(734\) | 31.9775 | − | 590.267i | 0.0435661 | − | 0.804178i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 265.989 | − | 150.460i | 0.361399 | − | 0.204430i | ||||
\(737\) | −390.447 | −0.529778 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 536.590 | − | 222.263i | 0.726103 | − | 0.300762i | 0.0111538 | − | 0.999938i | \(-0.496450\pi\) |
0.714950 | + | 0.699176i | \(0.246450\pi\) | |||||||
\(740\) | −260.610 | − | 324.155i | −0.352176 | − | 0.438048i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −193.793 | + | 68.2418i | −0.261177 | + | 0.0919700i | ||||
\(743\) | −907.324 | + | 907.324i | −1.22116 | + | 1.22116i | −0.253944 | + | 0.967219i | \(0.581728\pi\) |
−0.967219 | + | 0.253944i | \(0.918272\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 610.278 | − | 610.278i | 0.819165 | − | 0.819165i | ||||
\(746\) | 630.987 | + | 302.331i | 0.845827 | + | 0.405270i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 76.5279 | − | 139.770i | 0.102310 | − | 0.186858i | ||||
\(749\) | −361.249 | + | 149.634i | −0.482309 | + | 0.199779i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −662.862 | −0.882639 | −0.441320 | − | 0.897350i | \(-0.645489\pi\) | ||||
−0.441320 | + | 0.897350i | \(0.645489\pi\) | |||||||
\(752\) | 776.788 | + | 170.842i | 1.03296 | + | 0.227184i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.9476 | − | 13.4113i | 0.0198244 | − | 0.0177868i | ||||
\(755\) | 85.0132 | + | 205.240i | 0.112600 | + | 0.271841i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 76.1190 | − | 183.767i | 0.100553 | − | 0.242757i | −0.865595 | − | 0.500745i | \(-0.833059\pi\) |
0.966148 | + | 0.257988i | \(0.0830594\pi\) | |||||||
\(758\) | −804.266 | − | 385.356i | −1.06104 | − | 0.508385i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −845.370 | − | 138.478i | −1.11233 | − | 0.182208i | ||||
\(761\) | −435.811 | − | 435.811i | −0.572683 | − | 0.572683i | 0.360195 | − | 0.932877i | \(-0.382710\pi\) |
−0.932877 | + | 0.360195i | \(0.882710\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −373.176 | + | 900.926i | −0.489090 | + | 1.18077i | ||||
\(764\) | −146.110 | + | 1344.55i | −0.191244 | + | 1.75989i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −509.057 | − | 27.5780i | −0.664565 | − | 0.0360026i | ||||
\(767\) | 494.578i | 0.644821i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1422.48 | −1.84978 | −0.924889 | − | 0.380237i | \(-0.875843\pi\) | ||||
−0.924889 | + | 0.380237i | \(0.875843\pi\) | |||||||
\(770\) | −25.3770 | + | 468.429i | −0.0329572 | + | 0.608350i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −932.540 | − | 101.338i | −1.20795 | − | 0.131266i | ||||
\(773\) | 0.439715 | + | 0.182136i | 0.000568842 | + | 0.000235622i | 0.382968 | − | 0.923762i | \(-0.374902\pi\) |
−0.382399 | + | 0.923997i | \(0.624902\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.62867 | + | 3.62867i | −0.00468215 | + | 0.00468215i | ||||
\(776\) | −100.843 | + | 615.618i | −0.129952 | + | 0.793322i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −642.854 | + | 1341.68i | −0.826290 | + | 1.72453i | ||||
\(779\) | −722.878 | − | 299.426i | −0.927956 | − | 0.384372i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −429.160 | + | 177.764i | −0.549500 | + | 0.227610i | ||||
\(782\) | 58.2259 | + | 64.8960i | 0.0744576 | + | 0.0829872i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 98.7608 | − | 449.048i | 0.125970 | − | 0.572765i | ||||
\(785\) | 313.420i | 0.399262i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.0303 | + | 55.6002i | 0.0292635 | + | 0.0706482i | 0.937836 | − | 0.347079i | \(-0.112827\pi\) |
−0.908572 | + | 0.417728i | \(0.862827\pi\) | |||||||
\(788\) | 900.055 | + | 492.805i | 1.14220 | + | 0.625386i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 70.8832 | − | 147.938i | 0.0897255 | − | 0.187264i | ||||
\(791\) | 770.590 | + | 770.590i | 0.974197 | + | 0.974197i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −943.175 | − | 943.175i | −1.18938 | − | 1.18938i | ||||
\(794\) | 40.9110 | + | 116.179i | 0.0515252 | + | 0.146322i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −172.898 | + | 139.004i | −0.217208 | + | 0.174628i | ||||
\(797\) | −49.3444 | − | 119.128i | −0.0619127 | − | 0.149470i | 0.889895 | − | 0.456165i | \(-0.150777\pi\) |
−0.951808 | + | 0.306694i | \(0.900777\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 226.918i | 0.284003i | ||||||||
\(800\) | −437.482 | + | 247.468i | −0.546853 | + | 0.309335i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1405.96 | + | 76.1674i | 1.75307 | + | 0.0949718i | ||||
\(803\) | −595.542 | + | 246.682i | −0.741647 | + | 0.307200i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −237.138 | − | 98.2260i | −0.294582 | − | 0.122020i | ||||
\(806\) | −8.88651 | + | 3.12927i | −0.0110254 | + | 0.00388247i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 474.879 | − | 765.816i | 0.587721 | − | 0.947792i | ||||
\(809\) | −29.6470 | + | 29.6470i | −0.0366465 | + | 0.0366465i | −0.725193 | − | 0.688546i | \(-0.758249\pi\) |
0.688546 | + | 0.725193i | \(0.258249\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −755.209 | − | 312.818i | −0.931207 | − | 0.385719i | −0.135071 | − | 0.990836i | \(-0.543126\pi\) |
−0.796136 | + | 0.605117i | \(0.793126\pi\) | |||||||
\(812\) | 21.5427 | + | 11.7952i | 0.0265304 | + | 0.0145261i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 443.129 | − | 397.584i | 0.544385 | − | 0.488432i | ||||
\(815\) | −16.4144 | −0.0201404 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 183.741i | 0.224897i | ||||||||
\(818\) | 1112.61 | − | 998.251i | 1.36015 | − | 1.22036i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 260.703 | − | 76.2254i | 0.317930 | − | 0.0929578i | ||||
\(821\) | −120.712 | + | 291.425i | −0.147031 | + | 0.354964i | −0.980187 | − | 0.198074i | \(-0.936531\pi\) |
0.833156 | + | 0.553038i | \(0.186531\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 173.105 | + | 173.105i | 0.210334 | + | 0.210334i | 0.804409 | − | 0.594076i | \(-0.202482\pi\) |
−0.594076 | + | 0.804409i | \(0.702482\pi\) | |||||||
\(824\) | −506.056 | − | 704.326i | −0.614146 | − | 0.854764i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −570.529 | + | 200.904i | −0.690713 | + | 0.243225i | ||||
\(827\) | 59.9551 | − | 144.744i | 0.0724971 | − | 0.175023i | −0.883477 | − | 0.468475i | \(-0.844804\pi\) |
0.955974 | + | 0.293451i | \(0.0948038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 259.829 | + | 627.283i | 0.313425 | + | 0.756674i | 0.999573 | + | 0.0292124i | \(0.00929993\pi\) |
−0.686149 | + | 0.727461i | \(0.740700\pi\) | |||||||
\(830\) | −169.132 | − | 9.16269i | −0.203774 | − | 0.0110394i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −920.644 | + | 62.6710i | −1.10654 | + | 0.0753257i | ||||
\(833\) | 131.178 | 0.157476 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 657.240 | − | 272.238i | 0.787114 | − | 0.326033i | ||||
\(836\) | 132.466 | − | 1218.99i | 0.158452 | − | 1.45812i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −110.359 | − | 313.398i | −0.131693 | − | 0.373983i | ||||
\(839\) | −182.343 | + | 182.343i | −0.217333 | + | 0.217333i | −0.807374 | − | 0.590040i | \(-0.799112\pi\) |
0.590040 | + | 0.807374i | \(0.299112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 594.334 | − | 594.334i | 0.706699 | − | 0.706699i | ||||
\(842\) | −224.661 | + | 468.884i | −0.266818 | + | 0.556869i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 234.381 | + | 801.620i | 0.277703 | + | 0.949787i | ||||
\(845\) | 109.526 | − | 45.3671i | 0.129617 | − | 0.0536889i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 395.354 | 0.466770 | ||||||||
\(848\) | −106.671 | + | 152.888i | −0.125792 | + | 0.180293i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −95.7663 | − | 106.737i | −0.112666 | − | 0.125573i | ||||
\(851\) | 124.657 | + | 300.947i | 0.146482 | + | 0.353640i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −300.757 | + | 726.092i | −0.352588 | + | 0.851222i | 0.643712 | + | 0.765268i | \(0.277394\pi\) |
−0.996299 | + | 0.0859535i | \(0.972606\pi\) | |||||||
\(854\) | 704.886 | − | 1471.15i | 0.825393 | − | 1.72266i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −186.973 | + | 301.523i | −0.218426 | + | 0.352247i | ||||
\(857\) | 545.430 | + | 545.430i | 0.636441 | + | 0.636441i | 0.949676 | − | 0.313235i | \(-0.101413\pi\) |
−0.313235 | + | 0.949676i | \(0.601413\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 230.652 | − | 556.843i | 0.268512 | − | 0.648246i | −0.730901 | − | 0.682483i | \(-0.760900\pi\) |
0.999414 | + | 0.0342370i | \(0.0109001\pi\) | |||||||
\(860\) | −39.9660 | − | 49.7111i | −0.0464721 | − | 0.0578036i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 65.7063 | − | 1212.86i | 0.0762254 | − | 1.40703i | ||||
\(863\) | 980.846i | 1.13655i | 0.822837 | + | 0.568277i | \(0.192390\pi\) | ||||
−0.822837 | + | 0.568277i | \(0.807610\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 381.962 | 0.441574 | ||||||||
\(866\) | −466.076 | − | 25.2496i | −0.538195 | − | 0.0291565i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.21964 | − | 8.98004i | −0.00831756 | − | 0.0103457i | ||||
\(869\) | 216.933 | + | 89.8568i | 0.249636 | + | 0.103403i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −456.143 | + | 456.143i | −0.523701 | + | 0.523701i | ||||
\(872\) | 202.005 | + | 861.446i | 0.231657 | + | 0.987897i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 605.032 | + | 289.895i | 0.692256 | + | 0.331688i | ||||
\(875\) | 1010.82 | + | 418.696i | 1.15522 | + | 0.478509i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1395.56 | − | 578.059i | 1.59129 | − | 0.659132i | 0.601137 | − | 0.799146i | \(-0.294715\pi\) |
0.990150 | + | 0.140014i | \(0.0447146\pi\) | |||||||
\(878\) | −1046.00 | + | 938.491i | −1.19134 | + | 1.06890i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 229.307 | + | 358.610i | 0.260576 | + | 0.407511i | ||||
\(881\) | − | 1513.62i | − | 1.71807i | −0.511914 | − | 0.859037i | \(-0.671063\pi\) | ||
0.511914 | − | 0.859037i | \(-0.328937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −91.3318 | − | 220.494i | −0.103434 | − | 0.249711i | 0.863687 | − | 0.504028i | \(-0.168149\pi\) |
−0.967121 | + | 0.254317i | \(0.918149\pi\) | |||||||
\(884\) | −73.8833 | − | 252.692i | −0.0835784 | − | 0.285851i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 282.075 | + | 135.153i | 0.318369 | + | 0.152543i | ||||
\(887\) | −892.828 | − | 892.828i | −1.00657 | − | 1.00657i | −0.999978 | − | 0.00659168i | \(-0.997902\pi\) |
−0.00659168 | − | 0.999978i | \(-0.502098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 830.510 | + | 830.510i | 0.934207 | + | 0.934207i | ||||
\(890\) | 840.050 | − | 295.813i | 0.943877 | − | 0.332374i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −148.834 | + | 1369.62i | −0.166855 | + | 1.53545i | ||||
\(893\) | 668.203 | + | 1613.19i | 0.748268 | + | 1.80648i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 357.168i | 0.399071i | ||||||||
\(896\) | −446.273 | − | 1036.57i | −0.498073 | − | 1.15688i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.67187 | − | 30.8608i | 0.00186177 | − | 0.0343661i | ||||
\(899\) | 0.210208 | − | 0.0870710i | 0.000233824 | − | 9.68531e-5i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49.1388 | − | 20.3540i | −0.0545381 | − | 0.0225904i | ||||
\(902\) | 129.134 | + | 366.715i | 0.143164 | + | 0.406557i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 975.813 | + | 159.845i | 1.07944 | + | 0.176820i | ||||
\(905\) | 452.680 | − | 452.680i | 0.500199 | − | 0.500199i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −469.078 | − | 194.298i | −0.517175 | − | 0.214221i | 0.108800 | − | 0.994064i | \(-0.465299\pi\) |
−0.625976 | + | 0.779843i | \(0.715299\pi\) | |||||||
\(908\) | 283.676 | − | 82.9425i | 0.312419 | − | 0.0913464i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 517.600 | + | 576.894i | 0.568792 | + | 0.633950i | ||||
\(911\) | −469.566 | −0.515441 | −0.257720 | − | 0.966220i | \(-0.582971\pi\) | ||||
−0.257720 | + | 0.966220i | \(0.582971\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 242.446i | − | 0.265549i | ||||||
\(914\) | 177.246 | + | 197.550i | 0.193923 | + | 0.216138i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 158.816 | + | 86.9562i | 0.173380 | + | 0.0949303i | ||||
\(917\) | 832.872 | − | 2010.73i | 0.908257 | − | 2.19273i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 737.868 | + | 737.868i | 0.802903 | + | 0.802903i | 0.983548 | − | 0.180645i | \(-0.0578186\pi\) |
−0.180645 | + | 0.983548i | \(0.557819\pi\) | |||||||
\(920\) | −226.747 | + | 53.1710i | −0.246464 | + | 0.0577946i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −412.970 | − | 1172.75i | −0.447907 | − | 1.27197i | ||||
\(923\) | −293.696 | + | 709.045i | −0.318197 | + | 0.768196i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −205.027 | − | 494.979i | −0.221651 | − | 0.535113i | ||||
\(926\) | 61.4620 | − | 1134.51i | 0.0663736 | − | 1.22518i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 22.1192 | − | 2.71403i | 0.0238354 | − | 0.00292461i | ||||
\(929\) | −796.539 | −0.857416 | −0.428708 | − | 0.903443i | \(-0.641031\pi\) | ||||
−0.428708 | + | 0.903443i | \(0.641031\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 932.554 | − | 386.277i | 1.00167 | − | 0.414905i | ||||
\(932\) | 895.162 | − | 719.680i | 0.960475 | − | 0.772189i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 771.273 | − | 271.594i | 0.825774 | − | 0.290786i | ||||
\(935\) | −85.8723 | + | 85.8723i | −0.0918420 | + | 0.0918420i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 764.262 | − | 764.262i | 0.815648 | − | 0.815648i | −0.169826 | − | 0.985474i | \(-0.554321\pi\) |
0.985474 | + | 0.169826i | \(0.0543206\pi\) | |||||||
\(938\) | −711.484 | − | 340.900i | −0.758511 | − | 0.363433i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −531.670 | − | 291.104i | −0.565606 | − | 0.309685i | ||||
\(941\) | −113.549 | + | 47.0336i | −0.120669 | + | 0.0499826i | −0.442201 | − | 0.896916i | \(-0.645802\pi\) |
0.321532 | + | 0.946899i | \(0.395802\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −212.725 | −0.225583 | ||||||||
\(944\) | −314.042 | + | 450.104i | −0.332671 | + | 0.476805i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 67.9563 | − | 60.9717i | 0.0718354 | − | 0.0644521i | ||||
\(947\) | −396.726 | − | 957.782i | −0.418930 | − | 1.01139i | −0.982658 | − | 0.185425i | \(-0.940634\pi\) |
0.563729 | − | 0.825960i | \(-0.309366\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −407.560 | + | 983.937i | −0.429463 | + | 1.03681i | ||||
\(950\) | −995.118 | − | 476.801i | −1.04749 | − | 0.501896i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 261.485 | − | 187.877i | 0.274670 | − | 0.197349i | ||||
\(953\) | −391.136 | − | 391.136i | −0.410426 | − | 0.410426i | 0.471461 | − | 0.881887i | \(-0.343727\pi\) |
−0.881887 | + | 0.471461i | \(0.843727\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 394.443 | − | 952.270i | 0.413030 | − | 0.997142i | ||||
\(956\) | 348.632 | + | 37.8852i | 0.364677 | + | 0.0396289i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 654.799 | + | 35.4736i | 0.683506 | + | 0.0370288i | ||||
\(959\) | 1394.23i | 1.45383i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 960.893 | 0.999889 | ||||||||
\(962\) | 53.2089 | − | 982.171i | 0.0553107 | − | 1.02097i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.68740 | + | 61.5395i | −0.00693713 | + | 0.0638377i | ||||
\(965\) | 660.465 | + | 273.574i | 0.684420 | + | 0.283496i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.8939 | + | 22.8939i | −0.0236752 | + | 0.0236752i | −0.718845 | − | 0.695170i | \(-0.755329\pi\) |
0.695170 | + | 0.718845i | \(0.255329\pi\) | |||||||
\(968\) | 291.327 | − | 209.318i | 0.300958 | − | 0.216237i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 205.430 | − | 428.747i | 0.211784 | − | 0.442007i | ||||
\(971\) | 619.006 | + | 256.401i | 0.637493 | + | 0.264058i | 0.677933 | − | 0.735124i | \(-0.262876\pi\) |
−0.0404399 | + | 0.999182i | \(0.512876\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −280.154 | + | 116.044i | −0.287928 | + | 0.119264i | ||||
\(974\) | 278.597 | + | 310.512i | 0.286034 | + | 0.318801i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −259.476 | − | 1457.25i | −0.265856 | − | 1.49308i | ||||
\(977\) | 430.856i | 0.440999i | 0.975387 | + | 0.220500i | \(0.0707688\pi\) | ||||
−0.975387 | + | 0.220500i | \(0.929231\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 487.844 | + | 1177.76i | 0.498309 | + | 1.20302i | ||||
\(980\) | −168.282 | + | 307.349i | −0.171716 | + | 0.313621i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −560.123 | + | 1169.02i | −0.570390 | + | 1.19044i | ||||
\(983\) | −154.209 | − | 154.209i | −0.156876 | − | 0.156876i | 0.624305 | − | 0.781181i | \(-0.285382\pi\) |
−0.781181 | + | 0.624305i | \(0.785382\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −552.978 | − | 552.978i | −0.561399 | − | 0.561399i | ||||
\(986\) | 2.11180 | + | 5.99710i | 0.00214178 | + | 0.00608225i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1269.34 | − | 1578.85i | −1.28476 | − | 1.59803i | ||||
\(989\) | 19.1168 | + | 46.1520i | 0.0193294 | + | 0.0466653i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 966.543i | 0.975320i | 0.873033 | + | 0.487660i | \(0.162150\pi\) | ||||
−0.873033 | + | 0.487660i | \(0.837850\pi\) | |||||||
\(992\) | −10.0744 | − | 2.79478i | −0.0101556 | − | 0.00281732i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −937.234 | − | 50.7744i | −0.942891 | − | 0.0510809i | ||||
\(995\) | 156.201 | − | 64.7007i | 0.156986 | − | 0.0650258i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 732.694 | + | 303.492i | 0.734899 | + | 0.304405i | 0.718564 | − | 0.695461i | \(-0.244800\pi\) |
0.0163357 | + | 0.999867i | \(0.494800\pi\) | |||||||
\(998\) | 286.626 | − | 100.932i | 0.287201 | − | 0.101134i | ||||
\(999\) | 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 | 288.3.u.a.91.4 | 28 | ||
3.2 | odd | 2 | 32.3.h.a.27.4 | yes | 28 | ||
12.11 | even | 2 | 128.3.h.a.15.1 | 28 | |||
24.5 | odd | 2 | 256.3.h.b.31.1 | 28 | |||
24.11 | even | 2 | 256.3.h.a.31.7 | 28 | |||
32.19 | odd | 8 | inner | 288.3.u.a.19.4 | 28 | ||
96.29 | odd | 8 | 256.3.h.a.223.7 | 28 | |||
96.35 | even | 8 | 256.3.h.b.223.1 | 28 | |||
96.77 | odd | 8 | 128.3.h.a.111.1 | 28 | |||
96.83 | even | 8 | 32.3.h.a.19.4 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.19.4 | ✓ | 28 | 96.83 | even | 8 | ||
32.3.h.a.27.4 | yes | 28 | 3.2 | odd | 2 | ||
128.3.h.a.15.1 | 28 | 12.11 | even | 2 | |||
128.3.h.a.111.1 | 28 | 96.77 | odd | 8 | |||
256.3.h.a.31.7 | 28 | 24.11 | even | 2 | |||
256.3.h.a.223.7 | 28 | 96.29 | odd | 8 | |||
256.3.h.b.31.1 | 28 | 24.5 | odd | 2 | |||
256.3.h.b.223.1 | 28 | 96.35 | even | 8 | |||
288.3.u.a.19.4 | 28 | 32.19 | odd | 8 | inner | ||
288.3.u.a.91.4 | 28 | 1.1 | even | 1 | trivial |