Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(361,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.i (of order \(3\), 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: | \(34.6931230834\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 373.1 | ||
Root | \(-1.63746 + 1.52274i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.373 |
Dual form | 588.4.i.i.361.1 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | − | 2.59808i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.41238 | + | 11.1066i | −0.573540 | + | 0.993401i | 0.422658 | + | 0.906289i | \(0.361097\pi\) |
−0.996199 | + | 0.0871118i | \(0.972236\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.4124 | + | 31.8912i | 0.504685 | + | 0.874141i | 0.999985 | + | 0.00541879i | \(0.00172486\pi\) |
−0.495300 | + | 0.868722i | \(0.664942\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −87.1238 | −1.85875 | −0.929376 | − | 0.369134i | \(-0.879654\pi\) | ||||
−0.929376 | + | 0.369134i | \(0.879654\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 38.4743 | 0.662267 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 51.2990 | + | 88.8525i | 0.731873 | + | 1.26764i | 0.956082 | + | 0.293100i | \(0.0946868\pi\) |
−0.224209 | + | 0.974541i | \(0.571980\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 47.9124 | − | 82.9867i | 0.578519 | − | 1.00202i | −0.417131 | − | 0.908846i | \(-0.636964\pi\) |
0.995650 | − | 0.0931772i | \(-0.0297023\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 48.0000 | − | 83.1384i | 0.435161 | − | 0.753720i | −0.562148 | − | 0.827037i | \(-0.690025\pi\) |
0.997309 | + | 0.0733164i | \(0.0233583\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −19.7371 | − | 34.1857i | −0.157897 | − | 0.273486i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −212.021 | −1.35763 | −0.678815 | − | 0.734309i | \(-0.737506\pi\) | ||||
−0.678815 | + | 0.734309i | \(0.737506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −79.6238 | − | 137.912i | −0.461318 | − | 0.799026i | 0.537709 | − | 0.843130i | \(-0.319290\pi\) |
−0.999027 | + | 0.0441046i | \(0.985956\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 55.2371 | − | 95.6735i | 0.291380 | − | 0.504685i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −64.3351 | + | 111.432i | −0.285855 | + | 0.495115i | −0.972816 | − | 0.231579i | \(-0.925611\pi\) |
0.686961 | + | 0.726694i | \(0.258944\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 130.686 | + | 226.354i | 0.536576 | + | 0.929376i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 298.042 | 1.13527 | 0.567637 | − | 0.823279i | \(-0.307858\pi\) | ||||
0.567637 | + | 0.823279i | \(0.307858\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −33.3297 | −0.118203 | −0.0591016 | − | 0.998252i | \(-0.518824\pi\) | ||||
−0.0591016 | + | 0.998252i | \(0.518824\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −57.7114 | − | 99.9590i | −0.191180 | − | 0.331134i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 135.598 | − | 234.863i | 0.420830 | − | 0.728899i | −0.575191 | − | 0.818019i | \(-0.695072\pi\) |
0.996021 | + | 0.0891205i | \(0.0284056\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 153.897 | − | 266.557i | 0.422547 | − | 0.731873i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −224.134 | − | 388.212i | −0.580890 | − | 1.00613i | −0.995374 | − | 0.0960750i | \(-0.969371\pi\) |
0.414484 | − | 0.910057i | \(-0.363962\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −472.268 | −1.15783 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −287.474 | −0.668016 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −334.237 | − | 578.916i | −0.737525 | − | 1.27743i | −0.953607 | − | 0.301055i | \(-0.902661\pi\) |
0.216082 | − | 0.976375i | \(-0.430672\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −121.846 | + | 211.043i | −0.255750 | + | 0.442971i | −0.965099 | − | 0.261886i | \(-0.915656\pi\) |
0.709349 | + | 0.704857i | \(0.248989\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 558.670 | − | 967.645i | 1.06607 | − | 1.84649i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 167.789 | + | 290.618i | 0.305950 | + | 0.529921i | 0.977472 | − | 0.211063i | \(-0.0676927\pi\) |
−0.671522 | + | 0.740984i | \(0.734359\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −288.000 | −0.502480 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −339.608 | −0.567663 | −0.283831 | − | 0.958874i | \(-0.591606\pi\) | ||||
−0.283831 | + | 0.958874i | \(0.591606\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −459.160 | − | 795.288i | −0.736173 | − | 1.27509i | −0.954207 | − | 0.299147i | \(-0.903298\pi\) |
0.218034 | − | 0.975941i | \(-0.430036\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −59.2114 | + | 102.557i | −0.0911619 | + | 0.157897i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 68.1495 | − | 118.038i | 0.0970559 | − | 0.168106i | −0.813409 | − | 0.581692i | \(-0.802391\pi\) |
0.910465 | + | 0.413587i | \(0.135724\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −287.464 | −0.380160 | −0.190080 | − | 0.981769i | \(-0.560875\pi\) | ||||
−0.190080 | + | 0.981769i | \(0.560875\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1315.79 | −1.67903 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 318.031 | + | 550.846i | 0.391914 | + | 0.678815i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 80.9277 | − | 140.171i | 0.0963856 | − | 0.166945i | −0.813800 | − | 0.581144i | \(-0.802605\pi\) |
0.910186 | + | 0.414200i | \(0.135938\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −238.871 | + | 413.737i | −0.266342 | + | 0.461318i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 614.464 | + | 1064.28i | 0.663607 | + | 1.14940i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −182.680 | −0.191220 | −0.0956101 | − | 0.995419i | \(-0.530480\pi\) | ||||
−0.0956101 | + | 0.995419i | \(0.530480\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −331.423 | −0.336457 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −766.051 | − | 1326.84i | −0.754703 | − | 1.30718i | −0.945522 | − | 0.325558i | \(-0.894448\pi\) |
0.190819 | − | 0.981625i | \(-0.438886\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 243.954 | − | 422.541i | 0.233374 | − | 0.404215i | −0.725425 | − | 0.688301i | \(-0.758357\pi\) |
0.958799 | + | 0.284086i | \(0.0916901\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −246.176 | + | 426.389i | −0.222418 | + | 0.385239i | −0.955542 | − | 0.294856i | \(-0.904728\pi\) |
0.733124 | + | 0.680095i | \(0.238062\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −424.036 | − | 734.452i | −0.372617 | − | 0.645392i | 0.617350 | − | 0.786689i | \(-0.288206\pi\) |
−0.989967 | + | 0.141296i | \(0.954873\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 386.011 | 0.330077 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −736.350 | −0.613009 | −0.306505 | − | 0.951869i | \(-0.599159\pi\) | ||||
−0.306505 | + | 0.951869i | \(0.599159\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 615.588 | + | 1066.23i | 0.499164 | + | 0.864578i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 392.057 | − | 679.062i | 0.309792 | − | 0.536576i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5312 | + | 21.7046i | −0.00941485 | + | 0.0163070i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −447.062 | − | 774.335i | −0.327726 | − | 0.567637i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1096.85 | −0.784839 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2511.37 | −1.75471 | −0.877355 | − | 0.479841i | \(-0.840694\pi\) | ||||
−0.877355 | + | 0.479841i | \(0.840694\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 49.9946 | + | 86.5931i | 0.0341223 | + | 0.0591016i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −339.711 | + | 588.397i | −0.226570 | + | 0.392431i | −0.956789 | − | 0.290782i | \(-0.906085\pi\) |
0.730219 | + | 0.683213i | \(0.239418\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −173.134 | + | 299.877i | −0.110378 | + | 0.191180i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 82.2683 | + | 142.493i | 0.0513040 | + | 0.0888612i | 0.890537 | − | 0.454911i | \(-0.150329\pi\) |
−0.839233 | + | 0.543772i | \(0.816996\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 521.991 | 0.318523 | 0.159261 | − | 0.987236i | \(-0.449089\pi\) | ||||
0.159261 | + | 0.987236i | \(0.449089\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −813.588 | −0.485932 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1604.16 | − | 2778.48i | −0.938085 | − | 1.62481i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1359.56 | − | 2354.82i | 0.778656 | − | 1.34867i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1206.06 | − | 2088.96i | 0.663117 | − | 1.14855i | −0.316675 | − | 0.948534i | \(-0.602566\pi\) |
0.979792 | − | 0.200019i | \(-0.0641003\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 787.289 | + | 1363.62i | 0.424296 | + | 0.734902i | 0.996354 | − | 0.0853111i | \(-0.0271884\pi\) |
−0.572059 | + | 0.820213i | \(0.693855\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −923.382 | −0.487915 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2042.31 | 1.05834 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1039.37 | + | 1800.24i | 0.528349 | + | 0.915128i | 0.999454 | + | 0.0330505i | \(0.0105222\pi\) |
−0.471104 | + | 0.882078i | \(0.656144\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −672.402 | + | 1164.64i | −0.335377 | + | 0.580890i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1589.71 | − | 2753.46i | 0.763901 | − | 1.32312i | −0.176924 | − | 0.984224i | \(-0.556615\pi\) |
0.940826 | − | 0.338891i | \(-0.110052\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 708.402 | + | 1226.99i | 0.334237 | + | 0.578915i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2979.28 | 1.38050 | 0.690250 | − | 0.723571i | \(-0.257500\pi\) | ||||
0.690250 | + | 0.723571i | \(0.257500\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5393.55 | 2.45496 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 431.211 | + | 746.880i | 0.192840 | + | 0.334008i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.18518 | − | 14.1772i | 0.00359716 | − | 0.00623046i | −0.864221 | − | 0.503112i | \(-0.832188\pi\) |
0.867818 | + | 0.496882i | \(0.165522\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1002.71 | + | 1736.75i | −0.425810 | + | 0.737525i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1349.15 | − | 2336.79i | −0.563351 | − | 0.975753i | −0.997201 | − | 0.0747677i | \(-0.976178\pi\) |
0.433850 | − | 0.900985i | \(-0.357155\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −31.3297 | −0.0128659 | −0.00643293 | − | 0.999979i | \(-0.502048\pi\) | ||||
−0.00643293 | + | 0.999979i | \(0.502048\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 731.073 | 0.295314 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −825.082 | − | 1429.08i | −0.327899 | − | 0.567937i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1889.07 | + | 3271.97i | −0.738731 | + | 1.27952i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 772.587 | − | 1338.16i | 0.292683 | − | 0.506942i | −0.681760 | − | 0.731576i | \(-0.738785\pi\) |
0.974443 | + | 0.224634i | \(0.0721186\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 915.099 | + | 1585.00i | 0.341297 | + | 0.591143i | 0.984674 | − | 0.174406i | \(-0.0558006\pi\) |
−0.643377 | + | 0.765549i | \(0.722467\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3352.02 | −1.23099 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4728.45 | 1.71009 | 0.855047 | − | 0.518551i | \(-0.173528\pi\) | ||||
0.855047 | + | 0.518551i | \(0.173528\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −164.125 | − | 284.272i | −0.0584648 | − | 0.101264i | 0.835312 | − | 0.549777i | \(-0.185287\pi\) |
−0.893776 | + | 0.448513i | \(0.851954\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 503.366 | − | 871.855i | 0.176640 | − | 0.305950i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1911.15 | + | 3310.22i | −0.651126 | + | 1.12778i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 432.000 | + | 748.246i | 0.145054 | + | 0.251240i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3528.72 | 1.16788 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4935.76 | −1.61039 | −0.805193 | − | 0.593013i | \(-0.797938\pi\) | ||||
−0.805193 | + | 0.593013i | \(0.797938\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 509.412 | + | 882.327i | 0.163870 | + | 0.283831i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 213.723 | − | 370.179i | 0.0677943 | − | 0.117423i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1377.48 | + | 2385.86i | −0.425029 | + | 0.736173i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4469.36 | − | 7741.16i | −1.36037 | − | 2.35623i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3446.00 | −1.03480 | −0.517402 | − | 0.855742i | \(-0.673101\pi\) | ||||
−0.517402 | + | 0.855742i | \(0.673101\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 355.268 | 0.105265 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2862.37 | + | 4957.77i | 0.836927 | + | 1.44960i | 0.892452 | + | 0.451142i | \(0.148983\pi\) |
−0.0555255 | + | 0.998457i | \(0.517683\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1508.57 | − | 2612.93i | 0.435325 | − | 0.754004i | −0.561997 | − | 0.827139i | \(-0.689967\pi\) |
0.997322 | + | 0.0731345i | \(0.0233002\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −190.856 | + | 330.573i | −0.0536627 | + | 0.0929466i | −0.891609 | − | 0.452806i | \(-0.850423\pi\) |
0.837946 | + | 0.545753i | \(0.183756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1739.01 | + | 3012.06i | 0.482726 | + | 0.836106i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −408.897 | −0.112071 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1377.38 | −0.372785 | −0.186392 | − | 0.982475i | \(-0.559680\pi\) | ||||
−0.186392 | + | 0.982475i | \(0.559680\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2903.36 | + | 5028.77i | 0.776025 | + | 1.34411i | 0.934217 | + | 0.356706i | \(0.116100\pi\) |
−0.158192 | + | 0.987408i | \(0.550566\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −121.500 | + | 210.444i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4174.31 | + | 7230.11i | −1.07532 | + | 1.86251i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 431.196 | + | 746.854i | 0.109743 | + | 0.190080i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4348.52 | 1.09353 | 0.546765 | − | 0.837286i | \(-0.315859\pi\) | ||||
0.546765 | + | 0.837286i | \(0.315859\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3535.18 | 0.878477 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1973.69 | + | 3418.53i | 0.484695 | + | 0.839517i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2345.56 | + | 4062.62i | −0.569307 | + | 0.986068i | 0.427328 | + | 0.904097i | \(0.359455\pi\) |
−0.996635 | + | 0.0819713i | \(0.973878\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 954.094 | − | 1652.54i | 0.226272 | − | 0.391914i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3790.81 | + | 6565.87i | 0.888788 | + | 1.53943i | 0.841310 | + | 0.540553i | \(0.181785\pi\) |
0.0474778 | + | 0.998872i | \(0.484882\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5748.93 | 1.33266 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −485.566 | −0.111297 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1800.95 | − | 3119.33i | −0.408200 | − | 0.707023i | 0.586488 | − | 0.809958i | \(-0.300510\pi\) |
−0.994688 | + | 0.102935i | \(0.967177\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1918.13 | + | 3322.31i | −0.429957 | + | 0.744707i | −0.996869 | − | 0.0790710i | \(-0.974805\pi\) |
0.566912 | + | 0.823778i | \(0.308138\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 726.815 | − | 1258.88i | 0.159377 | − | 0.276048i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2701.52 | − | 4679.17i | −0.585988 | − | 1.01496i | −0.994751 | − | 0.102321i | \(-0.967373\pi\) |
0.408763 | − | 0.912640i | \(-0.365960\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1433.23 | 0.307545 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 150.842 | 0.0320230 | 0.0160115 | − | 0.999872i | \(-0.494903\pi\) | ||||
0.0160115 | + | 0.999872i | \(0.494903\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 908.571 | + | 1573.69i | 0.190844 | + | 0.330552i | 0.945530 | − | 0.325534i | \(-0.105544\pi\) |
−0.754686 | + | 0.656086i | \(0.772211\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1843.39 | − | 3192.85i | 0.383134 | − | 0.663607i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2806.68 | + | 4861.31i | −0.571275 | + | 0.989478i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 274.020 | + | 474.617i | 0.0552005 | + | 0.0956101i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2817.59 | 0.561792 | 0.280896 | − | 0.959738i | \(-0.409368\pi\) | ||||
0.280896 | + | 0.959738i | \(0.409368\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8573.02 | 1.69200 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 497.134 | + | 861.062i | 0.0971268 | + | 0.168228i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4181.94 | + | 7243.33i | −0.808856 | + | 1.40098i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2298.15 | + | 3980.52i | −0.435728 | + | 0.754703i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1562.64 | − | 2706.57i | −0.293365 | − | 0.508124i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8589.21 | −1.59678 | −0.798391 | − | 0.602139i | \(-0.794315\pi\) | ||||
−0.798391 | + | 0.602139i | \(0.794315\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1463.72 | −0.269477 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2999.15 | − | 5194.67i | −0.546836 | − | 0.947147i | −0.998489 | − | 0.0549538i | \(-0.982499\pi\) |
0.451653 | − | 0.892194i | \(-0.350834\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2481.64 | + | 4298.32i | −0.448148 | + | 0.776216i | −0.998266 | − | 0.0588717i | \(-0.981250\pi\) |
0.550117 | + | 0.835087i | \(0.314583\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1952.30 | − | 3381.49i | 0.345906 | − | 0.599127i | −0.639612 | − | 0.768698i | \(-0.720905\pi\) |
0.985518 | + | 0.169571i | \(0.0542383\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3903.81 | − | 6761.59i | −0.685176 | − | 1.18676i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1477.05 | 0.256826 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9831.43 | 1.69361 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1719.57 | + | 2978.39i | 0.293491 | + | 0.508342i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1272.11 | + | 2203.36i | −0.215131 | + | 0.372617i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1224.86 | − | 2121.52i | 0.203397 | − | 0.352295i | −0.746224 | − | 0.665695i | \(-0.768135\pi\) |
0.949621 | + | 0.313401i | \(0.101468\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −579.016 | − | 1002.89i | −0.0952850 | − | 0.165038i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4303.69 | −0.701898 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1770.59 | −0.286203 | −0.143101 | − | 0.989708i | \(-0.545707\pi\) | ||||
−0.143101 | + | 0.989708i | \(0.545707\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1104.53 | + | 1913.09i | 0.176960 | + | 0.306505i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2932.13 | − | 5078.59i | 0.465641 | − | 0.806513i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1846.76 | − | 3198.69i | 0.288193 | − | 0.499164i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2017.36 | + | 3494.17i | 0.312097 | + | 0.540567i | 0.978816 | − | 0.204741i | \(-0.0656353\pi\) |
−0.666719 | + | 0.745309i | \(0.732302\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6791.53 | −1.04167 | −0.520834 | − | 0.853658i | \(-0.674379\pi\) | ||||
−0.520834 | + | 0.853658i | \(0.674379\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2352.34 | −0.357717 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5078.40 | − | 8796.05i | −0.765712 | − | 1.32625i | −0.939870 | − | 0.341534i | \(-0.889054\pi\) |
0.174158 | − | 0.984718i | \(-0.444280\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2177.69 | − | 3771.88i | 0.325577 | − | 0.563917i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6421.36 | − | 11122.1i | 0.944029 | − | 1.63511i | 0.186347 | − | 0.982484i | \(-0.440335\pi\) |
0.757683 | − | 0.652623i | \(-0.226331\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1161.69 | − | 2012.11i | −0.169367 | − | 0.293353i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 75.1870 | 0.0108713 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11777.2 | 1.68890 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −957.408 | − | 1658.28i | −0.136175 | − | 0.235862i | 0.789871 | − | 0.613274i | \(-0.210148\pi\) |
−0.926046 | + | 0.377411i | \(0.876814\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1341.19 | + | 2323.00i | −0.189212 | + | 0.327726i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2857.43 | + | 4949.21i | −0.396654 | + | 0.687026i | −0.993311 | − | 0.115471i | \(-0.963162\pi\) |
0.596656 | + | 0.802497i | \(0.296496\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1645.27 | + | 2849.69i | 0.226564 | + | 0.392420i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18472.0 | 2.52350 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11570.3 | −1.56815 | −0.784075 | − | 0.620666i | \(-0.786862\pi\) | ||||
−0.784075 | + | 0.620666i | \(0.786862\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3767.06 | + | 6524.74i | 0.506541 | + | 0.877355i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3059.01 | − | 5298.36i | 0.408115 | − | 0.706876i | −0.586563 | − | 0.809903i | \(-0.699519\pi\) |
0.994679 | + | 0.103027i | \(0.0328528\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 149.984 | − | 259.779i | 0.0197005 | − | 0.0341223i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1629.23 | + | 2821.91i | 0.212353 | + | 0.367806i | 0.952450 | − | 0.304694i | \(-0.0985541\pi\) |
−0.740098 | + | 0.672499i | \(0.765221\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9849.41 | 1.27393 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2038.27 | 0.261621 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 874.000 | + | 1513.81i | 0.111331 | + | 0.192831i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 361.963 | − | 626.938i | 0.0457592 | − | 0.0792572i | −0.842239 | − | 0.539105i | \(-0.818763\pi\) |
0.887998 | + | 0.459848i | \(0.152096\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5514.91 | + | 9552.11i | −0.686787 | + | 1.18955i | 0.286085 | + | 0.958204i | \(0.407646\pi\) |
−0.972872 | + | 0.231346i | \(0.925687\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6937.12 | + | 12015.4i | 0.857475 | + | 1.48519i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1038.80 | 0.127453 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4738.25 | −0.577067 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1341.78 | + | 2324.03i | 0.162217 | + | 0.280968i | 0.935663 | − | 0.352894i | \(-0.114802\pi\) |
−0.773447 | + | 0.633861i | \(0.781469\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 246.805 | − | 427.479i | 0.0296204 | − | 0.0513040i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1843.33 | − | 3192.74i | 0.218037 | − | 0.377652i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −782.986 | − | 1356.17i | −0.0919497 | − | 0.159261i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10024.9 | −1.16885 | −0.584427 | − | 0.811446i | \(-0.698681\pi\) | ||||
−0.584427 | + | 0.811446i | \(0.698681\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5560.68 | −0.643731 | −0.321866 | − | 0.946785i | \(-0.604310\pi\) | ||||
−0.321866 | + | 0.946785i | \(0.604310\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1220.38 | + | 2113.76i | 0.140277 | + | 0.242966i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2024.99 | − | 3507.39i | 0.231121 | − | 0.400313i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4812.47 | + | 8335.44i | −0.541604 | + | 0.938085i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5763.11 | − | 9982.00i | −0.644081 | − | 1.11558i | −0.984513 | − | 0.175312i | \(-0.943906\pi\) |
0.340431 | − | 0.940269i | \(-0.389427\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2228.79 | −0.247365 | −0.123683 | − | 0.992322i | \(-0.539470\pi\) | ||||
−0.123683 | + | 0.992322i | \(0.539470\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8157.34 | −0.899114 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4599.59 | − | 7966.72i | −0.503497 | − | 0.872082i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2304.63 | − | 3991.74i | 0.250556 | − | 0.433975i | −0.713123 | − | 0.701039i | \(-0.752720\pi\) |
0.963679 | + | 0.267063i | \(0.0860533\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −531.662 | + | 920.865i | −0.0570203 | + | 0.0987621i | −0.893127 | − | 0.449805i | \(-0.851493\pi\) |
0.836106 | + | 0.548568i | \(0.184827\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1037.88 | + | 1797.66i | 0.110562 | + | 0.191499i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7236.37 | −0.765702 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12265.9 | −1.28923 | −0.644613 | − | 0.764509i | \(-0.722982\pi\) | ||||
−0.644613 | + | 0.764509i | \(0.722982\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5487.65 | + | 9504.89i | 0.572957 | + | 0.992390i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2361.87 | − | 4090.87i | 0.244967 | − | 0.424296i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8895.59 | − | 15407.6i | 0.910543 | − | 1.57711i | 0.0972436 | − | 0.995261i | \(-0.468997\pi\) |
0.813299 | − | 0.581846i | \(-0.197669\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1385.07 | + | 2399.02i | 0.140849 | + | 0.243958i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15368.9 | −1.55272 | −0.776358 | − | 0.630293i | \(-0.782935\pi\) | ||||
−0.776358 | + | 0.630293i | \(0.782935\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4104.98 | −0.412040 | −0.206020 | − | 0.978548i | \(-0.566051\pi\) | ||||
−0.206020 | + | 0.978548i | \(0.566051\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3063.46 | − | 5306.08i | −0.305516 | − | 0.529169i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1903.68 | − | 3297.27i | 0.188634 | − | 0.326723i | −0.756161 | − | 0.654385i | \(-0.772927\pi\) |
0.944795 | + | 0.327662i | \(0.106261\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3118.11 | − | 5400.73i | 0.305043 | − | 0.528349i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −613.679 | − | 1062.92i | −0.0596554 | − | 0.103326i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3782.61 | −0.365385 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4034.41 | 0.387260 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4937.33 | + | 8551.70i | 0.470965 | + | 0.815735i | 0.999448 | − | 0.0332085i | \(-0.0105725\pi\) |
−0.528484 | + | 0.848943i | \(0.677239\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5605.12 | − | 9708.35i | 0.531334 | − | 0.920297i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1171.41 | − | 2028.95i | 0.109673 | − | 0.189958i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3381.86 | + | 5857.56i | 0.314675 | + | 0.545033i | 0.979368 | − | 0.202083i | \(-0.0647711\pi\) |
−0.664693 | + | 0.747116i | \(0.731438\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9538.28 | −0.882077 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5574.29 | −0.512351 | −0.256175 | − | 0.966630i | \(-0.582462\pi\) | ||||
−0.256175 | + | 0.966630i | \(0.582462\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10876.5 | − | 18838.6i | −0.993612 | − | 1.72099i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2125.21 | − | 3680.97i | 0.192972 | − | 0.334237i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2893.73 | + | 5012.09i | −0.259601 | + | 0.449643i | −0.966135 | − | 0.258037i | \(-0.916925\pi\) |
0.706534 | + | 0.707679i | \(0.250258\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4468.92 | − | 7740.39i | −0.398516 | − | 0.690250i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8296.10 | −0.735397 | −0.367699 | − | 0.929945i | \(-0.619854\pi\) | ||||
−0.367699 | + | 0.929945i | \(0.619854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19648.8 | 1.73141 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8090.32 | − | 14012.9i | −0.708686 | − | 1.22748i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4880.19 | + | 8452.74i | −0.424972 | + | 0.736073i | −0.996418 | − | 0.0845670i | \(-0.973049\pi\) |
0.571446 | + | 0.820640i | \(0.306383\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1293.63 | − | 2240.64i | 0.111336 | − | 0.192840i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3128.65 | + | 5418.98i | 0.267699 | + | 0.463667i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9986.73 | 0.849547 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −49.1111 | −0.00415364 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3268.99 | − | 5662.06i | −0.274889 | − | 0.476121i | 0.695218 | − | 0.718799i | \(-0.255308\pi\) |
−0.970107 | + | 0.242677i | \(0.921974\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5171.92 | + | 8958.02i | −0.432413 | + | 0.748962i | −0.997081 | − | 0.0763570i | \(-0.975671\pi\) |
0.564667 | + | 0.825319i | \(0.309004\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8169.24 | − | 14149.5i | 0.675252 | − | 1.16957i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1475.50 | + | 2555.64i | 0.121271 | + | 0.210047i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6016.27 | 0.491683 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25966.5 | −2.11020 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3157.14 | − | 5468.33i | −0.255131 | − | 0.441900i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4047.44 | + | 7010.37i | −0.325251 | + | 0.563351i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3421.60 | − | 5926.38i | 0.271915 | − | 0.470970i | −0.697437 | − | 0.716646i | \(-0.745676\pi\) |
0.969352 | + | 0.245676i | \(0.0790098\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 46.9946 | + | 81.3970i | 0.00371405 | + | 0.00643293i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10876.3 | 0.854844 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18402.1 | −1.43842 | −0.719211 | − | 0.694791i | \(-0.755497\pi\) | ||||
−0.719211 | + | 0.694791i | \(0.755497\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1096.61 | − | 1899.38i | −0.0852498 | − | 0.147657i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10158.4 | + | 17594.9i | −0.785414 | + | 1.36038i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2475.25 | + | 4287.25i | −0.189312 | + | 0.327899i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −323.239 | − | 559.866i | −0.0245890 | − | 0.0425894i | 0.853469 | − | 0.521144i | \(-0.174494\pi\) |
−0.878058 | + | 0.478554i | \(0.841161\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2903.81 | 0.219710 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11334.4 | 0.853013 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3087.40 | + | 5347.53i | 0.231116 | + | 0.400305i | 0.958137 | − | 0.286311i | \(-0.0924289\pi\) |
−0.727021 | + | 0.686616i | \(0.759096\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4721.76 | − | 8178.32i | 0.351585 | − | 0.608964i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3418.59 | − | 5921.17i | 0.251871 | − | 0.436253i | −0.712170 | − | 0.702007i | \(-0.752287\pi\) |
0.964041 | + | 0.265754i | \(0.0856208\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2942.77 | + | 5097.03i | 0.215676 | + | 0.373562i | 0.953482 | − | 0.301451i | \(-0.0974711\pi\) |
−0.737805 | + | 0.675014i | \(0.764138\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4635.52 | −0.337961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3789.53 | −0.274842 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6001.62 | − | 10395.1i | −0.433017 | − | 0.750007i | 0.564115 | − | 0.825696i | \(-0.309218\pi\) |
−0.997131 | + | 0.0756896i | \(0.975884\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2745.30 | − | 4754.99i | 0.197048 | − | 0.341297i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8253.68 | − | 14295.8i | 0.586334 | − | 1.01556i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5028.03 | + | 8708.81i | 0.355357 | + | 0.615496i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12719.4 | 0.894358 | 0.447179 | − | 0.894445i | \(-0.352429\pi\) | ||||
0.447179 | + | 0.894445i | \(0.352429\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15259.9 | −1.06752 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7092.68 | − | 12284.9i | −0.493661 | − | 0.855047i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9580.20 | − | 16593.4i | 0.663426 | − | 1.14909i | −0.316283 | − | 0.948665i | \(-0.602435\pi\) |
0.979709 | − | 0.200423i | \(-0.0642317\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −492.374 | + | 852.817i | −0.0337547 | + | 0.0584648i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −533.983 | − | 924.885i | −0.0364240 | − | 0.0630881i | 0.847239 | − | 0.531212i | \(-0.178263\pi\) |
−0.883663 | + | 0.468124i | \(0.844930\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7554.96 | −0.512768 | −0.256384 | − | 0.966575i | \(-0.582531\pi\) | ||||
−0.256384 | + | 0.966575i | \(0.582531\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3020.20 | −0.203967 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −160.709 | − | 278.356i | −0.0107996 | − | 0.0187054i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5888.71 | + | 10199.5i | −0.393765 | + | 0.682020i | −0.992943 | − | 0.118595i | \(-0.962161\pi\) |
0.599178 | + | 0.800616i | \(0.295494\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11813.8 | + | 20462.1i | −0.782219 | + | 1.35484i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13426.5 | − | 23255.3i | −0.884649 | − | 1.53226i | −0.846115 | − | 0.533000i | \(-0.821065\pi\) |
−0.0385337 | − | 0.999257i | \(-0.512269\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11466.9 | 0.751855 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6816.72 | −0.444782 | −0.222391 | − | 0.974958i | \(-0.571386\pi\) | ||||
−0.222391 | + | 0.974958i | \(0.571386\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8356.74 | − | 14474.3i | −0.542627 | − | 0.939857i | −0.998752 | − | 0.0499414i | \(-0.984097\pi\) |
0.456126 | − | 0.889915i | \(-0.349237\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1296.00 | − | 2244.74i | 0.0837467 | − | 0.145054i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9500.53 | − | 16455.4i | 0.608034 | − | 1.05315i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5293.08 | − | 9167.89i | −0.337138 | − | 0.583940i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13201.3 | −0.836838 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 592.225 | 0.0373631 | 0.0186815 | − | 0.999825i | \(-0.494053\pi\) | ||||
0.0186815 | + | 0.999825i | \(0.494053\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7403.63 | + | 12823.5i | 0.464878 | + | 0.805193i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16103.9 | − | 27892.7i | 1.00640 | − | 1.74313i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1528.24 | − | 2646.98i | 0.0946104 | − | 0.163870i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3481.96 | − | 6030.92i | −0.214554 | − | 0.371618i | 0.738581 | − | 0.674165i | \(-0.235496\pi\) |
−0.953134 | + | 0.302547i | \(0.902163\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5466.06 | −0.335242 | −0.167621 | − | 0.985852i | \(-0.553608\pi\) | ||||
−0.167621 | + | 0.985852i | \(0.553608\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1282.34 | −0.0782821 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −618.633 | − | 1071.50i | −0.0375904 | − | 0.0651085i | 0.846618 | − | 0.532201i | \(-0.178635\pi\) |
−0.884209 | + | 0.467092i | \(0.845302\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12308.2 | − | 21318.4i | 0.744436 | − | 1.28940i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13575.9 | + | 23514.2i | −0.813578 | + | 1.40916i | 0.0967657 | + | 0.995307i | \(0.469150\pi\) |
−0.910344 | + | 0.413852i | \(0.864183\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4356.71 | − | 7546.05i | −0.259895 | − | 0.450151i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8264.88 | 0.490782 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5900.66 | 0.348797 | 0.174398 | − | 0.984675i | \(-0.444202\pi\) | ||||
0.174398 | + | 0.984675i | \(0.444202\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1809.49 | + | 3134.13i | 0.106477 | + | 0.184423i | 0.914341 | − | 0.404946i | \(-0.132710\pi\) |
−0.807864 | + | 0.589369i | \(0.799376\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13408.1 | + | 23223.5i | −0.785410 | + | 1.36037i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10177.0 | + | 17627.1i | −0.590787 | + | 1.02327i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5169.00 | + | 8952.98i | 0.298722 | + | 0.517402i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8973.86 | −0.516292 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13952.5 | −0.799151 | −0.399576 | − | 0.916700i | \(-0.630842\pi\) | ||||
−0.399576 | + | 0.916700i | \(0.630842\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −532.902 | − | 923.014i | −0.0303873 | − | 0.0526323i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14459.4 | + | 25044.5i | −0.820859 | + | 1.42177i | 0.0841848 | + | 0.996450i | \(0.473171\pi\) |
−0.905044 | + | 0.425319i | \(0.860162\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8587.12 | − | 14873.3i | 0.483200 | − | 0.836927i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5565.06 | + | 9638.97i | 0.311773 | + | 0.540007i | 0.978746 | − | 0.205075i | \(-0.0657437\pi\) |
−0.666973 | + | 0.745082i | \(0.732410\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2110.14 | −0.117700 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9051.44 | −0.502670 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19527.4 | + | 33822.5i | 1.07973 | + | 1.87015i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7012.64 | + | 12146.2i | −0.386069 | + | 0.668690i | −0.991917 | − | 0.126890i | \(-0.959501\pi\) |
0.605848 | + | 0.795580i | \(0.292834\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3347.20 | + | 5797.52i | −0.182686 | + | 0.316421i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15289.2 | + | 26481.7i | 0.830877 | + | 1.43912i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1145.14 | 0.0619644 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30366.7 | 1.63614 | 0.818070 | − | 0.575119i | \(-0.195044\pi\) | ||||
0.818070 | + | 0.575119i | \(0.195044\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6164.90 | + | 10677.9i | 0.330745 | + | 0.572867i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5217.03 | − | 9036.17i | 0.278702 | − | 0.482726i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8445.48 | + | 14628.0i | −0.447358 | + | 0.774847i | −0.998213 | − | 0.0597542i | \(-0.980968\pi\) |
0.550855 | + | 0.834601i | \(0.314302\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 613.346 | + | 1062.35i | 0.0323520 | + | 0.0560353i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15287.8 | −0.802989 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41145.8 | 2.15212 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2066.08 | + | 3578.55i | 0.107614 | + | 0.186392i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5503.61 | − | 9532.54i | 0.285466 | − | 0.494442i | −0.687256 | − | 0.726415i | \(-0.741185\pi\) |
0.972722 | + | 0.231973i | \(0.0745182\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8710.09 | − | 15086.3i | 0.448038 | − | 0.776025i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4184.68 | + | 7248.08i | 0.214366 | + | 0.371292i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14618.0 | 0.745737 | 0.372869 | − | 0.927884i | \(-0.378374\pi\) | ||||
0.372869 | + | 0.927884i | \(0.378374\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1709.78 | − | 2961.43i | −0.0865096 | − | 0.149839i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14261.1 | + | 24701.0i | −0.718617 | + | 1.24468i | 0.242930 | + | 0.970044i | \(0.421891\pi\) |
−0.961548 | + | 0.274638i | \(0.911442\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6178.77 | + | 10702.0i | −0.308817 | + | 0.534887i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10119.7 | − | 17527.9i | −0.503735 | − | 0.872495i | −0.999991 | − | 0.00431822i | \(-0.998625\pi\) |
0.496256 | − | 0.868176i | \(-0.334708\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25045.8 | 1.24168 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13977.6 | 0.690159 | 0.345079 | − | 0.938573i | \(-0.387852\pi\) | ||||
0.345079 | + | 0.938573i | \(0.387852\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15467.4 | + | 26790.4i | 0.760649 | + | 1.31748i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1293.59 | − | 2240.56i | 0.0633601 | − | 0.109743i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7513.90 | + | 13014.5i | −0.365095 | + | 0.632363i | −0.988791 | − | 0.149304i | \(-0.952297\pi\) |
0.623697 | + | 0.781667i | \(0.285630\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6522.78 | − | 11297.8i | −0.315675 | − | 0.546765i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20193.6 | −0.973403 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20769.4 | 0.997196 | 0.498598 | − | 0.866833i | \(-0.333848\pi\) | ||||
0.498598 | + | 0.866833i | \(0.333848\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5302.76 | − | 9184.66i | −0.253594 | − | 0.439238i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5605.57 | − | 9709.13i | 0.267019 | − | 0.462491i | −0.701071 | − | 0.713091i | \(-0.747295\pi\) |
0.968091 | + | 0.250600i | \(0.0806279\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5921.07 | − | 10255.6i | 0.279839 | − | 0.484695i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 29120.0 | + | 50437.3i | 1.37088 | + | 2.37443i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4305.86 | −0.201916 | −0.100958 | − | 0.994891i | \(-0.532191\pi\) | ||||
−0.100958 | + | 0.994891i | \(0.532191\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14073.3 | 0.657379 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8320.24 | + | 14411.1i | 0.387139 | + | 0.670544i | 0.992063 | − | 0.125739i | \(-0.0401302\pi\) |
−0.604925 | + | 0.796283i | \(0.706797\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3143.09 | + | 5443.99i | −0.145681 | + | 0.252328i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14279.9 | − | 24733.5i | 0.656778 | − | 1.13757i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6252.99 | − | 10830.5i | −0.286491 | − | 0.496217i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5724.56 | −0.261276 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26659.4 | −1.21212 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4883.53 | − | 8458.51i | −0.221193 | − | 0.383118i | 0.733977 | − | 0.679174i | \(-0.237662\pi\) |
−0.955171 | + | 0.296056i | \(0.904328\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11372.4 | − | 19697.6i | 0.513142 | − | 0.888788i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10615.6 | − | 18386.8i | 0.475375 | − | 0.823374i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8623.39 | − | 14936.2i | −0.384705 | − | 0.666328i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23118.5 | −1.02748 | −0.513738 | − | 0.857947i | \(-0.671740\pi\) | ||||
−0.513738 | + | 0.857947i | \(0.671740\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27824.2 | 1.23198 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 728.350 | + | 1261.54i | 0.0321285 | + | 0.0556483i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16908.4 | − | 29286.3i | 0.743071 | − | 1.28704i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5402.84 | + | 9358.00i | −0.235674 | + | 0.408200i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5230.33 | − | 9059.20i | −0.227304 | − | 0.393701i | 0.729705 | − | 0.683763i | \(-0.239658\pi\) |
−0.957008 | + | 0.290061i | \(0.906324\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9167.55 | 0.396937 | 0.198469 | − | 0.980107i | \(-0.436403\pi\) | ||||
0.198469 | + | 0.980107i | \(0.436403\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11508.8 | 0.496472 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20387.7 | + | 35312.5i | 0.876256 | + | 1.51772i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1596.91 | + | 2765.92i | −0.0683827 | + | 0.118442i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14413.7 | + | 24965.2i | −0.612717 | + | 1.06126i | 0.378064 | + | 0.925780i | \(0.376590\pi\) |
−0.990780 | + | 0.135477i | \(0.956743\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21397.2 | − | 37061.0i | −0.906268 | − | 1.56970i | −0.819206 | − | 0.573499i | \(-0.805586\pi\) |
−0.0870618 | − | 0.996203i | \(-0.527748\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4360.89 | −0.184032 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6028.87 | −0.253500 | −0.126750 | − | 0.991935i | \(-0.540455\pi\) | ||||
−0.126750 | + | 0.991935i | \(0.540455\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9703.71 | − | 16807.3i | −0.406542 | − | 0.704152i | 0.587957 | − | 0.808892i | \(-0.299932\pi\) |
−0.994500 | + | 0.104740i | \(0.966599\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8104.57 | + | 14037.5i | −0.338320 | + | 0.585988i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19104.3 | + | 33089.5i | −0.791773 | + | 1.37139i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2149.84 | − | 3723.63i | −0.0887806 | − | 0.153773i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10599.5 | 0.436156 | 0.218078 | − | 0.975931i | \(-0.430021\pi\) | ||||
0.218078 | + | 0.975931i | \(0.430021\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20563.8 | 0.843159 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −226.263 | − | 391.899i | −0.00924425 | − | 0.0160115i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34585.5 | + | 59903.8i | −1.40802 | + | 2.43876i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2725.71 | − | 4721.07i | 0.110184 | − | 0.190844i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6176.17 | + | 10697.4i | 0.248786 | + | 0.430909i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34766.1 | 1.39551 | 0.697754 | − | 0.716338i | \(-0.254183\pi\) | ||||
0.697754 | + | 0.716338i | \(0.254183\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11060.4 | −0.442405 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15002.0 | + | 25984.2i | 0.597968 | + | 1.03571i | 0.993121 | + | 0.117096i | \(0.0373584\pi\) |
−0.395153 | + | 0.918615i | \(0.629308\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13065.3 | + | 22629.8i | −0.518955 | + | 0.898857i | 0.480802 | + | 0.876829i | \(0.340345\pi\) |
−0.999757 | + | 0.0220275i | \(0.992988\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22334.2 | + | 38683.9i | −0.880955 | + | 1.52586i | −0.0306737 | + | 0.999529i | \(0.509765\pi\) |
−0.850281 | + | 0.526329i | \(0.823568\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 104.973 | + | 181.818i | 0.00412623 | + | 0.00714684i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16840.1 | 0.659652 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5019.18 | 0.195931 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14618.4 | − | 25319.8i | −0.568685 | − | 0.984992i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 822.061 | − | 1423.85i | 0.0318700 | − | 0.0552005i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1839.28 | + | 3185.72i | −0.0708187 | + | 0.122662i | −0.899260 | − | 0.437414i | \(-0.855895\pi\) |
0.828442 | + | 0.560075i | \(0.189228\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4226.38 | − | 7320.30i | −0.162175 | − | 0.280896i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33443.6 | 1.27894 | 0.639468 | − | 0.768817i | \(-0.279154\pi\) | ||||
0.639468 | + | 0.768817i | \(0.279154\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21095.4 | −0.803983 | −0.401991 | − | 0.915644i | \(-0.631682\pi\) | ||||
−0.401991 | + | 0.915644i | \(0.631682\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12859.5 | − | 22273.3i | −0.488439 | − | 0.846001i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7226.65 | − | 12516.9i | 0.273560 | − | 0.473819i | −0.696211 | − | 0.717837i | \(-0.745132\pi\) |
0.969771 | + | 0.244018i | \(0.0784656\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1491.40 | − | 2583.18i | 0.0560762 | − | 0.0971268i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12993.6 | − | 22505.7i | −0.486916 | − | 0.843363i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34604.9 | 1.29242 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25091.6 | 0.933986 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16881.9 | + | 29240.3i | 0.626299 | + | 1.08478i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22995.7 | − | 39829.8i | 0.850276 | − | 1.47272i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 200.898 | − | 347.965i | 0.00737909 | − | 0.0127810i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2602.04 | + | 4506.87i | 0.0952584 | + | 0.164992i | 0.909716 | − | 0.415230i | \(-0.136299\pi\) |
−0.814458 | + | 0.580223i | \(0.802966\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13788.9 | 0.503135 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31584.8 | 1.14868 | 0.574342 | − | 0.818616i | \(-0.305258\pi\) | ||||
0.574342 | + | 0.818616i | \(0.305258\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5292.90 | − | 9167.57i | −0.191861 | − | 0.332314i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4687.92 | + | 8119.71i | −0.169375 | + | 0.293365i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23315.3 | − | 40383.3i | 0.836889 | − | 1.44953i | −0.0555943 | − | 0.998453i | \(-0.517705\pi\) |
0.892483 | − | 0.451081i | \(-0.148961\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12883.8 | + | 22315.4i | 0.460951 | + | 0.798391i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29587.9 | 1.05514 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5079.16 | 0.180543 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2195.59 | + | 3802.87i | 0.0777912 | + | 0.134738i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19246.3 | + | 33335.6i | −0.679711 | + | 1.17729i | 0.295357 | + | 0.955387i | \(0.404561\pi\) |
−0.975068 | + | 0.221907i | \(0.928772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8997.44 | + | 15584.0i | −0.315716 | + | 0.546836i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −24226.9 | − | 41962.2i | −0.847384 | − | 1.46771i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39893.8 | −1.39090 | −0.695450 | − | 0.718574i | \(-0.744795\pi\) | ||||
−0.695450 | + | 0.718574i | \(0.744795\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14889.8 | 0.517477 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16315.4 | − | 28259.0i | −0.565213 | − | 0.978977i | −0.997030 | − | 0.0770161i | \(-0.975461\pi\) |
0.431817 | − | 0.901961i | \(-0.357873\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14306.0 | − | 24778.7i | 0.494027 | − | 0.855680i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15014.7 | + | 26006.1i | −0.515217 | + | 0.892382i | 0.484627 | + | 0.874721i | \(0.338955\pi\) |
−0.999844 | + | 0.0176614i | \(0.994378\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40003.7 | + | 69288.5i | 1.36836 | + | 2.37007i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11713.8 | −0.399418 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34963.6 | −1.18844 | −0.594220 | − | 0.804303i | \(-0.702539\pi\) | ||||
−0.594220 | + | 0.804303i | \(0.702539\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9908.24 | + | 17161.6i | 0.335731 | + | 0.581503i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11711.4 | + | 20284.8i | −0.395587 | + | 0.685176i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2215.61 | − | 3837.56i | 0.0743719 | − | 0.128816i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2215.58 | − | 3837.50i | −0.0741393 | − | 0.128413i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23471.8 | −0.782990 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20520.5 | 0.682414 | 0.341207 | − | 0.939988i | \(-0.389164\pi\) | ||||
0.341207 | + | 0.939988i | \(0.389164\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14747.1 | − | 25542.8i | −0.488902 | − | 0.846804i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19887.6 | − | 34446.4i | 0.657286 | − | 1.13845i | −0.324029 | − | 0.946047i | \(-0.605038\pi\) |
0.981315 | − | 0.192406i | \(-0.0616290\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5158.72 | − | 8935.16i | 0.169447 | − | 0.293491i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3586.02 | + | 6211.17i | 0.117428 | + | 0.203391i | 0.918748 | − | 0.394845i | \(-0.129202\pi\) |
−0.801320 | + | 0.598236i | \(0.795868\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5960.29 | 0.194578 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7632.65 | 0.248412 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24174.1 | + | 41870.8i | 0.784369 | + | 1.35857i | 0.929375 | + | 0.369137i | \(0.120347\pi\) |
−0.145006 | + | 0.989431i | \(0.546320\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30320.6 | + | 52516.9i | −0.980807 | + | 1.69881i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1599.83 | + | 2770.98i | −0.0514373 | + | 0.0890921i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18472.3 | − | 31994.9i | −0.592121 | − | 1.02558i | −0.993946 | − | 0.109867i | \(-0.964958\pi\) |
0.401826 | − | 0.915716i | \(-0.368376\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7349.18 | −0.234863 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4209.72 | 0.134128 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28294.8 | + | 49008.0i | 0.898802 | + | 1.55677i | 0.829028 | + | 0.559208i | \(0.188895\pi\) |
0.0697741 | + | 0.997563i | \(0.477772\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1737.05 | + | 3008.66i | −0.0550128 | + | 0.0952850i |
(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 | 588.4.i.i.373.1 | 4 | ||
3.2 | odd | 2 | 1764.4.k.z.1549.2 | 4 | |||
7.2 | even | 3 | 588.4.a.h.1.2 | 2 | |||
7.3 | odd | 6 | 84.4.i.b.25.2 | ✓ | 4 | ||
7.4 | even | 3 | inner | 588.4.i.i.361.1 | 4 | ||
7.5 | odd | 6 | 588.4.a.g.1.1 | 2 | |||
7.6 | odd | 2 | 84.4.i.b.37.2 | yes | 4 | ||
21.2 | odd | 6 | 1764.4.a.p.1.1 | 2 | |||
21.5 | even | 6 | 1764.4.a.x.1.2 | 2 | |||
21.11 | odd | 6 | 1764.4.k.z.361.2 | 4 | |||
21.17 | even | 6 | 252.4.k.d.109.1 | 4 | |||
21.20 | even | 2 | 252.4.k.d.37.1 | 4 | |||
28.3 | even | 6 | 336.4.q.h.193.2 | 4 | |||
28.19 | even | 6 | 2352.4.a.cb.1.1 | 2 | |||
28.23 | odd | 6 | 2352.4.a.bp.1.2 | 2 | |||
28.27 | even | 2 | 336.4.q.h.289.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.i.b.25.2 | ✓ | 4 | 7.3 | odd | 6 | ||
84.4.i.b.37.2 | yes | 4 | 7.6 | odd | 2 | ||
252.4.k.d.37.1 | 4 | 21.20 | even | 2 | |||
252.4.k.d.109.1 | 4 | 21.17 | even | 6 | |||
336.4.q.h.193.2 | 4 | 28.3 | even | 6 | |||
336.4.q.h.289.2 | 4 | 28.27 | even | 2 | |||
588.4.a.g.1.1 | 2 | 7.5 | odd | 6 | |||
588.4.a.h.1.2 | 2 | 7.2 | even | 3 | |||
588.4.i.i.361.1 | 4 | 7.4 | even | 3 | inner | ||
588.4.i.i.373.1 | 4 | 1.1 | even | 1 | trivial | ||
1764.4.a.p.1.1 | 2 | 21.2 | odd | 6 | |||
1764.4.a.x.1.2 | 2 | 21.5 | even | 6 | |||
1764.4.k.z.361.2 | 4 | 21.11 | odd | 6 | |||
1764.4.k.z.1549.2 | 4 | 3.2 | odd | 2 | |||
2352.4.a.bp.1.2 | 2 | 28.23 | odd | 6 | |||
2352.4.a.cb.1.1 | 2 | 28.19 | even | 6 |