Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(37,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.8684813214\) |
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: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(-1.63746 + 1.52274i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.37 |
Dual form | 252.4.k.d.109.1 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 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 | ||||||||
\(7\) | 6.32475 | − | 17.4068i | 0.341504 | − | 0.939880i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.4124 | − | 31.8912i | −0.504685 | − | 0.874141i | −0.999985 | − | 0.00541879i | \(-0.998275\pi\) |
0.495300 | − | 0.868722i | \(-0.335058\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 87.1238 | 1.85875 | 0.929376 | − | 0.369134i | \(-0.120346\pi\) | ||||
0.929376 | + | 0.369134i | \(0.120346\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 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 | \(0.363036\pi\) |
−0.995650 | + | 0.0931772i | \(0.970298\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −48.0000 | + | 83.1384i | −0.435161 | + | 0.753720i | −0.997309 | − | 0.0733164i | \(-0.976642\pi\) |
0.562148 | + | 0.827037i | \(0.309975\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −19.7371 | − | 34.1857i | −0.157897 | − | 0.273486i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 212.021 | 1.35763 | 0.678815 | − | 0.734309i | \(-0.262494\pi\) | ||||
0.678815 | + | 0.734309i | \(0.262494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 79.6238 | + | 137.912i | 0.461318 | + | 0.799026i | 0.999027 | − | 0.0441046i | \(-0.0140435\pi\) |
−0.537709 | + | 0.843130i | \(0.680710\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 152.773 | + | 181.865i | 0.737811 | + | 0.878310i | ||||
\(36\) | 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 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 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 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 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 | ||||||||
\(49\) | −262.995 | − | 220.188i | −0.766749 | − | 0.641947i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 224.134 | + | 388.212i | 0.580890 | + | 1.00613i | 0.995374 | + | 0.0960750i | \(0.0306289\pi\) |
−0.414484 | + | 0.910057i | \(0.636038\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 472.268 | 1.15783 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 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 | −0.709349 | − | 0.704857i | \(-0.751011\pi\) |
0.965099 | + | 0.261886i | \(0.0843444\pi\) | |||||||
\(62\) | 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 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 339.608 | 0.567663 | 0.283831 | − | 0.958874i | \(-0.408394\pi\) | ||||
0.283831 | + | 0.958874i | \(0.408394\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 459.160 | + | 795.288i | 0.736173 | + | 1.27509i | 0.954207 | + | 0.299147i | \(0.0967022\pi\) |
−0.218034 | + | 0.975941i | \(0.569964\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −671.578 | + | 118.797i | −0.993940 | + | 0.175821i | ||||
\(78\) | 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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 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 | ||||||||
\(91\) | 551.036 | − | 1516.55i | 0.634772 | − | 1.74700i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −614.464 | − | 1064.28i | −0.663607 | − | 1.14940i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 182.680 | 0.191220 | 0.0956101 | − | 0.995419i | \(-0.469520\pi\) | ||||
0.0956101 | + | 0.995419i | \(0.469520\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 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 | −0.958799 | − | 0.284086i | \(-0.908310\pi\) |
0.725425 | + | 0.688301i | \(0.241643\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 246.176 | − | 426.389i | 0.222418 | − | 0.385239i | −0.733124 | − | 0.680095i | \(-0.761938\pi\) |
0.955542 | + | 0.294856i | \(0.0952718\pi\) | |||||||
\(108\) | 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 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 736.350 | 0.613009 | 0.306505 | − | 0.951869i | \(-0.400841\pi\) | ||||
0.306505 | + | 0.951869i | \(0.400841\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −615.588 | − | 1066.23i | −0.499164 | − | 0.864578i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1871.09 | − | 330.983i | 1.44137 | − | 0.254968i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5312 | + | 21.7046i | −0.00941485 | + | 0.0163070i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||||||
\(133\) | 1141.50 | + | 1358.87i | 0.744215 | + | 0.885934i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −82.2683 | − | 142.493i | −0.0513040 | − | 0.0888612i | 0.839233 | − | 0.543772i | \(-0.183004\pi\) |
−0.890537 | + | 0.454911i | \(0.849671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −521.991 | −0.318523 | −0.159261 | − | 0.987236i | \(-0.550911\pi\) | ||||
−0.159261 | + | 0.987236i | \(0.550911\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 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 | \(0.397434\pi\) |
−0.979792 | + | 0.200019i | \(0.935900\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2042.31 | −1.05834 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1039.37 | − | 1800.24i | −0.528349 | − | 0.915128i | −0.999454 | − | 0.0330505i | \(-0.989478\pi\) |
0.471104 | − | 0.882078i | \(-0.343856\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1143.59 | + | 1361.36i | 0.559797 | + | 0.666398i | ||||
\(162\) | 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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 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 | ||||||||
\(175\) | −719.897 | + | 127.345i | −0.310966 | + | 0.0550077i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1349.15 | + | 2336.79i | 0.563351 | + | 0.975753i | 0.997201 | + | 0.0747677i | \(0.0238215\pi\) |
−0.433850 | + | 0.900985i | \(0.642845\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 31.3297 | 0.0128659 | 0.00643293 | − | 0.999979i | \(-0.497952\pi\) | ||||
0.00643293 | + | 0.999979i | \(0.497952\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | −0.974443 | − | 0.224634i | \(-0.927881\pi\) |
0.681760 | + | 0.731576i | \(0.261215\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4728.45 | −1.71009 | −0.855047 | − | 0.518551i | \(-0.826472\pi\) | ||||
−0.855047 | + | 0.518551i | \(0.826472\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 164.125 | + | 284.272i | 0.0584648 | + | 0.101264i | 0.893776 | − | 0.448513i | \(-0.148046\pi\) |
−0.835312 | + | 0.549777i | \(0.814713\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1340.98 | − | 3690.61i | 0.463637 | − | 1.27601i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1911.15 | + | 3310.22i | −0.651126 | + | 1.12778i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 213.723 | − | 370.179i | 0.0677943 | − | 0.117423i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2904.22 | − | 513.735i | 0.908530 | − | 0.160712i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4469.36 | + | 7741.16i | 1.36037 | + | 2.35623i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3446.00 | 1.03480 | 0.517402 | − | 0.855742i | \(-0.326899\pi\) | ||||
0.517402 | + | 0.855742i | \(0.326899\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 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 | −0.997322 | − | 0.0731345i | \(-0.976700\pi\) |
0.561997 | + | 0.827139i | \(0.310033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 190.856 | − | 330.573i | 0.0536627 | − | 0.0929466i | −0.837946 | − | 0.545753i | \(-0.816244\pi\) |
0.891609 | + | 0.452806i | \(0.149577\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1739.01 | + | 3012.06i | 0.482726 | + | 0.836106i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1377.38 | 0.372785 | 0.186392 | − | 0.982475i | \(-0.440320\pi\) | ||||
0.186392 | + | 0.982475i | \(0.440320\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2903.36 | − | 5028.77i | −0.776025 | − | 1.34411i | −0.934217 | − | 0.356706i | \(-0.883900\pi\) |
0.158192 | − | 0.987408i | \(-0.449434\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4131.95 | − | 1509.04i | 1.07747 | − | 0.393507i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4174.31 | + | 7230.11i | −1.07532 | + | 1.86251i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 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 | ||||||||
\(259\) | 1532.77 | + | 1824.65i | 0.367728 | + | 0.437753i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3790.81 | − | 6565.87i | −0.888788 | − | 1.53943i | −0.841310 | − | 0.540553i | \(-0.818215\pi\) |
−0.0474778 | − | 0.998872i | \(-0.515118\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5748.93 | −1.33266 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 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 | −0.566912 | − | 0.823778i | \(-0.691862\pi\) |
0.996869 | + | 0.0790710i | \(0.0251954\pi\) | |||||||
\(272\) | 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 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −150.842 | −0.0320230 | −0.0160115 | − | 0.999872i | \(-0.505097\pi\) | ||||
−0.0160115 | + | 0.999872i | \(0.505097\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −908.571 | − | 1573.69i | −0.190844 | − | 0.330552i | 0.754686 | − | 0.656086i | \(-0.227789\pi\) |
−0.945530 | + | 0.325534i | \(0.894456\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1885.04 | − | 5187.96i | 0.387701 | − | 1.06702i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2806.68 | + | 4861.31i | −0.571275 | + | 0.989478i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 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 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4181.94 | + | 7243.33i | −0.808856 | + | 1.40098i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −210.802 | + | 580.165i | −0.0403669 | + | 0.111097i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1562.64 | + | 2706.57i | 0.293365 | + | 0.508124i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8589.21 | 1.59678 | 0.798391 | − | 0.602139i | \(-0.205685\pi\) | ||||
0.798391 | + | 0.602139i | \(0.205685\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | −0.550117 | − | 0.835087i | \(-0.685417\pi\) |
0.998266 | + | 0.0588717i | \(0.0187503\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1952.30 | + | 3381.49i | −0.345906 | + | 0.599127i | −0.985518 | − | 0.169571i | \(-0.945762\pi\) |
0.639612 | + | 0.768698i | \(0.279095\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3903.81 | − | 6761.59i | −0.685176 | − | 1.18676i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9831.43 | −1.69361 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1719.57 | − | 2978.39i | −0.293491 | − | 0.508342i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3230.59 | − | 3845.78i | −0.541362 | − | 0.644452i | ||||
\(330\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2932.13 | − | 5078.59i | 0.465641 | − | 0.806513i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5496.15 | + | 3185.28i | −0.865201 | + | 0.501425i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2017.36 | − | 3494.17i | −0.312097 | − | 0.540567i | 0.666719 | − | 0.745309i | \(-0.267698\pi\) |
−0.978816 | + | 0.204741i | \(0.934365\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6791.53 | 1.04167 | 0.520834 | − | 0.853658i | \(-0.325621\pi\) | ||||
0.520834 | + | 0.853658i | \(0.325621\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 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 | \(0.559665\pi\) |
−0.757683 | + | 0.652623i | \(0.773669\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1161.69 | − | 2012.11i | −0.169367 | − | 0.293353i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11777.2 | −1.68890 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 957.408 | + | 1658.28i | 0.136175 | + | 0.235862i | 0.926046 | − | 0.377411i | \(-0.123186\pi\) |
−0.789871 | + | 0.613274i | \(0.789852\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8175.13 | − | 1446.12i | 1.14402 | − | 0.202369i | ||||
\(372\) | 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 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 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 | ||||||||
\(385\) | 2986.98 | − | 8220.69i | 0.395404 | − | 1.08822i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1629.23 | − | 2821.91i | −0.212353 | − | 0.367806i | 0.740098 | − | 0.672499i | \(-0.234779\pi\) |
−0.952450 | + | 0.304694i | \(0.901446\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9849.41 | −1.27393 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 874.000 | + | 1513.81i | 0.111331 | + | 0.192831i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −361.963 | + | 626.938i | −0.0457592 | + | 0.0792572i | −0.887998 | − | 0.459848i | \(-0.847904\pi\) |
0.842239 | + | 0.539105i | \(0.181237\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5514.91 | − | 9552.11i | 0.686787 | − | 1.18955i | −0.286085 | − | 0.958204i | \(-0.592354\pi\) |
0.972872 | − | 0.231346i | \(-0.0743128\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6937.12 | + | 12015.4i | 0.857475 | + | 1.48519i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4738.25 | 0.577067 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1341.78 | − | 2324.03i | −0.162217 | − | 0.280968i | 0.773447 | − | 0.633861i | \(-0.218531\pi\) |
−0.935663 | + | 0.352894i | \(0.885198\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12191.1 | + | 2156.51i | −1.45250 | + | 0.256937i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1843.33 | − | 3192.74i | 0.218037 | − | 0.377652i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2024.99 | − | 3507.39i | 0.231121 | − | 0.400313i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2902.94 | − | 3455.74i | −0.329000 | − | 0.391651i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5763.11 | + | 9982.00i | 0.644081 | + | 1.11558i | 0.984513 | + | 0.175312i | \(0.0560936\pi\) |
−0.340431 | + | 0.940269i | \(0.610573\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2228.79 | 0.247365 | 0.123683 | − | 0.992322i | \(-0.460530\pi\) | ||||
0.123683 | + | 0.992322i | \(0.460530\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4599.59 | − | 7966.72i | −0.503497 | − | 0.872082i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2304.63 | + | 3991.74i | −0.250556 | + | 0.433975i | −0.963679 | − | 0.267063i | \(-0.913947\pi\) |
0.713123 | + | 0.701039i | \(0.247280\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 531.662 | − | 920.865i | 0.0570203 | − | 0.0987621i | −0.836106 | − | 0.548568i | \(-0.815173\pi\) |
0.893127 | + | 0.449805i | \(0.148507\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1037.88 | + | 1797.66i | 0.110562 | + | 0.191499i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12265.9 | 1.28923 | 0.644613 | − | 0.764509i | \(-0.277018\pi\) | ||||
0.644613 | + | 0.764509i | \(0.277018\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5487.65 | − | 9504.89i | −0.572957 | − | 0.992390i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13310.2 | + | 15844.8i | 1.37141 | + | 1.63256i | ||||
\(456\) | 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 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 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 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 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 | ||||||||
\(469\) | 6119.96 | − | 1082.58i | 0.602545 | − | 0.106586i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 613.679 | + | 1062.92i | 0.0596554 | + | 0.103326i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3782.61 | 0.365385 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 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 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5574.29 | 0.512351 | 0.256175 | − | 0.966630i | \(-0.417538\pi\) | ||||
0.256175 | + | 0.966630i | \(0.417538\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10876.5 | + | 18838.6i | 0.993612 | + | 1.72099i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2147.94 | − | 5911.50i | 0.193859 | − | 0.533535i | ||||
\(498\) | 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 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 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 | ||||||||
\(511\) | 16747.5 | − | 2962.51i | 1.44984 | − | 0.256466i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3128.65 | − | 5418.98i | −0.267699 | − | 0.463667i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9986.73 | −0.849547 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 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 | −0.564667 | − | 0.825319i | \(-0.690996\pi\) |
0.997081 | + | 0.0763570i | \(0.0243289\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25966.5 | 2.11020 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3157.14 | + | 5468.33i | 0.255131 | + | 0.441900i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2179.68 | + | 12441.4i | −0.174184 | + | 0.994228i | ||||
\(540\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10158.4 | + | 17594.9i | −0.785414 | + | 1.36038i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1623.64 | − | 1932.83i | −0.124854 | − | 0.148630i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 323.239 | + | 559.866i | 0.0245890 | + | 0.0425894i | 0.878058 | − | 0.478554i | \(-0.158839\pi\) |
−0.853469 | + | 0.521144i | \(0.825506\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2903.81 | −0.219710 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 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 | −0.964041 | − | 0.265754i | \(-0.914379\pi\) |
0.712170 | + | 0.702007i | \(0.247713\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3789.53 | 0.274842 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6001.62 | + | 10395.1i | 0.433017 | + | 0.750007i | 0.997131 | − | 0.0756896i | \(-0.0241158\pi\) |
−0.564115 | + | 0.825696i | \(0.690782\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1818.14 | + | 5003.84i | −0.129826 | + | 0.357305i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8253.68 | − | 14295.8i | 0.586334 | − | 1.01556i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 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 | ||||||||
\(595\) | −8322.07 | + | 22903.8i | −0.573398 | + | 1.57809i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 533.983 | + | 924.885i | 0.0364240 | + | 0.0630881i | 0.883663 | − | 0.468124i | \(-0.155070\pi\) |
−0.847239 | + | 0.531212i | \(0.821737\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7554.96 | 0.512768 | 0.256384 | − | 0.966575i | \(-0.417469\pi\) | ||||
0.256384 | + | 0.966575i | \(0.417469\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −160.709 | − | 278.356i | −0.0107996 | − | 0.0187054i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5888.71 | − | 10199.5i | 0.393765 | − | 0.682020i | −0.599178 | − | 0.800616i | \(-0.704506\pi\) |
0.992943 | + | 0.118595i | \(0.0378392\pi\) | |||||||
\(608\) | 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 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6816.72 | 0.444782 | 0.222391 | − | 0.974958i | \(-0.428614\pi\) | ||||
0.222391 | + | 0.974958i | \(0.428614\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8356.74 | + | 14474.3i | 0.542627 | + | 0.939857i | 0.998752 | + | 0.0499414i | \(0.0159034\pi\) |
−0.456126 | + | 0.889915i | \(0.650763\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1928.08 | − | 2295.24i | −0.123992 | − | 0.147603i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9500.53 | − | 16455.4i | 0.608034 | − | 1.05315i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16103.9 | − | 27892.7i | 1.00640 | − | 1.74313i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22913.1 | − | 19183.6i | −1.42520 | − | 1.19322i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3481.96 | + | 6030.92i | 0.214554 | + | 0.371618i | 0.953134 | − | 0.302547i | \(-0.0978369\pi\) |
−0.738581 | + | 0.674165i | \(0.764504\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5466.06 | 0.335242 | 0.167621 | − | 0.985852i | \(-0.446392\pi\) | ||||
0.167621 | + | 0.985852i | \(0.446392\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 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 | \(-0.530850\pi\) |
0.910344 | − | 0.413852i | \(-0.135817\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4356.71 | − | 7546.05i | −0.259895 | − | 0.450151i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5900.66 | −0.348797 | −0.174398 | − | 0.984675i | \(-0.555798\pi\) | ||||
−0.174398 | + | 0.984675i | \(0.555798\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1809.49 | − | 3134.13i | −0.106477 | − | 0.184423i | 0.807864 | − | 0.589369i | \(-0.200624\pi\) |
−0.914341 | + | 0.404946i | \(0.867290\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22412.1 | + | 3964.54i | −1.30692 | + | 0.231186i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10177.0 | + | 17627.1i | −0.590787 | + | 1.02327i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 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 | ||||||||
\(679\) | 1155.41 | − | 3179.88i | 0.0653026 | − | 0.179724i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5565.06 | − | 9638.97i | −0.311773 | − | 0.540007i | 0.666973 | − | 0.745082i | \(-0.267590\pi\) |
−0.978746 | + | 0.205075i | \(0.934256\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2110.14 | 0.117700 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19527.4 | + | 33822.5i | 1.07973 | + | 1.87015i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7012.64 | − | 12146.2i | 0.386069 | − | 0.668690i | −0.605848 | − | 0.795580i | \(-0.707166\pi\) |
0.991917 | + | 0.126890i | \(0.0404995\pi\) | |||||||
\(692\) | 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 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30366.7 | −1.63614 | −0.818070 | − | 0.575119i | \(-0.804956\pi\) | ||||
−0.818070 | + | 0.575119i | \(0.804956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6164.90 | − | 10677.9i | −0.330745 | − | 0.572867i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27941.2 | + | 4942.59i | −1.48633 | + | 0.262921i | ||||
\(708\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15287.8 | −0.802989 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41145.8 | 2.15212 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 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 | ||||||||
\(721\) | 5812.14 | + | 6918.93i | 0.300216 | + | 0.357385i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4184.68 | − | 7248.08i | −0.214366 | − | 0.371292i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14618.0 | −0.745737 | −0.372869 | − | 0.927884i | \(-0.621626\pi\) | ||||
−0.372869 | + | 0.927884i | \(0.621626\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 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 | \(-0.578109\pi\) |
0.961548 | − | 0.274638i | \(-0.0885581\pi\) | |||||||
\(734\) | 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 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13977.6 | −0.690159 | −0.345079 | − | 0.938573i | \(-0.612148\pi\) | ||||
−0.345079 | + | 0.938573i | \(0.612148\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15467.4 | − | 26790.4i | −0.760649 | − | 1.31748i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5865.07 | − | 6981.94i | −0.286122 | − | 0.340607i | ||||
\(750\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 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 | ||||||||
\(763\) | −15466.4 | + | 2735.89i | −0.733842 | + | 0.129811i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29120.0 | − | 50437.3i | −1.37088 | − | 2.37443i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4305.86 | 0.201916 | 0.100958 | − | 0.994891i | \(-0.467809\pi\) | ||||
0.100958 | + | 0.994891i | \(0.467809\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26659.4 | 1.21212 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4883.53 | + | 8458.51i | 0.221193 | + | 0.383118i | 0.955171 | − | 0.296056i | \(-0.0956716\pi\) |
−0.733977 | + | 0.679174i | \(0.762338\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4657.23 | − | 12817.5i | 0.209345 | − | 0.576155i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10615.6 | − | 18386.8i | 0.475375 | − | 0.823374i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 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 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16908.4 | − | 29286.3i | 0.743071 | − | 1.28704i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22453.1 | + | 3971.79i | −0.983066 | + | 0.173897i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5230.33 | + | 9059.20i | 0.227304 | + | 0.393701i | 0.957008 | − | 0.290061i | \(-0.0936757\pi\) |
−0.729705 | + | 0.683763i | \(0.760342\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9167.55 | −0.396937 | −0.198469 | − | 0.980107i | \(-0.563597\pi\) | ||||
−0.198469 | + | 0.980107i | \(0.563597\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 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 | \(-0.623410\pi\) |
0.990780 | − | 0.135477i | \(-0.0432567\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6028.87 | 0.253500 | 0.126750 | − | 0.991935i | \(-0.459545\pi\) | ||||
0.126750 | + | 0.991935i | \(0.459545\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9703.71 | + | 16807.3i | 0.406542 | + | 0.704152i | 0.994500 | − | 0.104740i | \(-0.0334010\pi\) |
−0.587957 | + | 0.808892i | \(0.700068\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6072.84 | − | 34663.2i | 0.252595 | − | 1.44179i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19104.3 | + | 33089.5i | −0.791773 | + | 1.37139i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34585.5 | + | 59903.8i | −1.40802 | + | 2.43876i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 298.552 | + | 355.404i | 0.0121114 | + | 0.0144177i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6176.17 | − | 10697.4i | −0.248786 | − | 0.430909i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34766.1 | −1.39551 | −0.697754 | − | 0.716338i | \(-0.745817\pi\) | ||||
−0.697754 | + | 0.716338i | \(0.745817\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 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 | \(-0.659655\pi\) |
0.999757 | − | 0.0220275i | \(-0.00701214\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22334.2 | − | 38683.9i | 0.880955 | − | 1.52586i | 0.0306737 | − | 0.999529i | \(-0.490235\pi\) |
0.850281 | − | 0.526329i | \(-0.176432\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 104.973 | + | 181.818i | 0.00412623 | + | 0.00714684i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5019.18 | −0.195931 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14618.4 | + | 25319.8i | 0.568685 | + | 0.984992i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6937.28 | + | 19092.6i | −0.268026 | + | 0.737655i | ||||
\(876\) | 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 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 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 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 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 | ||||||||
\(889\) | −15883.8 | + | 43715.0i | −0.599242 | + | 1.64922i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12993.6 | + | 22505.7i | 0.486916 | + | 0.843363i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34604.9 | −1.29242 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31584.8 | −1.14868 | −0.574342 | − | 0.818616i | \(-0.694742\pi\) | ||||
−0.574342 | + | 0.818616i | \(0.694742\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5292.90 | + | 9167.57i | 0.191861 | + | 0.332314i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8093.54 | + | 9634.76i | 0.291464 | + | 0.346966i | ||||
\(918\) | 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 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29587.9 | 1.05514 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5079.16 | 0.180543 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 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 | ||||||||
\(931\) | 30873.4 | − | 11275.4i | 1.08682 | − | 0.396923i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24226.9 | + | 41962.2i | 0.847384 | + | 1.46771i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39893.8 | 1.39090 | 0.695450 | − | 0.718574i | \(-0.255205\pi\) | ||||
0.695450 | + | 0.718574i | \(0.255205\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 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 | \(-0.661045\pi\) |
0.999844 | − | 0.0176614i | \(-0.00562208\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40003.7 | + | 69288.5i | 1.36836 | + | 2.37007i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34963.6 | 1.18844 | 0.594220 | − | 0.804303i | \(-0.297461\pi\) | ||||
0.594220 | + | 0.804303i | \(0.297461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9908.24 | − | 17161.6i | −0.335731 | − | 0.581503i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3000.67 | + | 530.798i | −0.101039 | + | 0.0178732i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2215.61 | − | 3837.56i | 0.0743719 | − | 0.128816i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(973\) | −3301.46 | + | 9086.20i | −0.108777 | + | 0.299373i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3586.02 | − | 6211.17i | −0.117428 | − | 0.203391i | 0.801320 | − | 0.598236i | \(-0.204132\pi\) |
−0.918748 | + | 0.394845i | \(0.870798\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5960.29 | −0.194578 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4209.72 | −0.134128 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28294.8 | − | 49008.0i | −0.898802 | − | 1.55677i | −0.829028 | − | 0.559208i | \(-0.811105\pi\) |
−0.0697741 | − | 0.997563i | \(-0.522228\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 252.4.k.d.37.1 | 4 | ||
3.2 | odd | 2 | 84.4.i.b.37.2 | yes | 4 | ||
7.2 | even | 3 | 1764.4.a.x.1.2 | 2 | |||
7.3 | odd | 6 | 1764.4.k.z.361.2 | 4 | |||
7.4 | even | 3 | inner | 252.4.k.d.109.1 | 4 | ||
7.5 | odd | 6 | 1764.4.a.p.1.1 | 2 | |||
7.6 | odd | 2 | 1764.4.k.z.1549.2 | 4 | |||
12.11 | even | 2 | 336.4.q.h.289.2 | 4 | |||
21.2 | odd | 6 | 588.4.a.g.1.1 | 2 | |||
21.5 | even | 6 | 588.4.a.h.1.2 | 2 | |||
21.11 | odd | 6 | 84.4.i.b.25.2 | ✓ | 4 | ||
21.17 | even | 6 | 588.4.i.i.361.1 | 4 | |||
21.20 | even | 2 | 588.4.i.i.373.1 | 4 | |||
84.11 | even | 6 | 336.4.q.h.193.2 | 4 | |||
84.23 | even | 6 | 2352.4.a.cb.1.1 | 2 | |||
84.47 | odd | 6 | 2352.4.a.bp.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.i.b.25.2 | ✓ | 4 | 21.11 | odd | 6 | ||
84.4.i.b.37.2 | yes | 4 | 3.2 | odd | 2 | ||
252.4.k.d.37.1 | 4 | 1.1 | even | 1 | trivial | ||
252.4.k.d.109.1 | 4 | 7.4 | even | 3 | inner | ||
336.4.q.h.193.2 | 4 | 84.11 | even | 6 | |||
336.4.q.h.289.2 | 4 | 12.11 | even | 2 | |||
588.4.a.g.1.1 | 2 | 21.2 | odd | 6 | |||
588.4.a.h.1.2 | 2 | 21.5 | even | 6 | |||
588.4.i.i.361.1 | 4 | 21.17 | even | 6 | |||
588.4.i.i.373.1 | 4 | 21.20 | even | 2 | |||
1764.4.a.p.1.1 | 2 | 7.5 | odd | 6 | |||
1764.4.a.x.1.2 | 2 | 7.2 | even | 3 | |||
1764.4.k.z.361.2 | 4 | 7.3 | odd | 6 | |||
1764.4.k.z.1549.2 | 4 | 7.6 | odd | 2 | |||
2352.4.a.bp.1.2 | 2 | 84.47 | odd | 6 | |||
2352.4.a.cb.1.1 | 2 | 84.23 | even | 6 |