Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1584,2,Mod(17,1584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1584, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 5, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1584.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1584.cd (of order \(10\), degree \(4\), 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: | \(12.6483036802\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 1025.1 | ||
Root | \(1.90184 - 0.0324487i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1584.1025 |
Dual form | 1584.2.cd.c.17.1 |
$q$-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 \(\left(\mathbb{Z}/1584\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(353\) | \(991\) | \(1189\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.13811 | + | 0.694712i | −0.956190 | + | 0.310685i | −0.745228 | − | 0.666809i | \(-0.767659\pi\) |
−0.210962 | + | 0.977494i | \(0.567659\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.38116 | − | 3.27739i | 0.899995 | − | 1.23874i | −0.0704753 | − | 0.997514i | \(-0.522452\pi\) |
0.970470 | − | 0.241223i | \(-0.0775484\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.31656 | + | 0.0200544i | −0.999982 | + | 0.00604662i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.42495 | + | 1.43775i | 1.22726 | + | 0.398761i | 0.849721 | − | 0.527233i | \(-0.176771\pi\) |
0.377538 | + | 0.925994i | \(0.376771\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.0235753 | + | 0.0725574i | 0.00571786 | + | 0.0175978i | 0.953875 | − | 0.300205i | \(-0.0970551\pi\) |
−0.948157 | + | 0.317803i | \(0.897055\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.40822 | − | 1.93825i | −0.323068 | − | 0.444665i | 0.616333 | − | 0.787486i | \(-0.288618\pi\) |
−0.939401 | + | 0.342821i | \(0.888618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.22717i | − | 0.672912i | −0.941699 | − | 0.336456i | \(-0.890772\pi\) | ||
0.941699 | − | 0.336456i | \(-0.109228\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0437835 | − | 0.0318106i | 0.00875670 | − | 0.00636211i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.48796 | − | 1.08107i | −0.276307 | − | 0.200749i | 0.440998 | − | 0.897508i | \(-0.354625\pi\) |
−0.717305 | + | 0.696759i | \(0.754625\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.517528 | + | 1.59279i | −0.0929508 | + | 0.286073i | −0.986714 | − | 0.162466i | \(-0.948055\pi\) |
0.893763 | + | 0.448539i | \(0.148055\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.81433 | + | 8.66162i | −0.475709 | + | 1.46408i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.87906 | − | 4.27138i | −0.966511 | − | 0.702211i | −0.0118571 | − | 0.999930i | \(-0.503774\pi\) |
−0.954654 | + | 0.297718i | \(0.903774\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.82980 | − | 4.96214i | 1.06664 | − | 0.774956i | 0.0913313 | − | 0.995821i | \(-0.470888\pi\) |
0.975305 | + | 0.220864i | \(0.0708878\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.28086i | − | 0.652825i | −0.945227 | − | 0.326413i | \(-0.894160\pi\) | ||
0.945227 | − | 0.326413i | \(-0.105840\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.65360 | − | 5.02874i | −0.532932 | − | 0.733518i | 0.454642 | − | 0.890674i | \(-0.349767\pi\) |
−0.987574 | + | 0.157157i | \(0.949767\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.90822 | − | 8.95058i | −0.415460 | − | 1.27865i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.16884 | − | 0.379779i | −0.160552 | − | 0.0521666i | 0.227638 | − | 0.973746i | \(-0.426900\pi\) |
−0.388190 | + | 0.921579i | \(0.626900\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.07723 | − | 2.34694i | 0.954294 | − | 0.316461i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.341086 | + | 0.469465i | −0.0444056 | + | 0.0611191i | −0.830642 | − | 0.556806i | \(-0.812027\pi\) |
0.786237 | + | 0.617925i | \(0.212027\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.59710 | + | 1.16877i | −0.460561 | + | 0.149645i | −0.530102 | − | 0.847934i | \(-0.677847\pi\) |
0.0695411 | + | 0.997579i | \(0.477847\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.4598 | −1.29738 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.9984 | −1.58801 | −0.794003 | − | 0.607914i | \(-0.792007\pi\) | ||||
−0.794003 | + | 0.607914i | \(0.792007\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.06563 | − | 0.346245i | 0.126467 | − | 0.0410917i | −0.245100 | − | 0.969498i | \(-0.578821\pi\) |
0.371567 | + | 0.928406i | \(0.378821\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.82153 | − | 10.7654i | 0.915441 | − | 1.26000i | −0.0498335 | − | 0.998758i | \(-0.515869\pi\) |
0.965274 | − | 0.261239i | \(-0.0841309\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.83155 | + | 10.9174i | −0.892488 | + | 1.24416i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.627566 | − | 0.203908i | −0.0706066 | − | 0.0229415i | 0.273501 | − | 0.961872i | \(-0.411818\pi\) |
−0.344107 | + | 0.938930i | \(0.611818\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.15542 | − | 9.71138i | −0.346352 | − | 1.06596i | −0.960856 | − | 0.277048i | \(-0.910644\pi\) |
0.614504 | − | 0.788914i | \(-0.289356\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.100813 | − | 0.138757i | −0.0109347 | − | 0.0150503i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.58983i | − | 0.698520i | −0.937026 | − | 0.349260i | \(-0.886433\pi\) | ||
0.937026 | − | 0.349260i | \(-0.113567\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.2486 | − | 11.0787i | 1.59849 | − | 1.16137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.35745 | + | 3.16587i | 0.447065 | + | 0.324812i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.08168 | − | 15.6398i | 0.515966 | − | 1.58798i | −0.265551 | − | 0.964097i | \(-0.585554\pi\) |
0.781517 | − | 0.623883i | \(-0.214446\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.532095 | + | 1.63762i | −0.0529455 | + | 0.162949i | −0.974033 | − | 0.226406i | \(-0.927302\pi\) |
0.921087 | + | 0.389356i | \(0.127302\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.61382 | − | 1.89905i | −0.257548 | − | 0.187119i | 0.451518 | − | 0.892262i | \(-0.350883\pi\) |
−0.709065 | + | 0.705143i | \(0.750883\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.9884 | − | 8.71006i | 1.15896 | − | 0.842034i | 0.169314 | − | 0.985562i | \(-0.445845\pi\) |
0.989646 | + | 0.143529i | \(0.0458449\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.9258i | 1.42963i | 0.699313 | + | 0.714815i | \(0.253489\pi\) | ||||
−0.699313 | + | 0.714815i | \(0.746511\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.61055 | − | 9.09864i | −0.621868 | − | 0.855928i | 0.375619 | − | 0.926774i | \(-0.377430\pi\) |
−0.997487 | + | 0.0708461i | \(0.977430\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.24196 | + | 6.90004i | 0.209064 | + | 0.643432i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.293935 | + | 0.0955054i | 0.0269450 | + | 0.00875497i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9992 | − | 0.133023i | 0.999927 | − | 0.0120930i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.53559 | − | 8.99547i | 0.584561 | − | 0.804580i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.76481 | − | 1.87310i | 0.511544 | − | 0.166211i | −0.0418604 | − | 0.999123i | \(-0.513328\pi\) |
0.553404 | + | 0.832913i | \(0.313328\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.15083 | −0.624771 | −0.312385 | − | 0.949955i | \(-0.601128\pi\) | ||||
−0.312385 | + | 0.949955i | \(0.601128\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.70560 | −0.841582 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.1026 | + | 3.28252i | −0.863120 | + | 0.280445i | −0.706931 | − | 0.707283i | \(-0.749921\pi\) |
−0.156189 | + | 0.987727i | \(0.549921\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0311975 | − | 0.0429397i | 0.00264614 | − | 0.00364210i | −0.807692 | − | 0.589605i | \(-0.799284\pi\) |
0.810338 | + | 0.585963i | \(0.199284\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.7044 | − | 4.67966i | −1.22965 | − | 0.391333i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.93244 | + | 1.27773i | 0.326572 | + | 0.106110i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.30238 | + | 19.3967i | 0.516311 | + | 1.58904i | 0.780883 | + | 0.624677i | \(0.214769\pi\) |
−0.264572 | + | 0.964366i | \(0.585231\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.698980 | − | 0.962063i | −0.0568822 | − | 0.0782916i | 0.779628 | − | 0.626243i | \(-0.215408\pi\) |
−0.836510 | + | 0.547951i | \(0.815408\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3.76508i | − | 0.302419i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.40210 | − | 1.01868i | 0.111900 | − | 0.0812998i | −0.530428 | − | 0.847730i | \(-0.677969\pi\) |
0.642328 | + | 0.766430i | \(0.277969\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.5767 | − | 7.68443i | −0.833561 | − | 0.605618i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.309821 | − | 0.953532i | 0.0242671 | − | 0.0746864i | −0.938190 | − | 0.346122i | \(-0.887498\pi\) |
0.962457 | + | 0.271435i | \(0.0874984\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.17734 | + | 12.8565i | −0.323252 | + | 0.994868i | 0.648971 | + | 0.760813i | \(0.275200\pi\) |
−0.972223 | + | 0.234055i | \(0.924800\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.99579 | + | 5.08274i | 0.538138 | + | 0.390980i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.08619 | − | 4.42188i | 0.462724 | − | 0.336189i | −0.331875 | − | 0.943324i | \(-0.607681\pi\) |
0.794599 | + | 0.607135i | \(0.207681\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.219242i | − | 0.0165731i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.34750 | + | 10.1130i | 0.549178 | + | 0.755879i | 0.989900 | − | 0.141765i | \(-0.0452777\pi\) |
−0.440722 | + | 0.897643i | \(0.645278\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.56261 | − | 17.1200i | −0.413466 | − | 1.27252i | −0.913616 | − | 0.406578i | \(-0.866722\pi\) |
0.500150 | − | 0.865939i | \(-0.333278\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.5374 | + | 5.04842i | 1.14233 | + | 0.371167i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0796442 | − | 0.240168i | −0.00582416 | − | 0.0175629i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.7297 | + | 17.5209i | −0.921085 | + | 1.26777i | 0.0421514 | + | 0.999111i | \(0.486579\pi\) |
−0.963237 | + | 0.268654i | \(0.913421\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.93306 | + | 1.60285i | −0.355090 | + | 0.115376i | −0.481129 | − | 0.876650i | \(-0.659773\pi\) |
0.126040 | + | 0.992025i | \(0.459773\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.14679 | 0.366693 | 0.183347 | − | 0.983048i | \(-0.441307\pi\) | ||||
0.183347 | + | 0.983048i | \(0.441307\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.2595 | −1.71971 | −0.859855 | − | 0.510539i | \(-0.829446\pi\) | ||||
−0.859855 | + | 0.510539i | \(0.829446\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.08615 | + | 2.30243i | −0.497350 | + | 0.161599i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.1556 | + | 15.3543i | −0.779139 | + | 1.07239i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.70933 | + | 6.40009i | 0.325751 | + | 0.442704i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.8262 | + | 5.79210i | 1.22721 | + | 0.398744i | 0.849702 | − | 0.527263i | \(-0.176782\pi\) |
0.377506 | + | 0.926007i | \(0.376782\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.97397 | + | 9.15293i | 0.202823 | + | 0.624225i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.98787 | + | 5.48883i | 0.270714 | + | 0.372606i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.354958i | 0.0238771i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.44037 | + | 3.22612i | −0.297349 | + | 0.216037i | −0.726449 | − | 0.687220i | \(-0.758831\pi\) |
0.429100 | + | 0.903257i | \(0.358831\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.1352 | − | 8.09016i | −0.739066 | − | 0.536963i | 0.153352 | − | 0.988172i | \(-0.450993\pi\) |
−0.892419 | + | 0.451209i | \(0.850993\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.53035 | + | 20.0983i | −0.431538 | + | 1.32814i | 0.465056 | + | 0.885281i | \(0.346034\pi\) |
−0.896593 | + | 0.442855i | \(0.853966\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.62458 | − | 14.2330i | 0.302967 | − | 0.932435i | −0.677462 | − | 0.735558i | \(-0.736920\pi\) |
0.980428 | − | 0.196877i | \(-0.0630800\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.3053 | + | 8.21378i | 0.737477 | + | 0.535808i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.37274 | − | 3.17698i | 0.282849 | − | 0.205502i | −0.437310 | − | 0.899311i | \(-0.644069\pi\) |
0.720159 | + | 0.693809i | \(0.244069\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.7091i | 0.754252i | 0.926162 | + | 0.377126i | \(0.123088\pi\) | ||||
−0.926162 | + | 0.377126i | \(0.876912\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.4362 | + | 17.1169i | 0.794518 | + | 1.09356i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.44458 | − | 10.6013i | −0.219173 | − | 0.674546i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.4920 | + | 6.98319i | 1.35657 | + | 0.440775i | 0.894895 | − | 0.446276i | \(-0.147250\pi\) |
0.461671 | + | 0.887051i | \(0.347250\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0647190 | + | 10.7031i | 0.00406885 | + | 0.672900i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.1737 | + | 22.2612i | −1.00889 | + | 1.38862i | −0.0891801 | + | 0.996016i | \(0.528425\pi\) |
−0.919709 | + | 0.392601i | \(0.871575\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.9980 | + | 9.09709i | −1.73971 | + | 0.565266i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 32.0386 | 1.97559 | 0.987793 | − | 0.155773i | \(-0.0497868\pi\) | ||||
0.987793 | + | 0.155773i | \(0.0497868\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.76294 | 0.169726 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.7177 | − | 8.35619i | 1.56804 | − | 0.509486i | 0.609097 | − | 0.793096i | \(-0.291532\pi\) |
0.958940 | + | 0.283610i | \(0.0915322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.74690 | + | 12.0391i | −0.531336 | + | 0.731322i | −0.987333 | − | 0.158660i | \(-0.949283\pi\) |
0.455997 | + | 0.889981i | \(0.349283\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.144573 | + | 0.106380i | −0.00871807 | + | 0.00641495i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.49418 | − | 2.43501i | −0.450282 | − | 0.146305i | 0.0750927 | − | 0.997177i | \(-0.476075\pi\) |
−0.525374 | + | 0.850871i | \(0.676075\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.56034 | − | 20.1906i | −0.391357 | − | 1.20447i | −0.931763 | − | 0.363068i | \(-0.881729\pi\) |
0.540406 | − | 0.841405i | \(-0.318271\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.52460 | + | 3.47482i | 0.150072 | + | 0.206556i | 0.877434 | − | 0.479698i | \(-0.159254\pi\) |
−0.727362 | + | 0.686254i | \(0.759254\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 34.1996i | − | 2.01874i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7486 | − | 9.98893i | 0.808740 | − | 0.587584i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.4486 | − | 11.2241i | −0.902518 | − | 0.655717i | 0.0365938 | − | 0.999330i | \(-0.488349\pi\) |
−0.939111 | + | 0.343613i | \(0.888349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.403135 | − | 1.24072i | 0.0234714 | − | 0.0722376i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.63988 | − | 14.2801i | 0.268331 | − | 0.825838i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.0300 | − | 10.1934i | −0.808678 | − | 0.587539i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.87902 | − | 4.99790i | 0.393891 | − | 0.286179i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.86240i | − | 0.106293i | −0.998587 | − | 0.0531463i | \(-0.983075\pi\) | ||
0.998587 | − | 0.0531463i | \(-0.0169250\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.26339 | + | 7.24443i | 0.298459 | + | 0.410794i | 0.931739 | − | 0.363129i | \(-0.118292\pi\) |
−0.633279 | + | 0.773923i | \(0.718292\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.29558 | + | 16.2981i | 0.299324 | + | 0.921224i | 0.981735 | + | 0.190255i | \(0.0609316\pi\) |
−0.682411 | + | 0.730969i | \(0.739068\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.9678 | + | 8.43746i | 1.45850 | + | 0.473895i | 0.927611 | − | 0.373547i | \(-0.121859\pi\) |
0.530888 | + | 0.847442i | \(0.321859\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.95659 | + | 3.55558i | 0.277516 | + | 0.199075i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.107435 | − | 0.147872i | 0.00597785 | − | 0.00822781i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.239475 | − | 0.0778102i | 0.0132837 | − | 0.00431614i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.1809 | −1.38827 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.87217 | 0.322764 | 0.161382 | − | 0.986892i | \(-0.448405\pi\) | ||||
0.161382 | + | 0.986892i | \(0.448405\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.7919 | − | 9.03014i | 1.51844 | − | 0.493370i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.74004 | + | 13.4060i | −0.530574 | + | 0.730272i | −0.987218 | − | 0.159377i | \(-0.949051\pi\) |
0.456644 | + | 0.889650i | \(0.349051\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.68447 | − | 5.29296i | 0.0912193 | − | 0.286630i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.28988 | − | 3.01847i | −0.501606 | − | 0.162982i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.778158 | + | 2.39492i | 0.0417737 | + | 0.128566i | 0.969768 | − | 0.244027i | \(-0.0784686\pi\) |
−0.927995 | + | 0.372593i | \(0.878469\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.13104 | + | 7.06228i | 0.274658 | + | 0.378035i | 0.923955 | − | 0.382500i | \(-0.124937\pi\) |
−0.649297 | + | 0.760535i | \(0.724937\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.536500i | 0.0285550i | 0.999898 | + | 0.0142775i | \(0.00454483\pi\) | ||||
−0.999898 | + | 0.0142775i | \(0.995455\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.03789 | + | 1.48062i | −0.108160 | + | 0.0785829i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.7871 | − | 9.29040i | −0.674880 | − | 0.490329i | 0.196775 | − | 0.980449i | \(-0.436953\pi\) |
−0.871655 | + | 0.490120i | \(0.836953\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.09760 | − | 12.6111i | 0.215663 | − | 0.663742i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.24439 | + | 28.4513i | −0.483873 | + | 1.48921i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.4075 | + | 17.0065i | 1.22186 | + | 0.887734i | 0.996253 | − | 0.0864843i | \(-0.0275633\pi\) |
0.225608 | + | 0.974218i | \(0.427563\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.02788 | + | 2.92642i | −0.209117 | + | 0.151932i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 6.60935i | − | 0.342219i | −0.985252 | − | 0.171109i | \(-0.945265\pi\) | ||
0.985252 | − | 0.171109i | \(-0.0547352\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.02984 | − | 6.92297i | −0.259050 | − | 0.356551i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.478524 | − | 1.47275i | −0.0245801 | − | 0.0756498i | 0.938014 | − | 0.346597i | \(-0.112663\pi\) |
−0.962594 | + | 0.270948i | \(0.912663\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.8467 | − | 4.17415i | −0.656436 | − | 0.213289i | −0.0381861 | − | 0.999271i | \(-0.512158\pi\) |
−0.618250 | + | 0.785982i | \(0.712158\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.16021 | − | 28.7833i | 0.466847 | − | 1.46693i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.80471 | − | 12.1186i | 0.446416 | − | 0.614440i | −0.525206 | − | 0.850975i | \(-0.676012\pi\) |
0.971623 | + | 0.236535i | \(0.0760119\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.234155 | − | 0.0760817i | 0.0118417 | − | 0.00384762i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.48346 | 0.0746409 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.7132 | −1.03956 | −0.519782 | − | 0.854299i | \(-0.673987\pi\) | ||||
−0.519782 | + | 0.854299i | \(0.673987\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.7211 | − | 8.35730i | 1.28445 | − | 0.417343i | 0.414305 | − | 0.910138i | \(-0.364025\pi\) |
0.870146 | + | 0.492795i | \(0.164025\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.58007 | + | 6.30392i | −0.228149 | + | 0.314021i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.5839 | + | 14.0484i | 0.970739 | + | 0.696354i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.80668 | − | 1.88670i | −0.287122 | − | 0.0932915i | 0.161915 | − | 0.986805i | \(-0.448233\pi\) |
−0.449037 | + | 0.893513i | \(0.648233\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.726437 | + | 2.23574i | 0.0357456 | + | 0.110014i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.4932 | + | 18.5718i | 0.662357 | + | 0.911656i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.6619i | 1.74220i | 0.491110 | + | 0.871098i | \(0.336591\pi\) | ||||
−0.491110 | + | 0.871098i | \(0.663409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.5751 | + | 8.40982i | −0.564137 | + | 0.409870i | −0.832971 | − | 0.553317i | \(-0.813362\pi\) |
0.268834 | + | 0.963187i | \(0.413362\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.00334030 | + | 0.00242687i | 0.000162028 | + | 0.000117721i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.73477 | + | 14.5721i | −0.229131 | + | 0.705194i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.68944 | + | 8.27725i | −0.129546 | + | 0.398701i | −0.994702 | − | 0.102802i | \(-0.967219\pi\) |
0.865156 | + | 0.501503i | \(0.167219\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.3812 | + | 22.0733i | 1.46003 | + | 1.06077i | 0.983355 | + | 0.181693i | \(0.0581576\pi\) |
0.476673 | + | 0.879080i | \(0.341842\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.25507 | + | 4.54458i | −0.299221 | + | 0.217397i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.4669i | 1.54956i | 0.632232 | + | 0.774779i | \(0.282139\pi\) | ||||
−0.632232 | + | 0.774779i | \(0.717861\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.0630 | + | 15.2269i | 0.525618 | + | 0.723451i | 0.986455 | − | 0.164034i | \(-0.0524506\pi\) |
−0.460837 | + | 0.887485i | \(0.652451\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.57804 | + | 14.0897i | 0.217020 | + | 0.667918i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.86840 | − | 2.23168i | −0.324140 | − | 0.105319i | 0.142427 | − | 0.989805i | \(-0.454509\pi\) |
−0.466567 | + | 0.884486i | \(0.654509\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.5520 | + | 16.5942i | −1.06193 | + | 0.781392i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −24.9065 | + | 34.2809i | −1.16764 | + | 1.60711i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.01554 | − | 1.30473i | 0.187839 | − | 0.0610326i | −0.213587 | − | 0.976924i | \(-0.568515\pi\) |
0.401426 | + | 0.915891i | \(0.368515\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.1922 | 0.660997 | 0.330499 | − | 0.943806i | \(-0.392783\pi\) | ||||
0.330499 | + | 0.943806i | \(0.392783\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.3784 | 1.87654 | 0.938271 | − | 0.345902i | \(-0.112427\pi\) | ||||
0.938271 | + | 0.345902i | \(0.112427\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.7476 | − | 3.49210i | 0.497338 | − | 0.161595i | −0.0495980 | − | 0.998769i | \(-0.515794\pi\) |
0.546936 | + | 0.837174i | \(0.315794\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.9513 | + | 42.6008i | −1.42920 | + | 1.96712i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.0858500 | + | 14.1977i | 0.00394739 | + | 0.652813i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.123314 | − | 0.0400671i | −0.00565802 | − | 0.00183840i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.07597 | − | 21.7776i | −0.323309 | − | 0.995044i | −0.972198 | − | 0.234161i | \(-0.924766\pi\) |
0.648889 | − | 0.760883i | \(-0.275234\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.8733 | − | 27.3533i | −0.906145 | − | 1.24720i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 36.9698i | 1.67871i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.10169 | + | 4.43314i | −0.276494 | + | 0.200885i | −0.717387 | − | 0.696675i | \(-0.754662\pi\) |
0.440893 | + | 0.897560i | \(0.354662\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.8965 | − | 22.4476i | −1.39434 | − | 1.01305i | −0.995373 | − | 0.0960820i | \(-0.969369\pi\) |
−0.398967 | − | 0.916965i | \(-0.630631\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0433602 | − | 0.133449i | 0.00195285 | − | 0.00601024i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.40266 | − | 4.31695i | 0.0629181 | − | 0.193642i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.51994 | − | 4.73701i | −0.291873 | − | 0.212058i | 0.432207 | − | 0.901775i | \(-0.357735\pi\) |
−0.724079 | + | 0.689717i | \(0.757735\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.0846 | − | 15.3188i | 0.940115 | − | 0.683033i | −0.00833362 | − | 0.999965i | \(-0.502653\pi\) |
0.948448 | + | 0.316932i | \(0.102653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.87106i | − | 0.172260i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.4364 | + | 22.6228i | 0.728531 | + | 1.00274i | 0.999197 | + | 0.0400639i | \(0.0127561\pi\) |
−0.270666 | + | 0.962673i | \(0.587244\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.6581 | − | 51.2684i | −0.736911 | − | 2.26798i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.90792 | + | 2.24452i | 0.304399 | + | 0.0989054i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2182 | + | 16.6049i | 0.537357 | + | 0.730282i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.9804 | + | 26.1242i | −0.831545 | + | 1.14452i | 0.156088 | + | 0.987743i | \(0.450112\pi\) |
−0.987633 | + | 0.156781i | \(0.949888\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.5104 | + | 5.36454i | −0.721948 | + | 0.234575i | −0.646868 | − | 0.762602i | \(-0.723921\pi\) |
−0.0750804 | + | 0.997177i | \(0.523921\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.127769 | −0.00556572 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.5853 | 0.547189 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 37.3558 | − | 12.1376i | 1.61806 | − | 0.525740i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.5814 | + | 26.9515i | −0.846578 | + | 1.16522i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.82480 | + | 29.6269i | 0.423184 | + | 1.27612i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.58312 | − | 3.11375i | −0.412011 | − | 0.133870i | 0.0956753 | − | 0.995413i | \(-0.469499\pi\) |
−0.507686 | + | 0.861542i | \(0.669499\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.3691 | − | 31.9129i | −0.444165 | − | 1.36700i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.0244 | − | 19.3029i | −0.599639 | − | 0.825333i | 0.396036 | − | 0.918235i | \(-0.370386\pi\) |
−0.995675 | + | 0.0929023i | \(0.970386\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.40642i | 0.187720i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.16262 | + | 1.57124i | −0.0919640 | + | 0.0668158i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.6776 | − | 23.0151i | −1.34222 | − | 0.975181i | −0.999359 | − | 0.0357950i | \(-0.988604\pi\) |
−0.342862 | − | 0.939386i | \(-0.611396\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.15482 | − | 18.9426i | 0.260321 | − | 0.801185i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.55147 | + | 4.77494i | −0.0653868 | + | 0.201240i | −0.978412 | − | 0.206663i | \(-0.933740\pi\) |
0.913025 | + | 0.407903i | \(0.133740\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.4550 | + | 14.8614i | 0.860548 | + | 0.625225i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.69308 | − | 5.58935i | 0.322511 | − | 0.234318i | −0.414735 | − | 0.909942i | \(-0.636126\pi\) |
0.737246 | + | 0.675624i | \(0.236126\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 39.8291i | − | 1.66680i | −0.552673 | − | 0.833398i | \(-0.686392\pi\) | ||
0.552673 | − | 0.833398i | \(-0.313608\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.102658 | − | 0.141297i | −0.00428115 | − | 0.00589249i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.03506 | − | 12.4186i | −0.167982 | − | 0.516994i | 0.831262 | − | 0.555881i | \(-0.187619\pi\) |
−0.999244 | + | 0.0388866i | \(0.987619\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.3415 | − | 12.7828i | −1.63216 | − | 0.530321i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.88415 | + | 1.23612i | 0.160865 | + | 0.0511949i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.9608 | − | 19.2153i | 0.576222 | − | 0.793102i | −0.417053 | − | 0.908882i | \(-0.636937\pi\) |
0.993275 | + | 0.115780i | \(0.0369369\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.81602 | − | 1.23990i | 0.157236 | − | 0.0510891i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.1489 | 1.52552 | 0.762761 | − | 0.646680i | \(-0.223843\pi\) | ||||
0.762761 | + | 0.646680i | \(0.223843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.694814 | −0.0284846 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.26902 | + | 0.737248i | −0.0927095 | + | 0.0301231i | −0.355004 | − | 0.934865i | \(-0.615521\pi\) |
0.262295 | + | 0.964988i | \(0.415521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.99333 | − | 5.49635i | 0.162891 | − | 0.224201i | −0.719767 | − | 0.694216i | \(-0.755751\pi\) |
0.882658 | + | 0.470015i | \(0.155751\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.4250 | + | 7.92570i | −0.952363 | + | 0.322225i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.5143 | + | 12.5141i | 1.56325 | + | 0.507930i | 0.957673 | − | 0.287859i | \(-0.0929433\pi\) |
0.605575 | + | 0.795788i | \(0.292943\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.93688 | − | 27.5049i | −0.361547 | − | 1.11273i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.119072 | + | 0.163888i | 0.00480926 | + | 0.00661938i | 0.811415 | − | 0.584471i | \(-0.198698\pi\) |
−0.806606 | + | 0.591090i | \(0.798698\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 8.08426i | − | 0.325460i | −0.986671 | − | 0.162730i | \(-0.947970\pi\) | ||
0.986671 | − | 0.162730i | \(-0.0520299\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.9785 | − | 12.3356i | 0.682424 | − | 0.495810i | −0.191737 | − | 0.981446i | \(-0.561412\pi\) |
0.874161 | + | 0.485636i | \(0.161412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.5974 | − | 15.6914i | −0.865282 | − | 0.628664i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.80814 | + | 24.0310i | −0.312326 | + | 0.961239i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.171320 | − | 0.527268i | 0.00683097 | − | 0.0210236i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.6268 | − | 14.2597i | −0.781332 | − | 0.567671i | 0.124047 | − | 0.992276i | \(-0.460413\pi\) |
−0.905378 | + | 0.424606i | \(0.860413\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.0245 | + | 8.00977i | −0.437494 | + | 0.317858i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 43.7871i | − | 1.73491i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.48633 | − | 13.0568i | −0.374688 | − | 0.515713i | 0.579480 | − | 0.814987i | \(-0.303256\pi\) |
−0.954167 | + | 0.299273i | \(0.903256\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.88866 | − | 11.9681i | −0.153354 | − | 0.471975i | 0.844637 | − | 0.535340i | \(-0.179817\pi\) |
−0.997990 | + | 0.0633656i | \(0.979817\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.7701 | − | 9.34797i | −1.13107 | − | 0.367507i | −0.317087 | − | 0.948396i | \(-0.602705\pi\) |
−0.813982 | + | 0.580890i | \(0.802705\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.12182 | − | 1.56385i | 0.0440352 | − | 0.0613865i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.5162 | + | 15.8507i | −0.450664 | + | 0.620286i | −0.972540 | − | 0.232735i | \(-0.925232\pi\) |
0.521876 | + | 0.853021i | \(0.325232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.2892 | − | 4.96777i | 0.597399 | − | 0.194107i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.34943 | −0.0525664 | −0.0262832 | − | 0.999655i | \(-0.508367\pi\) | ||||
−0.0262832 | + | 0.999655i | \(0.508367\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.7859 | 1.11964 | 0.559821 | − | 0.828614i | \(-0.310870\pi\) | ||||
0.559821 | + | 0.828614i | \(0.310870\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.7516 | − | 6.74260i | 0.804712 | − | 0.261467i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.48879 | + | 4.80191i | −0.135086 | + | 0.185931i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.9066 | − | 3.94843i | 0.459648 | − | 0.152428i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.6864 | + | 6.72140i | 0.797400 | + | 0.259091i | 0.679252 | − | 0.733905i | \(-0.262304\pi\) |
0.118148 | + | 0.992996i | \(0.462304\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.84208 | − | 17.9801i | −0.224529 | − | 0.691030i | −0.998339 | − | 0.0576121i | \(-0.981651\pi\) |
0.773810 | − | 0.633418i | \(-0.218349\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39.1574 | − | 53.8955i | −1.50272 | − | 2.06832i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 33.7466i | − | 1.29128i | −0.763642 | − | 0.645640i | \(-0.776591\pi\) | ||
0.763642 | − | 0.645640i | \(-0.223409\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.3199 | − | 14.0367i | 0.738176 | − | 0.536316i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.62602 | − | 3.36100i | −0.176237 | − | 0.128044i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.50814 | − | 26.1854i | 0.323665 | − | 0.996138i | −0.648375 | − | 0.761321i | \(-0.724551\pi\) |
0.972040 | − | 0.234817i | \(-0.0754490\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.0368728 | + | 0.113483i | −0.00139867 | + | 0.00430465i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.521055 | + | 0.378569i | 0.0197364 | + | 0.0143393i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.43699 | + | 6.12983i | −0.318661 | + | 0.231521i | −0.735604 | − | 0.677412i | \(-0.763101\pi\) |
0.416943 | + | 0.908933i | \(0.363101\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.4101i | 0.656636i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.10011 | + | 5.64332i | 0.154201 | + | 0.212239i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.19477 | − | 19.0655i | −0.232649 | − | 0.716021i | −0.997425 | − | 0.0717239i | \(-0.977150\pi\) |
0.764775 | − | 0.644297i | \(-0.222850\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.14021 | + | 1.67015i | 0.192502 | + | 0.0625478i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 34.6907 | − | 0.209765i | 1.29736 | − | 0.00784477i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.01752 | − | 8.28241i | 0.224416 | − | 0.308882i | −0.681931 | − | 0.731417i | \(-0.738860\pi\) |
0.906347 | + | 0.422535i | \(0.138860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.4479 | + | 4.04456i | −0.463583 | + | 0.150627i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0995374 | −0.00369673 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.4456 | 0.535759 | 0.267880 | − | 0.963452i | \(-0.413677\pi\) | ||||
0.267880 | + | 0.963452i | \(0.413677\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.310608 | − | 0.100923i | 0.0114883 | − | 0.00373276i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.29622 | − | 5.91324i | 0.158685 | − | 0.218411i | −0.722270 | − | 0.691611i | \(-0.756901\pi\) |
0.880955 | + | 0.473200i | \(0.156901\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 43.1100 | − | 0.260675i | 1.58798 | − | 0.00960207i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.4909 | + | 4.05854i | 0.459485 | + | 0.149296i | 0.529608 | − | 0.848243i | \(-0.322339\pi\) |
−0.0701229 | + | 0.997538i | \(0.522339\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.9307 | + | 33.6412i | 0.401008 | + | 1.23418i | 0.924183 | + | 0.381950i | \(0.124747\pi\) |
−0.523175 | + | 0.852225i | \(0.675253\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.9503 | − | 37.0939i | −0.987383 | − | 1.35902i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 60.0306i | − | 2.19347i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.6629 | + | 13.5594i | −0.681018 | + | 0.494789i | −0.873695 | − | 0.486473i | \(-0.838283\pi\) |
0.192677 | + | 0.981262i | \(0.438283\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.16285 | + | 1.57140i | 0.0787141 | + | 0.0571892i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.02640 | − | 9.31430i | 0.109996 | − | 0.338534i | −0.880874 | − | 0.473350i | \(-0.843044\pi\) |
0.990871 | + | 0.134816i | \(0.0430445\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.9642 | + | 46.0550i | −0.542452 | + | 1.66949i | 0.184522 | + | 0.982828i | \(0.440926\pi\) |
−0.726973 | + | 0.686666i | \(0.759074\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.9176 | + | 35.5407i | 1.77094 | + | 1.28666i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.18426 | + | 1.58696i | −0.0788691 | + | 0.0573017i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 33.4223i | − | 1.20524i | −0.798029 | − | 0.602619i | \(-0.794124\pi\) | ||
0.798029 | − | 0.602619i | \(-0.205876\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.82924 | + | 5.27050i | 0.137728 | + | 0.189567i | 0.872310 | − | 0.488954i | \(-0.162621\pi\) |
−0.734581 | + | 0.678521i | \(0.762621\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0280083 | + | 0.0862007i | 0.00100609 | + | 0.00309642i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.2357 | − | 6.25007i | −0.689192 | − | 0.223932i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.52729 | + | 1.16971i | −0.126216 | + | 0.0418556i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.29014 | + | 3.15211i | −0.0817386 | + | 0.112503i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.5749 | + | 8.95962i | −0.982939 | + | 0.319376i | −0.756028 | − | 0.654539i | \(-0.772863\pi\) |
−0.226911 | + | 0.973916i | \(0.572863\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −45.5606 | −1.61995 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.5974 | −0.624901 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.7264 | + | 8.35900i | −0.911274 | + | 0.296091i | −0.726882 | − | 0.686762i | \(-0.759032\pi\) |
−0.184392 | + | 0.982853i | \(0.559032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.278738 | − | 0.383650i | 0.00986103 | − | 0.0135725i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.7247 | + | 35.8610i | −0.907805 | + | 1.26551i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27.9526 | + | 9.08234i | 0.985199 | + | 0.320110i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.9385 | − | 39.8205i | −0.454892 | − | 1.40001i | −0.871262 | − | 0.490818i | \(-0.836698\pi\) |
0.416370 | − | 0.909195i | \(-0.363302\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.51871 | + | 10.3486i | 0.264018 | + | 0.363389i | 0.920359 | − | 0.391075i | \(-0.127897\pi\) |
−0.656341 | + | 0.754464i | \(0.727897\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.25399i | 0.0789538i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.29738 | + | 6.02840i | −0.290289 | + | 0.210907i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.59682 | − | 6.97250i | −0.334931 | − | 0.243342i | 0.407589 | − | 0.913166i | \(-0.366370\pi\) |
−0.742520 | + | 0.669824i | \(0.766370\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.11976 | + | 24.9900i | −0.283037 | + | 0.871098i | 0.703943 | + | 0.710256i | \(0.251421\pi\) |
−0.986980 | + | 0.160842i | \(0.948579\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.99992 | − | 24.6212i | 0.278184 | − | 0.856163i | −0.710175 | − | 0.704025i | \(-0.751384\pi\) |
0.988359 | − | 0.152138i | \(-0.0486159\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0195 | − | 10.1858i | −0.486918 | − | 0.353766i | 0.317080 | − | 0.948399i | \(-0.397298\pi\) |
−0.803998 | + | 0.594632i | \(0.797298\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.580869 | − | 0.422026i | 0.0201259 | − | 0.0146223i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 30.3907i | − | 1.05171i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.2513 | + | 25.1207i | 0.630104 | + | 0.867264i | 0.998039 | − | 0.0625873i | \(-0.0199352\pi\) |
−0.367935 | + | 0.929851i | \(0.619935\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.91617 | − | 24.3635i | −0.272971 | − | 0.840120i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.4888 | − | 6.00737i | −0.636033 | − | 0.206660i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.7549 | − | 36.3654i | 0.884949 | − | 1.24953i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.7845 | + | 18.9727i | −0.472527 | + | 0.650377i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.303737 | − | 0.0986902i | 0.0103998 | − | 0.00337909i | −0.303812 | − | 0.952732i | \(-0.598260\pi\) |
0.314212 | + | 0.949353i | \(0.398260\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.2476 | −0.452528 | −0.226264 | − | 0.974066i | \(-0.572651\pi\) | ||||
−0.226264 | + | 0.974066i | \(0.572651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.58152 | 0.292798 | 0.146399 | − | 0.989226i | \(-0.453232\pi\) | ||||
0.146399 | + | 0.989226i | \(0.453232\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 51.0889 | − | 16.5998i | 1.73909 | − | 0.565063i | 0.744374 | − | 0.667763i | \(-0.232748\pi\) |
0.994712 | + | 0.102700i | \(0.0327482\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.94098 | + | 13.6826i | −0.338004 | + | 0.465222i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.08545 | + | 0.663690i | 0.0707441 | + | 0.0225141i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −57.5172 | − | 18.6885i | −1.94889 | − | 0.633234i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.9193 | − | 42.8394i | −0.470560 | − | 1.44823i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.8716 | − | 35.6092i | −0.873623 | − | 1.20244i | −0.978147 | − | 0.207916i | \(-0.933332\pi\) |
0.104524 | − | 0.994522i | \(-0.466668\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.44194i | 0.250725i | 0.992111 | + | 0.125363i | \(0.0400095\pi\) | ||||
−0.992111 | + | 0.125363i | \(0.959991\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.59369 | + | 5.51714i | −0.255548 | + | 0.185667i | −0.708182 | − | 0.706030i | \(-0.750484\pi\) |
0.452634 | + | 0.891696i | \(0.350484\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.5658 | − | 14.2154i | −0.656957 | − | 0.477307i | 0.208677 | − | 0.977985i | \(-0.433084\pi\) |
−0.865634 | + | 0.500678i | \(0.833084\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.58806 | − | 23.3537i | 0.254496 | − | 0.783257i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.60189 | + | 14.1632i | −0.153996 | + | 0.473952i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.7353 | − | 16.5182i | −0.759958 | − | 0.552142i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.49197 | − | 1.81052i | 0.0831119 | − | 0.0603843i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.0937613i | − | 0.00312364i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.7869 | + | 32.7399i | 0.790703 | + | 1.08831i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.0734 | + | 34.0803i | 0.367685 | + | 1.13162i | 0.948282 | + | 0.317428i | \(0.102819\pi\) |
−0.580597 | + | 0.814191i | \(0.697181\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.33061 | + | 2.70678i | 0.276005 | + | 0.0896796i | 0.443749 | − | 0.896151i | \(-0.353648\pi\) |
−0.167744 | + | 0.985831i | \(0.553648\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.6599 | + | 32.1451i | 0.352791 | + | 1.06385i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.0273 | + | 23.4360i | −0.562290 | + | 0.773926i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.4876 | − | 12.8303i | 1.30258 | − | 0.423233i | 0.426100 | − | 0.904676i | \(-0.359887\pi\) |
0.876477 | + | 0.481443i | \(0.159887\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.21318 | 0.171594 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.393281 | −0.0129310 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51.5363 | + | 16.7451i | −1.69085 | + | 0.549390i | −0.986967 | − | 0.160925i | \(-0.948552\pi\) |
−0.703883 | + | 0.710316i | \(0.748552\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.2531 | + | 18.2413i | −0.434351 | + | 0.597833i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.337136 | + | 0.458176i | 0.0110255 | + | 0.0149839i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.5444 | − | 5.37559i | −0.540480 | − | 0.175613i | 0.0260393 | − | 0.999661i | \(-0.491710\pi\) |
−0.566520 | + | 0.824048i | \(0.691710\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.64708 | + | 20.4576i | 0.216689 | + | 0.666899i | 0.999029 | + | 0.0440486i | \(0.0140256\pi\) |
−0.782341 | + | 0.622851i | \(0.785974\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0137 | − | 22.0410i | −0.521478 | − | 0.717753i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.7887i | 1.45544i | 0.685875 | + | 0.727719i | \(0.259420\pi\) | ||||
−0.685875 | + | 0.727719i | \(0.740580\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.0878 | − | 36.3909i | 1.62592 | − | 1.18130i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.11741 | − | 5.89765i | −0.262949 | − | 0.191043i | 0.448497 | − | 0.893784i | \(-0.351959\pi\) |
−0.711446 | + | 0.702741i | \(0.751959\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.0454 | − | 46.3049i | 0.486857 | − | 1.49839i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.2977 | + | 40.9262i | −0.429406 | + | 1.32158i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.8104 | + | 16.5727i | 0.735819 | + | 0.534604i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.43388 | − | 6.85412i | 0.303688 | − | 0.220642i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.32167i | 0.138976i | 0.997583 | + | 0.0694878i | \(0.0221365\pi\) | ||||
−0.997583 | + | 0.0694878i | \(0.977863\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.7344 | − | 46.4314i | −1.08259 | − | 1.49005i | −0.856640 | − | 0.515914i | \(-0.827452\pi\) |
−0.225947 | − | 0.974140i | \(-0.572548\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.0664437 | − | 0.204493i | −0.00213009 | − | 0.00655574i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.28130 | + | 1.06616i | 0.104978 | + | 0.0341095i | 0.361035 | − | 0.932552i | \(-0.382423\pi\) |
−0.256057 | + | 0.966662i | \(0.582423\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.132155 | + | 21.8556i | 0.00422369 | + | 0.698508i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.608167 | + | 0.837070i | −0.0193975 | + | 0.0266984i | −0.818606 | − | 0.574356i | \(-0.805253\pi\) |
0.799208 | + | 0.601054i | \(0.205253\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.0044 | + | 3.57554i | −0.350628 | + | 0.113926i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.8151 | −0.439294 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.78910 | −0.310961 | −0.155481 | − | 0.987839i | \(-0.549693\pi\) | ||||
−0.155481 | + | 0.987839i | \(0.549693\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 51.8693 | − | 16.8534i | 1.64437 | − | 0.534288i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.82690 | + | 9.39642i | −0.216210 | + | 0.297588i | −0.903321 | − | 0.428965i | \(-0.858878\pi\) |
0.687111 | + | 0.726552i | \(0.258878\pi\) | |||||||
\(998\) | 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 | 1584.2.cd.c.1025.1 | 16 | ||
3.2 | odd | 2 | inner | 1584.2.cd.c.1025.4 | 16 | ||
4.3 | odd | 2 | 99.2.j.a.35.1 | yes | 16 | ||
11.6 | odd | 10 | inner | 1584.2.cd.c.17.4 | 16 | ||
12.11 | even | 2 | 99.2.j.a.35.4 | yes | 16 | ||
33.17 | even | 10 | inner | 1584.2.cd.c.17.1 | 16 | ||
36.7 | odd | 6 | 891.2.u.c.134.4 | 32 | |||
36.11 | even | 6 | 891.2.u.c.134.1 | 32 | |||
36.23 | even | 6 | 891.2.u.c.431.4 | 32 | |||
36.31 | odd | 6 | 891.2.u.c.431.1 | 32 | |||
44.7 | even | 10 | 1089.2.d.g.1088.14 | 16 | |||
44.15 | odd | 10 | 1089.2.d.g.1088.4 | 16 | |||
44.39 | even | 10 | 99.2.j.a.17.4 | yes | 16 | ||
132.59 | even | 10 | 1089.2.d.g.1088.13 | 16 | |||
132.83 | odd | 10 | 99.2.j.a.17.1 | ✓ | 16 | ||
132.95 | odd | 10 | 1089.2.d.g.1088.3 | 16 | |||
396.83 | odd | 30 | 891.2.u.c.215.1 | 32 | |||
396.259 | even | 30 | 891.2.u.c.215.4 | 32 | |||
396.347 | odd | 30 | 891.2.u.c.512.4 | 32 | |||
396.391 | even | 30 | 891.2.u.c.512.1 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.j.a.17.1 | ✓ | 16 | 132.83 | odd | 10 | ||
99.2.j.a.17.4 | yes | 16 | 44.39 | even | 10 | ||
99.2.j.a.35.1 | yes | 16 | 4.3 | odd | 2 | ||
99.2.j.a.35.4 | yes | 16 | 12.11 | even | 2 | ||
891.2.u.c.134.1 | 32 | 36.11 | even | 6 | |||
891.2.u.c.134.4 | 32 | 36.7 | odd | 6 | |||
891.2.u.c.215.1 | 32 | 396.83 | odd | 30 | |||
891.2.u.c.215.4 | 32 | 396.259 | even | 30 | |||
891.2.u.c.431.1 | 32 | 36.31 | odd | 6 | |||
891.2.u.c.431.4 | 32 | 36.23 | even | 6 | |||
891.2.u.c.512.1 | 32 | 396.391 | even | 30 | |||
891.2.u.c.512.4 | 32 | 396.347 | odd | 30 | |||
1089.2.d.g.1088.3 | 16 | 132.95 | odd | 10 | |||
1089.2.d.g.1088.4 | 16 | 44.15 | odd | 10 | |||
1089.2.d.g.1088.13 | 16 | 132.59 | even | 10 | |||
1089.2.d.g.1088.14 | 16 | 44.7 | even | 10 | |||
1584.2.cd.c.17.1 | 16 | 33.17 | even | 10 | inner | ||
1584.2.cd.c.17.4 | 16 | 11.6 | odd | 10 | inner | ||
1584.2.cd.c.1025.1 | 16 | 1.1 | even | 1 | trivial | ||
1584.2.cd.c.1025.4 | 16 | 3.2 | odd | 2 | inner |