Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,4,Mod(73,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.73");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.7444125612\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 20x^{8} + 11x^{7} + 284x^{6} + 98x^{5} + 1567x^{4} + 780x^{3} + 6513x^{2} + 972x + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{10} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 73.2 | ||
Root | \(1.25497 + 2.17367i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.73 |
Dual form | 216.4.i.b.145.2 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.15936 | − | 5.47217i | −0.282581 | − | 0.489445i | 0.689438 | − | 0.724344i | \(-0.257857\pi\) |
−0.972020 | + | 0.234899i | \(0.924524\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.7898 | − | 25.6167i | 0.798574 | − | 1.38317i | −0.121971 | − | 0.992534i | \(-0.538921\pi\) |
0.920545 | − | 0.390637i | \(-0.127745\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −24.5762 | + | 42.5672i | −0.673636 | + | 1.16677i | 0.303230 | + | 0.952917i | \(0.401935\pi\) |
−0.976866 | + | 0.213854i | \(0.931398\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.13278 | − | 15.8184i | −0.194844 | − | 0.337481i | 0.752005 | − | 0.659157i | \(-0.229087\pi\) |
−0.946850 | + | 0.321677i | \(0.895754\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −63.7873 | −0.910041 | −0.455021 | − | 0.890481i | \(-0.650368\pi\) | ||||
−0.455021 | + | 0.890481i | \(0.650368\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −52.0413 | −0.628374 | −0.314187 | − | 0.949361i | \(-0.601732\pi\) | ||||
−0.314187 | + | 0.949361i | \(0.601732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −74.6939 | − | 129.374i | −0.677164 | − | 1.17288i | −0.975831 | − | 0.218525i | \(-0.929876\pi\) |
0.298668 | − | 0.954357i | \(-0.403458\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 42.5369 | − | 73.6761i | 0.340295 | − | 0.589409i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 59.7077 | − | 103.417i | 0.382326 | − | 0.662207i | −0.609069 | − | 0.793118i | \(-0.708457\pi\) |
0.991394 | + | 0.130910i | \(0.0417899\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −151.846 | − | 263.005i | −0.879755 | − | 1.52378i | −0.851610 | − | 0.524176i | \(-0.824373\pi\) |
−0.0281446 | − | 0.999604i | \(-0.508960\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −186.905 | −0.902649 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 170.764 | 0.758743 | 0.379371 | − | 0.925244i | \(-0.376140\pi\) | ||||
0.379371 | + | 0.925244i | \(0.376140\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 21.8453 | + | 37.8371i | 0.0832112 | + | 0.144126i | 0.904628 | − | 0.426203i | \(-0.140149\pi\) |
−0.821416 | + | 0.570329i | \(0.806816\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −223.434 | + | 386.999i | −0.792403 | + | 1.37248i | 0.132072 | + | 0.991240i | \(0.457837\pi\) |
−0.924475 | + | 0.381242i | \(0.875496\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −111.000 | + | 192.257i | −0.344488 | + | 0.596671i | −0.985261 | − | 0.171060i | \(-0.945281\pi\) |
0.640772 | + | 0.767731i | \(0.278614\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −265.976 | − | 460.685i | −0.775441 | − | 1.34310i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 67.3089 | 0.174445 | 0.0872226 | − | 0.996189i | \(-0.472201\pi\) | ||||
0.0872226 | + | 0.996189i | \(0.472201\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 310.579 | 0.761428 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −233.898 | − | 405.123i | −0.516117 | − | 0.893941i | −0.999825 | − | 0.0187118i | \(-0.994044\pi\) |
0.483708 | − | 0.875230i | \(-0.339290\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 237.504 | − | 411.369i | 0.498512 | − | 0.863449i | −0.501486 | − | 0.865166i | \(-0.667213\pi\) |
0.999999 | + | 0.00171696i | \(0.000546525\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −57.7074 | + | 99.9522i | −0.110119 | + | 0.190731i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 120.490 | + | 208.695i | 0.219704 | + | 0.380539i | 0.954718 | − | 0.297514i | \(-0.0961574\pi\) |
−0.735013 | + | 0.678053i | \(0.762824\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −550.486 | −0.920150 | −0.460075 | − | 0.887880i | \(-0.652177\pi\) | ||||
−0.460075 | + | 0.887880i | \(0.652177\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 552.924 | 0.886505 | 0.443252 | − | 0.896397i | \(-0.353825\pi\) | ||||
0.443252 | + | 0.896397i | \(0.353825\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 726.953 | + | 1259.12i | 1.07590 | + | 1.86351i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −456.657 | + | 790.953i | −0.650354 | + | 1.12645i | 0.332683 | + | 0.943039i | \(0.392046\pi\) |
−0.983037 | + | 0.183407i | \(0.941287\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 333.953 | − | 578.423i | 0.441639 | − | 0.764941i | −0.556172 | − | 0.831067i | \(-0.687730\pi\) |
0.997811 | + | 0.0661257i | \(0.0210638\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 201.527 | + | 349.055i | 0.257161 | + | 0.445416i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1430.73 | 1.70402 | 0.852008 | − | 0.523529i | \(-0.175385\pi\) | ||||
0.852008 | + | 0.523529i | \(0.175385\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −540.288 | −0.622391 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 164.417 | + | 284.779i | 0.177567 | + | 0.307555i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −832.861 | + | 1442.56i | −0.871796 | + | 1.50999i | −0.0116584 | + | 0.999932i | \(0.503711\pi\) |
−0.860137 | + | 0.510063i | \(0.829622\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 342.343 | − | 592.955i | 0.337271 | − | 0.584171i | −0.646647 | − | 0.762789i | \(-0.723829\pi\) |
0.983918 | + | 0.178618i | \(0.0571627\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 150.346 | + | 260.407i | 0.143825 | + | 0.249113i | 0.928934 | − | 0.370245i | \(-0.120726\pi\) |
−0.785109 | + | 0.619358i | \(0.787393\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1950.79 | 1.76252 | 0.881261 | − | 0.472631i | \(-0.156696\pi\) | ||||
0.881261 | + | 0.472631i | \(0.156696\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1637.17 | 1.43865 | 0.719323 | − | 0.694676i | \(-0.244452\pi\) | ||||
0.719323 | + | 0.694676i | \(0.244452\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −690.570 | − | 1196.10i | −0.574897 | − | 0.995751i | −0.996053 | − | 0.0887628i | \(-0.971709\pi\) |
0.421156 | − | 0.906988i | \(-0.361625\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −471.970 | + | 817.475i | −0.382708 | + | 0.662869i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −943.402 | + | 1634.02i | −0.726735 | + | 1.25874i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −542.475 | − | 939.594i | −0.407570 | − | 0.705931i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1327.40 | −0.949808 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1571.28 | 1.09786 | 0.548931 | − | 0.835868i | \(-0.315035\pi\) | ||||
0.548931 | + | 0.835868i | \(0.315035\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −72.1901 | − | 125.037i | −0.0481472 | − | 0.0833934i | 0.840947 | − | 0.541117i | \(-0.181998\pi\) |
−0.889095 | + | 0.457723i | \(0.848665\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −769.681 | + | 1333.13i | −0.501803 | + | 0.869148i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 761.191 | − | 1318.42i | 0.474693 | − | 0.822193i | −0.524887 | − | 0.851172i | \(-0.675892\pi\) |
0.999580 | + | 0.0289792i | \(0.00922566\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −788.882 | − | 1366.38i | −0.481382 | − | 0.833778i | 0.518390 | − | 0.855144i | \(-0.326532\pi\) |
−0.999772 | + | 0.0213665i | \(0.993198\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 897.795 | 0.525017 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −754.552 | −0.432152 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1167.63 | + | 2022.39i | 0.641984 | + | 1.11195i | 0.984989 | + | 0.172616i | \(0.0552219\pi\) |
−0.343005 | + | 0.939334i | \(0.611445\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 862.918 | − | 1494.62i | 0.465055 | − | 0.805498i | −0.534149 | − | 0.845390i | \(-0.679368\pi\) |
0.999204 | + | 0.0398919i | \(0.0127014\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −959.473 | + | 1661.86i | −0.497205 | + | 0.861184i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.4834 | + | 32.0143i | 0.00939579 | + | 0.0162740i | 0.870685 | − | 0.491841i | \(-0.163676\pi\) |
−0.861289 | + | 0.508115i | \(0.830343\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4418.83 | −2.16306 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1112.17 | 0.534430 | 0.267215 | − | 0.963637i | \(-0.413897\pi\) | ||||
0.267215 | + | 0.963637i | \(0.413897\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −828.243 | − | 1434.56i | −0.383781 | − | 0.664728i | 0.607819 | − | 0.794076i | \(-0.292045\pi\) |
−0.991599 | + | 0.129348i | \(0.958711\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 931.685 | − | 1613.73i | 0.424071 | − | 0.734513i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −317.108 | + | 549.248i | −0.139360 | + | 0.241379i | −0.927255 | − | 0.374431i | \(-0.877838\pi\) |
0.787894 | + | 0.615810i | \(0.211171\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1258.23 | − | 2179.31i | −0.543502 | − | 0.941374i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 374.805 | 0.156504 | 0.0782521 | − | 0.996934i | \(-0.475066\pi\) | ||||
0.0782521 | + | 0.996934i | \(0.475066\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −859.130 | −0.352810 | −0.176405 | − | 0.984318i | \(-0.556447\pi\) | ||||
−0.176405 | + | 0.984318i | \(0.556447\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −539.505 | − | 934.451i | −0.214407 | − | 0.371363i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1567.65 | − | 2715.25i | 0.613036 | − | 1.06181i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1538.37 | − | 2664.54i | 0.582789 | − | 1.00942i | −0.412359 | − | 0.911022i | \(-0.635295\pi\) |
0.995147 | − | 0.0983978i | \(-0.0313718\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −68.3081 | − | 118.313i | −0.0254763 | − | 0.0441262i | 0.853006 | − | 0.521901i | \(-0.174777\pi\) |
−0.878482 | + | 0.477775i | \(0.841444\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3635.05 | −1.31465 | −0.657326 | − | 0.753606i | \(-0.728313\pi\) | ||||
−0.657326 | + | 0.753606i | \(0.728313\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1611.10 | −0.573909 | −0.286955 | − | 0.957944i | \(-0.592643\pi\) | ||||
−0.286955 | + | 0.957944i | \(0.592643\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1766.13 | − | 3059.03i | −0.610631 | − | 1.05764i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 138.034 | − | 239.082i | 0.0470279 | − | 0.0814547i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1278.98 | − | 2215.25i | 0.423295 | − | 0.733168i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1646.97 | + | 2852.63i | 0.537355 | + | 0.930726i | 0.999045 | + | 0.0436847i | \(0.0139097\pi\) |
−0.461691 | + | 0.887041i | \(0.652757\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2823.63 | 0.895674 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8983.10 | −2.81020 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 582.556 | + | 1009.02i | 0.177316 | + | 0.307121i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −519.225 | + | 899.324i | −0.155919 | + | 0.270059i | −0.933393 | − | 0.358855i | \(-0.883167\pi\) |
0.777474 | + | 0.628914i | \(0.216500\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2314.33 | + | 4008.54i | −0.676686 | + | 1.17205i | 0.299287 | + | 0.954163i | \(0.403251\pi\) |
−0.975973 | + | 0.217891i | \(0.930082\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 172.157 | + | 298.184i | 0.0496787 | + | 0.0860460i | 0.889795 | − | 0.456360i | \(-0.150847\pi\) |
−0.840117 | + | 0.542406i | \(0.817514\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −401.177 | −0.112798 | −0.0563991 | − | 0.998408i | \(-0.517962\pi\) | ||||
−0.0563991 | + | 0.998408i | \(0.517962\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1402.75 | 0.389384 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1138.16 | + | 1971.35i | 0.308039 | + | 0.533539i | 0.977933 | − | 0.208917i | \(-0.0669939\pi\) |
−0.669894 | + | 0.742457i | \(0.733661\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −107.828 | + | 186.764i | −0.0288208 | + | 0.0499191i | −0.880076 | − | 0.474833i | \(-0.842509\pi\) |
0.851255 | + | 0.524752i | \(0.175842\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1680.63 | + | 2910.93i | −0.438251 | + | 0.759072i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 475.282 | + | 823.213i | 0.122435 | + | 0.212064i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 335.402 | 0.0843443 | 0.0421721 | − | 0.999110i | \(-0.486572\pi\) | ||||
0.0421721 | + | 0.999110i | \(0.486572\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7342.76 | 1.82465 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2253.80 | − | 3903.69i | −0.547035 | − | 0.947493i | −0.998476 | − | 0.0551917i | \(-0.982423\pi\) |
0.451441 | − | 0.892301i | \(-0.350910\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2525.57 | − | 4374.42i | 0.605912 | − | 1.04947i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1077.54 | − | 1866.35i | 0.252638 | − | 0.437582i | −0.711613 | − | 0.702571i | \(-0.752035\pi\) |
0.964251 | + | 0.264990i | \(0.0853685\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −212.653 | − | 368.326i | −0.0492950 | − | 0.0853814i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4048.11 | 0.917537 | 0.458768 | − | 0.888556i | \(-0.348291\pi\) | ||||
0.458768 | + | 0.888556i | \(0.348291\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −290.780 | −0.0651794 | −0.0325897 | − | 0.999469i | \(-0.510375\pi\) | ||||
−0.0325897 | + | 0.999469i | \(0.510375\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2090.79 | + | 3621.35i | 0.458470 | + | 0.794094i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1075.95 | − | 1863.60i | 0.233385 | − | 0.404235i | −0.725417 | − | 0.688310i | \(-0.758353\pi\) |
0.958802 | + | 0.284075i | \(0.0916864\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2135.57 | − | 3698.91i | 0.453371 | − | 0.785261i | −0.545222 | − | 0.838292i | \(-0.683555\pi\) |
0.998593 | + | 0.0530302i | \(0.0168880\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 82.4026 | + | 142.725i | 0.0173086 | + | 0.0299793i | 0.874550 | − | 0.484935i | \(-0.161157\pi\) |
−0.857241 | + | 0.514915i | \(0.827824\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1292.35 | 0.265801 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −844.176 | −0.171825 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2744.86 | + | 4754.24i | 0.547292 | + | 0.947937i | 0.998459 | + | 0.0554975i | \(0.0176745\pi\) |
−0.451167 | + | 0.892439i | \(0.648992\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1477.93 | + | 2559.86i | −0.291690 | + | 0.505223i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1364.33 | + | 2363.08i | −0.263883 | + | 0.457059i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6609.08 | + | 11447.3i | 1.26559 | + | 2.19206i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3001.44 | −0.563481 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6126.58 | −1.13897 | −0.569483 | − | 0.822003i | \(-0.692857\pi\) | ||||
−0.569483 | + | 0.822003i | \(0.692857\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −73.0772 | − | 126.573i | −0.0133242 | − | 0.0230782i | 0.859286 | − | 0.511495i | \(-0.170908\pi\) |
−0.872611 | + | 0.488417i | \(0.837575\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2123.90 | + | 3678.71i | −0.383546 | + | 0.664322i | −0.991566 | − | 0.129600i | \(-0.958631\pi\) |
0.608020 | + | 0.793922i | \(0.291964\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1793.68 | + | 3106.75i | −0.317802 | + | 0.550450i | −0.980029 | − | 0.198854i | \(-0.936278\pi\) |
0.662227 | + | 0.749303i | \(0.269612\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2934.77 | + | 5083.17i | 0.515096 | + | 0.892173i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3319.58 | 0.571846 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1553.92 | −0.265219 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3283.32 | + | 5686.88i | 0.550199 | + | 0.952973i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1246.46 | + | 2158.94i | −0.206984 | + | 0.358507i | −0.950763 | − | 0.309919i | \(-0.899698\pi\) |
0.743779 | + | 0.668426i | \(0.233032\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 761.341 | − | 1318.68i | 0.124169 | − | 0.215067i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 534.073 | + | 925.042i | 0.0863288 | + | 0.149526i | 0.905957 | − | 0.423370i | \(-0.139153\pi\) |
−0.819628 | + | 0.572896i | \(0.805820\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14927.2 | 2.37054 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5589.14 | −0.879841 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3042.61 | − | 5269.96i | −0.470709 | − | 0.815292i | 0.528730 | − | 0.848790i | \(-0.322669\pi\) |
−0.999439 | + | 0.0334980i | \(0.989335\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3533.63 | − | 6120.43i | 0.541979 | − | 0.938736i | −0.456811 | − | 0.889564i | \(-0.651008\pi\) |
0.998790 | − | 0.0491722i | \(-0.0156583\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5016.09 | − | 8688.12i | 0.756316 | − | 1.30998i | −0.188402 | − | 0.982092i | \(-0.560331\pi\) |
0.944718 | − | 0.327885i | \(-0.106336\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1739.18 | + | 3012.35i | 0.260017 | + | 0.450363i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7628.71 | −1.12153 | −0.560763 | − | 0.827976i | \(-0.689492\pi\) | ||||
−0.560763 | + | 0.827976i | \(0.689492\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4150.70 | −0.605146 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1746.88 | − | 3025.69i | −0.250510 | − | 0.433896i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 673.488 | − | 1166.52i | 0.0957924 | − | 0.165917i | −0.814147 | − | 0.580659i | \(-0.802795\pi\) |
0.909939 | + | 0.414742i | \(0.136128\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 995.486 | − | 1724.23i | 0.139307 | − | 0.241287i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 66.5062 | + | 115.192i | 0.00923206 | + | 0.0159904i | 0.870605 | − | 0.491983i | \(-0.163728\pi\) |
−0.861372 | + | 0.507974i | \(0.830395\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2181.19 | −0.297976 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2109.40 | 0.285891 | 0.142945 | − | 0.989731i | \(-0.454343\pi\) | ||||
0.142945 | + | 0.989731i | \(0.454343\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −119.054 | − | 206.207i | −0.0158835 | − | 0.0275110i | 0.857974 | − | 0.513692i | \(-0.171723\pi\) |
−0.873858 | + | 0.486181i | \(0.838389\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4593.41 | − | 7956.01i | 0.608056 | − | 1.05318i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.07864 | − | 7.06440i | 0.000531607 | − | 0.000920770i | −0.865759 | − | 0.500460i | \(-0.833164\pi\) |
0.866291 | + | 0.499540i | \(0.166497\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4764.53 | + | 8252.40i | 0.616247 | + | 1.06737i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5770.97 | 0.735112 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 347.061 | 0.0438753 | 0.0219376 | − | 0.999759i | \(-0.493016\pi\) | ||||
0.0219376 | + | 0.999759i | \(0.493016\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3515.36 | + | 6088.77i | 0.437777 | + | 0.758251i | 0.997518 | − | 0.0704161i | \(-0.0224327\pi\) |
−0.559741 | + | 0.828668i | \(0.689099\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2773.56 | + | 4803.94i | −0.342831 | + | 0.593800i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4196.73 | + | 7268.95i | −0.511116 | + | 0.885279i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7499.75 | − | 12990.0i | −0.906697 | − | 1.57044i | −0.818623 | − | 0.574331i | \(-0.805262\pi\) |
−0.0880735 | − | 0.996114i | \(-0.528071\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13837.2 | −1.64863 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4220.30 | −0.499196 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5234.16 | − | 9065.83i | −0.610275 | − | 1.05703i | −0.991194 | − | 0.132419i | \(-0.957725\pi\) |
0.380918 | − | 0.924609i | \(-0.375608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1898.54 | − | 3288.37i | 0.219784 | − | 0.380677i | −0.734958 | − | 0.678113i | \(-0.762798\pi\) |
0.954742 | + | 0.297436i | \(0.0961314\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2713.32 | + | 4699.60i | −0.309683 | + | 0.536387i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7025.27 | − | 12168.1i | −0.796198 | − | 1.37906i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16434.0 | −1.83665 | −0.918326 | − | 0.395825i | \(-0.870459\pi\) | ||||
−0.918326 | + | 0.395825i | \(0.870459\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15688.1 | 1.74116 | 0.870581 | − | 0.492024i | \(-0.163743\pi\) | ||||
0.870581 | + | 0.492024i | \(0.163743\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3887.17 | + | 6732.78i | 0.425512 | + | 0.737008i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 399.898 | − | 692.644i | 0.0434763 | − | 0.0753032i | −0.843468 | − | 0.537179i | \(-0.819490\pi\) |
0.886945 | + | 0.461876i | \(0.152823\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −981.481 | + | 1699.97i | −0.105263 | + | 0.182321i | −0.913846 | − | 0.406062i | \(-0.866902\pi\) |
0.808583 | + | 0.588383i | \(0.200235\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4520.20 | − | 7829.21i | −0.481523 | − | 0.834023i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4590.96 | 0.482541 | 0.241270 | − | 0.970458i | \(-0.422436\pi\) | ||||
0.241270 | + | 0.970458i | \(0.422436\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2147.49 | −0.224216 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1706.96 | + | 2956.55i | 0.175876 | + | 0.304626i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −797.352 | + | 1381.05i | −0.0816161 | + | 0.141363i | −0.903944 | − | 0.427650i | \(-0.859341\pi\) |
0.822328 | + | 0.569014i | \(0.192675\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2787.12 | + | 4827.44i | −0.281582 | + | 0.487714i | −0.971774 | − | 0.235912i | \(-0.924192\pi\) |
0.690193 | + | 0.723626i | \(0.257526\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6644.81 | − | 11509.1i | −0.666977 | − | 1.15524i | −0.978745 | − | 0.205080i | \(-0.934255\pi\) |
0.311768 | − | 0.950158i | \(-0.399079\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18331.8 | −1.81648 | −0.908238 | − | 0.418455i | \(-0.862572\pi\) | ||||
−0.908238 | + | 0.418455i | \(0.862572\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7128.09 | 0.701801 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10982.3 | − | 19021.9i | −1.06758 | − | 1.84911i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2213.68 | + | 3834.20i | −0.213833 | + | 0.370369i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9961.77 | − | 17254.3i | 0.950240 | − | 1.64586i | 0.205337 | − | 0.978691i | \(-0.434171\pi\) |
0.744903 | − | 0.667172i | \(-0.232496\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1559.55 | − | 2701.23i | −0.147837 | − | 0.256061i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10525.2 | 0.985413 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6788.63 | 0.631668 | 0.315834 | − | 0.948814i | \(-0.397716\pi\) | ||||
0.315834 | + | 0.948814i | \(0.397716\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3035.78 | − | 5258.12i | −0.279028 | − | 0.483291i | 0.692115 | − | 0.721787i | \(-0.256679\pi\) |
−0.971143 | + | 0.238496i | \(0.923346\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3808.60 | + | 6596.68i | −0.347932 | + | 0.602636i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8141.57 | + | 14101.6i | −0.734808 | + | 1.27272i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3663.64 | + | 6345.60i | 0.328671 | + | 0.569275i | 0.982248 | − | 0.187585i | \(-0.0600659\pi\) |
−0.653577 | + | 0.756860i | \(0.726733\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2121.18 | 0.188029 | 0.0940145 | − | 0.995571i | \(-0.470030\pi\) | ||||
0.0940145 | + | 0.995571i | \(0.470030\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4326.33 | −0.381226 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5680.40 | − | 9838.74i | −0.494655 | − | 0.856767i | 0.505326 | − | 0.862928i | \(-0.331372\pi\) |
−0.999981 | + | 0.00616140i | \(0.998039\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8177.64 | − | 14164.1i | 0.707940 | − | 1.22619i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 949.992 | − | 1645.43i | 0.0812847 | − | 0.140789i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5455.89 | − | 9449.87i | −0.464119 | − | 0.803878i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9012.94 | 0.757897 | 0.378948 | − | 0.925418i | \(-0.376286\pi\) | ||||
0.378948 | + | 0.925418i | \(0.376286\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7991.81 | 0.668178 | 0.334089 | − | 0.942541i | \(-0.391571\pi\) | ||||
0.334089 | + | 0.942541i | \(0.391571\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9685.87 | + | 16776.4i | 0.800613 | + | 1.38670i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5074.87 | + | 8789.94i | −0.417101 | + | 0.722441i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 399.017 | − | 691.117i | 0.0324265 | − | 0.0561643i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6163.23 | − | 10675.0i | −0.498056 | − | 0.862658i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26146.7 | 2.08946 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19447.1 | −1.54546 | −0.772732 | − | 0.634732i | \(-0.781111\pi\) | ||||
−0.772732 | + | 0.634732i | \(0.781111\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5172.40 | − | 8958.86i | −0.406534 | − | 0.704138i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8386.46 | + | 14525.8i | −0.655537 | + | 1.13542i | 0.326221 | + | 0.945293i | \(0.394224\pi\) |
−0.981759 | + | 0.190131i | \(0.939109\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3107.27 | + | 5381.95i | −0.240243 | + | 0.416114i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13507.7 | + | 23396.1i | 1.03871 | + | 1.79910i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7836.27 | −0.596110 | −0.298055 | − | 0.954549i | \(-0.596338\pi\) | ||||
−0.298055 | + | 0.954549i | \(0.596338\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8162.29 | 0.617581 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12388.9 | + | 21458.3i | 0.927409 | + | 1.60632i | 0.787641 | + | 0.616134i | \(0.211302\pi\) |
0.139768 | + | 0.990184i | \(0.455364\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4363.52 | + | 7557.83i | −0.324911 | + | 0.562762i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5785.67 | − | 10021.1i | 0.426270 | − | 0.738322i | −0.570268 | − | 0.821459i | \(-0.693161\pi\) |
0.996538 | + | 0.0831371i | \(0.0264939\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 97.6465 | + | 169.129i | 0.00715653 | + | 0.0123955i | 0.869581 | − | 0.493789i | \(-0.164389\pi\) |
−0.862425 | + | 0.506185i | \(0.831055\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12709.0 | −0.921743 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5912.60 | −0.426594 | −0.213297 | − | 0.976987i | \(-0.568420\pi\) | ||||
−0.213297 | + | 0.976987i | \(0.568420\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9878.18 | − | 17109.5i | −0.705363 | − | 1.22172i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1654.19 | + | 2865.15i | −0.117512 | + | 0.203538i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 574.756 | − | 995.507i | 0.0404135 | − | 0.0699983i | −0.845111 | − | 0.534591i | \(-0.820466\pi\) |
0.885525 | + | 0.464592i | \(0.153799\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7902.28 | + | 13687.2i | 0.552815 | + | 0.957503i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6387.66 | 0.442344 | 0.221172 | − | 0.975235i | \(-0.429012\pi\) | ||||
0.221172 | + | 0.975235i | \(0.429012\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11922.2 | 0.821448 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8626.38 | + | 14941.3i | 0.588421 | + | 1.01918i | 0.994439 | + | 0.105310i | \(0.0335836\pi\) |
−0.406018 | + | 0.913865i | \(0.633083\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3790.51 | + | 6565.36i | −0.257268 | + | 0.445602i | −0.965509 | − | 0.260369i | \(-0.916156\pi\) |
0.708241 | + | 0.705971i | \(0.249489\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3427.74 | + | 5937.03i | −0.230343 | + | 0.398966i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7895.62 | − | 13675.6i | −0.527963 | − | 0.914458i | −0.999469 | − | 0.0325952i | \(-0.989623\pi\) |
0.471506 | − | 0.881863i | \(-0.343711\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4054.94 | 0.268487 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16043.4 | 1.05708 | 0.528538 | − | 0.848910i | \(-0.322740\pi\) | ||||
0.528538 | + | 0.848910i | \(0.322740\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12582.2 | + | 21793.1i | 0.820975 | + | 1.42197i | 0.904957 | + | 0.425503i | \(0.139903\pi\) |
−0.0839822 | + | 0.996467i | \(0.526764\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −158.460 | + | 274.460i | −0.0102892 | + | 0.0178215i | −0.871124 | − | 0.491063i | \(-0.836609\pi\) |
0.860835 | + | 0.508884i | \(0.169942\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21160.3 | − | 36650.6i | 1.36078 | − | 2.35695i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1123.40 | − | 1945.78i | −0.0718974 | − | 0.124530i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10892.6 | −0.690487 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24816.8 | 1.56567 | 0.782837 | − | 0.622227i | \(-0.213772\pi\) | ||||
0.782837 | + | 0.622227i | \(0.213772\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4964.23 | − | 8598.30i | −0.310235 | − | 0.537343i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4858.21 | + | 8414.66i | −0.302181 | + | 0.523393i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9911.62 | + | 17167.4i | −0.610742 | + | 1.05784i | 0.380374 | + | 0.924833i | \(0.375795\pi\) |
−0.991116 | + | 0.133003i | \(0.957538\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3047.77 | − | 5278.88i | −0.186924 | − | 0.323762i | 0.757299 | − | 0.653068i | \(-0.226518\pi\) |
−0.944223 | + | 0.329306i | \(0.893185\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7321.69 | −0.444892 | −0.222446 | − | 0.974945i | \(-0.571404\pi\) | ||||
−0.222446 | + | 0.974945i | \(0.571404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22993.3 | 1.39070 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3367.87 | + | 5833.31i | 0.201830 | + | 0.349579i | 0.949118 | − | 0.314921i | \(-0.101978\pi\) |
−0.747288 | + | 0.664500i | \(0.768645\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −456.149 | + | 790.073i | −0.0272110 | + | 0.0471308i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11500.6 | + | 19919.6i | −0.679818 | + | 1.17748i | 0.295217 | + | 0.955430i | \(0.404608\pi\) |
−0.975035 | + | 0.222050i | \(0.928725\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12856.4 | − | 22268.0i | −0.756517 | − | 1.31033i | −0.944617 | − | 0.328176i | \(-0.893566\pi\) |
0.188099 | − | 0.982150i | \(-0.439767\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9726.79 | 0.567201 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17839.2 | −1.03559 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11673.9 | + | 20219.7i | 0.671631 | + | 1.16330i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2310.89 | + | 4002.58i | −0.132360 | + | 0.229254i | −0.924586 | − | 0.380974i | \(-0.875589\pi\) |
0.792226 | + | 0.610228i | \(0.208922\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9136.02 | − | 15824.1i | 0.518650 | − | 0.898328i | −0.481115 | − | 0.876657i | \(-0.659768\pi\) |
0.999765 | − | 0.0216704i | \(-0.00689844\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24635.7 | + | 42670.3i | 1.39239 | + | 2.41169i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30350.5 | 1.70034 | 0.850169 | − | 0.526510i | \(-0.176500\pi\) | ||||
0.850169 | + | 0.526510i | \(0.176500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9619.50 | −0.536558 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −614.718 | − | 1064.72i | −0.0339897 | − | 0.0588718i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5417.32 | − | 9383.07i | 0.298241 | − | 0.516568i | −0.677493 | − | 0.735529i | \(-0.736933\pi\) |
0.975734 | + | 0.218961i | \(0.0702668\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4984.72 | + | 8633.79i | −0.272059 | + | 0.471220i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1393.45 | − | 2413.53i | −0.0757257 | − | 0.131161i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12323.5 | 0.663982 | 0.331991 | − | 0.943283i | \(-0.392280\pi\) | ||||
0.331991 | + | 0.943283i | \(0.392280\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8886.81 | −0.476774 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10126.4 | − | 17539.4i | −0.538672 | − | 0.933008i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16451.2 | + | 28494.4i | −0.871424 | + | 1.50935i | −0.0108993 | + | 0.999941i | \(0.503469\pi\) |
−0.860524 | + | 0.509409i | \(0.829864\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22684.0 | + | 39289.8i | −1.19148 | + | 2.06370i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2836.45 | − | 4912.88i | −0.148360 | − | 0.256967i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8518.05 | 0.441821 | 0.220911 | − | 0.975294i | \(-0.429097\pi\) | ||||
0.220911 | + | 0.975294i | \(0.429097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8894.34 | 0.459421 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5079.56 | − | 8798.06i | −0.260207 | − | 0.450692i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18606.1 | + | 32226.8i | −0.949193 | + | 1.64405i | −0.202064 | + | 0.979372i | \(0.564765\pi\) |
−0.747129 | + | 0.664679i | \(0.768568\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14252.2 | − | 24685.6i | 0.721120 | − | 1.24902i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10477.0 | − | 18146.8i | −0.527938 | − | 0.914415i | −0.999470 | − | 0.0325659i | \(-0.989632\pi\) |
0.471532 | − | 0.881849i | \(-0.343701\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11844.7 | −0.592002 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28544.4 | 1.42087 | 0.710435 | − | 0.703763i | \(-0.248498\pi\) | ||||
0.710435 | + | 0.703763i | \(0.248498\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7505.41 | − | 12999.7i | −0.370588 | − | 0.641877i | 0.619068 | − | 0.785337i | \(-0.287510\pi\) |
−0.989656 | + | 0.143460i | \(0.954177\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7377.90 | − | 12778.9i | 0.362826 | − | 0.628433i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28851.8 | − | 49972.7i | 1.40750 | − | 2.43787i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7331.27 | − | 12698.1i | −0.356221 | − | 0.616992i | 0.631105 | − | 0.775697i | \(-0.282602\pi\) |
−0.987326 | + | 0.158705i | \(0.949268\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10905.1 | −0.525663 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36100.7 | −1.73329 | −0.866646 | − | 0.498924i | \(-0.833729\pi\) | ||||
−0.866646 | + | 0.498924i | \(0.833729\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8415.28 | − | 14575.7i | −0.400859 | − | 0.694308i | 0.592971 | − | 0.805224i | \(-0.297955\pi\) |
−0.993830 | + | 0.110916i | \(0.964622\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24213.4 | − | 41938.8i | 1.14886 | − | 1.98989i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4272.28 | + | 7399.80i | −0.201125 | + | 0.348359i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3711.90 | + | 6429.19i | 0.174063 | + | 0.301486i | 0.939837 | − | 0.341624i | \(-0.110977\pi\) |
−0.765774 | + | 0.643110i | \(0.777644\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13516.7 | −0.628929 | −0.314464 | − | 0.949269i | \(-0.601825\pi\) | ||||
−0.314464 | + | 0.949269i | \(0.601825\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25836.3 | −1.19751 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1136.86 | − | 1969.10i | −0.0522878 | − | 0.0905651i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13528.8 | − | 23432.6i | 0.619846 | − | 1.07360i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 116.792 | − | 202.289i | 0.00531015 | − | 0.00919746i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2191.09 | + | 3795.08i | 0.0992426 | + | 0.171893i | 0.911371 | − | 0.411585i | \(-0.135025\pi\) |
−0.812129 | + | 0.583478i | \(0.801691\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −40853.6 | −1.83639 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8676.28 | −0.388529 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2171.85 | + | 3761.75i | 0.0965254 | + | 0.167187i | 0.910244 | − | 0.414072i | \(-0.135894\pi\) |
−0.813719 | + | 0.581259i | \(0.802560\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7080.37 | − | 12263.6i | 0.313499 | − | 0.542996i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13588.7 | + | 23536.4i | −0.597181 | + | 1.03435i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13960.7 | + | 24180.6i | 0.611241 | + | 1.05870i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14546.1 | 0.632155 | 0.316077 | − | 0.948733i | \(-0.397634\pi\) | ||||
0.316077 | + | 0.948733i | \(0.397634\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22663.2 | −0.981272 | −0.490636 | − | 0.871365i | \(-0.663236\pi\) | ||||
−0.490636 | + | 0.871365i | \(0.663236\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3513.75 | − | 6086.00i | −0.151020 | − | 0.261574i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11627.8 | − | 20139.9i | 0.497925 | − | 0.862432i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18211.0 | + | 31542.4i | −0.774139 | + | 1.34085i | 0.161138 | + | 0.986932i | \(0.448484\pi\) |
−0.935277 | + | 0.353917i | \(0.884850\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3934.78 | − | 6815.24i | −0.166656 | − | 0.288656i | 0.770586 | − | 0.637336i | \(-0.219964\pi\) |
−0.937242 | + | 0.348679i | \(0.886630\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22101.6 | −0.929322 | −0.464661 | − | 0.885489i | \(-0.653824\pi\) | ||||
−0.464661 | + | 0.885489i | \(0.653824\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17056.2 | 0.714580 | 0.357290 | − | 0.933994i | \(-0.383701\pi\) | ||||
0.357290 | + | 0.933994i | \(0.383701\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16965.9 | + | 29385.8i | 0.705684 | + | 1.22228i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5233.43 | + | 9064.57i | −0.216899 | + | 0.375679i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11472.3 | − | 19870.6i | 0.472072 | − | 0.817653i | −0.527417 | − | 0.849606i | \(-0.676840\pi\) |
0.999489 | + | 0.0319535i | \(0.0101729\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5064.48 | + | 8771.94i | 0.207654 | + | 0.359668i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11774.1 | −0.479339 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32092.4 | −1.30190 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12755.1 | − | 22092.4i | −0.513793 | − | 0.889916i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15435.6 | − | 26735.3i | 0.619584 | − | 1.07315i | −0.369978 | − | 0.929041i | \(-0.620635\pi\) |
0.989562 | − | 0.144110i | \(-0.0460320\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7544.95 | + | 13068.2i | −0.300736 | + | 0.520890i | −0.976303 | − | 0.216409i | \(-0.930566\pi\) |
0.675567 | + | 0.737299i | \(0.263899\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3876.35 | − | 6714.03i | −0.153969 | − | 0.266682i | 0.778714 | − | 0.627379i | \(-0.215872\pi\) |
−0.932683 | + | 0.360697i | \(0.882539\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22050.5 | 0.869765 | 0.434883 | − | 0.900487i | \(-0.356790\pi\) | ||||
0.434883 | + | 0.900487i | \(0.356790\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4007.44 | 0.157522 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22445.8 | − | 38877.2i | −0.876203 | − | 1.51763i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2200.82 | − | 3811.93i | 0.0856163 | − | 0.148292i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19631.9 | + | 34003.5i | −0.758492 | + | 1.31375i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17186.7 | − | 29768.3i | −0.661749 | − | 1.14618i | −0.980156 | − | 0.198229i | \(-0.936481\pi\) |
0.318407 | − | 0.947954i | \(-0.396852\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14030.0 | 0.536531 | 0.268266 | − | 0.963345i | \(-0.413550\pi\) | ||||
0.268266 | + | 0.963345i | \(0.413550\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14608.8 | −0.556767 | −0.278383 | − | 0.960470i | \(-0.589799\pi\) | ||||
−0.278383 | + | 0.960470i | \(0.589799\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12326.8 | + | 21350.6i | 0.466620 | + | 0.808209i | 0.999273 | − | 0.0381243i | \(-0.0121383\pi\) |
−0.532653 | + | 0.846334i | \(0.678805\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23238.9 | − | 40250.9i | 0.876724 | − | 1.51853i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5776.57 | − | 10005.3i | 0.216467 | − | 0.374933i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1184.14 | − | 2051.00i | −0.0442252 | − | 0.0766003i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36265.6 | −1.34541 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4293.46 | −0.158752 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2714.30 | + | 4701.30i | 0.0996975 | + | 0.172681i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8151.01 | − | 14118.0i | 0.298401 | − | 0.516846i | −0.677369 | − | 0.735643i | \(-0.736880\pi\) |
0.975770 | + | 0.218797i | \(0.0702133\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15514.2 | − | 26871.4i | 0.564225 | − | 0.977266i | −0.432896 | − | 0.901444i | \(-0.642508\pi\) |
0.997121 | − | 0.0758225i | \(-0.0241582\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16414.5 | + | 28430.8i | 0.595008 | + | 1.03058i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4270.71 | −0.153796 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21538.9 | 0.773126 | 0.386563 | − | 0.922263i | \(-0.373662\pi\) | ||||
0.386563 | + | 0.922263i | \(0.373662\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5027.47 | + | 8707.83i | 0.179286 | + | 0.310533i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7263.79 | − | 12581.3i | 0.258197 | − | 0.447210i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23463.6 | − | 40640.2i | 0.828650 | − | 1.43526i | −0.0704469 | − | 0.997516i | \(-0.522443\pi\) |
0.899097 | − | 0.437749i | \(-0.144224\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13841.8 | + | 23974.6i | 0.487267 | + | 0.843971i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19811.0 | −0.692931 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35694.0 | 1.24447 | 0.622237 | − | 0.782829i | \(-0.286224\pi\) | ||||
0.622237 | + | 0.782829i | \(0.286224\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3239.14 | + | 5610.36i | 0.112214 | + | 0.194360i | 0.916663 | − | 0.399662i | \(-0.130873\pi\) |
−0.804449 | + | 0.594022i | \(0.797539\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3263.42 | − | 5652.41i | 0.112695 | − | 0.195194i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25776.7 | + | 44646.5i | −0.884509 | + | 1.53201i | −0.0382335 | + | 0.999269i | \(0.512173\pi\) |
−0.846275 | + | 0.532746i | \(0.821160\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5049.73 | − | 8746.40i | −0.172731 | − | 0.299178i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14395.3 | −0.489306 | −0.244653 | − | 0.969611i | \(-0.578674\pi\) | ||||
−0.244653 | + | 0.969611i | \(0.578674\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19441.1 | −0.658741 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22515.7 | − | 38998.4i | −0.758156 | − | 1.31316i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31219.1 | + | 54073.0i | −1.04794 | + | 1.81508i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −431.619 | + | 747.586i | −0.0143982 | + | 0.0249385i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7338.24 | − | 12710.2i | −0.244035 | − | 0.422681i | 0.717825 | − | 0.696224i | \(-0.245138\pi\) |
−0.961860 | + | 0.273543i | \(0.911805\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36879.2 | 1.21886 | 0.609429 | − | 0.792841i | \(-0.291399\pi\) | ||||
0.609429 | + | 0.792841i | \(0.291399\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −46669.6 | −1.53768 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16256.4 | + | 28157.0i | 0.532333 | + | 0.922029i | 0.999287 | + | 0.0377469i | \(0.0120181\pi\) |
−0.466954 | + | 0.884282i | \(0.654649\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35161.9 | + | 60902.2i | −1.14789 | + | 1.98820i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9772.57 | − | 16926.6i | 0.317087 | − | 0.549211i | −0.662792 | − | 0.748804i | \(-0.730629\pi\) |
0.979879 | + | 0.199593i | \(0.0639620\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11484.4 | + | 19891.6i | 0.371496 | + | 0.643451i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 66756.6 | 2.14635 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9818.92 | −0.314741 | −0.157370 | − | 0.987540i | \(-0.550302\pi\) | ||||
−0.157370 | + | 0.987540i | \(0.550302\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5090.04 | + | 8816.21i | 0.162176 | + | 0.280897i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5712.93 | + | 9895.08i | −0.181475 | + | 0.314323i | −0.942383 | − | 0.334536i | \(-0.891420\pi\) |
0.760908 | + | 0.648859i | \(0.224754\pi\) | |||||||
\(998\) | 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 | 216.4.i.b.73.2 | 10 | ||
3.2 | odd | 2 | 72.4.i.b.25.1 | ✓ | 10 | ||
4.3 | odd | 2 | 432.4.i.f.289.2 | 10 | |||
9.2 | odd | 6 | 648.4.a.l.1.2 | 5 | |||
9.4 | even | 3 | inner | 216.4.i.b.145.2 | 10 | ||
9.5 | odd | 6 | 72.4.i.b.49.1 | yes | 10 | ||
9.7 | even | 3 | 648.4.a.k.1.4 | 5 | |||
12.11 | even | 2 | 144.4.i.f.97.5 | 10 | |||
36.7 | odd | 6 | 1296.4.a.bc.1.4 | 5 | |||
36.11 | even | 6 | 1296.4.a.bd.1.2 | 5 | |||
36.23 | even | 6 | 144.4.i.f.49.5 | 10 | |||
36.31 | odd | 6 | 432.4.i.f.145.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.4.i.b.25.1 | ✓ | 10 | 3.2 | odd | 2 | ||
72.4.i.b.49.1 | yes | 10 | 9.5 | odd | 6 | ||
144.4.i.f.49.5 | 10 | 36.23 | even | 6 | |||
144.4.i.f.97.5 | 10 | 12.11 | even | 2 | |||
216.4.i.b.73.2 | 10 | 1.1 | even | 1 | trivial | ||
216.4.i.b.145.2 | 10 | 9.4 | even | 3 | inner | ||
432.4.i.f.145.2 | 10 | 36.31 | odd | 6 | |||
432.4.i.f.289.2 | 10 | 4.3 | odd | 2 | |||
648.4.a.k.1.4 | 5 | 9.7 | even | 3 | |||
648.4.a.l.1.2 | 5 | 9.2 | odd | 6 | |||
1296.4.a.bc.1.4 | 5 | 36.7 | odd | 6 | |||
1296.4.a.bd.1.2 | 5 | 36.11 | even | 6 |