Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(89,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.89");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.y (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 89.3 | ||
Character | \(\chi\) | \(=\) | 900.89 |
Dual form | 900.3.y.a.809.3 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) |
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 | ||||||||
\(5\) | −4.98271 | − | 0.415486i | −0.996541 | − | 0.0830972i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.91927i | 0.559896i | 0.960015 | + | 0.279948i | \(0.0903172\pi\) | ||||
−0.960015 | + | 0.279948i | \(0.909683\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.92910 | − | 2.65518i | −0.175373 | − | 0.241380i | 0.712278 | − | 0.701898i | \(-0.247664\pi\) |
−0.887650 | + | 0.460518i | \(0.847664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.5122 | − | 15.8451i | 0.885550 | − | 1.21886i | −0.0893023 | − | 0.996005i | \(-0.528464\pi\) |
0.974853 | − | 0.222851i | \(-0.0715363\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.71776 | + | 20.6751i | 0.395162 | + | 1.21618i | 0.928835 | + | 0.370493i | \(0.120811\pi\) |
−0.533673 | + | 0.845691i | \(0.679189\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.10679 | − | 21.8724i | −0.374041 | − | 1.15118i | −0.944123 | − | 0.329593i | \(-0.893088\pi\) |
0.570082 | − | 0.821588i | \(-0.306912\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.27008 | + | 3.82894i | −0.229134 | + | 0.166476i | −0.696429 | − | 0.717626i | \(-0.745229\pi\) |
0.467295 | + | 0.884102i | \(0.345229\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.6547 | + | 4.14049i | 0.986190 | + | 0.165620i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −20.7268 | − | 6.73453i | −0.714716 | − | 0.232225i | −0.0709851 | − | 0.997477i | \(-0.522614\pi\) |
−0.643731 | + | 0.765252i | \(0.722614\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 12.6700 | + | 38.9943i | 0.408710 | + | 1.25788i | 0.917757 | + | 0.397141i | \(0.129998\pi\) |
−0.509048 | + | 0.860738i | \(0.670002\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.62840 | − | 19.5286i | 0.0465258 | − | 0.557960i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −19.7719 | + | 27.2137i | −0.534375 | + | 0.735505i | −0.987789 | − | 0.155796i | \(-0.950206\pi\) |
0.453414 | + | 0.891300i | \(0.350206\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −25.6093 | + | 35.2482i | −0.624618 | + | 0.859712i | −0.997679 | − | 0.0680944i | \(-0.978308\pi\) |
0.373061 | + | 0.927807i | \(0.378308\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 31.4782i | 0.732050i | 0.930605 | + | 0.366025i | \(0.119282\pi\) | ||||
−0.930605 | + | 0.366025i | \(0.880718\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.51163 | + | 20.0408i | −0.138545 | + | 0.426399i | −0.996125 | − | 0.0879530i | \(-0.971967\pi\) |
0.857579 | + | 0.514352i | \(0.171967\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 33.6393 | 0.686516 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −17.8194 | + | 54.8425i | −0.336215 | + | 1.03476i | 0.629905 | + | 0.776672i | \(0.283094\pi\) |
−0.966120 | + | 0.258092i | \(0.916906\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.50895 | + | 14.0315i | 0.154708 | + | 0.255118i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −31.1679 | + | 42.8990i | −0.528270 | + | 0.727101i | −0.986866 | − | 0.161544i | \(-0.948353\pi\) |
0.458596 | + | 0.888645i | \(0.348353\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −41.6382 | + | 30.2519i | −0.682593 | + | 0.495933i | −0.874217 | − | 0.485536i | \(-0.838625\pi\) |
0.191624 | + | 0.981468i | \(0.438625\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −63.9451 | + | 74.1685i | −0.983771 | + | 1.14105i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 73.5135 | − | 23.8860i | 1.09722 | − | 0.356507i | 0.296186 | − | 0.955130i | \(-0.404285\pi\) |
0.801031 | + | 0.598623i | \(0.204285\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 93.7744 | + | 30.4691i | 1.32077 | + | 0.429143i | 0.882758 | − | 0.469828i | \(-0.155684\pi\) |
0.438008 | + | 0.898971i | \(0.355684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 31.0857 | + | 42.7858i | 0.425831 | + | 0.586107i | 0.966990 | − | 0.254814i | \(-0.0820142\pi\) |
−0.541159 | + | 0.840920i | \(0.682014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.4064 | − | 7.56067i | 0.135148 | − | 0.0981905i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −18.3643 | + | 56.5197i | −0.232460 | + | 0.715439i | 0.764988 | + | 0.644044i | \(0.222745\pi\) |
−0.997448 | + | 0.0713942i | \(0.977255\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −34.6261 | − | 106.568i | −0.417182 | − | 1.28396i | −0.910284 | − | 0.413984i | \(-0.864137\pi\) |
0.493102 | − | 0.869971i | \(-0.335863\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.8824 | − | 105.809i | −0.292734 | − | 1.24482i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 56.4115 | + | 77.6438i | 0.633837 | + | 0.872402i | 0.998268 | − | 0.0588286i | \(-0.0187365\pi\) |
−0.364431 | + | 0.931230i | \(0.618737\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 62.1013 | + | 45.1193i | 0.682432 | + | 0.495816i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 26.3233 | + | 111.937i | 0.277088 | + | 1.17828i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.4495 | − | 5.01984i | −0.159273 | − | 0.0517510i | 0.228295 | − | 0.973592i | \(-0.426685\pi\) |
−0.387568 | + | 0.921841i | \(0.626685\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.92444i | 0.0586578i | 0.999570 | + | 0.0293289i | \(0.00933702\pi\) | ||||
−0.999570 | + | 0.0293289i | \(0.990663\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 139.464 | + | 45.3146i | 1.35402 | + | 0.439948i | 0.894042 | − | 0.447982i | \(-0.147857\pi\) |
0.459978 | + | 0.887930i | \(0.347857\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −209.615 | −1.95902 | −0.979509 | − | 0.201403i | \(-0.935450\pi\) | ||||
−0.979509 | + | 0.201403i | \(0.935450\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 71.6458 | + | 52.0538i | 0.657301 | + | 0.477557i | 0.865751 | − | 0.500476i | \(-0.166842\pi\) |
−0.208449 | + | 0.978033i | \(0.566842\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 56.5402 | + | 41.0789i | 0.500356 | + | 0.363530i | 0.809153 | − | 0.587598i | \(-0.199926\pi\) |
−0.308797 | + | 0.951128i | \(0.599926\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 27.8501 | − | 16.8888i | 0.242175 | − | 0.146859i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −81.0315 | + | 26.3287i | −0.680937 | + | 0.221250i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 34.0625 | − | 104.834i | 0.281508 | − | 0.866394i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −121.127 | − | 30.8746i | −0.969016 | − | 0.246997i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −46.7583 | − | 64.3573i | −0.368176 | − | 0.506750i | 0.584228 | − | 0.811589i | \(-0.301397\pi\) |
−0.952404 | + | 0.304839i | \(0.901397\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −111.634 | + | 36.2721i | −0.852167 | + | 0.276886i | −0.702354 | − | 0.711828i | \(-0.747867\pi\) |
−0.149814 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 85.7240 | − | 27.8534i | 0.644542 | − | 0.209424i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 44.3045 | + | 32.1891i | 0.323391 | + | 0.234957i | 0.737621 | − | 0.675215i | \(-0.235949\pi\) |
−0.414230 | + | 0.910172i | \(0.635949\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −195.185 | + | 141.810i | −1.40421 | + | 1.02022i | −0.410074 | + | 0.912052i | \(0.634497\pi\) |
−0.994133 | + | 0.108164i | \(0.965503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −64.2797 | −0.449509 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 100.477 | + | 42.1679i | 0.692947 | + | 0.290813i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 67.3024i | 0.451694i | 0.974163 | + | 0.225847i | \(0.0725150\pi\) | ||||
−0.974163 | + | 0.225847i | \(0.927485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −86.9606 | −0.575898 | −0.287949 | − | 0.957646i | \(-0.592973\pi\) | ||||
−0.287949 | + | 0.957646i | \(0.592973\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −46.9294 | − | 199.561i | −0.302770 | − | 1.28749i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 113.116i | − | 0.720483i | −0.932859 | − | 0.360242i | \(-0.882694\pi\) | ||
0.932859 | − | 0.360242i | \(-0.117306\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.0067 | − | 20.6549i | −0.0932090 | − | 0.128291i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.5822 | − | 26.9526i | 0.120136 | − | 0.165354i | −0.744713 | − | 0.667385i | \(-0.767414\pi\) |
0.864850 | + | 0.502031i | \(0.167414\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.98196 | + | 15.3329i | 0.0298321 | + | 0.0918137i | 0.964864 | − | 0.262750i | \(-0.0846294\pi\) |
−0.935032 | + | 0.354564i | \(0.884629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −66.3143 | − | 204.094i | −0.392392 | − | 1.20766i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 210.342 | − | 152.822i | 1.21585 | − | 0.883365i | 0.220099 | − | 0.975477i | \(-0.429362\pi\) |
0.995749 | + | 0.0921123i | \(0.0293619\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.2277 | + | 96.6286i | −0.0927298 | + | 0.552164i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 248.594 | + | 80.7731i | 1.38879 | + | 0.451247i | 0.905550 | − | 0.424239i | \(-0.139458\pi\) |
0.483244 | + | 0.875486i | \(0.339458\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 90.6204 | + | 278.901i | 0.500665 | + | 1.54089i | 0.807938 | + | 0.589267i | \(0.200584\pi\) |
−0.307273 | + | 0.951621i | \(0.599416\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 109.824 | − | 127.383i | 0.593646 | − | 0.688556i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 41.9369 | − | 57.7213i | 0.224262 | − | 0.308670i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.1808 | − | 30.5293i | 0.116130 | − | 0.159839i | −0.746995 | − | 0.664830i | \(-0.768504\pi\) |
0.863125 | + | 0.504991i | \(0.168504\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 152.054i | 0.787847i | 0.919143 | + | 0.393924i | \(0.128883\pi\) | ||||
−0.919143 | + | 0.393924i | \(0.871117\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −84.6500 | + | 260.526i | −0.429696 | + | 1.32247i | 0.468730 | + | 0.883342i | \(0.344712\pi\) |
−0.898426 | + | 0.439126i | \(0.855288\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −246.402 | −1.23820 | −0.619101 | − | 0.785311i | \(-0.712503\pi\) | ||||
−0.619101 | + | 0.785311i | \(0.712503\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 26.3945 | − | 81.2338i | 0.130022 | − | 0.400166i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 142.249 | − | 164.991i | 0.693897 | − | 0.804835i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −44.3655 | + | 61.0639i | −0.212275 | + | 0.292172i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −84.7429 | + | 61.5693i | −0.401625 | + | 0.291798i | −0.770203 | − | 0.637799i | \(-0.779845\pi\) |
0.368577 | + | 0.929597i | \(0.379845\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.0787 | − | 156.846i | 0.0608313 | − | 0.729518i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −152.829 | + | 49.6572i | −0.704282 | + | 0.228835i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 404.936 | + | 131.572i | 1.83229 | + | 0.595347i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −110.794 | − | 152.495i | −0.496833 | − | 0.683833i | 0.484797 | − | 0.874627i | \(-0.338894\pi\) |
−0.981630 | + | 0.190794i | \(0.938894\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.5710 | − | 20.7581i | 0.125864 | − | 0.0914452i | −0.523072 | − | 0.852288i | \(-0.675214\pi\) |
0.648936 | + | 0.760843i | \(0.275214\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −32.5334 | + | 100.128i | −0.142067 | + | 0.437238i | −0.996622 | − | 0.0821229i | \(-0.973830\pi\) |
0.854555 | + | 0.519361i | \(0.173830\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 36.0883 | + | 111.068i | 0.154885 | + | 0.476688i | 0.998149 | − | 0.0608116i | \(-0.0193689\pi\) |
−0.843264 | + | 0.537500i | \(0.819369\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 40.7722 | − | 97.1517i | 0.173499 | − | 0.413411i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −117.529 | − | 161.765i | −0.491753 | − | 0.676840i | 0.488957 | − | 0.872308i | \(-0.337377\pi\) |
−0.980710 | + | 0.195468i | \(0.937377\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 193.762 | + | 140.776i | 0.803992 | + | 0.584135i | 0.912083 | − | 0.410006i | \(-0.134474\pi\) |
−0.108090 | + | 0.994141i | \(0.534474\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −167.615 | − | 13.9767i | −0.684142 | − | 0.0570476i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −428.386 | − | 139.191i | −1.73436 | − | 0.563526i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 413.644i | − | 1.64798i | −0.566601 | − | 0.823992i | \(-0.691742\pi\) | ||
0.566601 | − | 0.823992i | \(-0.308258\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.3330 | + | 6.60660i | 0.0803677 | + | 0.0261131i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.9908 | 0.0427660 | 0.0213830 | − | 0.999771i | \(-0.493193\pi\) | ||||
0.0213830 | + | 0.999771i | \(0.493193\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −106.658 | − | 77.4914i | −0.411806 | − | 0.299195i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −203.928 | − | 148.162i | −0.775391 | − | 0.563354i | 0.128201 | − | 0.991748i | \(-0.459080\pi\) |
−0.903592 | + | 0.428394i | \(0.859080\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 111.575 | − | 265.860i | 0.421038 | − | 1.00325i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 305.833 | − | 99.3712i | 1.13693 | − | 0.369410i | 0.320722 | − | 0.947173i | \(-0.396075\pi\) |
0.816204 | + | 0.577764i | \(0.196075\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −138.402 | + | 425.957i | −0.510707 | + | 1.57180i | 0.280252 | + | 0.959927i | \(0.409582\pi\) |
−0.790959 | + | 0.611869i | \(0.790418\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −36.5677 | − | 73.4502i | −0.132974 | − | 0.267092i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −266.645 | − | 367.006i | −0.962619 | − | 1.32493i | −0.945688 | − | 0.325074i | \(-0.894611\pi\) |
−0.0169303 | − | 0.999857i | \(-0.505389\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 493.513 | − | 160.352i | 1.75628 | − | 0.570648i | 0.759472 | − | 0.650540i | \(-0.225457\pi\) |
0.996804 | + | 0.0798916i | \(0.0254574\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 183.224 | − | 59.5330i | 0.647434 | − | 0.210364i | 0.0331515 | − | 0.999450i | \(-0.489446\pi\) |
0.614282 | + | 0.789086i | \(0.289446\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −138.147 | − | 100.370i | −0.481349 | − | 0.349721i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −148.527 | + | 107.911i | −0.513934 | + | 0.373395i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −37.9439 | −0.129501 | −0.0647507 | − | 0.997901i | \(-0.520625\pi\) | ||||
−0.0647507 | + | 0.997901i | \(0.520625\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 173.125 | − | 200.803i | 0.586863 | − | 0.680689i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 127.584i | 0.426704i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −123.371 | −0.409872 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 220.040 | − | 133.436i | 0.721443 | − | 0.437496i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 182.514i | − | 0.594507i | −0.954799 | − | 0.297253i | \(-0.903929\pi\) | ||
0.954799 | − | 0.297253i | \(-0.0960706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 80.1499 | + | 110.317i | 0.257717 | + | 0.354716i | 0.918195 | − | 0.396129i | \(-0.129647\pi\) |
−0.660478 | + | 0.750845i | \(0.729647\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.71068 | − | 6.48370i | 0.0150501 | − | 0.0207147i | −0.801426 | − | 0.598094i | \(-0.795925\pi\) |
0.816476 | + | 0.577380i | \(0.195925\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −98.9966 | − | 304.680i | −0.312292 | − | 0.961137i | −0.976855 | − | 0.213904i | \(-0.931382\pi\) |
0.664562 | − | 0.747233i | \(-0.268618\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.1026 | + | 68.0248i | 0.0692872 | + | 0.213244i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 404.474 | − | 293.868i | 1.25224 | − | 0.909807i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 349.436 | − | 342.991i | 1.07519 | − | 1.05536i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −78.5452 | − | 25.5209i | −0.238739 | − | 0.0775710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −83.1059 | − | 255.774i | −0.251075 | − | 0.772730i | −0.994578 | − | 0.103997i | \(-0.966837\pi\) |
0.743502 | − | 0.668733i | \(-0.233163\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −376.221 | + | 88.4731i | −1.12305 | + | 0.264099i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 338.343 | − | 465.689i | 1.00398 | − | 1.38187i | 0.0811363 | − | 0.996703i | \(-0.474145\pi\) |
0.922848 | − | 0.385163i | \(-0.125855\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 79.0950 | − | 108.865i | 0.231950 | − | 0.319252i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 323.886i | 0.944274i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 41.5770 | − | 127.961i | 0.119818 | − | 0.368763i | −0.873103 | − | 0.487536i | \(-0.837896\pi\) |
0.992921 | + | 0.118773i | \(0.0378959\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −446.343 | −1.27892 | −0.639461 | − | 0.768824i | \(-0.720842\pi\) | ||||
−0.639461 | + | 0.768824i | \(0.720842\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 107.030 | − | 329.405i | 0.303202 | − | 0.933159i | −0.677140 | − | 0.735854i | \(-0.736781\pi\) |
0.980342 | − | 0.197305i | \(-0.0632189\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −454.591 | − | 190.781i | −1.28054 | − | 0.537411i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −233.133 | + | 320.880i | −0.649395 | + | 0.893815i | −0.999073 | − | 0.0430546i | \(-0.986291\pi\) |
0.349678 | + | 0.936870i | \(0.386291\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −135.842 | + | 98.6950i | −0.376294 | + | 0.273393i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −137.114 | − | 226.105i | −0.375655 | − | 0.619465i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −506.808 | + | 164.672i | −1.38095 | + | 0.448697i | −0.902981 | − | 0.429681i | \(-0.858626\pi\) |
−0.477967 | + | 0.878378i | \(0.658626\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −214.943 | − | 69.8391i | −0.579360 | − | 0.188246i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 173.642 | + | 238.997i | 0.465527 | + | 0.640743i | 0.975643 | − | 0.219362i | \(-0.0703977\pi\) |
−0.510116 | + | 0.860105i | \(0.670398\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −345.319 | + | 250.889i | −0.915966 | + | 0.665488i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.1751 | + | 89.7918i | −0.0769792 | + | 0.236918i | −0.982140 | − | 0.188152i | \(-0.939750\pi\) |
0.905161 | + | 0.425069i | \(0.139750\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −175.807 | − | 541.077i | −0.459025 | − | 1.41273i | −0.866344 | − | 0.499448i | \(-0.833536\pi\) |
0.407319 | − | 0.913286i | \(-0.366464\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −54.9932 | + | 33.3489i | −0.142840 | + | 0.0866205i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 289.468 | + | 398.419i | 0.744135 | + | 1.02421i | 0.998370 | + | 0.0570713i | \(0.0181762\pi\) |
−0.254235 | + | 0.967142i | \(0.581824\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −114.567 | − | 83.2378i | −0.293010 | − | 0.212884i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 114.987 | − | 273.991i | 0.291107 | − | 0.693647i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 354.512 | + | 115.188i | 0.892977 | + | 0.290146i | 0.719335 | − | 0.694663i | \(-0.244447\pi\) |
0.173642 | + | 0.984809i | \(0.444447\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 410.370i | 1.02337i | 0.859174 | + | 0.511683i | \(0.170978\pi\) | ||||
−0.859174 | + | 0.511683i | \(0.829022\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 763.728 | + | 248.150i | 1.89511 | + | 0.615758i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 110.399 | 0.271251 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −446.694 | − | 324.542i | −1.09216 | − | 0.793502i | −0.112398 | − | 0.993663i | \(-0.535853\pi\) |
−0.979763 | + | 0.200162i | \(0.935853\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −168.133 | − | 122.156i | −0.407101 | − | 0.295776i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 128.254 | + | 545.385i | 0.309046 | + | 1.31418i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 471.125 | − | 153.078i | 1.12440 | − | 0.365341i | 0.312957 | − | 0.949767i | \(-0.398681\pi\) |
0.811447 | + | 0.584427i | \(0.198681\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −148.946 | + | 458.410i | −0.353792 | + | 1.08886i | 0.602914 | + | 0.797806i | \(0.294006\pi\) |
−0.956707 | + | 0.291054i | \(0.905994\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 80.0194 | + | 537.555i | 0.188281 | + | 1.26484i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −118.565 | − | 163.191i | −0.277671 | − | 0.382181i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 187.019 | − | 60.7663i | 0.433920 | − | 0.140989i | −0.0839090 | − | 0.996473i | \(-0.526741\pi\) |
0.517829 | + | 0.855484i | \(0.326741\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 666.372 | − | 216.518i | 1.53897 | − | 0.500040i | 0.587875 | − | 0.808952i | \(-0.299965\pi\) |
0.951091 | + | 0.308911i | \(0.0999646\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 121.202 | + | 88.0581i | 0.277349 | + | 0.201506i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −205.621 | + | 149.393i | −0.468385 | + | 0.340302i | −0.796812 | − | 0.604228i | \(-0.793482\pi\) |
0.328426 | + | 0.944530i | \(0.393482\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 735.899 | 1.66117 | 0.830586 | − | 0.556890i | \(-0.188006\pi\) | ||||
0.830586 | + | 0.556890i | \(0.188006\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −248.822 | − | 410.314i | −0.559151 | − | 0.922055i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 320.333i | 0.713436i | 0.934212 | + | 0.356718i | \(0.116104\pi\) | ||||
−0.934212 | + | 0.356718i | \(0.883896\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 142.993 | 0.317058 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −290.686 | − | 250.618i | −0.638871 | − | 0.550809i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 371.347i | − | 0.812577i | −0.913745 | − | 0.406288i | \(-0.866823\pi\) | ||
0.913745 | − | 0.406288i | \(-0.133177\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 287.569 | + | 395.805i | 0.623794 | + | 0.858578i | 0.997622 | − | 0.0689195i | \(-0.0219552\pi\) |
−0.373829 | + | 0.927498i | \(0.621955\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 55.0271 | − | 75.7382i | 0.118849 | − | 0.163582i | −0.745447 | − | 0.666564i | \(-0.767764\pi\) |
0.864296 | + | 0.502983i | \(0.167764\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 88.5517 | + | 272.534i | 0.189618 | + | 0.583585i | 0.999997 | − | 0.00232117i | \(-0.000738851\pi\) |
−0.810379 | + | 0.585906i | \(0.800739\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 93.6157 | + | 288.120i | 0.199607 | + | 0.614327i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 83.5801 | − | 60.7245i | 0.176702 | − | 0.128382i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −84.6533 | − | 568.685i | −0.178218 | − | 1.19723i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −143.020 | − | 46.4699i | −0.298580 | − | 0.0970144i | 0.155896 | − | 0.987773i | \(-0.450173\pi\) |
−0.454476 | + | 0.890759i | \(0.650173\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 203.587 | + | 626.576i | 0.423257 | + | 1.30265i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 74.8946 | + | 31.4315i | 0.154422 | + | 0.0648071i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −276.674 | + | 380.809i | −0.568119 | + | 0.781948i | −0.992330 | − | 0.123615i | \(-0.960551\pi\) |
0.424212 | + | 0.905563i | \(0.360551\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 89.7565 | − | 123.539i | 0.182804 | − | 0.251607i | −0.707774 | − | 0.706439i | \(-0.750300\pi\) |
0.890578 | + | 0.454831i | \(0.150300\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 473.769i | − | 0.960993i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −119.417 | + | 367.527i | −0.240275 | + | 0.739491i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −708.670 | −1.42018 | −0.710090 | − | 0.704110i | \(-0.751346\pi\) | ||||
−0.710090 | + | 0.704110i | \(0.751346\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 57.1391 | − | 175.856i | 0.113597 | − | 0.349614i | −0.878055 | − | 0.478559i | \(-0.841159\pi\) |
0.991652 | + | 0.128945i | \(0.0411591\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.46152 | − | 29.5197i | 0.00487430 | − | 0.0584549i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −246.414 | + | 339.160i | −0.484115 | + | 0.666327i | −0.979289 | − | 0.202467i | \(-0.935104\pi\) |
0.495174 | + | 0.868794i | \(0.335104\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −167.689 | + | 121.833i | −0.328159 | + | 0.238421i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −676.081 | − | 283.735i | −1.31278 | − | 0.550942i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 65.7734 | − | 21.3711i | 0.127221 | − | 0.0413367i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −338.109 | − | 109.858i | −0.648961 | − | 0.210860i | −0.0340051 | − | 0.999422i | \(-0.510826\pi\) |
−0.614956 | + | 0.788561i | \(0.710826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 481.758 | + | 663.083i | 0.921144 | + | 1.26785i | 0.963215 | + | 0.268731i | \(0.0866042\pi\) |
−0.0420716 | + | 0.999115i | \(0.513396\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −721.098 | + | 523.908i | −1.36831 | + | 0.994133i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −150.357 | + | 462.751i | −0.284229 | + | 0.874766i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 263.694 | + | 811.565i | 0.494735 | + | 1.52264i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1044.45 | + | 87.0921i | 1.95224 | + | 0.162789i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −64.8936 | − | 89.3184i | −0.120396 | − | 0.165711i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 356.350 | + | 258.904i | 0.658688 | + | 0.478565i | 0.866220 | − | 0.499663i | \(-0.166543\pi\) |
−0.207532 | + | 0.978228i | \(0.566543\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −335.363 | − | 289.136i | −0.615344 | − | 0.530526i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.72191 | − | 1.85916i | −0.0104605 | − | 0.00339883i | 0.303782 | − | 0.952742i | \(-0.401751\pi\) |
−0.314243 | + | 0.949343i | \(0.601751\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 501.206i | 0.909629i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −221.516 | − | 71.9749i | −0.400571 | − | 0.130153i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −511.337 | −0.918020 | −0.459010 | − | 0.888431i | \(-0.651796\pi\) | ||||
−0.459010 | + | 0.888431i | \(0.651796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 498.775 | + | 362.381i | 0.892263 | + | 0.648267i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −677.355 | − | 492.127i | −1.20312 | − | 0.874116i | −0.208529 | − | 0.978016i | \(-0.566868\pi\) |
−0.994588 | + | 0.103901i | \(0.966868\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −264.656 | − | 228.176i | −0.468417 | − | 0.403851i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 178.776 | − | 58.0878i | 0.314193 | − | 0.102088i | −0.147676 | − | 0.989036i | \(-0.547179\pi\) |
0.461869 | + | 0.886948i | \(0.347179\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −142.570 | + | 438.785i | −0.249685 | + | 0.768451i | 0.745146 | + | 0.666902i | \(0.232380\pi\) |
−0.994831 | + | 0.101549i | \(0.967620\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −145.786 | + | 72.5808i | −0.253541 | + | 0.126227i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −144.165 | − | 198.426i | −0.249852 | − | 0.343892i | 0.665607 | − | 0.746302i | \(-0.268173\pi\) |
−0.915460 | + | 0.402410i | \(0.868173\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 417.670 | − | 135.709i | 0.718881 | − | 0.233579i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 179.992 | − | 58.4830i | 0.308734 | − | 0.100314i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −40.9156 | − | 29.7269i | −0.0697029 | − | 0.0506421i | 0.552388 | − | 0.833587i | \(-0.313717\pi\) |
−0.622091 | + | 0.782945i | \(0.713717\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 762.857 | − | 554.248i | 1.29517 | − | 0.940998i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −373.871 | −0.630473 | −0.315237 | − | 0.949013i | \(-0.602084\pi\) | ||||
−0.315237 | + | 0.949013i | \(0.602084\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 414.695 | − | 97.5209i | 0.696967 | − | 0.163901i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 152.760i | 0.255025i | 0.991837 | + | 0.127513i | \(0.0406993\pi\) | ||||
−0.991837 | + | 0.127513i | \(0.959301\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 442.462 | 0.736210 | 0.368105 | − | 0.929784i | \(-0.380007\pi\) | ||||
0.368105 | + | 0.929784i | \(0.380007\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −213.280 | + | 508.203i | −0.352530 | + | 0.840005i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 66.9050i | 0.110222i | 0.998480 | + | 0.0551112i | \(0.0175513\pi\) | ||||
−0.998480 | + | 0.0551112i | \(0.982449\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 242.585 | + | 333.890i | 0.397030 | + | 0.546465i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −610.239 | + | 839.923i | −0.995497 | + | 1.37018i | −0.0674487 | + | 0.997723i | \(0.521486\pi\) |
−0.928048 | + | 0.372461i | \(0.878514\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.2157 | − | 65.2952i | −0.0343852 | − | 0.105827i | 0.932391 | − | 0.361452i | \(-0.117719\pi\) |
−0.966776 | + | 0.255625i | \(0.917719\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −279.981 | − | 861.692i | −0.452311 | − | 1.39207i | −0.874263 | − | 0.485452i | \(-0.838655\pi\) |
0.421952 | − | 0.906618i | \(-0.361345\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −304.307 | + | 221.092i | −0.488454 | + | 0.354883i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 590.713 | + | 204.166i | 0.945140 | + | 0.326665i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −695.469 | − | 225.972i | −1.10567 | − | 0.359255i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 173.326 | + | 533.442i | 0.274685 | + | 0.845392i | 0.989303 | + | 0.145877i | \(0.0466005\pi\) |
−0.714618 | + | 0.699515i | \(0.753400\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 206.243 | + | 340.101i | 0.324793 | + | 0.535592i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 387.261 | − | 533.019i | 0.607945 | − | 0.836764i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 500.539 | − | 688.933i | 0.780873 | − | 1.07478i | −0.214312 | − | 0.976765i | \(-0.568751\pi\) |
0.995185 | − | 0.0980139i | \(-0.0312490\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 279.237i | − | 0.434272i | −0.976141 | − | 0.217136i | \(-0.930328\pi\) | ||
0.976141 | − | 0.217136i | \(-0.0696716\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −54.2292 | + | 166.900i | −0.0838164 | + | 0.257960i | −0.984178 | − | 0.177182i | \(-0.943302\pi\) |
0.900362 | + | 0.435142i | \(0.143302\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 174.030 | 0.268152 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −58.0638 | + | 178.702i | −0.0889185 | + | 0.273663i | −0.985621 | − | 0.168971i | \(-0.945956\pi\) |
0.896703 | + | 0.442633i | \(0.145956\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 571.310 | − | 134.351i | 0.872229 | − | 0.205116i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −733.416 | + | 1009.46i | −1.11292 | + | 1.53181i | −0.295885 | + | 0.955224i | \(0.595615\pi\) |
−0.817038 | + | 0.576584i | \(0.804385\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −65.0567 | + | 47.2665i | −0.0984217 | + | 0.0715076i | −0.635908 | − | 0.771765i | \(-0.719374\pi\) |
0.537486 | + | 0.843273i | \(0.319374\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −438.710 | + | 103.168i | −0.659715 | + | 0.155140i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 135.018 | − | 43.8699i | 0.202425 | − | 0.0657720i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 160.648 | + | 52.1978i | 0.239416 | + | 0.0777911i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −310.068 | − | 426.772i | −0.460725 | − | 0.634133i | 0.513934 | − | 0.857830i | \(-0.328188\pi\) |
−0.974659 | + | 0.223696i | \(0.928188\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 345.000 | − | 250.657i | 0.509601 | − | 0.370247i | −0.303071 | − | 0.952968i | \(-0.598012\pi\) |
0.812672 | + | 0.582721i | \(0.198012\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.6741 | − | 60.5507i | 0.0289752 | − | 0.0891764i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 268.621 | + | 826.730i | 0.393296 | + | 1.21044i | 0.930281 | + | 0.366848i | \(0.119563\pi\) |
−0.536985 | + | 0.843592i | \(0.680437\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −207.382 | − | 178.797i | −0.302748 | − | 0.261017i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 663.846 | + | 913.706i | 0.963492 | + | 1.32613i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −424.247 | − | 308.234i | −0.613961 | − | 0.446069i | 0.236846 | − | 0.971547i | \(-0.423886\pi\) |
−0.850807 | + | 0.525478i | \(0.823886\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1031.47 | − | 625.502i | 1.48413 | − | 0.900002i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −900.799 | − | 292.687i | −1.29239 | − | 0.419924i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 465.185i | 0.663602i | 0.943349 | + | 0.331801i | \(0.107656\pi\) | ||||
−0.943349 | + | 0.331801i | \(0.892344\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 735.744 | + | 239.058i | 1.04658 | + | 0.340054i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.2195 | −0.0328423 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 562.969 | + | 409.021i | 0.794032 | + | 0.576898i | 0.909157 | − | 0.416453i | \(-0.136727\pi\) |
−0.115125 | + | 0.993351i | \(0.536727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −216.079 | − | 156.990i | −0.303056 | − | 0.220183i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 320.287 | + | 26.7073i | 0.447954 | + | 0.0373529i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −638.711 | + | 207.530i | −0.888332 | + | 0.288637i | −0.717413 | − | 0.696648i | \(-0.754674\pi\) |
−0.170919 | + | 0.985285i | \(0.554674\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −177.600 | + | 546.598i | −0.246325 | + | 0.758111i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −483.129 | − | 251.857i | −0.666384 | − | 0.347389i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −191.108 | − | 263.037i | −0.262871 | − | 0.361812i | 0.657096 | − | 0.753807i | \(-0.271785\pi\) |
−0.919967 | + | 0.391996i | \(0.871785\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −650.815 | + | 211.463i | −0.890308 | + | 0.289279i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 516.306 | − | 167.758i | 0.704374 | − | 0.228865i | 0.0651386 | − | 0.997876i | \(-0.479251\pi\) |
0.639235 | + | 0.769011i | \(0.279251\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −205.237 | − | 149.113i | −0.278476 | − | 0.202324i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1085.93 | + | 788.976i | −1.46946 | + | 1.06763i | −0.488693 | + | 0.872456i | \(0.662526\pi\) |
−0.980769 | + | 0.195171i | \(0.937474\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −983.917 | −1.32425 | −0.662125 | − | 0.749394i | \(-0.730345\pi\) | ||||
−0.662125 | + | 0.749394i | \(0.730345\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.9632 | − | 335.348i | 0.0375345 | − | 0.450132i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 821.538i | − | 1.09685i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 841.325 | 1.12027 | 0.560137 | − | 0.828400i | \(-0.310749\pi\) | ||||
0.560137 | + | 0.828400i | \(0.310749\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 433.299 | + | 36.1309i | 0.573906 | + | 0.0478555i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 337.631i | 0.446012i | 0.974817 | + | 0.223006i | \(0.0715870\pi\) | ||||
−0.974817 | + | 0.223006i | \(0.928413\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −216.485 | − | 297.966i | −0.284475 | − | 0.391546i | 0.642735 | − | 0.766089i | \(-0.277800\pi\) |
−0.927210 | + | 0.374543i | \(0.877800\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −204.013 | + | 280.800i | −0.267382 | + | 0.368020i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 320.929 | + | 987.719i | 0.418422 | + | 1.28777i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 263.712 | + | 811.621i | 0.342928 | + | 1.05542i | 0.962684 | + | 0.270629i | \(0.0872316\pi\) |
−0.619756 | + | 0.784795i | \(0.712768\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1016.04 | − | 738.200i | 1.31442 | − | 0.954980i | 0.314433 | − | 0.949280i | \(-0.398185\pi\) |
0.999984 | − | 0.00570041i | \(-0.00181451\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 150.920 | + | 1013.85i | 0.194736 | + | 1.30820i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 952.964 | + | 309.637i | 1.22332 | + | 0.397480i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −99.9991 | − | 307.766i | −0.128040 | − | 0.394066i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −46.9981 | + | 563.623i | −0.0598702 | + | 0.717991i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −514.243 | + | 707.795i | −0.653422 | + | 0.899358i | −0.999241 | − | 0.0389430i | \(-0.987601\pi\) |
0.345820 | + | 0.938301i | \(0.387601\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −160.999 | + | 221.597i | −0.203539 | + | 0.280147i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1008.03i | 1.27116i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −82.5788 | + | 254.151i | −0.103612 | + | 0.318885i | −0.989402 | − | 0.145201i | \(-0.953617\pi\) |
0.885790 | + | 0.464086i | \(0.153617\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −458.089 | −0.573328 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 53.6365 | − | 165.076i | 0.0667951 | − | 0.205574i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 66.1919 | + | 109.152i | 0.0822260 | + | 0.135593i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 787.718 | − | 1084.20i | 0.973694 | − | 1.34017i | 0.0335353 | − | 0.999438i | \(-0.489323\pi\) |
0.940159 | − | 0.340737i | \(-0.110677\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 611.355 | − | 444.175i | 0.753829 | − | 0.547689i | −0.143183 | − | 0.989696i | \(-0.545734\pi\) |
0.897011 | + | 0.442008i | \(0.145734\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −108.771 | + | 126.161i | −0.133461 | + | 0.154799i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 688.504 | − | 223.708i | 0.842722 | − | 0.273817i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −755.137 | − | 245.359i | −0.919778 | − | 0.298854i | −0.189402 | − | 0.981900i | \(-0.560655\pi\) |
−0.730376 | + | 0.683046i | \(0.760655\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −643.168 | − | 885.245i | −0.781492 | − | 1.07563i | −0.995116 | − | 0.0987156i | \(-0.968527\pi\) |
0.213624 | − | 0.976916i | \(-0.431473\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 516.929 | − | 375.571i | 0.625065 | − | 0.454137i | −0.229622 | − | 0.973280i | \(-0.573749\pi\) |
0.854687 | + | 0.519143i | \(0.173749\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −248.173 | + | 763.798i | −0.299364 | + | 0.921348i | 0.682356 | + | 0.731020i | \(0.260955\pi\) |
−0.981720 | + | 0.190328i | \(0.939045\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 225.981 | + | 695.497i | 0.271285 | + | 0.834931i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.4530 | − | 78.4692i | −0.0220994 | − | 0.0939751i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 500.862 | + | 689.377i | 0.596975 | + | 0.821666i | 0.995427 | − | 0.0955235i | \(-0.0304525\pi\) |
−0.398452 | + | 0.917189i | \(0.630452\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −296.139 | − | 215.157i | −0.352127 | − | 0.255835i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 245.626 | + | 1044.50i | 0.290682 | + | 1.23609i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 410.872 | + | 133.500i | 0.485090 | + | 0.157615i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 219.124i | − | 0.257490i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 358.654 | + | 116.534i | 0.420462 | + | 0.136616i | 0.511604 | − | 0.859222i | \(-0.329052\pi\) |
−0.0911417 | + | 0.995838i | \(0.529052\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1224.38 | −1.42868 | −0.714340 | − | 0.699799i | \(-0.753273\pi\) | ||||
−0.714340 | + | 0.699799i | \(0.753273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1243.79 | − | 903.670i | −1.44796 | − | 1.05200i | −0.986303 | − | 0.164941i | \(-0.947257\pi\) |
−0.461653 | − | 0.887061i | \(-0.652743\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −439.239 | − | 319.126i | −0.508968 | − | 0.369787i | 0.303464 | − | 0.952843i | \(-0.401857\pi\) |
−0.812432 | + | 0.583056i | \(0.801857\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1111.57 | + | 674.074i | −1.28505 | + | 0.779276i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 185.496 | − | 60.2714i | 0.213460 | − | 0.0693572i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 467.823 | − | 1439.81i | 0.537110 | − | 1.65305i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 121.006 | − | 474.730i | 0.138292 | − | 0.542548i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 210.629 | + | 289.906i | 0.240170 | + | 0.330565i | 0.912038 | − | 0.410105i | \(-0.134508\pi\) |
−0.671869 | + | 0.740670i | \(0.734508\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 461.872 | − | 150.071i | 0.524258 | − | 0.170342i | −0.0349186 | − | 0.999390i | \(-0.511117\pi\) |
0.559177 | + | 0.829048i | \(0.311117\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 768.885 | − | 249.826i | 0.870765 | − | 0.282929i | 0.160647 | − | 0.987012i | \(-0.448642\pi\) |
0.710117 | + | 0.704083i | \(0.248642\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.2028 | − | 28.4825i | −0.0441971 | − | 0.0321111i | 0.565467 | − | 0.824771i | \(-0.308696\pi\) |
−0.609664 | + | 0.792660i | \(0.708696\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 252.234 | − | 183.259i | 0.283728 | − | 0.206140i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 484.617 | 0.542684 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1205.11 | − | 505.756i | −1.34649 | − | 0.565091i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 893.551i | − | 0.993939i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1253.58 | −1.39132 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −335.655 | − | 1427.33i | −0.370890 | − | 1.57716i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 669.083i | − | 0.737688i | −0.929491 | − | 0.368844i | \(-0.879754\pi\) | ||
0.929491 | − | 0.368844i | \(-0.120246\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −873.093 | − | 1201.71i | −0.958390 | − | 1.31911i | −0.947698 | − | 0.319168i | \(-0.896597\pi\) |
−0.0106915 | − | 0.999943i | \(-0.503403\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −216.161 | + | 297.519i | −0.236758 | + | 0.325870i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −142.160 | − | 437.524i | −0.155027 | − | 0.477125i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −169.678 | − | 522.215i | −0.184633 | − | 0.568242i | 0.815309 | − | 0.579026i | \(-0.196567\pi\) |
−0.999942 | + | 0.0107842i | \(0.996567\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1562.33 | − | 1135.10i | 1.69267 | − | 1.22979i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −600.149 | + | 589.081i | −0.648809 | + | 0.636844i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −589.067 | − | 191.400i | −0.634088 | − | 0.206028i | −0.0257026 | − | 0.999670i | \(-0.508182\pi\) |
−0.608385 | + | 0.793642i | \(0.708182\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −239.067 | − | 735.774i | −0.256786 | − | 0.790305i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −232.942 | + | 270.184i | −0.249136 | + | 0.288967i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 293.703 | − | 404.247i | 0.313450 | − | 0.431427i | −0.623003 | − | 0.782219i | \(-0.714088\pi\) |
0.936453 | + | 0.350792i | \(0.114088\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −648.463 | + | 892.532i | −0.689121 | + | 0.948493i | −0.999998 | − | 0.00195660i | \(-0.999377\pi\) |
0.310877 | + | 0.950450i | \(0.399377\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 283.817i | − | 0.300973i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 159.120 | − | 489.721i | 0.168025 | − | 0.517129i | −0.831221 | − | 0.555942i | \(-0.812358\pi\) |
0.999246 | + | 0.0388130i | \(0.0123577\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1035.81 | 1.09147 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −215.793 | + | 664.143i | −0.226436 | + | 0.696898i | 0.771707 | + | 0.635978i | \(0.219403\pi\) |
−0.998143 | + | 0.0609193i | \(0.980597\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −123.205 | + | 142.903i | −0.129010 | + | 0.149636i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −126.158 | + | 173.642i | −0.131552 | + | 0.181065i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −582.559 | + | 423.254i | −0.606201 | + | 0.440431i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 63.1765 | − | 757.643i | 0.0654679 | − | 0.785122i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 926.107 | − | 300.910i | 0.957712 | − | 0.311179i | 0.211866 | − | 0.977299i | \(-0.432046\pi\) |
0.745845 | + | 0.666119i | \(0.232046\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1633.95 | + | 530.903i | 1.68275 | + | 0.546759i | 0.985442 | − | 0.170010i | \(-0.0543801\pi\) |
0.697310 | + | 0.716770i | \(0.254380\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −555.792 | − | 764.982i | −0.571215 | − | 0.786210i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 962.183 | − | 699.067i | 0.984834 | − | 0.715524i | 0.0260503 | − | 0.999661i | \(-0.491707\pi\) |
0.958784 | + | 0.284137i | \(0.0917070\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 97.3346 | − | 299.565i | 0.0994225 | − | 0.305991i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 161.024 | + | 495.580i | 0.163808 | + | 0.504150i | 0.998946 | − | 0.0458900i | \(-0.0146124\pi\) |
−0.835138 | + | 0.550040i | \(0.814612\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 530.031 | − | 1262.95i | 0.538103 | − | 1.28219i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −120.528 | − | 165.892i | −0.121868 | − | 0.167738i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 641.848 | + | 466.330i | 0.647677 | + | 0.470565i | 0.862479 | − | 0.506093i | \(-0.168911\pi\) |
−0.214802 | + | 0.976658i | \(0.568911\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1227.75 | + | 102.377i | 1.23392 | + | 0.102891i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −138.298 | − | 44.9356i | −0.138714 | − | 0.0450708i | 0.238837 | − | 0.971060i | \(-0.423234\pi\) |
−0.377551 | + | 0.925989i | \(0.623234\pi\) | |||||||
\(998\) | 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 | 900.3.y.a.89.3 | ✓ | 80 | |
3.2 | odd | 2 | inner | 900.3.y.a.89.18 | yes | 80 | |
25.9 | even | 10 | inner | 900.3.y.a.809.18 | yes | 80 | |
75.59 | odd | 10 | inner | 900.3.y.a.809.3 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.3.y.a.89.3 | ✓ | 80 | 1.1 | even | 1 | trivial | |
900.3.y.a.89.18 | yes | 80 | 3.2 | odd | 2 | inner | |
900.3.y.a.809.3 | yes | 80 | 75.59 | odd | 10 | inner | |
900.3.y.a.809.18 | yes | 80 | 25.9 | even | 10 | inner |