Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(485,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.485");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.b (of order \(2\), degree \(1\), 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: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.65306824704.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 2x^{6} + 20x^{5} + x^{4} - 40x^{3} + 36x^{2} - 12x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 485.1 | ||
Root | \(2.75726 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.485 |
Dual form | 1089.3.b.g.485.8 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.89935i | − 1.94967i | −0.222917 | − | 0.974837i | \(-0.571558\pi\) | ||||
0.222917 | − | 0.974837i | \(-0.428442\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −11.2049 | −2.80123 | ||||||||
\(5\) | 6.10332i | 1.22066i | 0.792145 | + | 0.610332i | \(0.208964\pi\) | ||||
−0.792145 | + | 0.610332i | \(0.791036\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.61086 | −0.372980 | −0.186490 | − | 0.982457i | \(-0.559711\pi\) | ||||
−0.186490 | + | 0.982457i | \(0.559711\pi\) | |||||||
\(8\) | 28.0945i | 3.51182i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 23.7990 | 2.37990 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.69890 | 0.592223 | 0.296111 | − | 0.955153i | \(-0.404310\pi\) | ||||
0.296111 | + | 0.955153i | \(0.404310\pi\) | |||||||
\(14\) | 10.1807i | 0.727190i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.7307 | 4.04567 | ||||||||
\(17\) | − 27.5859i | − 1.62270i | −0.584559 | − | 0.811351i | \(-0.698732\pi\) | ||||
0.584559 | − | 0.811351i | \(-0.301268\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.63254 | −0.191186 | −0.0955930 | − | 0.995420i | \(-0.530475\pi\) | ||||
−0.0955930 | + | 0.995420i | \(0.530475\pi\) | |||||||
\(20\) | − 68.3873i | − 3.41937i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22.4470i | 0.975957i | 0.872856 | + | 0.487979i | \(0.162266\pi\) | ||||
−0.872856 | + | 0.487979i | \(0.837734\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.2506 | −0.490023 | ||||||||
\(26\) | − 30.0207i | − 1.15464i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 29.2545 | 1.04480 | ||||||||
\(29\) | − 16.9284i | − 0.583738i | −0.956458 | − | 0.291869i | \(-0.905723\pi\) | ||||
0.956458 | − | 0.291869i | \(-0.0942771\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.26034 | 0.105172 | 0.0525862 | − | 0.998616i | \(-0.483254\pi\) | ||||
0.0525862 | + | 0.998616i | \(0.483254\pi\) | |||||||
\(32\) | − 140.030i | − 4.37592i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −107.567 | −3.16374 | ||||||||
\(35\) | − 15.9349i | − 0.455284i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 15.0843 | 0.407683 | 0.203841 | − | 0.979004i | \(-0.434657\pi\) | ||||
0.203841 | + | 0.979004i | \(0.434657\pi\) | |||||||
\(38\) | 14.1645i | 0.372751i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −171.470 | −4.28675 | ||||||||
\(41\) | 40.2542i | 0.981809i | 0.871214 | + | 0.490904i | \(0.163334\pi\) | ||||
−0.871214 | + | 0.490904i | \(0.836666\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −69.4624 | −1.61540 | −0.807702 | − | 0.589590i | \(-0.799289\pi\) | ||||
−0.807702 | + | 0.589590i | \(0.799289\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 87.5288 | 1.90280 | ||||||||
\(47\) | − 21.7183i | − 0.462091i | −0.972943 | − | 0.231045i | \(-0.925785\pi\) | ||||
0.972943 | − | 0.231045i | \(-0.0742146\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −42.1834 | −0.860886 | ||||||||
\(50\) | 47.7693i | 0.955385i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −86.2656 | −1.65895 | ||||||||
\(53\) | − 12.1729i | − 0.229677i | −0.993384 | − | 0.114839i | \(-0.963365\pi\) | ||||
0.993384 | − | 0.114839i | \(-0.0366351\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 73.3509i | − 1.30984i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −66.0098 | −1.13810 | ||||||||
\(59\) | − 34.0467i | − 0.577063i | −0.957470 | − | 0.288532i | \(-0.906833\pi\) | ||||
0.957470 | − | 0.288532i | \(-0.0931670\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −61.3863 | −1.00633 | −0.503166 | − | 0.864190i | \(-0.667832\pi\) | ||||
−0.503166 | + | 0.864190i | \(0.667832\pi\) | |||||||
\(62\) | − 12.7132i | − 0.205052i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −287.101 | −4.48596 | ||||||||
\(65\) | 46.9889i | 0.722906i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 54.6101 | 0.815076 | 0.407538 | − | 0.913188i | \(-0.366387\pi\) | ||||
0.407538 | + | 0.913188i | \(0.366387\pi\) | |||||||
\(68\) | 309.098i | 4.54557i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −62.1359 | −0.887655 | ||||||||
\(71\) | 11.5967i | 0.163334i | 0.996660 | + | 0.0816670i | \(0.0260244\pi\) | ||||
−0.996660 | + | 0.0816670i | \(0.973976\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −41.7131 | −0.571412 | −0.285706 | − | 0.958317i | \(-0.592228\pi\) | ||||
−0.285706 | + | 0.958317i | \(0.592228\pi\) | |||||||
\(74\) | − 58.8188i | − 0.794849i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 40.7023 | 0.535557 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −96.9294 | −1.22695 | −0.613477 | − | 0.789712i | \(-0.710230\pi\) | ||||
−0.613477 | + | 0.789712i | \(0.710230\pi\) | |||||||
\(80\) | 395.073i | 4.93841i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 156.965 | 1.91421 | ||||||||
\(83\) | − 89.8729i | − 1.08281i | −0.840763 | − | 0.541403i | \(-0.817893\pi\) | ||||
0.840763 | − | 0.541403i | \(-0.182107\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 168.366 | 1.98078 | ||||||||
\(86\) | 270.858i | 3.14951i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 117.316i | − 1.31816i | −0.752074 | − | 0.659078i | \(-0.770947\pi\) | ||||
0.752074 | − | 0.659078i | \(-0.229053\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.1007 | −0.220887 | ||||||||
\(92\) | − 251.517i | − 2.73388i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −84.6871 | −0.900927 | ||||||||
\(95\) | − 22.1705i | − 0.233374i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.47681 | −0.0770806 | −0.0385403 | − | 0.999257i | \(-0.512271\pi\) | ||||
−0.0385403 | + | 0.999257i | \(0.512271\pi\) | |||||||
\(98\) | 164.488i | 1.67845i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 137.267 | 1.37267 | ||||||||
\(101\) | − 55.4534i | − 0.549044i | −0.961581 | − | 0.274522i | \(-0.911480\pi\) | ||||
0.961581 | − | 0.274522i | \(-0.0885196\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −167.207 | −1.62337 | −0.811683 | − | 0.584098i | \(-0.801448\pi\) | ||||
−0.811683 | + | 0.584098i | \(0.801448\pi\) | |||||||
\(104\) | 216.297i | 2.07978i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −47.4664 | −0.447796 | ||||||||
\(107\) | − 37.0923i | − 0.346657i | −0.984864 | − | 0.173329i | \(-0.944548\pi\) | ||||
0.984864 | − | 0.173329i | \(-0.0554523\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 97.9327 | 0.898465 | 0.449232 | − | 0.893415i | \(-0.351697\pi\) | ||||
0.449232 | + | 0.893415i | \(0.351697\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −169.003 | −1.50895 | ||||||||
\(113\) | − 207.091i | − 1.83267i | −0.400416 | − | 0.916334i | \(-0.631134\pi\) | ||||
0.400416 | − | 0.916334i | \(-0.368866\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −137.001 | −1.19132 | ||||||||
\(116\) | 189.682i | 1.63519i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −132.760 | −1.12509 | ||||||||
\(119\) | 72.0230i | 0.605235i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 239.367i | 1.96202i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −36.5319 | −0.294612 | ||||||||
\(125\) | 77.8139i | 0.622511i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −182.507 | −1.43707 | −0.718533 | − | 0.695493i | \(-0.755186\pi\) | ||||
−0.718533 | + | 0.695493i | \(0.755186\pi\) | |||||||
\(128\) | 559.391i | 4.37024i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 183.226 | 1.40943 | ||||||||
\(131\) | − 163.461i | − 1.24780i | −0.781506 | − | 0.623898i | \(-0.785548\pi\) | ||||
0.781506 | − | 0.623898i | \(-0.214452\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.48404 | 0.0713086 | ||||||||
\(134\) | − 212.944i | − 1.58913i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 775.014 | 5.69863 | ||||||||
\(137\) | − 199.563i | − 1.45666i | −0.685224 | − | 0.728332i | \(-0.740296\pi\) | ||||
0.685224 | − | 0.728332i | \(-0.259704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.75894 | −0.0198485 | −0.00992425 | − | 0.999951i | \(-0.503159\pi\) | ||||
−0.00992425 | + | 0.999951i | \(0.503159\pi\) | |||||||
\(140\) | 178.550i | 1.27536i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 45.2196 | 0.318448 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 103.320 | 0.712549 | ||||||||
\(146\) | 162.654i | 1.11407i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −169.018 | −1.14201 | ||||||||
\(149\) | − 79.7092i | − 0.534961i | −0.963563 | − | 0.267481i | \(-0.913809\pi\) | ||||
0.963563 | − | 0.267481i | \(-0.0861911\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 149.776 | 0.991894 | 0.495947 | − | 0.868353i | \(-0.334821\pi\) | ||||
0.495947 | + | 0.868353i | \(0.334821\pi\) | |||||||
\(152\) | − 102.054i | − 0.671411i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.8989i | 0.128380i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −273.723 | −1.74346 | −0.871730 | − | 0.489986i | \(-0.837002\pi\) | ||||
−0.871730 | + | 0.489986i | \(0.837002\pi\) | |||||||
\(158\) | 377.962i | 2.39216i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 854.646 | 5.34154 | ||||||||
\(161\) | − 58.6060i | − 0.364012i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 289.639 | 1.77693 | 0.888464 | − | 0.458946i | \(-0.151773\pi\) | ||||
0.888464 | + | 0.458946i | \(0.151773\pi\) | |||||||
\(164\) | − 451.045i | − 2.75027i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −350.446 | −2.11112 | ||||||||
\(167\) | 47.9894i | 0.287362i | 0.989624 | + | 0.143681i | \(0.0458939\pi\) | ||||
−0.989624 | + | 0.143681i | \(0.954106\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −109.727 | −0.649272 | ||||||||
\(170\) | − 656.518i | − 3.86187i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 778.321 | 4.52512 | ||||||||
\(173\) | − 35.0195i | − 0.202425i | −0.994865 | − | 0.101212i | \(-0.967728\pi\) | ||||
0.994865 | − | 0.101212i | \(-0.0322722\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 31.9845 | 0.182769 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −457.456 | −2.56998 | ||||||||
\(179\) | − 190.174i | − 1.06242i | −0.847239 | − | 0.531212i | \(-0.821737\pi\) | ||||
0.847239 | − | 0.531212i | \(-0.178263\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −78.2856 | −0.432517 | −0.216258 | − | 0.976336i | \(-0.569385\pi\) | ||||
−0.216258 | + | 0.976336i | \(0.569385\pi\) | |||||||
\(182\) | 78.3798i | 0.430658i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −630.639 | −3.42738 | ||||||||
\(185\) | 92.0642i | 0.497644i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 243.352i | 1.29442i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −86.4507 | −0.455004 | ||||||||
\(191\) | − 99.6608i | − 0.521784i | −0.965368 | − | 0.260892i | \(-0.915983\pi\) | ||||
0.965368 | − | 0.260892i | \(-0.0840167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −29.9880 | −0.155378 | −0.0776891 | − | 0.996978i | \(-0.524754\pi\) | ||||
−0.0776891 | + | 0.996978i | \(0.524754\pi\) | |||||||
\(194\) | 29.1547i | 0.150282i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 472.662 | 2.41154 | ||||||||
\(197\) | − 82.2920i | − 0.417726i | −0.977945 | − | 0.208863i | \(-0.933024\pi\) | ||||
0.977945 | − | 0.208863i | \(-0.0669763\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 217.671 | 1.09383 | 0.546913 | − | 0.837189i | \(-0.315803\pi\) | ||||
0.546913 | + | 0.837189i | \(0.315803\pi\) | |||||||
\(200\) | − 344.174i | − 1.72087i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −216.232 | −1.07046 | ||||||||
\(203\) | 44.1977i | 0.217723i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −245.684 | −1.19846 | ||||||||
\(206\) | 651.997i | 3.16504i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 498.355 | 2.39594 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 105.008 | 0.497669 | 0.248834 | − | 0.968546i | \(-0.419952\pi\) | ||||
0.248834 | + | 0.968546i | \(0.419952\pi\) | |||||||
\(212\) | 136.396i | 0.643380i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −144.636 | −0.675869 | ||||||||
\(215\) | − 423.952i | − 1.97187i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.51230 | −0.0392272 | ||||||||
\(218\) | − 381.874i | − 1.75171i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 212.381i | − 0.961002i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 238.589 | 1.06991 | 0.534953 | − | 0.844882i | \(-0.320329\pi\) | ||||
0.534953 | + | 0.844882i | \(0.320329\pi\) | |||||||
\(224\) | 365.598i | 1.63213i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −807.522 | −3.57310 | ||||||||
\(227\) | 326.217i | 1.43708i | 0.695485 | + | 0.718540i | \(0.255190\pi\) | ||||
−0.695485 | + | 0.718540i | \(0.744810\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 233.208 | 1.01837 | 0.509187 | − | 0.860656i | \(-0.329946\pi\) | ||||
0.509187 | + | 0.860656i | \(0.329946\pi\) | |||||||
\(230\) | 534.216i | 2.32268i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 475.596 | 2.04998 | ||||||||
\(233\) | − 65.6551i | − 0.281781i | −0.990025 | − | 0.140891i | \(-0.955003\pi\) | ||||
0.990025 | − | 0.140891i | \(-0.0449966\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 132.554 | 0.564058 | ||||||||
\(236\) | 381.491i | 1.61649i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 280.843 | 1.18001 | ||||||||
\(239\) | 214.400i | 0.897072i | 0.893765 | + | 0.448536i | \(0.148054\pi\) | ||||
−0.893765 | + | 0.448536i | \(0.851946\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 404.958 | 1.68032 | 0.840161 | − | 0.542337i | \(-0.182460\pi\) | ||||
0.840161 | + | 0.542337i | \(0.182460\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 687.829 | 2.81897 | ||||||||
\(245\) | − 257.459i | − 1.05085i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −27.9665 | −0.113225 | ||||||||
\(248\) | 91.5978i | 0.369346i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 303.424 | 1.21369 | ||||||||
\(251\) | 300.918i | 1.19888i | 0.800420 | + | 0.599439i | \(0.204610\pi\) | ||||
−0.800420 | + | 0.599439i | \(0.795390\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 711.660i | 2.80181i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1032.85 | 4.03458 | ||||||||
\(257\) | − 424.503i | − 1.65176i | −0.563844 | − | 0.825881i | \(-0.690678\pi\) | ||||
0.563844 | − | 0.825881i | \(-0.309322\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −39.3829 | −0.152058 | ||||||||
\(260\) | − 526.507i | − 2.02503i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −637.393 | −2.43280 | ||||||||
\(263\) | 306.813i | 1.16659i | 0.812261 | + | 0.583294i | \(0.198236\pi\) | ||||
−0.812261 | + | 0.583294i | \(0.801764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 74.2951 | 0.280359 | ||||||||
\(266\) | − 36.9816i | − 0.139029i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −611.902 | −2.28322 | ||||||||
\(269\) | 248.773i | 0.924809i | 0.886669 | + | 0.462404i | \(0.153013\pi\) | ||||
−0.886669 | + | 0.462404i | \(0.846987\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −230.792 | −0.851631 | −0.425816 | − | 0.904810i | \(-0.640013\pi\) | ||||
−0.425816 | + | 0.904810i | \(0.640013\pi\) | |||||||
\(272\) | − 1785.66i | − 6.56492i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −778.166 | −2.84002 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −442.379 | −1.59703 | −0.798517 | − | 0.601972i | \(-0.794382\pi\) | ||||
−0.798517 | + | 0.601972i | \(0.794382\pi\) | |||||||
\(278\) | 10.7581i | 0.0386981i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 447.684 | 1.59887 | ||||||||
\(281\) | − 219.013i | − 0.779407i | −0.920940 | − | 0.389704i | \(-0.872577\pi\) | ||||
0.920940 | − | 0.389704i | \(-0.127423\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 144.620 | 0.511023 | 0.255512 | − | 0.966806i | \(-0.417756\pi\) | ||||
0.255512 | + | 0.966806i | \(0.417756\pi\) | |||||||
\(284\) | − 129.940i | − 0.457537i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 105.098i | − 0.366195i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −471.984 | −1.63316 | ||||||||
\(290\) | − 402.879i | − 1.38924i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 467.392 | 1.60066 | ||||||||
\(293\) | − 103.257i | − 0.352412i | −0.984353 | − | 0.176206i | \(-0.943618\pi\) | ||||
0.984353 | − | 0.176206i | \(-0.0563824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 207.798 | 0.704401 | ||||||||
\(296\) | 423.786i | 1.43171i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −310.814 | −1.04300 | ||||||||
\(299\) | 172.817i | 0.577984i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 181.357 | 0.602514 | ||||||||
\(302\) | − 584.029i | − 1.93387i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −235.137 | −0.773476 | ||||||||
\(305\) | − 374.660i | − 1.22839i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −332.933 | −1.08447 | −0.542237 | − | 0.840226i | \(-0.682422\pi\) | ||||
−0.542237 | + | 0.840226i | \(0.682422\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 77.5929 | 0.250300 | ||||||||
\(311\) | 534.673i | 1.71921i | 0.510962 | + | 0.859603i | \(0.329289\pi\) | ||||
−0.510962 | + | 0.859603i | \(0.670711\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −312.885 | −0.999631 | −0.499816 | − | 0.866132i | \(-0.666599\pi\) | ||||
−0.499816 | + | 0.866132i | \(0.666599\pi\) | |||||||
\(314\) | 1067.34i | 3.39918i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1086.09 | 3.43699 | ||||||||
\(317\) | 260.003i | 0.820200i | 0.912041 | + | 0.410100i | \(0.134506\pi\) | ||||
−0.912041 | + | 0.410100i | \(0.865494\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − 1752.27i | − 5.47585i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −228.525 | −0.709706 | ||||||||
\(323\) | 100.207i | 0.310238i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −94.3159 | −0.290203 | ||||||||
\(326\) | − 1129.41i | − 3.46443i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1130.92 | −3.44793 | ||||||||
\(329\) | 56.7034i | 0.172351i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −545.194 | −1.64711 | −0.823555 | − | 0.567236i | \(-0.808013\pi\) | ||||
−0.823555 | + | 0.567236i | \(0.808013\pi\) | |||||||
\(332\) | 1007.02i | 3.03319i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 187.128 | 0.560262 | ||||||||
\(335\) | 333.303i | 0.994934i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −321.319 | −0.953468 | −0.476734 | − | 0.879048i | \(-0.658180\pi\) | ||||
−0.476734 | + | 0.879048i | \(0.658180\pi\) | |||||||
\(338\) | 427.864i | 1.26587i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1886.53 | −5.54861 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 238.067 | 0.694073 | ||||||||
\(344\) | − 1951.51i | − 5.67301i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −136.553 | −0.394662 | ||||||||
\(347\) | − 307.133i | − 0.885111i | −0.896741 | − | 0.442555i | \(-0.854072\pi\) | ||||
0.896741 | − | 0.442555i | \(-0.145928\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −483.011 | −1.38399 | −0.691993 | − | 0.721904i | \(-0.743267\pi\) | ||||
−0.691993 | + | 0.721904i | \(0.743267\pi\) | |||||||
\(350\) | − 124.719i | − 0.356340i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 137.108i | − 0.388408i | −0.980961 | − | 0.194204i | \(-0.937788\pi\) | ||||
0.980961 | − | 0.194204i | \(-0.0622124\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −70.7785 | −0.199376 | ||||||||
\(356\) | 1314.52i | 3.69246i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −741.555 | −2.07138 | ||||||||
\(359\) | 236.029i | 0.657463i | 0.944423 | + | 0.328731i | \(0.106621\pi\) | ||||
−0.944423 | + | 0.328731i | \(0.893379\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −347.805 | −0.963448 | ||||||||
\(362\) | 305.263i | 0.843268i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 225.227 | 0.618757 | ||||||||
\(365\) | − 254.589i | − 0.697503i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −332.474 | −0.905924 | −0.452962 | − | 0.891530i | \(-0.649633\pi\) | ||||
−0.452962 | + | 0.891530i | \(0.649633\pi\) | |||||||
\(368\) | 1453.01i | 3.94840i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 358.990 | 0.970244 | ||||||||
\(371\) | 31.7817i | 0.0856650i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 191.412 | 0.513169 | 0.256585 | − | 0.966522i | \(-0.417403\pi\) | ||||
0.256585 | + | 0.966522i | \(0.417403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 610.165 | 1.62278 | ||||||||
\(377\) | − 130.330i | − 0.345703i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −387.997 | −1.02374 | −0.511870 | − | 0.859063i | \(-0.671047\pi\) | ||||
−0.511870 | + | 0.859063i | \(0.671047\pi\) | |||||||
\(380\) | 248.419i | 0.653735i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −388.612 | −1.01731 | ||||||||
\(383\) | 119.163i | 0.311131i | 0.987826 | + | 0.155566i | \(0.0497200\pi\) | ||||
−0.987826 | + | 0.155566i | \(0.950280\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 116.934i | 0.302937i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 83.7772 | 0.215921 | ||||||||
\(389\) | − 204.409i | − 0.525473i | −0.964868 | − | 0.262736i | \(-0.915375\pi\) | ||||
0.964868 | − | 0.262736i | \(-0.0846249\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 619.222 | 1.58369 | ||||||||
\(392\) | − 1185.12i | − 3.02327i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −320.885 | −0.814430 | ||||||||
\(395\) | − 591.592i | − 1.49770i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 543.945 | 1.37014 | 0.685069 | − | 0.728478i | \(-0.259772\pi\) | ||||
0.685069 | + | 0.728478i | \(0.259772\pi\) | |||||||
\(398\) | − 848.777i | − 2.13261i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −792.988 | −1.98247 | ||||||||
\(401\) | 112.010i | 0.279326i | 0.990199 | + | 0.139663i | \(0.0446020\pi\) | ||||
−0.990199 | + | 0.139663i | \(0.955398\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.1010 | 0.0622855 | ||||||||
\(404\) | 621.352i | 1.53800i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 172.342 | 0.424488 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 156.376 | 0.382337 | 0.191168 | − | 0.981557i | \(-0.438772\pi\) | ||||
0.191168 | + | 0.981557i | \(0.438772\pi\) | |||||||
\(410\) | 958.009i | 2.33661i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1873.54 | 4.54742 | ||||||||
\(413\) | 88.8912i | 0.215233i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 548.524 | 1.32174 | ||||||||
\(416\) | − 1078.07i | − 2.59152i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 618.122i | − 1.47523i | −0.675221 | − | 0.737616i | \(-0.735952\pi\) | ||||
0.675221 | − | 0.737616i | \(-0.264048\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 289.351 | 0.687295 | 0.343647 | − | 0.939099i | \(-0.388338\pi\) | ||||
0.343647 | + | 0.939099i | \(0.388338\pi\) | |||||||
\(422\) | − 409.464i | − 0.970293i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 341.992 | 0.806585 | ||||||||
\(425\) | 337.944i | 0.795161i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 160.271 | 0.375342 | ||||||||
\(428\) | 415.617i | 0.971068i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1653.14 | −3.84450 | ||||||||
\(431\) | 608.054i | 1.41080i | 0.708811 | + | 0.705399i | \(0.249232\pi\) | ||||
−0.708811 | + | 0.705399i | \(0.750768\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −39.7517 | −0.0918054 | −0.0459027 | − | 0.998946i | \(-0.514616\pi\) | ||||
−0.0459027 | + | 0.998946i | \(0.514616\pi\) | |||||||
\(434\) | 33.1924i | 0.0764803i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1097.33 | −2.51681 | ||||||||
\(437\) | − 81.5396i | − 0.186589i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 474.376 | 1.08058 | 0.540292 | − | 0.841478i | \(-0.318314\pi\) | ||||
0.540292 | + | 0.841478i | \(0.318314\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −828.149 | −1.87364 | ||||||||
\(443\) | − 140.746i | − 0.317711i | −0.987302 | − | 0.158855i | \(-0.949220\pi\) | ||||
0.987302 | − | 0.158855i | \(-0.0507804\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 716.017 | 1.60903 | ||||||||
\(446\) | − 930.343i | − 2.08597i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 749.582 | 1.67317 | ||||||||
\(449\) | − 193.508i | − 0.430976i | −0.976506 | − | 0.215488i | \(-0.930866\pi\) | ||||
0.976506 | − | 0.215488i | \(-0.0691342\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 2320.44i | 5.13373i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1272.04 | 2.80184 | ||||||||
\(455\) | − 122.681i | − 0.269629i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.5272 | 0.0689874 | 0.0344937 | − | 0.999405i | \(-0.489018\pi\) | ||||
0.0344937 | + | 0.999405i | \(0.489018\pi\) | |||||||
\(458\) | − 909.358i | − 1.98550i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1535.09 | 3.33715 | ||||||||
\(461\) | − 502.003i | − 1.08894i | −0.838779 | − | 0.544471i | \(-0.816730\pi\) | ||||
0.838779 | − | 0.544471i | \(-0.183270\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 786.087 | 1.69781 | 0.848906 | − | 0.528544i | \(-0.177262\pi\) | ||||
0.848906 | + | 0.528544i | \(0.177262\pi\) | |||||||
\(464\) | − 1095.79i | − 2.36161i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −256.012 | −0.549382 | ||||||||
\(467\) | − 538.345i | − 1.15277i | −0.817177 | − | 0.576387i | \(-0.804462\pi\) | ||||
0.817177 | − | 0.576387i | \(-0.195538\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −142.579 | −0.304007 | ||||||||
\(470\) | − 516.873i | − 1.09973i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 956.527 | 2.02654 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 44.5006 | 0.0936856 | ||||||||
\(476\) | − 807.013i | − 1.69541i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 836.022 | 1.74900 | ||||||||
\(479\) | 54.9462i | 0.114710i | 0.998354 | + | 0.0573551i | \(0.0182667\pi\) | ||||
−0.998354 | + | 0.0573551i | \(0.981733\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 116.132 | 0.241439 | ||||||||
\(482\) | − 1579.07i | − 3.27608i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 45.6334i | − 0.0940895i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 281.751 | 0.578543 | 0.289272 | − | 0.957247i | \(-0.406587\pi\) | ||||
0.289272 | + | 0.957247i | \(0.406587\pi\) | |||||||
\(488\) | − 1724.62i | − 3.53406i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1003.92 | −2.04882 | ||||||||
\(491\) | 575.037i | 1.17116i | 0.810616 | + | 0.585578i | \(0.199132\pi\) | ||||
−0.810616 | + | 0.585578i | \(0.800868\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −466.986 | −0.947233 | ||||||||
\(494\) | 109.051i | 0.220752i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 211.044 | 0.425493 | ||||||||
\(497\) | − 30.2774i | − 0.0609203i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −173.598 | −0.347892 | −0.173946 | − | 0.984755i | \(-0.555652\pi\) | ||||
−0.173946 | + | 0.984755i | \(0.555652\pi\) | |||||||
\(500\) | − 871.899i | − 1.74380i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1173.39 | 2.33742 | ||||||||
\(503\) | 195.789i | 0.389242i | 0.980879 | + | 0.194621i | \(0.0623477\pi\) | ||||
−0.980879 | + | 0.194621i | \(0.937652\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 338.450 | 0.670199 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2044.98 | 4.02555 | ||||||||
\(509\) | − 176.019i | − 0.345813i | −0.984938 | − | 0.172906i | \(-0.944684\pi\) | ||||
0.984938 | − | 0.172906i | \(-0.0553158\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 108.907 | 0.213125 | ||||||||
\(512\) | − 1789.90i | − 3.49589i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1655.29 | −3.22040 | ||||||||
\(515\) | − 1020.52i | − 1.98159i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 153.568i | 0.296463i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1320.13 | −2.53871 | ||||||||
\(521\) | 907.916i | 1.74264i | 0.490714 | + | 0.871321i | \(0.336736\pi\) | ||||
−0.490714 | + | 0.871321i | \(0.663264\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 439.027 | 0.839441 | 0.419720 | − | 0.907654i | \(-0.362128\pi\) | ||||
0.419720 | + | 0.907654i | \(0.362128\pi\) | |||||||
\(524\) | 1831.57i | 3.49537i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1196.37 | 2.27447 | ||||||||
\(527\) | − 89.9396i | − 0.170663i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.1315 | 0.0475076 | ||||||||
\(530\) | − 289.703i | − 0.546609i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −106.268 | −0.199752 | ||||||||
\(533\) | 309.913i | 0.581450i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 226.387 | 0.423152 | ||||||||
\(536\) | 1534.24i | 2.86240i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 970.055 | 1.80308 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.4729 | 0.0748113 | 0.0374057 | − | 0.999300i | \(-0.488091\pi\) | ||||
0.0374057 | + | 0.999300i | \(0.488091\pi\) | |||||||
\(542\) | 899.939i | 1.66040i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3862.85 | −7.10082 | ||||||||
\(545\) | 597.715i | 1.09672i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −178.824 | −0.326918 | −0.163459 | − | 0.986550i | \(-0.552265\pi\) | ||||
−0.163459 | + | 0.986550i | \(0.552265\pi\) | |||||||
\(548\) | 2236.09i | 4.08046i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 61.4930i | 0.111603i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 253.069 | 0.457630 | ||||||||
\(554\) | 1724.99i | 3.11370i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 30.9137 | 0.0556003 | ||||||||
\(557\) | − 358.907i | − 0.644357i | −0.946679 | − | 0.322179i | \(-0.895585\pi\) | ||||
0.946679 | − | 0.322179i | \(-0.104415\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −534.784 | −0.956680 | ||||||||
\(560\) | − 1031.48i | − 1.84193i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −854.010 | −1.51959 | ||||||||
\(563\) | − 205.504i | − 0.365016i | −0.983204 | − | 0.182508i | \(-0.941578\pi\) | ||||
0.983204 | − | 0.182508i | \(-0.0584216\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1263.95 | 2.23707 | ||||||||
\(566\) | − 563.922i | − 0.996329i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −325.804 | −0.573599 | ||||||||
\(569\) | 63.9111i | 0.112322i | 0.998422 | + | 0.0561609i | \(0.0178860\pi\) | ||||
−0.998422 | + | 0.0561609i | \(0.982114\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −645.953 | −1.13127 | −0.565633 | − | 0.824657i | \(-0.691368\pi\) | ||||
−0.565633 | + | 0.824657i | \(0.691368\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −409.814 | −0.713961 | ||||||||
\(575\) | − 274.989i | − 0.478241i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.5030 | −0.0528648 | −0.0264324 | − | 0.999651i | \(-0.508415\pi\) | ||||
−0.0264324 | + | 0.999651i | \(0.508415\pi\) | |||||||
\(578\) | 1840.43i | 3.18414i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1157.69 | −1.99601 | ||||||||
\(581\) | 234.646i | 0.403865i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − 1171.91i | − 2.00670i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −402.634 | −0.687088 | ||||||||
\(587\) | 433.560i | 0.738604i | 0.929309 | + | 0.369302i | \(0.120403\pi\) | ||||
−0.929309 | + | 0.369302i | \(0.879597\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.8433 | −0.0201075 | ||||||||
\(590\) | − 810.278i | − 1.37335i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 976.415 | 1.64935 | ||||||||
\(593\) | − 583.923i | − 0.984693i | −0.870399 | − | 0.492347i | \(-0.836139\pi\) | ||||
0.870399 | − | 0.492347i | \(-0.163861\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −439.580 | −0.738790 | ||||||||
\(596\) | 893.136i | 1.49855i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 673.875 | 1.12688 | ||||||||
\(599\) | − 62.6790i | − 0.104639i | −0.998630 | − | 0.0523197i | \(-0.983339\pi\) | ||||
0.998630 | − | 0.0523197i | \(-0.0166615\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 456.794 | 0.760057 | 0.380028 | − | 0.924975i | \(-0.375914\pi\) | ||||
0.380028 | + | 0.924975i | \(0.375914\pi\) | |||||||
\(602\) | − 707.173i | − 1.17471i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1678.23 | −2.77852 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −849.069 | −1.39880 | −0.699398 | − | 0.714732i | \(-0.746549\pi\) | ||||
−0.699398 | + | 0.714732i | \(0.746549\pi\) | |||||||
\(608\) | 508.662i | 0.836616i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1460.93 | −2.39497 | ||||||||
\(611\) | − 167.207i | − 0.273661i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −217.267 | −0.354433 | −0.177216 | − | 0.984172i | \(-0.556709\pi\) | ||||
−0.177216 | + | 0.984172i | \(0.556709\pi\) | |||||||
\(614\) | 1298.22i | 2.11437i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 417.676i | − 0.676947i | −0.940976 | − | 0.338473i | \(-0.890090\pi\) | ||||
0.940976 | − | 0.338473i | \(-0.109910\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 542.307 | 0.876101 | 0.438051 | − | 0.898950i | \(-0.355669\pi\) | ||||
0.438051 | + | 0.898950i | \(0.355669\pi\) | |||||||
\(620\) | − 222.966i | − 0.359623i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2084.88 | 3.35189 | ||||||||
\(623\) | 306.295i | 0.491646i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −781.188 | −1.24990 | ||||||||
\(626\) | 1220.05i | 1.94896i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3067.05 | 4.88384 | ||||||||
\(629\) | − 416.114i | − 0.661548i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −660.757 | −1.04716 | −0.523579 | − | 0.851977i | \(-0.675404\pi\) | ||||
−0.523579 | + | 0.851977i | \(0.675404\pi\) | |||||||
\(632\) | − 2723.19i | − 4.30884i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1013.84 | 1.59912 | ||||||||
\(635\) | − 1113.90i | − 1.75418i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −324.766 | −0.509836 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3414.14 | −5.33460 | ||||||||
\(641\) | 656.483i | 1.02416i | 0.858939 | + | 0.512078i | \(0.171124\pi\) | ||||
−0.858939 | + | 0.512078i | \(0.828876\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 193.650 | 0.301166 | 0.150583 | − | 0.988597i | \(-0.451885\pi\) | ||||
0.150583 | + | 0.988597i | \(0.451885\pi\) | |||||||
\(644\) | 656.676i | 1.01968i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 390.742 | 0.604863 | ||||||||
\(647\) | − 484.835i | − 0.749359i | −0.927154 | − | 0.374679i | \(-0.877753\pi\) | ||||
0.927154 | − | 0.374679i | \(-0.122247\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 367.771i | 0.565801i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3245.39 | −4.97759 | ||||||||
\(653\) | − 530.535i | − 0.812457i | −0.913771 | − | 0.406229i | \(-0.866844\pi\) | ||||
0.913771 | − | 0.406229i | \(-0.133156\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 997.658 | 1.52314 | ||||||||
\(656\) | 2605.68i | 3.97207i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 221.106 | 0.336028 | ||||||||
\(659\) | 513.861i | 0.779759i | 0.920866 | + | 0.389880i | \(0.127483\pi\) | ||||
−0.920866 | + | 0.389880i | \(0.872517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 356.601 | 0.539487 | 0.269743 | − | 0.962932i | \(-0.413061\pi\) | ||||
0.269743 | + | 0.962932i | \(0.413061\pi\) | |||||||
\(662\) | 2125.90i | 3.21133i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2524.94 | 3.80262 | ||||||||
\(665\) | 57.8842i | 0.0870439i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 379.992 | 0.569703 | ||||||||
\(668\) | − 537.718i | − 0.804967i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1299.66 | 1.93980 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 551.643 | 0.819677 | 0.409839 | − | 0.912158i | \(-0.365585\pi\) | ||||
0.409839 | + | 0.912158i | \(0.365585\pi\) | |||||||
\(674\) | 1252.93i | 1.85895i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1229.48 | 1.81876 | ||||||||
\(677\) | − 673.629i | − 0.995021i | −0.867458 | − | 0.497510i | \(-0.834248\pi\) | ||||
0.867458 | − | 0.497510i | \(-0.165752\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.5209 | 0.0287495 | ||||||||
\(680\) | 4730.16i | 6.95612i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 22.2083i | − 0.0325158i | −0.999868 | − | 0.0162579i | \(-0.994825\pi\) | ||||
0.999868 | − | 0.0162579i | \(-0.00517528\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1218.00 | 1.77810 | ||||||||
\(686\) | − 928.307i | − 1.35322i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4496.35 | −6.53539 | ||||||||
\(689\) | − 93.7179i | − 0.136020i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −932.929 | −1.35011 | −0.675057 | − | 0.737766i | \(-0.735881\pi\) | ||||
−0.675057 | + | 0.737766i | \(0.735881\pi\) | |||||||
\(692\) | 392.391i | 0.567039i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1197.62 | −1.72568 | ||||||||
\(695\) | − 16.8387i | − 0.0242284i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1110.45 | 1.59318 | ||||||||
\(698\) | 1883.43i | 2.69832i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −358.384 | −0.511978 | ||||||||
\(701\) | − 690.617i | − 0.985188i | −0.870259 | − | 0.492594i | \(-0.836049\pi\) | ||||
0.870259 | − | 0.492594i | \(-0.163951\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −54.7941 | −0.0779433 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −534.633 | −0.757270 | ||||||||
\(707\) | 144.781i | 0.204782i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −432.626 | −0.610192 | −0.305096 | − | 0.952322i | \(-0.598689\pi\) | ||||
−0.305096 | + | 0.952322i | \(0.598689\pi\) | |||||||
\(710\) | 275.990i | 0.388719i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3295.94 | 4.62912 | ||||||||
\(713\) | 73.1850i | 0.102644i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2130.89i | 2.97610i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 920.360 | 1.28184 | ||||||||
\(719\) | 1085.00i | 1.50904i | 0.656274 | + | 0.754522i | \(0.272131\pi\) | ||||
−0.656274 | + | 0.754522i | \(0.727869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 436.553 | 0.605483 | ||||||||
\(722\) | 1356.21i | 1.87841i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 877.184 | 1.21158 | ||||||||
\(725\) | 207.383i | 0.286045i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 688.568 | 0.947137 | 0.473568 | − | 0.880757i | \(-0.342966\pi\) | ||||
0.473568 | + | 0.880757i | \(0.342966\pi\) | |||||||
\(728\) | − 564.721i | − 0.775716i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −992.730 | −1.35990 | ||||||||
\(731\) | 1916.19i | 2.62132i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 259.491 | 0.354012 | 0.177006 | − | 0.984210i | \(-0.443359\pi\) | ||||
0.177006 | + | 0.984210i | \(0.443359\pi\) | |||||||
\(734\) | 1296.43i | 1.76626i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3143.25 | 4.27071 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −195.434 | −0.264457 | −0.132228 | − | 0.991219i | \(-0.542213\pi\) | ||||
−0.132228 | + | 0.991219i | \(0.542213\pi\) | |||||||
\(740\) | − 1031.57i | − 1.39402i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 123.928 | 0.167019 | ||||||||
\(743\) | 322.257i | 0.433725i | 0.976202 | + | 0.216862i | \(0.0695823\pi\) | ||||
−0.976202 | + | 0.216862i | \(0.930418\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 486.491 | 0.653008 | ||||||||
\(746\) | − 746.383i | − 1.00051i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 96.8429i | 0.129296i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 407.900 | 0.543142 | 0.271571 | − | 0.962418i | \(-0.412457\pi\) | ||||
0.271571 | + | 0.962418i | \(0.412457\pi\) | |||||||
\(752\) | − 1405.84i | − 1.86947i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −508.202 | −0.674009 | ||||||||
\(755\) | 914.131i | 1.21077i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 596.605 | 0.788118 | 0.394059 | − | 0.919085i | \(-0.371071\pi\) | ||||
0.394059 | + | 0.919085i | \(0.371071\pi\) | |||||||
\(758\) | 1512.94i | 1.99596i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 622.871 | 0.819567 | ||||||||
\(761\) | − 671.334i | − 0.882174i | −0.897464 | − | 0.441087i | \(-0.854593\pi\) | ||||
0.897464 | − | 0.441087i | \(-0.145407\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −255.689 | −0.335109 | ||||||||
\(764\) | 1116.69i | 1.46164i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 464.659 | 0.606605 | ||||||||
\(767\) | − 262.122i | − 0.341750i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −947.641 | −1.23230 | −0.616151 | − | 0.787628i | \(-0.711309\pi\) | ||||
−0.616151 | + | 0.787628i | \(0.711309\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 336.013 | 0.435251 | ||||||||
\(773\) | 1038.33i | 1.34325i | 0.740893 | + | 0.671623i | \(0.234403\pi\) | ||||
−0.740893 | + | 0.671623i | \(0.765597\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −39.9411 | −0.0515369 | ||||||||
\(776\) | − 210.058i | − 0.270693i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −797.062 | −1.02450 | ||||||||
\(779\) | − 146.225i | − 0.187708i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − 2414.56i | − 3.08768i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2730.56 | −3.48286 | ||||||||
\(785\) | − 1670.62i | − 2.12818i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.9336 | 0.0164340 | 0.00821702 | − | 0.999966i | \(-0.497384\pi\) | ||||
0.00821702 | + | 0.999966i | \(0.497384\pi\) | |||||||
\(788\) | 922.076i | 1.17015i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2306.82 | −2.92003 | ||||||||
\(791\) | 540.687i | 0.683548i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −472.607 | −0.595973 | ||||||||
\(794\) | − 2121.03i | − 2.67133i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2438.99 | −3.06406 | ||||||||
\(797\) | 459.455i | 0.576480i | 0.957558 | + | 0.288240i | \(0.0930701\pi\) | ||||
−0.957558 | + | 0.288240i | \(0.906930\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −599.119 | −0.749836 | ||||||||
\(800\) | 1715.44i | 2.14430i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 436.765 | 0.544595 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 357.692 | 0.444337 | ||||||||
\(806\) | − 97.8778i | − 0.121436i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1557.94 | 1.92814 | ||||||||
\(809\) | 1546.11i | 1.91113i | 0.294773 | + | 0.955567i | \(0.404756\pi\) | ||||
−0.294773 | + | 0.955567i | \(0.595244\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1461.97 | −1.80268 | −0.901340 | − | 0.433112i | \(-0.857415\pi\) | ||||
−0.901340 | + | 0.433112i | \(0.857415\pi\) | |||||||
\(812\) | − 495.232i | − 0.609892i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1767.76i | 2.16903i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 252.325 | 0.308843 | ||||||||
\(818\) | − 609.764i | − 0.745433i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2752.87 | 3.35716 | ||||||||
\(821\) | − 795.413i | − 0.968834i | −0.874837 | − | 0.484417i | \(-0.839032\pi\) | ||||
0.874837 | − | 0.484417i | \(-0.160968\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −73.3941 | −0.0891788 | −0.0445894 | − | 0.999005i | \(-0.514198\pi\) | ||||
−0.0445894 | + | 0.999005i | \(0.514198\pi\) | |||||||
\(824\) | − 4697.59i | − 5.70096i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 346.618 | 0.419634 | ||||||||
\(827\) | 858.149i | 1.03766i | 0.854876 | + | 0.518832i | \(0.173633\pi\) | ||||
−0.854876 | + | 0.518832i | \(0.826367\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 116.737 | 0.140816 | 0.0704081 | − | 0.997518i | \(-0.477570\pi\) | ||||
0.0704081 | + | 0.997518i | \(0.477570\pi\) | |||||||
\(830\) | − 2138.89i | − 2.57697i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2210.36 | −2.65669 | ||||||||
\(833\) | 1163.67i | 1.39696i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −292.895 | −0.350772 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2410.27 | −2.87622 | ||||||||
\(839\) | 119.850i | 0.142849i | 0.997446 | + | 0.0714243i | \(0.0227544\pi\) | ||||
−0.997446 | + | 0.0714243i | \(0.977246\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 554.429 | 0.659250 | ||||||||
\(842\) | − 1128.28i | − 1.34000i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1176.61 | −1.39409 | ||||||||
\(845\) | − 669.699i | − 0.792544i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 787.960i | − 0.929199i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1317.76 | 1.55031 | ||||||||
\(851\) | 338.597i | 0.397881i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 480.900 | 0.563775 | 0.281887 | − | 0.959447i | \(-0.409040\pi\) | ||||
0.281887 | + | 0.959447i | \(0.409040\pi\) | |||||||
\(854\) | − 624.952i | − 0.731794i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1042.09 | 1.21740 | ||||||||
\(857\) | 898.929i | 1.04893i | 0.851433 | + | 0.524463i | \(0.175734\pi\) | ||||
−0.851433 | + | 0.524463i | \(0.824266\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −892.879 | −1.03944 | −0.519720 | − | 0.854337i | \(-0.673964\pi\) | ||||
−0.519720 | + | 0.854337i | \(0.673964\pi\) | |||||||
\(860\) | 4750.35i | 5.52366i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2371.01 | 2.75060 | ||||||||
\(863\) | − 1385.04i | − 1.60491i | −0.596712 | − | 0.802455i | \(-0.703527\pi\) | ||||
0.596712 | − | 0.802455i | \(-0.296473\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 213.735 | 0.247093 | ||||||||
\(866\) | 155.006i | 0.178991i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 95.3797 | 0.109884 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 420.437 | 0.482706 | ||||||||
\(872\) | 2751.37i | 3.15524i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −317.951 | −0.363789 | ||||||||
\(875\) | − 203.161i | − 0.232184i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.82028 | 0.0100573 | 0.00502867 | − | 0.999987i | \(-0.498399\pi\) | ||||
0.00502867 | + | 0.999987i | \(0.498399\pi\) | |||||||
\(878\) | − 1849.76i | − 2.10679i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 871.048i | − 0.988704i | −0.869262 | − | 0.494352i | \(-0.835405\pi\) | ||||
0.869262 | − | 0.494352i | \(-0.164595\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −426.150 | −0.482616 | −0.241308 | − | 0.970449i | \(-0.577576\pi\) | ||||
−0.241308 | + | 0.970449i | \(0.577576\pi\) | |||||||
\(884\) | 2379.72i | 2.69199i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −548.818 | −0.619433 | ||||||||
\(887\) | − 1032.71i | − 1.16427i | −0.813091 | − | 0.582136i | \(-0.802217\pi\) | ||||
0.813091 | − | 0.582136i | \(-0.197783\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 476.501 | 0.535997 | ||||||||
\(890\) | − 2792.00i | − 3.13708i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2673.38 | −2.99706 | ||||||||
\(893\) | 78.8924i | 0.0883454i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1160.69 | 1.29686 | ||||||||
\(896\) | − 1460.49i | − 1.63001i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −754.557 | −0.840264 | ||||||||
\(899\) | − 55.1924i | − 0.0613931i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −335.801 | −0.372698 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5818.14 | 6.43599 | ||||||||
\(905\) | − 477.802i | − 0.527958i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1283.21 | 1.41479 | 0.707393 | − | 0.706820i | \(-0.249871\pi\) | ||||
0.707393 | + | 0.706820i | \(0.249871\pi\) | |||||||
\(908\) | − 3655.24i | − 4.02560i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −478.378 | −0.525690 | ||||||||
\(911\) | − 1125.40i | − 1.23535i | −0.786433 | − | 0.617675i | \(-0.788075\pi\) | ||||
0.786433 | − | 0.617675i | \(-0.211925\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − 122.936i | − 0.134503i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2613.07 | −2.85270 | ||||||||
\(917\) | 426.775i | 0.465403i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1149.37 | 1.25067 | 0.625336 | − | 0.780356i | \(-0.284962\pi\) | ||||
0.625336 | + | 0.780356i | \(0.284962\pi\) | |||||||
\(920\) | − 3848.99i | − 4.18369i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1957.48 | −2.12308 | ||||||||
\(923\) | 89.2819i | 0.0967301i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −184.791 | −0.199774 | ||||||||
\(926\) | − 3065.23i | − 3.31018i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2370.48 | −2.55439 | ||||||||
\(929\) | − 250.860i | − 0.270032i | −0.990843 | − | 0.135016i | \(-0.956891\pi\) | ||||
0.990843 | − | 0.135016i | \(-0.0431087\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 153.233 | 0.164589 | ||||||||
\(932\) | 735.661i | 0.789335i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2099.20 | −2.24753 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 817.848 | 0.872837 | 0.436418 | − | 0.899744i | \(-0.356247\pi\) | ||||
0.436418 | + | 0.899744i | \(0.356247\pi\) | |||||||
\(938\) | 555.966i | 0.592715i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1485.25 | −1.58006 | ||||||||
\(941\) | 1289.31i | 1.37015i | 0.728472 | + | 0.685076i | \(0.240231\pi\) | ||||
−0.728472 | + | 0.685076i | \(0.759769\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −903.586 | −0.958203 | ||||||||
\(944\) | − 2203.87i | − 2.33461i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 16.5616i | − 0.0174885i | −0.999962 | − | 0.00874423i | \(-0.997217\pi\) | ||||
0.999962 | − | 0.00874423i | \(-0.00278341\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −321.145 | −0.338403 | ||||||||
\(950\) | − 173.524i | − 0.182656i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2023.45 | −2.12548 | ||||||||
\(953\) | 905.921i | 0.950599i | 0.879824 | + | 0.475300i | \(0.157660\pi\) | ||||
−0.879824 | + | 0.475300i | \(0.842340\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 608.262 | 0.636924 | ||||||||
\(956\) | − 2402.34i | − 2.51291i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 214.254 | 0.223648 | ||||||||
\(959\) | 521.031i | 0.543307i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −950.370 | −0.988939 | ||||||||
\(962\) | − 452.840i | − 0.470728i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4537.52 | −4.70697 | ||||||||
\(965\) | − 183.027i | − 0.189665i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1034.62 | 1.06993 | 0.534965 | − | 0.844874i | \(-0.320325\pi\) | ||||
0.534965 | + | 0.844874i | \(0.320325\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −177.941 | −0.183444 | ||||||||
\(971\) | − 1733.52i | − 1.78529i | −0.450757 | − | 0.892647i | \(-0.648846\pi\) | ||||
0.450757 | − | 0.892647i | \(-0.351154\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.20321 | 0.00740309 | ||||||||
\(974\) | − 1098.64i | − 1.12797i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3973.58 | −4.07129 | ||||||||
\(977\) | 835.320i | 0.854985i | 0.904019 | + | 0.427492i | \(0.140603\pi\) | ||||
−0.904019 | + | 0.427492i | \(0.859397\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 2884.81i | 2.94368i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2242.27 | 2.28337 | ||||||||
\(983\) | 1505.21i | 1.53124i | 0.643294 | + | 0.765619i | \(0.277567\pi\) | ||||
−0.643294 | + | 0.765619i | \(0.722433\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 502.255 | 0.509904 | ||||||||
\(986\) | 1820.94i | 1.84680i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 313.363 | 0.317169 | ||||||||
\(989\) | − 1559.22i | − 1.57657i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −141.776 | −0.143064 | −0.0715318 | − | 0.997438i | \(-0.522789\pi\) | ||||
−0.0715318 | + | 0.997438i | \(0.522789\pi\) | |||||||
\(992\) | − 456.544i | − 0.460226i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −118.062 | −0.118775 | ||||||||
\(995\) | 1328.52i | 1.33520i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1566.45 | 1.57116 | 0.785579 | − | 0.618761i | \(-0.212365\pi\) | ||||
0.785579 | + | 0.618761i | \(0.212365\pi\) | |||||||
\(998\) | 676.919i | 0.678276i | ||||||||
\(999\) | 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 | 1089.3.b.g.485.1 | 8 | ||
3.2 | odd | 2 | inner | 1089.3.b.g.485.8 | 8 | ||
11.10 | odd | 2 | 99.3.b.a.89.8 | yes | 8 | ||
33.32 | even | 2 | 99.3.b.a.89.1 | ✓ | 8 | ||
44.43 | even | 2 | 1584.3.i.b.881.6 | 8 | |||
132.131 | odd | 2 | 1584.3.i.b.881.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.3.b.a.89.1 | ✓ | 8 | 33.32 | even | 2 | ||
99.3.b.a.89.8 | yes | 8 | 11.10 | odd | 2 | ||
1089.3.b.g.485.1 | 8 | 1.1 | even | 1 | trivial | ||
1089.3.b.g.485.8 | 8 | 3.2 | odd | 2 | inner | ||
1584.3.i.b.881.3 | 8 | 132.131 | odd | 2 | |||
1584.3.i.b.881.6 | 8 | 44.43 | even | 2 |