Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,3,Mod(129,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.129");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.s (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.2071158433\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 36x^{14} + 522x^{12} + 3644x^{10} + 12219x^{8} + 15156x^{6} + 15478x^{4} - 10992x^{2} + 11025 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(-0.707107 + 3.42121i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.257 |
Dual form | 448.3.s.g.129.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −4.19011 | + | 2.41916i | −1.39670 | + | 0.806387i | −0.994046 | − | 0.108963i | \(-0.965247\pi\) |
−0.402658 | + | 0.915351i | \(0.631914\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.0446470 | + | 0.0257769i | 0.00892939 | + | 0.00515539i | 0.504458 | − | 0.863436i | \(-0.331692\pi\) |
−0.495529 | + | 0.868592i | \(0.665026\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.12357 | + | 3.39144i | 0.874796 | + | 0.484491i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.20469 | − | 12.4789i | 0.800521 | − | 1.38654i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.894964 | − | 1.55012i | −0.0813604 | − | 0.140920i | 0.822474 | − | 0.568803i | \(-0.192593\pi\) |
−0.903835 | + | 0.427882i | \(0.859260\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.87602i | − | 0.452002i | −0.974127 | − | 0.226001i | \(-0.927435\pi\) | ||
0.974127 | − | 0.226001i | \(-0.0725652\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.249434 | −0.0166290 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.0248 | − | 13.2934i | 1.35440 | − | 0.781962i | 0.365536 | − | 0.930797i | \(-0.380886\pi\) |
0.988862 | + | 0.148835i | \(0.0475523\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 22.8134 | + | 13.1713i | 1.20071 | + | 0.693227i | 0.960712 | − | 0.277547i | \(-0.0895215\pi\) |
0.239993 | + | 0.970775i | \(0.422855\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −33.8629 | + | 0.603422i | −1.61252 | + | 0.0287344i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −12.8386 | + | 22.2371i | −0.558199 | + | 0.966830i | 0.439448 | + | 0.898268i | \(0.355174\pi\) |
−0.997647 | + | 0.0685614i | \(0.978159\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.4987 | − | 21.6483i | −0.499947 | − | 0.865933i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.1723i | 0.969345i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 27.1749 | 0.937066 | 0.468533 | − | 0.883446i | \(-0.344783\pi\) | ||||
0.468533 | + | 0.883446i | \(0.344783\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −25.7249 | + | 14.8523i | −0.829837 | + | 0.479106i | −0.853797 | − | 0.520606i | \(-0.825706\pi\) |
0.0239601 | + | 0.999713i | \(0.492373\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.50000 | + | 4.33013i | 0.227273 | + | 0.131216i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.185978 | + | 0.309264i | 0.00531366 | + | 0.00883612i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −30.8629 | + | 53.4561i | −0.834132 | + | 1.44476i | 0.0606029 | + | 0.998162i | \(0.480698\pi\) |
−0.894735 | + | 0.446597i | \(0.852636\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.2150 | + | 24.6212i | 0.364488 | + | 0.631312i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 65.7376i | 1.60336i | 0.597755 | + | 0.801679i | \(0.296059\pi\) | ||||
−0.597755 | + | 0.801679i | \(0.703941\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.52546 | −0.221522 | −0.110761 | − | 0.993847i | \(-0.535329\pi\) | ||||
−0.110761 | + | 0.993847i | \(0.535329\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.643335 | − | 0.371430i | 0.0142963 | − | 0.00825399i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 61.2978 | + | 35.3903i | 1.30421 | + | 0.752986i | 0.981123 | − | 0.193384i | \(-0.0619463\pi\) |
0.323086 | + | 0.946370i | \(0.395280\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 25.9963 | + | 41.5354i | 0.530537 | + | 0.847662i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −64.3176 | + | 111.401i | −1.26113 | + | 2.18434i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.86555 | + | 8.42738i | 0.0918028 | + | 0.159007i | 0.908270 | − | 0.418385i | \(-0.137404\pi\) |
−0.816467 | + | 0.577392i | \(0.804070\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.0922778i | − | 0.00167778i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −127.454 | −2.23604 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 54.3535 | − | 31.3810i | 0.921246 | − | 0.531881i | 0.0372134 | − | 0.999307i | \(-0.488152\pi\) |
0.884032 | + | 0.467426i | \(0.154819\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 66.1830 | + | 38.2108i | 1.08497 | + | 0.626406i | 0.932232 | − | 0.361861i | \(-0.117859\pi\) |
0.152735 | + | 0.988267i | \(0.451192\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 86.4398 | − | 51.9811i | 1.37206 | − | 0.825098i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.151466 | − | 0.262346i | 0.00233024 | − | 0.00403610i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −51.5236 | − | 89.2415i | −0.769009 | − | 1.33196i | −0.938101 | − | 0.346363i | \(-0.887417\pi\) |
0.169091 | − | 0.985600i | \(-0.445917\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 124.234i | − | 1.80050i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −90.1681 | −1.26997 | −0.634986 | − | 0.772523i | \(-0.718994\pi\) | ||||
−0.634986 | + | 0.772523i | \(0.718994\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −28.8184 | + | 16.6383i | −0.394773 | + | 0.227922i | −0.684226 | − | 0.729270i | \(-0.739860\pi\) |
0.289453 | + | 0.957192i | \(0.406527\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 104.742 | + | 60.4726i | 1.39656 | + | 0.806302i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.223235 | − | 12.5275i | −0.00289915 | − | 0.162695i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −32.4323 | + | 56.1743i | −0.410535 | + | 0.711068i | −0.994948 | − | 0.100389i | \(-0.967991\pi\) |
0.584413 | + | 0.811456i | \(0.301325\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.52712 | + | 2.64505i | 0.0188534 | + | 0.0326550i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 29.1364i | 0.351041i | 0.984476 | + | 0.175520i | \(0.0561608\pi\) | ||||
−0.984476 | + | 0.175520i | \(0.943839\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.37065 | 0.0161253 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −113.866 | + | 65.7405i | −1.30880 | + | 0.755638i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.7689 | + | 10.8362i | 0.210887 | + | 0.121755i | 0.601723 | − | 0.798705i | \(-0.294481\pi\) |
−0.390837 | + | 0.920460i | \(0.627814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.9281 | − | 35.9822i | 0.218991 | − | 0.395409i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 71.8602 | − | 124.466i | 0.772691 | − | 1.33834i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.679033 | + | 1.17612i | 0.00714771 | + | 0.0123802i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 123.061i | − | 1.26867i | −0.773056 | − | 0.634337i | \(-0.781273\pi\) | ||
0.773056 | − | 0.634337i | \(-0.218727\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −25.7918 | −0.260523 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 48.9543 | − | 28.2638i | 0.484696 | − | 0.279840i | −0.237675 | − | 0.971345i | \(-0.576385\pi\) |
0.722372 | + | 0.691505i | \(0.243052\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −25.6062 | − | 14.7838i | −0.248604 | − | 0.143532i | 0.370521 | − | 0.928824i | \(-0.379179\pi\) |
−0.619125 | + | 0.785293i | \(0.712513\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.52743 | − | 0.845941i | −0.0145469 | − | 0.00805658i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.9054 | − | 25.8169i | 0.139303 | − | 0.241279i | −0.787930 | − | 0.615765i | \(-0.788847\pi\) |
0.927233 | + | 0.374485i | \(0.122181\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 40.7751 | + | 70.6246i | 0.374084 | + | 0.647932i | 0.990189 | − | 0.139731i | \(-0.0446239\pi\) |
−0.616106 | + | 0.787663i | \(0.711291\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 298.649i | − | 2.69053i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 43.3994 | 0.384065 | 0.192033 | − | 0.981389i | \(-0.438492\pi\) | ||||
0.192033 | + | 0.981389i | \(0.438492\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.14641 | + | 0.661879i | −0.00996876 | + | 0.00575547i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −73.3262 | − | 42.3349i | −0.626720 | − | 0.361837i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 186.077 | − | 3.31582i | 1.56368 | − | 0.0278640i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 58.8981 | − | 102.014i | 0.486761 | − | 0.843095i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −159.030 | − | 275.448i | −1.29293 | − | 2.23942i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.57756i | − | 0.0206205i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 94.0304 | 0.740397 | 0.370199 | − | 0.928953i | \(-0.379290\pi\) | ||||
0.370199 | + | 0.928953i | \(0.379290\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 39.9127 | − | 23.0436i | 0.309401 | − | 0.178633i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 108.932 | + | 62.8918i | 0.831540 | + | 0.480090i | 0.854380 | − | 0.519649i | \(-0.173937\pi\) |
−0.0228396 | + | 0.999739i | \(0.507271\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 95.0298 | + | 158.026i | 0.714510 | + | 1.18816i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.674642 | + | 1.16851i | −0.00499735 | + | 0.00865566i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 124.928 | + | 216.382i | 0.911884 | + | 1.57943i | 0.811400 | + | 0.584491i | \(0.198706\pi\) |
0.100484 | + | 0.994939i | \(0.467961\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.08301i | 0.0149857i | 0.999972 | + | 0.00749284i | \(0.00238507\pi\) | ||||
−0.999972 | + | 0.00749284i | \(0.997615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −342.460 | −2.42879 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.10856 | + | 5.25883i | −0.0636962 | + | 0.0367750i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.21328 | + | 0.700486i | 0.00836743 | + | 0.00483094i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −209.408 | − | 111.149i | −1.42455 | − | 0.756114i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.8122 | + | 18.7273i | −0.0725652 | + | 0.125687i | −0.900025 | − | 0.435838i | \(-0.856452\pi\) |
0.827460 | + | 0.561525i | \(0.189785\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −44.0090 | − | 76.2258i | −0.291450 | − | 0.504807i | 0.682703 | − | 0.730696i | \(-0.260804\pi\) |
−0.974153 | + | 0.225890i | \(0.927471\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 383.098i | − | 2.50391i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.53139 | −0.00987992 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −142.568 | + | 82.3115i | −0.908075 | + | 0.524277i | −0.879811 | − | 0.475323i | \(-0.842331\pi\) |
−0.0282634 | + | 0.999601i | \(0.508998\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −40.7744 | − | 23.5411i | −0.256443 | − | 0.148057i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −154.034 | + | 92.6292i | −0.956731 | + | 0.575337i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −82.4420 | + | 142.794i | −0.505779 | + | 0.876035i | 0.494199 | + | 0.869349i | \(0.335462\pi\) |
−0.999978 | + | 0.00668599i | \(0.997872\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.223235 | + | 0.386654i | 0.00135294 | + | 0.00234336i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.8929i | 0.113131i | 0.998399 | + | 0.0565655i | \(0.0180150\pi\) | ||||
−0.998399 | + | 0.0565655i | \(0.981985\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 134.472 | 0.795695 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 328.727 | − | 189.791i | 1.92238 | − | 1.10989i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 85.2911 | + | 49.2428i | 0.493012 | + | 0.284641i | 0.725823 | − | 0.687881i | \(-0.241459\pi\) |
−0.232811 | + | 0.972522i | \(0.574792\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.11760 | − | 174.954i | −0.0178148 | − | 0.999735i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −151.831 | + | 262.980i | −0.857805 | + | 1.48576i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −35.1481 | − | 60.8784i | −0.196358 | − | 0.340103i | 0.750987 | − | 0.660317i | \(-0.229578\pi\) |
−0.947345 | + | 0.320215i | \(0.896245\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 204.167i | 1.12800i | 0.825776 | + | 0.563999i | \(0.190738\pi\) | ||||
−0.825776 | + | 0.563999i | \(0.809262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −369.752 | −2.02050 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.75587 | + | 1.59110i | −0.0148966 | + | 0.00860055i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −41.2127 | − | 23.7942i | −0.220389 | − | 0.127242i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −88.7617 | + | 160.268i | −0.469639 | + | 0.847980i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 95.3517 | − | 165.154i | 0.499224 | − | 0.864681i | −0.500776 | − | 0.865577i | \(-0.666952\pi\) |
1.00000 | 0.000896163i | \(0.000285258\pi\) | ||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −42.7740 | − | 74.0868i | −0.221627 | − | 0.383869i | 0.733675 | − | 0.679500i | \(-0.237803\pi\) |
−0.955302 | + | 0.295631i | \(0.904470\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.46568i | 0.00751631i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −275.164 | −1.39677 | −0.698386 | − | 0.715721i | \(-0.746098\pi\) | ||||
−0.698386 | + | 0.715721i | \(0.746098\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −179.161 | + | 103.439i | −0.900308 | + | 0.519793i | −0.877300 | − | 0.479942i | \(-0.840658\pi\) |
−0.0230082 | + | 0.999735i | \(0.507324\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 431.779 | + | 249.288i | 2.14816 | + | 1.24024i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 166.408 | + | 92.1620i | 0.819742 | + | 0.454000i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.69452 | + | 2.93499i | −0.00826593 | + | 0.0143170i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 184.996 | + | 320.423i | 0.893701 | + | 1.54793i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 47.1514i | − | 0.225605i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 78.7325 | 0.373140 | 0.186570 | − | 0.982442i | \(-0.440263\pi\) | ||||
0.186570 | + | 0.982442i | \(0.440263\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 377.814 | − | 218.131i | 1.77378 | − | 1.02409i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.425283 | − | 0.245537i | −0.00197806 | − | 0.00114203i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −207.899 | + | 3.70467i | −0.958061 | + | 0.0170722i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 80.5017 | − | 139.433i | 0.367588 | − | 0.636680i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −78.1120 | − | 135.294i | −0.353448 | − | 0.612190i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 155.408i | − | 0.696896i | −0.937328 | − | 0.348448i | \(-0.886709\pi\) | ||
0.937328 | − | 0.348448i | \(-0.113291\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −360.196 | −1.60087 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −70.8987 | + | 40.9334i | −0.312329 | + | 0.180323i | −0.647968 | − | 0.761667i | \(-0.724381\pi\) |
0.335639 | + | 0.941991i | \(0.391048\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 355.669 | + | 205.346i | 1.55314 | + | 0.896707i | 0.997883 | + | 0.0650290i | \(0.0207140\pi\) |
0.555258 | + | 0.831678i | \(0.312619\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 31.2415 | + | 51.9516i | 0.135244 | + | 0.224899i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.9359 | + | 32.7979i | −0.0812699 | + | 0.140764i | −0.903796 | − | 0.427964i | \(-0.859231\pi\) |
0.822526 | + | 0.568728i | \(0.192564\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.82451 | + | 3.16014i | 0.00776387 | + | 0.0134474i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 313.836i | − | 1.32420i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 428.133 | 1.79135 | 0.895676 | − | 0.444707i | \(-0.146692\pi\) | ||||
0.895676 | + | 0.444707i | \(0.146692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 180.155 | − | 104.012i | 0.747530 | − | 0.431587i | −0.0772706 | − | 0.997010i | \(-0.524621\pi\) |
0.824801 | + | 0.565423i | \(0.191287\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −216.791 | − | 125.164i | −0.892143 | − | 0.515079i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.0900009 | + | 2.52454i | 0.000367350 | + | 0.0103042i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 77.3949 | − | 134.052i | 0.313340 | − | 0.542721i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −70.4856 | − | 122.085i | −0.283075 | − | 0.490300i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 375.625i | 1.49652i | 0.663408 | + | 0.748258i | \(0.269109\pi\) | ||||
−0.663408 | + | 0.748258i | \(0.730891\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 45.9603 | 0.181661 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.74317 | + | 3.31582i | −0.0225222 | + | 0.0130032i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −62.4373 | − | 36.0482i | −0.242947 | − | 0.140265i | 0.373584 | − | 0.927597i | \(-0.378129\pi\) |
−0.616530 | + | 0.787331i | \(0.711462\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −370.284 | + | 222.673i | −1.42967 | + | 0.859741i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 195.787 | − | 339.113i | 0.750141 | − | 1.29928i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 104.550 | + | 181.086i | 0.397529 | + | 0.688541i | 0.993420 | − | 0.114524i | \(-0.0365344\pi\) |
−0.595891 | + | 0.803065i | \(0.703201\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.501676i | 0.00189312i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −104.858 | −0.392728 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 244.956 | − | 141.425i | 0.910616 | − | 0.525744i | 0.0299865 | − | 0.999550i | \(-0.490454\pi\) |
0.880629 | + | 0.473806i | \(0.157120\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −171.410 | − | 98.9636i | −0.632509 | − | 0.365179i | 0.149214 | − | 0.988805i | \(-0.452326\pi\) |
−0.781723 | + | 0.623625i | \(0.785659\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.54572 | + | 198.979i | 0.0129880 | + | 0.728861i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −22.3717 | + | 38.7490i | −0.0813517 | + | 0.140905i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −118.659 | − | 205.524i | −0.428372 | − | 0.741963i | 0.568356 | − | 0.822783i | \(-0.307580\pi\) |
−0.996729 | + | 0.0808197i | \(0.974246\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 428.025i | 1.53414i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −239.870 | −0.853628 | −0.426814 | − | 0.904339i | \(-0.640364\pi\) | ||||
−0.426814 | + | 0.904339i | \(0.640364\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −119.663 | + | 69.0872i | −0.422836 | + | 0.244124i | −0.696290 | − | 0.717761i | \(-0.745167\pi\) |
0.273454 | + | 0.961885i | \(0.411834\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.69044 | − | 3.28538i | −0.0199665 | − | 0.0115276i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −222.945 | + | 402.549i | −0.776812 | + | 1.40261i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 208.927 | − | 361.872i | 0.722930 | − | 1.25215i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 297.705 | + | 515.641i | 1.02304 | + | 1.77196i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 385.332i | − | 1.31513i | −0.753400 | − | 0.657563i | \(-0.771587\pi\) | ||
0.753400 | − | 0.657563i | \(-0.228413\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.23562 | 0.0109682 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 40.5703 | − | 23.4233i | 0.136600 | − | 0.0788663i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 130.666 | + | 75.4398i | 0.437009 | + | 0.252307i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −58.3299 | − | 32.3050i | −0.193787 | − | 0.107326i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −136.749 | + | 236.857i | −0.451318 | + | 0.781706i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.96991 | + | 3.41199i | 0.00645873 | + | 0.0111868i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 222.533i | − | 0.724864i | −0.932010 | − | 0.362432i | \(-0.881946\pi\) | ||
0.932010 | − | 0.362432i | \(-0.118054\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 143.057 | 0.462968 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 171.841 | − | 99.2124i | 0.552543 | − | 0.319011i | −0.197604 | − | 0.980282i | \(-0.563316\pi\) |
0.750147 | + | 0.661271i | \(0.229983\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −328.619 | − | 189.729i | −1.04990 | − | 0.606161i | −0.127280 | − | 0.991867i | \(-0.540625\pi\) |
−0.922622 | + | 0.385705i | \(0.873958\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.19919 | − | 0.0926473i | 0.0165054 | − | 0.000294118i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −129.813 | + | 224.843i | −0.409505 | + | 0.709284i | −0.994834 | − | 0.101512i | \(-0.967632\pi\) |
0.585329 | + | 0.810796i | \(0.300965\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.3206 | − | 42.1245i | −0.0762400 | − | 0.132052i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 144.234i | 0.449327i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 700.364 | 2.16831 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −127.206 | + | 73.4425i | −0.391403 | + | 0.225977i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −341.705 | − | 197.283i | −1.04497 | − | 0.603313i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 255.338 | + | 424.603i | 0.776103 | + | 1.29059i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 273.589 | − | 473.869i | 0.826552 | − | 1.43163i | −0.0741761 | − | 0.997245i | \(-0.523633\pi\) |
0.900728 | − | 0.434384i | \(-0.143034\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 444.715 | + | 770.269i | 1.33548 | + | 2.31312i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 5.31248i | − | 0.0158582i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −408.705 | −1.21277 | −0.606387 | − | 0.795170i | \(-0.707382\pi\) | ||||
−0.606387 | + | 0.795170i | \(0.707382\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −181.848 | + | 104.990i | −0.536425 | + | 0.309705i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 46.0458 | + | 26.5846i | 0.135032 | + | 0.0779606i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3257 | + | 342.510i | 0.0534276 | + | 0.998572i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.20238 | − | 5.54669i | 0.00928227 | − | 0.0160774i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 133.575 | + | 231.358i | 0.384941 | + | 0.666738i | 0.991761 | − | 0.128102i | \(-0.0408884\pi\) |
−0.606820 | + | 0.794839i | \(0.707555\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 466.080i | − | 1.33547i | −0.744398 | − | 0.667736i | \(-0.767263\pi\) | ||
0.744398 | − | 0.667736i | \(-0.232737\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 153.789 | 0.438146 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 230.205 | − | 132.909i | 0.652139 | − | 0.376513i | −0.137136 | − | 0.990552i | \(-0.543790\pi\) |
0.789275 | + | 0.614039i | \(0.210456\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.02573 | − | 2.32426i | −0.0113401 | − | 0.00654720i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −771.664 | + | 464.045i | −2.16152 | + | 1.29985i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 144.903 | − | 250.979i | 0.403628 | − | 0.699105i | −0.590532 | − | 0.807014i | \(-0.701082\pi\) |
0.994161 | + | 0.107909i | \(0.0344155\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 166.467 | + | 288.330i | 0.461128 | + | 0.798698i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 569.936i | 1.57007i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.71554 | −0.00470011 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.07460 | + | 3.50717i | −0.0165520 | + | 0.00955632i | −0.508253 | − | 0.861208i | \(-0.669709\pi\) |
0.491701 | + | 0.870764i | \(0.336375\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 820.333 | + | 473.619i | 2.22312 | + | 1.28352i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.21363 | + | 68.1069i | 0.00327125 | + | 0.183576i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −286.998 | + | 497.096i | −0.769433 | + | 1.33270i | 0.168438 | + | 0.985712i | \(0.446128\pi\) |
−0.937871 | + | 0.346984i | \(0.887206\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.23553 | + | 10.8002i | 0.0166281 | + | 0.0288007i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 159.680i | − | 0.423555i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −678.807 | −1.79105 | −0.895524 | − | 0.445014i | \(-0.853199\pi\) | ||||
−0.895524 | + | 0.445014i | \(0.853199\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −393.998 | + | 227.475i | −1.03412 | + | 0.597047i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 358.444 | + | 206.948i | 0.935886 | + | 0.540334i | 0.888668 | − | 0.458550i | \(-0.151631\pi\) |
0.0472179 | + | 0.998885i | \(0.484964\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.312954 | − | 0.565070i | 0.000812868 | − | 0.00146771i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −68.6280 | + | 118.867i | −0.177333 | + | 0.307150i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 69.2438 | + | 119.934i | 0.178005 | + | 0.308313i | 0.941197 | − | 0.337858i | \(-0.109702\pi\) |
−0.763192 | + | 0.646171i | \(0.776369\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 682.672i | 1.74596i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −608.582 | −1.54855 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.89600 | + | 1.67201i | −0.00733166 | + | 0.00423293i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.62003 | − | 2.09002i | −0.00911846 | − | 0.00526455i | 0.495434 | − | 0.868646i | \(-0.335009\pi\) |
−0.504552 | + | 0.863381i | \(0.668342\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −780.475 | − | 432.253i | −1.95608 | − | 1.08334i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 301.027 | − | 521.394i | 0.750690 | − | 1.30023i | −0.196798 | − | 0.980444i | \(-0.563054\pi\) |
0.947489 | − | 0.319790i | \(-0.103612\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 87.2724 | + | 151.160i | 0.216557 | + | 0.375088i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.157458i | 0.000388785i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 110.485 | 0.271461 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −155.272 | + | 89.6463i | −0.379638 | + | 0.219184i | −0.677661 | − | 0.735375i | \(-0.737006\pi\) |
0.298023 | + | 0.954559i | \(0.403673\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1046.93 | − | 604.443i | −2.54726 | − | 1.47066i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 439.264 | − | 7.82750i | 1.06359 | − | 0.0189528i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.751046 | + | 1.30085i | −0.00180975 | + | 0.00313458i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.03914 | − | 8.72804i | −0.0120843 | − | 0.0209305i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 605.541i | − | 1.44521i | −0.691263 | − | 0.722603i | \(-0.742946\pi\) | ||
0.691263 | − | 0.722603i | \(-0.257054\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −582.852 | −1.38445 | −0.692224 | − | 0.721683i | \(-0.743369\pi\) | ||||
−0.692224 | + | 0.721683i | \(0.743369\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 883.264 | − | 509.953i | 2.08809 | − | 1.20556i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −575.558 | − | 332.299i | −1.35425 | − | 0.781879i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 275.687 | + | 458.442i | 0.645637 | + | 1.07363i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25.4439 | − | 44.0702i | 0.0593098 | − | 0.102728i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 137.702 | + | 238.507i | 0.319495 | + | 0.553382i | 0.980383 | − | 0.197103i | \(-0.0631534\pi\) |
−0.660888 | + | 0.750485i | \(0.729820\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 27.7972i | − | 0.0641967i | −0.999485 | − | 0.0320984i | \(-0.989781\pi\) | ||
0.999485 | − | 0.0320984i | \(-0.0102190\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.77836 | −0.0155824 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −585.783 | + | 338.202i | −1.34047 | + | 0.773918i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −254.750 | − | 147.080i | −0.580295 | − | 0.335034i | 0.180955 | − | 0.983491i | \(-0.442081\pi\) |
−0.761251 | + | 0.648458i | \(0.775414\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 705.611 | − | 25.1554i | 1.60003 | − | 0.0570416i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 145.445 | − | 251.918i | 0.328319 | − | 0.568665i | −0.653860 | − | 0.756616i | \(-0.726851\pi\) |
0.982178 | + | 0.187951i | \(0.0601847\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.558650 | + | 0.967610i | 0.00125539 | + | 0.00217440i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 104.626i | − | 0.234063i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 433.407 | 0.965271 | 0.482635 | − | 0.875821i | \(-0.339680\pi\) | ||||
0.482635 | + | 0.875821i | \(0.339680\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 101.901 | − | 58.8328i | 0.225946 | − | 0.130450i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 368.805 | + | 212.930i | 0.814139 | + | 0.470043i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.81724 | − | 1.09281i | 0.00399394 | − | 0.00240178i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.6828 | − | 49.6801i | 0.0627632 | − | 0.108709i | −0.832936 | − | 0.553369i | \(-0.813342\pi\) |
0.895700 | + | 0.444660i | \(0.146675\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 347.918 | + | 602.612i | 0.757991 | + | 1.31288i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 567.060i | − | 1.23007i | −0.788501 | − | 0.615033i | \(-0.789143\pi\) | ||
0.788501 | − | 0.615033i | \(-0.210857\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.548177 | 0.00118397 | 0.000591984 | − | 1.00000i | \(-0.499812\pi\) | ||||
0.000591984 | 1.00000i | \(0.499812\pi\) | ||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.41668 | − | 3.70467i | 0.0137993 | − | 0.00796704i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −88.5154 | − | 51.1044i | −0.189540 | − | 0.109431i | 0.402227 | − | 0.915540i | \(-0.368236\pi\) |
−0.591767 | + | 0.806109i | \(0.701570\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.8518 | − | 721.216i | −0.0274025 | − | 1.53777i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 398.250 | − | 689.789i | 0.845541 | − | 1.46452i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.52495 | + | 14.7656i | 0.0180231 | + | 0.0312170i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 658.496i | − | 1.38631i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 140.219 | 0.293960 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −389.828 | + | 225.067i | −0.813837 | + | 0.469869i | −0.848287 | − | 0.529537i | \(-0.822365\pi\) |
0.0344496 | + | 0.999406i | \(0.489032\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 314.109 | + | 181.351i | 0.653034 | + | 0.377029i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 421.333 | − | 760.759i | 0.872326 | − | 1.57507i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.17215 | − | 5.49432i | 0.00654051 | − | 0.0113285i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −470.386 | − | 814.732i | −0.965885 | − | 1.67296i | −0.707219 | − | 0.706995i | \(-0.750050\pi\) |
−0.258666 | − | 0.965967i | \(-0.583283\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 797.762i | − | 1.63142i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 514.670 | 1.04821 | 0.524103 | − | 0.851655i | \(-0.324401\pi\) | ||||
0.524103 | + | 0.851655i | \(0.324401\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 625.696 | − | 361.246i | 1.26916 | − | 0.732750i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.15152 | − | 0.664832i | −0.00232631 | − | 0.00134310i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −552.151 | − | 305.799i | −1.11097 | − | 0.615290i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 124.004 | − | 214.780i | 0.248504 | − | 0.430422i | −0.714607 | − | 0.699526i | \(-0.753394\pi\) |
0.963111 | + | 0.269105i | \(0.0867277\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −45.7049 | − | 79.1633i | −0.0912274 | − | 0.158011i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 164.798i | − | 0.327630i | −0.986491 | − | 0.163815i | \(-0.947620\pi\) | ||
0.986491 | − | 0.163815i | \(-0.0523800\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.91422 | 0.00577073 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −563.454 | + | 325.310i | −1.11135 | + | 0.641638i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −109.542 | − | 63.2438i | −0.215209 | − | 0.124251i | 0.388521 | − | 0.921440i | \(-0.372986\pi\) |
−0.603730 | + | 0.797189i | \(0.706320\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −232.900 | + | 4.15017i | −0.455773 | + | 0.00812167i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −344.724 | + | 597.079i | −0.671977 | + | 1.16390i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.762160 | − | 1.32010i | −0.00147992 | − | 0.00256330i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 126.692i | − | 0.245053i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −476.505 | −0.918122 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −44.7559 | + | 25.8398i | −0.0859039 | + | 0.0495966i | −0.542337 | − | 0.840161i | \(-0.682460\pi\) |
0.456433 | + | 0.889758i | \(0.349127\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 297.579 | + | 171.808i | 0.568986 | + | 0.328504i | 0.756744 | − | 0.653711i | \(-0.226789\pi\) |
−0.187758 | + | 0.982215i | \(0.560122\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 436.304 | + | 725.533i | 0.831056 | + | 1.38197i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −394.874 | + | 683.942i | −0.749286 | + | 1.29780i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −65.1585 | − | 112.858i | −0.123173 | − | 0.213342i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 904.361i | − | 1.70313i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 386.276 | 0.724720 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.33096 | − | 0.768430i | 0.00248778 | − | 0.00143632i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 294.549 | + | 170.058i | 0.548509 | + | 0.316682i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 41.1193 | − | 77.4702i | 0.0762881 | − | 0.143730i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 382.006 | − | 661.654i | 0.706111 | − | 1.22302i | −0.260177 | − | 0.965561i | \(-0.583781\pi\) |
0.966289 | − | 0.257460i | \(-0.0828856\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −493.914 | − | 855.485i | −0.909603 | − | 1.57548i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.20423i | 0.00771419i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −59.3354 | −0.108474 | −0.0542371 | − | 0.998528i | \(-0.517273\pi\) | ||||
−0.0542371 | + | 0.998528i | \(0.517273\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 953.655 | − | 550.593i | 1.73708 | − | 1.00290i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 619.952 | + | 357.929i | 1.12514 | + | 0.649600i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −389.113 | + | 233.996i | −0.703640 | + | 0.423139i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.69826 | − | 13.3338i | 0.0138707 | − | 0.0240248i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −365.048 | − | 632.281i | −0.655382 | − | 1.13515i | −0.981798 | − | 0.189929i | \(-0.939174\pi\) |
0.326416 | − | 0.945226i | \(-0.394159\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 55.9718i | 0.100128i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 230.248 | 0.410424 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −412.415 | + | 238.108i | −0.732531 | + | 0.422927i | −0.819347 | − | 0.573298i | \(-0.805664\pi\) |
0.0868167 | + | 0.996224i | \(0.472331\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.93765 | + | 1.11870i | 0.00342947 | + | 0.00198000i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.380917 | + | 21.3763i | 0.000671811 | + | 0.0377007i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −208.701 | + | 361.480i | −0.366785 | + | 0.635291i | −0.989061 | − | 0.147508i | \(-0.952875\pi\) |
0.622276 | + | 0.782798i | \(0.286208\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −492.001 | − | 852.171i | −0.861648 | − | 1.49242i | −0.870337 | − | 0.492456i | \(-0.836099\pi\) |
0.00868931 | − | 0.999962i | \(-0.497234\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 922.685i | 1.61027i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 641.861 | 1.11628 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 80.3564 | − | 46.3938i | 0.139266 | − | 0.0804052i | −0.428748 | − | 0.903424i | \(-0.641045\pi\) |
0.568014 | + | 0.823019i | \(0.307712\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 358.456 | + | 206.955i | 0.619095 | + | 0.357435i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −98.8141 | + | 178.419i | −0.170076 | + | 0.307089i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.70898 | − | 15.0844i | 0.0149382 | − | 0.0258738i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.18253 | − | 3.78025i | −0.00373082 | − | 0.00646196i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 648.667i | 1.10506i | 0.833495 | + | 0.552528i | \(0.186337\pi\) | ||||
−0.833495 | + | 0.552528i | \(0.813663\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −782.498 | −1.32852 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1152.97 | − | 665.667i | 1.95088 | − | 1.12634i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −453.392 | − | 261.766i | −0.764574 | − | 0.441427i | 0.0663617 | − | 0.997796i | \(-0.478861\pi\) |
−0.830936 | + | 0.556369i | \(0.812194\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.39327 | + | 4.64847i | 0.0141063 | + | 0.00781255i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 500.471 | − | 866.841i | 0.838309 | − | 1.45199i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −445.522 | − | 771.668i | −0.743777 | − | 1.28826i | −0.950764 | − | 0.309916i | \(-0.899699\pi\) |
0.206987 | − | 0.978344i | \(-0.433634\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 502.034i | 0.835331i | 0.908601 | + | 0.417666i | \(0.137152\pi\) | ||||
−0.908601 | + | 0.417666i | \(0.862848\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1484.85 | −2.46243 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.25924 | − | 3.03642i | 0.00869296 | − | 0.00501888i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −263.638 | − | 152.212i | −0.434330 | − | 0.250760i | 0.266860 | − | 0.963735i | \(-0.414014\pi\) |
−0.701189 | + | 0.712975i | \(0.747347\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −920.221 | + | 16.3979i | −1.51104 | + | 0.0269260i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 207.954 | − | 360.187i | 0.340351 | − | 0.589505i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −249.053 | − | 431.373i | −0.406286 | − | 0.703708i | 0.588184 | − | 0.808727i | \(-0.299843\pi\) |
−0.994470 | + | 0.105019i | \(0.966510\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 16.3972i | − | 0.0266622i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 242.250 | 0.392626 | 0.196313 | − | 0.980541i | \(-0.437103\pi\) | ||||
0.196313 | + | 0.980541i | \(0.437103\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −468.171 | + | 270.298i | −0.756334 | + | 0.436669i | −0.827978 | − | 0.560761i | \(-0.810509\pi\) |
0.0716442 | + | 0.997430i | \(0.477175\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −581.996 | − | 336.016i | −0.937192 | − | 0.541088i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 78.1824 | + | 130.010i | 0.125493 | + | 0.208684i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.400 | + | 541.093i | −0.499841 | + | 0.865749i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 114.067 | + | 197.570i | 0.181925 | + | 0.315103i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1641.09i | 2.60904i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 808.138 | 1.28073 | 0.640363 | − | 0.768073i | \(-0.278784\pi\) | ||||
0.640363 | + | 0.768073i | \(0.278784\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −329.898 | + | 190.467i | −0.521166 | + | 0.300895i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.19817 | + | 2.42382i | 0.00661130 | + | 0.00381703i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 244.063 | − | 152.755i | 0.383144 | − | 0.239804i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −649.633 | + | 1125.20i | −1.01664 | + | 1.76087i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −155.277 | − | 268.947i | −0.242241 | − | 0.419574i | 0.719111 | − | 0.694895i | \(-0.244549\pi\) |
−0.961352 | + | 0.275321i | \(0.911216\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 342.761i | − | 0.533065i | −0.963826 | − | 0.266533i | \(-0.914122\pi\) | ||
0.963826 | − | 0.266533i | \(-0.0858780\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.37598 | 0.00368369 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 447.656 | − | 258.454i | 0.691895 | − | 0.399466i | −0.112427 | − | 0.993660i | \(-0.535862\pi\) |
0.804321 | + | 0.594195i | \(0.202529\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −97.2889 | − | 56.1698i | −0.149906 | − | 0.0865482i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 862.159 | − | 518.465i | 1.32436 | − | 0.796413i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −381.777 | + | 661.256i | −0.584650 | + | 1.01264i | 0.410269 | + | 0.911965i | \(0.365435\pi\) |
−0.994919 | + | 0.100679i | \(0.967898\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.24231 | + | 5.61585i | 0.00495010 | + | 0.00857382i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 479.496i | 0.729827i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 593.617 | 0.900785 | 0.450392 | − | 0.892831i | \(-0.351284\pi\) | ||||
0.450392 | + | 0.892831i | \(0.351284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 275.162 | − | 158.865i | 0.416282 | − | 0.240340i | −0.277204 | − | 0.960811i | \(-0.589408\pi\) |
0.693485 | + | 0.720471i | \(0.256074\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 654.596 | + | 377.931i | 0.987325 | + | 0.570032i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.169374 | + | 9.50495i | 0.000254698 | + | 0.0142932i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −348.887 | + | 604.291i | −0.523070 | + | 0.905983i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 375.957 | + | 651.176i | 0.561968 | + | 0.973358i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 136.789i | − | 0.203859i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 567.441 | 0.843152 | 0.421576 | − | 0.906793i | \(-0.361477\pi\) | ||||
0.421576 | + | 0.906793i | \(0.361477\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 566.587 | − | 327.119i | 0.839388 | − | 0.484621i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 541.094 | + | 312.401i | 0.799253 | + | 0.461449i | 0.843210 | − | 0.537584i | \(-0.180663\pi\) |
−0.0439568 | + | 0.999033i | \(0.513996\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 417.355 | − | 753.576i | 0.614661 | − | 1.10983i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 198.049 | − | 343.031i | 0.290821 | − | 0.503717i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 46.4425 | + | 80.4407i | 0.0679977 | + | 0.117776i | 0.898020 | − | 0.439955i | \(-0.145006\pi\) |
−0.830022 | + | 0.557731i | \(0.811672\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.8811i | 0.0188045i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1987.06 | −2.89237 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 49.5194 | − | 28.5901i | 0.0718715 | − | 0.0414950i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 422.387 | + | 243.865i | 0.611269 | + | 0.352916i | 0.773462 | − | 0.633843i | \(-0.218523\pi\) |
−0.162193 | + | 0.986759i | \(0.551857\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −157.938 | − | 87.4711i | −0.227904 | − | 0.126221i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.0536936 | + | 0.0930000i | −7.72570e−5 | + | 0.000133813i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 873.874 | + | 1513.59i | 1.25376 | + | 2.17158i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 183.236i | − | 0.262140i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −548.723 | −0.782772 | −0.391386 | − | 0.920227i | \(-0.628004\pi\) | ||||
−0.391386 | + | 0.920227i | \(0.628004\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1408.17 | + | 813.010i | −2.00309 | + | 1.15649i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.2898 | − | 8.82756i | −0.0216876 | − | 0.0125214i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 395.630 | − | 7.04996i | 0.559590 | − | 0.00997166i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −125.886 | + | 218.041i | −0.177555 | + | 0.307533i | −0.941042 | − | 0.338289i | \(-0.890152\pi\) |
0.763488 | + | 0.645822i | \(0.223485\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 467.329 | + | 809.437i | 0.657284 | + | 1.13845i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 762.730i | − | 1.06975i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.542226 | −0.000758358 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1793.93 | + | 1035.72i | −2.50199 | + | 1.44452i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 348.643 | + | 201.289i | 0.484900 | + | 0.279957i | 0.722456 | − | 0.691417i | \(-0.243013\pi\) |
−0.237556 | + | 0.971374i | \(0.576346\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −106.663 | − | 177.371i | −0.147938 | − | 0.246007i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −503.246 | + | 871.647i | −0.696052 | + | 1.20560i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −339.650 | − | 588.291i | −0.468483 | − | 0.811437i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 419.973i | 0.577680i | 0.957377 | + | 0.288840i | \(0.0932695\pi\) | ||||
−0.957377 | + | 0.288840i | \(0.906730\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1183.68 | 1.62371 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −219.322 | + | 126.625i | −0.300030 | + | 0.173222i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −382.547 | − | 220.863i | −0.521892 | − | 0.301314i | 0.215817 | − | 0.976434i | \(-0.430759\pi\) |
−0.737708 | + | 0.675120i | \(0.764092\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.48437 | − | 10.3604i | −0.00882228 | − | 0.0140957i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −92.2236 | + | 159.736i | −0.125134 | + | 0.216738i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 219.526 | + | 380.231i | 0.297059 | + | 0.514521i | 0.975462 | − | 0.220169i | \(-0.0706610\pi\) |
−0.678403 | + | 0.734690i | \(0.737328\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 748.924i | 1.01069i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −882.165 | −1.18730 | −0.593651 | − | 0.804723i | \(-0.702314\pi\) | ||||
−0.593651 | + | 0.804723i | \(0.702314\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.965466 | + | 0.557412i | −0.00129593 | + | 0.000748204i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 363.589 | + | 209.918i | 0.486733 | + | 0.281015i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 178.830 | − | 107.541i | 0.238759 | − | 0.143579i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 57.8178 | − | 100.143i | 0.0769877 | − | 0.133347i | −0.824961 | − | 0.565189i | \(-0.808803\pi\) |
0.901949 | + | 0.431843i | \(0.142136\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −908.699 | − | 1573.91i | −1.20677 | − | 2.09019i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 4.53767i | − | 0.00601015i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 885.222 | 1.16938 | 0.584691 | − | 0.811256i | \(-0.301216\pi\) | ||||
0.584691 | + | 0.811256i | \(0.301216\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −192.579 | + | 111.185i | −0.253727 | + | 0.146489i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 479.807 | + | 277.017i | 0.630495 | + | 0.364017i | 0.780944 | − | 0.624601i | \(-0.214738\pi\) |
−0.150448 | + | 0.988618i | \(0.548072\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.1707 | + | 570.761i | 0.0133299 | + | 0.748049i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.87509 | − | 17.1042i | 0.0129086 | − | 0.0223584i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −184.395 | − | 319.382i | −0.240411 | − | 0.416405i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 502.045i | 0.652854i | 0.945222 | + | 0.326427i | \(0.105845\pi\) | ||||
−0.945222 | + | 0.326427i | \(0.894155\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 348.826 | 0.452433 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1029.64 | − | 594.462i | 1.33200 | − | 0.769032i | 0.346396 | − | 0.938088i | \(-0.387405\pi\) |
0.985606 | + | 0.169057i | \(0.0540721\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 643.055 | + | 371.268i | 0.829748 | + | 0.479055i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1012.85 | − | 1828.80i | 1.30354 | − | 2.35367i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −865.852 | + | 1499.70i | −1.11149 | + | 1.92516i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 80.6972 | + | 139.772i | 0.103325 | + | 0.178965i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 711.230i | 0.908340i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.48695 | −0.0108114 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −245.089 | + | 141.502i | −0.311421 | + | 0.179799i | −0.647562 | − | 0.762013i | \(-0.724211\pi\) |
0.336141 | + | 0.941812i | \(0.390878\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −876.154 | − | 505.848i | −1.11046 | − | 0.641125i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 265.759 | + | 147.186i | 0.335979 | + | 0.186076i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 224.527 | − | 388.893i | 0.283136 | − | 0.490407i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.21363 | − | 2.10208i | −0.00152658 | − | 0.00264412i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 999.015i | − | 1.25347i | −0.779233 | − | 0.626735i | \(-0.784391\pi\) | ||
0.779233 | − | 0.626735i | \(-0.215609\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1881.83 | 2.35523 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 270.448 | − | 156.143i | 0.337638 | − | 0.194936i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 51.5830 | + | 29.7814i | 0.0642378 | + | 0.0370877i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.26483 | + | 0.165095i | −0.0115091 | + | 0.000205087i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −684.261 | + | 1185.17i | −0.847907 | + | 1.46862i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −353.113 | − | 611.610i | −0.436481 | − | 0.756007i | 0.560934 | − | 0.827860i | \(-0.310442\pi\) |
−0.997415 | + | 0.0718530i | \(0.977109\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 357.615i | − | 0.440955i | −0.975392 | − | 0.220478i | \(-0.929238\pi\) | ||
0.975392 | − | 0.220478i | \(-0.0707616\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 957.636 | 1.17790 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.36157 | + | 4.25020i | −0.00903260 | + | 0.00521497i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −217.308 | − | 125.463i | −0.265983 | − | 0.153565i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −305.442 | − | 507.922i | −0.372945 | − | 0.620173i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −668.782 | + | 1158.36i | −0.814594 | + | 1.41092i | 0.0950249 | + | 0.995475i | \(0.469707\pi\) |
−0.909619 | + | 0.415443i | \(0.863626\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −239.300 | − | 414.480i | −0.290766 | − | 0.503621i | 0.683225 | − | 0.730207i | \(-0.260577\pi\) |
−0.973991 | + | 0.226587i | \(0.927243\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 216.483i | − | 0.262404i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −572.317 | −0.692040 | −0.346020 | − | 0.938227i | \(-0.612467\pi\) | ||||
−0.346020 | + | 0.938227i | \(0.612467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1027.50 | + | 593.229i | −1.23945 | + | 0.715596i | −0.968981 | − | 0.247133i | \(-0.920511\pi\) |
−0.270467 | + | 0.962729i | \(0.587178\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 994.390 | + | 574.112i | 1.19662 | + | 0.690868i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1150.70 | + | 610.765i | 1.38140 | + | 0.733212i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.487001 | + | 0.843510i | −0.000583234 | + | 0.00101019i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −388.719 | − | 673.281i | −0.464419 | − | 0.804398i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 979.116i | − | 1.16700i | −0.812112 | − | 0.583502i | \(-0.801682\pi\) | ||
0.812112 | − | 0.583502i | \(-0.198318\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −102.524 | −0.121908 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1005.08 | − | 580.283i | 1.19227 | − | 0.688355i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.00378 | + | 3.46629i | 0.00710507 | + | 0.00410211i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 706.642 | − | 424.944i | 0.834288 | − | 0.501705i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 334.266 | − | 578.966i | 0.393718 | − | 0.681939i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −792.472 | − | 1372.60i | −0.931224 | − | 1.61293i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 683.331i | − | 0.801091i | −0.916277 | − | 0.400546i | \(-0.868821\pi\) | ||
0.916277 | − | 0.400546i | \(-0.131179\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.5689 | 0.0228876 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.04833 | + | 4.06936i | −0.00822443 | + | 0.00474837i | −0.504107 | − | 0.863641i | \(-0.668178\pi\) |
0.495882 | + | 0.868390i | \(0.334845\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 911.901 | + | 526.487i | 1.06158 | + | 0.612906i | 0.925870 | − | 0.377842i | \(-0.123334\pi\) |
0.135715 | + | 0.990748i | \(0.456667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −39.6675 | − | 2226.07i | −0.0460715 | − | 2.58544i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 521.994 | − | 904.120i | 0.604860 | − | 1.04765i | −0.387214 | − | 0.921990i | \(-0.626562\pi\) |
0.992074 | − | 0.125658i | \(-0.0401043\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.53866 | + | 4.39708i | 0.00293486 | + | 0.00508333i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2021.71i | 2.33185i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 116.103 | 0.133605 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −524.385 | + | 302.754i | −0.602050 | + | 0.347593i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1535.67 | − | 886.619i | −1.75907 | − | 1.01560i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.74162 | − | 15.7839i | 0.00999042 | − | 0.0180387i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 403.776 | − | 699.361i | 0.460406 | − | 0.797447i | −0.538575 | − | 0.842578i | \(-0.681037\pi\) |
0.998981 | + | 0.0451308i | \(0.0143705\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 932.180 | + | 1614.58i | 1.06050 | + | 1.83684i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 681.043i | 0.773034i | 0.922282 | + | 0.386517i | \(0.126322\pi\) | ||||
−0.922282 | + | 0.386517i | \(0.873678\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −996.177 | −1.12817 | −0.564086 | − | 0.825716i | \(-0.690772\pi\) | ||||
−0.564086 | + | 0.825716i | \(0.690772\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.5576 | + | 7.82750i | −0.0153194 | + | 0.00884463i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −236.794 | − | 136.713i | −0.266961 | − | 0.154130i | 0.360545 | − | 0.932742i | \(-0.382591\pi\) |
−0.627506 | + | 0.778612i | \(0.715924\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 575.802 | + | 318.898i | 0.647697 | + | 0.358716i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.73344 | − | 4.73446i | 0.00306783 | − | 0.00531364i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 932.275 | + | 1614.75i | 1.04398 | + | 1.80823i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.62405i | − | 0.00404921i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −730.004 | −0.813829 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −699.073 | + | 403.610i | −0.777612 | + | 0.448954i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 224.056 | + | 129.359i | 0.248675 | + | 0.143573i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 322.560 | − | 5.74787i | 0.357209 | − | 0.00636531i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.26281 | + | 9.11546i | −0.00581526 | + | 0.0100723i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.9679 | + | 27.6573i | 0.0176052 | + | 0.0304932i | 0.874694 | − | 0.484676i | \(-0.161062\pi\) |
−0.857089 | + | 0.515169i | \(0.827729\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 814.527i | − | 0.896070i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1257.16 | −1.37998 | −0.689991 | − | 0.723818i | \(-0.742385\pi\) | ||||
−0.689991 | + | 0.723818i | \(0.742385\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.1650 | − | 26.0760i | 0.0494688 | − | 0.0285608i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.5083 | − | 9.53107i | −0.0180419 | − | 0.0104165i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 453.758 | + | 754.558i | 0.494829 | + | 0.822855i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −691.491 | + | 1197.70i | −0.752438 | + | 1.30326i | 0.194200 | + | 0.980962i | \(0.437789\pi\) |
−0.946638 | + | 0.322299i | \(0.895544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 538.344 | + | 932.439i | 0.584521 | + | 1.01242i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 529.829i | 0.574030i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1542.98 | 1.66809 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −368.970 | + | 213.025i | −0.398026 | + | 0.229800i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −424.420 | − | 245.039i | −0.456857 | − | 0.263766i | 0.253865 | − | 0.967240i | \(-0.418298\pi\) |
−0.710722 | + | 0.703473i | \(0.751631\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.9880 | + | 1289.97i | 0.0493964 | + | 1.38557i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −480.022 | + | 831.422i | −0.514493 | + | 0.891128i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.22668 | − | 2.12467i | −0.00131196 | − | 0.00227238i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1136.61i | 1.21303i | 0.795072 | + | 0.606515i | \(0.207433\pi\) | ||||
−0.795072 | + | 0.606515i | \(0.792567\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1835.94 | 1.95520 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −458.248 | + | 264.570i | −0.486980 | + | 0.281158i | −0.723321 | − | 0.690512i | \(-0.757385\pi\) |
0.236341 | + | 0.971670i | \(0.424052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1461.81 | − | 843.978i | −1.55017 | − | 0.894993i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.09416 | + | 4.86748i | −0.00856525 | + | 0.00515077i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 582.080 | − | 1008.19i | 0.614657 | − | 1.06462i | −0.375788 | − | 0.926706i | \(-0.622628\pi\) |
0.990445 | − | 0.137911i | \(-0.0440388\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 97.7672 | + | 169.338i | 0.103021 | + | 0.178438i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1256.16i | − | 1.32088i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −616.861 | −0.647283 | −0.323642 | − | 0.946180i | \(-0.604907\pi\) | ||||
−0.323642 | + | 0.946180i | \(0.604907\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.51433 | − | 4.91575i | 0.00891553 | − | 0.00514738i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 203.812 | + | 117.671i | 0.212970 | + | 0.122958i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.1614 | + | 1748.72i | 0.0324936 | + | 1.82348i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −39.3184 | + | 68.1015i | −0.0409141 | + | 0.0708652i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −214.777 | − | 372.005i | −0.223029 | − | 0.386298i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 4.41034i | − | 0.00457030i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 624.887 | 0.646212 | 0.323106 | − | 0.946363i | \(-0.395273\pi\) | ||||
0.323106 | + | 0.946363i | \(0.395273\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2934.60 | + | 1694.29i | −3.02849 | + | 1.74850i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 644.984 | + | 372.382i | 0.664248 | + | 0.383504i | 0.793894 | − | 0.608057i | \(-0.208051\pi\) |
−0.129646 | + | 0.991560i | \(0.541384\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.06439 | + | 12.7555i | −0.00726042 | + | 0.0131094i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 355.338 | − | 615.464i | 0.364450 | − | 0.631245i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 342.196 | + | 592.702i | 0.350252 | + | 0.606655i | 0.986294 | − | 0.165000i | \(-0.0527625\pi\) |
−0.636041 | + | 0.771655i | \(0.719429\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 38.7922i | − | 0.0396243i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1175.09 | 1.19785 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −787.512 | + | 454.670i | −0.801131 | + | 0.462533i | −0.843867 | − | 0.536553i | \(-0.819726\pi\) |
0.0427352 | + | 0.999086i | \(0.486393\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.2852 | − | 7.09289i | −0.0124723 | − | 0.00720091i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2097.08 | − | 1161.43i | −2.12470 | − | 1.17673i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 122.293 | − | 211.818i | 0.123654 | − | 0.214174i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −662.509 | − | 1147.50i | −0.668526 | − | 1.15792i | −0.978316 | − | 0.207116i | \(-0.933592\pi\) |
0.309791 | − | 0.950805i | \(-0.399741\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2647.42i | 2.66608i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.6653 | −0.0107189 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −811.560 | + | 468.554i | −0.814002 | + | 0.469964i | −0.848344 | − | 0.529446i | \(-0.822400\pi\) |
0.0343418 | + | 0.999410i | \(0.489067\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1399.07 | − | 807.753i | −1.40047 | − | 0.808562i |
(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 | 448.3.s.g.257.1 | 16 | ||
4.3 | odd | 2 | inner | 448.3.s.g.257.8 | 16 | ||
7.3 | odd | 6 | inner | 448.3.s.g.129.1 | 16 | ||
8.3 | odd | 2 | 224.3.s.a.33.1 | ✓ | 16 | ||
8.5 | even | 2 | 224.3.s.a.33.8 | yes | 16 | ||
28.3 | even | 6 | inner | 448.3.s.g.129.8 | 16 | ||
56.3 | even | 6 | 224.3.s.a.129.1 | yes | 16 | ||
56.5 | odd | 6 | 1568.3.c.h.97.1 | 16 | |||
56.19 | even | 6 | 1568.3.c.h.97.15 | 16 | |||
56.37 | even | 6 | 1568.3.c.h.97.16 | 16 | |||
56.45 | odd | 6 | 224.3.s.a.129.8 | yes | 16 | ||
56.51 | odd | 6 | 1568.3.c.h.97.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.s.a.33.1 | ✓ | 16 | 8.3 | odd | 2 | ||
224.3.s.a.33.8 | yes | 16 | 8.5 | even | 2 | ||
224.3.s.a.129.1 | yes | 16 | 56.3 | even | 6 | ||
224.3.s.a.129.8 | yes | 16 | 56.45 | odd | 6 | ||
448.3.s.g.129.1 | 16 | 7.3 | odd | 6 | inner | ||
448.3.s.g.129.8 | 16 | 28.3 | even | 6 | inner | ||
448.3.s.g.257.1 | 16 | 1.1 | even | 1 | trivial | ||
448.3.s.g.257.8 | 16 | 4.3 | odd | 2 | inner | ||
1568.3.c.h.97.1 | 16 | 56.5 | odd | 6 | |||
1568.3.c.h.97.2 | 16 | 56.51 | odd | 6 | |||
1568.3.c.h.97.15 | 16 | 56.19 | even | 6 | |||
1568.3.c.h.97.16 | 16 | 56.37 | even | 6 |