Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,3,Mod(19,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.m (of order \(4\), degree \(2\), 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: | \(3.92371580679\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6x^{14} + 10x^{12} + 88x^{10} - 752x^{8} + 1408x^{6} + 2560x^{4} - 24576x^{2} + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 91.1 | ||
Root | \(0.136762 + 1.99532i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.91 |
Dual form | 144.3.m.b.19.1 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.99532 | + | 0.136762i | −0.997659 | + | 0.0683808i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.96259 | − | 0.545766i | 0.990648 | − | 0.136441i | ||||
\(5\) | −0.227650 | − | 0.227650i | −0.0455300 | − | 0.0455300i | 0.683975 | − | 0.729505i | \(-0.260250\pi\) |
−0.729505 | + | 0.683975i | \(0.760250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.90219 | 0.557456 | 0.278728 | − | 0.960370i | \(-0.410087\pi\) | ||||
0.278728 | + | 0.960370i | \(0.410087\pi\) | |||||||
\(8\) | −7.83199 | + | 1.63091i | −0.978999 | + | 0.203863i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.485368 | + | 0.423100i | 0.0485368 | + | 0.0423100i | ||||
\(11\) | 2.21045 | − | 2.21045i | 0.200950 | − | 0.200950i | −0.599457 | − | 0.800407i | \(-0.704617\pi\) |
0.800407 | + | 0.599457i | \(0.204617\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.08526 | − | 5.08526i | 0.391174 | − | 0.391174i | −0.483932 | − | 0.875106i | \(-0.660792\pi\) |
0.875106 | + | 0.483932i | \(0.160792\pi\) | |||||||
\(14\) | −7.78612 | + | 0.533670i | −0.556152 | + | 0.0381193i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.4043 | − | 4.32530i | 0.962767 | − | 0.270331i | ||||
\(17\) | 18.8341 | 1.10789 | 0.553943 | − | 0.832555i | \(-0.313123\pi\) | ||||
0.553943 | + | 0.832555i | \(0.313123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.7651 | + | 11.7651i | 0.619216 | + | 0.619216i | 0.945330 | − | 0.326114i | \(-0.105739\pi\) |
−0.326114 | + | 0.945330i | \(0.605739\pi\) | |||||||
\(20\) | −1.02633 | − | 0.777840i | −0.0513164 | − | 0.0388920i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.10825 | + | 4.71286i | −0.186739 | + | 0.214221i | ||||
\(23\) | 35.4354 | 1.54067 | 0.770335 | − | 0.637640i | \(-0.220089\pi\) | ||||
0.770335 | + | 0.637640i | \(0.220089\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 24.8964i | − | 0.995854i | ||||||
\(26\) | −9.45124 | + | 10.8422i | −0.363509 | + | 0.417007i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 15.4628 | − | 2.12968i | 0.552243 | − | 0.0760602i | ||||
\(29\) | 21.2499 | − | 21.2499i | 0.732755 | − | 0.732755i | −0.238410 | − | 0.971165i | \(-0.576626\pi\) |
0.971165 | + | 0.238410i | \(0.0766261\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 35.9691i | 1.16029i | 0.814512 | + | 0.580146i | \(0.197005\pi\) | ||||
−0.814512 | + | 0.580146i | \(0.802995\pi\) | |||||||
\(32\) | −30.1449 | + | 10.7371i | −0.942028 | + | 0.335533i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −37.5799 | + | 2.57578i | −1.10529 | + | 0.0757581i | ||||
\(35\) | −0.888334 | − | 0.888334i | −0.0253810 | − | 0.0253810i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −34.4199 | − | 34.4199i | −0.930267 | − | 0.930267i | 0.0674555 | − | 0.997722i | \(-0.478512\pi\) |
−0.997722 | + | 0.0674555i | \(0.978512\pi\) | |||||||
\(38\) | −25.0842 | − | 21.8661i | −0.660110 | − | 0.575425i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.15423 | + | 1.41168i | 0.0538557 | + | 0.0352919i | ||||
\(41\) | 44.1055i | 1.07574i | 0.843026 | + | 0.537872i | \(0.180772\pi\) | ||||
−0.843026 | + | 0.537872i | \(0.819228\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −28.3018 | + | 28.3018i | −0.658180 | + | 0.658180i | −0.954949 | − | 0.296769i | \(-0.904091\pi\) |
0.296769 | + | 0.954949i | \(0.404091\pi\) | |||||||
\(44\) | 7.55273 | − | 9.96550i | 0.171653 | − | 0.226489i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −70.7049 | + | 4.84620i | −1.53706 | + | 0.105352i | ||||
\(47\) | − | 32.8802i | − | 0.699579i | −0.936828 | − | 0.349790i | \(-0.886253\pi\) | ||
0.936828 | − | 0.349790i | \(-0.113747\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −33.7729 | −0.689242 | ||||||||
\(50\) | 3.40486 | + | 49.6762i | 0.0680973 | + | 0.993523i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 17.3754 | − | 22.9262i | 0.334143 | − | 0.440888i | ||||
\(53\) | −42.1450 | − | 42.1450i | −0.795189 | − | 0.795189i | 0.187144 | − | 0.982333i | \(-0.440077\pi\) |
−0.982333 | + | 0.187144i | \(0.940077\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00642 | −0.0182985 | ||||||||
\(56\) | −30.5620 | + | 6.36412i | −0.545749 | + | 0.113645i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −39.4941 | + | 45.3065i | −0.680933 | + | 0.781146i | ||||
\(59\) | −66.9935 | + | 66.9935i | −1.13548 | + | 1.13548i | −0.146233 | + | 0.989250i | \(0.546715\pi\) |
−0.989250 | + | 0.146233i | \(0.953285\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 17.3728 | − | 17.3728i | 0.284800 | − | 0.284800i | −0.550220 | − | 0.835020i | \(-0.685456\pi\) |
0.835020 | + | 0.550220i | \(0.185456\pi\) | |||||||
\(62\) | −4.91919 | − | 71.7697i | −0.0793417 | − | 1.15758i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 58.6803 | − | 25.5465i | 0.916879 | − | 0.399164i | ||||
\(65\) | −2.31532 | −0.0356203 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 39.6756 | + | 39.6756i | 0.592174 | + | 0.592174i | 0.938218 | − | 0.346044i | \(-0.112475\pi\) |
−0.346044 | + | 0.938218i | \(0.612475\pi\) | |||||||
\(68\) | 74.6317 | − | 10.2790i | 1.09752 | − | 0.151162i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.89400 | + | 1.65102i | 0.0270571 | + | 0.0235860i | ||||
\(71\) | 63.0272 | 0.887707 | 0.443853 | − | 0.896099i | \(-0.353611\pi\) | ||||
0.443853 | + | 0.896099i | \(0.353611\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 75.4549i | − | 1.03363i | −0.856097 | − | 0.516815i | \(-0.827118\pi\) | ||
0.856097 | − | 0.516815i | \(-0.172882\pi\) | |||||||
\(74\) | 73.3859 | + | 63.9713i | 0.991702 | + | 0.864477i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 53.0413 | + | 40.1993i | 0.697912 | + | 0.528939i | ||||
\(77\) | 8.62561 | − | 8.62561i | 0.112021 | − | 0.112021i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 59.1583i | 0.748839i | 0.927259 | + | 0.374419i | \(0.122158\pi\) | ||||
−0.927259 | + | 0.374419i | \(0.877842\pi\) | |||||||
\(80\) | −4.49144 | − | 2.52213i | −0.0561430 | − | 0.0315266i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.03194 | − | 88.0046i | −0.0735603 | − | 1.07323i | ||||
\(83\) | −71.2155 | − | 71.2155i | −0.858018 | − | 0.858018i | 0.133086 | − | 0.991104i | \(-0.457511\pi\) |
−0.991104 | + | 0.133086i | \(0.957511\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.28757 | − | 4.28757i | −0.0504420 | − | 0.0504420i | ||||
\(86\) | 52.6004 | − | 60.3416i | 0.611633 | − | 0.701647i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −13.7072 | + | 20.9173i | −0.155764 | + | 0.237696i | ||||
\(89\) | 150.671i | 1.69293i | 0.532443 | + | 0.846466i | \(0.321274\pi\) | ||||
−0.532443 | + | 0.846466i | \(0.678726\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.8437 | − | 19.8437i | 0.218062 | − | 0.218062i | ||||
\(92\) | 140.416 | − | 19.3394i | 1.52626 | − | 0.210211i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.49675 | + | 65.6065i | 0.0478378 | + | 0.697942i | ||||
\(95\) | − | 5.35665i | − | 0.0563858i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 51.5586 | 0.531532 | 0.265766 | − | 0.964038i | \(-0.414375\pi\) | ||||
0.265766 | + | 0.964038i | \(0.414375\pi\) | |||||||
\(98\) | 67.3876 | − | 4.61883i | 0.687629 | − | 0.0471309i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.5876 | − | 98.6541i | −0.135876 | − | 0.986541i | ||||
\(101\) | −139.414 | − | 139.414i | −1.38034 | − | 1.38034i | −0.844010 | − | 0.536327i | \(-0.819811\pi\) |
−0.536327 | − | 0.844010i | \(-0.680189\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 67.9691 | 0.659894 | 0.329947 | − | 0.943999i | \(-0.392969\pi\) | ||||
0.329947 | + | 0.943999i | \(0.392969\pi\) | |||||||
\(104\) | −31.5341 | + | 48.1213i | −0.303213 | + | 0.462705i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 89.8565 | + | 78.3289i | 0.847703 | + | 0.738952i | ||||
\(107\) | −129.801 | + | 129.801i | −1.21309 | + | 1.21309i | −0.243090 | + | 0.970004i | \(0.578161\pi\) |
−0.970004 | + | 0.243090i | \(0.921839\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 30.1323 | − | 30.1323i | 0.276443 | − | 0.276443i | −0.555244 | − | 0.831687i | \(-0.687375\pi\) |
0.831687 | + | 0.555244i | \(0.187375\pi\) | |||||||
\(110\) | 2.00812 | − | 0.137639i | 0.0182557 | − | 0.00125127i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 60.1105 | − | 16.8781i | 0.536701 | − | 0.150698i | ||||
\(113\) | −5.11034 | −0.0452243 | −0.0226121 | − | 0.999744i | \(-0.507198\pi\) | ||||
−0.0226121 | + | 0.999744i | \(0.507198\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.06687 | − | 8.06687i | −0.0701467 | − | 0.0701467i | ||||
\(116\) | 72.6072 | − | 95.8021i | 0.625924 | − | 0.825880i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 124.511 | − | 142.836i | 1.05518 | − | 1.21047i | ||||
\(119\) | 73.4942 | 0.617598 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 111.228i | 0.919238i | ||||||||
\(122\) | −32.2884 | + | 37.0403i | −0.264659 | + | 0.303609i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 19.6307 | + | 142.531i | 0.158312 | + | 1.14944i | ||||
\(125\) | −11.3589 | + | 11.3589i | −0.0908712 | + | 0.0908712i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 123.225i | − | 0.970277i | −0.874437 | − | 0.485138i | \(-0.838769\pi\) | ||
0.874437 | − | 0.485138i | \(-0.161231\pi\) | |||||||
\(128\) | −113.592 | + | 58.9986i | −0.887438 | + | 0.460927i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.61980 | − | 0.316646i | 0.0355369 | − | 0.00243574i | ||||
\(131\) | −76.2899 | − | 76.2899i | −0.582365 | − | 0.582365i | 0.353187 | − | 0.935553i | \(-0.385098\pi\) |
−0.935553 | + | 0.353187i | \(0.885098\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 45.9098 | + | 45.9098i | 0.345186 | + | 0.345186i | ||||
\(134\) | −84.5917 | − | 73.7394i | −0.631281 | − | 0.550294i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −147.508 | + | 30.7166i | −1.08462 | + | 0.225857i | ||||
\(137\) | 73.0194i | 0.532988i | 0.963837 | + | 0.266494i | \(0.0858653\pi\) | ||||
−0.963837 | + | 0.266494i | \(0.914135\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.5250 | − | 16.5250i | 0.118885 | − | 0.118885i | −0.645162 | − | 0.764046i | \(-0.723210\pi\) |
0.764046 | + | 0.645162i | \(0.223210\pi\) | |||||||
\(140\) | −4.00493 | − | 3.03528i | −0.0286066 | − | 0.0216806i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −125.759 | + | 8.61969i | −0.885629 | + | 0.0607021i | ||||
\(143\) | − | 22.4814i | − | 0.157213i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.67507 | −0.0667246 | ||||||||
\(146\) | 10.3193 | + | 150.557i | 0.0706804 | + | 1.03121i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −155.177 | − | 117.607i | −1.04849 | − | 0.794640i | ||||
\(149\) | −22.0334 | − | 22.0334i | −0.147875 | − | 0.147875i | 0.629293 | − | 0.777168i | \(-0.283344\pi\) |
−0.777168 | + | 0.629293i | \(0.783344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −161.017 | −1.06634 | −0.533168 | − | 0.846010i | \(-0.678999\pi\) | ||||
−0.533168 | + | 0.846010i | \(0.678999\pi\) | |||||||
\(152\) | −111.332 | − | 72.9565i | −0.732448 | − | 0.479977i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −16.0312 | + | 18.3905i | −0.104099 | + | 0.119419i | ||||
\(155\) | 8.18836 | − | 8.18836i | 0.0528281 | − | 0.0528281i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −151.888 | + | 151.888i | −0.967441 | + | 0.967441i | −0.999486 | − | 0.0320455i | \(-0.989798\pi\) |
0.0320455 | + | 0.999486i | \(0.489798\pi\) | |||||||
\(158\) | −8.09058 | − | 118.040i | −0.0512062 | − | 0.747086i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.30678 | + | 4.41820i | 0.0581674 | + | 0.0276137i | ||||
\(161\) | 138.276 | 0.858856 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −186.334 | − | 186.334i | −1.14315 | − | 1.14315i | −0.987870 | − | 0.155283i | \(-0.950371\pi\) |
−0.155283 | − | 0.987870i | \(-0.549629\pi\) | |||||||
\(164\) | 24.0713 | + | 174.772i | 0.146776 | + | 1.06568i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 151.837 | + | 132.358i | 0.914682 | + | 0.797338i | ||||
\(167\) | 199.590 | 1.19515 | 0.597576 | − | 0.801813i | \(-0.296131\pi\) | ||||
0.597576 | + | 0.801813i | \(0.296131\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 117.280i | 0.693966i | ||||||||
\(170\) | 9.14145 | + | 7.96870i | 0.0537732 | + | 0.0468747i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −96.7022 | + | 127.594i | −0.562222 | + | 0.741828i | ||||
\(173\) | 138.631 | − | 138.631i | 0.801333 | − | 0.801333i | −0.181971 | − | 0.983304i | \(-0.558248\pi\) |
0.983304 | + | 0.181971i | \(0.0582477\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 97.1504i | − | 0.555145i | ||||||
\(176\) | 24.4895 | − | 43.6112i | 0.139145 | − | 0.247791i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −20.6060 | − | 300.637i | −0.115764 | − | 1.68897i | ||||
\(179\) | 148.572 | + | 148.572i | 0.830010 | + | 0.830010i | 0.987518 | − | 0.157508i | \(-0.0503458\pi\) |
−0.157508 | + | 0.987518i | \(0.550346\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 99.6006 | + | 99.6006i | 0.550280 | + | 0.550280i | 0.926522 | − | 0.376242i | \(-0.122784\pi\) |
−0.376242 | + | 0.926522i | \(0.622784\pi\) | |||||||
\(182\) | −36.8806 | + | 42.3083i | −0.202641 | + | 0.232463i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −277.530 | + | 57.7918i | −1.50831 | + | 0.314086i | ||||
\(185\) | 15.6714i | 0.0847101i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 41.6318 | − | 41.6318i | 0.222630 | − | 0.222630i | ||||
\(188\) | −17.9449 | − | 130.291i | −0.0954516 | − | 0.693037i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.732584 | + | 10.6882i | 0.00385571 | + | 0.0562539i | ||||
\(191\) | − | 149.517i | − | 0.782812i | −0.920218 | − | 0.391406i | \(-0.871989\pi\) | ||
0.920218 | − | 0.391406i | \(-0.128011\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −52.8254 | −0.273707 | −0.136853 | − | 0.990591i | \(-0.543699\pi\) | ||||
−0.136853 | + | 0.990591i | \(0.543699\pi\) | |||||||
\(194\) | −102.876 | + | 7.05123i | −0.530288 | + | 0.0363466i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −133.828 | + | 18.4321i | −0.682797 | + | 0.0940412i | ||||
\(197\) | 108.072 | + | 108.072i | 0.548590 | + | 0.548590i | 0.926033 | − | 0.377443i | \(-0.123197\pi\) |
−0.377443 | + | 0.926033i | \(0.623197\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.24707 | −0.0112918 | −0.00564590 | − | 0.999984i | \(-0.501797\pi\) | ||||
−0.00564590 | + | 0.999984i | \(0.501797\pi\) | |||||||
\(200\) | 40.6036 | + | 194.988i | 0.203018 | + | 0.974940i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 297.242 | + | 259.109i | 1.47149 | + | 1.28272i | ||||
\(203\) | 82.9212 | − | 82.9212i | 0.408479 | − | 0.408479i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.0406 | − | 10.0406i | 0.0489787 | − | 0.0489787i | ||||
\(206\) | −135.620 | + | 9.29556i | −0.658349 | + | 0.0451241i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 56.3395 | − | 100.330i | 0.270863 | − | 0.482356i | ||||
\(209\) | 52.0124 | 0.248863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 50.4041 | + | 50.4041i | 0.238882 | + | 0.238882i | 0.816387 | − | 0.577505i | \(-0.195974\pi\) |
−0.577505 | + | 0.816387i | \(0.695974\pi\) | |||||||
\(212\) | −190.005 | − | 144.002i | −0.896249 | − | 0.679256i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 241.243 | − | 276.746i | 1.12730 | − | 1.29321i | ||||
\(215\) | 12.8858 | 0.0599339 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 140.358i | 0.646812i | ||||||||
\(218\) | −56.0026 | + | 64.2445i | −0.256893 | + | 0.294699i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.98802 | + | 0.549268i | −0.0181274 | + | 0.00249667i | ||||
\(221\) | 95.7760 | − | 95.7760i | 0.433376 | − | 0.433376i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 230.340i | − | 1.03291i | −0.856313 | − | 0.516457i | \(-0.827251\pi\) | ||
0.856313 | − | 0.516457i | \(-0.172749\pi\) | |||||||
\(224\) | −117.631 | + | 41.8981i | −0.525140 | + | 0.187045i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.1968 | − | 0.698898i | 0.0451184 | − | 0.00309247i | ||||
\(227\) | −12.1395 | − | 12.1395i | −0.0534779 | − | 0.0534779i | 0.679862 | − | 0.733340i | \(-0.262040\pi\) |
−0.733340 | + | 0.679862i | \(0.762040\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 39.1259 | + | 39.1259i | 0.170855 | + | 0.170855i | 0.787355 | − | 0.616500i | \(-0.211450\pi\) |
−0.616500 | + | 0.787355i | \(0.711450\pi\) | |||||||
\(230\) | 17.1992 | + | 14.9927i | 0.0747792 | + | 0.0651858i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −131.772 | + | 201.086i | −0.567985 | + | 0.866748i | ||||
\(233\) | − | 36.6784i | − | 0.157418i | −0.996898 | − | 0.0787090i | \(-0.974920\pi\) | ||
0.996898 | − | 0.0787090i | \(-0.0250798\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.48518 | + | 7.48518i | −0.0318518 | + | 0.0318518i | ||||
\(236\) | −228.905 | + | 302.031i | −0.969937 | + | 1.27979i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −146.644 | + | 10.0512i | −0.616152 | + | 0.0422318i | ||||
\(239\) | 147.098i | 0.615474i | 0.951471 | + | 0.307737i | \(0.0995717\pi\) | ||||
−0.951471 | + | 0.307737i | \(0.900428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 205.488 | 0.852649 | 0.426324 | − | 0.904570i | \(-0.359808\pi\) | ||||
0.426324 | + | 0.904570i | \(0.359808\pi\) | |||||||
\(242\) | −15.2117 | − | 221.935i | −0.0628582 | − | 0.917086i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 59.3600 | − | 78.3229i | 0.243278 | − | 0.320996i | ||||
\(245\) | 7.68839 | + | 7.68839i | 0.0313812 | + | 0.0313812i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 119.657 | 0.484442 | ||||||||
\(248\) | −58.6622 | − | 281.710i | −0.236541 | − | 1.13593i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 21.1112 | − | 24.2181i | 0.0844447 | − | 0.0968724i | ||||
\(251\) | 55.4867 | − | 55.4867i | 0.221063 | − | 0.221063i | −0.587883 | − | 0.808946i | \(-0.700039\pi\) |
0.808946 | + | 0.587883i | \(0.200039\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 78.3282 | − | 78.3282i | 0.309598 | − | 0.309598i | ||||
\(254\) | 16.8525 | + | 245.873i | 0.0663483 | + | 0.968005i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 218.584 | − | 133.256i | 0.853842 | − | 0.520532i | ||||
\(257\) | −142.878 | −0.555944 | −0.277972 | − | 0.960589i | \(-0.589662\pi\) | ||||
−0.277972 | + | 0.960589i | \(0.589662\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −134.313 | − | 134.313i | −0.518583 | − | 0.518583i | ||||
\(260\) | −9.17466 | + | 1.26362i | −0.0352872 | + | 0.00486008i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 162.656 | + | 141.789i | 0.620825 | + | 0.541180i | ||||
\(263\) | −242.691 | −0.922780 | −0.461390 | − | 0.887197i | \(-0.652649\pi\) | ||||
−0.461390 | + | 0.887197i | \(0.652649\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.1886i | 0.0724099i | ||||||||
\(266\) | −97.8833 | − | 85.3259i | −0.367982 | − | 0.320774i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 178.872 | + | 135.565i | 0.667433 | + | 0.505839i | ||||
\(269\) | −292.665 | + | 292.665i | −1.08797 | + | 1.08797i | −0.0922353 | + | 0.995737i | \(0.529401\pi\) |
−0.995737 | + | 0.0922353i | \(0.970599\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 258.180i | 0.952694i | 0.879257 | + | 0.476347i | \(0.158039\pi\) | ||||
−0.879257 | + | 0.476347i | \(0.841961\pi\) | |||||||
\(272\) | 290.125 | − | 81.4629i | 1.06664 | − | 0.299496i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.98625 | − | 145.697i | −0.0364462 | − | 0.531741i | ||||
\(275\) | −55.0322 | − | 55.0322i | −0.200117 | − | 0.200117i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 63.2023 | + | 63.2023i | 0.228167 | + | 0.228167i | 0.811927 | − | 0.583759i | \(-0.198419\pi\) |
−0.583759 | + | 0.811927i | \(0.698419\pi\) | |||||||
\(278\) | −30.7126 | + | 35.2325i | −0.110477 | + | 0.126736i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.40622 | + | 5.50864i | 0.0300222 | + | 0.0196737i | ||||
\(281\) | − | 421.406i | − | 1.49966i | −0.661628 | − | 0.749832i | \(-0.730134\pi\) | ||
0.661628 | − | 0.749832i | \(-0.269866\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 275.707 | − | 275.707i | 0.974229 | − | 0.974229i | −0.0254475 | − | 0.999676i | \(-0.508101\pi\) |
0.999676 | + | 0.0254475i | \(0.00810107\pi\) | |||||||
\(284\) | 249.751 | − | 34.3981i | 0.879405 | − | 0.121120i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.07459 | + | 44.8576i | 0.0107503 | + | 0.156845i | ||||
\(287\) | 172.108i | 0.599681i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 65.7217 | 0.227411 | ||||||||
\(290\) | 19.3049 | − | 1.32318i | 0.0665685 | − | 0.00456268i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −41.1807 | − | 298.997i | −0.141030 | − | 1.02396i | ||||
\(293\) | 181.330 | + | 181.330i | 0.618873 | + | 0.618873i | 0.945242 | − | 0.326369i | \(-0.105825\pi\) |
−0.326369 | + | 0.945242i | \(0.605825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.5021 | 0.103397 | ||||||||
\(296\) | 325.712 | + | 213.441i | 1.10038 | + | 0.721083i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 46.9769 | + | 40.9503i | 0.157641 | + | 0.137417i | ||||
\(299\) | 180.198 | − | 180.198i | 0.602669 | − | 0.602669i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −110.439 | + | 110.439i | −0.366907 | + | 0.366907i | ||||
\(302\) | 321.280 | − | 22.0209i | 1.06384 | − | 0.0729169i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 232.121 | + | 130.345i | 0.763555 | + | 0.428768i | ||||
\(305\) | −7.90985 | −0.0259339 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 279.027 | + | 279.027i | 0.908883 | + | 0.908883i | 0.996182 | − | 0.0872996i | \(-0.0278237\pi\) |
−0.0872996 | + | 0.996182i | \(0.527824\pi\) | |||||||
\(308\) | 29.4722 | − | 38.8873i | 0.0956890 | − | 0.126258i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.2185 | + | 17.4582i | −0.0490920 | + | 0.0563169i | ||||
\(311\) | −414.511 | −1.33283 | −0.666417 | − | 0.745579i | \(-0.732173\pi\) | ||||
−0.666417 | + | 0.745579i | \(0.732173\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 331.008i | − | 1.05753i | −0.848767 | − | 0.528767i | \(-0.822654\pi\) | ||
0.848767 | − | 0.528767i | \(-0.177346\pi\) | |||||||
\(314\) | 282.293 | − | 323.838i | 0.899022 | − | 1.03133i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 32.2866 | + | 234.420i | 0.102173 | + | 0.741836i | ||||
\(317\) | −194.563 | + | 194.563i | −0.613764 | + | 0.613764i | −0.943925 | − | 0.330161i | \(-0.892897\pi\) |
0.330161 | + | 0.943925i | \(0.392897\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 93.9437i | − | 0.294494i | ||||||
\(320\) | −19.1742 | − | 7.54290i | −0.0599195 | − | 0.0235716i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −275.904 | + | 18.9108i | −0.856846 | + | 0.0587293i | ||||
\(323\) | 221.585 | + | 221.585i | 0.686021 | + | 0.686021i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −126.604 | − | 126.604i | −0.389552 | − | 0.389552i | ||||
\(326\) | 397.279 | + | 346.312i | 1.21865 | + | 1.06231i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −71.9320 | − | 345.434i | −0.219305 | − | 1.05315i | ||||
\(329\) | − | 128.305i | − | 0.389985i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −462.054 | + | 462.054i | −1.39593 | + | 1.39593i | −0.584641 | + | 0.811292i | \(0.698765\pi\) |
−0.811292 | + | 0.584641i | \(0.801235\pi\) | |||||||
\(332\) | −321.065 | − | 243.331i | −0.967063 | − | 0.732925i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −398.246 | + | 27.2963i | −1.19235 | + | 0.0817254i | ||||
\(335\) | − | 18.0643i | − | 0.0539233i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −472.439 | −1.40190 | −0.700948 | − | 0.713212i | \(-0.747240\pi\) | ||||
−0.700948 | + | 0.713212i | \(0.747240\pi\) | |||||||
\(338\) | −16.0394 | − | 234.012i | −0.0474540 | − | 0.692342i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −19.3299 | − | 14.6499i | −0.0568527 | − | 0.0430879i | ||||
\(341\) | 79.5078 | + | 79.5078i | 0.233161 | + | 0.233161i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −322.996 | −0.941679 | ||||||||
\(344\) | 175.502 | − | 267.817i | 0.510179 | − | 0.778537i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −257.653 | + | 295.572i | −0.744662 | + | 0.854253i | ||||
\(347\) | 92.8976 | − | 92.8976i | 0.267716 | − | 0.267716i | −0.560463 | − | 0.828179i | \(-0.689377\pi\) |
0.828179 | + | 0.560463i | \(0.189377\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 264.708 | − | 264.708i | 0.758475 | − | 0.758475i | −0.217570 | − | 0.976045i | \(-0.569813\pi\) |
0.976045 | + | 0.217570i | \(0.0698129\pi\) | |||||||
\(350\) | 13.2864 | + | 193.846i | 0.0379613 | + | 0.553846i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −42.9001 | + | 90.3676i | −0.121875 | + | 0.256726i | ||||
\(353\) | −413.360 | −1.17099 | −0.585495 | − | 0.810676i | \(-0.699100\pi\) | ||||
−0.585495 | + | 0.810676i | \(0.699100\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.3481 | − | 14.3481i | −0.0404173 | − | 0.0404173i | ||||
\(356\) | 82.2311 | + | 597.048i | 0.230986 | + | 1.67710i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −316.767 | − | 276.129i | −0.884824 | − | 0.771311i | ||||
\(359\) | −625.198 | −1.74150 | −0.870749 | − | 0.491728i | \(-0.836365\pi\) | ||||
−0.870749 | + | 0.491728i | \(0.836365\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 84.1643i | − | 0.233142i | ||||||
\(362\) | −212.357 | − | 185.113i | −0.586620 | − | 0.511363i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 67.8024 | − | 89.4624i | 0.186270 | − | 0.245776i | ||||
\(365\) | −17.1773 | + | 17.1773i | −0.0470611 | + | 0.0470611i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 601.904i | 1.64007i | 0.572316 | + | 0.820033i | \(0.306045\pi\) | ||||
−0.572316 | + | 0.820033i | \(0.693955\pi\) | |||||||
\(368\) | 545.857 | − | 153.269i | 1.48331 | − | 0.416491i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.14324 | − | 31.2694i | −0.00579254 | − | 0.0845118i | ||||
\(371\) | −164.458 | − | 164.458i | −0.443283 | − | 0.443283i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −493.026 | − | 493.026i | −1.32179 | − | 1.32179i | −0.912330 | − | 0.409455i | \(-0.865719\pi\) |
−0.409455 | − | 0.912330i | \(-0.634281\pi\) | |||||||
\(374\) | −77.3750 | + | 88.7622i | −0.206885 | + | 0.237332i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 53.6246 | + | 257.518i | 0.142619 | + | 0.684888i | ||||
\(377\) | − | 216.122i | − | 0.573269i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −144.970 | + | 144.970i | −0.382506 | + | 0.382506i | −0.872004 | − | 0.489498i | \(-0.837180\pi\) |
0.489498 | + | 0.872004i | \(0.337180\pi\) | |||||||
\(380\) | −2.92348 | − | 21.2262i | −0.00769337 | − | 0.0558585i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.4482 | + | 298.334i | 0.0535293 | + | 0.780979i | ||||
\(383\) | 417.764i | 1.09077i | 0.838187 | + | 0.545384i | \(0.183616\pi\) | ||||
−0.838187 | + | 0.545384i | \(0.816384\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.92724 | −0.0102006 | ||||||||
\(386\) | 105.403 | − | 7.22448i | 0.273066 | − | 0.0187163i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 204.306 | − | 28.1389i | 0.526561 | − | 0.0725230i | ||||
\(389\) | 144.751 | + | 144.751i | 0.372109 | + | 0.372109i | 0.868245 | − | 0.496136i | \(-0.165248\pi\) |
−0.496136 | + | 0.868245i | \(0.665248\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 667.392 | 1.70689 | ||||||||
\(392\) | 264.509 | − | 55.0804i | 0.674768 | − | 0.140511i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −230.418 | − | 200.858i | −0.584819 | − | 0.509793i | ||||
\(395\) | 13.4674 | − | 13.4674i | 0.0340946 | − | 0.0340946i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −105.531 | + | 105.531i | −0.265822 | + | 0.265822i | −0.827414 | − | 0.561592i | \(-0.810189\pi\) |
0.561592 | + | 0.827414i | \(0.310189\pi\) | |||||||
\(398\) | 4.48362 | − | 0.307313i | 0.0112654 | − | 0.000772142i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −107.684 | − | 383.510i | −0.269210 | − | 0.958776i | ||||
\(401\) | −529.383 | −1.32016 | −0.660078 | − | 0.751197i | \(-0.729477\pi\) | ||||
−0.660078 | + | 0.751197i | \(0.729477\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 182.912 | + | 182.912i | 0.453876 | + | 0.453876i | ||||
\(404\) | −628.529 | − | 476.354i | −1.55576 | − | 1.17909i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −154.114 | + | 176.795i | −0.379591 | + | 0.435455i | ||||
\(407\) | −152.167 | −0.373874 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 371.204i | − | 0.907590i | −0.891106 | − | 0.453795i | \(-0.850070\pi\) | ||
0.891106 | − | 0.453795i | \(-0.149930\pi\) | |||||||
\(410\) | −18.6611 | + | 21.4074i | −0.0455148 | + | 0.0522132i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 269.334 | − | 37.0952i | 0.653723 | − | 0.0900369i | ||||
\(413\) | −261.422 | + | 261.422i | −0.632982 | + | 0.632982i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.4244i | 0.0781311i | ||||||||
\(416\) | −98.6940 | + | 207.895i | −0.237245 | + | 0.499748i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −103.781 | + | 7.11330i | −0.248281 | + | 0.0170175i | ||||
\(419\) | 124.486 | + | 124.486i | 0.297103 | + | 0.297103i | 0.839878 | − | 0.542775i | \(-0.182626\pi\) |
−0.542775 | + | 0.839878i | \(0.682626\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 51.7267 | + | 51.7267i | 0.122866 | + | 0.122866i | 0.765866 | − | 0.643000i | \(-0.222310\pi\) |
−0.643000 | + | 0.765866i | \(0.722310\pi\) | |||||||
\(422\) | −107.465 | − | 93.6788i | −0.254658 | − | 0.221988i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 398.814 | + | 261.345i | 0.940599 | + | 0.616379i | ||||
\(425\) | − | 468.899i | − | 1.10329i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 67.7922 | − | 67.7922i | 0.158764 | − | 0.158764i | ||||
\(428\) | −443.508 | + | 585.189i | −1.03623 | + | 1.36727i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −25.7112 | + | 1.76228i | −0.0597936 | + | 0.00409833i | ||||
\(431\) | − | 424.978i | − | 0.986029i | −0.870021 | − | 0.493014i | \(-0.835895\pi\) | ||
0.870021 | − | 0.493014i | \(-0.164105\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 283.151 | 0.653927 | 0.326964 | − | 0.945037i | \(-0.393975\pi\) | ||||
0.326964 | + | 0.945037i | \(0.393975\pi\) | |||||||
\(434\) | −19.1956 | − | 280.059i | −0.0442295 | − | 0.645298i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 102.957 | − | 135.847i | 0.236140 | − | 0.311576i | ||||
\(437\) | 416.901 | + | 416.901i | 0.954008 | + | 0.954008i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −701.459 | −1.59786 | −0.798928 | − | 0.601427i | \(-0.794599\pi\) | ||||
−0.798928 | + | 0.601427i | \(0.794599\pi\) | |||||||
\(440\) | 7.88226 | − | 1.64137i | 0.0179142 | − | 0.00373040i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −178.005 | + | 204.202i | −0.402727 | + | 0.461996i | ||||
\(443\) | 272.651 | − | 272.651i | 0.615464 | − | 0.615464i | −0.328900 | − | 0.944365i | \(-0.606678\pi\) |
0.944365 | + | 0.328900i | \(0.106678\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 34.3002 | − | 34.3002i | 0.0770792 | − | 0.0770792i | ||||
\(446\) | 31.5016 | + | 459.601i | 0.0706314 | + | 1.03050i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 228.982 | − | 99.6875i | 0.511120 | − | 0.222517i | ||||
\(449\) | 614.711 | 1.36907 | 0.684534 | − | 0.728981i | \(-0.260006\pi\) | ||||
0.684534 | + | 0.728981i | \(0.260006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 97.4931 | + | 97.4931i | 0.216171 | + | 0.216171i | ||||
\(452\) | −20.2502 | + | 2.78905i | −0.0448013 | + | 0.00617046i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 25.8823 | + | 22.5619i | 0.0570096 | + | 0.0496959i | ||||
\(455\) | −9.03482 | −0.0198567 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 117.859i | − | 0.257898i | −0.991651 | − | 0.128949i | \(-0.958840\pi\) | ||
0.991651 | − | 0.128949i | \(-0.0411603\pi\) | |||||||
\(458\) | −83.4195 | − | 72.7177i | −0.182139 | − | 0.158772i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −36.3683 | − | 27.5631i | −0.0790616 | − | 0.0599198i | ||||
\(461\) | 262.235 | − | 262.235i | 0.568839 | − | 0.568839i | −0.362964 | − | 0.931803i | \(-0.618235\pi\) |
0.931803 | + | 0.362964i | \(0.118235\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 192.234i | 0.415192i | 0.978215 | + | 0.207596i | \(0.0665640\pi\) | ||||
−0.978215 | + | 0.207596i | \(0.933436\pi\) | |||||||
\(464\) | 235.427 | − | 419.251i | 0.507386 | − | 0.903559i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.01619 | + | 73.1851i | 0.0107644 | + | 0.157049i | ||||
\(467\) | 529.169 | + | 529.169i | 1.13312 | + | 1.13312i | 0.989655 | + | 0.143470i | \(0.0458259\pi\) |
0.143470 | + | 0.989655i | \(0.454174\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 154.822 | + | 154.822i | 0.330111 | + | 0.330111i | ||||
\(470\) | 13.9116 | − | 15.9590i | 0.0295992 | − | 0.0339553i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 415.433 | − | 633.953i | 0.880154 | − | 1.34312i | ||||
\(473\) | 125.119i | 0.264523i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 292.908 | − | 292.908i | 0.616649 | − | 0.616649i | ||||
\(476\) | 291.227 | − | 40.1106i | 0.611822 | − | 0.0842660i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.1174 | − | 293.508i | −0.0420866 | − | 0.614033i | ||||
\(479\) | − | 1.43750i | − | 0.00300104i | −0.999999 | − | 0.00150052i | \(-0.999522\pi\) | ||
0.999999 | − | 0.00150052i | \(-0.000477630\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −350.068 | −0.727792 | ||||||||
\(482\) | −410.015 | + | 28.1029i | −0.850653 | + | 0.0583048i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 60.7043 | + | 440.751i | 0.125422 | + | 0.910642i | ||||
\(485\) | −11.7373 | − | 11.7373i | −0.0242006 | − | 0.0242006i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 701.238 | 1.43991 | 0.719957 | − | 0.694019i | \(-0.244162\pi\) | ||||
0.719957 | + | 0.694019i | \(0.244162\pi\) | |||||||
\(488\) | −107.730 | + | 164.397i | −0.220759 | + | 0.336880i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.3923 | − | 14.2893i | −0.0334536 | − | 0.0291619i | ||||
\(491\) | 519.668 | − | 519.668i | 1.05839 | − | 1.05839i | 0.0602007 | − | 0.998186i | \(-0.480826\pi\) |
0.998186 | − | 0.0602007i | \(-0.0191741\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 400.222 | − | 400.222i | 0.811809 | − | 0.811809i | ||||
\(494\) | −238.754 | + | 16.3645i | −0.483308 | + | 0.0331265i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 155.577 | + | 554.077i | 0.313663 | + | 1.11709i | ||||
\(497\) | 245.944 | 0.494858 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 359.284 | + | 359.284i | 0.720009 | + | 0.720009i | 0.968607 | − | 0.248598i | \(-0.0799698\pi\) |
−0.248598 | + | 0.968607i | \(0.579970\pi\) | |||||||
\(500\) | −38.8114 | + | 51.2100i | −0.0776228 | + | 0.102420i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −103.125 | + | 118.302i | −0.205429 | + | 0.235662i | ||||
\(503\) | 174.376 | 0.346671 | 0.173335 | − | 0.984863i | \(-0.444546\pi\) | ||||
0.173335 | + | 0.984863i | \(0.444546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 63.4752i | 0.125693i | ||||||||
\(506\) | −145.577 | + | 167.002i | −0.287702 | + | 0.330043i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −67.2521 | − | 488.291i | −0.132386 | − | 0.961203i | ||||
\(509\) | 314.247 | − | 314.247i | 0.617381 | − | 0.617381i | −0.327478 | − | 0.944859i | \(-0.606199\pi\) |
0.944859 | + | 0.327478i | \(0.106199\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 294.440i | − | 0.576203i | ||||||
\(512\) | −417.920 | + | 295.782i | −0.816249 | + | 0.577700i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 285.086 | − | 19.5402i | 0.554643 | − | 0.0380159i | ||||
\(515\) | −15.4732 | − | 15.4732i | −0.0300450 | − | 0.0300450i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −72.6801 | − | 72.6801i | −0.140580 | − | 0.140580i | ||||
\(518\) | 286.366 | + | 249.628i | 0.552830 | + | 0.481908i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 18.1336 | − | 3.77607i | 0.0348722 | − | 0.00726167i | ||||
\(521\) | − | 468.678i | − | 0.899575i | −0.893136 | − | 0.449787i | \(-0.851500\pi\) | ||
0.893136 | − | 0.449787i | \(-0.148500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −417.239 | + | 417.239i | −0.797780 | + | 0.797780i | −0.982745 | − | 0.184965i | \(-0.940783\pi\) |
0.184965 | + | 0.982745i | \(0.440783\pi\) | |||||||
\(524\) | −343.942 | − | 260.669i | −0.656378 | − | 0.497460i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 484.246 | − | 33.1908i | 0.920620 | − | 0.0631004i | ||||
\(527\) | 677.443i | 1.28547i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 726.667 | 1.37366 | ||||||||
\(530\) | −2.62427 | − | 38.2874i | −0.00495144 | − | 0.0722404i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 206.978 | + | 156.866i | 0.389056 | + | 0.294860i | ||||
\(533\) | 224.288 | + | 224.288i | 0.420803 | + | 0.420803i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 59.0984 | 0.110464 | ||||||||
\(536\) | −375.447 | − | 246.032i | −0.700460 | − | 0.459015i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 543.934 | − | 623.984i | 1.01103 | − | 1.15982i | ||||
\(539\) | −74.6533 | + | 74.6533i | −0.138503 | + | 0.138503i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −163.152 | + | 163.152i | −0.301574 | + | 0.301574i | −0.841629 | − | 0.540055i | \(-0.818403\pi\) |
0.540055 | + | 0.841629i | \(0.318403\pi\) | |||||||
\(542\) | −35.3091 | − | 515.152i | −0.0651460 | − | 0.950464i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −567.751 | + | 202.222i | −1.04366 | + | 0.371732i | ||||
\(545\) | −13.7192 | −0.0251729 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −595.267 | − | 595.267i | −1.08824 | − | 1.08824i | −0.995710 | − | 0.0925300i | \(-0.970505\pi\) |
−0.0925300 | − | 0.995710i | \(-0.529495\pi\) | |||||||
\(548\) | 39.8515 | + | 289.346i | 0.0727217 | + | 0.528004i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 117.333 | + | 102.280i | 0.213333 | + | 0.185964i | ||||
\(551\) | 500.015 | 0.907468 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 230.847i | 0.417445i | ||||||||
\(554\) | −134.752 | − | 117.465i | −0.243235 | − | 0.212031i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 56.4629 | − | 74.5004i | 0.101552 | − | 0.133994i | ||||
\(557\) | −370.177 | + | 370.177i | −0.664590 | + | 0.664590i | −0.956459 | − | 0.291868i | \(-0.905723\pi\) |
0.291868 | + | 0.956459i | \(0.405723\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 287.843i | 0.514926i | ||||||||
\(560\) | −17.5265 | − | 9.84184i | −0.0312973 | − | 0.0175747i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 57.6321 | + | 840.839i | 0.102548 | + | 1.49615i | ||||
\(563\) | −426.543 | − | 426.543i | −0.757625 | − | 0.757625i | 0.218264 | − | 0.975890i | \(-0.429960\pi\) |
−0.975890 | + | 0.218264i | \(0.929960\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.16337 | + | 1.16337i | 0.00205906 | + | 0.00205906i | ||||
\(566\) | −512.417 | + | 587.829i | −0.905330 | + | 1.03857i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −493.628 | + | 102.791i | −0.869064 | + | 0.180971i | ||||
\(569\) | 291.547i | 0.512385i | 0.966626 | + | 0.256192i | \(0.0824680\pi\) | ||||
−0.966626 | + | 0.256192i | \(0.917532\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 569.328 | − | 569.328i | 0.997071 | − | 0.997071i | −0.00292477 | − | 0.999996i | \(-0.500931\pi\) |
0.999996 | + | 0.00292477i | \(0.000930984\pi\) | |||||||
\(572\) | −12.2696 | − | 89.0847i | −0.0214503 | − | 0.155743i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −23.5378 | − | 343.411i | −0.0410066 | − | 0.598277i | ||||
\(575\) | − | 882.212i | − | 1.53428i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −360.847 | −0.625385 | −0.312692 | − | 0.949854i | \(-0.601231\pi\) | ||||
−0.312692 | + | 0.949854i | \(0.601231\pi\) | |||||||
\(578\) | −131.136 | + | 8.98820i | −0.226878 | + | 0.0155505i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −38.3384 | + | 5.28032i | −0.0661006 | + | 0.00910401i | ||||
\(581\) | −277.897 | − | 277.897i | −0.478308 | − | 0.478308i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −186.319 | −0.319586 | ||||||||
\(584\) | 123.060 | + | 590.963i | 0.210719 | + | 1.01192i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −386.610 | − | 337.012i | −0.659744 | − | 0.575106i | ||||
\(587\) | −373.439 | + | 373.439i | −0.636183 | + | 0.636183i | −0.949612 | − | 0.313429i | \(-0.898522\pi\) |
0.313429 | + | 0.949612i | \(0.398522\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −423.180 | + | 423.180i | −0.718472 | + | 0.718472i | ||||
\(590\) | −60.8615 | + | 4.17152i | −0.103155 | + | 0.00707037i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −679.089 | − | 381.337i | −1.14711 | − | 0.644151i | ||||
\(593\) | 608.053 | 1.02538 | 0.512692 | − | 0.858572i | \(-0.328648\pi\) | ||||
0.512692 | + | 0.858572i | \(0.328648\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.7309 | − | 16.7309i | −0.0281192 | − | 0.0281192i | ||||
\(596\) | −99.3343 | − | 75.2842i | −0.166668 | − | 0.126316i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −334.909 | + | 384.197i | −0.560048 | + | 0.642470i | ||||
\(599\) | 211.563 | 0.353194 | 0.176597 | − | 0.984283i | \(-0.443491\pi\) | ||||
0.176597 | + | 0.984283i | \(0.443491\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 343.381i | 0.571349i | 0.958327 | + | 0.285674i | \(0.0922176\pi\) | ||||
−0.958327 | + | 0.285674i | \(0.907782\pi\) | |||||||
\(602\) | 205.257 | − | 235.465i | 0.340959 | − | 0.391137i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −638.043 | + | 87.8774i | −1.05636 | + | 0.145492i | ||||
\(605\) | 25.3210 | − | 25.3210i | 0.0418529 | − | 0.0418529i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1006.23i | − | 1.65771i | −0.559461 | − | 0.828856i | \(-0.688992\pi\) | ||
0.559461 | − | 0.828856i | \(-0.311008\pi\) | |||||||
\(608\) | −480.981 | − | 228.336i | −0.791087 | − | 0.375552i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.7827 | − | 1.08176i | 0.0258732 | − | 0.00177338i | ||||
\(611\) | −167.204 | − | 167.204i | −0.273657 | − | 0.273657i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 380.705 | + | 380.705i | 0.621052 | + | 0.621052i | 0.945801 | − | 0.324748i | \(-0.105280\pi\) |
−0.324748 | + | 0.945801i | \(0.605280\pi\) | |||||||
\(614\) | −594.908 | − | 518.587i | −0.968905 | − | 0.844605i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −53.4882 | + | 81.6233i | −0.0868314 | + | 0.132505i | ||||
\(617\) | 693.808i | 1.12449i | 0.826972 | + | 0.562243i | \(0.190061\pi\) | ||||
−0.826972 | + | 0.562243i | \(0.809939\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −619.279 | + | 619.279i | −1.00045 | + | 1.00045i | −0.000450619 | 1.00000i | \(0.500143\pi\) | |
−1.00000 | 0.000450619i | \(0.999857\pi\) | ||||||||
\(620\) | 27.9782 | − | 36.9160i | 0.0451261 | − | 0.0595420i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 827.082 | − | 56.6892i | 1.32971 | − | 0.0911403i | ||||
\(623\) | 587.947i | 0.943736i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −617.237 | −0.987579 | ||||||||
\(626\) | 45.2692 | + | 660.467i | 0.0723151 | + | 1.05506i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −518.976 | + | 684.767i | −0.826394 | + | 1.09039i | ||||
\(629\) | −648.266 | − | 648.266i | −1.03063 | − | 1.03063i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1007.91 | −1.59732 | −0.798661 | − | 0.601781i | \(-0.794458\pi\) | ||||
−0.798661 | + | 0.601781i | \(0.794458\pi\) | |||||||
\(632\) | −96.4816 | − | 463.327i | −0.152661 | − | 0.733113i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 361.607 | − | 414.824i | 0.570358 | − | 0.654297i | ||||
\(635\) | −28.0522 | + | 28.0522i | −0.0441767 | + | 0.0441767i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −171.744 | + | 171.744i | −0.269613 | + | 0.269613i | ||||
\(638\) | 12.8479 | + | 187.448i | 0.0201377 | + | 0.293805i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 39.2903 | + | 12.4282i | 0.0613910 | + | 0.0194191i | ||||
\(641\) | −511.481 | −0.797943 | −0.398971 | − | 0.916963i | \(-0.630633\pi\) | ||||
−0.398971 | + | 0.916963i | \(0.630633\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −497.727 | − | 497.727i | −0.774071 | − | 0.774071i | 0.204745 | − | 0.978815i | \(-0.434364\pi\) |
−0.978815 | + | 0.204745i | \(0.934364\pi\) | |||||||
\(644\) | 547.931 | − | 75.4662i | 0.850824 | − | 0.117184i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −472.437 | − | 411.828i | −0.731326 | − | 0.637505i | ||||
\(647\) | 59.8694 | 0.0925339 | 0.0462669 | − | 0.998929i | \(-0.485268\pi\) | ||||
0.0462669 | + | 0.998929i | \(0.485268\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 296.172i | 0.456351i | ||||||||
\(650\) | 269.931 | + | 235.301i | 0.415278 | + | 0.362002i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −840.060 | − | 636.671i | −1.28844 | − | 0.976489i | ||||
\(653\) | 489.952 | − | 489.952i | 0.750310 | − | 0.750310i | −0.224227 | − | 0.974537i | \(-0.571986\pi\) |
0.974537 | + | 0.224227i | \(0.0719858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.7348i | 0.0530302i | ||||||||
\(656\) | 190.769 | + | 679.414i | 0.290807 | + | 1.03569i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 17.5472 | + | 256.009i | 0.0266675 | + | 0.389072i | ||||
\(659\) | 234.984 | + | 234.984i | 0.356577 | + | 0.356577i | 0.862549 | − | 0.505973i | \(-0.168866\pi\) |
−0.505973 | + | 0.862549i | \(0.668866\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 305.060 | + | 305.060i | 0.461512 | + | 0.461512i | 0.899151 | − | 0.437639i | \(-0.144185\pi\) |
−0.437639 | + | 0.899151i | \(0.644185\pi\) | |||||||
\(662\) | 858.753 | − | 985.136i | 1.29721 | − | 1.48812i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 673.905 | + | 441.614i | 1.01492 | + | 0.665081i | ||||
\(665\) | − | 20.9027i | − | 0.0314326i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 752.998 | − | 752.998i | 1.12893 | − | 1.12893i | ||||
\(668\) | 790.895 | − | 108.930i | 1.18397 | − | 0.163068i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.47050 | + | 36.0441i | 0.00368732 | + | 0.0537971i | ||||
\(671\) | − | 76.8036i | − | 0.114461i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 458.738 | 0.681632 | 0.340816 | − | 0.940130i | \(-0.389297\pi\) | ||||
0.340816 | + | 0.940130i | \(0.389297\pi\) | |||||||
\(674\) | 942.666 | − | 64.6115i | 1.39861 | − | 0.0958628i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 64.0076 | + | 464.734i | 0.0946858 | + | 0.687476i | ||||
\(677\) | 171.344 | + | 171.344i | 0.253094 | + | 0.253094i | 0.822238 | − | 0.569144i | \(-0.192725\pi\) |
−0.569144 | + | 0.822238i | \(0.692725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 201.192 | 0.296306 | ||||||||
\(680\) | 40.5729 | + | 26.5876i | 0.0596660 | + | 0.0390994i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −169.517 | − | 147.770i | −0.248559 | − | 0.216671i | ||||
\(683\) | −769.447 | + | 769.447i | −1.12657 | + | 1.12657i | −0.135838 | + | 0.990731i | \(0.543373\pi\) |
−0.990731 | + | 0.135838i | \(0.956627\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.6229 | − | 16.6229i | 0.0242670 | − | 0.0242670i | ||||
\(686\) | 644.480 | − | 44.1734i | 0.939475 | − | 0.0643927i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −313.555 | + | 558.382i | −0.455748 | + | 0.811601i | ||||
\(689\) | −428.636 | −0.622114 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.7951 | + | 44.7951i | 0.0648264 | + | 0.0648264i | 0.738777 | − | 0.673950i | \(-0.235404\pi\) |
−0.673950 | + | 0.738777i | \(0.735404\pi\) | |||||||
\(692\) | 473.677 | − | 624.996i | 0.684504 | − | 0.903174i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −172.655 | + | 198.065i | −0.248783 | + | 0.285396i | ||||
\(695\) | −7.52381 | −0.0108256 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 830.686i | 1.19180i | ||||||||
\(698\) | −491.975 | + | 564.378i | −0.704835 | + | 0.808565i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −53.0214 | − | 384.967i | −0.0757448 | − | 0.549954i | ||||
\(701\) | 31.7012 | − | 31.7012i | 0.0452229 | − | 0.0452229i | −0.684134 | − | 0.729357i | \(-0.739820\pi\) |
0.729357 | + | 0.684134i | \(0.239820\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 809.907i | − | 1.15207i | ||||||
\(704\) | 73.2406 | − | 186.179i | 0.104035 | − | 0.264459i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 824.784 | − | 56.5317i | 1.16825 | − | 0.0800732i | ||||
\(707\) | −544.021 | − | 544.021i | −0.769478 | − | 0.769478i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 256.706 | + | 256.706i | 0.362068 | + | 0.362068i | 0.864574 | − | 0.502506i | \(-0.167589\pi\) |
−0.502506 | + | 0.864574i | \(0.667589\pi\) | |||||||
\(710\) | 30.5914 | + | 26.6668i | 0.0430864 | + | 0.0375589i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −245.730 | − | 1180.05i | −0.345127 | − | 1.65738i | ||||
\(713\) | 1274.58i | 1.78763i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.11789 | + | 5.11789i | −0.00715789 | + | 0.00715789i | ||||
\(716\) | 669.815 | + | 507.644i | 0.935496 | + | 0.709000i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1247.47 | − | 85.5030i | 1.73742 | − | 0.119085i | ||||
\(719\) | − | 1368.29i | − | 1.90305i | −0.307574 | − | 0.951524i | \(-0.599517\pi\) | ||
0.307574 | − | 0.951524i | \(-0.400483\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 265.229 | 0.367862 | ||||||||
\(722\) | 11.5104 | + | 167.935i | 0.0159424 | + | 0.232596i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 449.035 | + | 340.318i | 0.620215 | + | 0.470053i | ||||
\(725\) | −529.045 | − | 529.045i | −0.729717 | − | 0.729717i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.5336 | 0.0516281 | 0.0258141 | − | 0.999667i | \(-0.491782\pi\) | ||||
0.0258141 | + | 0.999667i | \(0.491782\pi\) | |||||||
\(728\) | −123.052 | + | 187.779i | −0.169028 | + | 0.257938i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 31.9250 | − | 36.6234i | 0.0437329 | − | 0.0501691i | ||||
\(731\) | −533.037 | + | 533.037i | −0.729189 | + | 0.729189i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −385.216 | + | 385.216i | −0.525534 | + | 0.525534i | −0.919237 | − | 0.393704i | \(-0.871194\pi\) |
0.393704 | + | 0.919237i | \(0.371194\pi\) | |||||||
\(734\) | −82.3174 | − | 1200.99i | −0.112149 | − | 1.63623i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1068.20 | + | 380.472i | −1.45135 | + | 0.516945i | ||||
\(737\) | 175.402 | 0.237995 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −889.039 | − | 889.039i | −1.20303 | − | 1.20303i | −0.973240 | − | 0.229790i | \(-0.926196\pi\) |
−0.229790 | − | 0.973240i | \(-0.573804\pi\) | |||||||
\(740\) | 8.55289 | + | 62.0992i | 0.0115580 | + | 0.0839179i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 350.638 | + | 305.655i | 0.472557 | + | 0.411933i | ||||
\(743\) | 506.252 | 0.681362 | 0.340681 | − | 0.940179i | \(-0.389342\pi\) | ||||
0.340681 | + | 0.940179i | \(0.389342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0318i | 0.0134655i | ||||||||
\(746\) | 1051.17 | + | 916.317i | 1.40908 | + | 1.22831i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 142.248 | − | 187.691i | 0.190172 | − | 0.250924i | ||||
\(749\) | −506.509 | + | 506.509i | −0.676247 | + | 0.676247i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 456.844i | 0.608314i | 0.952622 | + | 0.304157i | \(0.0983748\pi\) | ||||
−0.952622 | + | 0.304157i | \(0.901625\pi\) | |||||||
\(752\) | −142.217 | − | 506.496i | −0.189118 | − | 0.673532i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 29.5572 | + | 431.233i | 0.0392006 | + | 0.571927i | ||||
\(755\) | 36.6554 | + | 36.6554i | 0.0485502 | + | 0.0485502i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −221.708 | − | 221.708i | −0.292877 | − | 0.292877i | 0.545339 | − | 0.838216i | \(-0.316401\pi\) |
−0.838216 | + | 0.545339i | \(0.816401\pi\) | |||||||
\(758\) | 269.434 | − | 309.087i | 0.355454 | − | 0.407766i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.73621 | + | 41.9533i | 0.0114950 | + | 0.0552017i | ||||
\(761\) | 205.900i | 0.270566i | 0.990807 | + | 0.135283i | \(0.0431943\pi\) | ||||
−0.990807 | + | 0.135283i | \(0.956806\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 117.582 | − | 117.582i | 0.154105 | − | 0.154105i | ||||
\(764\) | −81.6013 | − | 592.475i | −0.106808 | − | 0.775491i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −57.1340 | − | 833.572i | −0.0745875 | − | 1.08821i | ||||
\(767\) | 681.359i | 0.888342i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 900.133 | 1.17052 | 0.585262 | − | 0.810844i | \(-0.300992\pi\) | ||||
0.585262 | + | 0.810844i | \(0.300992\pi\) | |||||||
\(770\) | 7.83609 | − | 0.537095i | 0.0101767 | − | 0.000697526i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −209.325 | + | 28.8303i | −0.271147 | + | 0.0373449i | ||||
\(773\) | −870.407 | − | 870.407i | −1.12601 | − | 1.12601i | −0.990819 | − | 0.135193i | \(-0.956835\pi\) |
−0.135193 | − | 0.990819i | \(-0.543165\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 895.498 | 1.15548 | ||||||||
\(776\) | −403.807 | + | 84.0873i | −0.520369 | + | 0.108360i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −308.620 | − | 269.027i | −0.396683 | − | 0.345793i | ||||
\(779\) | −518.907 | + | 518.907i | −0.666119 | + | 0.666119i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 139.318 | − | 139.318i | 0.178385 | − | 0.178385i | ||||
\(782\) | −1331.66 | + | 91.2736i | −1.70289 | + | 0.116718i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −520.247 | + | 146.078i | −0.663580 | + | 0.186324i | ||||
\(785\) | 69.1547 | 0.0880951 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1005.24 | + | 1005.24i | 1.27730 | + | 1.27730i | 0.942171 | + | 0.335133i | \(0.108781\pi\) |
0.335133 | + | 0.942171i | \(0.391219\pi\) | |||||||
\(788\) | 487.228 | + | 369.264i | 0.618310 | + | 0.468609i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −25.0299 | + | 28.7135i | −0.0316834 | + | 0.0363462i | ||||
\(791\) | −19.9415 | −0.0252106 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 176.691i | − | 0.222813i | ||||||
\(794\) | 196.136 | − | 225.002i | 0.247023 | − | 0.283377i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.90421 | + | 1.22637i | −0.0111862 | + | 0.00154067i | ||||
\(797\) | 434.779 | − | 434.779i | 0.545520 | − | 0.545520i | −0.379622 | − | 0.925142i | \(-0.623946\pi\) |
0.925142 | + | 0.379622i | \(0.123946\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 619.268i | − | 0.775054i | ||||||
\(800\) | 267.313 | + | 750.498i | 0.334142 | + | 0.938123i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1056.29 | − | 72.3992i | 1.31707 | − | 0.0902733i | ||||
\(803\) | −166.789 | − | 166.789i | −0.207708 | − | 0.207708i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.4785 | − | 31.4785i | −0.0391037 | − | 0.0391037i | ||||
\(806\) | −389.983 | − | 339.952i | −0.483850 | − | 0.421777i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1319.26 | + | 864.519i | 1.63275 | + | 1.06995i | ||||
\(809\) | 50.0002i | 0.0618049i | 0.999522 | + | 0.0309024i | \(0.00983812\pi\) | ||||
−0.999522 | + | 0.0309024i | \(0.990162\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.9957 | + | 36.9957i | −0.0456173 | + | 0.0456173i | −0.729547 | − | 0.683930i | \(-0.760269\pi\) |
0.683930 | + | 0.729547i | \(0.260269\pi\) | |||||||
\(812\) | 283.327 | − | 373.839i | 0.348925 | − | 0.460392i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 303.621 | − | 20.8106i | 0.372999 | − | 0.0255658i | ||||
\(815\) | 84.8378i | 0.104096i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −665.947 | −0.815112 | ||||||||
\(818\) | 50.7665 | + | 740.671i | 0.0620617 | + | 0.905465i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 34.3071 | − | 45.2667i | 0.0418379 | − | 0.0552033i | ||||
\(821\) | −297.373 | − | 297.373i | −0.362208 | − | 0.362208i | 0.502417 | − | 0.864625i | \(-0.332444\pi\) |
−0.864625 | + | 0.502417i | \(0.832444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −345.052 | −0.419262 | −0.209631 | − | 0.977781i | \(-0.567226\pi\) | ||||
−0.209631 | + | 0.977781i | \(0.567226\pi\) | |||||||
\(824\) | −532.333 | + | 110.851i | −0.646036 | + | 0.134528i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 485.867 | − | 557.372i | 0.588217 | − | 0.674785i | ||||
\(827\) | −426.416 | + | 426.416i | −0.515618 | + | 0.515618i | −0.916242 | − | 0.400624i | \(-0.868793\pi\) |
0.400624 | + | 0.916242i | \(0.368793\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 897.159 | − | 897.159i | 1.08222 | − | 1.08222i | 0.0859157 | − | 0.996302i | \(-0.472618\pi\) |
0.996302 | − | 0.0859157i | \(-0.0273816\pi\) | |||||||
\(830\) | −4.43441 | − | 64.6970i | −0.00534267 | − | 0.0779482i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 168.494 | − | 428.315i | 0.202517 | − | 0.514802i | ||||
\(833\) | −636.080 | −0.763602 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −45.4367 | − | 45.4367i | −0.0544152 | − | 0.0544152i | ||||
\(836\) | 206.104 | − | 28.3866i | 0.246536 | − | 0.0339552i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −265.414 | − | 231.364i | −0.316723 | − | 0.276091i | ||||
\(839\) | 708.037 | 0.843906 | 0.421953 | − | 0.906618i | \(-0.361345\pi\) | ||||
0.421953 | + | 0.906618i | \(0.361345\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 62.1159i | − | 0.0738595i | ||||||
\(842\) | −110.285 | − | 96.1370i | −0.130980 | − | 0.114177i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 227.240 | + | 172.222i | 0.269241 | + | 0.204054i | ||||
\(845\) | 26.6989 | − | 26.6989i | 0.0315963 | − | 0.0315963i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 434.033i | 0.512435i | ||||||||
\(848\) | −831.503 | − | 466.924i | −0.980546 | − | 0.550618i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 64.1274 | + | 935.603i | 0.0754440 | + | 1.10071i | ||||
\(851\) | −1219.68 | − | 1219.68i | −1.43323 | − | 1.43323i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 795.484 | + | 795.484i | 0.932572 | + | 0.932572i | 0.997866 | − | 0.0652942i | \(-0.0207986\pi\) |
−0.0652942 | + | 0.997866i | \(0.520799\pi\) | |||||||
\(854\) | −125.996 | + | 144.538i | −0.147536 | + | 0.169249i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 804.907 | − | 1228.29i | 0.940312 | − | 1.43492i | ||||
\(857\) | 1447.28i | 1.68877i | 0.535735 | + | 0.844386i | \(0.320034\pi\) | ||||
−0.535735 | + | 0.844386i | \(0.679966\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −99.6061 | + | 99.6061i | −0.115956 | + | 0.115956i | −0.762704 | − | 0.646748i | \(-0.776129\pi\) |
0.646748 | + | 0.762704i | \(0.276129\pi\) | |||||||
\(860\) | 51.0611 | − | 7.03262i | 0.0593734 | − | 0.00817747i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 58.1207 | + | 847.967i | 0.0674254 | + | 0.983721i | ||||
\(863\) | − | 549.773i | − | 0.637049i | −0.947915 | − | 0.318525i | \(-0.896813\pi\) | ||
0.947915 | − | 0.318525i | \(-0.103187\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −63.1185 | −0.0729694 | ||||||||
\(866\) | −564.976 | + | 38.7241i | −0.652397 | + | 0.0447161i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 76.6028 | + | 556.183i | 0.0882520 | + | 0.640763i | ||||
\(869\) | 130.766 | + | 130.766i | 0.150479 | + | 0.150479i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 403.522 | 0.463286 | ||||||||
\(872\) | −186.853 | + | 285.139i | −0.214281 | + | 0.326994i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −888.867 | − | 774.835i | −1.01701 | − | 0.886539i | ||||
\(875\) | −44.3246 | + | 44.3246i | −0.0506567 | + | 0.0506567i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −165.469 | + | 165.469i | −0.188677 | + | 0.188677i | −0.795124 | − | 0.606447i | \(-0.792594\pi\) |
0.606447 | + | 0.795124i | \(0.292594\pi\) | |||||||
\(878\) | 1399.63 | − | 95.9326i | 1.59412 | − | 0.109263i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15.5031 | + | 4.35305i | −0.0176172 | + | 0.00494665i | ||||
\(881\) | 1046.60 | 1.18796 | 0.593982 | − | 0.804479i | \(-0.297555\pi\) | ||||
0.593982 | + | 0.804479i | \(0.297555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 338.581 | + | 338.581i | 0.383444 | + | 0.383444i | 0.872341 | − | 0.488897i | \(-0.162601\pi\) |
−0.488897 | + | 0.872341i | \(0.662601\pi\) | |||||||
\(884\) | 327.250 | − | 431.793i | 0.370192 | − | 0.488453i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −506.737 | + | 581.313i | −0.571938 | + | 0.656109i | ||||
\(887\) | 1486.13 | 1.67546 | 0.837728 | − | 0.546088i | \(-0.183883\pi\) | ||||
0.837728 | + | 0.546088i | \(0.183883\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 480.848i | − | 0.540887i | ||||||
\(890\) | −63.7489 | + | 73.1309i | −0.0716280 | + | 0.0821695i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −125.711 | − | 912.742i | −0.140932 | − | 1.02325i | ||||
\(893\) | 386.840 | − | 386.840i | 0.433191 | − | 0.433191i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 67.6447i | − | 0.0755807i | ||||||
\(896\) | −443.258 | + | 230.224i | −0.494708 | + | 0.256947i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1226.54 | + | 84.0689i | −1.36586 | + | 0.0936179i | ||||
\(899\) | 764.339 | + | 764.339i | 0.850210 | + | 0.850210i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −793.761 | − | 793.761i | −0.880978 | − | 0.880978i | ||||
\(902\) | −207.863 | − | 181.197i | −0.230447 | − | 0.200883i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 40.0242 | − | 8.33449i | 0.0442745 | − | 0.00921957i | ||||
\(905\) | − | 45.3482i | − | 0.0501085i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −66.8336 | + | 66.8336i | −0.0736864 | + | 0.0736864i | −0.742989 | − | 0.669303i | \(-0.766593\pi\) |
0.669303 | + | 0.742989i | \(0.266593\pi\) | |||||||
\(908\) | −54.7291 | − | 41.4785i | −0.0602744 | − | 0.0456812i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 18.0273 | − | 1.23562i | 0.0198103 | − | 0.00135782i | ||||
\(911\) | 227.208i | 0.249406i | 0.992194 | + | 0.124703i | \(0.0397977\pi\) | ||||
−0.992194 | + | 0.124703i | \(0.960202\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −314.837 | −0.344838 | ||||||||
\(914\) | 16.1186 | + | 235.167i | 0.0176352 | + | 0.257294i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 176.393 | + | 133.686i | 0.192569 | + | 0.145946i | ||||
\(917\) | −297.698 | − | 297.698i | −0.324643 | − | 0.324643i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1375.00 | −1.49619 | −0.748097 | − | 0.663589i | \(-0.769032\pi\) | ||||
−0.748097 | + | 0.663589i | \(0.769032\pi\) | |||||||
\(920\) | 76.3360 | + | 50.0233i | 0.0829739 | + | 0.0543732i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −487.378 | + | 559.106i | −0.528610 | + | 0.606405i | ||||
\(923\) | 320.509 | − | 320.509i | 0.347247 | − | 0.347247i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −856.929 | + | 856.929i | −0.926410 | + | 0.926410i | ||||
\(926\) | −26.2902 | − | 383.568i | −0.0283912 | − | 0.414220i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −412.415 | + | 868.737i | −0.444413 | + | 0.936139i | ||||
\(929\) | 1788.04 | 1.92470 | 0.962348 | − | 0.271822i | \(-0.0876262\pi\) | ||||
0.962348 | + | 0.271822i | \(0.0876262\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −397.342 | − | 397.342i | −0.426790 | − | 0.426790i | ||||
\(932\) | −20.0178 | − | 145.341i | −0.0214783 | − | 0.155946i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1128.23 | − | 983.491i | −1.20796 | − | 1.05299i | ||||
\(935\) | −18.9549 | −0.0202727 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 768.834i | − | 0.820527i | −0.911967 | − | 0.410263i | \(-0.865437\pi\) | ||
0.911967 | − | 0.410263i | \(-0.134563\pi\) | |||||||
\(938\) | −330.093 | − | 287.746i | −0.351912 | − | 0.306765i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −25.5756 | + | 33.7459i | −0.0272081 | + | 0.0358999i | ||||
\(941\) | 1016.85 | − | 1016.85i | 1.08061 | − | 1.08061i | 0.0841571 | − | 0.996453i | \(-0.473180\pi\) |
0.996453 | − | 0.0841571i | \(-0.0268197\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1562.90i | 1.65737i | ||||||||
\(944\) | −742.220 | + | 1321.75i | −0.786250 | + | 1.40016i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.1115 | − | 249.653i | −0.0180883 | − | 0.263904i | ||||
\(947\) | 476.431 | + | 476.431i | 0.503095 | + | 0.503095i | 0.912398 | − | 0.409304i | \(-0.134228\pi\) |
−0.409304 | + | 0.912398i | \(0.634228\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −383.708 | − | 383.708i | −0.404329 | − | 0.404329i | ||||
\(950\) | −544.387 | + | 624.504i | −0.573039 | + | 0.657373i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −575.606 | + | 119.862i | −0.604628 | + | 0.125906i | ||||
\(953\) | − | 577.529i | − | 0.606011i | −0.952989 | − | 0.303006i | \(-0.902010\pi\) | ||
0.952989 | − | 0.303006i | \(-0.0979901\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34.0375 | + | 34.0375i | −0.0356414 | + | 0.0356414i | ||||
\(956\) | 80.2812 | + | 582.890i | 0.0839761 | + | 0.609718i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.196594 | + | 2.86827i | 0.000205213 | + | 0.00299401i | ||||
\(959\) | 284.936i | 0.297118i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −332.773 | −0.346278 | ||||||||
\(962\) | 698.497 | − | 47.8758i | 0.726088 | − | 0.0497670i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 814.266 | − | 112.148i | 0.844675 | − | 0.116337i | ||||
\(965\) | 12.0257 | + | 12.0257i | 0.0124619 | + | 0.0124619i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 864.047 | 0.893534 | 0.446767 | − | 0.894650i | \(-0.352575\pi\) | ||||
0.446767 | + | 0.894650i | \(0.352575\pi\) | |||||||
\(968\) | −181.402 | − | 871.136i | −0.187399 | − | 0.899934i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 25.0249 | + | 21.8145i | 0.0257989 | + | 0.0224891i | ||||
\(971\) | 898.515 | − | 898.515i | 0.925350 | − | 0.925350i | −0.0720505 | − | 0.997401i | \(-0.522954\pi\) |
0.997401 | + | 0.0720505i | \(0.0229543\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 64.4836 | − | 64.4836i | 0.0662730 | − | 0.0662730i | ||||
\(974\) | −1399.19 | + | 95.9024i | −1.43654 | + | 0.0984624i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 192.473 | − | 342.759i | 0.197206 | − | 0.351187i | ||||
\(977\) | −538.131 | −0.550799 | −0.275400 | − | 0.961330i | \(-0.588810\pi\) | ||||
−0.275400 | + | 0.961330i | \(0.588810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 333.051 | + | 333.051i | 0.340195 | + | 0.340195i | ||||
\(980\) | 34.6620 | + | 26.2699i | 0.0353694 | + | 0.0268060i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −965.833 | + | 1107.97i | −0.983536 | + | 1.12828i | ||||
\(983\) | 759.452 | 0.772586 | 0.386293 | − | 0.922376i | \(-0.373755\pi\) | ||||
0.386293 | + | 0.922376i | \(0.373755\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 49.2052i | − | 0.0499546i | ||||||
\(986\) | −743.835 | + | 853.305i | −0.754396 | + | 0.865421i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 474.153 | − | 65.3048i | 0.479912 | − | 0.0660980i | ||||
\(989\) | −1002.88 | + | 1002.88i | −1.01404 | + | 1.01404i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 514.565i | − | 0.519238i | −0.965711 | − | 0.259619i | \(-0.916403\pi\) | ||
0.965711 | − | 0.259619i | \(-0.0835969\pi\) | |||||||
\(992\) | −386.202 | − | 1084.28i | −0.389316 | − | 1.09303i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −490.737 | + | 33.6357i | −0.493699 | + | 0.0338388i | ||||
\(995\) | 0.511545 | + | 0.511545i | 0.000514115 | + | 0.000514115i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1249.59 | − | 1249.59i | −1.25335 | − | 1.25335i | −0.954208 | − | 0.299145i | \(-0.903299\pi\) |
−0.299145 | − | 0.954208i | \(-0.596701\pi\) | |||||||
\(998\) | −766.023 | − | 667.751i | −0.767558 | − | 0.669089i | ||||
\(999\) | 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 | 144.3.m.b.91.1 | yes | 16 | |
3.2 | odd | 2 | inner | 144.3.m.b.91.8 | yes | 16 | |
4.3 | odd | 2 | 576.3.m.b.271.4 | 16 | |||
8.3 | odd | 2 | 1152.3.m.d.415.5 | 16 | |||
8.5 | even | 2 | 1152.3.m.e.415.5 | 16 | |||
12.11 | even | 2 | 576.3.m.b.271.5 | 16 | |||
16.3 | odd | 4 | inner | 144.3.m.b.19.1 | ✓ | 16 | |
16.5 | even | 4 | 1152.3.m.d.991.5 | 16 | |||
16.11 | odd | 4 | 1152.3.m.e.991.5 | 16 | |||
16.13 | even | 4 | 576.3.m.b.559.4 | 16 | |||
24.5 | odd | 2 | 1152.3.m.e.415.4 | 16 | |||
24.11 | even | 2 | 1152.3.m.d.415.4 | 16 | |||
48.5 | odd | 4 | 1152.3.m.d.991.4 | 16 | |||
48.11 | even | 4 | 1152.3.m.e.991.4 | 16 | |||
48.29 | odd | 4 | 576.3.m.b.559.5 | 16 | |||
48.35 | even | 4 | inner | 144.3.m.b.19.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.m.b.19.1 | ✓ | 16 | 16.3 | odd | 4 | inner | |
144.3.m.b.19.8 | yes | 16 | 48.35 | even | 4 | inner | |
144.3.m.b.91.1 | yes | 16 | 1.1 | even | 1 | trivial | |
144.3.m.b.91.8 | yes | 16 | 3.2 | odd | 2 | inner | |
576.3.m.b.271.4 | 16 | 4.3 | odd | 2 | |||
576.3.m.b.271.5 | 16 | 12.11 | even | 2 | |||
576.3.m.b.559.4 | 16 | 16.13 | even | 4 | |||
576.3.m.b.559.5 | 16 | 48.29 | odd | 4 | |||
1152.3.m.d.415.4 | 16 | 24.11 | even | 2 | |||
1152.3.m.d.415.5 | 16 | 8.3 | odd | 2 | |||
1152.3.m.d.991.4 | 16 | 48.5 | odd | 4 | |||
1152.3.m.d.991.5 | 16 | 16.5 | even | 4 | |||
1152.3.m.e.415.4 | 16 | 24.5 | odd | 2 | |||
1152.3.m.e.415.5 | 16 | 8.5 | even | 2 | |||
1152.3.m.e.991.4 | 16 | 48.11 | even | 4 | |||
1152.3.m.e.991.5 | 16 | 16.11 | odd | 4 |