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 | 91.8 | ||
Root | \(-0.136762 - 1.99532i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.91 |
Dual form | 144.3.m.b.19.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | 0.729505 | − | 0.683975i | \(-0.239750\pi\) |
−0.683975 | + | 0.729505i | \(0.739750\pi\) | |||||||
\(6\) | 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 | −0.800407 | − | 0.599457i | \(-0.795383\pi\) |
0.599457 | + | 0.800407i | \(0.295383\pi\) | |||||||
\(12\) | 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 | \(-0.686877\pi\) | ||||
−0.553943 | + | 0.832555i | \(0.686877\pi\) | |||||||
\(18\) | 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 | \(-0.779911\pi\) | ||||
−0.770335 | + | 0.637640i | \(0.779911\pi\) | |||||||
\(24\) | 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 | −0.971165 | − | 0.238410i | \(-0.923374\pi\) |
0.238410 | + | 0.971165i | \(0.423374\pi\) | |||||||
\(30\) | 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 | \(-0.819228\pi\) | ||
0.843026 | − | 0.537872i | \(-0.180772\pi\) | |||||||
\(42\) | 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 | \(0.113747\pi\) | ||||
−0.936828 | + | 0.349790i | \(0.886253\pi\) | |||||||
\(48\) | 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 | 0.982333 | − | 0.187144i | \(-0.0599230\pi\) |
−0.187144 | + | 0.982333i | \(0.559923\pi\) | |||||||
\(54\) | 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 | \(-0.453285\pi\) |
0.989250 | − | 0.146233i | \(-0.0467149\pi\) | |||||||
\(60\) | 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 | \(-0.646389\pi\) | ||||
−0.443853 | + | 0.896099i | \(0.646389\pi\) | |||||||
\(72\) | 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 | 0.991104 | − | 0.133086i | \(-0.0424887\pi\) |
−0.133086 | + | 0.991104i | \(0.542489\pi\) | |||||||
\(84\) | 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 | \(-0.678726\pi\) | ||
0.532443 | − | 0.846466i | \(-0.321274\pi\) | |||||||
\(90\) | 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 | \(0.180189\pi\) |
0.536327 | + | 0.844010i | \(0.319811\pi\) | |||||||
\(102\) | 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 | \(-0.421839\pi\) |
0.970004 | − | 0.243090i | \(-0.0781609\pi\) | |||||||
\(108\) | 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 | \(-0.492802\pi\) | ||||
0.0226121 | + | 0.999744i | \(0.492802\pi\) | |||||||
\(114\) | 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 | 0.935553 | − | 0.353187i | \(-0.114902\pi\) |
−0.353187 | + | 0.935553i | \(0.614902\pi\) | |||||||
\(132\) | 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 | \(-0.914135\pi\) | ||
0.963837 | − | 0.266494i | \(-0.0858653\pi\) | |||||||
\(138\) | 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 | 0.777168 | − | 0.629293i | \(-0.216656\pi\) |
−0.629293 | + | 0.777168i | \(0.716656\pi\) | |||||||
\(150\) | 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 | \(-0.703869\pi\) | ||||
−0.597576 | + | 0.801813i | \(0.703869\pi\) | |||||||
\(168\) | 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 | −0.983304 | − | 0.181971i | \(-0.941752\pi\) |
0.181971 | + | 0.983304i | \(0.441752\pi\) | |||||||
\(174\) | 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 | 0.157508 | − | 0.987518i | \(-0.449654\pi\) |
−0.987518 | + | 0.157508i | \(0.949654\pi\) | |||||||
\(180\) | 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 | \(0.128011\pi\) | ||||
−0.920218 | + | 0.391406i | \(0.871989\pi\) | |||||||
\(192\) | 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 | 0.377443 | − | 0.926033i | \(-0.376803\pi\) |
−0.926033 | + | 0.377443i | \(0.876803\pi\) | |||||||
\(198\) | 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 | 0.733340 | − | 0.679862i | \(-0.237960\pi\) |
−0.679862 | + | 0.733340i | \(0.737960\pi\) | |||||||
\(228\) | 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 | \(0.0250798\pi\) | ||||
−0.996898 | + | 0.0787090i | \(0.974920\pi\) | |||||||
\(234\) | 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 | \(-0.900428\pi\) | ||
0.951471 | − | 0.307737i | \(-0.0995717\pi\) | |||||||
\(240\) | 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 | −0.808946 | − | 0.587883i | \(-0.799961\pi\) |
0.587883 | + | 0.808946i | \(0.299961\pi\) | |||||||
\(252\) | 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 | \(-0.410338\pi\) | ||||
0.277972 | + | 0.960589i | \(0.410338\pi\) | |||||||
\(258\) | 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 | \(-0.347351\pi\) | ||||
0.461390 | + | 0.887197i | \(0.347351\pi\) | |||||||
\(264\) | 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 | \(-0.470599\pi\) |
0.995737 | − | 0.0922353i | \(-0.0294012\pi\) | |||||||
\(270\) | 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 | \(0.269866\pi\) | ||||
−0.661628 | + | 0.749832i | \(0.730134\pi\) | |||||||
\(282\) | 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 | 0.326369 | − | 0.945242i | \(-0.394175\pi\) |
−0.945242 | + | 0.326369i | \(0.894175\pi\) | |||||||
\(294\) | 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 | \(-0.267827\pi\) | ||||
0.666417 | + | 0.745579i | \(0.267827\pi\) | |||||||
\(312\) | 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 | −0.330161 | − | 0.943925i | \(-0.607103\pi\) |
0.943925 | + | 0.330161i | \(0.107103\pi\) | |||||||
\(318\) | 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 | −0.828179 | − | 0.560463i | \(-0.810623\pi\) |
0.560463 | + | 0.828179i | \(0.310623\pi\) | |||||||
\(348\) | 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 | \(-0.300900\pi\) | ||||
0.585495 | + | 0.810676i | \(0.300900\pi\) | |||||||
\(354\) | 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 | \(-0.163635\pi\) | ||||
0.870749 | + | 0.491728i | \(0.163635\pi\) | |||||||
\(360\) | 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 | \(-0.816384\pi\) | ||
0.838187 | − | 0.545384i | \(-0.183616\pi\) | |||||||
\(384\) | 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 | 0.496136 | − | 0.868245i | \(-0.334752\pi\) |
−0.868245 | + | 0.496136i | \(0.834752\pi\) | |||||||
\(390\) | 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 | \(-0.270523\pi\) | ||||
0.660078 | + | 0.751197i | \(0.270523\pi\) | |||||||
\(402\) | 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 | 0.542775 | − | 0.839878i | \(-0.317374\pi\) |
−0.839878 | + | 0.542775i | \(0.817374\pi\) | |||||||
\(420\) | 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 | \(0.164105\pi\) | ||||
−0.870021 | + | 0.493014i | \(0.835895\pi\) | |||||||
\(432\) | 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 | −0.944365 | − | 0.328900i | \(-0.893322\pi\) |
0.328900 | + | 0.944365i | \(0.393322\pi\) | |||||||
\(444\) | 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 | \(-0.739994\pi\) | ||||
−0.684534 | + | 0.728981i | \(0.739994\pi\) | |||||||
\(450\) | 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 | −0.931803 | − | 0.362964i | \(-0.881765\pi\) |
0.362964 | + | 0.931803i | \(0.381765\pi\) | |||||||
\(462\) | 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 | \(-0.954174\pi\) |
−0.143470 | − | 0.989655i | \(-0.545826\pi\) | |||||||
\(468\) | 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 | \(0.000477630\pi\) | ||||
−0.999999 | + | 0.00150052i | \(0.999522\pi\) | |||||||
\(480\) | 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 | \(0.519174\pi\) |
−0.998186 | + | 0.0602007i | \(0.980826\pi\) | |||||||
\(492\) | 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 | \(-0.555454\pi\) | ||||
−0.173335 | + | 0.984863i | \(0.555454\pi\) | |||||||
\(504\) | 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 | −0.944859 | − | 0.327478i | \(-0.893801\pi\) |
0.327478 | + | 0.944859i | \(0.393801\pi\) | |||||||
\(510\) | 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 | \(0.148500\pi\) | ||||
−0.893136 | + | 0.449787i | \(0.851500\pi\) | |||||||
\(522\) | 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 | −0.291868 | − | 0.956459i | \(-0.594277\pi\) |
0.956459 | + | 0.291868i | \(0.0942769\pi\) | |||||||
\(558\) | 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 | 0.975890 | − | 0.218264i | \(-0.0700395\pi\) |
−0.218264 | + | 0.975890i | \(0.570040\pi\) | |||||||
\(564\) | 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 | \(-0.917532\pi\) | ||
0.966626 | − | 0.256192i | \(-0.0824680\pi\) | |||||||
\(570\) | 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 | −0.313429 | − | 0.949612i | \(-0.601478\pi\) |
0.949612 | + | 0.313429i | \(0.101478\pi\) | |||||||
\(588\) | 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 | \(-0.671352\pi\) | ||||
−0.512692 | + | 0.858572i | \(0.671352\pi\) | |||||||
\(594\) | 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 | \(-0.556509\pi\) | ||||
−0.176597 | + | 0.984283i | \(0.556509\pi\) | |||||||
\(600\) | 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 | \(-0.809939\pi\) | ||
0.826972 | − | 0.562243i | \(-0.190061\pi\) | |||||||
\(618\) | 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 | \(-0.369367\pi\) | ||||
0.398971 | + | 0.916963i | \(0.369367\pi\) | |||||||
\(642\) | 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 | \(-0.514732\pi\) | ||||
−0.0462669 | + | 0.998929i | \(0.514732\pi\) | |||||||
\(648\) | 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 | −0.974537 | − | 0.224227i | \(-0.928014\pi\) |
0.224227 | + | 0.974537i | \(0.428014\pi\) | |||||||
\(654\) | 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 | 0.505973 | − | 0.862549i | \(-0.331134\pi\) |
−0.862549 | + | 0.505973i | \(0.831134\pi\) | |||||||
\(660\) | 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 | 0.569144 | − | 0.822238i | \(-0.307275\pi\) |
−0.822238 | + | 0.569144i | \(0.807275\pi\) | |||||||
\(678\) | 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 | \(-0.456627\pi\) |
0.990731 | − | 0.135838i | \(-0.0433728\pi\) | |||||||
\(684\) | 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 | −0.729357 | − | 0.684134i | \(-0.760180\pi\) |
0.684134 | + | 0.729357i | \(0.260180\pi\) | |||||||
\(702\) | 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 | \(0.400483\pi\) | ||||
−0.307574 | + | 0.951524i | \(0.599517\pi\) | |||||||
\(720\) | 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 | \(-0.610658\pi\) | ||||
−0.340681 | + | 0.940179i | \(0.610658\pi\) | |||||||
\(744\) | 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 | \(-0.956806\pi\) | ||
0.990807 | − | 0.135283i | \(-0.0431943\pi\) | |||||||
\(762\) | 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 | \(0.0431654\pi\) |
0.135193 | + | 0.990819i | \(0.456835\pi\) | |||||||
\(774\) | 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 | −0.925142 | − | 0.379622i | \(-0.876054\pi\) |
0.379622 | + | 0.925142i | \(0.376054\pi\) | |||||||
\(798\) | 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 | \(-0.990162\pi\) | ||
0.999522 | − | 0.0309024i | \(-0.00983812\pi\) | |||||||
\(810\) | 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 | 0.864625 | − | 0.502417i | \(-0.167556\pi\) |
−0.502417 | + | 0.864625i | \(0.667556\pi\) | |||||||
\(822\) | 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 | −0.400624 | − | 0.916242i | \(-0.631207\pi\) |
0.916242 | + | 0.400624i | \(0.131207\pi\) | |||||||
\(828\) | 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 | \(-0.638655\pi\) | ||||
−0.421953 | + | 0.906618i | \(0.638655\pi\) | |||||||
\(840\) | 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 | \(-0.679966\pi\) | ||
0.535735 | − | 0.844386i | \(-0.320034\pi\) | |||||||
\(858\) | 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 | \(0.103187\pi\) | ||||
−0.947915 | + | 0.318525i | \(0.896813\pi\) | |||||||
\(864\) | 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 | \(-0.702445\pi\) | ||||
−0.593982 | + | 0.804479i | \(0.702445\pi\) | |||||||
\(882\) | 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 | \(-0.816117\pi\) | ||||
−0.837728 | + | 0.546088i | \(0.816117\pi\) | |||||||
\(888\) | 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 | \(-0.960202\pi\) | ||
0.992194 | − | 0.124703i | \(-0.0397977\pi\) | |||||||
\(912\) | 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 | \(-0.912374\pi\) | ||||
−0.962348 | + | 0.271822i | \(0.912374\pi\) | |||||||
\(930\) | 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 | \(0.526820\pi\) |
−0.996453 | + | 0.0841571i | \(0.973180\pi\) | |||||||
\(942\) | 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 | 0.409304 | − | 0.912398i | \(-0.365772\pi\) |
−0.912398 | + | 0.409304i | \(0.865772\pi\) | |||||||
\(948\) | 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 | \(0.0979901\pi\) | ||||
−0.952989 | + | 0.303006i | \(0.902010\pi\) | |||||||
\(954\) | 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 | −0.997401 | − | 0.0720505i | \(-0.977046\pi\) |
0.0720505 | + | 0.997401i | \(0.477046\pi\) | |||||||
\(972\) | 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 | \(-0.411190\pi\) | ||||
0.275400 | + | 0.961330i | \(0.411190\pi\) | |||||||
\(978\) | 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 | \(-0.626245\pi\) | ||||
−0.386293 | + | 0.922376i | \(0.626245\pi\) | |||||||
\(984\) | 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.91.8 | yes | 16 | |
3.2 | odd | 2 | inner | 144.3.m.b.91.1 | yes | 16 | |
4.3 | odd | 2 | 576.3.m.b.271.5 | 16 | |||
8.3 | odd | 2 | 1152.3.m.d.415.4 | 16 | |||
8.5 | even | 2 | 1152.3.m.e.415.4 | 16 | |||
12.11 | even | 2 | 576.3.m.b.271.4 | 16 | |||
16.3 | odd | 4 | inner | 144.3.m.b.19.8 | yes | 16 | |
16.5 | even | 4 | 1152.3.m.d.991.4 | 16 | |||
16.11 | odd | 4 | 1152.3.m.e.991.4 | 16 | |||
16.13 | even | 4 | 576.3.m.b.559.5 | 16 | |||
24.5 | odd | 2 | 1152.3.m.e.415.5 | 16 | |||
24.11 | even | 2 | 1152.3.m.d.415.5 | 16 | |||
48.5 | odd | 4 | 1152.3.m.d.991.5 | 16 | |||
48.11 | even | 4 | 1152.3.m.e.991.5 | 16 | |||
48.29 | odd | 4 | 576.3.m.b.559.4 | 16 | |||
48.35 | even | 4 | inner | 144.3.m.b.19.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.m.b.19.1 | ✓ | 16 | 48.35 | even | 4 | inner | |
144.3.m.b.19.8 | yes | 16 | 16.3 | odd | 4 | inner | |
144.3.m.b.91.1 | yes | 16 | 3.2 | odd | 2 | inner | |
144.3.m.b.91.8 | yes | 16 | 1.1 | even | 1 | trivial | |
576.3.m.b.271.4 | 16 | 12.11 | even | 2 | |||
576.3.m.b.271.5 | 16 | 4.3 | odd | 2 | |||
576.3.m.b.559.4 | 16 | 48.29 | odd | 4 | |||
576.3.m.b.559.5 | 16 | 16.13 | even | 4 | |||
1152.3.m.d.415.4 | 16 | 8.3 | odd | 2 | |||
1152.3.m.d.415.5 | 16 | 24.11 | even | 2 | |||
1152.3.m.d.991.4 | 16 | 16.5 | even | 4 | |||
1152.3.m.d.991.5 | 16 | 48.5 | odd | 4 | |||
1152.3.m.e.415.4 | 16 | 8.5 | even | 2 | |||
1152.3.m.e.415.5 | 16 | 24.5 | odd | 2 | |||
1152.3.m.e.991.4 | 16 | 16.11 | odd | 4 | |||
1152.3.m.e.991.5 | 16 | 48.11 | even | 4 |