Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,3,Mod(19,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.f (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.94278685509\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + 1552 x^{8} - 3648 x^{7} + 6784 x^{6} - 9216 x^{5} + 19456 x^{4} - 30720 x^{3} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Root | \(-1.59523 - 1.20633i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.19 |
Dual form | 108.3.f.c.91.1 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.59523 | − | 1.20633i | −0.797615 | − | 0.603167i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.08951 | + | 3.84876i | 0.272378 | + | 0.962190i | ||||
\(5\) | −1.10093 | − | 1.90686i | −0.220185 | − | 0.381372i | 0.734679 | − | 0.678415i | \(-0.237333\pi\) |
−0.954864 | + | 0.297043i | \(0.903999\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.23844 | − | 4.17912i | −1.03406 | − | 0.597017i | −0.115917 | − | 0.993259i | \(-0.536981\pi\) |
−0.918146 | + | 0.396242i | \(0.870314\pi\) | |||||||
\(8\) | 2.90487 | − | 7.45397i | 0.363109 | − | 0.931747i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.544081 | + | 4.36996i | −0.0544081 | + | 0.436996i | ||||
\(11\) | −4.54769 | − | 2.62561i | −0.413426 | − | 0.238692i | 0.278835 | − | 0.960339i | \(-0.410052\pi\) |
−0.692261 | + | 0.721648i | \(0.743385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.37788 | − | 12.7789i | −0.567529 | − | 0.982990i | −0.996809 | − | 0.0798182i | \(-0.974566\pi\) |
0.429280 | − | 0.903171i | \(-0.358767\pi\) | |||||||
\(14\) | 6.50556 | + | 15.3986i | 0.464683 | + | 1.09990i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −13.6259 | + | 8.38655i | −0.851620 | + | 0.524159i | ||||
\(17\) | −28.2789 | −1.66346 | −0.831732 | − | 0.555178i | \(-0.812650\pi\) | ||||
−0.831732 | + | 0.555178i | \(0.812650\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.1376i | 1.00724i | 0.863925 | + | 0.503620i | \(0.167999\pi\) | ||||
−0.863925 | + | 0.503620i | \(0.832001\pi\) | |||||||
\(20\) | 6.13957 | − | 6.31475i | 0.306979 | − | 0.315737i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.08724 | + | 9.67448i | 0.185784 | + | 0.439749i | ||||
\(23\) | 3.16702 | − | 1.82848i | 0.137696 | − | 0.0794990i | −0.429569 | − | 0.903034i | \(-0.641335\pi\) |
0.567266 | + | 0.823535i | \(0.308001\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.0759 | − | 17.4520i | 0.403037 | − | 0.698081i | ||||
\(26\) | −3.64618 | + | 29.2854i | −0.140238 | + | 1.12636i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.19805 | − | 32.4122i | 0.292787 | − | 1.15758i | ||||
\(29\) | 12.3355 | − | 21.3657i | 0.425362 | − | 0.736748i | −0.571092 | − | 0.820886i | \(-0.693480\pi\) |
0.996454 | + | 0.0841375i | \(0.0268135\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 32.9674 | − | 19.0338i | 1.06347 | − | 0.613992i | 0.137077 | − | 0.990560i | \(-0.456229\pi\) |
0.926389 | + | 0.376568i | \(0.122896\pi\) | |||||||
\(32\) | 31.8535 | + | 3.05895i | 0.995421 | + | 0.0955923i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 45.1113 | + | 34.1138i | 1.32680 | + | 1.00335i | ||||
\(35\) | 18.4036i | 0.525817i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.21977 | −0.114048 | −0.0570239 | − | 0.998373i | \(-0.518161\pi\) | ||||
−0.0570239 | + | 0.998373i | \(0.518161\pi\) | |||||||
\(38\) | 23.0863 | − | 30.5288i | 0.607535 | − | 0.803390i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −17.4117 | + | 2.66709i | −0.435293 | + | 0.0666773i | ||||
\(41\) | 9.92483 | + | 17.1903i | 0.242069 | + | 0.419276i | 0.961303 | − | 0.275492i | \(-0.0888406\pi\) |
−0.719235 | + | 0.694767i | \(0.755507\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −20.1894 | − | 11.6564i | −0.469521 | − | 0.271078i | 0.246518 | − | 0.969138i | \(-0.420714\pi\) |
−0.716039 | + | 0.698060i | \(0.754047\pi\) | |||||||
\(44\) | 5.15057 | − | 20.3636i | 0.117058 | − | 0.462809i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.25787 | − | 0.903640i | −0.157780 | − | 0.0196444i | ||||
\(47\) | 25.8538 | + | 14.9267i | 0.550082 | + | 0.317590i | 0.749155 | − | 0.662395i | \(-0.230460\pi\) |
−0.199073 | + | 0.979985i | \(0.563793\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.4300 | + | 18.0654i | 0.212858 | + | 0.368681i | ||||
\(50\) | −37.1264 | + | 15.6850i | −0.742528 | + | 0.313701i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 41.1445 | − | 42.3184i | 0.791240 | − | 0.813816i | ||||
\(53\) | 32.1118 | 0.605883 | 0.302942 | − | 0.953009i | \(-0.402031\pi\) | ||||
0.302942 | + | 0.953009i | \(0.402031\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.5624i | 0.210225i | ||||||||
\(56\) | −52.1778 | + | 41.8154i | −0.931746 | + | 0.746703i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −45.4521 | + | 19.2025i | −0.783657 | + | 0.331077i | ||||
\(59\) | −7.96159 | + | 4.59663i | −0.134942 | + | 0.0779089i | −0.565951 | − | 0.824439i | \(-0.691491\pi\) |
0.431009 | + | 0.902348i | \(0.358158\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40.8215 | + | 70.7049i | −0.669205 | + | 1.15910i | 0.308922 | + | 0.951087i | \(0.400032\pi\) |
−0.978127 | + | 0.208009i | \(0.933302\pi\) | |||||||
\(62\) | −75.5517 | − | 9.40656i | −1.21858 | − | 0.151719i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −47.1234 | − | 43.3057i | −0.736304 | − | 0.676651i | ||||
\(65\) | −16.2450 | + | 28.1372i | −0.249923 | + | 0.432879i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.86179 | + | 3.96166i | −0.102415 | + | 0.0591292i | −0.550333 | − | 0.834946i | \(-0.685499\pi\) |
0.447918 | + | 0.894075i | \(0.352166\pi\) | |||||||
\(68\) | −30.8102 | − | 108.839i | −0.453091 | − | 1.60057i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 22.2009 | − | 29.3579i | 0.317155 | − | 0.419399i | ||||
\(71\) | − | 62.9286i | − | 0.886318i | −0.896443 | − | 0.443159i | \(-0.853858\pi\) | ||
0.896443 | − | 0.443159i | \(-0.146142\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33.3218 | 0.456463 | 0.228232 | − | 0.973607i | \(-0.426706\pi\) | ||||
0.228232 | + | 0.973607i | \(0.426706\pi\) | |||||||
\(74\) | 6.73149 | + | 5.09045i | 0.0909661 | + | 0.0687899i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −73.6560 | + | 20.8506i | −0.969157 | + | 0.274351i | ||||
\(77\) | 21.9454 | + | 38.0106i | 0.285006 | + | 0.493644i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −53.7133 | − | 31.0114i | −0.679916 | − | 0.392549i | 0.119908 | − | 0.992785i | \(-0.461740\pi\) |
−0.799823 | + | 0.600236i | \(0.795073\pi\) | |||||||
\(80\) | 30.9931 | + | 16.7497i | 0.387414 | + | 0.209372i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.90489 | − | 39.3951i | 0.0598157 | − | 0.480429i | ||||
\(83\) | −103.056 | − | 59.4995i | −1.24164 | − | 0.716861i | −0.272212 | − | 0.962237i | \(-0.587755\pi\) |
−0.969428 | + | 0.245376i | \(0.921089\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 31.1329 | + | 53.9238i | 0.366270 | + | 0.634398i | ||||
\(86\) | 18.1453 | + | 42.9498i | 0.210992 | + | 0.499416i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −32.7816 | + | 26.2713i | −0.372519 | + | 0.298537i | ||||
\(89\) | 107.361 | 1.20630 | 0.603152 | − | 0.797626i | \(-0.293911\pi\) | ||||
0.603152 | + | 0.797626i | \(0.293911\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 123.332i | 1.35530i | ||||||||
\(92\) | 10.4879 | + | 10.1969i | 0.113999 | + | 0.110836i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −23.2362 | − | 54.9999i | −0.247193 | − | 0.585106i | ||||
\(95\) | 36.4927 | − | 21.0690i | 0.384133 | − | 0.221779i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.78621 | − | 3.09380i | 0.0184145 | − | 0.0318949i | −0.856671 | − | 0.515863i | \(-0.827471\pi\) |
0.875086 | + | 0.483968i | \(0.160805\pi\) | |||||||
\(98\) | 5.15457 | − | 41.4005i | 0.0525976 | − | 0.422454i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 78.1465 | + | 19.7656i | 0.781465 | + | 0.197656i | ||||
\(101\) | −7.54688 | + | 13.0716i | −0.0747216 | + | 0.129422i | −0.900965 | − | 0.433891i | \(-0.857140\pi\) |
0.826244 | + | 0.563313i | \(0.190473\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 112.813 | − | 65.1324i | 1.09527 | − | 0.632353i | 0.160294 | − | 0.987069i | \(-0.448756\pi\) |
0.934974 | + | 0.354716i | \(0.115422\pi\) | |||||||
\(104\) | −116.685 | + | 17.8736i | −1.12197 | + | 0.171861i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −51.2257 | − | 38.7376i | −0.483261 | − | 0.365449i | ||||
\(107\) | 51.2733i | 0.479190i | 0.970873 | + | 0.239595i | \(0.0770146\pi\) | ||||
−0.970873 | + | 0.239595i | \(0.922985\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −25.4737 | −0.233704 | −0.116852 | − | 0.993149i | \(-0.537280\pi\) | ||||
−0.116852 | + | 0.993149i | \(0.537280\pi\) | |||||||
\(110\) | 13.9481 | − | 18.4447i | 0.126801 | − | 0.167679i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 133.679 | − | 3.76124i | 1.19356 | − | 0.0335825i | ||||
\(113\) | −76.1529 | − | 131.901i | −0.673919 | − | 1.16726i | −0.976783 | − | 0.214229i | \(-0.931276\pi\) |
0.302864 | − | 0.953034i | \(-0.402057\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.97330 | − | 4.02603i | −0.0606374 | − | 0.0350090i | ||||
\(116\) | 95.6712 | + | 24.1982i | 0.824751 | + | 0.208605i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 18.2456 | + | 2.27167i | 0.154624 | + | 0.0192514i | ||||
\(119\) | 204.695 | + | 118.181i | 1.72013 | + | 0.993116i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −46.7124 | − | 80.9082i | −0.386053 | − | 0.668663i | ||||
\(122\) | 150.413 | − | 63.5461i | 1.23290 | − | 0.520870i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 109.175 | + | 106.146i | 0.880443 | + | 0.856019i | ||||
\(125\) | −99.4176 | −0.795341 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 147.428i | − | 1.16085i | −0.814314 | − | 0.580425i | \(-0.802886\pi\) | ||
0.814314 | − | 0.580425i | \(-0.197114\pi\) | |||||||
\(128\) | 22.9316 | + | 125.929i | 0.179153 | + | 0.983821i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 59.8573 | − | 25.2883i | 0.460441 | − | 0.194525i | ||||
\(131\) | −112.889 | + | 65.1766i | −0.861750 | + | 0.497532i | −0.864598 | − | 0.502464i | \(-0.832427\pi\) |
0.00284803 | + | 0.999996i | \(0.499093\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 79.9782 | − | 138.526i | 0.601340 | − | 1.04155i | ||||
\(134\) | 15.7252 | + | 1.95787i | 0.117352 | + | 0.0146109i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −82.1465 | + | 210.790i | −0.604018 | + | 1.54993i | ||||
\(137\) | −49.9179 | + | 86.4604i | −0.364364 | + | 0.631098i | −0.988674 | − | 0.150079i | \(-0.952047\pi\) |
0.624310 | + | 0.781177i | \(0.285380\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −82.7828 | + | 47.7947i | −0.595560 | + | 0.343847i | −0.767293 | − | 0.641297i | \(-0.778397\pi\) |
0.171733 | + | 0.985144i | \(0.445063\pi\) | |||||||
\(140\) | −70.8310 | + | 20.0509i | −0.505936 | + | 0.143221i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −75.9129 | + | 100.385i | −0.534598 | + | 0.706940i | ||||
\(143\) | 77.4857i | 0.541858i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −54.3218 | −0.374633 | ||||||||
\(146\) | −53.1560 | − | 40.1973i | −0.364082 | − | 0.275324i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.59749 | − | 16.2409i | −0.0310641 | − | 0.109736i | ||||
\(149\) | −34.3382 | − | 59.4755i | −0.230458 | − | 0.399164i | 0.727485 | − | 0.686123i | \(-0.240689\pi\) |
−0.957943 | + | 0.286959i | \(0.907356\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 91.2633 | + | 52.6909i | 0.604393 | + | 0.348946i | 0.770768 | − | 0.637116i | \(-0.219873\pi\) |
−0.166375 | + | 0.986063i | \(0.553206\pi\) | |||||||
\(152\) | 142.651 | + | 55.5922i | 0.938493 | + | 0.365738i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.8455 | − | 87.1092i | 0.0704255 | − | 0.565644i | ||||
\(155\) | −72.5894 | − | 41.9095i | −0.468319 | − | 0.270384i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −107.502 | − | 186.200i | −0.684729 | − | 1.18598i | −0.973522 | − | 0.228593i | \(-0.926587\pi\) |
0.288794 | − | 0.957391i | \(-0.406746\pi\) | |||||||
\(158\) | 48.2749 | + | 114.267i | 0.305538 | + | 0.723206i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −29.2353 | − | 64.1077i | −0.182721 | − | 0.400673i | ||||
\(161\) | −30.5657 | −0.189849 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 33.7439i | 0.207018i | 0.994629 | + | 0.103509i | \(0.0330071\pi\) | ||||
−0.994629 | + | 0.103509i | \(0.966993\pi\) | |||||||
\(164\) | −55.3481 | + | 56.9273i | −0.337489 | + | 0.347118i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 92.6219 | + | 219.236i | 0.557963 | + | 1.32070i | ||||
\(167\) | 131.565 | − | 75.9589i | 0.787812 | − | 0.454843i | −0.0513797 | − | 0.998679i | \(-0.516362\pi\) |
0.839192 | + | 0.543836i | \(0.183029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −24.3663 | + | 42.2036i | −0.144179 | + | 0.249726i | ||||
\(170\) | 15.3860 | − | 123.578i | 0.0905060 | − | 0.726927i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 22.8659 | − | 90.4040i | 0.132941 | − | 0.525605i | ||||
\(173\) | 59.4003 | − | 102.884i | 0.343354 | − | 0.594707i | −0.641699 | − | 0.766957i | \(-0.721770\pi\) |
0.985053 | + | 0.172249i | \(0.0551035\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −145.868 | + | 84.2170i | −0.833532 | + | 0.481240i | ||||
\(176\) | 83.9862 | − | 2.36307i | 0.477194 | − | 0.0134265i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −171.265 | − | 129.513i | −0.962166 | − | 0.727603i | ||||
\(179\) | − | 218.189i | − | 1.21894i | −0.792811 | − | 0.609468i | \(-0.791383\pi\) | ||
0.792811 | − | 0.609468i | \(-0.208617\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 184.078 | 1.01701 | 0.508503 | − | 0.861060i | \(-0.330199\pi\) | ||||
0.508503 | + | 0.861060i | \(0.330199\pi\) | |||||||
\(182\) | 148.780 | − | 196.743i | 0.817472 | − | 1.08101i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.42965 | − | 28.9183i | −0.0240742 | − | 0.157165i | ||||
\(185\) | 4.64565 | + | 8.04650i | 0.0251116 | + | 0.0434946i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 128.603 | + | 74.2492i | 0.687719 | + | 0.397055i | ||||
\(188\) | −29.2813 | + | 115.768i | −0.155752 | + | 0.615788i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −83.6305 | − | 10.4124i | −0.440160 | − | 0.0548021i | ||||
\(191\) | −215.775 | − | 124.578i | −1.12971 | − | 0.652239i | −0.185849 | − | 0.982578i | \(-0.559503\pi\) |
−0.943862 | + | 0.330339i | \(0.892837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 125.086 | + | 216.656i | 0.648115 | + | 1.12257i | 0.983573 | + | 0.180513i | \(0.0577758\pi\) |
−0.335457 | + | 0.942055i | \(0.608891\pi\) | |||||||
\(194\) | −6.58158 | + | 2.78056i | −0.0339256 | + | 0.0143328i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −58.1656 | + | 59.8252i | −0.296763 | + | 0.305231i | ||||
\(197\) | −255.674 | −1.29784 | −0.648919 | − | 0.760858i | \(-0.724779\pi\) | ||||
−0.648919 | + | 0.760858i | \(0.724779\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 309.110i | − | 1.55332i | −0.629921 | − | 0.776659i | \(-0.716913\pi\) | ||
0.629921 | − | 0.776659i | \(-0.283087\pi\) | |||||||
\(200\) | −100.818 | − | 125.802i | −0.504088 | − | 0.629008i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 27.8077 | − | 11.7481i | 0.137662 | − | 0.0581589i | ||||
\(203\) | −178.580 | + | 103.103i | −0.879702 | + | 0.507896i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.8530 | − | 37.8505i | 0.106600 | − | 0.184636i | ||||
\(206\) | −258.533 | − | 32.1887i | −1.25502 | − | 0.156256i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 207.701 | + | 112.249i | 0.998563 | + | 0.539658i | ||||
\(209\) | 50.2478 | − | 87.0317i | 0.240420 | − | 0.416420i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −341.158 | + | 196.968i | −1.61686 | + | 0.933497i | −0.629140 | + | 0.777292i | \(0.716593\pi\) |
−0.987725 | + | 0.156205i | \(0.950074\pi\) | |||||||
\(212\) | 34.9862 | + | 123.591i | 0.165029 | + | 0.582975i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 61.8528 | − | 81.7927i | 0.289032 | − | 0.382209i | ||||
\(215\) | 51.3311i | 0.238750i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −318.177 | −1.46626 | ||||||||
\(218\) | 40.6364 | + | 30.7298i | 0.186405 | + | 0.140962i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −44.5009 | + | 12.5974i | −0.202277 | + | 0.0572608i | ||||
\(221\) | 208.638 | + | 361.372i | 0.944064 | + | 1.63517i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 89.4002 | + | 51.6152i | 0.400898 | + | 0.231458i | 0.686871 | − | 0.726779i | \(-0.258984\pi\) |
−0.285974 | + | 0.958238i | \(0.592317\pi\) | |||||||
\(224\) | −217.786 | − | 155.261i | −0.972258 | − | 0.693131i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −37.6350 | + | 302.278i | −0.166527 | + | 1.33751i | ||||
\(227\) | 122.210 | + | 70.5578i | 0.538369 | + | 0.310828i | 0.744418 | − | 0.667714i | \(-0.232727\pi\) |
−0.206049 | + | 0.978542i | \(0.566061\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 105.572 | + | 182.856i | 0.461012 | + | 0.798496i | 0.999012 | − | 0.0444490i | \(-0.0141532\pi\) |
−0.538000 | + | 0.842945i | \(0.680820\pi\) | |||||||
\(230\) | 6.26726 | + | 14.8346i | 0.0272490 | + | 0.0644982i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −123.426 | − | 154.013i | −0.532010 | − | 0.663849i | ||||
\(233\) | 280.109 | 1.20219 | 0.601093 | − | 0.799179i | \(-0.294732\pi\) | ||||
0.601093 | + | 0.799179i | \(0.294732\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 65.7328i | − | 0.279714i | ||||||
\(236\) | −26.3656 | − | 25.6342i | −0.111719 | − | 0.108619i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −183.970 | − | 435.456i | −0.772983 | − | 1.82965i | ||||
\(239\) | 339.349 | − | 195.923i | 1.41987 | − | 0.819762i | 0.423583 | − | 0.905857i | \(-0.360772\pi\) |
0.996287 | + | 0.0860949i | \(0.0274388\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.6786 | + | 41.0125i | −0.0982514 | + | 0.170176i | −0.910961 | − | 0.412493i | \(-0.864658\pi\) |
0.812710 | + | 0.582669i | \(0.197992\pi\) | |||||||
\(242\) | −23.0854 | + | 185.418i | −0.0953943 | + | 0.766190i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −316.602 | − | 80.0783i | −1.29755 | − | 0.328190i | ||||
\(245\) | 22.9654 | − | 39.7772i | 0.0937363 | − | 0.162356i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 244.557 | − | 141.195i | 0.990107 | − | 0.571639i | ||||
\(248\) | −46.1110 | − | 301.029i | −0.185931 | − | 1.21383i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 158.594 | + | 119.931i | 0.634376 | + | 0.479724i | ||||
\(251\) | 389.416i | 1.55146i | 0.631065 | + | 0.775730i | \(0.282618\pi\) | ||||
−0.631065 | + | 0.775730i | \(0.717382\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.2035 | −0.0759030 | ||||||||
\(254\) | −177.847 | + | 235.181i | −0.700187 | + | 0.925911i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 115.332 | − | 228.549i | 0.450514 | − | 0.892769i | ||||
\(257\) | 32.5409 | + | 56.3625i | 0.126618 | + | 0.219310i | 0.922364 | − | 0.386321i | \(-0.126254\pi\) |
−0.795746 | + | 0.605631i | \(0.792921\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 30.5445 | + | 17.6349i | 0.117933 | + | 0.0680884i | ||||
\(260\) | −125.992 | − | 31.8673i | −0.484586 | − | 0.122567i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 258.709 | + | 32.2105i | 0.987439 | + | 0.122941i | ||||
\(263\) | 124.773 | + | 72.0378i | 0.474423 | + | 0.273908i | 0.718089 | − | 0.695951i | \(-0.245017\pi\) |
−0.243667 | + | 0.969859i | \(0.578350\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −35.3527 | − | 61.2327i | −0.133406 | − | 0.231067i | ||||
\(266\) | −294.693 | + | 124.501i | −1.10787 | + | 0.468048i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −22.7235 | − | 22.0931i | −0.0847891 | − | 0.0824370i | ||||
\(269\) | 72.4113 | 0.269187 | 0.134593 | − | 0.990901i | \(-0.457027\pi\) | ||||
0.134593 | + | 0.990901i | \(0.457027\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 35.4695i | 0.130884i | 0.997856 | + | 0.0654419i | \(0.0208457\pi\) | ||||
−0.997856 | + | 0.0654419i | \(0.979154\pi\) | |||||||
\(272\) | 385.326 | − | 237.162i | 1.41664 | − | 0.871920i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 183.931 | − | 77.7064i | 0.671280 | − | 0.283600i | ||||
\(275\) | −91.6443 | + | 52.9109i | −0.333252 | + | 0.192403i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −166.922 | + | 289.118i | −0.602607 | + | 1.04375i | 0.389818 | + | 0.920892i | \(0.372538\pi\) |
−0.992425 | + | 0.122854i | \(0.960795\pi\) | |||||||
\(278\) | 189.714 | + | 23.6203i | 0.682424 | + | 0.0849651i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 137.180 | + | 53.4600i | 0.489928 | + | 0.190929i | ||||
\(281\) | 20.5385 | − | 35.5737i | 0.0730906 | − | 0.126597i | −0.827164 | − | 0.561961i | \(-0.810047\pi\) |
0.900254 | + | 0.435364i | \(0.143380\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 218.583 | − | 126.199i | 0.772378 | − | 0.445933i | −0.0613442 | − | 0.998117i | \(-0.519539\pi\) |
0.833722 | + | 0.552184i | \(0.186205\pi\) | |||||||
\(284\) | 242.197 | − | 68.5615i | 0.852806 | − | 0.241414i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 93.4737 | − | 123.607i | 0.326831 | − | 0.432194i | ||||
\(287\) | − | 165.908i | − | 0.578077i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 510.695 | 1.76711 | ||||||||
\(290\) | 86.6558 | + | 65.5303i | 0.298813 | + | 0.225967i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 36.3046 | + | 128.248i | 0.124331 | + | 0.439205i | ||||
\(293\) | −20.3415 | − | 35.2325i | −0.0694248 | − | 0.120247i | 0.829223 | − | 0.558917i | \(-0.188783\pi\) |
−0.898648 | + | 0.438670i | \(0.855450\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.5302 | + | 10.1211i | 0.0594245 | + | 0.0343088i | ||||
\(296\) | −12.2579 | + | 31.4540i | −0.0414117 | + | 0.106264i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.9701 | + | 136.300i | −0.0569465 | + | 0.457384i | ||||
\(299\) | −46.7317 | − | 26.9806i | −0.156293 | − | 0.0902361i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 97.4266 | + | 168.748i | 0.323677 | + | 0.560624i | ||||
\(302\) | −82.0231 | − | 194.148i | −0.271600 | − | 0.642875i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −160.498 | − | 260.767i | −0.527955 | − | 0.857787i | ||||
\(305\) | 179.766 | 0.589396 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 136.830i | 0.445701i | 0.974853 | + | 0.222850i | \(0.0715361\pi\) | ||||
−0.974853 | + | 0.222850i | \(0.928464\pi\) | |||||||
\(308\) | −122.384 | + | 125.876i | −0.397351 | + | 0.408688i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 65.2398 | + | 154.422i | 0.210451 | + | 0.498137i | ||||
\(311\) | −371.260 | + | 214.347i | −1.19376 | + | 0.689219i | −0.959158 | − | 0.282871i | \(-0.908713\pi\) |
−0.234605 | + | 0.972091i | \(0.575380\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.98705 | − | 10.3699i | 0.0191280 | − | 0.0331306i | −0.856303 | − | 0.516474i | \(-0.827244\pi\) |
0.875431 | + | 0.483343i | \(0.160578\pi\) | |||||||
\(314\) | −53.1281 | + | 426.715i | −0.169198 | + | 1.35896i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 60.8341 | − | 240.517i | 0.192513 | − | 0.761130i | ||||
\(317\) | 23.5266 | − | 40.7493i | 0.0742164 | − | 0.128547i | −0.826529 | − | 0.562894i | \(-0.809688\pi\) |
0.900745 | + | 0.434348i | \(0.143021\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −112.196 | + | 64.7763i | −0.351711 | + | 0.203061i | ||||
\(320\) | −30.6984 | + | 137.534i | −0.0959324 | + | 0.429794i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 48.7593 | + | 36.8725i | 0.151426 | + | 0.114511i | ||||
\(323\) | − | 541.189i | − | 1.67551i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −297.356 | −0.914941 | ||||||||
\(326\) | 40.7065 | − | 53.8293i | 0.124867 | − | 0.165121i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 156.966 | − | 24.0438i | 0.478556 | − | 0.0733042i | ||||
\(329\) | −124.761 | − | 216.092i | −0.379213 | − | 0.656816i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 73.1501 | + | 42.2332i | 0.220997 | + | 0.127593i | 0.606412 | − | 0.795151i | \(-0.292608\pi\) |
−0.385415 | + | 0.922743i | \(0.625942\pi\) | |||||||
\(332\) | 116.718 | − | 461.464i | 0.351561 | − | 1.38995i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −301.508 | − | 37.5392i | −0.902717 | − | 0.112393i | ||||
\(335\) | 15.1086 | + | 8.72297i | 0.0451004 | + | 0.0260387i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −252.558 | − | 437.443i | −0.749430 | − | 1.29805i | −0.948096 | − | 0.317983i | \(-0.896994\pi\) |
0.198667 | − | 0.980067i | \(-0.436339\pi\) | |||||||
\(338\) | 89.7815 | − | 37.9306i | 0.265626 | − | 0.112221i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −173.620 | + | 178.574i | −0.510648 | + | 0.525217i | ||||
\(341\) | −199.901 | −0.586219 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 235.200i | 0.685714i | ||||||||
\(344\) | −145.534 | + | 116.631i | −0.423064 | + | 0.339044i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −218.870 | + | 92.4675i | −0.632572 | + | 0.267247i | ||||
\(347\) | 424.751 | − | 245.230i | 1.22407 | − | 0.706715i | 0.258284 | − | 0.966069i | \(-0.416843\pi\) |
0.965782 | + | 0.259354i | \(0.0835097\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 186.972 | − | 323.845i | 0.535736 | − | 0.927923i | −0.463391 | − | 0.886154i | \(-0.653367\pi\) |
0.999127 | − | 0.0417686i | \(-0.0132992\pi\) | |||||||
\(350\) | 334.287 | + | 41.6203i | 0.955105 | + | 0.118915i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −136.828 | − | 97.5458i | −0.388716 | − | 0.277119i | ||||
\(353\) | −297.026 | + | 514.465i | −0.841434 | + | 1.45741i | 0.0472483 | + | 0.998883i | \(0.484955\pi\) |
−0.888682 | + | 0.458523i | \(0.848379\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −119.996 | + | 69.2796i | −0.338016 | + | 0.195154i | ||||
\(356\) | 116.971 | + | 413.207i | 0.328571 | + | 1.16069i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −263.209 | + | 348.062i | −0.735222 | + | 0.972241i | ||||
\(359\) | 410.893i | 1.14455i | 0.820062 | + | 0.572274i | \(0.193939\pi\) | ||||
−0.820062 | + | 0.572274i | \(0.806061\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.24690 | −0.0145343 | ||||||||
\(362\) | −293.647 | − | 222.060i | −0.811180 | − | 0.613425i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −474.676 | + | 134.372i | −1.30405 | + | 0.369154i | ||||
\(365\) | −36.6848 | − | 63.5400i | −0.100506 | − | 0.174082i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −466.176 | − | 269.147i | −1.27023 | − | 0.733370i | −0.295203 | − | 0.955435i | \(-0.595387\pi\) |
−0.975032 | + | 0.222064i | \(0.928721\pi\) | |||||||
\(368\) | −27.8189 | + | 51.4750i | −0.0755948 | + | 0.139878i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.29590 | − | 18.4402i | 0.00620512 | − | 0.0498384i | ||||
\(371\) | −232.440 | − | 134.199i | −0.626522 | − | 0.361722i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −74.9606 | − | 129.836i | −0.200967 | − | 0.348085i | 0.747873 | − | 0.663841i | \(-0.231075\pi\) |
−0.948840 | + | 0.315757i | \(0.897742\pi\) | |||||||
\(374\) | −115.583 | − | 273.583i | −0.309044 | − | 0.731506i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 186.365 | − | 149.354i | 0.495653 | − | 0.397217i | ||||
\(377\) | −364.039 | −0.965621 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 184.361i | − | 0.486442i | −0.969971 | − | 0.243221i | \(-0.921796\pi\) | ||
0.969971 | − | 0.243221i | \(-0.0782040\pi\) | |||||||
\(380\) | 120.849 | + | 117.497i | 0.318024 | + | 0.309201i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 193.928 | + | 459.027i | 0.507665 | + | 1.20164i | ||||
\(383\) | −180.514 | + | 104.220i | −0.471315 | + | 0.272114i | −0.716790 | − | 0.697289i | \(-0.754389\pi\) |
0.245475 | + | 0.969403i | \(0.421056\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 48.3206 | − | 83.6937i | 0.125508 | − | 0.217386i | ||||
\(386\) | 61.8181 | − | 496.511i | 0.160150 | − | 1.28630i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.8534 | + | 3.50395i | 0.0357047 | + | 0.00903080i | ||||
\(389\) | 150.914 | − | 261.390i | 0.387953 | − | 0.671954i | −0.604221 | − | 0.796816i | \(-0.706516\pi\) |
0.992174 | + | 0.124863i | \(0.0398491\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −89.5597 | + | 51.7073i | −0.229053 | + | 0.132244i | ||||
\(392\) | 164.957 | − | 25.2677i | 0.420808 | − | 0.0644585i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 407.859 | + | 308.428i | 1.03517 | + | 0.782813i | ||||
\(395\) | 136.565i | 0.345734i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −246.672 | −0.621341 | −0.310670 | − | 0.950518i | \(-0.600553\pi\) | ||||
−0.310670 | + | 0.950518i | \(0.600553\pi\) | |||||||
\(398\) | −372.890 | + | 493.102i | −0.936911 | + | 1.23895i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.06842 | + | 322.302i | 0.0226711 | + | 0.805755i | ||||
\(401\) | −377.516 | − | 653.877i | −0.941437 | − | 1.63062i | −0.762734 | − | 0.646713i | \(-0.776143\pi\) |
−0.178703 | − | 0.983903i | \(-0.557190\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −486.460 | − | 280.858i | −1.20710 | − | 0.696917i | ||||
\(404\) | −58.5318 | − | 14.8045i | −0.144881 | − | 0.0366447i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 409.252 | + | 50.9539i | 1.00801 | + | 0.125502i | ||||
\(407\) | 19.1902 | + | 11.0794i | 0.0471503 | + | 0.0272222i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 130.730 | + | 226.432i | 0.319634 | + | 0.553622i | 0.980412 | − | 0.196959i | \(-0.0631067\pi\) |
−0.660778 | + | 0.750582i | \(0.729773\pi\) | |||||||
\(410\) | −80.5209 | + | 34.0182i | −0.196392 | + | 0.0829712i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 373.590 | + | 363.226i | 0.906771 | + | 0.881617i | ||||
\(413\) | 76.8394 | 0.186052 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 262.018i | 0.631369i | ||||||||
\(416\) | −195.921 | − | 429.620i | −0.470964 | − | 1.03274i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −185.146 | + | 78.2199i | −0.442933 | + | 0.187129i | ||||
\(419\) | −340.246 | + | 196.441i | −0.812043 | + | 0.468833i | −0.847665 | − | 0.530532i | \(-0.821992\pi\) |
0.0356217 | + | 0.999365i | \(0.488659\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 102.451 | − | 177.450i | 0.243351 | − | 0.421496i | −0.718316 | − | 0.695717i | \(-0.755087\pi\) |
0.961667 | + | 0.274221i | \(0.0884200\pi\) | |||||||
\(422\) | 781.835 | + | 97.3423i | 1.85269 | + | 0.230669i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 93.2807 | − | 239.361i | 0.220002 | − | 0.564530i | ||||
\(425\) | −284.936 | + | 493.524i | −0.670438 | + | 1.16123i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 590.968 | − | 341.196i | 1.38400 | − | 0.799053i | ||||
\(428\) | −197.339 | + | 55.8629i | −0.461072 | + | 0.130521i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 61.9225 | − | 81.8850i | 0.144006 | − | 0.190430i | ||||
\(431\) | − | 462.725i | − | 1.07361i | −0.843707 | − | 0.536803i | \(-0.819632\pi\) | ||
0.843707 | − | 0.536803i | \(-0.180368\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 190.574 | 0.440126 | 0.220063 | − | 0.975486i | \(-0.429374\pi\) | ||||
0.220063 | + | 0.975486i | \(0.429374\pi\) | |||||||
\(434\) | 507.566 | + | 383.828i | 1.16951 | + | 0.884397i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −27.7539 | − | 98.0421i | −0.0636558 | − | 0.224867i | ||||
\(437\) | 34.9926 | + | 60.6090i | 0.0800747 | + | 0.138693i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 379.279 | + | 218.977i | 0.863962 | + | 0.498809i | 0.865337 | − | 0.501190i | \(-0.167104\pi\) |
−0.00137479 | + | 0.999999i | \(0.500438\pi\) | |||||||
\(440\) | 86.1858 | + | 33.5873i | 0.195877 | + | 0.0763347i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 103.110 | − | 828.159i | 0.233280 | − | 1.87366i | ||||
\(443\) | 721.993 | + | 416.843i | 1.62978 | + | 0.940954i | 0.984157 | + | 0.177297i | \(0.0567354\pi\) |
0.645623 | + | 0.763657i | \(0.276598\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −118.196 | − | 204.722i | −0.265610 | − | 0.460050i | ||||
\(446\) | −80.3486 | − | 190.185i | −0.180154 | − | 0.426423i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 160.121 | + | 510.400i | 0.357413 | + | 1.13929i | ||||
\(449\) | 480.789 | 1.07080 | 0.535399 | − | 0.844599i | \(-0.320161\pi\) | ||||
0.535399 | + | 0.844599i | \(0.320161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 104.235i | − | 0.231119i | ||||||
\(452\) | 424.685 | − | 436.802i | 0.939568 | − | 0.966376i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −109.836 | − | 259.982i | −0.241930 | − | 0.572647i | ||||
\(455\) | 235.177 | − | 135.779i | 0.516872 | − | 0.298416i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 109.313 | − | 189.336i | 0.239197 | − | 0.414302i | −0.721287 | − | 0.692636i | \(-0.756449\pi\) |
0.960484 | + | 0.278334i | \(0.0897824\pi\) | |||||||
\(458\) | 52.1739 | − | 419.051i | 0.113917 | − | 0.914959i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.89775 | − | 31.2250i | 0.0171690 | − | 0.0678804i | ||||
\(461\) | 358.474 | − | 620.894i | 0.777600 | − | 1.34684i | −0.155722 | − | 0.987801i | \(-0.549770\pi\) |
0.933322 | − | 0.359042i | \(-0.116896\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.6250 | + | 15.3719i | −0.0575053 | + | 0.0332007i | −0.528477 | − | 0.848948i | \(-0.677237\pi\) |
0.470972 | + | 0.882148i | \(0.343903\pi\) | |||||||
\(464\) | 11.1021 | + | 394.580i | 0.0239268 | + | 0.850387i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −446.838 | − | 337.905i | −0.958881 | − | 0.725119i | ||||
\(467\) | 458.639i | 0.982096i | 0.871133 | + | 0.491048i | \(0.163386\pi\) | ||||
−0.871133 | + | 0.491048i | \(0.836614\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 66.2249 | 0.141204 | ||||||||
\(470\) | −79.2958 | + | 104.859i | −0.168714 | + | 0.223104i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.1357 | + | 72.6981i | 0.0235927 | + | 0.154021i | ||||
\(473\) | 61.2101 | + | 106.019i | 0.129408 | + | 0.224142i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 333.989 | + | 192.829i | 0.703135 | + | 0.405955i | ||||
\(476\) | −231.832 | + | 916.582i | −0.487041 | + | 1.92559i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −777.688 | − | 96.8260i | −1.62696 | − | 0.202565i | ||||
\(479\) | −570.477 | − | 329.365i | −1.19098 | − | 0.687610i | −0.232448 | − | 0.972609i | \(-0.574674\pi\) |
−0.958528 | + | 0.284999i | \(0.908007\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.1329 | + | 53.9238i | 0.0647254 | + | 0.112108i | ||||
\(482\) | 87.2476 | − | 36.8601i | 0.181012 | − | 0.0764732i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 260.503 | − | 267.935i | 0.538228 | − | 0.553585i | ||||
\(485\) | −7.86593 | −0.0162184 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 715.589i | 1.46938i | 0.678402 | + | 0.734691i | \(0.262673\pi\) | ||||
−0.678402 | + | 0.734691i | \(0.737327\pi\) | |||||||
\(488\) | 408.451 | + | 509.671i | 0.836990 | + | 1.04441i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −84.6198 | + | 35.7499i | −0.172693 | + | 0.0729589i | ||||
\(491\) | 574.179 | − | 331.502i | 1.16941 | − | 0.675157i | 0.215866 | − | 0.976423i | \(-0.430742\pi\) |
0.953540 | + | 0.301266i | \(0.0974091\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −348.834 | + | 604.198i | −0.707574 | + | 1.22555i | ||||
\(494\) | −560.452 | − | 69.7790i | −1.13452 | − | 0.141253i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −289.584 | + | 535.836i | −0.583839 | + | 1.08031i | ||||
\(497\) | −262.986 | + | 455.505i | −0.529147 | + | 0.916509i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 458.706 | − | 264.834i | 0.919251 | − | 0.530730i | 0.0358546 | − | 0.999357i | \(-0.488585\pi\) |
0.883396 | + | 0.468627i | \(0.155251\pi\) | |||||||
\(500\) | −108.317 | − | 382.635i | −0.216634 | − | 0.765269i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 469.766 | − | 621.208i | 0.935790 | − | 1.23747i | ||||
\(503\) | 68.3537i | 0.135892i | 0.997689 | + | 0.0679460i | \(0.0216446\pi\) | ||||
−0.997689 | + | 0.0679460i | \(0.978355\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.2342 | 0.0658103 | ||||||||
\(506\) | 30.6339 | + | 23.1658i | 0.0605413 | + | 0.0457822i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 567.415 | − | 160.625i | 1.11696 | − | 0.316190i | ||||
\(509\) | 400.473 | + | 693.640i | 0.786784 | + | 1.36275i | 0.927927 | + | 0.372761i | \(0.121589\pi\) |
−0.141143 | + | 0.989989i | \(0.545078\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −241.198 | − | 139.256i | −0.472012 | − | 0.272516i | ||||
\(512\) | −459.687 | + | 225.460i | −0.897826 | + | 0.440351i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.0818 | − | 129.166i | 0.0312876 | − | 0.251297i | ||||
\(515\) | −248.396 | − | 143.412i | −0.482323 | − | 0.278469i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −78.3834 | − | 135.764i | −0.151612 | − | 0.262600i | ||||
\(518\) | −27.4520 | − | 64.9786i | −0.0529961 | − | 0.125441i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 162.544 | + | 202.825i | 0.312585 | + | 0.390047i | ||||
\(521\) | 208.227 | 0.399668 | 0.199834 | − | 0.979830i | \(-0.435960\pi\) | ||||
0.199834 | + | 0.979830i | \(0.435960\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.5350i | 0.0583843i | 0.999574 | + | 0.0291921i | \(0.00929347\pi\) | ||||
−0.999574 | + | 0.0291921i | \(0.990707\pi\) | |||||||
\(524\) | −373.844 | − | 363.473i | −0.713442 | − | 0.693651i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −112.140 | − | 265.435i | −0.213194 | − | 0.504629i | ||||
\(527\) | −932.283 | + | 538.254i | −1.76904 | + | 1.02135i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −257.813 | + | 446.546i | −0.487360 | + | 0.844132i | ||||
\(530\) | −17.4714 | + | 140.327i | −0.0329650 | + | 0.264769i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 620.292 | + | 156.891i | 1.16596 | + | 0.294907i | ||||
\(533\) | 146.448 | − | 253.656i | 0.274762 | − | 0.475903i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 97.7710 | − | 56.4481i | 0.182749 | − | 0.105510i | ||||
\(536\) | 9.59747 | + | 62.6557i | 0.0179057 | + | 0.116895i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −115.513 | − | 87.3522i | −0.214707 | − | 0.162365i | ||||
\(539\) | − | 109.541i | − | 0.203230i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 526.091 | 0.972442 | 0.486221 | − | 0.873836i | \(-0.338375\pi\) | ||||
0.486221 | + | 0.873836i | \(0.338375\pi\) | |||||||
\(542\) | 42.7881 | − | 56.5820i | 0.0789448 | − | 0.104395i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −900.780 | − | 86.5038i | −1.65585 | − | 0.159014i | ||||
\(545\) | 28.0446 | + | 48.5747i | 0.0514580 | + | 0.0891279i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −823.276 | − | 475.318i | −1.50507 | − | 0.868955i | −0.999983 | − | 0.00588962i | \(-0.998125\pi\) |
−0.505092 | − | 0.863066i | \(-0.668541\pi\) | |||||||
\(548\) | −387.151 | − | 97.9224i | −0.706481 | − | 0.178691i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 210.022 | + | 26.1487i | 0.381858 | + | 0.0475432i | ||||
\(551\) | 408.888 | + | 236.071i | 0.742083 | + | 0.428442i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 259.201 | + | 448.949i | 0.468717 | + | 0.811842i | ||||
\(554\) | 615.052 | − | 259.845i | 1.11020 | − | 0.469034i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −274.143 | − | 266.538i | −0.493063 | − | 0.479385i | ||||
\(557\) | −978.257 | −1.75630 | −0.878148 | − | 0.478390i | \(-0.841221\pi\) | ||||
−0.878148 | + | 0.478390i | \(0.841221\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 343.997i | 0.615379i | ||||||||
\(560\) | −154.343 | − | 250.766i | −0.275612 | − | 0.447796i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −75.6773 | + | 31.9719i | −0.134657 | + | 0.0568895i | ||||
\(563\) | 925.131 | − | 534.125i | 1.64322 | − | 0.948712i | 0.663538 | − | 0.748143i | \(-0.269054\pi\) |
0.979680 | − | 0.200569i | \(-0.0642792\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −167.677 | + | 290.426i | −0.296774 | + | 0.514028i | ||||
\(566\) | −500.928 | − | 62.3680i | −0.885032 | − | 0.110191i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −469.068 | − | 182.799i | −0.825824 | − | 0.321830i | ||||
\(569\) | 481.775 | − | 834.459i | 0.846705 | − | 1.46654i | −0.0374271 | − | 0.999299i | \(-0.511916\pi\) |
0.884132 | − | 0.467237i | \(-0.154750\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 243.132 | − | 140.372i | 0.425800 | − | 0.245836i | −0.271756 | − | 0.962366i | \(-0.587604\pi\) |
0.697556 | + | 0.716531i | \(0.254271\pi\) | |||||||
\(572\) | −298.224 | + | 84.4217i | −0.521370 | + | 0.147590i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −200.141 | + | 264.661i | −0.348677 | + | 0.461083i | ||||
\(575\) | − | 73.6944i | − | 0.128164i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −552.228 | −0.957068 | −0.478534 | − | 0.878069i | \(-0.658832\pi\) | ||||
−0.478534 | + | 0.878069i | \(0.658832\pi\) | |||||||
\(578\) | −814.676 | − | 616.069i | −1.40947 | − | 1.06586i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −59.1843 | − | 209.072i | −0.102042 | − | 0.360469i | ||||
\(581\) | 497.311 | + | 861.367i | 0.855956 | + | 1.48256i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −146.034 | − | 84.3130i | −0.250488 | − | 0.144619i | ||||
\(584\) | 96.7956 | − | 248.380i | 0.165746 | − | 0.425308i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.0528 | + | 80.7425i | −0.0171550 | + | 0.137786i | ||||
\(587\) | 141.476 | + | 81.6811i | 0.241015 | + | 0.139150i | 0.615643 | − | 0.788025i | \(-0.288896\pi\) |
−0.374628 | + | 0.927175i | \(0.622230\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 364.260 | + | 630.917i | 0.618438 | + | 1.07117i | ||||
\(590\) | −15.7553 | − | 37.2928i | −0.0267039 | − | 0.0632081i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 57.4982 | − | 35.3893i | 0.0971253 | − | 0.0597792i | ||||
\(593\) | 818.460 | 1.38020 | 0.690101 | − | 0.723713i | \(-0.257566\pi\) | ||||
0.690101 | + | 0.723713i | \(0.257566\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 520.433i | − | 0.874677i | ||||||
\(596\) | 191.495 | − | 196.959i | 0.321300 | − | 0.330468i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 42.0002 | + | 99.4143i | 0.0702345 | + | 0.166245i | ||||
\(599\) | −398.849 | + | 230.275i | −0.665857 | + | 0.384433i | −0.794505 | − | 0.607257i | \(-0.792270\pi\) |
0.128648 | + | 0.991690i | \(0.458936\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 162.324 | − | 281.153i | 0.270090 | − | 0.467809i | −0.698795 | − | 0.715322i | \(-0.746280\pi\) |
0.968885 | + | 0.247513i | \(0.0796132\pi\) | |||||||
\(602\) | 48.1486 | − | 386.721i | 0.0799811 | − | 0.642393i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −103.362 | + | 408.658i | −0.171129 | + | 0.676587i | ||||
\(605\) | −102.854 | + | 178.148i | −0.170006 | + | 0.294459i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −764.054 | + | 441.127i | −1.25874 | + | 0.726733i | −0.972829 | − | 0.231524i | \(-0.925629\pi\) |
−0.285909 | + | 0.958257i | \(0.592295\pi\) | |||||||
\(608\) | −58.5409 | + | 609.598i | −0.0962845 | + | 1.00263i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −286.767 | − | 216.858i | −0.470111 | − | 0.355504i | ||||
\(611\) | − | 440.510i | − | 0.720966i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.4869 | 0.0317895 | 0.0158947 | − | 0.999874i | \(-0.494940\pi\) | ||||
0.0158947 | + | 0.999874i | \(0.494940\pi\) | |||||||
\(614\) | 165.063 | − | 218.275i | 0.268832 | − | 0.355497i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 347.079 | − | 53.1648i | 0.563440 | − | 0.0863065i | ||||
\(617\) | 48.3314 | + | 83.7124i | 0.0783329 | + | 0.135677i | 0.902531 | − | 0.430625i | \(-0.141707\pi\) |
−0.824198 | + | 0.566302i | \(0.808374\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 363.937 | + | 210.119i | 0.587944 | + | 0.339449i | 0.764284 | − | 0.644880i | \(-0.223093\pi\) |
−0.176340 | + | 0.984329i | \(0.556426\pi\) | |||||||
\(620\) | 82.2126 | − | 325.040i | 0.132601 | − | 0.524258i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 850.820 | + | 105.931i | 1.36788 | + | 0.170307i | ||||
\(623\) | −777.127 | − | 448.674i | −1.24739 | − | 0.720184i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −142.447 | − | 246.725i | −0.227915 | − | 0.394760i | ||||
\(626\) | −22.0603 | + | 9.31995i | −0.0352401 | + | 0.0148881i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 599.512 | − | 616.618i | 0.954638 | − | 0.981875i | ||||
\(629\) | 119.330 | 0.189714 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 483.230i | − | 0.765816i | −0.923787 | − | 0.382908i | \(-0.874923\pi\) | ||
0.923787 | − | 0.382908i | \(-0.125077\pi\) | |||||||
\(632\) | −387.188 | + | 310.294i | −0.612640 | + | 0.490971i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −86.6876 | + | 36.6235i | −0.136731 | + | 0.0577658i | ||||
\(635\) | −281.124 | + | 162.307i | −0.442715 | + | 0.255602i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 153.903 | − | 266.568i | 0.241606 | − | 0.418475i | ||||
\(638\) | 257.120 | + | 32.0127i | 0.403010 | + | 0.0501767i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 214.883 | − | 182.366i | 0.335755 | − | 0.284947i | ||||
\(641\) | 45.2967 | − | 78.4562i | 0.0706657 | − | 0.122397i | −0.828528 | − | 0.559948i | \(-0.810821\pi\) |
0.899193 | + | 0.437552i | \(0.144154\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −453.773 | + | 261.986i | −0.705713 | + | 0.407444i | −0.809472 | − | 0.587159i | \(-0.800246\pi\) |
0.103759 | + | 0.994602i | \(0.466913\pi\) | |||||||
\(644\) | −33.3017 | − | 117.640i | −0.0517107 | − | 0.182671i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −652.855 | + | 863.321i | −1.01061 | + | 1.33641i | ||||
\(647\) | − | 31.3018i | − | 0.0483799i | −0.999707 | − | 0.0241900i | \(-0.992299\pi\) | ||
0.999707 | − | 0.0241900i | \(-0.00770066\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.2758 | 0.0743848 | ||||||||
\(650\) | 474.351 | + | 358.711i | 0.729771 | + | 0.551863i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −129.872 | + | 36.7645i | −0.199191 | + | 0.0563872i | ||||
\(653\) | −445.115 | − | 770.961i | −0.681646 | − | 1.18065i | −0.974478 | − | 0.224481i | \(-0.927931\pi\) |
0.292833 | − | 0.956164i | \(-0.405402\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 248.565 | + | 143.509i | 0.379489 | + | 0.219098i | ||||
\(656\) | −279.402 | − | 150.999i | −0.425918 | − | 0.230181i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −61.6574 | + | 495.221i | −0.0937042 | + | 0.752615i | ||||
\(659\) | 41.1783 | + | 23.7743i | 0.0624860 | + | 0.0360763i | 0.530918 | − | 0.847423i | \(-0.321847\pi\) |
−0.468432 | + | 0.883500i | \(0.655181\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.8421 | − | 43.0278i | −0.0375826 | − | 0.0650950i | 0.846622 | − | 0.532194i | \(-0.178632\pi\) |
−0.884205 | + | 0.467099i | \(0.845299\pi\) | |||||||
\(662\) | −65.7437 | − | 155.615i | −0.0993108 | − | 0.235068i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −742.872 | + | 595.339i | −1.11878 | + | 0.896595i | ||||
\(665\) | −352.200 | −0.529624 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 90.2207i | − | 0.135263i | ||||||
\(668\) | 435.689 | + | 423.603i | 0.652229 | + | 0.634136i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.5789 | − | 32.1412i | −0.0202670 | − | 0.0479720i | ||||
\(671\) | 371.287 | − | 214.362i | 0.553333 | − | 0.319467i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.4365 | + | 28.4688i | −0.0244227 | + | 0.0423013i | −0.877978 | − | 0.478700i | \(-0.841108\pi\) |
0.853556 | + | 0.521002i | \(0.174441\pi\) | |||||||
\(674\) | −124.815 | + | 1002.49i | −0.185185 | + | 1.48738i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −188.979 | − | 47.7986i | −0.279555 | − | 0.0707079i | ||||
\(677\) | −457.417 | + | 792.269i | −0.675653 | + | 1.17026i | 0.300625 | + | 0.953742i | \(0.402805\pi\) |
−0.976278 | + | 0.216522i | \(0.930529\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.8587 | + | 14.9296i | −0.0380836 | + | 0.0219876i | ||||
\(680\) | 492.384 | − | 75.4223i | 0.724094 | − | 0.110915i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 318.888 | + | 241.147i | 0.467577 | + | 0.353588i | ||||
\(683\) | 870.646i | 1.27474i | 0.770559 | + | 0.637369i | \(0.219977\pi\) | ||||
−0.770559 | + | 0.637369i | \(0.780023\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 219.824 | 0.320910 | ||||||||
\(686\) | 283.730 | − | 375.198i | 0.413600 | − | 0.546936i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 372.856 | − | 10.4908i | 0.541942 | − | 0.0152483i | ||||
\(689\) | −236.917 | − | 410.352i | −0.343856 | − | 0.595577i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 800.188 | + | 461.988i | 1.15801 | + | 0.668580i | 0.950827 | − | 0.309722i | \(-0.100236\pi\) |
0.207187 | + | 0.978301i | \(0.433569\pi\) | |||||||
\(692\) | 460.695 | + | 116.524i | 0.665744 | + | 0.168387i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −973.405 | − | 121.194i | −1.40260 | − | 0.174631i | ||||
\(695\) | 182.275 | + | 105.237i | 0.262267 | + | 0.151420i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −280.663 | − | 486.123i | −0.402673 | − | 0.697450i | ||||
\(698\) | −688.929 | + | 291.056i | −0.987004 | + | 0.416986i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −483.056 | − | 469.656i | −0.690080 | − | 0.670937i | ||||
\(701\) | −1191.44 | −1.69963 | −0.849815 | − | 0.527082i | \(-0.823286\pi\) | ||||
−0.849815 | + | 0.527082i | \(0.823286\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 80.7561i | − | 0.114874i | ||||||
\(704\) | 100.599 | + | 320.668i | 0.142896 | + | 0.455495i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1094.44 | − | 462.376i | 1.55020 | − | 0.654923i | ||||
\(707\) | 109.255 | − | 63.0786i | 0.154534 | − | 0.0892201i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 655.954 | − | 1136.15i | 0.925182 | − | 1.60246i | 0.133914 | − | 0.990993i | \(-0.457246\pi\) |
0.791268 | − | 0.611469i | \(-0.209421\pi\) | |||||||
\(710\) | 274.995 | + | 34.2383i | 0.387317 | + | 0.0482229i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 311.870 | − | 800.266i | 0.438020 | − | 1.12397i | ||||
\(713\) | 69.6056 | − | 120.560i | 0.0976236 | − | 0.169089i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 147.754 | − | 85.3059i | 0.206649 | − | 0.119309i | ||||
\(716\) | 839.759 | − | 237.720i | 1.17285 | − | 0.332011i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 495.674 | − | 655.468i | 0.690354 | − | 0.912909i | ||||
\(719\) | − | 245.763i | − | 0.341813i | −0.985287 | − | 0.170906i | \(-0.945330\pi\) | ||
0.985287 | − | 0.170906i | \(-0.0546695\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1088.78 | −1.51010 | ||||||||
\(722\) | 8.37001 | + | 6.32952i | 0.0115928 | + | 0.00876664i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 200.556 | + | 708.473i | 0.277011 | + | 0.978554i | ||||
\(725\) | −248.583 | − | 430.559i | −0.342873 | − | 0.593874i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1041.96 | + | 601.573i | 1.43323 | + | 0.827473i | 0.997365 | − | 0.0725411i | \(-0.0231108\pi\) |
0.435860 | + | 0.900014i | \(0.356444\pi\) | |||||||
\(728\) | 919.314 | + | 358.264i | 1.26279 | + | 0.492121i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −18.1298 | + | 145.615i | −0.0248353 | + | 0.199473i | ||||
\(731\) | 570.934 | + | 329.629i | 0.781032 | + | 0.450929i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −510.693 | − | 884.546i | −0.696716 | − | 1.20675i | −0.969599 | − | 0.244700i | \(-0.921310\pi\) |
0.272883 | − | 0.962047i | \(-0.412023\pi\) | |||||||
\(734\) | 418.977 | + | 991.716i | 0.570813 | + | 1.35111i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 106.474 | − | 48.5556i | 0.144665 | − | 0.0659723i | ||||
\(737\) | 41.6070 | 0.0564546 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 259.300i | − | 0.350879i | −0.984490 | − | 0.175439i | \(-0.943865\pi\) | ||
0.984490 | − | 0.175439i | \(-0.0561346\pi\) | |||||||
\(740\) | −25.9076 | + | 26.6467i | −0.0350102 | + | 0.0360091i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 208.905 | + | 494.478i | 0.281544 | + | 0.666412i | ||||
\(743\) | −100.270 | + | 57.8907i | −0.134953 | + | 0.0779149i | −0.565956 | − | 0.824435i | \(-0.691493\pi\) |
0.431004 | + | 0.902350i | \(0.358160\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −75.6076 | + | 130.956i | −0.101487 | + | 0.175780i | ||||
\(746\) | −37.0458 | + | 297.545i | −0.0496593 | + | 0.398854i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −145.652 | + | 575.859i | −0.194723 | + | 0.769866i | ||||
\(749\) | 214.277 | − | 371.139i | 0.286084 | − | 0.495513i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −543.581 | + | 313.837i | −0.723809 | + | 0.417891i | −0.816153 | − | 0.577836i | \(-0.803897\pi\) |
0.0923438 | + | 0.995727i | \(0.470564\pi\) | |||||||
\(752\) | −477.466 | + | 13.4342i | −0.634928 | + | 0.0178646i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 580.726 | + | 439.153i | 0.770194 | + | 0.582431i | ||||
\(755\) | − | 232.035i | − | 0.307331i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.5546 | 0.0654618 | 0.0327309 | − | 0.999464i | \(-0.489580\pi\) | ||||
0.0327309 | + | 0.999464i | \(0.489580\pi\) | |||||||
\(758\) | −222.402 | + | 294.099i | −0.293406 | + | 0.387993i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −51.0416 | − | 333.218i | −0.0671601 | − | 0.438445i | ||||
\(761\) | 13.0738 | + | 22.6446i | 0.0171798 | + | 0.0297563i | 0.874488 | − | 0.485048i | \(-0.161198\pi\) |
−0.857308 | + | 0.514804i | \(0.827865\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 184.390 | + | 106.458i | 0.241664 | + | 0.139525i | ||||
\(764\) | 244.380 | − | 966.195i | 0.319869 | − | 1.26465i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 413.684 | + | 51.5057i | 0.540058 | + | 0.0672398i | ||||
\(767\) | 117.479 | + | 67.8267i | 0.153167 | + | 0.0884312i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 93.5875 | + | 162.098i | 0.121700 | + | 0.210791i | 0.920438 | − | 0.390888i | \(-0.127832\pi\) |
−0.798738 | + | 0.601679i | \(0.794499\pi\) | |||||||
\(770\) | −178.045 | + | 75.2199i | −0.231227 | + | 0.0976881i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −697.573 | + | 717.476i | −0.903592 | + | 0.929373i | ||||
\(773\) | 877.069 | 1.13463 | 0.567315 | − | 0.823501i | \(-0.307982\pi\) | ||||
0.567315 | + | 0.823501i | \(0.307982\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 767.131i | − | 0.989847i | ||||||
\(776\) | −17.8724 | − | 22.3015i | −0.0230315 | − | 0.0287390i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −556.066 | + | 234.925i | −0.714737 | + | 0.301960i | ||||
\(779\) | −328.981 | + | 189.937i | −0.422312 | + | 0.243822i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −165.226 | + | 286.179i | −0.211557 | + | 0.366427i | ||||
\(782\) | 205.245 | + | 25.5539i | 0.262461 | + | 0.0326777i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −293.625 | − | 158.685i | −0.374522 | − | 0.202405i | ||||
\(785\) | −236.704 | + | 409.984i | −0.301534 | + | 0.522272i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −577.106 | + | 333.192i | −0.733298 | + | 0.423370i | −0.819628 | − | 0.572897i | \(-0.805820\pi\) |
0.0863293 | + | 0.996267i | \(0.472486\pi\) | |||||||
\(788\) | −278.560 | − | 984.028i | −0.353503 | − | 1.24877i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 164.743 | − | 217.852i | 0.208536 | − | 0.275763i | ||||
\(791\) | 1273.01i | 1.60936i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1204.70 | 1.51917 | ||||||||
\(794\) | 393.499 | + | 297.569i | 0.495590 | + | 0.374772i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1189.69 | − | 336.780i | 1.49459 | − | 0.423090i | ||||
\(797\) | −90.8816 | − | 157.412i | −0.114030 | − | 0.197505i | 0.803362 | − | 0.595491i | \(-0.203043\pi\) |
−0.917391 | + | 0.397986i | \(0.869709\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −731.118 | − | 422.111i | −0.915041 | − | 0.528299i | ||||
\(800\) | 374.338 | − | 525.085i | 0.467923 | − | 0.656357i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −186.570 | + | 1498.49i | −0.232631 | + | 1.86845i | ||||
\(803\) | −151.537 | − | 87.4900i | −0.188714 | − | 0.108954i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 33.6505 | + | 58.2844i | 0.0418019 | + | 0.0724030i | ||||
\(806\) | 437.207 | + | 1034.87i | 0.542440 | + | 1.28395i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 75.5125 | + | 94.2255i | 0.0934560 | + | 0.116616i | ||||
\(809\) | −114.921 | −0.142053 | −0.0710266 | − | 0.997474i | \(-0.522628\pi\) | ||||
−0.0710266 | + | 0.997474i | \(0.522628\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1378.48i | − | 1.69973i | −0.526997 | − | 0.849867i | \(-0.676682\pi\) | ||
0.526997 | − | 0.849867i | \(-0.323318\pi\) | |||||||
\(812\) | −591.383 | − | 574.978i | −0.728305 | − | 0.708101i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.2472 | − | 40.8240i | −0.0211882 | − | 0.0501524i | ||||
\(815\) | 64.3449 | − | 37.1496i | 0.0789508 | − | 0.0455823i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 223.075 | − | 386.377i | 0.273041 | − | 0.472921i | ||||
\(818\) | 64.6074 | − | 518.915i | 0.0789822 | − | 0.634370i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 169.487 | + | 42.8683i | 0.206691 | + | 0.0522784i | ||||
\(821\) | 160.807 | − | 278.526i | 0.195867 | − | 0.339252i | −0.751317 | − | 0.659941i | \(-0.770581\pi\) |
0.947184 | + | 0.320689i | \(0.103915\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 56.6805 | − | 32.7245i | 0.0688706 | − | 0.0397625i | −0.465169 | − | 0.885222i | \(-0.654007\pi\) |
0.534040 | + | 0.845459i | \(0.320673\pi\) | |||||||
\(824\) | −157.789 | − | 1030.10i | −0.191492 | − | 1.25013i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −122.576 | − | 92.6940i | −0.148398 | − | 0.112220i | ||||
\(827\) | − | 778.406i | − | 0.941240i | −0.882336 | − | 0.470620i | \(-0.844030\pi\) | ||
0.882336 | − | 0.470620i | \(-0.155970\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −81.3426 | −0.0981214 | −0.0490607 | − | 0.998796i | \(-0.515623\pi\) | ||||
−0.0490607 | + | 0.998796i | \(0.515623\pi\) | |||||||
\(830\) | 316.081 | − | 417.979i | 0.380821 | − | 0.503589i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −205.726 | + | 921.688i | −0.247267 | + | 1.10780i | ||||
\(833\) | −294.950 | − | 510.869i | −0.354082 | − | 0.613288i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −289.686 | − | 167.250i | −0.346929 | − | 0.200299i | ||||
\(836\) | 389.710 | + | 98.5695i | 0.466160 | + | 0.117906i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 779.744 | + | 97.0820i | 0.930483 | + | 0.115850i | ||||
\(839\) | −553.733 | − | 319.698i | −0.659992 | − | 0.381046i | 0.132282 | − | 0.991212i | \(-0.457769\pi\) |
−0.792274 | + | 0.610166i | \(0.791103\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 116.171 | + | 201.214i | 0.138135 | + | 0.239256i | ||||
\(842\) | −377.496 | + | 159.483i | −0.448333 | + | 0.189410i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1129.78 | − | 1098.44i | −1.33860 | − | 1.30147i | ||||
\(845\) | 107.302 | 0.126984 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 780.866i | 0.921920i | ||||||||
\(848\) | −437.553 | + | 269.307i | −0.515982 | + | 0.317579i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1049.89 | − | 443.555i | 1.23517 | − | 0.521829i | ||||
\(851\) | −13.3641 | + | 7.71575i | −0.0157040 | + | 0.00906668i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.8069 | + | 67.2155i | −0.0454946 | + | 0.0787989i | −0.887876 | − | 0.460083i | \(-0.847820\pi\) |
0.842381 | + | 0.538882i | \(0.181153\pi\) | |||||||
\(854\) | −1354.33 | − | 168.620i | −1.58586 | − | 0.197448i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 382.190 | + | 148.942i | 0.446484 | + | 0.173998i | ||||
\(857\) | −436.010 | + | 755.192i | −0.508763 | + | 0.881204i | 0.491185 | + | 0.871055i | \(0.336564\pi\) |
−0.999948 | + | 0.0101489i | \(0.996769\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 136.909 | − | 79.0444i | 0.159382 | − | 0.0920191i | −0.418188 | − | 0.908361i | \(-0.637335\pi\) |
0.577570 | + | 0.816342i | \(0.304001\pi\) | |||||||
\(860\) | −197.561 | + | 55.9260i | −0.229722 | + | 0.0650302i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −558.201 | + | 738.152i | −0.647565 | + | 0.856324i | ||||
\(863\) | − | 685.963i | − | 0.794859i | −0.917633 | − | 0.397429i | \(-0.869902\pi\) | ||
0.917633 | − | 0.397429i | \(-0.130098\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −261.581 | −0.302406 | ||||||||
\(866\) | −304.010 | − | 229.897i | −0.351051 | − | 0.265469i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −346.658 | − | 1224.59i | −0.399376 | − | 1.41082i | ||||
\(869\) | 162.848 | + | 282.060i | 0.187396 | + | 0.324580i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 101.251 | + | 58.4573i | 0.116247 | + | 0.0671151i | ||||
\(872\) | −73.9978 | + | 189.880i | −0.0848598 | + | 0.217752i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 17.2935 | − | 138.898i | 0.0197866 | − | 0.158922i | ||||
\(875\) | 719.629 | + | 415.478i | 0.822433 | + | 0.474832i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 458.905 | + | 794.847i | 0.523267 | + | 0.906325i | 0.999633 | + | 0.0270780i | \(0.00862025\pi\) |
−0.476366 | + | 0.879247i | \(0.658046\pi\) | |||||||
\(878\) | −340.878 | − | 806.857i | −0.388244 | − | 0.918971i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −96.9686 | − | 157.548i | −0.110192 | − | 0.179032i | ||||
\(881\) | 657.430 | 0.746231 | 0.373116 | − | 0.927785i | \(-0.378289\pi\) | ||||
0.373116 | + | 0.927785i | \(0.378289\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 618.879i | 0.700882i | 0.936585 | + | 0.350441i | \(0.113968\pi\) | ||||
−0.936585 | + | 0.350441i | \(0.886032\pi\) | |||||||
\(884\) | −1163.52 | + | 1196.72i | −1.31620 | + | 1.35375i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −648.892 | − | 1535.92i | −0.732384 | − | 1.73355i | ||||
\(887\) | 110.844 | − | 63.9959i | 0.124965 | − | 0.0721487i | −0.436214 | − | 0.899843i | \(-0.643681\pi\) |
0.561180 | + | 0.827694i | \(0.310348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −616.119 | + | 1067.15i | −0.693047 | + | 1.20039i | ||||
\(890\) | −58.4131 | + | 469.164i | −0.0656327 | + | 0.527150i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −101.252 | + | 400.315i | −0.113511 | + | 0.448784i | ||||
\(893\) | −285.661 | + | 494.780i | −0.319890 | + | 0.554065i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −416.056 | + | 240.210i | −0.464867 | + | 0.268391i | ||||
\(896\) | 360.284 | − | 1007.36i | 0.402102 | − | 1.12429i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −766.968 | − | 579.992i | −0.854085 | − | 0.645871i | ||||
\(899\) | − | 939.164i | − | 1.04468i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −908.086 | −1.00786 | ||||||||
\(902\) | −125.742 | + | 166.278i | −0.139404 | + | 0.184344i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1204.40 | + | 184.487i | −1.33230 | + | 0.204079i | ||||
\(905\) | −202.656 | − | 351.011i | −0.223930 | − | 0.387858i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.7946 | − | 7.96431i | −0.0152090 | − | 0.00878094i | 0.492376 | − | 0.870382i | \(-0.336128\pi\) |
−0.507585 | + | 0.861602i | \(0.669462\pi\) | |||||||
\(908\) | −138.411 | + | 547.230i | −0.152435 | + | 0.602676i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −538.957 | − | 67.1027i | −0.592260 | − | 0.0737393i | ||||
\(911\) | −43.9255 | − | 25.3604i | −0.0482168 | − | 0.0278380i | 0.475698 | − | 0.879609i | \(-0.342196\pi\) |
−0.523915 | + | 0.851771i | \(0.675529\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 312.445 | + | 541.170i | 0.342218 | + | 0.592738i | ||||
\(914\) | −402.782 | + | 170.166i | −0.440681 | + | 0.186177i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −588.746 | + | 605.544i | −0.642735 | + | 0.661074i | ||||
\(917\) | 1089.52 | 1.18814 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1065.04i | 1.15892i | 0.815002 | + | 0.579458i | \(0.196736\pi\) | ||||
−0.815002 | + | 0.579458i | \(0.803264\pi\) | |||||||
\(920\) | −50.2665 | + | 40.2837i | −0.0546375 | + | 0.0437866i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1320.85 | + | 558.030i | −1.43260 | + | 0.605239i | ||||
\(923\) | −804.156 | + | 464.279i | −0.871241 | + | 0.503011i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −42.5181 | + | 73.6434i | −0.0459655 | + | 0.0796145i | ||||
\(926\) | 61.0166 | + | 7.59686i | 0.0658927 | + | 0.00820396i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 458.285 | − | 642.838i | 0.493841 | − | 0.692713i | ||||
\(929\) | −171.699 | + | 297.392i | −0.184822 | + | 0.320121i | −0.943516 | − | 0.331326i | \(-0.892504\pi\) |
0.758695 | + | 0.651446i | \(0.225837\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −345.727 | + | 199.606i | −0.371351 | + | 0.214399i | ||||
\(932\) | 305.183 | + | 1078.07i | 0.327449 | + | 1.15673i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 553.272 | − | 731.634i | 0.592368 | − | 0.783334i | ||||
\(935\) | − | 326.971i | − | 0.349702i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −267.742 | −0.285744 | −0.142872 | − | 0.989741i | \(-0.545634\pi\) | ||||
−0.142872 | + | 0.989741i | \(0.545634\pi\) | |||||||
\(938\) | −105.644 | − | 79.8894i | −0.112627 | − | 0.0851699i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 252.990 | − | 71.6168i | 0.269138 | − | 0.0761881i | ||||
\(941\) | 610.126 | + | 1056.77i | 0.648380 | + | 1.12303i | 0.983510 | + | 0.180855i | \(0.0578865\pi\) |
−0.335130 | + | 0.942172i | \(0.608780\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 62.8642 | + | 36.2946i | 0.0666640 | + | 0.0384885i | ||||
\(944\) | 69.9342 | − | 129.404i | 0.0740828 | − | 0.137080i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.2503 | − | 242.964i | 0.0319770 | − | 0.256833i | ||||
\(947\) | −1395.84 | − | 805.888i | −1.47396 | − | 0.850991i | −0.474390 | − | 0.880315i | \(-0.657331\pi\) |
−0.999570 | + | 0.0293240i | \(0.990665\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −245.845 | − | 425.815i | −0.259056 | − | 0.448699i | ||||
\(950\) | −300.173 | − | 710.509i | −0.315972 | − | 0.747904i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1475.53 | − | 1182.49i | 1.54993 | − | 1.24211i | ||||
\(953\) | −242.459 | −0.254416 | −0.127208 | − | 0.991876i | \(-0.540602\pi\) | ||||
−0.127208 | + | 0.991876i | \(0.540602\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 548.603i | 0.574453i | ||||||||
\(956\) | 1123.79 | + | 1092.61i | 1.17551 | + | 1.14290i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 512.717 | + | 1213.60i | 0.535196 | + | 1.26681i | ||||
\(959\) | 722.656 | − | 417.226i | 0.753552 | − | 0.435063i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 244.068 | − | 422.739i | 0.253973 | − | 0.439895i | ||||
\(962\) | 15.3860 | − | 123.578i | 0.0159938 | − | 0.128459i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −183.646 | − | 46.4496i | −0.190504 | − | 0.0481842i | ||||
\(965\) | 275.421 | − | 477.043i | 0.285411 | − | 0.494346i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1543.81 | − | 891.320i | 1.59650 | − | 0.921737i | 0.604340 | − | 0.796726i | \(-0.293437\pi\) |
0.992155 | − | 0.125011i | \(-0.0398966\pi\) | |||||||
\(968\) | −738.781 | + | 113.165i | −0.763204 | + | 0.116906i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.5480 | + | 9.48894i | 0.0129360 | + | 0.00978242i | ||||
\(971\) | 645.136i | 0.664404i | 0.943208 | + | 0.332202i | \(0.107792\pi\) | ||||
−0.943208 | + | 0.332202i | \(0.892208\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 798.958 | 0.821129 | ||||||||
\(974\) | 863.240 | − | 1141.53i | 0.886283 | − | 1.17200i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −36.7397 | − | 1305.77i | −0.0376431 | − | 1.33788i | ||||
\(977\) | 689.779 | + | 1194.73i | 0.706017 | + | 1.22286i | 0.966323 | + | 0.257331i | \(0.0828431\pi\) |
−0.260306 | + | 0.965526i | \(0.583824\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −488.244 | − | 281.888i | −0.498717 | − | 0.287935i | ||||
\(980\) | 178.114 | + | 45.0505i | 0.181749 | + | 0.0459699i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1315.85 | − | 163.830i | −1.33997 | − | 0.166833i | ||||
\(983\) | 639.804 | + | 369.391i | 0.650869 | + | 0.375779i | 0.788789 | − | 0.614664i | \(-0.210708\pi\) |
−0.137920 | + | 0.990443i | \(0.544042\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 281.478 | + | 487.534i | 0.285764 | + | 0.494959i | ||||
\(986\) | 1285.34 | − | 543.024i | 1.30359 | − | 0.550734i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 809.872 | + | 787.406i | 0.819709 | + | 0.796970i | ||||
\(989\) | −85.2536 | −0.0862018 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1533.69i | − | 1.54762i | −0.633416 | − | 0.773811i | \(-0.718348\pi\) | ||
0.633416 | − | 0.773811i | \(-0.281652\pi\) | |||||||
\(992\) | 1108.35 | − | 505.445i | 1.11729 | − | 0.509522i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 969.014 | − | 409.386i | 0.974863 | − | 0.411857i | ||||
\(995\) | −589.430 | + | 340.307i | −0.592391 | + | 0.342017i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −871.274 | + | 1509.09i | −0.873896 | + | 1.51363i | −0.0159621 | + | 0.999873i | \(0.505081\pi\) |
−0.857934 | + | 0.513760i | \(0.828252\pi\) | |||||||
\(998\) | −1051.22 | − | 130.882i | −1.05333 | − | 0.131144i | ||||
\(999\) | 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 | 108.3.f.c.19.1 | 16 | ||
3.2 | odd | 2 | 36.3.f.c.7.8 | yes | 16 | ||
4.3 | odd | 2 | inner | 108.3.f.c.19.7 | 16 | ||
8.3 | odd | 2 | 1728.3.o.g.127.4 | 16 | |||
8.5 | even | 2 | 1728.3.o.g.127.3 | 16 | |||
9.2 | odd | 6 | 324.3.d.i.163.3 | 8 | |||
9.4 | even | 3 | inner | 108.3.f.c.91.7 | 16 | ||
9.5 | odd | 6 | 36.3.f.c.31.2 | yes | 16 | ||
9.7 | even | 3 | 324.3.d.g.163.6 | 8 | |||
12.11 | even | 2 | 36.3.f.c.7.2 | ✓ | 16 | ||
24.5 | odd | 2 | 576.3.o.g.511.5 | 16 | |||
24.11 | even | 2 | 576.3.o.g.511.4 | 16 | |||
36.7 | odd | 6 | 324.3.d.g.163.5 | 8 | |||
36.11 | even | 6 | 324.3.d.i.163.4 | 8 | |||
36.23 | even | 6 | 36.3.f.c.31.8 | yes | 16 | ||
36.31 | odd | 6 | inner | 108.3.f.c.91.1 | 16 | ||
72.5 | odd | 6 | 576.3.o.g.319.4 | 16 | |||
72.13 | even | 6 | 1728.3.o.g.1279.4 | 16 | |||
72.59 | even | 6 | 576.3.o.g.319.5 | 16 | |||
72.67 | odd | 6 | 1728.3.o.g.1279.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.c.7.2 | ✓ | 16 | 12.11 | even | 2 | ||
36.3.f.c.7.8 | yes | 16 | 3.2 | odd | 2 | ||
36.3.f.c.31.2 | yes | 16 | 9.5 | odd | 6 | ||
36.3.f.c.31.8 | yes | 16 | 36.23 | even | 6 | ||
108.3.f.c.19.1 | 16 | 1.1 | even | 1 | trivial | ||
108.3.f.c.19.7 | 16 | 4.3 | odd | 2 | inner | ||
108.3.f.c.91.1 | 16 | 36.31 | odd | 6 | inner | ||
108.3.f.c.91.7 | 16 | 9.4 | even | 3 | inner | ||
324.3.d.g.163.5 | 8 | 36.7 | odd | 6 | |||
324.3.d.g.163.6 | 8 | 9.7 | even | 3 | |||
324.3.d.i.163.3 | 8 | 9.2 | odd | 6 | |||
324.3.d.i.163.4 | 8 | 36.11 | even | 6 | |||
576.3.o.g.319.4 | 16 | 72.5 | odd | 6 | |||
576.3.o.g.319.5 | 16 | 72.59 | even | 6 | |||
576.3.o.g.511.4 | 16 | 24.11 | even | 2 | |||
576.3.o.g.511.5 | 16 | 24.5 | odd | 2 | |||
1728.3.o.g.127.3 | 16 | 8.5 | even | 2 | |||
1728.3.o.g.127.4 | 16 | 8.3 | odd | 2 | |||
1728.3.o.g.1279.3 | 16 | 72.67 | odd | 6 | |||
1728.3.o.g.1279.4 | 16 | 72.13 | even | 6 |