Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,3,Mod(5,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.k (of order \(18\), degree \(6\), 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: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 29.4 | ||
Character | \(\chi\) | \(=\) | 108.29 |
Dual form | 108.3.k.a.41.4 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.0634556 | − | 2.99933i | 0.0211519 | − | 0.999776i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.64904 | + | 6.73227i | 1.12981 | + | 1.34645i | 0.930404 | + | 0.366536i | \(0.119456\pi\) |
0.199404 | + | 0.979917i | \(0.436099\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.05297 | − | 1.47516i | 0.578995 | − | 0.210737i | −0.0358873 | − | 0.999356i | \(-0.511426\pi\) |
0.614882 | + | 0.788619i | \(0.289204\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.99195 | − | 0.380648i | −0.999105 | − | 0.0422943i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.6606 | − | 15.0883i | 1.15096 | − | 1.37166i | 0.234219 | − | 0.972184i | \(-0.424747\pi\) |
0.916742 | − | 0.399479i | \(-0.130809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.31536 | − | 7.45976i | −0.101181 | − | 0.573828i | −0.992677 | − | 0.120799i | \(-0.961454\pi\) |
0.891496 | − | 0.453029i | \(-0.149657\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 20.5507 | − | 16.5161i | 1.37005 | − | 1.10108i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.16520 | + | 1.82743i | −0.186188 | + | 0.107496i | −0.590197 | − | 0.807259i | \(-0.700950\pi\) |
0.404009 | + | 0.914755i | \(0.367617\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.8333 | + | 29.1562i | −0.885964 | + | 1.53453i | −0.0413596 | + | 0.999144i | \(0.513169\pi\) |
−0.844605 | + | 0.535391i | \(0.820164\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.16730 | − | 12.2498i | −0.198443 | − | 0.583323i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.05125 | − | 2.88830i | 0.0457067 | − | 0.125578i | −0.914739 | − | 0.404045i | \(-0.867604\pi\) |
0.960446 | + | 0.278467i | \(0.0898262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.07052 | + | 51.4415i | −0.362821 | + | 2.05766i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.71228 | + | 26.9457i | −0.0634178 | + | 0.997987i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 23.9443 | + | 4.22203i | 0.825667 | + | 0.145587i | 0.570487 | − | 0.821306i | \(-0.306754\pi\) |
0.255179 | + | 0.966894i | \(0.417865\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −27.1255 | − | 9.87288i | −0.875016 | − | 0.318480i | −0.134820 | − | 0.990870i | \(-0.543045\pi\) |
−0.740197 | + | 0.672390i | \(0.765268\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −44.4514 | − | 38.9307i | −1.34701 | − | 1.17972i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 32.8265 | + | 18.9524i | 0.937901 | + | 0.541497i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −14.9004 | − | 25.8083i | −0.402714 | − | 0.697522i | 0.591338 | − | 0.806424i | \(-0.298600\pi\) |
−0.994052 | + | 0.108902i | \(0.965267\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −22.4577 | + | 3.47182i | −0.575839 | + | 0.0890211i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −22.6547 | + | 3.99463i | −0.552552 | + | 0.0974299i | −0.442951 | − | 0.896546i | \(-0.646069\pi\) |
−0.109601 | + | 0.993976i | \(0.534957\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.85241 | − | 5.74986i | −0.159358 | − | 0.133718i | 0.559622 | − | 0.828748i | \(-0.310946\pi\) |
−0.718980 | + | 0.695031i | \(0.755391\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −48.2333 | − | 62.6865i | −1.07185 | − | 1.39303i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.60489 | + | 9.90435i | 0.0766997 | + | 0.210731i | 0.972117 | − | 0.234498i | \(-0.0753446\pi\) |
−0.895417 | + | 0.445229i | \(0.853122\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −23.2857 | + | 19.5391i | −0.475219 | + | 0.398756i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.28021 | + | 9.60944i | 0.103534 | + | 0.188420i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 70.8948i | 1.33764i | 0.743426 | + | 0.668818i | \(0.233200\pi\) | ||||
−0.743426 | + | 0.668818i | \(0.766800\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 173.099 | 3.14725 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 86.3808 | + | 52.3388i | 1.51545 | + | 0.918224i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −43.8902 | − | 52.3064i | −0.743903 | − | 0.886549i | 0.252814 | − | 0.967515i | \(-0.418644\pi\) |
−0.996717 | + | 0.0809663i | \(0.974199\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −99.7950 | + | 36.3224i | −1.63598 | + | 0.595449i | −0.986330 | − | 0.164781i | \(-0.947308\pi\) |
−0.649653 | + | 0.760231i | \(0.725086\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −37.0056 | + | 11.7218i | −0.587390 | + | 0.186060i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 42.7906 | − | 50.9958i | 0.658317 | − | 0.784551i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.27685 | − | 24.2552i | −0.0638336 | − | 0.362018i | −0.999947 | − | 0.0103194i | \(-0.996715\pi\) |
0.936113 | − | 0.351699i | \(-0.114396\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.59625 | − | 3.33634i | −0.124583 | − | 0.0483527i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 29.9139 | − | 17.2708i | 0.421323 | − | 0.243251i | −0.274320 | − | 0.961638i | \(-0.588453\pi\) |
0.695643 | + | 0.718387i | \(0.255119\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 20.9190 | − | 36.2328i | 0.286562 | − | 0.496340i | −0.686425 | − | 0.727201i | \(-0.740821\pi\) |
0.972987 | + | 0.230861i | \(0.0741542\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 153.714 | + | 30.4697i | 2.04953 | + | 0.406263i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 29.0553 | − | 79.8287i | 0.377341 | − | 1.03674i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.78445 | − | 49.8191i | 0.111196 | − | 0.630621i | −0.877368 | − | 0.479818i | \(-0.840703\pi\) |
0.988564 | − | 0.150804i | \(-0.0481861\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 80.7102 | + | 6.84554i | 0.996422 | + | 0.0845129i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −30.9208 | − | 5.45218i | −0.372540 | − | 0.0656889i | −0.0157564 | − | 0.999876i | \(-0.505016\pi\) |
−0.356784 | + | 0.934187i | \(0.616127\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −30.1831 | − | 10.9857i | −0.355095 | − | 0.129244i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.1827 | − | 71.5490i | 0.163019 | − | 0.822403i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 40.0231 | + | 23.1073i | 0.449697 | + | 0.259633i | 0.707702 | − | 0.706511i | \(-0.249732\pi\) |
−0.258005 | + | 0.966144i | \(0.583065\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.3354 | − | 28.2938i | −0.179510 | − | 0.310921i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −31.3333 | + | 80.7318i | −0.336917 | + | 0.868084i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −291.379 | + | 51.3780i | −3.06715 | + | 0.540821i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 84.8132 | + | 71.1668i | 0.874363 | + | 0.733678i | 0.965012 | − | 0.262205i | \(-0.0844497\pi\) |
−0.0906489 | + | 0.995883i | \(0.528894\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −119.587 | + | 130.854i | −1.20795 | + | 1.32176i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −27.7555 | − | 76.2576i | −0.274807 | − | 0.755026i | −0.997930 | − | 0.0643070i | \(-0.979516\pi\) |
0.723123 | − | 0.690719i | \(-0.242706\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 120.693 | − | 101.273i | 1.17177 | − | 0.983234i | 0.171775 | − | 0.985136i | \(-0.445050\pi\) |
0.999998 | + | 0.00190171i | \(0.000605335\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 58.9275 | − | 97.2549i | 0.561214 | − | 0.926237i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 60.6265i | 0.566603i | 0.959031 | + | 0.283301i | \(0.0914297\pi\) | ||||
−0.959031 | + | 0.283301i | \(0.908570\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.0119 | 0.119375 | 0.0596876 | − | 0.998217i | \(-0.480990\pi\) | ||||
0.0596876 | + | 0.998217i | \(0.480990\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −78.3531 | + | 43.0536i | −0.705884 | + | 0.387870i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 72.3782 | + | 86.2570i | 0.640515 | + | 0.763336i | 0.984452 | − | 0.175657i | \(-0.0562048\pi\) |
−0.343936 | + | 0.938993i | \(0.611760\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 25.3834 | − | 9.23879i | 0.220725 | − | 0.0803373i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.98807 | + | 67.5785i | 0.0768211 | + | 0.577594i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.1327 | + | 12.0757i | −0.0851487 | + | 0.101476i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −46.3548 | − | 262.891i | −0.383098 | − | 2.17265i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.5436 | + | 68.2022i | 0.0857206 | + | 0.554490i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −207.284 | + | 119.676i | −1.65827 | + | 0.957405i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 28.4023 | − | 49.1942i | 0.223640 | − | 0.387356i | −0.732270 | − | 0.681014i | \(-0.761539\pi\) |
0.955911 | + | 0.293658i | \(0.0948726\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.6805 | + | 20.1878i | −0.137058 | + | 0.156494i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.65602 | − | 12.7923i | 0.0355421 | − | 0.0976511i | −0.920652 | − | 0.390384i | \(-0.872342\pi\) |
0.956194 | + | 0.292733i | \(0.0945646\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −25.2149 | + | 143.001i | −0.189586 | + | 1.07519i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −191.078 | + | 140.690i | −1.41539 | + | 1.04215i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 176.617 | + | 31.1423i | 1.28917 | + | 0.227316i | 0.775871 | − | 0.630892i | \(-0.217311\pi\) |
0.513302 | + | 0.858208i | \(0.328422\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −108.775 | − | 39.5907i | −0.782551 | − | 0.284825i | −0.0803153 | − | 0.996770i | \(-0.525593\pi\) |
−0.702236 | + | 0.711944i | \(0.747815\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 29.9351 | − | 10.1838i | 0.212306 | − | 0.0722252i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −129.208 | − | 74.5984i | −0.903554 | − | 0.521667i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 106.839 | + | 185.050i | 0.736819 | + | 1.27621i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 57.1265 | + | 71.0815i | 0.388615 | + | 0.483547i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −77.5851 | + | 13.6804i | −0.520706 | + | 0.0918145i | −0.427823 | − | 0.903863i | \(-0.640719\pi\) |
−0.0928828 | + | 0.995677i | \(0.529608\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −31.2173 | − | 26.1944i | −0.206737 | − | 0.173473i | 0.533540 | − | 0.845775i | \(-0.320861\pi\) |
−0.740277 | + | 0.672302i | \(0.765306\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.1569 | − | 15.2273i | 0.190568 | − | 0.0995250i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −86.7663 | − | 238.388i | −0.559783 | − | 1.53799i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −140.499 | + | 117.893i | −0.894901 | + | 0.750911i | −0.969187 | − | 0.246326i | \(-0.920777\pi\) |
0.0742864 | + | 0.997237i | \(0.476332\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 212.637 | + | 4.49867i | 1.33734 | + | 0.0282935i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 13.2569i | − | 0.0823413i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −225.642 | −1.38431 | −0.692154 | − | 0.721750i | \(-0.743338\pi\) | ||||
−0.692154 | + | 0.721750i | \(0.743338\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.9841 | − | 519.179i | 0.0665701 | − | 3.14654i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 119.618 | + | 142.556i | 0.716278 | + | 0.853627i | 0.994263 | − | 0.106959i | \(-0.0341112\pi\) |
−0.277986 | + | 0.960585i | \(0.589667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 104.890 | − | 38.1769i | 0.620652 | − | 0.225899i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 162.463 | − | 255.763i | 0.950073 | − | 1.49569i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 89.4213 | − | 106.568i | 0.516886 | − | 0.616001i | −0.442956 | − | 0.896544i | \(-0.646070\pi\) |
0.959841 | + | 0.280543i | \(0.0905145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 39.1219 | + | 221.871i | 0.223553 | + | 1.26783i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −159.669 | + | 128.322i | −0.902085 | + | 0.724984i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 125.967 | − | 72.7273i | 0.703728 | − | 0.406298i | −0.105006 | − | 0.994472i | \(-0.533486\pi\) |
0.808735 | + | 0.588174i | \(0.200153\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 125.541 | − | 217.444i | 0.693599 | − | 1.20135i | −0.277052 | − | 0.960855i | \(-0.589357\pi\) |
0.970651 | − | 0.240494i | \(-0.0773094\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 102.610 | + | 301.623i | 0.560712 | + | 1.64821i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 89.5752 | − | 246.106i | 0.484190 | − | 1.33030i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.5005 | + | 70.8938i | −0.0668475 | + | 0.379111i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 32.8093 | + | 111.736i | 0.173594 | + | 0.591194i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −28.3584 | − | 5.00035i | −0.148473 | − | 0.0261798i | 0.0989175 | − | 0.995096i | \(-0.468462\pi\) |
−0.247391 | + | 0.968916i | \(0.579573\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 84.8880 | + | 30.8967i | 0.439834 | + | 0.160087i | 0.552439 | − | 0.833553i | \(-0.313697\pi\) |
−0.112605 | + | 0.993640i | \(0.535919\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −150.238 | − | 131.579i | −0.770451 | − | 0.674764i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 246.767 | + | 142.471i | 1.25263 | + | 0.723204i | 0.971630 | − | 0.236505i | \(-0.0760020\pi\) |
0.280996 | + | 0.959709i | \(0.409335\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 78.3479 | + | 135.703i | 0.393708 | + | 0.681922i | 0.992935 | − | 0.118657i | \(-0.0378588\pi\) |
−0.599227 | + | 0.800579i | \(0.704525\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −73.0208 | + | 11.2886i | −0.363288 | + | 0.0561620i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 103.274 | − | 18.2099i | 0.508738 | − | 0.0897042i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −154.870 | − | 129.951i | −0.755463 | − | 0.633909i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.5523 | + | 25.5713i | −0.0509771 | + | 0.123533i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 226.797 | + | 623.120i | 1.08515 | + | 2.98143i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 142.593 | − | 119.650i | 0.675795 | − | 0.567060i | −0.238979 | − | 0.971025i | \(-0.576813\pi\) |
0.914774 | + | 0.403965i | \(0.132368\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −49.9027 | − | 90.8177i | −0.234285 | − | 0.426374i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 78.6134i | − | 0.365644i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −124.503 | −0.573746 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −107.347 | − | 65.0422i | −0.490168 | − | 0.296996i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.7956 | + | 21.2079i | 0.0805229 | + | 0.0959634i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −50.7592 | + | 18.4748i | −0.227620 | + | 0.0828468i | −0.453312 | − | 0.891352i | \(-0.649758\pi\) |
0.225693 | + | 0.974199i | \(0.427536\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 101.143 | − | 459.107i | 0.449524 | − | 2.04047i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −184.955 | + | 220.421i | −0.814781 | + | 0.971018i | −0.999932 | − | 0.0116918i | \(-0.996278\pi\) |
0.185150 | + | 0.982710i | \(0.440723\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 38.3441 | + | 217.460i | 0.167441 | + | 0.949608i | 0.946511 | + | 0.322671i | \(0.104581\pi\) |
−0.779070 | + | 0.626937i | \(0.784308\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −237.589 | − | 92.2119i | −1.02852 | − | 0.399186i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 351.012 | − | 202.657i | 1.50649 | − | 0.869772i | 0.506517 | − | 0.862230i | \(-0.330933\pi\) |
0.999972 | − | 0.00754192i | \(-0.00240069\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −46.3145 | + | 80.2191i | −0.197083 | + | 0.341358i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −148.866 | − | 29.5087i | −0.628128 | − | 0.124509i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 113.967 | − | 313.121i | 0.476848 | − | 1.31013i | −0.435306 | − | 0.900283i | \(-0.643360\pi\) |
0.912154 | − | 0.409847i | \(-0.134418\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.43972 | − | 30.8502i | 0.0225714 | − | 0.128009i | −0.971440 | − | 0.237286i | \(-0.923742\pi\) |
0.994011 | + | 0.109277i | \(0.0348534\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 25.6535 | − | 241.642i | 0.105570 | − | 0.994412i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −263.084 | − | 46.3889i | −1.07381 | − | 0.189342i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 239.640 | + | 87.2218i | 0.970202 | + | 0.353125i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.3150 | + | 92.3958i | −0.0735541 | + | 0.371068i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 86.8677 | + | 50.1531i | 0.346086 | + | 0.199813i | 0.662960 | − | 0.748655i | \(-0.269300\pi\) |
−0.316874 | + | 0.948468i | \(0.602633\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.2700 | − | 52.4292i | −0.119644 | − | 0.207230i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −34.8652 | + | 89.8319i | −0.136726 | + | 0.352282i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −389.385 | + | 68.6591i | −1.51512 | + | 0.267156i | −0.868512 | − | 0.495669i | \(-0.834923\pi\) |
−0.646605 | + | 0.762825i | \(0.723812\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −98.4623 | − | 82.6197i | −0.380163 | − | 0.318995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −213.699 | − | 47.0787i | −0.818770 | − | 0.180378i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −107.565 | − | 295.532i | −0.408992 | − | 1.12370i | −0.957721 | − | 0.287697i | \(-0.907110\pi\) |
0.548729 | − | 0.836000i | \(-0.315112\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −477.282 | + | 400.487i | −1.80107 | + | 1.51127i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 71.8461 | − | 118.576i | 0.269087 | − | 0.444105i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 182.669i | − | 0.679069i | −0.940594 | − | 0.339534i | \(-0.889731\pi\) | ||
0.940594 | − | 0.339534i | \(-0.110269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −461.198 | −1.70184 | −0.850919 | − | 0.525297i | \(-0.823954\pi\) | ||||
−0.850919 | + | 0.525297i | \(0.823954\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −85.8989 | + | 47.1999i | −0.314648 | + | 0.172893i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 661.326 | + | 788.138i | 2.40482 | + | 2.86596i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −148.424 | + | 54.0220i | −0.535827 | + | 0.195025i | −0.595738 | − | 0.803179i | \(-0.703141\pi\) |
0.0599111 | + | 0.998204i | \(0.480918\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 240.153 | + | 99.1017i | 0.860764 | + | 0.355203i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −131.821 | + | 157.098i | −0.469113 | + | 0.559067i | −0.947778 | − | 0.318930i | \(-0.896676\pi\) |
0.478665 | + | 0.877998i | \(0.341121\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 70.6906 | + | 400.906i | 0.249790 | + | 1.41663i | 0.809100 | + | 0.587671i | \(0.199955\pi\) |
−0.559310 | + | 0.828959i | \(0.688934\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 135.610 | + | 877.202i | 0.475824 | + | 3.07790i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −85.9258 | + | 49.6093i | −0.299393 | + | 0.172855i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −137.821 | + | 238.713i | −0.476889 | + | 0.825996i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 218.834 | − | 249.867i | 0.752008 | − | 0.858649i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 146.516 | − | 402.550i | 0.500055 | − | 1.37389i | −0.391166 | − | 0.920320i | \(-0.627928\pi\) |
0.891221 | − | 0.453570i | \(-0.149850\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 104.202 | − | 590.962i | 0.353229 | − | 2.00326i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 384.885 | + | 366.983i | 1.29591 | + | 1.23563i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −22.9288 | − | 4.04297i | −0.0766849 | − | 0.0135216i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −36.2545 | − | 13.1956i | −0.120447 | − | 0.0438391i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −230.483 | + | 78.4089i | −0.760670 | + | 0.258775i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −808.278 | − | 466.660i | −2.65009 | − | 1.53003i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −50.5433 | − | 87.5435i | −0.164636 | − | 0.285158i | 0.771890 | − | 0.635756i | \(-0.219312\pi\) |
−0.936526 | + | 0.350598i | \(0.885978\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −296.093 | − | 368.423i | −0.958229 | − | 1.19231i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.38442 | − | 1.30207i | 0.0237441 | − | 0.00418673i | −0.161764 | − | 0.986830i | \(-0.551718\pi\) |
0.185508 | + | 0.982643i | \(0.440607\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 353.344 | + | 296.491i | 1.12889 | + | 0.947254i | 0.999019 | − | 0.0442760i | \(-0.0140981\pi\) |
0.129875 | + | 0.991530i | \(0.458543\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −287.960 | − | 182.914i | −0.914159 | − | 0.580681i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.7695 | + | 62.5587i | 0.0718281 | + | 0.197346i | 0.970412 | − | 0.241456i | \(-0.0776250\pi\) |
−0.898584 | + | 0.438802i | \(0.855403\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 366.852 | − | 307.826i | 1.15001 | − | 0.964971i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 181.839 | + | 3.84709i | 0.566476 | + | 0.0119847i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 123.047i | − | 0.380950i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 395.672 | 1.21745 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.825677 | − | 39.0269i | 0.00252501 | − | 0.119348i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.2210 | + | 34.8242i | 0.0888175 | + | 0.105849i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 250.644 | − | 91.2269i | 0.757233 | − | 0.275610i | 0.0655866 | − | 0.997847i | \(-0.479108\pi\) |
0.691646 | + | 0.722237i | \(0.256886\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 124.160 | + | 237.739i | 0.372853 | + | 0.713930i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 139.133 | − | 165.812i | 0.415321 | − | 0.494960i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −94.3310 | − | 534.978i | −0.279914 | − | 1.58747i | −0.722907 | − | 0.690945i | \(-0.757194\pi\) |
0.442993 | − | 0.896525i | \(-0.353917\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 263.306 | − | 211.613i | 0.776714 | − | 0.624226i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −492.390 | + | 284.281i | −1.44396 | + | 0.833669i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −171.223 | + | 296.568i | −0.499194 | + | 0.864629i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −26.0995 | − | 76.7194i | −0.0756506 | − | 0.222375i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −142.664 | + | 391.967i | −0.411136 | + | 1.12959i | 0.545452 | + | 0.838142i | \(0.316358\pi\) |
−0.956588 | + | 0.291445i | \(0.905864\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 76.3391 | − | 432.940i | 0.218737 | − | 1.24052i | −0.655567 | − | 0.755137i | \(-0.727570\pi\) |
0.874304 | − | 0.485380i | \(-0.161319\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 203.260 | − | 22.6700i | 0.579089 | − | 0.0645868i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.4788 | − | 2.02403i | −0.0325180 | − | 0.00573380i | 0.157366 | − | 0.987540i | \(-0.449700\pi\) |
−0.189883 | + | 0.981807i | \(0.560811\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 285.257 | + | 103.825i | 0.803540 | + | 0.292465i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 35.5760 | + | 31.1576i | 0.0996526 | + | 0.0872761i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 192.363 | + | 111.061i | 0.535831 | + | 0.309362i | 0.743387 | − | 0.668861i | \(-0.233218\pi\) |
−0.207557 | + | 0.978223i | \(0.566551\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −386.221 | − | 668.955i | −1.06986 | − | 1.85306i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −791.439 | + | 122.351i | −2.18027 | + | 0.337056i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 362.101 | − | 63.8483i | 0.992059 | − | 0.174927i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 185.653 | + | 155.782i | 0.505868 | + | 0.424473i | 0.859672 | − | 0.510846i | \(-0.170668\pi\) |
−0.353805 | + | 0.935319i | \(0.615112\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 205.230 | − | 27.2960i | 0.556179 | − | 0.0739729i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 104.581 | + | 287.334i | 0.281890 | + | 0.774485i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 445.391 | − | 373.728i | 1.19408 | − | 1.00195i | 0.194299 | − | 0.980942i | \(-0.437757\pi\) |
0.999779 | − | 0.0210080i | \(-0.00668756\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 345.793 | + | 629.308i | 0.922115 | + | 1.67815i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 184.172i | − | 0.488521i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −225.207 | −0.594213 | −0.297107 | − | 0.954844i | \(-0.596022\pi\) | ||||
−0.297107 | + | 0.954844i | \(0.596022\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −145.747 | − | 88.3095i | −0.382539 | − | 0.231783i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.3855 | + | 30.2532i | 0.0662806 | + | 0.0789902i | 0.798166 | − | 0.602438i | \(-0.205804\pi\) |
−0.731885 | + | 0.681428i | \(0.761359\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 701.562 | − | 255.348i | 1.82224 | − | 0.663241i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 59.4278 | + | 54.3108i | 0.153560 | + | 0.140338i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −143.473 | + | 170.984i | −0.368824 | + | 0.439548i | −0.918254 | − | 0.395992i | \(-0.870401\pi\) |
0.549429 | + | 0.835540i | \(0.314845\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.95073 | + | 11.0631i | 0.00498908 | + | 0.0282945i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −38.0729 | − | 14.7767i | −0.0968775 | − | 0.0375997i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 385.019 | − | 222.291i | 0.974732 | − | 0.562762i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −81.7197 | + | 141.543i | −0.205843 | + | 0.356531i | −0.950401 | − | 0.311027i | \(-0.899327\pi\) |
0.744558 | + | 0.667558i | \(0.232660\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 427.306 | + | 84.7019i | 1.07094 | + | 0.212286i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 98.9356 | − | 271.823i | 0.246722 | − | 0.677864i | −0.753079 | − | 0.657930i | \(-0.771432\pi\) |
0.999801 | − | 0.0199338i | \(-0.00634555\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.9696 | + | 215.336i | −0.0942173 | + | 0.534333i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 409.849 | + | 582.033i | 1.01197 | + | 1.43712i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −578.051 | − | 101.926i | −1.42027 | − | 0.250433i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −85.1579 | − | 30.9950i | −0.208210 | − | 0.0757823i | 0.235810 | − | 0.971799i | \(-0.424226\pi\) |
−0.444020 | + | 0.896017i | \(0.646448\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 104.613 | − | 527.756i | 0.254534 | − | 1.28408i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −255.046 | − | 147.251i | −0.617544 | − | 0.356539i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −137.968 | − | 238.967i | −0.332452 | − | 0.575824i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −125.648 | + | 323.739i | −0.301314 | + | 0.776352i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −636.775 | + | 112.281i | −1.51975 | + | 0.267973i | −0.870334 | − | 0.492462i | \(-0.836097\pi\) |
−0.649415 | + | 0.760434i | \(0.724986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −94.6516 | − | 79.4221i | −0.224826 | − | 0.188651i | 0.523416 | − | 0.852077i | \(-0.324657\pi\) |
−0.748242 | + | 0.663426i | \(0.769102\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.6449 | − | 90.4315i | −0.0677184 | − | 0.213786i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −65.2957 | − | 179.398i | −0.153637 | − | 0.422114i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −350.884 | + | 294.427i | −0.821743 | + | 0.689524i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −231.944 | + | 382.804i | −0.540662 | + | 0.892317i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 679.383i | − | 1.57629i | −0.615487 | − | 0.788147i | \(-0.711041\pi\) | ||
0.615487 | − | 0.788147i | \(-0.288959\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 738.981 | 1.70665 | 0.853327 | − | 0.521376i | \(-0.174581\pi\) | ||||
0.853327 | + | 0.521376i | \(0.174581\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 561.805 | − | 308.702i | 1.29151 | − | 0.709660i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 66.5156 | + | 79.2702i | 0.152210 | + | 0.181396i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −294.308 | + | 107.120i | −0.670407 | + | 0.244008i | −0.654723 | − | 0.755869i | \(-0.727215\pi\) |
−0.0156837 | + | 0.999877i | \(0.504992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 216.822 | − | 166.831i | 0.491659 | − | 0.378300i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −316.952 | + | 377.729i | −0.715467 | + | 0.852661i | −0.994182 | − | 0.107713i | \(-0.965647\pi\) |
0.278715 | + | 0.960374i | \(0.410092\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 70.5273 | + | 399.980i | 0.158488 | + | 0.898832i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.1087 | + | 233.571i | 0.0807800 | + | 0.522531i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −403.766 | + | 233.114i | −0.899255 | + | 0.519185i | −0.876959 | − | 0.480566i | \(-0.840431\pi\) |
−0.0222969 | + | 0.999751i | \(0.507098\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −226.549 | + | 392.394i | −0.502326 | + | 0.870054i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −80.5466 | + | 91.9688i | −0.177807 | + | 0.203022i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 98.2018 | − | 269.807i | 0.215828 | − | 0.592983i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −65.2077 | + | 369.811i | −0.142687 | + | 0.809216i | 0.826509 | + | 0.562923i | \(0.190323\pi\) |
−0.969196 | + | 0.246292i | \(0.920788\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −43.8216 | − | 88.4175i | −0.0954718 | − | 0.192631i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −116.143 | − | 20.4791i | −0.251937 | − | 0.0444232i | 0.0462535 | − | 0.998930i | \(-0.485272\pi\) |
−0.298190 | + | 0.954507i | \(0.596383\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 82.8187 | + | 30.1435i | 0.178874 | + | 0.0651048i | 0.429905 | − | 0.902874i | \(-0.358547\pi\) |
−0.251030 | + | 0.967979i | \(0.580769\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −720.511 | + | 245.114i | −1.54949 | + | 0.527126i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 288.366 | + | 166.488i | 0.617486 | + | 0.356506i | 0.775890 | − | 0.630869i | \(-0.217301\pi\) |
−0.158403 | + | 0.987374i | \(0.550635\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −53.1143 | − | 91.9966i | −0.113250 | − | 0.196155i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 344.684 | + | 428.885i | 0.731814 | + | 0.910584i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −173.511 | + | 30.5947i | −0.366831 | + | 0.0646822i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1347.15 | − | 1130.39i | −2.83610 | − | 2.37977i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26.9860 | − | 637.482i | 0.0565744 | − | 1.33644i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −143.904 | − | 395.374i | −0.300427 | − | 0.825416i | −0.994426 | − | 0.105440i | \(-0.966375\pi\) |
0.693999 | − | 0.719976i | \(-0.255847\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −172.924 | + | 145.101i | −0.359510 | + | 0.301665i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −39.7619 | − | 0.841227i | −0.0823228 | − | 0.00174167i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 973.009i | 2.00620i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 212.098 | 0.435519 | 0.217760 | − | 0.976002i | \(-0.430125\pi\) | ||||
0.217760 | + | 0.976002i | \(0.430125\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.3183 | + | 676.775i | −0.0292807 | + | 1.38400i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −173.315 | − | 206.549i | −0.352983 | − | 0.420669i | 0.560111 | − | 0.828418i | \(-0.310758\pi\) |
−0.913094 | + | 0.407748i | \(0.866314\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −83.5041 | + | 30.3930i | −0.169380 | + | 0.0616491i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1556.49 | − | 65.8897i | −3.14443 | − | 0.133110i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 95.7630 | − | 114.126i | 0.192682 | − | 0.229629i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 61.6379 | + | 349.566i | 0.123523 | + | 0.700533i | 0.982174 | + | 0.187973i | \(0.0601918\pi\) |
−0.858651 | + | 0.512560i | \(0.828697\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 435.162 | − | 349.729i | 0.868586 | − | 0.698062i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 410.636 | − | 237.081i | 0.816374 | − | 0.471333i | −0.0327908 | − | 0.999462i | \(-0.510439\pi\) |
0.849164 | + | 0.528129i | \(0.177106\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 356.595 | − | 617.640i | 0.706128 | − | 1.22305i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −107.849 | − | 317.023i | −0.212720 | − | 0.625291i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −28.2600 | + | 77.6437i | −0.0555206 | + | 0.152542i | −0.964353 | − | 0.264621i | \(-0.914753\pi\) |
0.908832 | + | 0.417163i | \(0.136975\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.3349 | − | 177.709i | 0.0613208 | − | 0.347768i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −756.808 | − | 503.508i | −1.47526 | − | 0.981498i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1363.60 | + | 240.439i | 2.64776 | + | 0.466871i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 195.080 | + | 71.0032i | 0.377330 | + | 0.137337i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −313.959 | − | 274.966i | −0.604930 | − | 0.529800i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 489.450 | + | 282.584i | 0.939444 | + | 0.542388i | 0.889786 | − | 0.456378i | \(-0.150853\pi\) |
0.0496582 | + | 0.998766i | \(0.484187\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 340.114 | + | 589.095i | 0.650314 | + | 1.12638i | 0.983047 | + | 0.183356i | \(0.0586960\pi\) |
−0.332733 | + | 0.943021i | \(0.607971\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 667.947 | − | 103.260i | 1.27228 | − | 0.196686i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 103.900 | − | 18.3203i | 0.197153 | − | 0.0347634i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 398.000 | + | 333.962i | 0.752364 | + | 0.631308i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 374.748 | + | 487.043i | 0.705741 | + | 0.917218i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 59.5979 | + | 163.744i | 0.111816 | + | 0.307212i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −408.154 | + | 342.482i | −0.762904 | + | 0.640153i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −210.140 | − | 382.433i | −0.391322 | − | 0.712165i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 598.718i | 1.11079i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 53.2254 | 0.0983833 | 0.0491916 | − | 0.998789i | \(-0.484335\pi\) | ||||
0.0491916 | + | 0.998789i | \(0.484335\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −644.220 | − | 390.338i | −1.18641 | − | 0.718855i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 73.5047 | + | 87.5995i | 0.134871 | + | 0.160733i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −128.793 | + | 46.8768i | −0.235453 | + | 0.0856981i | −0.457052 | − | 0.889440i | \(-0.651095\pi\) |
0.221599 | + | 0.975138i | \(0.428873\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 911.177 | − | 288.622i | 1.65970 | − | 0.525724i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −526.161 | + | 627.054i | −0.954920 | + | 1.13803i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −37.8880 | − | 214.873i | −0.0685135 | − | 0.388560i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −732.468 | − | 284.282i | −1.31976 | − | 0.512220i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 519.540 | − | 299.956i | 0.932746 | − | 0.538521i | 0.0450671 | − | 0.998984i | \(-0.485650\pi\) |
0.887679 | + | 0.460463i | \(0.152317\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.8792 | + | 58.6805i | −0.0606068 | + | 0.104974i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 211.841 | + | 41.9917i | 0.377612 | + | 0.0748515i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 75.8301 | − | 208.342i | 0.134689 | − | 0.370056i | −0.853952 | − | 0.520352i | \(-0.825801\pi\) |
0.988641 | + | 0.150296i | \(0.0480228\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −171.838 | + | 974.539i | −0.304137 | + | 1.72485i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 337.214 | − | 91.3156i | 0.594734 | − | 0.161050i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −121.585 | − | 21.4387i | −0.213681 | − | 0.0376778i | 0.0657826 | − | 0.997834i | \(-0.479046\pi\) |
−0.279464 | + | 0.960156i | \(0.590157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −704.732 | − | 256.501i | −1.23421 | − | 0.449215i | −0.359171 | − | 0.933272i | \(-0.616940\pi\) |
−0.875036 | + | 0.484057i | \(0.839163\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.7972 | + | 84.7388i | −0.0293145 | + | 0.147886i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 139.043 | + | 80.2765i | 0.241814 | + | 0.139611i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.9521 | − | 27.6299i | −0.0276467 | − | 0.0478855i | 0.851871 | − | 0.523752i | \(-0.175468\pi\) |
−0.879518 | + | 0.475866i | \(0.842135\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 98.0560 | − | 252.647i | 0.169354 | − | 0.436350i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −133.364 | + | 23.5157i | −0.229542 | + | 0.0404745i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1069.68 | + | 897.569i | 1.83479 | + | 1.53957i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −404.182 | + | 442.264i | −0.690910 | + | 0.756006i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −43.4593 | − | 119.403i | −0.0740363 | − | 0.203413i | 0.897154 | − | 0.441717i | \(-0.145631\pi\) |
−0.971190 | + | 0.238304i | \(0.923408\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 744.468 | − | 624.683i | 1.26395 | − | 1.06058i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 442.977 | − | 731.096i | 0.749538 | − | 1.23705i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 606.986i | − | 1.02359i | −0.859109 | − | 0.511793i | \(-0.828981\pi\) | ||
0.859109 | − | 0.511793i | \(-0.171019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −138.537 | −0.232835 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 411.988 | − | 226.380i | 0.690097 | − | 0.379196i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −168.791 | − | 201.157i | −0.281787 | − | 0.335821i | 0.606522 | − | 0.795067i | \(-0.292564\pi\) |
−0.888309 | + | 0.459246i | \(0.848120\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −998.384 | + | 363.382i | −1.66120 | + | 0.604629i | −0.990551 | − | 0.137142i | \(-0.956208\pi\) |
−0.670653 | + | 0.741771i | \(0.733986\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 29.2245 | + | 219.730i | 0.0484652 | + | 0.364394i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1507.99 | − | 1797.16i | 2.49255 | − | 2.97051i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −180.588 | − | 1024.16i | −0.297509 | − | 1.68725i | −0.656828 | − | 0.754040i | \(-0.728102\pi\) |
0.359320 | − | 0.933215i | \(-0.383009\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −48.0643 | − | 310.907i | −0.0789233 | − | 0.510521i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 69.1423 | − | 39.9193i | 0.113163 | − | 0.0653344i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 244.419 | − | 423.347i | 0.398726 | − | 0.690614i | −0.594843 | − | 0.803842i | \(-0.702786\pi\) |
0.993569 | + | 0.113228i | \(0.0361190\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −399.594 | + | 456.260i | −0.649746 | + | 0.741886i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 122.120 | − | 335.523i | 0.197926 | − | 0.543797i | −0.800533 | − | 0.599288i | \(-0.795450\pi\) |
0.998459 | + | 0.0554913i | \(0.0176725\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −53.2686 | + | 302.101i | −0.0860559 | + | 0.488047i | 0.911068 | + | 0.412257i | \(0.135259\pi\) |
−0.997124 | + | 0.0757908i | \(0.975852\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 76.0271 | + | 33.2723i | 0.122427 | + | 0.0535786i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 196.299 | + | 34.6128i | 0.315087 | + | 0.0555583i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −749.523 | − | 272.804i | −1.19924 | − | 0.436486i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1883.33 | − | 640.699i | 3.00372 | − | 1.02185i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 94.3257 | + | 54.4590i | 0.149961 | + | 0.0865803i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 403.300 | + | 698.535i | 0.639144 | + | 1.10703i | 0.985621 | + | 0.168971i | \(0.0540444\pi\) |
−0.346477 | + | 0.938058i | \(0.612622\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −349.820 | − | 435.275i | −0.552638 | − | 0.687638i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 491.634 | − | 86.6884i | 0.774227 | − | 0.136517i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 176.386 | + | 148.005i | 0.276901 | + | 0.232347i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −275.559 | + | 143.912i | −0.431234 | + | 0.225214i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 196.557 | + | 540.037i | 0.306642 | + | 0.842492i | 0.993306 | + | 0.115516i | \(0.0368523\pi\) |
−0.686664 | + | 0.726975i | \(0.740925\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −499.279 | + | 418.945i | −0.776484 | + | 0.651548i | −0.942361 | − | 0.334599i | \(-0.891399\pi\) |
0.165876 | + | 0.986147i | \(0.446955\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −235.788 | − | 4.98846i | −0.365562 | − | 0.00773405i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 653.900i | 1.01066i | 0.862925 | + | 0.505332i | \(0.168630\pi\) | ||||
−0.862925 | + | 0.505332i | \(0.831370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1344.89 | −2.07225 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.90040 | + | 373.425i | −0.0121358 | + | 0.573617i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −691.419 | − | 824.001i | −1.05883 | − | 1.26187i | −0.963865 | − | 0.266390i | \(-0.914169\pi\) |
−0.0949693 | − | 0.995480i | \(-0.530275\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 112.423 | − | 40.9187i | 0.171638 | − | 0.0624713i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −201.895 | + | 317.841i | −0.307298 | + | 0.483776i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 624.556 | − | 744.317i | 0.947733 | − | 1.12946i | −0.0437255 | − | 0.999044i | \(-0.513923\pi\) |
0.991459 | − | 0.130421i | \(-0.0416329\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.91401 | − | 56.2251i | −0.0149985 | − | 0.0850607i | 0.976390 | − | 0.216017i | \(-0.0693065\pi\) |
−0.991388 | + | 0.130956i | \(0.958195\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 64.7387 | − | 52.0290i | 0.0976452 | − | 0.0784751i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1105.16 | + | 638.064i | −1.66189 | + | 0.959494i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 37.3661 | − | 64.7200i | 0.0560211 | − | 0.0970314i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 52.1912 | + | 153.416i | 0.0780137 | + | 0.229321i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −715.419 | + | 1965.60i | −1.06620 | + | 2.92936i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −57.6515 | + | 326.958i | −0.0856634 | + | 0.485821i | 0.911548 | + | 0.411194i | \(0.134888\pi\) |
−0.997211 | + | 0.0746277i | \(0.976223\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1370.59 | − | 332.493i | −2.03051 | − | 0.492583i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 389.350 | + | 68.6529i | 0.575111 | + | 0.101408i | 0.453636 | − | 0.891187i | \(-0.350127\pi\) |
0.121475 | + | 0.992595i | \(0.461238\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 448.727 | + | 163.323i | 0.660865 | + | 0.240535i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 649.379 | + | 568.729i | 0.953567 | + | 0.835138i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 74.8054 | + | 43.1889i | 0.109525 | + | 0.0632341i | 0.553762 | − | 0.832675i | \(-0.313192\pi\) |
−0.444237 | + | 0.895909i | \(0.646525\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 788.057 | + | 1364.95i | 1.15045 | + | 1.99263i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 654.668 | − | 101.207i | 0.952937 | − | 0.147318i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 528.858 | − | 93.2519i | 0.767573 | − | 0.135344i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 460.719 | + | 386.589i | 0.666742 | + | 0.559463i | 0.912099 | − | 0.409970i | \(-0.134461\pi\) |
−0.245357 | + | 0.969433i | \(0.578905\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −291.650 | + | 706.755i | −0.420851 | + | 1.01985i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −347.937 | − | 955.949i | −0.500629 | − | 1.37547i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 64.4066 | − | 54.0436i | 0.0924055 | − | 0.0775374i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −585.561 | − | 1065.66i | −0.837712 | − | 1.52455i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 839.245i | 1.19721i | 0.801044 | + | 0.598606i | \(0.204278\pi\) | ||||
−0.801044 | + | 0.598606i | \(0.795722\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1003.29 | 1.42716 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 237.665 | + | 144.003i | 0.337113 | + | 0.204259i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −224.984 | − | 268.126i | −0.318224 | − | 0.379244i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −500.860 | + | 182.298i | −0.706432 | + | 0.257120i | −0.670155 | − | 0.742222i | \(-0.733772\pi\) |
−0.0362774 | + | 0.999342i | \(0.511550\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −97.9529 | + | 444.627i | −0.137768 | + | 0.625354i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −57.0317 | + | 67.9677i | −0.0799883 | + | 0.0953263i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −227.686 | − | 1291.27i | −0.318442 | − | 1.80598i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −931.921 | − | 361.693i | −1.29975 | − | 0.504453i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −903.864 | + | 521.846i | −1.25711 | + | 0.725794i | −0.972512 | − | 0.232852i | \(-0.925194\pi\) |
−0.284600 | + | 0.958646i | \(0.591861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 339.769 | − | 588.497i | 0.471247 | − | 0.816224i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −92.1846 | − | 18.2731i | −0.127503 | − | 0.0252740i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −434.375 | + | 1193.44i | −0.599138 | + | 1.64612i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 144.189 | − | 817.738i | 0.198335 | − | 1.12481i | −0.709255 | − | 0.704952i | \(-0.750968\pi\) |
0.907589 | − | 0.419859i | \(-0.137921\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −723.136 | − | 92.2770i | −0.991956 | − | 0.126580i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.1967 | + | 5.67715i | 0.0440448 | + | 0.00776628i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −948.261 | − | 345.139i | −1.29367 | − | 0.470858i | −0.398741 | − | 0.917064i | \(-0.630553\pi\) |
−0.894930 | + | 0.446206i | \(0.852775\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −155.830 | + | 786.133i | −0.212013 | + | 1.06957i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −420.117 | − | 242.555i | −0.570037 | − | 0.329111i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −397.795 | − | 689.001i | −0.538288 | − | 0.932342i | −0.998996 | − | 0.0447908i | \(-0.985738\pi\) |
0.460708 | − | 0.887552i | \(-0.347595\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 276.813 | − | 713.224i | 0.373567 | − | 0.962515i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 82.1407 | − | 14.4836i | 0.110553 | − | 0.0194934i | −0.118098 | − | 0.993002i | \(-0.537680\pi\) |
0.228651 | + | 0.973509i | \(0.426569\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −530.381 | − | 445.043i | −0.711921 | − | 0.597373i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 275.963 | + | 60.7957i | 0.369429 | + | 0.0813865i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 89.4337 | + | 245.717i | 0.119404 | + | 0.328060i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 378.125 | − | 317.285i | 0.503496 | − | 0.422483i | −0.355338 | − | 0.934738i | \(-0.615634\pi\) |
0.858833 | + | 0.512255i | \(0.171190\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 155.938 | − | 257.362i | 0.207089 | − | 0.341783i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 358.137i | − | 0.474353i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −488.264 | −0.644998 | −0.322499 | − | 0.946570i | \(-0.604523\pi\) | ||||
−0.322499 | + | 0.946570i | \(0.604523\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −159.173 | + | 87.4628i | −0.209714 | + | 0.115234i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −54.9049 | − | 65.4331i | −0.0721483 | − | 0.0859830i | 0.728763 | − | 0.684766i | \(-0.240096\pi\) |
−0.800911 | + | 0.598783i | \(0.795651\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 52.7367 | − | 19.1946i | 0.0691176 | − | 0.0251567i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 267.223 | + | 110.272i | 0.349311 | + | 0.144147i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −332.462 | + | 396.212i | −0.433457 | + | 0.516574i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 158.722 | + | 900.158i | 0.206401 | + | 1.17056i | 0.895220 | + | 0.445624i | \(0.147018\pi\) |
−0.688819 | + | 0.724933i | \(0.741871\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 181.223 | + | 1172.25i | 0.235049 | + | 1.52043i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1171.92 | − | 676.608i | 1.51607 | − | 0.875301i | 0.516243 | − | 0.856442i | \(-0.327330\pi\) |
0.999822 | − | 0.0188590i | \(-0.00600335\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 753.918 | − | 1305.82i | 0.972798 | − | 1.68494i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −254.052 | + | 290.078i | −0.326965 | + | 0.373331i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 264.885 | − | 727.766i | 0.340032 | − | 0.934230i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 118.141 | − | 670.009i | 0.151268 | − | 0.857886i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −154.765 | + | 637.966i | −0.197656 | + | 0.814772i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1587.37 | − | 279.897i | −2.02213 | − | 0.356556i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 571.286 | + | 207.931i | 0.725903 | + | 0.264207i | 0.678430 | − | 0.734665i | \(-0.262661\pi\) |
0.0474733 | + | 0.998873i | \(0.484883\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −893.225 | + | 303.870i | −1.13210 | + | 0.385133i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 420.589 | + | 242.827i | 0.531718 | + | 0.306988i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 402.222 | + | 696.670i | 0.507216 | + | 0.878524i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1170.91 | + | 1456.94i | 1.47284 | + | 1.83263i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1368.77 | + | 241.352i | −1.71741 | + | 0.302825i | −0.943721 | − | 0.330743i | \(-0.892701\pi\) |
−0.773687 | + | 0.633569i | \(0.781589\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.5097 | − | 24.7616i | −0.0369333 | − | 0.0309907i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −351.089 | − | 223.015i | −0.438314 | − | 0.278420i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −281.844 | − | 774.361i | −0.350989 | − | 0.964335i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 89.2493 | − | 74.8890i | 0.110869 | − | 0.0930298i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −547.886 | − | 11.5914i | −0.678917 | − | 0.0143636i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 422.581i | 0.522350i | 0.965291 | + | 0.261175i | \(0.0841100\pi\) | ||||
−0.965291 | + | 0.261175i | \(0.915890\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 336.669 | 0.415129 | 0.207564 | − | 0.978221i | \(-0.433446\pi\) | ||||
0.207564 | + | 0.978221i | \(0.433446\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.2656 | + | 1383.28i | −0.0359971 | + | 1.70146i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1274.66 | − | 1519.08i | −1.56400 | − | 1.86391i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 282.993 | − | 103.001i | 0.346380 | − | 0.126072i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 136.117 | + | 260.634i | 0.166199 | + | 0.318235i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −275.130 | + | 327.887i | −0.335116 | + | 0.399375i | −0.907118 | − | 0.420877i | \(-0.861722\pi\) |
0.572002 | + | 0.820252i | \(0.306167\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 94.1304 | + | 533.840i | 0.114375 | + | 0.648651i | 0.987058 | + | 0.160364i | \(0.0512669\pi\) |
−0.872683 | + | 0.488287i | \(0.837622\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2405.85 | − | 1933.52i | 2.91618 | − | 2.34366i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −266.300 | + | 153.748i | −0.322008 | + | 0.185911i | −0.652287 | − | 0.757972i | \(-0.726190\pi\) |
0.330280 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −165.593 | + | 286.816i | −0.199751 | + | 0.345978i | −0.948447 | − | 0.316934i | \(-0.897347\pi\) |
0.748697 | + | 0.662912i | \(0.230680\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 152.611 | + | 448.601i | 0.183648 | + | 0.539833i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37.9978 | − | 104.398i | 0.0456156 | − | 0.125328i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −283.993 | + | 1610.61i | −0.340112 | + | 1.92887i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 312.478 | − | 714.009i | 0.373330 | − | 0.853058i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 747.773 | + | 131.853i | 0.891267 | + | 0.157154i | 0.600486 | − | 0.799635i | \(-0.294974\pi\) |
0.290781 | + | 0.956790i | \(0.406085\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −234.776 | − | 85.4514i | −0.279163 | − | 0.101607i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 462.823 | + | 405.343i | 0.549019 | + | 0.480833i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 849.546 | + | 490.486i | 1.00538 | + | 0.580456i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −575.681 | − | 997.108i | −0.679670 | − | 1.17722i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1206.94 | − | 186.585i | 1.42160 | − | 0.219770i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −90.2063 | + | 15.9058i | −0.106000 | + | 0.0186907i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −398.713 | − | 334.560i | −0.467424 | − | 0.392216i | 0.378430 | − | 0.925630i | \(-0.376464\pi\) |
−0.845854 | + | 0.533414i | \(0.820909\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2639.62 | − | 351.075i | 3.08728 | − | 0.410614i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 386.012 | + | 1060.56i | 0.450422 | + | 1.23752i | 0.932428 | + | 0.361356i | \(0.117686\pi\) |
−0.482006 | + | 0.876168i | \(0.660092\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 596.284 | − | 500.341i | 0.694160 | − | 0.582470i | −0.225945 | − | 0.974140i | \(-0.572547\pi\) |
0.920106 | + | 0.391670i | \(0.128103\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 143.342 | + | 260.868i | 0.166483 | + | 0.302982i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1131.63i | − | 1.31127i | −0.755078 | − | 0.655635i | \(-0.772401\pi\) | ||
0.755078 | − | 0.655635i | \(-0.227599\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1222.59 | 1.41340 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 707.233 | + | 428.518i | 0.815725 | + | 0.494254i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −640.469 | − | 763.281i | −0.737018 | − | 0.878344i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −175.313 | + | 63.8086i | −0.201277 | + | 0.0732590i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −735.547 | − | 672.212i | −0.842551 | − | 0.770002i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −663.575 | + | 790.818i | −0.758372 | + | 0.903792i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −104.520 | − | 592.762i | −0.119179 | − | 0.675898i | −0.984596 | − | 0.174845i | \(-0.944057\pi\) |
0.865417 | − | 0.501052i | \(-0.167054\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1198.08 | − | 464.994i | −1.36301 | − | 0.529004i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 661.931 | − | 382.166i | 0.751340 | − | 0.433786i | −0.0748378 | − | 0.997196i | \(-0.523844\pi\) |
0.826178 | + | 0.563409i | \(0.190511\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.19534 | − | 5.53449i | 0.00361873 | − | 0.00626782i | −0.864210 | − | 0.503131i | \(-0.832181\pi\) |
0.867829 | + | 0.496863i | \(0.165515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1765.88 | − | 350.037i | −1.99534 | − | 0.395522i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 246.492 | − | 677.231i | 0.277894 | − | 0.763507i | −0.719707 | − | 0.694278i | \(-0.755724\pi\) |
0.997601 | − | 0.0692290i | \(-0.0220539\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42.5442 | − | 241.280i | 0.0478563 | − | 0.271407i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1125.13 | − | 1131.11i | 1.26277 | − | 1.26948i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −349.455 | − | 61.6183i | −0.391327 | − | 0.0690015i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1201.21 | + | 437.206i | 1.34214 | + | 0.488499i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.5811 | + | 68.5144i | −0.0151406 | + | 0.0763818i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −607.819 | − | 350.924i | −0.676105 | − | 0.390350i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −129.555 | − | 224.396i | −0.143790 | − | 0.249052i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −41.8784 | + | 107.902i | −0.0463770 | + | 0.119493i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2173.08 | − | 383.173i | 2.40119 | − | 0.423395i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −982.519 | − | 824.431i | −1.08326 | − | 0.908965i | −0.0870746 | − | 0.996202i | \(-0.527752\pi\) |
−0.996188 | + | 0.0872369i | \(0.972196\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 220.549 | + | 696.270i | 0.242628 | + | 0.765973i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 76.4002 | + | 209.908i | 0.0838641 | + | 0.230415i | 0.974536 | − | 0.224233i | \(-0.0719875\pi\) |
−0.890672 | + | 0.454647i | \(0.849765\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −473.740 | + | 397.515i | −0.518883 | + | 0.435394i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1450.96 | + | 2394.68i | −1.58574 | + | 2.61714i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 58.7151i | − | 0.0640296i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 606.971 | 0.660469 | 0.330235 | − | 0.943899i | \(-0.392872\pi\) | ||||
0.330235 | + | 0.943899i | \(0.392872\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −265.779 | + | 146.041i | −0.288577 | + | 0.158568i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −168.184 | − | 200.434i | −0.182214 | − | 0.217154i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1462.77 | − | 532.406i | 1.58138 | − | 0.575574i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1123.81 | + | 864.701i | −1.21231 | + | 0.932795i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 363.623 | − | 433.349i | 0.391413 | − | 0.466468i | −0.533969 | − | 0.845504i | \(-0.679300\pi\) |
0.925382 | + | 0.379036i | \(0.123744\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −177.708 | − | 1007.83i | −0.190878 | − | 1.08252i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.43676 | − | 22.2309i | −0.00368356 | − | 0.0238273i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −547.892 | + | 316.325i | −0.585980 | + | 0.338316i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 174.168 | − | 301.667i | 0.185878 | − | 0.321950i | −0.757994 | − | 0.652262i | \(-0.773820\pi\) |
0.943872 | + | 0.330311i | \(0.107154\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 911.695 | − | 1040.98i | 0.970921 | − | 1.10861i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −591.614 | + | 1625.45i | −0.628708 | + | 1.72736i | 0.0558865 | + | 0.998437i | \(0.482202\pi\) |
−0.684595 | + | 0.728924i | \(0.740021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.2781 | + | 69.6328i | −0.0130203 | + | 0.0738418i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −566.893 | + | 852.080i | −0.599887 | + | 0.901672i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −200.007 | − | 35.2667i | −0.211201 | − | 0.0372404i | 0.0670465 | − | 0.997750i | \(-0.478642\pi\) |
−0.278247 | + | 0.960509i | \(0.589754\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −297.804 | − | 108.392i | −0.313808 | − | 0.114217i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 189.079 | − | 64.3236i | 0.198821 | − | 0.0676378i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 223.234 | + | 128.884i | 0.234243 | + | 0.135241i | 0.612528 | − | 0.790449i | \(-0.290153\pi\) |
−0.378285 | + | 0.925689i | \(0.623486\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −126.534 | − | 219.163i | −0.132496 | − | 0.229490i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −899.992 | − | 1119.84i | −0.940430 | − | 1.17016i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 761.761 | − | 134.319i | 0.794329 | − | 0.140062i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −97.8491 | − | 82.1051i | −0.101820 | − | 0.0854372i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 23.0774 | − | 545.150i | 0.0239641 | − | 0.566096i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 271.531 | + | 746.026i | 0.281379 | + | 0.773084i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −940.814 | + | 789.437i | −0.972921 | + | 0.816377i | −0.983006 | − | 0.183572i | \(-0.941234\pi\) |
0.0100857 | + | 0.999949i | \(0.496790\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −369.058 | − | 7.80801i | −0.380865 | − | 0.00805780i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1295.87i | 1.33458i | 0.744800 | + | 0.667288i | \(0.232545\pi\) | ||||
−0.744800 | + | 0.667288i | \(0.767455\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −499.262 | −0.513117 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 25.1076 | − | 1186.75i | 0.0257514 | − | 1.21718i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 480.625 | + | 572.787i | 0.491940 | + | 0.586271i | 0.953710 | − | 0.300729i | \(-0.0972299\pi\) |
−0.461770 | + | 0.887000i | \(0.652785\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 855.365 | − | 311.327i | 0.873713 | − | 0.318005i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −117.002 | − | 4.95296i | −0.119268 | − | 0.00504888i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 95.9650 | − | 114.367i | 0.0976246 | − | 0.116344i | −0.715020 | − | 0.699104i | \(-0.753583\pi\) |
0.812645 | + | 0.582759i | \(0.198027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 434.845 | + | 2466.13i | 0.441467 | + | 2.50368i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 106.303 | − | 85.4335i | 0.107704 | − | 0.0865588i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.8109 | + | 13.7472i | −0.0240758 | + | 0.0139002i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −289.456 | + | 501.353i | −0.292085 | + | 0.505906i | −0.974303 | − | 0.225243i | \(-0.927682\pi\) |
0.682217 | + | 0.731149i | \(0.261016\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −257.715 | − | 757.553i | −0.259532 | − | 0.762893i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −470.995 | + | 1294.05i | −0.473362 | + | 1.30055i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 262.672 | − | 1489.69i | 0.263463 | − | 1.49417i | −0.509914 | − | 0.860225i | \(-0.670323\pi\) |
0.773377 | − | 0.633947i | \(-0.218566\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 720.935 | − | 357.311i | 0.721657 | − | 0.357669i |
(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.k.a.29.4 | ✓ | 36 | |
3.2 | odd | 2 | 324.3.k.a.89.1 | 36 | |||
4.3 | odd | 2 | 432.3.bc.b.353.3 | 36 | |||
27.11 | odd | 18 | 2916.3.c.b.1457.2 | 36 | |||
27.13 | even | 9 | 324.3.k.a.233.1 | 36 | |||
27.14 | odd | 18 | inner | 108.3.k.a.41.4 | yes | 36 | |
27.16 | even | 9 | 2916.3.c.b.1457.35 | 36 | |||
108.95 | even | 18 | 432.3.bc.b.257.3 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.k.a.29.4 | ✓ | 36 | 1.1 | even | 1 | trivial | |
108.3.k.a.41.4 | yes | 36 | 27.14 | odd | 18 | inner | |
324.3.k.a.89.1 | 36 | 3.2 | odd | 2 | |||
324.3.k.a.233.1 | 36 | 27.13 | even | 9 | |||
432.3.bc.b.257.3 | 36 | 108.95 | even | 18 | |||
432.3.bc.b.353.3 | 36 | 4.3 | odd | 2 | |||
2916.3.c.b.1457.2 | 36 | 27.11 | odd | 18 | |||
2916.3.c.b.1457.35 | 36 | 27.16 | even | 9 |