Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,5,Mod(8,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.8");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.g (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.61794870793\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.4 | ||
Character | \(\chi\) | \(=\) | 35.8 |
Dual form | 35.5.g.a.22.4 |
$q$-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 \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.97419 | + | 2.97419i | −0.743548 | + | 0.743548i | −0.973259 | − | 0.229711i | \(-0.926222\pi\) |
0.229711 | + | 0.973259i | \(0.426222\pi\) | |||||||
\(3\) | −1.22954 | − | 1.22954i | −0.136615 | − | 0.136615i | 0.635492 | − | 0.772107i | \(-0.280797\pi\) |
−0.772107 | + | 0.635492i | \(0.780797\pi\) | |||||||
\(4\) | − | 1.69164i | − | 0.105728i | ||||||
\(5\) | −22.1755 | − | 11.5432i | −0.887021 | − | 0.461729i | ||||
\(6\) | 7.31376 | 0.203160 | ||||||||
\(7\) | 13.0958 | − | 13.0958i | 0.267261 | − | 0.267261i | ||||
\(8\) | −42.5558 | − | 42.5558i | −0.664935 | − | 0.664935i | ||||
\(9\) | − | 77.9765i | − | 0.962673i | ||||||
\(10\) | 100.286 | − | 31.6225i | 1.00286 | − | 0.316225i | ||||
\(11\) | 17.6226 | 0.145642 | 0.0728208 | − | 0.997345i | \(-0.476800\pi\) | ||||
0.0728208 | + | 0.997345i | \(0.476800\pi\) | |||||||
\(12\) | −2.07994 | + | 2.07994i | −0.0144440 | + | 0.0144440i | ||||
\(13\) | −160.405 | − | 160.405i | −0.949144 | − | 0.949144i | 0.0496243 | − | 0.998768i | \(-0.484198\pi\) |
−0.998768 | + | 0.0496243i | \(0.984198\pi\) | |||||||
\(14\) | 77.8989i | 0.397443i | ||||||||
\(15\) | 13.0728 | + | 41.4585i | 0.0581015 | + | 0.184260i | ||||
\(16\) | 280.205 | 1.09455 | ||||||||
\(17\) | −324.451 | + | 324.451i | −1.12267 | + | 1.12267i | −0.131328 | + | 0.991339i | \(0.541924\pi\) |
−0.991339 | + | 0.131328i | \(0.958076\pi\) | |||||||
\(18\) | 231.917 | + | 231.917i | 0.715793 | + | 0.715793i | ||||
\(19\) | 468.403i | 1.29752i | 0.760995 | + | 0.648758i | \(0.224711\pi\) | ||||
−0.760995 | + | 0.648758i | \(0.775289\pi\) | |||||||
\(20\) | −19.5270 | + | 37.5130i | −0.0488175 | + | 0.0937826i | ||||
\(21\) | −32.2036 | −0.0730239 | ||||||||
\(22\) | −52.4131 | + | 52.4131i | −0.108291 | + | 0.108291i | ||||
\(23\) | −625.505 | − | 625.505i | −1.18243 | − | 1.18243i | −0.979113 | − | 0.203315i | \(-0.934828\pi\) |
−0.203315 | − | 0.979113i | \(-0.565172\pi\) | |||||||
\(24\) | 104.648i | 0.181680i | ||||||||
\(25\) | 358.508 | + | 511.954i | 0.573613 | + | 0.819126i | ||||
\(26\) | 954.152 | 1.41147 | ||||||||
\(27\) | −195.468 | + | 195.468i | −0.268131 | + | 0.268131i | ||||
\(28\) | −22.1534 | − | 22.1534i | −0.0282569 | − | 0.0282569i | ||||
\(29\) | − | 755.645i | − | 0.898508i | −0.893404 | − | 0.449254i | \(-0.851690\pi\) | ||
0.893404 | − | 0.449254i | \(-0.148310\pi\) | |||||||
\(30\) | −162.187 | − | 84.4243i | −0.180207 | − | 0.0938048i | ||||
\(31\) | 553.934 | 0.576414 | 0.288207 | − | 0.957568i | \(-0.406941\pi\) | ||||
0.288207 | + | 0.957568i | \(0.406941\pi\) | |||||||
\(32\) | −152.489 | + | 152.489i | −0.148915 | + | 0.148915i | ||||
\(33\) | −21.6677 | − | 21.6677i | −0.0198969 | − | 0.0198969i | ||||
\(34\) | − | 1929.96i | − | 1.66951i | ||||||
\(35\) | −441.574 | + | 139.239i | −0.360469 | + | 0.113664i | ||||
\(36\) | −131.908 | −0.101781 | ||||||||
\(37\) | 555.586 | − | 555.586i | 0.405834 | − | 0.405834i | −0.474449 | − | 0.880283i | \(-0.657353\pi\) |
0.880283 | + | 0.474449i | \(0.157353\pi\) | |||||||
\(38\) | −1393.12 | − | 1393.12i | −0.964766 | − | 0.964766i | ||||
\(39\) | 394.449i | 0.259335i | ||||||||
\(40\) | 452.467 | + | 1434.93i | 0.282792 | + | 0.896830i | ||||
\(41\) | −1685.09 | −1.00243 | −0.501215 | − | 0.865323i | \(-0.667113\pi\) | ||||
−0.501215 | + | 0.865323i | \(0.667113\pi\) | |||||||
\(42\) | 95.7796 | − | 95.7796i | 0.0542968 | − | 0.0542968i | ||||
\(43\) | −416.902 | − | 416.902i | −0.225474 | − | 0.225474i | 0.585325 | − | 0.810799i | \(-0.300967\pi\) |
−0.810799 | + | 0.585325i | \(0.800967\pi\) | |||||||
\(44\) | − | 29.8112i | − | 0.0153983i | ||||||
\(45\) | −900.099 | + | 1729.17i | −0.444493 | + | 0.853911i | ||||
\(46\) | 3720.74 | 1.75839 | ||||||||
\(47\) | −319.293 | + | 319.293i | −0.144542 | + | 0.144542i | −0.775675 | − | 0.631133i | \(-0.782590\pi\) |
0.631133 | + | 0.775675i | \(0.282590\pi\) | |||||||
\(48\) | −344.522 | − | 344.522i | −0.149532 | − | 0.149532i | ||||
\(49\) | − | 343.000i | − | 0.142857i | ||||||
\(50\) | −2588.92 | − | 456.377i | −1.03557 | − | 0.182551i | ||||
\(51\) | 797.849 | 0.306747 | ||||||||
\(52\) | −271.348 | + | 271.348i | −0.100351 | + | 0.100351i | ||||
\(53\) | 3352.34 | + | 3352.34i | 1.19343 | + | 1.19343i | 0.976098 | + | 0.217329i | \(0.0697345\pi\) |
0.217329 | + | 0.976098i | \(0.430266\pi\) | |||||||
\(54\) | − | 1162.72i | − | 0.398737i | ||||||
\(55\) | −390.791 | − | 203.422i | −0.129187 | − | 0.0672469i | ||||
\(56\) | −1114.60 | −0.355422 | ||||||||
\(57\) | 575.920 | − | 575.920i | 0.177261 | − | 0.177261i | ||||
\(58\) | 2247.43 | + | 2247.43i | 0.668084 | + | 0.668084i | ||||
\(59\) | − | 4679.64i | − | 1.34434i | −0.740398 | − | 0.672168i | \(-0.765363\pi\) | ||
0.740398 | − | 0.672168i | \(-0.234637\pi\) | |||||||
\(60\) | 70.1329 | − | 22.1145i | 0.0194813 | − | 0.00614293i | ||||
\(61\) | 848.263 | 0.227966 | 0.113983 | − | 0.993483i | \(-0.463639\pi\) | ||||
0.113983 | + | 0.993483i | \(0.463639\pi\) | |||||||
\(62\) | −1647.51 | + | 1647.51i | −0.428592 | + | 0.428592i | ||||
\(63\) | −1021.16 | − | 1021.16i | −0.257285 | − | 0.257285i | ||||
\(64\) | 3576.21i | 0.873098i | ||||||||
\(65\) | 1705.48 | + | 5408.66i | 0.403664 | + | 1.28016i | ||||
\(66\) | 128.888 | 0.0295885 | ||||||||
\(67\) | 2472.93 | − | 2472.93i | 0.550886 | − | 0.550886i | −0.375811 | − | 0.926696i | \(-0.622636\pi\) |
0.926696 | + | 0.375811i | \(0.122636\pi\) | |||||||
\(68\) | 548.854 | + | 548.854i | 0.118697 | + | 0.118697i | ||||
\(69\) | 1538.16i | 0.323076i | ||||||||
\(70\) | 899.203 | − | 1727.45i | 0.183511 | − | 0.352541i | ||||
\(71\) | −2453.67 | −0.486743 | −0.243371 | − | 0.969933i | \(-0.578253\pi\) | ||||
−0.243371 | + | 0.969933i | \(0.578253\pi\) | |||||||
\(72\) | −3318.35 | + | 3318.35i | −0.640114 | + | 0.640114i | ||||
\(73\) | −2349.08 | − | 2349.08i | −0.440811 | − | 0.440811i | 0.451474 | − | 0.892284i | \(-0.350898\pi\) |
−0.892284 | + | 0.451474i | \(0.850898\pi\) | |||||||
\(74\) | 3304.84i | 0.603514i | ||||||||
\(75\) | 188.667 | − | 1070.27i | 0.0335408 | − | 0.190270i | ||||
\(76\) | 792.371 | 0.137183 | ||||||||
\(77\) | 230.782 | − | 230.782i | 0.0389243 | − | 0.0389243i | ||||
\(78\) | −1173.17 | − | 1173.17i | −0.192828 | − | 0.192828i | ||||
\(79\) | − | 1766.38i | − | 0.283028i | −0.989936 | − | 0.141514i | \(-0.954803\pi\) | ||
0.989936 | − | 0.141514i | \(-0.0451970\pi\) | |||||||
\(80\) | −6213.69 | − | 3234.46i | −0.970888 | − | 0.505385i | ||||
\(81\) | −5835.43 | −0.889411 | ||||||||
\(82\) | 5011.77 | − | 5011.77i | 0.745355 | − | 0.745355i | ||||
\(83\) | −885.758 | − | 885.758i | −0.128576 | − | 0.128576i | 0.639890 | − | 0.768466i | \(-0.278980\pi\) |
−0.768466 | + | 0.639890i | \(0.778980\pi\) | |||||||
\(84\) | 54.4769i | 0.00772065i | ||||||||
\(85\) | 10940.1 | − | 3449.66i | 1.51420 | − | 0.477462i | ||||
\(86\) | 2479.89 | 0.335302 | ||||||||
\(87\) | −929.094 | + | 929.094i | −0.122750 | + | 0.122750i | ||||
\(88\) | −749.945 | − | 749.945i | −0.0968421 | − | 0.0968421i | ||||
\(89\) | 3514.86i | 0.443740i | 0.975076 | + | 0.221870i | \(0.0712160\pi\) | ||||
−0.975076 | + | 0.221870i | \(0.928784\pi\) | |||||||
\(90\) | −2465.81 | − | 7819.95i | −0.304422 | − | 0.965426i | ||||
\(91\) | −4201.27 | −0.507339 | ||||||||
\(92\) | −1058.13 | + | 1058.13i | −0.125015 | + | 0.125015i | ||||
\(93\) | −681.083 | − | 681.083i | −0.0787470 | − | 0.0787470i | ||||
\(94\) | − | 1899.28i | − | 0.214948i | ||||||
\(95\) | 5406.88 | − | 10387.1i | 0.599101 | − | 1.15092i | ||||
\(96\) | 374.983 | 0.0406883 | ||||||||
\(97\) | 421.287 | − | 421.287i | 0.0447748 | − | 0.0447748i | −0.684365 | − | 0.729140i | \(-0.739920\pi\) |
0.729140 | + | 0.684365i | \(0.239920\pi\) | |||||||
\(98\) | 1020.15 | + | 1020.15i | 0.106221 | + | 0.106221i | ||||
\(99\) | − | 1374.15i | − | 0.140205i | ||||||
\(100\) | 866.042 | − | 606.468i | 0.0866042 | − | 0.0606468i | ||||
\(101\) | 9326.25 | 0.914249 | 0.457124 | − | 0.889403i | \(-0.348879\pi\) | ||||
0.457124 | + | 0.889403i | \(0.348879\pi\) | |||||||
\(102\) | −2372.96 | + | 2372.96i | −0.228081 | + | 0.228081i | ||||
\(103\) | −3554.31 | − | 3554.31i | −0.335028 | − | 0.335028i | 0.519464 | − | 0.854492i | \(-0.326132\pi\) |
−0.854492 | + | 0.519464i | \(0.826132\pi\) | |||||||
\(104\) | 13652.4i | 1.26224i | ||||||||
\(105\) | 714.131 | + | 371.733i | 0.0647738 | + | 0.0337172i | ||||
\(106\) | −19941.0 | −1.77474 | ||||||||
\(107\) | 5312.92 | − | 5312.92i | 0.464051 | − | 0.464051i | −0.435930 | − | 0.899981i | \(-0.643580\pi\) |
0.899981 | + | 0.435930i | \(0.143580\pi\) | |||||||
\(108\) | 330.661 | + | 330.661i | 0.0283489 | + | 0.0283489i | ||||
\(109\) | 9313.69i | 0.783915i | 0.919983 | + | 0.391957i | \(0.128202\pi\) | ||||
−0.919983 | + | 0.391957i | \(0.871798\pi\) | |||||||
\(110\) | 1767.30 | − | 557.272i | 0.146058 | − | 0.0460556i | ||||
\(111\) | −1366.23 | −0.110886 | ||||||||
\(112\) | 3669.50 | − | 3669.50i | 0.292531 | − | 0.292531i | ||||
\(113\) | 10930.8 | + | 10930.8i | 0.856043 | + | 0.856043i | 0.990869 | − | 0.134826i | \(-0.0430477\pi\) |
−0.134826 | + | 0.990869i | \(0.543048\pi\) | |||||||
\(114\) | 3425.79i | 0.263604i | ||||||||
\(115\) | 6650.56 | + | 21091.2i | 0.502878 | + | 1.59480i | ||||
\(116\) | −1278.28 | −0.0949971 | ||||||||
\(117\) | −12507.8 | + | 12507.8i | −0.913714 | + | 0.913714i | ||||
\(118\) | 13918.1 | + | 13918.1i | 0.999579 | + | 0.999579i | ||||
\(119\) | 8497.89i | 0.600091i | ||||||||
\(120\) | 1207.97 | − | 2320.62i | 0.0838871 | − | 0.161154i | ||||
\(121\) | −14330.4 | −0.978789 | ||||||||
\(122\) | −2522.90 | + | 2522.90i | −0.169504 | + | 0.169504i | ||||
\(123\) | 2071.88 | + | 2071.88i | 0.136947 | + | 0.136947i | ||||
\(124\) | − | 937.058i | − | 0.0609429i | ||||||
\(125\) | −2040.52 | − | 15491.2i | −0.130593 | − | 0.991436i | ||||
\(126\) | 6074.28 | 0.382608 | ||||||||
\(127\) | 14279.3 | − | 14279.3i | 0.885318 | − | 0.885318i | −0.108751 | − | 0.994069i | \(-0.534685\pi\) |
0.994069 | + | 0.108751i | \(0.0346852\pi\) | |||||||
\(128\) | −13076.2 | − | 13076.2i | −0.798106 | − | 0.798106i | ||||
\(129\) | 1025.19i | 0.0616064i | ||||||||
\(130\) | −21158.8 | − | 11014.0i | −1.25200 | − | 0.651715i | ||||
\(131\) | −9187.71 | −0.535383 | −0.267692 | − | 0.963505i | \(-0.586261\pi\) | ||||
−0.267692 | + | 0.963505i | \(0.586261\pi\) | |||||||
\(132\) | −36.6539 | + | 36.6539i | −0.00210365 | + | 0.00210365i | ||||
\(133\) | 6134.12 | + | 6134.12i | 0.346776 | + | 0.346776i | ||||
\(134\) | 14709.9i | 0.819220i | ||||||||
\(135\) | 6590.92 | − | 2078.27i | 0.361642 | − | 0.114034i | ||||
\(136\) | 27614.5 | 1.49300 | ||||||||
\(137\) | −2649.32 | + | 2649.32i | −0.141154 | + | 0.141154i | −0.774153 | − | 0.632999i | \(-0.781824\pi\) |
0.632999 | + | 0.774153i | \(0.281824\pi\) | |||||||
\(138\) | −4574.79 | − | 4574.79i | −0.240222 | − | 0.240222i | ||||
\(139\) | − | 29935.3i | − | 1.54937i | −0.632349 | − | 0.774684i | \(-0.717909\pi\) | ||
0.632349 | − | 0.774684i | \(-0.282091\pi\) | |||||||
\(140\) | 235.542 | + | 746.985i | 0.0120174 | + | 0.0381115i | ||||
\(141\) | 785.166 | 0.0394933 | ||||||||
\(142\) | 7297.69 | − | 7297.69i | 0.361917 | − | 0.361917i | ||||
\(143\) | −2826.76 | − | 2826.76i | −0.138235 | − | 0.138235i | ||||
\(144\) | − | 21849.4i | − | 1.05369i | ||||||
\(145\) | −8722.58 | + | 16756.8i | −0.414867 | + | 0.796996i | ||||
\(146\) | 13973.2 | 0.655528 | ||||||||
\(147\) | −421.731 | + | 421.731i | −0.0195165 | + | 0.0195165i | ||||
\(148\) | −939.853 | − | 939.853i | −0.0429078 | − | 0.0429078i | ||||
\(149\) | − | 35767.7i | − | 1.61108i | −0.592538 | − | 0.805542i | \(-0.701874\pi\) | ||
0.592538 | − | 0.805542i | \(-0.298126\pi\) | |||||||
\(150\) | 2622.04 | + | 3744.31i | 0.116535 | + | 0.166414i | ||||
\(151\) | −41532.5 | −1.82152 | −0.910760 | − | 0.412936i | \(-0.864503\pi\) | ||||
−0.910760 | + | 0.412936i | \(0.864503\pi\) | |||||||
\(152\) | 19933.3 | − | 19933.3i | 0.862764 | − | 0.862764i | ||||
\(153\) | 25299.5 | + | 25299.5i | 1.08076 | + | 1.08076i | ||||
\(154\) | 1372.78i | 0.0578842i | ||||||||
\(155\) | −12283.8 | − | 6394.18i | −0.511291 | − | 0.266147i | ||||
\(156\) | 667.266 | 0.0274189 | ||||||||
\(157\) | −20305.2 | + | 20305.2i | −0.823774 | + | 0.823774i | −0.986647 | − | 0.162873i | \(-0.947924\pi\) |
0.162873 | + | 0.986647i | \(0.447924\pi\) | |||||||
\(158\) | 5253.55 | + | 5253.55i | 0.210445 | + | 0.210445i | ||||
\(159\) | − | 8243.65i | − | 0.326081i | ||||||
\(160\) | 5141.75 | − | 1621.32i | 0.200850 | − | 0.0633326i | ||||
\(161\) | −16383.0 | −0.632035 | ||||||||
\(162\) | 17355.7 | − | 17355.7i | 0.661320 | − | 0.661320i | ||||
\(163\) | −24246.0 | − | 24246.0i | −0.912567 | − | 0.912567i | 0.0839065 | − | 0.996474i | \(-0.473260\pi\) |
−0.996474 | + | 0.0839065i | \(0.973260\pi\) | |||||||
\(164\) | 2850.56i | 0.105985i | ||||||||
\(165\) | 230.378 | + | 730.607i | 0.00846199 | + | 0.0268359i | ||||
\(166\) | 5268.83 | 0.191204 | ||||||||
\(167\) | −29647.0 | + | 29647.0i | −1.06303 | + | 1.06303i | −0.0651591 | + | 0.997875i | \(0.520755\pi\) |
−0.997875 | + | 0.0651591i | \(0.979245\pi\) | |||||||
\(168\) | 1370.45 | + | 1370.45i | 0.0485561 | + | 0.0485561i | ||||
\(169\) | 22898.7i | 0.801747i | ||||||||
\(170\) | −22277.9 | + | 42797.9i | −0.770863 | + | 1.48089i | ||||
\(171\) | 36524.4 | 1.24908 | ||||||||
\(172\) | −705.248 | + | 705.248i | −0.0238388 | + | 0.0238388i | ||||
\(173\) | −4080.56 | − | 4080.56i | −0.136341 | − | 0.136341i | 0.635642 | − | 0.771984i | \(-0.280735\pi\) |
−0.771984 | + | 0.635642i | \(0.780735\pi\) | |||||||
\(174\) | − | 5526.61i | − | 0.182541i | ||||||
\(175\) | 11399.4 | + | 2009.49i | 0.372225 | + | 0.0656161i | ||||
\(176\) | 4937.94 | 0.159412 | ||||||||
\(177\) | −5753.79 | + | 5753.79i | −0.183657 | + | 0.183657i | ||||
\(178\) | −10453.9 | − | 10453.9i | −0.329942 | − | 0.329942i | ||||
\(179\) | − | 20997.6i | − | 0.655335i | −0.944793 | − | 0.327668i | \(-0.893737\pi\) | ||
0.944793 | − | 0.327668i | \(-0.106263\pi\) | |||||||
\(180\) | 2925.14 | + | 1522.65i | 0.0902819 | + | 0.0469952i | ||||
\(181\) | 22890.3 | 0.698705 | 0.349352 | − | 0.936991i | \(-0.386402\pi\) | ||||
0.349352 | + | 0.936991i | \(0.386402\pi\) | |||||||
\(182\) | 12495.4 | − | 12495.4i | 0.377231 | − | 0.377231i | ||||
\(183\) | −1042.97 | − | 1042.97i | −0.0311437 | − | 0.0311437i | ||||
\(184\) | 53237.7i | 1.57248i | ||||||||
\(185\) | −18733.7 | + | 5907.17i | −0.547368 | + | 0.172598i | ||||
\(186\) | 4051.34 | 0.117104 | ||||||||
\(187\) | −5717.68 | + | 5717.68i | −0.163507 | + | 0.163507i | ||||
\(188\) | 540.130 | + | 540.130i | 0.0152821 | + | 0.0152821i | ||||
\(189\) | 5119.61i | 0.143322i | ||||||||
\(190\) | 14812.1 | + | 46974.3i | 0.410308 | + | 1.30123i | ||||
\(191\) | 57786.8 | 1.58402 | 0.792012 | − | 0.610506i | \(-0.209034\pi\) | ||||
0.792012 | + | 0.610506i | \(0.209034\pi\) | |||||||
\(192\) | 4397.08 | − | 4397.08i | 0.119278 | − | 0.119278i | ||||
\(193\) | −10258.8 | − | 10258.8i | −0.275412 | − | 0.275412i | 0.555863 | − | 0.831274i | \(-0.312388\pi\) |
−0.831274 | + | 0.555863i | \(0.812388\pi\) | |||||||
\(194\) | 2505.97i | 0.0665845i | ||||||||
\(195\) | 4553.21 | − | 8747.11i | 0.119742 | − | 0.230036i | ||||
\(196\) | −580.233 | −0.0151039 | ||||||||
\(197\) | 14590.3 | − | 14590.3i | 0.375951 | − | 0.375951i | −0.493688 | − | 0.869639i | \(-0.664351\pi\) |
0.869639 | + | 0.493688i | \(0.164351\pi\) | |||||||
\(198\) | 4086.99 | + | 4086.99i | 0.104249 | + | 0.104249i | ||||
\(199\) | − | 50015.5i | − | 1.26299i | −0.775381 | − | 0.631493i | \(-0.782442\pi\) | ||
0.775381 | − | 0.631493i | \(-0.217558\pi\) | |||||||
\(200\) | 6530.00 | − | 37043.2i | 0.163250 | − | 0.926081i | ||||
\(201\) | −6081.11 | −0.150519 | ||||||||
\(202\) | −27738.1 | + | 27738.1i | −0.679788 | + | 0.679788i | ||||
\(203\) | −9895.78 | − | 9895.78i | −0.240136 | − | 0.240136i | ||||
\(204\) | − | 1349.67i | − | 0.0324316i | ||||||
\(205\) | 37367.7 | + | 19451.3i | 0.889177 | + | 0.462851i | ||||
\(206\) | 21142.4 | 0.498219 | ||||||||
\(207\) | −48774.7 | + | 48774.7i | −1.13829 | + | 1.13829i | ||||
\(208\) | −44946.3 | − | 44946.3i | −1.03888 | − | 1.03888i | ||||
\(209\) | 8254.50i | 0.188972i | ||||||||
\(210\) | −3229.57 | + | 1018.36i | −0.0732328 | + | 0.0230920i | ||||
\(211\) | −37327.4 | −0.838422 | −0.419211 | − | 0.907889i | \(-0.637693\pi\) | ||||
−0.419211 | + | 0.907889i | \(0.637693\pi\) | |||||||
\(212\) | 5670.95 | − | 5670.95i | 0.126178 | − | 0.126178i | ||||
\(213\) | 3016.88 | + | 3016.88i | 0.0664965 | + | 0.0664965i | ||||
\(214\) | 31603.3i | 0.690089i | ||||||||
\(215\) | 4432.63 | + | 14057.4i | 0.0958925 | + | 0.304108i | ||||
\(216\) | 16636.6 | 0.356579 | ||||||||
\(217\) | 7254.21 | − | 7254.21i | 0.154053 | − | 0.154053i | ||||
\(218\) | −27700.7 | − | 27700.7i | −0.582878 | − | 0.582878i | ||||
\(219\) | 5776.57i | 0.120443i | ||||||||
\(220\) | −344.117 | + | 661.078i | −0.00710985 | + | 0.0136586i | ||||
\(221\) | 104087. | 2.13114 | ||||||||
\(222\) | 4063.43 | − | 4063.43i | 0.0824492 | − | 0.0824492i | ||||
\(223\) | 9094.35 | + | 9094.35i | 0.182878 | + | 0.182878i | 0.792609 | − | 0.609731i | \(-0.208722\pi\) |
−0.609731 | + | 0.792609i | \(0.708722\pi\) | |||||||
\(224\) | 3993.94i | 0.0795987i | ||||||||
\(225\) | 39920.4 | − | 27955.2i | 0.788550 | − | 0.552202i | ||||
\(226\) | −65020.7 | −1.27302 | ||||||||
\(227\) | −30816.0 | + | 30816.0i | −0.598032 | + | 0.598032i | −0.939789 | − | 0.341757i | \(-0.888978\pi\) |
0.341757 | + | 0.939789i | \(0.388978\pi\) | |||||||
\(228\) | −974.250 | − | 974.250i | −0.0187413 | − | 0.0187413i | ||||
\(229\) | − | 13976.7i | − | 0.266522i | −0.991081 | − | 0.133261i | \(-0.957455\pi\) | ||
0.991081 | − | 0.133261i | \(-0.0425448\pi\) | |||||||
\(230\) | −82509.5 | − | 42949.3i | −1.55973 | − | 0.811897i | ||||
\(231\) | −567.511 | −0.0106353 | ||||||||
\(232\) | −32157.1 | + | 32157.1i | −0.597449 | + | 0.597449i | ||||
\(233\) | 6660.07 | + | 6660.07i | 0.122678 | + | 0.122678i | 0.765780 | − | 0.643102i | \(-0.222353\pi\) |
−0.643102 | + | 0.765780i | \(0.722353\pi\) | |||||||
\(234\) | − | 74401.4i | − | 1.35878i | ||||||
\(235\) | 10766.2 | − | 3394.83i | 0.194951 | − | 0.0614727i | ||||
\(236\) | −7916.26 | −0.142133 | ||||||||
\(237\) | −2171.83 | + | 2171.83i | −0.0386660 | + | 0.0386660i | ||||
\(238\) | −25274.4 | − | 25274.4i | −0.446196 | − | 0.446196i | ||||
\(239\) | − | 7840.64i | − | 0.137264i | −0.997642 | − | 0.0686318i | \(-0.978137\pi\) | ||
0.997642 | − | 0.0686318i | \(-0.0218634\pi\) | |||||||
\(240\) | 3663.07 | + | 11616.9i | 0.0635949 | + | 0.201681i | ||||
\(241\) | −79730.7 | −1.37275 | −0.686375 | − | 0.727247i | \(-0.740799\pi\) | ||||
−0.686375 | + | 0.727247i | \(0.740799\pi\) | |||||||
\(242\) | 42621.5 | − | 42621.5i | 0.727776 | − | 0.727776i | ||||
\(243\) | 23007.7 | + | 23007.7i | 0.389638 | + | 0.389638i | ||||
\(244\) | − | 1434.96i | − | 0.0241023i | ||||||
\(245\) | −3959.32 | + | 7606.21i | −0.0659612 | + | 0.126717i | ||||
\(246\) | −12324.3 | −0.203654 | ||||||||
\(247\) | 75134.4 | − | 75134.4i | 1.23153 | − | 1.23153i | ||||
\(248\) | −23573.1 | − | 23573.1i | −0.383278 | − | 0.383278i | ||||
\(249\) | 2178.15i | 0.0351308i | ||||||||
\(250\) | 52142.7 | + | 40004.9i | 0.834283 | + | 0.640078i | ||||
\(251\) | 55697.0 | 0.884065 | 0.442032 | − | 0.896999i | \(-0.354258\pi\) | ||||
0.442032 | + | 0.896999i | \(0.354258\pi\) | |||||||
\(252\) | −1727.44 | + | 1727.44i | −0.0272021 | + | 0.0272021i | ||||
\(253\) | −11023.0 | − | 11023.0i | −0.172211 | − | 0.172211i | ||||
\(254\) | 84938.7i | 1.31655i | ||||||||
\(255\) | −17692.7 | − | 9209.74i | −0.272091 | − | 0.141634i | ||||
\(256\) | 20562.7 | 0.313762 | ||||||||
\(257\) | 53468.3 | − | 53468.3i | 0.809525 | − | 0.809525i | −0.175037 | − | 0.984562i | \(-0.556005\pi\) |
0.984562 | + | 0.175037i | \(0.0560046\pi\) | |||||||
\(258\) | −3049.12 | − | 3049.12i | −0.0458073 | − | 0.0458073i | ||||
\(259\) | − | 14551.7i | − | 0.216927i | ||||||
\(260\) | 9149.52 | − | 2885.06i | 0.135348 | − | 0.0426784i | ||||
\(261\) | −58922.6 | −0.864969 | ||||||||
\(262\) | 27326.0 | − | 27326.0i | 0.398083 | − | 0.398083i | ||||
\(263\) | 78703.8 | + | 78703.8i | 1.13785 | + | 1.13785i | 0.988835 | + | 0.149013i | \(0.0476097\pi\) |
0.149013 | + | 0.988835i | \(0.452390\pi\) | |||||||
\(264\) | 1844.17i | 0.0264602i | ||||||||
\(265\) | −35643.1 | − | 113037.i | −0.507556 | − | 1.60964i | ||||
\(266\) | −36488.1 | −0.515689 | ||||||||
\(267\) | 4321.66 | − | 4321.66i | 0.0606216 | − | 0.0606216i | ||||
\(268\) | −4183.31 | − | 4183.31i | −0.0582438 | − | 0.0582438i | ||||
\(269\) | 83582.2i | 1.15507i | 0.816365 | + | 0.577536i | \(0.195986\pi\) | ||||
−0.816365 | + | 0.577536i | \(0.804014\pi\) | |||||||
\(270\) | −13421.5 | + | 25783.8i | −0.184108 | + | 0.353688i | ||||
\(271\) | 32293.6 | 0.439721 | 0.219861 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219861 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(272\) | −90912.6 | + | 90912.6i | −1.22881 | + | 1.22881i | ||||
\(273\) | 5165.62 | + | 5165.62i | 0.0693102 | + | 0.0693102i | ||||
\(274\) | − | 15759.2i | − | 0.209910i | ||||||
\(275\) | 6317.86 | + | 9021.97i | 0.0835419 | + | 0.119299i | ||||
\(276\) | 2602.02 | 0.0341580 | ||||||||
\(277\) | −58656.0 | + | 58656.0i | −0.764456 | + | 0.764456i | −0.977124 | − | 0.212668i | \(-0.931785\pi\) |
0.212668 | + | 0.977124i | \(0.431785\pi\) | |||||||
\(278\) | 89033.5 | + | 89033.5i | 1.15203 | + | 1.15203i | ||||
\(279\) | − | 43193.8i | − | 0.554898i | ||||||
\(280\) | 24717.0 | + | 12866.1i | 0.315267 | + | 0.164109i | ||||
\(281\) | −60425.2 | −0.765254 | −0.382627 | − | 0.923903i | \(-0.624980\pi\) | ||||
−0.382627 | + | 0.923903i | \(0.624980\pi\) | |||||||
\(282\) | −2335.24 | + | 2335.24i | −0.0293652 | + | 0.0293652i | ||||
\(283\) | 72566.2 | + | 72566.2i | 0.906070 | + | 0.906070i | 0.995952 | − | 0.0898824i | \(-0.0286491\pi\) |
−0.0898824 | + | 0.995952i | \(0.528649\pi\) | |||||||
\(284\) | 4150.73i | 0.0514622i | ||||||||
\(285\) | −19419.3 | + | 6123.36i | −0.239080 | + | 0.0753876i | ||||
\(286\) | 16814.7 | 0.205568 | ||||||||
\(287\) | −22067.5 | + | 22067.5i | −0.267911 | + | 0.267911i | ||||
\(288\) | 11890.6 | + | 11890.6i | 0.143357 | + | 0.143357i | ||||
\(289\) | − | 127016.i | − | 1.52076i | ||||||
\(290\) | −23895.4 | − | 75780.7i | −0.284131 | − | 0.901078i | ||||
\(291\) | −1035.98 | −0.0122339 | ||||||||
\(292\) | −3973.80 | + | 3973.80i | −0.0466059 | + | 0.0466059i | ||||
\(293\) | −15395.9 | − | 15395.9i | −0.179336 | − | 0.179336i | 0.611730 | − | 0.791067i | \(-0.290474\pi\) |
−0.791067 | + | 0.611730i | \(0.790474\pi\) | |||||||
\(294\) | − | 2508.62i | − | 0.0290229i | ||||||
\(295\) | −54018.0 | + | 103773.i | −0.620719 | + | 1.19245i | ||||
\(296\) | −47286.8 | −0.539706 | ||||||||
\(297\) | −3444.65 | + | 3444.65i | −0.0390510 | + | 0.0390510i | ||||
\(298\) | 106380. | + | 106380.i | 1.19792 | + | 1.19792i | ||||
\(299\) | 200669.i | 2.24459i | ||||||||
\(300\) | −1810.51 | − | 319.157i | −0.0201167 | − | 0.00354619i | ||||
\(301\) | −10919.3 | −0.120521 | ||||||||
\(302\) | 123526. | − | 123526.i | 1.35439 | − | 1.35439i | ||||
\(303\) | −11467.0 | − | 11467.0i | −0.124900 | − | 0.124900i | ||||
\(304\) | 131249.i | 1.42020i | ||||||||
\(305\) | −18810.7 | − | 9791.68i | −0.202211 | − | 0.105259i | ||||
\(306\) | −150491. | −1.60720 | ||||||||
\(307\) | 40854.0 | − | 40854.0i | 0.433469 | − | 0.433469i | −0.456338 | − | 0.889807i | \(-0.650839\pi\) |
0.889807 | + | 0.456338i | \(0.150839\pi\) | |||||||
\(308\) | −390.401 | − | 390.401i | −0.00411538 | − | 0.00411538i | ||||
\(309\) | 8740.32i | 0.0915399i | ||||||||
\(310\) | 55551.8 | − | 17516.8i | 0.578063 | − | 0.182277i | ||||
\(311\) | −124994. | −1.29231 | −0.646157 | − | 0.763205i | \(-0.723625\pi\) | ||||
−0.646157 | + | 0.763205i | \(0.723625\pi\) | |||||||
\(312\) | 16786.1 | − | 16786.1i | 0.172441 | − | 0.172441i | ||||
\(313\) | −27798.6 | − | 27798.6i | −0.283749 | − | 0.283749i | 0.550853 | − | 0.834602i | \(-0.314302\pi\) |
−0.834602 | + | 0.550853i | \(0.814302\pi\) | |||||||
\(314\) | − | 120783.i | − | 1.22503i | ||||||
\(315\) | 10857.3 | + | 34432.4i | 0.109421 | + | 0.347013i | ||||
\(316\) | −2988.08 | −0.0299239 | ||||||||
\(317\) | 83808.0 | − | 83808.0i | 0.834002 | − | 0.834002i | −0.154060 | − | 0.988062i | \(-0.549235\pi\) |
0.988062 | + | 0.154060i | \(0.0492348\pi\) | |||||||
\(318\) | 24518.2 | + | 24518.2i | 0.242457 | + | 0.242457i | ||||
\(319\) | − | 13316.5i | − | 0.130860i | ||||||
\(320\) | 41280.9 | − | 79304.3i | 0.403134 | − | 0.774456i | ||||
\(321\) | −13064.9 | −0.126793 | ||||||||
\(322\) | 48726.1 | − | 48726.1i | 0.469948 | − | 0.469948i | ||||
\(323\) | −151974. | − | 151974.i | −1.45668 | − | 1.45668i | ||||
\(324\) | 9871.45i | 0.0940353i | ||||||||
\(325\) | 24613.5 | − | 139627.i | 0.233027 | − | 1.32191i | ||||
\(326\) | 144225. | 1.35708 | ||||||||
\(327\) | 11451.5 | − | 11451.5i | 0.107095 | − | 0.107095i | ||||
\(328\) | 71710.2 | + | 71710.2i | 0.666551 | + | 0.666551i | ||||
\(329\) | 8362.81i | 0.0772610i | ||||||||
\(330\) | −2858.15 | − | 1487.78i | −0.0262457 | − | 0.0136619i | ||||
\(331\) | −37373.1 | −0.341117 | −0.170558 | − | 0.985348i | \(-0.554557\pi\) | ||||
−0.170558 | + | 0.985348i | \(0.554557\pi\) | |||||||
\(332\) | −1498.38 | + | 1498.38i | −0.0135940 | + | 0.0135940i | ||||
\(333\) | −43322.7 | − | 43322.7i | −0.390685 | − | 0.390685i | ||||
\(334\) | − | 176352.i | − | 1.58083i | ||||||
\(335\) | −83384.0 | + | 26292.9i | −0.743007 | + | 0.234288i | ||||
\(336\) | −9023.59 | −0.0799283 | ||||||||
\(337\) | −7169.19 | + | 7169.19i | −0.0631263 | + | 0.0631263i | −0.737965 | − | 0.674839i | \(-0.764213\pi\) |
0.674839 | + | 0.737965i | \(0.264213\pi\) | |||||||
\(338\) | −68105.1 | − | 68105.1i | −0.596138 | − | 0.596138i | ||||
\(339\) | − | 26879.7i | − | 0.233897i | ||||||
\(340\) | −5835.59 | − | 18506.7i | −0.0504809 | − | 0.160092i | ||||
\(341\) | 9761.77 | 0.0839498 | ||||||||
\(342\) | −108631. | + | 108631.i | −0.928754 | + | 0.928754i | ||||
\(343\) | −4491.86 | − | 4491.86i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 35483.2i | 0.299851i | ||||||||
\(345\) | 17755.4 | − | 34109.6i | 0.149173 | − | 0.286575i | ||||
\(346\) | 24272.7 | 0.202753 | ||||||||
\(347\) | 9680.63 | − | 9680.63i | 0.0803979 | − | 0.0803979i | −0.665764 | − | 0.746162i | \(-0.731894\pi\) |
0.746162 | + | 0.665764i | \(0.231894\pi\) | |||||||
\(348\) | 1571.69 | + | 1571.69i | 0.0129781 | + | 0.0129781i | ||||
\(349\) | − | 72057.7i | − | 0.591602i | −0.955250 | − | 0.295801i | \(-0.904413\pi\) | ||
0.955250 | − | 0.295801i | \(-0.0955866\pi\) | |||||||
\(350\) | −39880.6 | + | 27927.4i | −0.325556 | + | 0.227979i | ||||
\(351\) | 62708.0 | 0.508990 | ||||||||
\(352\) | −2687.26 | + | 2687.26i | −0.0216883 | + | 0.0216883i | ||||
\(353\) | 52704.4 | + | 52704.4i | 0.422958 | + | 0.422958i | 0.886221 | − | 0.463263i | \(-0.153321\pi\) |
−0.463263 | + | 0.886221i | \(0.653321\pi\) | |||||||
\(354\) | − | 34225.7i | − | 0.273115i | ||||||
\(355\) | 54411.5 | + | 28323.3i | 0.431751 | + | 0.224743i | ||||
\(356\) | 5945.89 | 0.0469155 | ||||||||
\(357\) | 10448.5 | − | 10448.5i | 0.0819816 | − | 0.0819816i | ||||
\(358\) | 62450.9 | + | 62450.9i | 0.487273 | + | 0.487273i | ||||
\(359\) | 232709.i | 1.80561i | 0.430046 | + | 0.902807i | \(0.358497\pi\) | ||||
−0.430046 | + | 0.902807i | \(0.641503\pi\) | |||||||
\(360\) | 111891. | − | 35281.8i | 0.863354 | − | 0.272236i | ||||
\(361\) | −89080.8 | −0.683549 | ||||||||
\(362\) | −68080.0 | + | 68080.0i | −0.519520 | + | 0.519520i | ||||
\(363\) | 17619.8 | + | 17619.8i | 0.133717 | + | 0.133717i | ||||
\(364\) | 7107.04i | 0.0536397i | ||||||||
\(365\) | 24976.2 | + | 79208.1i | 0.187474 | + | 0.594543i | ||||
\(366\) | 6203.99 | 0.0463137 | ||||||||
\(367\) | −44132.8 | + | 44132.8i | −0.327664 | + | 0.327664i | −0.851698 | − | 0.524033i | \(-0.824427\pi\) |
0.524033 | + | 0.851698i | \(0.324427\pi\) | |||||||
\(368\) | −175269. | − | 175269.i | −1.29423 | − | 1.29423i | ||||
\(369\) | 131397.i | 0.965012i | ||||||||
\(370\) | 38148.5 | − | 73286.6i | 0.278660 | − | 0.535329i | ||||
\(371\) | 87803.1 | 0.637914 | ||||||||
\(372\) | −1152.15 | + | 1152.15i | −0.00832573 | + | 0.00832573i | ||||
\(373\) | 90918.1 | + | 90918.1i | 0.653480 | + | 0.653480i | 0.953829 | − | 0.300349i | \(-0.0971031\pi\) |
−0.300349 | + | 0.953829i | \(0.597103\pi\) | |||||||
\(374\) | − | 34010.9i | − | 0.243151i | ||||||
\(375\) | −16538.1 | + | 21555.9i | −0.117604 | + | 0.153286i | ||||
\(376\) | 27175.6 | 0.192222 | ||||||||
\(377\) | −121210. | + | 121210.i | −0.852813 | + | 0.852813i | ||||
\(378\) | −15226.7 | − | 15226.7i | −0.106567 | − | 0.106567i | ||||
\(379\) | 90612.2i | 0.630824i | 0.948955 | + | 0.315412i | \(0.102143\pi\) | ||||
−0.948955 | + | 0.315412i | \(0.897857\pi\) | |||||||
\(380\) | −17571.2 | − | 9146.51i | −0.121684 | − | 0.0633415i | ||||
\(381\) | −35113.8 | −0.241896 | ||||||||
\(382\) | −171869. | + | 171869.i | −1.17780 | + | 1.17780i | ||||
\(383\) | −178249. | − | 178249.i | −1.21515 | − | 1.21515i | −0.969310 | − | 0.245840i | \(-0.920936\pi\) |
−0.245840 | − | 0.969310i | \(-0.579064\pi\) | |||||||
\(384\) | 32155.3i | 0.218067i | ||||||||
\(385\) | −7781.69 | + | 2453.75i | −0.0524992 | + | 0.0165542i | ||||
\(386\) | 61023.4 | 0.409564 | ||||||||
\(387\) | −32508.5 | + | 32508.5i | −0.217058 | + | 0.217058i | ||||
\(388\) | −712.666 | − | 712.666i | −0.00473394 | − | 0.00473394i | ||||
\(389\) | − | 125379.i | − | 0.828564i | −0.910149 | − | 0.414282i | \(-0.864033\pi\) | ||
0.910149 | − | 0.414282i | \(-0.135967\pi\) | |||||||
\(390\) | 12473.5 | + | 39557.7i | 0.0820084 | + | 0.260077i | ||||
\(391\) | 405891. | 2.65495 | ||||||||
\(392\) | −14596.6 | + | 14596.6i | −0.0949907 | + | 0.0949907i | ||||
\(393\) | 11296.6 | + | 11296.6i | 0.0731415 | + | 0.0731415i | ||||
\(394\) | 86788.7i | 0.559076i | ||||||||
\(395\) | −20389.7 | + | 39170.4i | −0.130682 | + | 0.251052i | ||||
\(396\) | −2324.57 | −0.0148235 | ||||||||
\(397\) | 187283. | − | 187283.i | 1.18828 | − | 1.18828i | 0.210735 | − | 0.977543i | \(-0.432414\pi\) |
0.977543 | − | 0.210735i | \(-0.0675858\pi\) | |||||||
\(398\) | 148756. | + | 148756.i | 0.939091 | + | 0.939091i | ||||
\(399\) | − | 15084.3i | − | 0.0947498i | ||||||
\(400\) | 100456. | + | 143452.i | 0.627848 | + | 0.896574i | ||||
\(401\) | −159884. | −0.994296 | −0.497148 | − | 0.867666i | \(-0.665619\pi\) | ||||
−0.497148 | + | 0.867666i | \(0.665619\pi\) | |||||||
\(402\) | 18086.4 | − | 18086.4i | 0.111918 | − | 0.111918i | ||||
\(403\) | −88853.9 | − | 88853.9i | −0.547100 | − | 0.547100i | ||||
\(404\) | − | 15776.7i | − | 0.0966613i | ||||||
\(405\) | 129404. | + | 67359.6i | 0.788926 | + | 0.410667i | ||||
\(406\) | 58863.9 | 0.357106 | ||||||||
\(407\) | 9790.89 | − | 9790.89i | 0.0591062 | − | 0.0591062i | ||||
\(408\) | −33953.1 | − | 33953.1i | −0.203967 | − | 0.203967i | ||||
\(409\) | 99389.4i | 0.594146i | 0.954855 | + | 0.297073i | \(0.0960105\pi\) | ||||
−0.954855 | + | 0.297073i | \(0.903989\pi\) | |||||||
\(410\) | −168991. | + | 53286.7i | −1.00530 | + | 0.316994i | ||||
\(411\) | 6514.89 | 0.0385676 | ||||||||
\(412\) | −6012.62 | + | 6012.62i | −0.0354217 | + | 0.0354217i | ||||
\(413\) | −61283.6 | − | 61283.6i | −0.359289 | − | 0.359289i | ||||
\(414\) | − | 290130.i | − | 1.69275i | ||||||
\(415\) | 9417.66 | + | 29866.6i | 0.0546823 | + | 0.173416i | ||||
\(416\) | 48920.2 | 0.282684 | ||||||||
\(417\) | −36806.6 | + | 36806.6i | −0.211667 | + | 0.211667i | ||||
\(418\) | −24550.5 | − | 24550.5i | −0.140510 | − | 0.140510i | ||||
\(419\) | 155849.i | 0.887721i | 0.896096 | + | 0.443860i | \(0.146391\pi\) | ||||
−0.896096 | + | 0.443860i | \(0.853609\pi\) | |||||||
\(420\) | 628.838 | − | 1208.05i | 0.00356484 | − | 0.00684838i | ||||
\(421\) | 150890. | 0.851325 | 0.425663 | − | 0.904882i | \(-0.360041\pi\) | ||||
0.425663 | + | 0.904882i | \(0.360041\pi\) | |||||||
\(422\) | 111019. | − | 111019.i | 0.623407 | − | 0.623407i | ||||
\(423\) | 24897.4 | + | 24897.4i | 0.139147 | + | 0.139147i | ||||
\(424\) | − | 285323.i | − | 1.58710i | ||||||
\(425\) | −282422. | − | 49785.5i | −1.56358 | − | 0.275629i | ||||
\(426\) | −17945.6 | −0.0988867 | ||||||||
\(427\) | 11108.7 | − | 11108.7i | 0.0609266 | − | 0.0609266i | ||||
\(428\) | −8987.56 | − | 8987.56i | −0.0490630 | − | 0.0490630i | ||||
\(429\) | 6951.22i | 0.0377700i | ||||||||
\(430\) | −54992.9 | − | 28625.9i | −0.297420 | − | 0.154818i | ||||
\(431\) | 39190.3 | 0.210972 | 0.105486 | − | 0.994421i | \(-0.466360\pi\) | ||||
0.105486 | + | 0.994421i | \(0.466360\pi\) | |||||||
\(432\) | −54770.9 | + | 54770.9i | −0.293483 | + | 0.293483i | ||||
\(433\) | −132917. | − | 132917.i | −0.708933 | − | 0.708933i | 0.257378 | − | 0.966311i | \(-0.417142\pi\) |
−0.966311 | + | 0.257378i | \(0.917142\pi\) | |||||||
\(434\) | 43150.8i | 0.229092i | ||||||||
\(435\) | 31327.9 | − | 9878.42i | 0.165559 | − | 0.0522046i | ||||
\(436\) | 15755.4 | 0.0828814 | ||||||||
\(437\) | 292989. | − | 292989.i | 1.53422 | − | 1.53422i | ||||
\(438\) | −17180.6 | − | 17180.6i | −0.0895551 | − | 0.0895551i | ||||
\(439\) | − | 163837.i | − | 0.850124i | −0.905164 | − | 0.425062i | \(-0.860252\pi\) | ||
0.905164 | − | 0.425062i | \(-0.139748\pi\) | |||||||
\(440\) | 7973.65 | + | 25287.2i | 0.0411862 | + | 0.130616i | ||||
\(441\) | −26745.9 | −0.137525 | ||||||||
\(442\) | −309575. | + | 309575.i | −1.58461 | + | 1.58461i | ||||
\(443\) | 27337.1 | + | 27337.1i | 0.139298 | + | 0.139298i | 0.773317 | − | 0.634019i | \(-0.218596\pi\) |
−0.634019 | + | 0.773317i | \(0.718596\pi\) | |||||||
\(444\) | 2311.17i | 0.0117237i | ||||||||
\(445\) | 40572.8 | − | 77943.9i | 0.204887 | − | 0.393607i | ||||
\(446\) | −54096.7 | −0.271957 | ||||||||
\(447\) | −43977.7 | + | 43977.7i | −0.220099 | + | 0.220099i | ||||
\(448\) | 46833.3 | + | 46833.3i | 0.233345 | + | 0.233345i | ||||
\(449\) | 160196.i | 0.794617i | 0.917685 | + | 0.397308i | \(0.130056\pi\) | ||||
−0.917685 | + | 0.397308i | \(0.869944\pi\) | |||||||
\(450\) | −35586.6 | + | 201875.i | −0.175737 | + | 0.996914i | ||||
\(451\) | −29695.6 | −0.145995 | ||||||||
\(452\) | 18491.0 | − | 18491.0i | 0.0905073 | − | 0.0905073i | ||||
\(453\) | 51065.7 | + | 51065.7i | 0.248847 | + | 0.248847i | ||||
\(454\) | − | 183305.i | − | 0.889331i | ||||||
\(455\) | 93165.4 | + | 48496.2i | 0.450020 | + | 0.234253i | ||||
\(456\) | −49017.5 | −0.235733 | ||||||||
\(457\) | −106963. | + | 106963.i | −0.512153 | + | 0.512153i | −0.915186 | − | 0.403033i | \(-0.867956\pi\) |
0.403033 | + | 0.915186i | \(0.367956\pi\) | |||||||
\(458\) | 41569.3 | + | 41569.3i | 0.198172 | + | 0.198172i | ||||
\(459\) | − | 126839.i | − | 0.602044i | ||||||
\(460\) | 35678.8 | − | 11250.4i | 0.168614 | − | 0.0531681i | ||||
\(461\) | −23815.9 | −0.112064 | −0.0560318 | − | 0.998429i | \(-0.517845\pi\) | ||||
−0.0560318 | + | 0.998429i | \(0.517845\pi\) | |||||||
\(462\) | 1687.89 | − | 1687.89i | 0.00790787 | − | 0.00790787i | ||||
\(463\) | −122436. | − | 122436.i | −0.571147 | − | 0.571147i | 0.361302 | − | 0.932449i | \(-0.382332\pi\) |
−0.932449 | + | 0.361302i | \(0.882332\pi\) | |||||||
\(464\) | − | 211735.i | − | 0.983462i | ||||||
\(465\) | 7241.48 | + | 22965.2i | 0.0334905 | + | 0.106210i | ||||
\(466\) | −39616.7 | −0.182434 | ||||||||
\(467\) | 37772.5 | − | 37772.5i | 0.173198 | − | 0.173198i | −0.615185 | − | 0.788383i | \(-0.710919\pi\) |
0.788383 | + | 0.615185i | \(0.210919\pi\) | |||||||
\(468\) | 21158.8 | + | 21158.8i | 0.0966048 | + | 0.0966048i | ||||
\(469\) | − | 64769.9i | − | 0.294461i | ||||||
\(470\) | −21923.8 | + | 42117.5i | −0.0992476 | + | 0.190663i | ||||
\(471\) | 49932.0 | 0.225080 | ||||||||
\(472\) | −199146. | + | 199146.i | −0.893896 | + | 0.893896i | ||||
\(473\) | −7346.90 | − | 7346.90i | −0.0328384 | − | 0.0328384i | ||||
\(474\) | − | 12918.9i | − | 0.0575000i | ||||||
\(475\) | −239801. | + | 167927.i | −1.06283 | + | 0.744273i | ||||
\(476\) | 14375.4 | 0.0634462 | ||||||||
\(477\) | 261403. | − | 261403.i | 1.14888 | − | 1.14888i | ||||
\(478\) | 23319.6 | + | 23319.6i | 0.102062 | + | 0.102062i | ||||
\(479\) | − | 181209.i | − | 0.789787i | −0.918727 | − | 0.394893i | \(-0.870782\pi\) | ||
0.918727 | − | 0.394893i | \(-0.129218\pi\) | |||||||
\(480\) | −8315.45 | − | 4328.51i | −0.0360914 | − | 0.0187869i | ||||
\(481\) | −178238. | −0.770389 | ||||||||
\(482\) | 237135. | − | 237135.i | 1.02071 | − | 1.02071i | ||||
\(483\) | 20143.5 | + | 20143.5i | 0.0863456 | + | 0.0863456i | ||||
\(484\) | 24242.0i | 0.103485i | ||||||||
\(485\) | −14205.3 | + | 4479.25i | −0.0603901 | + | 0.0190424i | ||||
\(486\) | −136859. | −0.579429 | ||||||||
\(487\) | 38680.6 | − | 38680.6i | 0.163093 | − | 0.163093i | −0.620842 | − | 0.783935i | \(-0.713209\pi\) |
0.783935 | + | 0.620842i | \(0.213209\pi\) | |||||||
\(488\) | −36098.5 | − | 36098.5i | −0.151583 | − | 0.151583i | ||||
\(489\) | 59622.7i | 0.249341i | ||||||||
\(490\) | −10846.5 | − | 34398.1i | −0.0451751 | − | 0.143266i | ||||
\(491\) | 281643. | 1.16825 | 0.584126 | − | 0.811663i | \(-0.301437\pi\) | ||||
0.584126 | + | 0.811663i | \(0.301437\pi\) | |||||||
\(492\) | 3504.87 | − | 3504.87i | 0.0144791 | − | 0.0144791i | ||||
\(493\) | 245170. | + | 245170.i | 1.00873 | + | 1.00873i | ||||
\(494\) | 446928.i | 1.83140i | ||||||||
\(495\) | −15862.1 | + | 30472.5i | −0.0647367 | + | 0.124365i | ||||
\(496\) | 155215. | 0.630914 | ||||||||
\(497\) | −32132.8 | + | 32132.8i | −0.130088 | + | 0.130088i | ||||
\(498\) | −6478.22 | − | 6478.22i | −0.0261214 | − | 0.0261214i | ||||
\(499\) | − | 460535.i | − | 1.84953i | −0.380536 | − | 0.924766i | \(-0.624260\pi\) | ||
0.380536 | − | 0.924766i | \(-0.375740\pi\) | |||||||
\(500\) | −26205.5 | + | 3451.82i | −0.104822 | + | 0.0138073i | ||||
\(501\) | 72904.1 | 0.290453 | ||||||||
\(502\) | −165653. | + | 165653.i | −0.657345 | + | 0.657345i | ||||
\(503\) | 51536.3 | + | 51536.3i | 0.203694 | + | 0.203694i | 0.801580 | − | 0.597887i | \(-0.203993\pi\) |
−0.597887 | + | 0.801580i | \(0.703993\pi\) | |||||||
\(504\) | 86913.0i | 0.342155i | ||||||||
\(505\) | −206815. | − | 107655.i | −0.810958 | − | 0.422135i | ||||
\(506\) | 65569.3 | 0.256094 | ||||||||
\(507\) | 28154.8 | − | 28154.8i | 0.109531 | − | 0.109531i | ||||
\(508\) | −24155.4 | − | 24155.4i | −0.0936025 | − | 0.0936025i | ||||
\(509\) | 159178.i | 0.614395i | 0.951646 | + | 0.307198i | \(0.0993912\pi\) | ||||
−0.951646 | + | 0.307198i | \(0.900609\pi\) | |||||||
\(510\) | 80013.1 | − | 25230.0i | 0.307624 | − | 0.0970012i | ||||
\(511\) | −61526.2 | −0.235623 | ||||||||
\(512\) | 148061. | − | 148061.i | 0.564808 | − | 0.564808i | ||||
\(513\) | −91557.7 | − | 91557.7i | −0.347904 | − | 0.347904i | ||||
\(514\) | 318050.i | 1.20384i | ||||||||
\(515\) | 37790.6 | + | 119847.i | 0.142485 | + | 0.451869i | ||||
\(516\) | 1734.26 | 0.00651350 | ||||||||
\(517\) | −5626.79 | + | 5626.79i | −0.0210513 | + | 0.0210513i | ||||
\(518\) | 43279.5 | + | 43279.5i | 0.161296 | + | 0.161296i | ||||
\(519\) | 10034.4i | 0.0372526i | ||||||||
\(520\) | 157592. | − | 302748.i | 0.582811 | − | 1.11963i | ||||
\(521\) | 302546. | 1.11459 | 0.557295 | − | 0.830314i | \(-0.311839\pi\) | ||||
0.557295 | + | 0.830314i | \(0.311839\pi\) | |||||||
\(522\) | 175247. | − | 175247.i | 0.643146 | − | 0.643146i | ||||
\(523\) | 286177. | + | 286177.i | 1.04624 | + | 1.04624i | 0.998878 | + | 0.0473640i | \(0.0150821\pi\) |
0.0473640 | + | 0.998878i | \(0.484918\pi\) | |||||||
\(524\) | 15542.3i | 0.0566048i | ||||||||
\(525\) | −11545.2 | − | 16486.7i | −0.0418875 | − | 0.0598158i | ||||
\(526\) | −468161. | −1.69209 | ||||||||
\(527\) | −179724. | + | 179724.i | −0.647121 | + | 0.647121i | ||||
\(528\) | −6071.38 | − | 6071.38i | −0.0217781 | − | 0.0217781i | ||||
\(529\) | 502672.i | 1.79628i | ||||||||
\(530\) | 442202. | + | 230183.i | 1.57423 | + | 0.819449i | ||||
\(531\) | −364901. | −1.29416 | ||||||||
\(532\) | 10376.7 | − | 10376.7i | 0.0366638 | − | 0.0366638i | ||||
\(533\) | 270297. | + | 270297.i | 0.951450 | + | 0.951450i | ||||
\(534\) | 25706.9i | 0.0901502i | ||||||||
\(535\) | −179145. | + | 56488.6i | −0.625889 | + | 0.197357i | ||||
\(536\) | −210475. | −0.732606 | ||||||||
\(537\) | −25817.3 | + | 25817.3i | −0.0895288 | + | 0.0895288i | ||||
\(538\) | −248589. | − | 248589.i | −0.858852 | − | 0.858852i | ||||
\(539\) | − | 6044.56i | − | 0.0208059i | ||||||
\(540\) | −3515.69 | − | 11149.5i | −0.0120566 | − | 0.0382355i | ||||
\(541\) | −266396. | −0.910192 | −0.455096 | − | 0.890442i | \(-0.650395\pi\) | ||||
−0.455096 | + | 0.890442i | \(0.650395\pi\) | |||||||
\(542\) | −96047.3 | + | 96047.3i | −0.326954 | + | 0.326954i | ||||
\(543\) | −28144.4 | − | 28144.4i | −0.0954537 | − | 0.0954537i | ||||
\(544\) | − | 98950.7i | − | 0.334365i | ||||||
\(545\) | 107510. | − | 206536.i | 0.361956 | − | 0.695349i | ||||
\(546\) | −30727.1 | −0.103071 | ||||||||
\(547\) | −243105. | + | 243105.i | −0.812492 | + | 0.812492i | −0.985007 | − | 0.172515i | \(-0.944811\pi\) |
0.172515 | + | 0.985007i | \(0.444811\pi\) | |||||||
\(548\) | 4481.71 | + | 4481.71i | 0.0149239 | + | 0.0149239i | ||||
\(549\) | − | 66144.5i | − | 0.219457i | ||||||
\(550\) | −45623.6 | − | 8042.56i | −0.150822 | − | 0.0265870i | ||||
\(551\) | 353947. | 1.16583 | ||||||||
\(552\) | 65457.8 | − | 65457.8i | 0.214824 | − | 0.214824i | ||||
\(553\) | −23132.1 | − | 23132.1i | −0.0756425 | − | 0.0756425i | ||||
\(554\) | − | 348908.i | − | 1.13682i | ||||||
\(555\) | 30296.8 | + | 15770.7i | 0.0983584 | + | 0.0511993i | ||||
\(556\) | −50639.9 | −0.163811 | ||||||||
\(557\) | −22586.2 | + | 22586.2i | −0.0728003 | + | 0.0728003i | −0.742569 | − | 0.669769i | \(-0.766393\pi\) |
0.669769 | + | 0.742569i | \(0.266393\pi\) | |||||||
\(558\) | 128467. | + | 128467.i | 0.412593 | + | 0.412593i | ||||
\(559\) | 133746.i | 0.428015i | ||||||||
\(560\) | −123731. | + | 39015.3i | −0.394551 | + | 0.124411i | ||||
\(561\) | 14060.2 | 0.0446751 | ||||||||
\(562\) | 179716. | − | 179716.i | 0.569003 | − | 0.569003i | ||||
\(563\) | −422208. | − | 422208.i | −1.33202 | − | 1.33202i | −0.903565 | − | 0.428451i | \(-0.859059\pi\) |
−0.428451 | − | 0.903565i | \(-0.640941\pi\) | |||||||
\(564\) | − | 1328.22i | − | 0.00417553i | ||||||
\(565\) | −116220. | − | 368573.i | −0.364069 | − | 1.15459i | ||||
\(566\) | −431652. | −1.34741 | ||||||||
\(567\) | −76419.6 | + | 76419.6i | −0.237705 | + | 0.237705i | ||||
\(568\) | 104418. | + | 104418.i | 0.323652 | + | 0.323652i | ||||
\(569\) | 400419.i | 1.23677i | 0.785874 | + | 0.618387i | \(0.212213\pi\) | ||||
−0.785874 | + | 0.618387i | \(0.787787\pi\) | |||||||
\(570\) | 39544.7 | − | 75968.7i | 0.121713 | − | 0.233822i | ||||
\(571\) | 281832. | 0.864406 | 0.432203 | − | 0.901776i | \(-0.357736\pi\) | ||||
0.432203 | + | 0.901776i | \(0.357736\pi\) | |||||||
\(572\) | −4781.87 | + | 4781.87i | −0.0146152 | + | 0.0146152i | ||||
\(573\) | −71051.0 | − | 71051.0i | −0.216402 | − | 0.216402i | ||||
\(574\) | − | 131266.i | − | 0.398409i | ||||||
\(575\) | 95980.9 | − | 544478.i | 0.290302 | − | 1.64682i | ||||
\(576\) | 278860. | 0.840507 | ||||||||
\(577\) | −112269. | + | 112269.i | −0.337215 | + | 0.337215i | −0.855318 | − | 0.518103i | \(-0.826638\pi\) |
0.518103 | + | 0.855318i | \(0.326638\pi\) | |||||||
\(578\) | 377769. | + | 377769.i | 1.13076 | + | 1.13076i | ||||
\(579\) | 25227.2i | 0.0752509i | ||||||||
\(580\) | 28346.6 | + | 14755.5i | 0.0842645 | + | 0.0438629i | ||||
\(581\) | −23199.4 | −0.0687266 | ||||||||
\(582\) | 3081.19 | − | 3081.19i | 0.00909646 | − | 0.00909646i | ||||
\(583\) | 59077.0 | + | 59077.0i | 0.173813 | + | 0.173813i | ||||
\(584\) | 199934.i | 0.586221i | ||||||||
\(585\) | 421749. | − | 132987.i | 1.23237 | − | 0.388596i | ||||
\(586\) | 91580.5 | 0.266691 | ||||||||
\(587\) | 154399. | − | 154399.i | 0.448094 | − | 0.448094i | −0.446627 | − | 0.894720i | \(-0.647375\pi\) |
0.894720 | + | 0.446627i | \(0.147375\pi\) | |||||||
\(588\) | 713.418 | + | 713.418i | 0.00206343 | + | 0.00206343i | ||||
\(589\) | 259465.i | 0.747907i | ||||||||
\(590\) | −147982. | − | 469302.i | −0.425113 | − | 1.34818i | ||||
\(591\) | −35878.6 | −0.102721 | ||||||||
\(592\) | 155678. | − | 155678.i | 0.444205 | − | 0.444205i | ||||
\(593\) | −202843. | − | 202843.i | −0.576835 | − | 0.576835i | 0.357195 | − | 0.934030i | \(-0.383733\pi\) |
−0.934030 | + | 0.357195i | \(0.883733\pi\) | |||||||
\(594\) | − | 20490.1i | − | 0.0580726i | ||||||
\(595\) | 98092.9 | − | 188445.i | 0.277079 | − | 0.532293i | ||||
\(596\) | −60506.1 | −0.170336 | ||||||||
\(597\) | −61496.0 | + | 61496.0i | −0.172543 | + | 0.172543i | ||||
\(598\) | −596827. | − | 596827.i | −1.66896 | − | 1.66896i | ||||
\(599\) | − | 495814.i | − | 1.38186i | −0.722921 | − | 0.690931i | \(-0.757201\pi\) | ||
0.722921 | − | 0.690931i | \(-0.242799\pi\) | |||||||
\(600\) | −53574.9 | + | 37517.2i | −0.148819 | + | 0.104214i | ||||
\(601\) | −552708. | −1.53020 | −0.765098 | − | 0.643914i | \(-0.777309\pi\) | ||||
−0.765098 | + | 0.643914i | \(0.777309\pi\) | |||||||
\(602\) | 32476.2 | − | 32476.2i | 0.0896132 | − | 0.0896132i | ||||
\(603\) | −192830. | − | 192830.i | −0.530323 | − | 0.530323i | ||||
\(604\) | 70258.0i | 0.192585i | ||||||||
\(605\) | 317785. | + | 165419.i | 0.868206 | + | 0.451935i | ||||
\(606\) | 68210.0 | 0.185739 | ||||||||
\(607\) | 60231.6 | − | 60231.6i | 0.163473 | − | 0.163473i | −0.620630 | − | 0.784103i | \(-0.713123\pi\) |
0.784103 | + | 0.620630i | \(0.213123\pi\) | |||||||
\(608\) | −71426.6 | − | 71426.6i | −0.193220 | − | 0.193220i | ||||
\(609\) | 24334.5i | 0.0656126i | ||||||||
\(610\) | 85068.9 | − | 26824.2i | 0.228618 | − | 0.0720888i | ||||
\(611\) | 102433. | 0.274382 | ||||||||
\(612\) | 42797.7 | − | 42797.7i | 0.114266 | − | 0.114266i | ||||
\(613\) | 376210. | + | 376210.i | 1.00117 | + | 1.00117i | 0.999999 | + | 0.00117501i | \(0.000374018\pi\) |
0.00117501 | + | 0.999999i | \(0.499626\pi\) | |||||||
\(614\) | 243016.i | 0.644610i | ||||||||
\(615\) | −22028.8 | − | 69861.1i | −0.0582427 | − | 0.184708i | ||||
\(616\) | −19642.3 | −0.0517643 | ||||||||
\(617\) | −127411. | + | 127411.i | −0.334685 | + | 0.334685i | −0.854363 | − | 0.519677i | \(-0.826052\pi\) |
0.519677 | + | 0.854363i | \(0.326052\pi\) | |||||||
\(618\) | −25995.4 | − | 25995.4i | −0.0680643 | − | 0.0680643i | ||||
\(619\) | − | 527739.i | − | 1.37733i | −0.725080 | − | 0.688665i | \(-0.758197\pi\) | ||
0.725080 | − | 0.688665i | \(-0.241803\pi\) | |||||||
\(620\) | −10816.7 | + | 20779.7i | −0.0281391 | + | 0.0540576i | ||||
\(621\) | 244532. | 0.634092 | ||||||||
\(622\) | 371756. | − | 371756.i | 0.960898 | − | 0.960898i | ||||
\(623\) | 46029.9 | + | 46029.9i | 0.118594 | + | 0.118594i | ||||
\(624\) | 110526.i | 0.283855i | ||||||||
\(625\) | −133569. | + | 367079.i | −0.341936 | + | 0.939723i | ||||
\(626\) | 165357. | 0.421962 | ||||||||
\(627\) | 10149.2 | − | 10149.2i | 0.0258165 | − | 0.0258165i | ||||
\(628\) | 34349.1 | + | 34349.1i | 0.0870956 | + | 0.0870956i | ||||
\(629\) | 360521.i | 0.911232i | ||||||||
\(630\) | −134700. | − | 70116.7i | −0.339381 | − | 0.176661i | ||||
\(631\) | −594356. | −1.49275 | −0.746376 | − | 0.665524i | \(-0.768208\pi\) | ||||
−0.746376 | + | 0.665524i | \(0.768208\pi\) | |||||||
\(632\) | −75169.7 | + | 75169.7i | −0.188195 | + | 0.188195i | ||||
\(633\) | 45895.4 | + | 45895.4i | 0.114541 | + | 0.114541i | ||||
\(634\) | 498522.i | 1.24024i | ||||||||
\(635\) | −481480. | + | 151822.i | −1.19407 | + | 0.376519i | ||||
\(636\) | −13945.3 | −0.0344757 | ||||||||
\(637\) | −55019.0 | + | 55019.0i | −0.135592 | + | 0.135592i | ||||
\(638\) | 39605.7 | + | 39605.7i | 0.0973008 | + | 0.0973008i | ||||
\(639\) | 191329.i | 0.468574i | ||||||||
\(640\) | 139030. | + | 440912.i | 0.339428 | + | 1.07644i | ||||
\(641\) | −720768. | −1.75420 | −0.877100 | − | 0.480307i | \(-0.840525\pi\) | ||||
−0.877100 | + | 0.480307i | \(0.840525\pi\) | |||||||
\(642\) | 38857.4 | − | 38857.4i | 0.0942767 | − | 0.0942767i | ||||
\(643\) | 22321.8 | + | 22321.8i | 0.0539892 | + | 0.0539892i | 0.733586 | − | 0.679597i | \(-0.237845\pi\) |
−0.679597 | + | 0.733586i | \(0.737845\pi\) | |||||||
\(644\) | 27714.1i | 0.0668235i | ||||||||
\(645\) | 11834.0 | − | 22734.2i | 0.0284455 | − | 0.0546462i | ||||
\(646\) | 903999. | 2.16622 | ||||||||
\(647\) | 61507.7 | − | 61507.7i | 0.146934 | − | 0.146934i | −0.629813 | − | 0.776747i | \(-0.716869\pi\) |
0.776747 | + | 0.629813i | \(0.216869\pi\) | |||||||
\(648\) | 248331. | + | 248331.i | 0.591400 | + | 0.591400i | ||||
\(649\) | − | 82467.5i | − | 0.195791i | ||||||
\(650\) | 342072. | + | 488482.i | 0.809637 | + | 1.15617i | ||||
\(651\) | −17838.6 | −0.0420920 | ||||||||
\(652\) | −41015.5 | + | 41015.5i | −0.0964835 | + | 0.0964835i | ||||
\(653\) | 406395. | + | 406395.i | 0.953064 | + | 0.953064i | 0.998947 | − | 0.0458828i | \(-0.0146101\pi\) |
−0.0458828 | + | 0.998947i | \(0.514610\pi\) | |||||||
\(654\) | 68118.1i | 0.159260i | ||||||||
\(655\) | 203742. | + | 106056.i | 0.474896 | + | 0.247202i | ||||
\(656\) | −472169. | −1.09721 | ||||||||
\(657\) | −183173. | + | 183173.i | −0.424356 | + | 0.424356i | ||||
\(658\) | −24872.6 | − | 24872.6i | −0.0574473 | − | 0.0574473i | ||||
\(659\) | − | 128094.i | − | 0.294956i | −0.989065 | − | 0.147478i | \(-0.952884\pi\) | ||
0.989065 | − | 0.147478i | \(-0.0471156\pi\) | |||||||
\(660\) | 1235.93 | − | 389.716i | 0.00283729 | − | 0.000894665i | ||||
\(661\) | −328592. | −0.752062 | −0.376031 | − | 0.926607i | \(-0.622711\pi\) | ||||
−0.376031 | + | 0.926607i | \(0.622711\pi\) | |||||||
\(662\) | 111155. | − | 111155.i | 0.253637 | − | 0.253637i | ||||
\(663\) | −127979. | − | 127979.i | −0.291147 | − | 0.291147i | ||||
\(664\) | 75388.3i | 0.170989i | ||||||||
\(665\) | −65219.9 | − | 206835.i | −0.147481 | − | 0.467714i | ||||
\(666\) | 257700. | 0.580986 | ||||||||
\(667\) | −472660. | + | 472660.i | −1.06242 | + | 1.06242i | ||||
\(668\) | 50152.0 | + | 50152.0i | 0.112392 | + | 0.112392i | ||||
\(669\) | − | 22363.7i | − | 0.0499679i | ||||||
\(670\) | 169800. | − | 326200.i | 0.378257 | − | 0.726666i | ||||
\(671\) | 14948.6 | 0.0332014 | ||||||||
\(672\) | 4910.70 | − | 4910.70i | 0.0108744 | − | 0.0108744i | ||||
\(673\) | 595757. | + | 595757.i | 1.31534 | + | 1.31534i | 0.917417 | + | 0.397927i | \(0.130270\pi\) |
0.397927 | + | 0.917417i | \(0.369730\pi\) | |||||||
\(674\) | − | 42645.1i | − | 0.0938749i | ||||||
\(675\) | −170147. | − | 29993.6i | −0.373437 | − | 0.0658296i | ||||
\(676\) | 38736.4 | 0.0847668 | ||||||||
\(677\) | −249719. | + | 249719.i | −0.544846 | + | 0.544846i | −0.924946 | − | 0.380099i | \(-0.875890\pi\) |
0.380099 | + | 0.924946i | \(0.375890\pi\) | |||||||
\(678\) | 79945.4 | + | 79945.4i | 0.173914 | + | 0.173914i | ||||
\(679\) | − | 11034.2i | − | 0.0239332i | ||||||
\(680\) | −612367. | − | 318761.i | −1.32432 | − | 0.689361i | ||||
\(681\) | 75778.8 | 0.163401 | ||||||||
\(682\) | −29033.4 | + | 29033.4i | −0.0624207 | + | 0.0624207i | ||||
\(683\) | −392090. | − | 392090.i | −0.840512 | − | 0.840512i | 0.148413 | − | 0.988925i | \(-0.452583\pi\) |
−0.988925 | + | 0.148413i | \(0.952583\pi\) | |||||||
\(684\) | − | 61786.3i | − | 0.132063i | ||||||
\(685\) | 89331.9 | − | 28168.4i | 0.190382 | − | 0.0600318i | ||||
\(686\) | 26719.3 | 0.0567776 | ||||||||
\(687\) | −17184.8 | + | 17184.8i | −0.0364109 | + | 0.0364109i | ||||
\(688\) | −116818. | − | 116818.i | −0.246793 | − | 0.246793i | ||||
\(689\) | − | 1.07547e6i | − | 2.26547i | ||||||
\(690\) | 48640.6 | + | 154256.i | 0.102165 | + | 0.324000i | ||||
\(691\) | 905394. | 1.89619 | 0.948094 | − | 0.317990i | \(-0.103008\pi\) | ||||
0.948094 | + | 0.317990i | \(0.103008\pi\) | |||||||
\(692\) | −6902.84 | + | 6902.84i | −0.0144150 | + | 0.0144150i | ||||
\(693\) | −17995.6 | − | 17995.6i | −0.0374714 | − | 0.0374714i | ||||
\(694\) | 57584.1i | 0.119559i | ||||||||
\(695\) | −345550. | + | 663832.i | −0.715388 | + | 1.37432i | ||||
\(696\) | 79076.7 | 0.163241 | ||||||||
\(697\) | 546727. | − | 546727.i | 1.12540 | − | 1.12540i | ||||
\(698\) | 214314. | + | 214314.i | 0.439885 | + | 0.439885i | ||||
\(699\) | − | 16377.6i | − | 0.0335194i | ||||||
\(700\) | 3399.34 | − | 19283.7i | 0.00693743 | − | 0.0393545i | ||||
\(701\) | 528653. | 1.07581 | 0.537904 | − | 0.843006i | \(-0.319216\pi\) | ||||
0.537904 | + | 0.843006i | \(0.319216\pi\) | |||||||
\(702\) | −186506. | + | 186506.i | −0.378458 | + | 0.378458i | ||||
\(703\) | 260239. | + | 260239.i | 0.526576 | + | 0.526576i | ||||
\(704\) | 63022.2i | 0.127159i | ||||||||
\(705\) | −17411.5 | − | 9063.35i | −0.0350314 | − | 0.0182352i | ||||
\(706\) | −313506. | −0.628980 | ||||||||
\(707\) | 122135. | − | 122135.i | 0.244343 | − | 0.244343i | ||||
\(708\) | 9733.34 | + | 9733.34i | 0.0194176 | + | 0.0194176i | ||||
\(709\) | − | 684824.i | − | 1.36234i | −0.732124 | − | 0.681172i | \(-0.761471\pi\) | ||
0.732124 | − | 0.681172i | \(-0.238529\pi\) | |||||||
\(710\) | −246069. | + | 77591.3i | −0.488135 | + | 0.153921i | ||||
\(711\) | −137736. | −0.272463 | ||||||||
\(712\) | 149578. | − | 149578.i | 0.295058 | − | 0.295058i | ||||
\(713\) | −346488. | − | 346488.i | −0.681569 | − | 0.681569i | ||||
\(714\) | 62151.5i | 0.121915i | ||||||||
\(715\) | 30055.0 | + | 95314.9i | 0.0587902 | + | 0.186444i | ||||
\(716\) | −35520.4 | −0.0692870 | ||||||||
\(717\) | −9640.36 | + | 9640.36i | −0.0187523 | + | 0.0187523i | ||||
\(718\) | −692122. | − | 692122.i | −1.34256 | − | 1.34256i | ||||
\(719\) | − | 485616.i | − | 0.939367i | −0.882835 | − | 0.469683i | \(-0.844368\pi\) | ||
0.882835 | − | 0.469683i | \(-0.155632\pi\) | |||||||
\(720\) | −252212. | + | 484521.i | −0.486520 | + | 0.934648i | ||||
\(721\) | −93093.1 | −0.179080 | ||||||||
\(722\) | 264943. | − | 264943.i | 0.508252 | − | 0.508252i | ||||
\(723\) | 98031.9 | + | 98031.9i | 0.187539 | + | 0.187539i | ||||
\(724\) | − | 38722.1i | − | 0.0738724i | ||||||
\(725\) | 386856. | − | 270905.i | 0.735992 | − | 0.515396i | ||||
\(726\) | −104809. | −0.198851 | ||||||||
\(727\) | 650933. | − | 650933.i | 1.23159 | − | 1.23159i | 0.268243 | − | 0.963351i | \(-0.413557\pi\) |
0.963351 | − | 0.268243i | \(-0.0864428\pi\) | |||||||
\(728\) | 178788. | + | 178788.i | 0.337347 | + | 0.337347i | ||||
\(729\) | 416092.i | 0.782950i | ||||||||
\(730\) | −309864. | − | 161296.i | −0.581467 | − | 0.302676i | ||||
\(731\) | 270528. | 0.506265 | ||||||||
\(732\) | −1764.33 | + | 1764.33i | −0.00329275 | + | 0.00329275i | ||||
\(733\) | 34579.8 | + | 34579.8i | 0.0643599 | + | 0.0643599i | 0.738554 | − | 0.674194i | \(-0.235509\pi\) |
−0.674194 | + | 0.738554i | \(0.735509\pi\) | |||||||
\(734\) | − | 262519.i | − | 0.487268i | ||||||
\(735\) | 14220.3 | − | 4483.98i | 0.0263228 | − | 0.00830021i | ||||
\(736\) | 190766. | 0.352164 | ||||||||
\(737\) | 43579.5 | − | 43579.5i | 0.0802319 | − | 0.0802319i | ||||
\(738\) | −390800. | − | 390800.i | −0.717533 | − | 0.717533i | ||||
\(739\) | 206401.i | 0.377941i | 0.981983 | + | 0.188970i | \(0.0605150\pi\) | ||||
−0.981983 | + | 0.188970i | \(0.939485\pi\) | |||||||
\(740\) | 9992.81 | + | 31690.7i | 0.0182484 | + | 0.0578719i | ||||
\(741\) | −184761. | −0.336491 | ||||||||
\(742\) | −261143. | + | 261143.i | −0.474320 | + | 0.474320i | ||||
\(743\) | −601192. | − | 601192.i | −1.08902 | − | 1.08902i | −0.995630 | − | 0.0933899i | \(-0.970230\pi\) |
−0.0933899 | − | 0.995630i | \(-0.529770\pi\) | |||||||
\(744\) | 57968.0i | 0.104723i | ||||||||
\(745\) | −412874. | + | 793167.i | −0.743884 | + | 1.42907i | ||||
\(746\) | −540816. | −0.971788 | ||||||||
\(747\) | −69068.3 | + | 69068.3i | −0.123776 | + | 0.123776i | ||||
\(748\) | 9672.26 | + | 9672.26i | 0.0172872 | + | 0.0172872i | ||||
\(749\) | − | 139154.i | − | 0.248046i | ||||||
\(750\) | −14923.9 | − | 113299.i | −0.0265313 | − | 0.201420i | ||||
\(751\) | 565097. | 1.00194 | 0.500972 | − | 0.865463i | \(-0.332976\pi\) | ||||
0.500972 | + | 0.865463i | \(0.332976\pi\) | |||||||
\(752\) | −89467.5 | + | 89467.5i | −0.158208 | + | 0.158208i | ||||
\(753\) | −68481.5 | − | 68481.5i | −0.120777 | − | 0.120777i | ||||
\(754\) | − | 721001.i | − | 1.26822i | ||||||
\(755\) | 921005. | + | 479418.i | 1.61573 | + | 0.841048i | ||||
\(756\) | 8660.54 | 0.0151531 | ||||||||
\(757\) | −282485. | + | 282485.i | −0.492951 | + | 0.492951i | −0.909235 | − | 0.416284i | \(-0.863332\pi\) |
0.416284 | + | 0.909235i | \(0.363332\pi\) | |||||||
\(758\) | −269498. | − | 269498.i | −0.469048 | − | 0.469048i | ||||
\(759\) | 27106.5i | 0.0470532i | ||||||||
\(760\) | −672126. | + | 211937.i | −1.16365 | + | 0.366927i | ||||
\(761\) | −157487. | −0.271942 | −0.135971 | − | 0.990713i | \(-0.543415\pi\) | ||||
−0.135971 | + | 0.990713i | \(0.543415\pi\) | |||||||
\(762\) | 104435. | − | 104435.i | 0.179861 | − | 0.179861i | ||||
\(763\) | 121970. | + | 121970.i | 0.209510 | + | 0.209510i | ||||
\(764\) | − | 97754.5i | − | 0.167475i | ||||||
\(765\) | −268993. | − | 853068.i | −0.459640 | − | 1.45768i | ||||
\(766\) | 1.06030e6 | 1.80705 | ||||||||
\(767\) | −750638. | + | 750638.i | −1.27597 | + | 1.27597i | ||||
\(768\) | −25282.6 | − | 25282.6i | −0.0428647 | − | 0.0428647i | ||||
\(769\) | 801382.i | 1.35515i | 0.735455 | + | 0.677574i | \(0.236969\pi\) | ||||
−0.735455 | + | 0.677574i | \(0.763031\pi\) | |||||||
\(770\) | 15846.3 | − | 30442.2i | 0.0267268 | − | 0.0513445i | ||||
\(771\) | −131483. | −0.221187 | ||||||||
\(772\) | −17354.2 | + | 17354.2i | −0.0291186 | + | 0.0291186i | ||||
\(773\) | 407066. | + | 407066.i | 0.681249 | + | 0.681249i | 0.960282 | − | 0.279033i | \(-0.0900139\pi\) |
−0.279033 | + | 0.960282i | \(0.590014\pi\) | |||||||
\(774\) | − | 193373.i | − | 0.322786i | ||||||
\(775\) | 198590. | + | 283589.i | 0.330639 | + | 0.472156i | ||||
\(776\) | −35856.4 | −0.0595447 | ||||||||
\(777\) | −17891.9 | + | 17891.9i | −0.0296356 | + | 0.0296356i | ||||
\(778\) | 372902. | + | 372902.i | 0.616077 | + | 0.616077i | ||||
\(779\) | − | 789300.i | − | 1.30067i | ||||||
\(780\) | −14797.0 | − | 7702.39i | −0.0243211 | − | 0.0126601i | ||||
\(781\) | −43240.1 | −0.0708900 | ||||||||
\(782\) | −1.20720e6 | + | 1.20720e6i | −1.97408 | + | 1.97408i | ||||
\(783\) | 147704. | + | 147704.i | 0.240918 | + | 0.240918i | ||||
\(784\) | − | 96110.2i | − | 0.156364i | ||||||
\(785\) | 684666. | − | 215891.i | 1.11106 | − | 0.350345i | ||||
\(786\) | −67196.7 | −0.108768 | ||||||||
\(787\) | 384677. | − | 384677.i | 0.621079 | − | 0.621079i | −0.324728 | − | 0.945807i | \(-0.605273\pi\) |
0.945807 | + | 0.324728i | \(0.105273\pi\) | |||||||
\(788\) | −24681.6 | − | 24681.6i | −0.0397484 | − | 0.0397484i | ||||
\(789\) | − | 193539.i | − | 0.310895i | ||||||
\(790\) | −55857.4 | − | 177143.i | −0.0895007 | − | 0.283838i | ||||
\(791\) | 286295. | 0.457574 | ||||||||
\(792\) | −58478.1 | + | 58478.1i | −0.0932272 | + | 0.0932272i | ||||
\(793\) | −136066. | − | 136066.i | −0.216373 | − | 0.216373i | ||||
\(794\) | 1.11403e6i | 1.76708i | ||||||||
\(795\) | −95158.2 | + | 182807.i | −0.150561 | + | 0.289241i | ||||
\(796\) | −84608.3 | −0.133533 | ||||||||
\(797\) | 168513. | − | 168513.i | 0.265287 | − | 0.265287i | −0.561911 | − | 0.827198i | \(-0.689933\pi\) |
0.827198 | + | 0.561911i | \(0.189933\pi\) | |||||||
\(798\) | 44863.5 | + | 44863.5i | 0.0704510 | + | 0.0704510i | ||||
\(799\) | − | 207190.i | − | 0.324545i | ||||||
\(800\) | −132736. | − | 23398.8i | −0.207400 | − | 0.0365607i | ||||
\(801\) | 274077. | 0.427176 | ||||||||
\(802\) | 475525. | − | 475525.i | 0.739307 | − | 0.739307i | ||||
\(803\) | −41397.0 | − | 41397.0i | −0.0642004 | − | 0.0642004i | ||||
\(804\) | 10287.1i | 0.0159140i | ||||||||
\(805\) | 363301. | + | 189112.i | 0.560628 | + | 0.291829i | ||||
\(806\) | 528537. | 0.813590 | ||||||||
\(807\) | 102767. | − | 102767.i | 0.157801 | − | 0.157801i | ||||
\(808\) | −396886. | − | 396886.i | −0.607916 | − | 0.607916i | ||||
\(809\) | − | 154337.i | − | 0.235816i | −0.993025 | − | 0.117908i | \(-0.962381\pi\) | ||
0.993025 | − | 0.117908i | \(-0.0376188\pi\) | |||||||
\(810\) | −585212. | + | 184531.i | −0.891955 | + | 0.281254i | ||||
\(811\) | 196780. | 0.299185 | 0.149592 | − | 0.988748i | \(-0.452204\pi\) | ||||
0.149592 | + | 0.988748i | \(0.452204\pi\) | |||||||
\(812\) | −16740.1 | + | 16740.1i | −0.0253890 | + | 0.0253890i | ||||
\(813\) | −39706.1 | − | 39706.1i | −0.0600726 | − | 0.0600726i | ||||
\(814\) | 58240.0i | 0.0878967i | ||||||||
\(815\) | 257791. | + | 817545.i | 0.388108 | + | 1.23082i | ||||
\(816\) | 223561. | 0.335750 | ||||||||
\(817\) | 195278. | − | 195278.i | 0.292556 | − | 0.292556i | ||||
\(818\) | −295603. | − | 295603.i | −0.441776 | − | 0.441776i | ||||
\(819\) | 327600.i | 0.488401i | ||||||||
\(820\) | 32904.6 | − | 63212.7i | 0.0489361 | − | 0.0940105i | ||||
\(821\) | −392342. | −0.582074 | −0.291037 | − | 0.956712i | \(-0.594000\pi\) | ||||
−0.291037 | + | 0.956712i | \(0.594000\pi\) | |||||||
\(822\) | −19376.5 | + | 19376.5i | −0.0286769 | + | 0.0286769i | ||||
\(823\) | −292221. | − | 292221.i | −0.431432 | − | 0.431432i | 0.457683 | − | 0.889115i | \(-0.348679\pi\) |
−0.889115 | + | 0.457683i | \(0.848679\pi\) | |||||||
\(824\) | 302513.i | 0.445543i | ||||||||
\(825\) | 3324.81 | − | 18860.9i | 0.00488494 | − | 0.0277111i | ||||
\(826\) | 364538. | 0.534297 | ||||||||
\(827\) | −652551. | + | 652551.i | −0.954122 | + | 0.954122i | −0.998993 | − | 0.0448712i | \(-0.985712\pi\) |
0.0448712 | + | 0.998993i | \(0.485712\pi\) | |||||||
\(828\) | 82509.2 | + | 82509.2i | 0.120349 | + | 0.120349i | ||||
\(829\) | 604523.i | 0.879637i | 0.898087 | + | 0.439819i | \(0.144957\pi\) | ||||
−0.898087 | + | 0.439819i | \(0.855043\pi\) | |||||||
\(830\) | −116839. | − | 60819.2i | −0.169602 | − | 0.0882846i | ||||
\(831\) | 144239. | 0.208873 | ||||||||
\(832\) | 573643. | − | 573643.i | 0.828695 | − | 0.828695i | ||||
\(833\) | 111287. | + | 111287.i | 0.160381 | + | 0.160381i | ||||
\(834\) | − | 218940.i | − | 0.314770i | ||||||
\(835\) | 999658. | − | 315216.i | 1.43377 | − | 0.452100i | ||||
\(836\) | 13963.7 | 0.0199796 | ||||||||
\(837\) | −108276. | + | 108276.i | −0.154555 | + | 0.154555i | ||||
\(838\) | −463525. | − | 463525.i | −0.660063 | − | 0.660063i | ||||
\(839\) | 61209.4i | 0.0869549i | 0.999054 | + | 0.0434775i | \(0.0138437\pi\) | ||||
−0.999054 | + | 0.0434775i | \(0.986156\pi\) | |||||||
\(840\) | −14571.0 | − | 46209.8i | −0.0206506 | − | 0.0654901i | ||||
\(841\) | 136281. | 0.192683 | ||||||||
\(842\) | −448775. | + | 448775.i | −0.633001 | + | 0.633001i | ||||
\(843\) | 74295.0 | + | 74295.0i | 0.104545 | + | 0.104545i | ||||
\(844\) | 63144.5i | 0.0886443i | ||||||||
\(845\) | 264325. | − | 507791.i | 0.370190 | − | 0.711167i | ||||
\(846\) | −148099. | −0.206924 | ||||||||
\(847\) | −187669. | + | 187669.i | −0.261592 | + | 0.261592i | ||||
\(848\) | 939341. | + | 939341.i | 1.30627 | + | 1.30627i | ||||
\(849\) | − | 178446.i | − | 0.247566i | ||||||
\(850\) | 988050. | − | 691906.i | 1.36754 | − | 0.957656i | ||||
\(851\) | −695044. | −0.959739 | ||||||||
\(852\) | 5103.48 | − | 5103.48i | 0.00703052 | − | 0.00703052i | ||||
\(853\) | −587656. | − | 587656.i | −0.807654 | − | 0.807654i | 0.176625 | − | 0.984278i | \(-0.443482\pi\) |
−0.984278 | + | 0.176625i | \(0.943482\pi\) | |||||||
\(854\) | 66078.7i | 0.0906037i | ||||||||
\(855\) | −809949. | − | 421610.i | −1.10796 | − | 0.576738i | ||||
\(856\) | −452191. | −0.617127 | ||||||||
\(857\) | −162064. | + | 162064.i | −0.220661 | + | 0.220661i | −0.808777 | − | 0.588116i | \(-0.799870\pi\) |
0.588116 | + | 0.808777i | \(0.299870\pi\) | |||||||
\(858\) | −20674.3 | − | 20674.3i | −0.0280838 | − | 0.0280838i | ||||
\(859\) | 1.21163e6i | 1.64204i | 0.570897 | + | 0.821022i | \(0.306596\pi\) | ||||
−0.570897 | + | 0.821022i | \(0.693404\pi\) | |||||||
\(860\) | 23780.1 | − | 7498.42i | 0.0321526 | − | 0.0101385i | ||||
\(861\) | 54265.7 | 0.0732014 | ||||||||
\(862\) | −116560. | + | 116560.i | −0.156868 | + | 0.156868i | ||||
\(863\) | 199163. | + | 199163.i | 0.267416 | + | 0.267416i | 0.828058 | − | 0.560642i | \(-0.189446\pi\) |
−0.560642 | + | 0.828058i | \(0.689446\pi\) | |||||||
\(864\) | − | 59613.5i | − | 0.0798577i | ||||||
\(865\) | 43385.8 | + | 137591.i | 0.0579849 | + | 0.183890i | ||||
\(866\) | 790643. | 1.05425 | ||||||||
\(867\) | −156171. | + | 156171.i | −0.207760 | + | 0.207760i | ||||
\(868\) | −12271.5 | − | 12271.5i | −0.0162877 | − | 0.0162877i | ||||
\(869\) | − | 31128.2i | − | 0.0412207i | ||||||
\(870\) | −63794.9 | + | 122556.i | −0.0842844 | + | 0.161918i | ||||
\(871\) | −793341. | −1.04574 | ||||||||
\(872\) | 396352. | − | 396352.i | 0.521252 | − | 0.521252i | ||||
\(873\) | −32850.4 | − | 32850.4i | −0.0431035 | − | 0.0431035i | ||||
\(874\) | 1.74281e6i | 2.28153i | ||||||||
\(875\) | −229592. | − | 176147.i | −0.299875 | − | 0.230070i | ||||
\(876\) | 9771.88 | 0.0127341 | ||||||||
\(877\) | −67773.5 | + | 67773.5i | −0.0881172 | + | 0.0881172i | −0.749791 | − | 0.661674i | \(-0.769846\pi\) |
0.661674 | + | 0.749791i | \(0.269846\pi\) | |||||||
\(878\) | 487282. | + | 487282.i | 0.632108 | + | 0.632108i | ||||
\(879\) | 37859.6i | 0.0490002i | ||||||||
\(880\) | −109501. | − | 56999.7i | −0.141402 | − | 0.0736050i | ||||
\(881\) | 623471. | 0.803276 | 0.401638 | − | 0.915799i | \(-0.368441\pi\) | ||||
0.401638 | + | 0.915799i | \(0.368441\pi\) | |||||||
\(882\) | 79547.5 | − | 79547.5i | 0.102256 | − | 0.102256i | ||||
\(883\) | −660163. | − | 660163.i | −0.846701 | − | 0.846701i | 0.143019 | − | 0.989720i | \(-0.454319\pi\) |
−0.989720 | + | 0.143019i | \(0.954319\pi\) | |||||||
\(884\) | − | 176078.i | − | 0.225321i | ||||||
\(885\) | 194010. | − | 61176.1i | 0.247707 | − | 0.0781079i | ||||
\(886\) | −162612. | −0.207150 | ||||||||
\(887\) | 846037. | − | 846037.i | 1.07533 | − | 1.07533i | 0.0784092 | − | 0.996921i | \(-0.475016\pi\) |
0.996921 | − | 0.0784092i | \(-0.0249841\pi\) | |||||||
\(888\) | 58141.0 | + | 58141.0i | 0.0737320 | + | 0.0737320i | ||||
\(889\) | − | 373997.i | − | 0.473222i | ||||||
\(890\) | 111149. | + | 352492.i | 0.140322 | + | 0.445009i | ||||
\(891\) | −102836. | −0.129535 | ||||||||
\(892\) | 15384.4 | − | 15384.4i | 0.0193353 | − | 0.0193353i | ||||
\(893\) | −149558. | − | 149558.i | −0.187546 | − | 0.187546i | ||||
\(894\) | − | 261596.i | − | 0.327308i | ||||||
\(895\) | −242380. | + | 465633.i | −0.302587 | + | 0.581296i | ||||
\(896\) | −342486. | −0.426605 | ||||||||
\(897\) | 246730. | − | 246730.i | 0.306645 | − | 0.306645i | ||||
\(898\) | −476452. | − | 476452.i | −0.590836 | − | 0.590836i | ||||
\(899\) | − | 418578.i | − | 0.517913i | ||||||
\(900\) | −47290.2 | − | 67530.9i | −0.0583830 | − | 0.0833715i | ||||
\(901\) | −2.17534e6 | −2.67964 | ||||||||
\(902\) | 88320.5 | − | 88320.5i | 0.108555 | − | 0.108555i | ||||
\(903\) | 13425.7 | + | 13425.7i | 0.0164650 | + | 0.0164650i | ||||
\(904\) | − | 930339.i | − | 1.13842i | ||||||
\(905\) | −507604. | − | 264227.i | −0.619766 | − | 0.322612i | ||||
\(906\) | −303759. | −0.370060 | ||||||||
\(907\) | −67185.8 | + | 67185.8i | −0.0816701 | + | 0.0816701i | −0.746762 | − | 0.665092i | \(-0.768392\pi\) |
0.665092 | + | 0.746762i | \(0.268392\pi\) | |||||||
\(908\) | 52129.6 | + | 52129.6i | 0.0632285 | + | 0.0632285i | ||||
\(909\) | − | 727228.i | − | 0.880122i | ||||||
\(910\) | −421329. | + | 132855.i | −0.508790 | + | 0.160433i | ||||
\(911\) | −286850. | −0.345635 | −0.172818 | − | 0.984954i | \(-0.555287\pi\) | ||||
−0.172818 | + | 0.984954i | \(0.555287\pi\) | |||||||
\(912\) | 161375. | − | 161375.i | 0.194020 | − | 0.194020i | ||||
\(913\) | −15609.4 | − | 15609.4i | −0.0187260 | − | 0.0187260i | ||||
\(914\) | − | 636255.i | − | 0.761621i | ||||||
\(915\) | 11089.2 | + | 35167.7i | 0.0132452 | + | 0.0420050i | ||||
\(916\) | −23643.5 | −0.0281787 | ||||||||
\(917\) | −120320. | + | 120320.i | −0.143087 | + | 0.143087i | ||||
\(918\) | 377244. | + | 377244.i | 0.447649 | + | 0.447649i | ||||
\(919\) | − | 184400.i | − | 0.218339i | −0.994023 | − | 0.109169i | \(-0.965181\pi\) | ||
0.994023 | − | 0.109169i | \(-0.0348191\pi\) | |||||||
\(920\) | 614535. | − | 1.18057e6i | 0.726057 | − | 1.39482i | ||||
\(921\) | −100463. | −0.118437 | ||||||||
\(922\) | 70833.0 | − | 70833.0i | 0.0833247 | − | 0.0833247i | ||||
\(923\) | 393582. | + | 393582.i | 0.461989 | + | 0.461989i | ||||
\(924\) | 960.026i | 0.00112445i | ||||||||
\(925\) | 483617. | + | 85252.3i | 0.565221 | + | 0.0996374i | ||||
\(926\) | 728297. | 0.849350 | ||||||||
\(927\) | −277153. | + | 277153.i | −0.322522 | + | 0.322522i | ||||
\(928\) | 115228. | + | 115228.i | 0.133802 | + | 0.133802i | ||||
\(929\) | − | 223434.i | − | 0.258891i | −0.991587 | − | 0.129446i | \(-0.958680\pi\) | ||
0.991587 | − | 0.129446i | \(-0.0413198\pi\) | |||||||
\(930\) | −89840.6 | − | 46765.5i | −0.103874 | − | 0.0540704i | ||||
\(931\) | 160662. | 0.185359 | ||||||||
\(932\) | 11266.5 | − | 11266.5i | 0.0129705 | − | 0.0129705i | ||||
\(933\) | 153685. | + | 153685.i | 0.176550 | + | 0.176550i | ||||
\(934\) | 224685.i | 0.257562i | ||||||||
\(935\) | 192793. | − | 60792.1i | 0.220530 | − | 0.0695383i | ||||
\(936\) | 1.06456e6 | 1.21512 | ||||||||
\(937\) | 799998. | − | 799998.i | 0.911192 | − | 0.911192i | −0.0851740 | − | 0.996366i | \(-0.527145\pi\) |
0.996366 | + | 0.0851740i | \(0.0271446\pi\) | |||||||
\(938\) | 192638. | + | 192638.i | 0.218946 | + | 0.218946i | ||||
\(939\) | 68358.9i | 0.0775289i | ||||||||
\(940\) | −5742.83 | − | 18212.5i | −0.00649936 | − | 0.0206117i | ||||
\(941\) | −1.67631e6 | −1.89311 | −0.946554 | − | 0.322545i | \(-0.895462\pi\) | ||||
−0.946554 | + | 0.322545i | \(0.895462\pi\) | |||||||
\(942\) | −148507. | + | 148507.i | −0.167358 | + | 0.167358i | ||||
\(943\) | 1.05403e6 | + | 1.05403e6i | 1.18530 | + | 1.18530i | ||||
\(944\) | − | 1.31126e6i | − | 1.47144i | ||||||
\(945\) | 59096.7 | − | 113530.i | 0.0661759 | − | 0.127130i | ||||
\(946\) | 43702.2 | 0.0488339 | ||||||||
\(947\) | 45066.2 | − | 45066.2i | 0.0502517 | − | 0.0502517i | −0.681534 | − | 0.731786i | \(-0.738687\pi\) |
0.731786 | + | 0.681534i | \(0.238687\pi\) | |||||||
\(948\) | 3673.96 | + | 3673.96i | 0.00408806 | + | 0.00408806i | ||||
\(949\) | 753610.i | 0.836785i | ||||||||
\(950\) | 213768. | − | 1.21266e6i | 0.236862 | − | 1.34367i | ||||
\(951\) | −206090. | −0.227875 | ||||||||
\(952\) | 361634. | − | 361634.i | 0.399021 | − | 0.399021i | ||||
\(953\) | 148966. | + | 148966.i | 0.164022 | + | 0.164022i | 0.784346 | − | 0.620324i | \(-0.212999\pi\) |
−0.620324 | + | 0.784346i | \(0.712999\pi\) | |||||||
\(954\) | 1.55493e6i | 1.70849i | ||||||||
\(955\) | −1.28145e6 | − | 667045.i | −1.40506 | − | 0.731389i | ||||
\(956\) | −13263.5 | −0.0145126 | ||||||||
\(957\) | −16373.1 | + | 16373.1i | −0.0178775 | + | 0.0178775i | ||||
\(958\) | 538952. | + | 538952.i | 0.587245 | + | 0.587245i | ||||
\(959\) | 69390.0i | 0.0754501i | ||||||||
\(960\) | −148264. | + | 46751.2i | −0.160877 | + | 0.0507283i | ||||
\(961\) | −616678. | −0.667747 | ||||||||
\(962\) | 530114. | − | 530114.i | 0.572821 | − | 0.572821i | ||||
\(963\) | −414283. | − | 414283.i | −0.446729 | − | 0.446729i | ||||
\(964\) | 134876.i | 0.145138i | ||||||||
\(965\) | 109075. | + | 345914.i | 0.117131 | + | 0.371462i | ||||
\(966\) | −119821. | −0.128404 | ||||||||
\(967\) | 205113. | − | 205113.i | 0.219352 | − | 0.219352i | −0.588874 | − | 0.808225i | \(-0.700428\pi\) |
0.808225 | + | 0.588874i | \(0.200428\pi\) | |||||||
\(968\) | 609844. | + | 609844.i | 0.650830 | + | 0.650830i | ||||
\(969\) | 373715.i | 0.398009i | ||||||||
\(970\) | 28927.0 | − | 55571.3i | 0.0307440 | − | 0.0590619i | ||||
\(971\) | −57664.8 | −0.0611606 | −0.0305803 | − | 0.999532i | \(-0.509736\pi\) | ||||
−0.0305803 | + | 0.999532i | \(0.509736\pi\) | |||||||
\(972\) | 38920.9 | − | 38920.9i | 0.0411955 | − | 0.0411955i | ||||
\(973\) | −392027. | − | 392027.i | −0.414086 | − | 0.414086i | ||||
\(974\) | 230087.i | 0.242535i | ||||||||
\(975\) | −201940. | + | 141413.i | −0.212428 | + | 0.148758i | ||||
\(976\) | 237687. | 0.249520 | ||||||||
\(977\) | 161161. | − | 161161.i | 0.168838 | − | 0.168838i | −0.617630 | − | 0.786469i | \(-0.711907\pi\) |
0.786469 | + | 0.617630i | \(0.211907\pi\) | |||||||
\(978\) | −177329. | − | 177329.i | −0.185397 | − | 0.185397i | ||||
\(979\) | 61941.1i | 0.0646269i | ||||||||
\(980\) | 12867.0 | + | 6697.76i | 0.0133975 | + | 0.00697392i | ||||
\(981\) | 726249. | 0.754653 | ||||||||
\(982\) | −837662. | + | 837662.i | −0.868652 | + | 0.868652i | ||||
\(983\) | 392165. | + | 392165.i | 0.405847 | + | 0.405847i | 0.880287 | − | 0.474441i | \(-0.157350\pi\) |
−0.474441 | + | 0.880287i | \(0.657350\pi\) | |||||||
\(984\) | − | 176341.i | − | 0.182122i | ||||||
\(985\) | −491967. | + | 155129.i | −0.507064 | + | 0.159889i | ||||
\(986\) | −1.45836e6 | −1.50007 | ||||||||
\(987\) | 10282.4 | − | 10282.4i | 0.0105550 | − | 0.0105550i | ||||
\(988\) | −127100. | − | 127100.i | −0.130207 | − | 0.130207i | ||||
\(989\) | 521548.i | 0.533214i | ||||||||
\(990\) | −43454.1 | − | 137808.i | −0.0443364 | − | 0.140606i | ||||
\(991\) | 988822. | 1.00686 | 0.503432 | − | 0.864035i | \(-0.332070\pi\) | ||||
0.503432 | + | 0.864035i | \(0.332070\pi\) | |||||||
\(992\) | −84469.1 | + | 84469.1i | −0.0858370 | + | 0.0858370i | ||||
\(993\) | 45951.6 | + | 45951.6i | 0.0466018 | + | 0.0466018i | ||||
\(994\) | − | 191138.i | − | 0.193453i | ||||||
\(995\) | −577340. | + | 1.10912e6i | −0.583157 | + | 1.12030i | ||||
\(996\) | 3684.64 | 0.00371430 | ||||||||
\(997\) | 952325. | − | 952325.i | 0.958064 | − | 0.958064i | −0.0410911 | − | 0.999155i | \(-0.513083\pi\) |
0.999155 | + | 0.0410911i | \(0.0130834\pi\) | |||||||
\(998\) | 1.36972e6 | + | 1.36972e6i | 1.37522 | + | 1.37522i | ||||
\(999\) | 217198.i | 0.217633i |
(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 | 35.5.g.a.8.4 | ✓ | 24 | |
5.2 | odd | 4 | inner | 35.5.g.a.22.4 | yes | 24 | |
5.3 | odd | 4 | 175.5.g.c.57.9 | 24 | |||
5.4 | even | 2 | 175.5.g.c.43.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.5.g.a.8.4 | ✓ | 24 | 1.1 | even | 1 | trivial | |
35.5.g.a.22.4 | yes | 24 | 5.2 | odd | 4 | inner | |
175.5.g.c.43.9 | 24 | 5.4 | even | 2 | |||
175.5.g.c.57.9 | 24 | 5.3 | odd | 4 |