Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [351,4,Mod(127,351)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(351, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("351.127");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 351 = 3^{3} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 351.l (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.7096704120\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 117) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.31 | ||
Character | \(\chi\) | \(=\) | 351.199 |
Dual form | 351.4.l.a.127.10 |
$q$-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 \(\left(\mathbb{Z}/351\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.67076i | 1.29781i | 0.760870 | + | 0.648904i | \(0.224772\pi\) | ||||
−0.760870 | + | 0.648904i | \(0.775228\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.47446 | −0.684307 | ||||||||
\(5\) | −15.6805 | − | 9.05312i | −1.40250 | − | 0.809736i | −0.407854 | − | 0.913047i | \(-0.633723\pi\) |
−0.994649 | + | 0.103311i | \(0.967056\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 27.0172 | + | 15.5984i | 1.45879 | + | 0.842235i | 0.998952 | − | 0.0457664i | \(-0.0145730\pi\) |
0.459841 | + | 0.888001i | \(0.347906\pi\) | |||||||
\(8\) | 9.27065i | 0.409709i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 33.2318 | − | 57.5592i | 1.05088 | − | 1.82018i | ||||
\(11\) | − | 5.30011i | − | 0.145277i | −0.997358 | − | 0.0726383i | \(-0.976858\pi\) | ||
0.997358 | − | 0.0726383i | \(-0.0231419\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.93395 | + | 46.7068i | −0.0839293 | + | 0.996472i | ||||
\(14\) | −57.2580 | + | 99.1737i | −1.09306 | + | 1.89323i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −77.8260 | −1.21603 | ||||||||
\(17\) | 1.95690 | + | 3.38945i | 0.0279187 | + | 0.0483566i | 0.879647 | − | 0.475627i | \(-0.157779\pi\) |
−0.851728 | + | 0.523983i | \(0.824445\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.5736 | − | 11.3008i | 0.236342 | − | 0.136452i | −0.377152 | − | 0.926151i | \(-0.623097\pi\) |
0.613494 | + | 0.789699i | \(0.289763\pi\) | |||||||
\(20\) | 85.8420 | + | 49.5609i | 0.959743 | + | 0.554108i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 19.4554 | 0.188541 | ||||||||
\(23\) | 27.9664 | + | 48.4393i | 0.253539 | + | 0.439143i | 0.964498 | − | 0.264091i | \(-0.0850719\pi\) |
−0.710958 | + | 0.703234i | \(0.751739\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 101.418 | + | 175.661i | 0.811344 | + | 1.40529i | ||||
\(26\) | −171.449 | − | 14.4406i | −1.29323 | − | 0.108924i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −147.905 | − | 85.3928i | −0.998263 | − | 0.576347i | ||||
\(29\) | −294.507 | −1.88581 | −0.942905 | − | 0.333060i | \(-0.891919\pi\) | ||||
−0.942905 | + | 0.333060i | \(0.891919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −150.573 | − | 86.9333i | −0.872377 | − | 0.503667i | −0.00423943 | − | 0.999991i | \(-0.501349\pi\) |
−0.868137 | + | 0.496324i | \(0.834683\pi\) | |||||||
\(32\) | − | 211.515i | − | 1.16847i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.4419 | + | 7.18331i | −0.0627577 | + | 0.0362332i | ||||
\(35\) | −282.428 | − | 489.180i | −1.36398 | − | 2.36247i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −328.880 | − | 189.879i | −1.46129 | − | 0.843674i | −0.462215 | − | 0.886768i | \(-0.652945\pi\) |
−0.999071 | + | 0.0430940i | \(0.986279\pi\) | |||||||
\(38\) | 41.4826 | + | 71.8500i | 0.177089 | + | 0.306726i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 83.9283 | − | 145.368i | 0.331756 | − | 0.574618i | ||||
\(41\) | −114.876 | + | 66.3235i | −0.437575 | + | 0.252634i | −0.702568 | − | 0.711616i | \(-0.747963\pi\) |
0.264994 | + | 0.964250i | \(0.414630\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 30.3001 | − | 52.4813i | 0.107459 | − | 0.186124i | −0.807281 | − | 0.590167i | \(-0.799062\pi\) |
0.914740 | + | 0.404043i | \(0.132395\pi\) | |||||||
\(44\) | 29.0152i | 0.0994138i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −177.809 | + | 102.658i | −0.569924 | + | 0.329046i | ||||
\(47\) | −229.733 | + | 132.636i | −0.712978 | + | 0.411638i | −0.812163 | − | 0.583431i | \(-0.801710\pi\) |
0.0991849 | + | 0.995069i | \(0.468376\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 315.121 | + | 545.805i | 0.918719 | + | 1.59127i | ||||
\(50\) | −644.809 | + | 372.281i | −1.82380 | + | 1.05297i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 21.5362 | − | 255.694i | 0.0574334 | − | 0.681893i | ||||
\(53\) | 446.339 | 1.15678 | 0.578390 | − | 0.815761i | \(-0.303681\pi\) | ||||
0.578390 | + | 0.815761i | \(0.303681\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −47.9825 | + | 83.1082i | −0.117636 | + | 0.203751i | ||||
\(56\) | −144.607 | + | 250.467i | −0.345071 | + | 0.597681i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 1081.06i | − | 2.44742i | ||||||
\(59\) | 253.923i | 0.560304i | 0.959956 | + | 0.280152i | \(0.0903849\pi\) | ||||
−0.959956 | + | 0.280152i | \(0.909615\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −176.091 | + | 304.998i | −0.369608 | + | 0.640180i | −0.989504 | − | 0.144504i | \(-0.953841\pi\) |
0.619896 | + | 0.784684i | \(0.287175\pi\) | |||||||
\(62\) | 319.111 | − | 552.716i | 0.653663 | − | 1.13218i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 153.812 | 0.300415 | ||||||||
\(65\) | 484.528 | − | 696.770i | 0.924590 | − | 1.32959i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −387.416 | + | 223.675i | −0.706424 | + | 0.407854i | −0.809735 | − | 0.586795i | \(-0.800389\pi\) |
0.103312 | + | 0.994649i | \(0.467056\pi\) | |||||||
\(68\) | −10.7130 | − | 18.5554i | −0.0191050 | − | 0.0330908i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1795.66 | − | 1036.73i | 3.06604 | − | 1.77018i | ||||
\(71\) | 260.787 | − | 150.566i | 0.435912 | − | 0.251674i | −0.265950 | − | 0.963987i | \(-0.585686\pi\) |
0.701862 | + | 0.712313i | \(0.252352\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 86.9083i | 0.139340i | 0.997570 | + | 0.0696702i | \(0.0221947\pi\) | ||||
−0.997570 | + | 0.0696702i | \(0.977805\pi\) | |||||||
\(74\) | 697.000 | − | 1207.24i | 1.09493 | − | 1.89647i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −107.155 | + | 61.8659i | −0.161730 | + | 0.0933751i | ||||
\(77\) | 82.6732 | − | 143.194i | 0.122357 | − | 0.211929i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −243.931 | − | 422.500i | −0.347397 | − | 0.601709i | 0.638389 | − | 0.769714i | \(-0.279601\pi\) |
−0.985786 | + | 0.168005i | \(0.946268\pi\) | |||||||
\(80\) | 1220.35 | + | 704.568i | 1.70549 | + | 0.984664i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −243.457 | − | 421.681i | −0.327870 | − | 0.567888i | ||||
\(83\) | −842.406 | + | 486.363i | −1.11405 | + | 0.643196i | −0.939875 | − | 0.341519i | \(-0.889059\pi\) |
−0.174174 | + | 0.984715i | \(0.555725\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 70.8642i | − | 0.0904271i | ||||||
\(86\) | 192.646 | + | 111.224i | 0.241553 | + | 0.139461i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 49.1355 | 0.0595211 | ||||||||
\(89\) | 789.927 | + | 456.065i | 0.940810 | + | 0.543177i | 0.890214 | − | 0.455542i | \(-0.150555\pi\) |
0.0505959 | + | 0.998719i | \(0.483888\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −834.836 | + | 1200.52i | −0.961699 | + | 1.38296i | ||||
\(92\) | −153.101 | − | 265.179i | −0.173499 | − | 0.300509i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −486.875 | − | 843.293i | −0.534227 | − | 0.925309i | ||||
\(95\) | −409.231 | −0.441960 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.9039 | − | 6.87274i | −0.0124604 | − | 0.00719403i | 0.493757 | − | 0.869600i | \(-0.335623\pi\) |
−0.506217 | + | 0.862406i | \(0.668957\pi\) | |||||||
\(98\) | −2003.52 | + | 1156.73i | −2.06516 | + | 1.19232i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −555.208 | − | 961.649i | −0.555208 | − | 0.961649i | ||||
\(101\) | −905.068 | −0.891660 | −0.445830 | − | 0.895118i | \(-0.647091\pi\) | ||||
−0.445830 | + | 0.895118i | \(0.647091\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 784.818 | − | 1359.35i | 0.750781 | − | 1.30039i | −0.196664 | − | 0.980471i | \(-0.563011\pi\) |
0.947445 | − | 0.319920i | \(-0.103656\pi\) | |||||||
\(104\) | −433.002 | − | 36.4703i | −0.408263 | − | 0.0343866i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1638.40i | 1.50128i | ||||||||
\(107\) | −436.686 | + | 756.363i | −0.394542 | + | 0.683368i | −0.993043 | − | 0.117755i | \(-0.962430\pi\) |
0.598500 | + | 0.801123i | \(0.295764\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1947.88i | 1.71168i | 0.517240 | + | 0.855841i | \(0.326960\pi\) | ||||
−0.517240 | + | 0.855841i | \(0.673040\pi\) | |||||||
\(110\) | −305.070 | − | 176.132i | −0.264430 | − | 0.152669i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2102.64 | − | 1213.96i | −1.77394 | − | 1.02418i | ||||
\(113\) | 1325.76 | 1.10369 | 0.551846 | − | 0.833946i | \(-0.313924\pi\) | ||||
0.551846 | + | 0.833946i | \(0.313924\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1012.73i | − | 0.821200i | ||||||
\(116\) | 1612.26 | 1.29047 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −932.089 | −0.727167 | ||||||||
\(119\) | 122.098i | 0.0940565i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1302.91 | 0.978895 | ||||||||
\(122\) | −1119.57 | − | 646.386i | −0.830831 | − | 0.479681i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 824.305 | + | 475.912i | 0.596974 | + | 0.344663i | ||||
\(125\) | − | 1409.32i | − | 1.00842i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 881.977 | − | 1527.63i | 0.616243 | − | 1.06736i | −0.373922 | − | 0.927460i | \(-0.621987\pi\) |
0.990165 | − | 0.139904i | \(-0.0446794\pi\) | |||||||
\(128\) | − | 1127.51i | − | 0.778585i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2557.67 | + | 1778.59i | 1.72556 | + | 1.19994i | ||||
\(131\) | −464.088 | + | 803.823i | −0.309523 | + | 0.536110i | −0.978258 | − | 0.207391i | \(-0.933503\pi\) |
0.668735 | + | 0.743501i | \(0.266836\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 705.100 | 0.459699 | ||||||||
\(134\) | −821.055 | − | 1422.11i | −0.529316 | − | 0.916803i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −31.4224 | + | 18.1418i | −0.0198121 | + | 0.0114385i | ||||
\(137\) | 790.102 | + | 456.166i | 0.492722 | + | 0.284473i | 0.725703 | − | 0.688008i | \(-0.241515\pi\) |
−0.232981 | + | 0.972481i | \(0.574848\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2425.50 | −1.48006 | −0.740030 | − | 0.672574i | \(-0.765189\pi\) | ||||
−0.740030 | + | 0.672574i | \(0.765189\pi\) | |||||||
\(140\) | 1546.14 | + | 2678.00i | 0.933378 | + | 1.61666i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 552.689 | + | 957.286i | 0.326624 | + | 0.565730i | ||||
\(143\) | 247.551 | + | 20.8504i | 0.144764 | + | 0.0121930i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4618.00 | + | 2666.20i | 2.64486 | + | 1.52701i | ||||
\(146\) | −319.019 | −0.180837 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1800.44 | + | 1039.49i | 0.999969 | + | 0.577332i | ||||
\(149\) | − | 593.988i | − | 0.326587i | −0.986578 | − | 0.163293i | \(-0.947788\pi\) | ||
0.986578 | − | 0.163293i | \(-0.0522117\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1410.87 | + | 814.564i | −0.760362 | + | 0.438995i | −0.829426 | − | 0.558617i | \(-0.811332\pi\) |
0.0690639 | + | 0.997612i | \(0.477999\pi\) | |||||||
\(152\) | 104.766 | + | 181.460i | 0.0559056 | + | 0.0968313i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 525.631 | + | 303.473i | 0.275043 | + | 0.158796i | ||||
\(155\) | 1574.03 | + | 2726.31i | 0.815674 | + | 1.41279i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1393.74 | + | 2414.03i | −0.708489 | + | 1.22714i | 0.256928 | + | 0.966430i | \(0.417290\pi\) |
−0.965417 | + | 0.260709i | \(0.916044\pi\) | |||||||
\(158\) | 1550.90 | − | 895.410i | 0.780903 | − | 0.450854i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1914.87 | + | 3316.65i | −0.946149 | + | 1.63878i | ||||
\(161\) | 1744.93i | 0.854159i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −658.915 | + | 380.425i | −0.316627 | + | 0.182805i | −0.649888 | − | 0.760030i | \(-0.725184\pi\) |
0.333261 | + | 0.942835i | \(0.391851\pi\) | |||||||
\(164\) | 628.882 | − | 363.085i | 0.299436 | − | 0.172879i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1785.32 | − | 3092.27i | −0.834746 | − | 1.44582i | ||||
\(167\) | −877.056 | + | 506.369i | −0.406399 | + | 0.234635i | −0.689241 | − | 0.724532i | \(-0.742056\pi\) |
0.282842 | + | 0.959166i | \(0.408723\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2166.05 | − | 367.484i | −0.985912 | − | 0.167266i | ||||
\(170\) | 260.125 | 0.117357 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −165.876 | + | 287.307i | −0.0735347 | + | 0.127366i | ||||
\(173\) | 880.012 | − | 1524.23i | 0.386740 | − | 0.669854i | −0.605269 | − | 0.796021i | \(-0.706934\pi\) |
0.992009 | + | 0.126167i | \(0.0402676\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6327.83i | 2.73337i | ||||||||
\(176\) | 412.486i | 0.176661i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1674.10 | + | 2899.63i | −0.704940 | + | 1.22099i | ||||
\(179\) | 1156.00 | − | 2002.26i | 0.482702 | − | 0.836065i | −0.517101 | − | 0.855925i | \(-0.672989\pi\) |
0.999803 | + | 0.0198600i | \(0.00632204\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −590.593 | −0.242533 | −0.121266 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121266 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(182\) | −4406.83 | − | 3064.48i | −1.79481 | − | 1.24810i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −449.064 | + | 259.267i | −0.179921 | + | 0.103877i | ||||
\(185\) | 3438.00 | + | 5954.79i | 1.36631 | + | 2.36651i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.9645 | − | 10.3718i | 0.00702509 | − | 0.00405594i | ||||
\(188\) | 1257.66 | − | 726.111i | 0.487896 | − | 0.281687i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 1502.19i | − | 0.573580i | ||||||
\(191\) | 1408.36 | − | 2439.36i | 0.533537 | − | 0.924114i | −0.465695 | − | 0.884945i | \(-0.654196\pi\) |
0.999233 | − | 0.0391685i | \(-0.0124709\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3108.07 | − | 1794.44i | 1.15919 | − | 0.669259i | 0.208080 | − | 0.978112i | \(-0.433279\pi\) |
0.951110 | + | 0.308853i | \(0.0999452\pi\) | |||||||
\(194\) | 25.2282 | − | 43.6965i | 0.00933648 | − | 0.0161713i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1725.11 | − | 2987.99i | −0.628686 | − | 1.08892i | ||||
\(197\) | 3226.92 | + | 1863.06i | 1.16705 | + | 0.673795i | 0.952983 | − | 0.303025i | \(-0.0979965\pi\) |
0.214064 | + | 0.976820i | \(0.431330\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 818.404 | + | 1417.52i | 0.291533 | + | 0.504950i | 0.974172 | − | 0.225805i | \(-0.0725013\pi\) |
−0.682639 | + | 0.730755i | \(0.739168\pi\) | |||||||
\(200\) | −1628.49 | + | 940.211i | −0.575759 | + | 0.332415i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 3322.29i | − | 1.15720i | ||||||
\(203\) | −7956.76 | − | 4593.83i | −2.75101 | − | 1.58830i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2401.74 | 0.818267 | ||||||||
\(206\) | 4989.83 | + | 2880.88i | 1.68766 | + | 0.974370i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 306.163 | − | 3635.00i | 0.102061 | − | 1.21174i | ||||
\(209\) | −59.8956 | − | 103.742i | −0.0198233 | − | 0.0343349i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1865.72 | + | 3231.53i | 0.608728 | + | 1.05435i | 0.991450 | + | 0.130485i | \(0.0416533\pi\) |
−0.382722 | + | 0.923863i | \(0.625013\pi\) | |||||||
\(212\) | −2443.46 | −0.791593 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2776.42 | − | 1602.97i | −0.886880 | − | 0.512041i | ||||
\(215\) | −950.239 | + | 548.620i | −0.301422 | + | 0.174026i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2712.04 | − | 4697.39i | −0.848412 | − | 1.46949i | ||||
\(218\) | −7150.20 | −2.22143 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 262.678 | − | 454.972i | 0.0804989 | − | 0.139428i | ||||
\(221\) | −166.009 | + | 78.0666i | −0.0505292 | + | 0.0237617i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2239.68i | 0.672556i | 0.941763 | + | 0.336278i | \(0.109168\pi\) | ||||
−0.941763 | + | 0.336278i | \(0.890832\pi\) | |||||||
\(224\) | 3299.30 | − | 5714.55i | 0.984123 | − | 1.70455i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4866.55i | 1.43238i | ||||||||
\(227\) | 1311.34 | + | 757.100i | 0.383420 | + | 0.221368i | 0.679305 | − | 0.733856i | \(-0.262281\pi\) |
−0.295885 | + | 0.955224i | \(0.595615\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2765.65 | + | 1596.75i | 0.798077 | + | 0.460770i | 0.842798 | − | 0.538230i | \(-0.180907\pi\) |
−0.0447214 | + | 0.998999i | \(0.514240\pi\) | |||||||
\(230\) | 3717.50 | 1.06576 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 2730.27i | − | 0.772633i | ||||||
\(233\) | −4521.57 | −1.27132 | −0.635661 | − | 0.771968i | \(-0.719272\pi\) | ||||
−0.635661 | + | 0.771968i | \(0.719272\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4803.09 | 1.33327 | ||||||||
\(236\) | − | 1390.09i | − | 0.383420i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −448.193 | −0.122067 | ||||||||
\(239\) | 616.585 | + | 355.985i | 0.166877 | + | 0.0963464i | 0.581112 | − | 0.813823i | \(-0.302618\pi\) |
−0.414236 | + | 0.910170i | \(0.635951\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −575.708 | − | 332.385i | −0.153878 | − | 0.0888416i | 0.421084 | − | 0.907022i | \(-0.361650\pi\) |
−0.574962 | + | 0.818180i | \(0.694983\pi\) | |||||||
\(242\) | 4782.66i | 1.27042i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 964.001 | − | 1669.70i | 0.252926 | − | 0.438080i | ||||
\(245\) | − | 11411.3i | − | 2.97568i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 450.824 | + | 958.678i | 0.116135 | + | 0.246960i | ||||
\(248\) | 805.928 | − | 1395.91i | 0.206357 | − | 0.357420i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5173.26 | 1.30874 | ||||||||
\(251\) | 3552.61 | + | 6153.31i | 0.893383 | + | 1.54738i | 0.835794 | + | 0.549044i | \(0.185008\pi\) |
0.0575887 | + | 0.998340i | \(0.481659\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 256.734 | − | 148.225i | 0.0637972 | − | 0.0368334i | ||||
\(254\) | 5607.56 | + | 3237.53i | 1.38523 | + | 0.799765i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5369.32 | 1.31087 | ||||||||
\(257\) | 3557.55 | + | 6161.86i | 0.863478 | + | 1.49559i | 0.868550 | + | 0.495601i | \(0.165052\pi\) |
−0.00507226 | + | 0.999987i | \(0.501615\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5923.62 | − | 10260.0i | −1.42114 | − | 2.46149i | ||||
\(260\) | −2652.53 | + | 3814.44i | −0.632703 | + | 0.909851i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2950.64 | − | 1703.55i | −0.695768 | − | 0.401702i | ||||
\(263\) | 5431.87 | 1.27355 | 0.636774 | − | 0.771050i | \(-0.280268\pi\) | ||||
0.636774 | + | 0.771050i | \(0.280268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6998.80 | − | 4040.76i | −1.62239 | − | 0.936686i | ||||
\(266\) | 2588.25i | 0.596601i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2120.89 | − | 1224.50i | 0.483411 | − | 0.279097i | ||||
\(269\) | −2049.04 | − | 3549.04i | −0.464431 | − | 0.804419i | 0.534744 | − | 0.845014i | \(-0.320408\pi\) |
−0.999176 | + | 0.0405953i | \(0.987075\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2034.93 | − | 1174.87i | −0.456138 | − | 0.263351i | 0.254281 | − | 0.967130i | \(-0.418161\pi\) |
−0.710419 | + | 0.703779i | \(0.751494\pi\) | |||||||
\(272\) | −152.298 | − | 263.787i | −0.0339500 | − | 0.0588032i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1674.47 | + | 2900.27i | −0.369192 | + | 0.639459i | ||||
\(275\) | 931.023 | − | 537.526i | 0.204156 | − | 0.117869i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1615.56 | − | 2798.24i | 0.350432 | − | 0.606967i | −0.635893 | − | 0.771777i | \(-0.719368\pi\) |
0.986325 | + | 0.164811i | \(0.0527013\pi\) | |||||||
\(278\) | − | 8903.42i | − | 1.92083i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4535.02 | − | 2618.30i | 0.967927 | − | 0.558833i | ||||
\(281\) | −660.709 | + | 381.461i | −0.140265 | + | 0.0809823i | −0.568491 | − | 0.822690i | \(-0.692472\pi\) |
0.428225 | + | 0.903672i | \(0.359139\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2153.83 | − | 3730.54i | −0.452409 | − | 0.783596i | 0.546126 | − | 0.837703i | \(-0.316102\pi\) |
−0.998535 | + | 0.0541071i | \(0.982769\pi\) | |||||||
\(284\) | −1427.67 | + | 824.265i | −0.298298 | + | 0.172222i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −76.5366 | + | 908.700i | −0.0158241 | + | 0.187876i | ||||
\(287\) | −4138.16 | −0.851108 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2448.84 | − | 4241.52i | 0.498441 | − | 0.863325i | ||||
\(290\) | −9786.99 | + | 16951.6i | −1.98176 | + | 3.43252i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 475.776i | − | 0.0953517i | ||||||
\(293\) | 1952.55i | 0.389314i | 0.980871 | + | 0.194657i | \(0.0623594\pi\) | ||||
−0.980871 | + | 0.194657i | \(0.937641\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2298.79 | − | 3981.63i | 0.453698 | − | 0.785828i | ||||
\(296\) | 1760.30 | − | 3048.93i | 0.345661 | − | 0.598702i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2180.39 | 0.423847 | ||||||||
\(299\) | −2372.46 | + | 1115.67i | −0.458873 | + | 0.215788i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1637.25 | − | 945.266i | 0.313520 | − | 0.181011i | ||||
\(302\) | −2990.07 | − | 5178.95i | −0.569732 | − | 0.986804i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1523.34 | + | 879.498i | −0.287399 | + | 0.165930i | ||||
\(305\) | 5522.37 | − | 3188.34i | 1.03675 | − | 0.598570i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4583.08i | − | 0.852021i | −0.904718 | − | 0.426011i | \(-0.859919\pi\) | ||
0.904718 | − | 0.426011i | \(-0.140081\pi\) | |||||||
\(308\) | −452.591 | + | 783.911i | −0.0837298 | + | 0.145024i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10007.6 | + | 5777.90i | −1.83353 | + | 1.05859i | ||||
\(311\) | 2718.46 | − | 4708.51i | 0.495658 | − | 0.858504i | −0.504330 | − | 0.863511i | \(-0.668260\pi\) |
0.999987 | + | 0.00500685i | \(0.00159374\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1428.47 | − | 2474.18i | −0.257961 | − | 0.446802i | 0.707734 | − | 0.706479i | \(-0.249717\pi\) |
−0.965696 | + | 0.259677i | \(0.916384\pi\) | |||||||
\(314\) | −8861.33 | − | 5116.09i | −1.59259 | − | 0.919483i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1335.39 | + | 2312.96i | 0.237726 | + | 0.411754i | ||||
\(317\) | −211.113 | + | 121.886i | −0.0374046 | + | 0.0215956i | −0.518586 | − | 0.855026i | \(-0.673541\pi\) |
0.481181 | + | 0.876621i | \(0.340208\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1560.92i | 0.273964i | ||||||||
\(320\) | −2411.85 | − | 1392.48i | −0.421333 | − | 0.243257i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6405.21 | −1.10853 | ||||||||
\(323\) | 76.6073 | + | 44.2292i | 0.0131967 | + | 0.00761913i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8603.54 | + | 4045.87i | −1.46843 | + | 0.690536i | ||||
\(326\) | −1396.45 | − | 2418.72i | −0.237245 | − | 0.410921i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −614.862 | − | 1064.97i | −0.103506 | − | 0.179278i | ||||
\(329\) | −8275.65 | −1.38678 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7686.80 | + | 4437.97i | 1.27645 | + | 0.736958i | 0.976194 | − | 0.216901i | \(-0.0695949\pi\) |
0.300255 | + | 0.953859i | \(0.402928\pi\) | |||||||
\(332\) | 4611.71 | − | 2662.57i | 0.762351 | − | 0.440144i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1858.76 | − | 3219.46i | −0.304511 | − | 0.527428i | ||||
\(335\) | 8099.81 | 1.32102 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2517.56 | + | 4360.54i | −0.406944 | + | 0.704848i | −0.994546 | − | 0.104302i | \(-0.966739\pi\) |
0.587601 | + | 0.809151i | \(0.300072\pi\) | |||||||
\(338\) | 1348.95 | − | 7951.04i | 0.217080 | − | 1.27952i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 387.943i | 0.0618799i | ||||||||
\(341\) | −460.756 | + | 798.052i | −0.0731710 | + | 0.126736i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8961.01i | 1.41064i | ||||||||
\(344\) | 486.536 | + | 280.902i | 0.0762565 | + | 0.0440267i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5595.06 | + | 3230.31i | 0.869342 | + | 0.501915i | ||||
\(347\) | 1047.29 | 0.162022 | 0.0810110 | − | 0.996713i | \(-0.474185\pi\) | ||||
0.0810110 | + | 0.996713i | \(0.474185\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3715.05i | 0.569805i | 0.958557 | + | 0.284902i | \(0.0919612\pi\) | ||||
−0.958557 | + | 0.284902i | \(0.908039\pi\) | |||||||
\(350\) | −23227.9 | −3.54739 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1121.05 | −0.169751 | ||||||||
\(353\) | 3215.70i | 0.484856i | 0.970169 | + | 0.242428i | \(0.0779439\pi\) | ||||
−0.970169 | + | 0.242428i | \(0.922056\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5452.35 | −0.815157 | ||||||||
\(356\) | −4324.42 | − | 2496.71i | −0.643803 | − | 0.371700i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7349.79 | + | 4243.40i | 1.08505 | + | 0.626455i | ||||
\(359\) | 2456.41i | 0.361126i | 0.983563 | + | 0.180563i | \(0.0577920\pi\) | ||||
−0.983563 | + | 0.180563i | \(0.942208\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3174.08 | + | 5497.67i | −0.462762 | + | 0.801527i | ||||
\(362\) | − | 2167.92i | − | 0.314761i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4570.27 | − | 6572.22i | 0.658097 | − | 0.946368i | ||||
\(365\) | 786.792 | − | 1362.76i | 0.112829 | − | 0.195425i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7207.65 | 1.02517 | 0.512583 | − | 0.858638i | \(-0.328689\pi\) | ||||
0.512583 | + | 0.858638i | \(0.328689\pi\) | |||||||
\(368\) | −2176.52 | − | 3769.84i | −0.308312 | − | 0.534012i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −21858.6 | + | 12620.1i | −3.07128 | + | 1.77320i | ||||
\(371\) | 12058.8 | + | 6962.17i | 1.68750 | + | 0.974280i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3618.03 | 0.502237 | 0.251118 | − | 0.967956i | \(-0.419202\pi\) | ||||
0.251118 | + | 0.967956i | \(0.419202\pi\) | |||||||
\(374\) | 38.0723 | + | 65.9432i | 0.00526383 | + | 0.00911722i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1229.62 | − | 2129.77i | −0.168652 | − | 0.292113i | ||||
\(377\) | 1158.57 | − | 13755.5i | 0.158275 | − | 1.87916i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3693.56 | + | 2132.48i | 0.500594 | + | 0.289018i | 0.728959 | − | 0.684557i | \(-0.240005\pi\) |
−0.228365 | + | 0.973576i | \(0.573338\pi\) | |||||||
\(380\) | 2240.32 | 0.302437 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8954.29 | + | 5169.76i | 1.19932 | + | 0.692429i | ||||
\(383\) | 2198.87i | 0.293360i | 0.989184 | + | 0.146680i | \(0.0468588\pi\) | ||||
−0.989184 | + | 0.146680i | \(0.953141\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2592.71 | + | 1496.90i | −0.343212 | + | 0.198154i | ||||
\(386\) | 6586.97 | + | 11409.0i | 0.868570 | + | 1.50441i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 65.1676 | + | 37.6245i | 0.00852676 | + | 0.00492293i | ||||
\(389\) | −4728.07 | − | 8189.26i | −0.616254 | − | 1.06738i | −0.990163 | − | 0.139917i | \(-0.955316\pi\) |
0.373910 | − | 0.927465i | \(-0.378017\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −109.455 | + | 189.582i | −0.0141570 | + | 0.0245206i | ||||
\(392\) | −5059.97 | + | 2921.37i | −0.651956 | + | 0.376407i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6838.84 | + | 11845.2i | −0.874457 | + | 1.51460i | ||||
\(395\) | 8833.33i | 1.12520i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 353.202 | − | 203.921i | 0.0446516 | − | 0.0257796i | −0.477508 | − | 0.878627i | \(-0.658460\pi\) |
0.522160 | + | 0.852848i | \(0.325127\pi\) | |||||||
\(398\) | −5203.36 | + | 3004.16i | −0.655329 | + | 0.378354i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7892.95 | − | 13671.0i | −0.986619 | − | 1.70887i | ||||
\(401\) | −9601.64 | + | 5543.51i | −1.19572 | + | 0.690348i | −0.959598 | − | 0.281375i | \(-0.909209\pi\) |
−0.236121 | + | 0.971724i | \(0.575876\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4652.72 | − | 6690.78i | 0.575108 | − | 0.827026i | ||||
\(404\) | 4954.76 | 0.610169 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16862.9 | − | 29207.3i | 2.06130 | − | 3.57028i | ||||
\(407\) | −1006.38 | + | 1743.10i | −0.122566 | + | 0.212291i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4555.43i | 0.550738i | 0.961339 | + | 0.275369i | \(0.0887999\pi\) | ||||
−0.961339 | + | 0.275369i | \(0.911200\pi\) | |||||||
\(410\) | 8816.20i | 1.06195i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4296.45 | + | 7441.68i | −0.513765 | + | 0.889867i | ||||
\(413\) | −3960.79 | + | 6860.29i | −0.471907 | + | 0.817368i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17612.4 | 2.08328 | ||||||||
\(416\) | 9879.19 | + | 832.089i | 1.16434 | + | 0.0980686i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 380.813 | − | 219.862i | 0.0445602 | − | 0.0257268i | ||||
\(419\) | −2619.83 | − | 4537.68i | −0.305458 | − | 0.529070i | 0.671905 | − | 0.740637i | \(-0.265476\pi\) |
−0.977363 | + | 0.211568i | \(0.932143\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2347.39 | + | 1355.27i | −0.271746 | + | 0.156892i | −0.629681 | − | 0.776854i | \(-0.716814\pi\) |
0.357935 | + | 0.933746i | \(0.383481\pi\) | |||||||
\(422\) | −11862.1 | + | 6848.61i | −1.36834 | + | 0.790013i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4137.85i | 0.473943i | ||||||||
\(425\) | −396.930 | + | 687.503i | −0.0453034 | + | 0.0784677i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9514.96 | + | 5493.47i | −1.07836 | + | 0.622594i | ||||
\(428\) | 2390.62 | − | 4140.67i | 0.269988 | − | 0.467633i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2013.85 | − | 3488.09i | −0.225853 | − | 0.391188i | ||||
\(431\) | 6956.90 | + | 4016.57i | 0.777499 | + | 0.448889i | 0.835543 | − | 0.549425i | \(-0.185153\pi\) |
−0.0580440 | + | 0.998314i | \(0.518486\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6078.19 | − | 10527.7i | −0.674594 | − | 1.16843i | −0.976587 | − | 0.215122i | \(-0.930985\pi\) |
0.301993 | − | 0.953310i | \(-0.402348\pi\) | |||||||
\(434\) | 17243.0 | − | 9955.24i | 1.90712 | − | 1.10108i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 10663.6i | − | 1.17132i | ||||||
\(437\) | 1094.81 | + | 632.088i | 0.119844 | + | 0.0691919i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9173.30 | 0.997307 | 0.498654 | − | 0.866801i | \(-0.333828\pi\) | ||||
0.498654 | + | 0.866801i | \(0.333828\pi\) | |||||||
\(440\) | −770.467 | − | 444.829i | −0.0834786 | − | 0.0481964i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −286.564 | − | 609.378i | −0.0308381 | − | 0.0655773i | ||||
\(443\) | −2512.51 | − | 4351.80i | −0.269465 | − | 0.466727i | 0.699259 | − | 0.714869i | \(-0.253514\pi\) |
−0.968724 | + | 0.248141i | \(0.920180\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8257.61 | − | 14302.6i | −0.879660 | − | 1.52361i | ||||
\(446\) | −8221.31 | −0.872848 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4155.59 | + | 2399.23i | 0.438243 | + | 0.253020i | ||||
\(449\) | −1955.56 | + | 1129.04i | −0.205542 | + | 0.118670i | −0.599238 | − | 0.800571i | \(-0.704530\pi\) |
0.393696 | + | 0.919241i | \(0.371196\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 351.522 | + | 608.853i | 0.0367018 | + | 0.0635694i | ||||
\(452\) | −7257.82 | −0.755264 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2779.13 | + | 4813.60i | −0.287293 | + | 0.497606i | ||||
\(455\) | 23959.1 | − | 11266.9i | 2.46862 | − | 1.16088i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14006.0i | 1.43364i | 0.697257 | + | 0.716821i | \(0.254404\pi\) | ||||
−0.697257 | + | 0.716821i | \(0.745596\pi\) | |||||||
\(458\) | −5861.29 | + | 10152.0i | −0.597991 | + | 1.03575i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5544.17i | 0.561953i | ||||||||
\(461\) | −6714.29 | − | 3876.50i | −0.678342 | − | 0.391641i | 0.120888 | − | 0.992666i | \(-0.461426\pi\) |
−0.799230 | + | 0.601025i | \(0.794759\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6468.88 | + | 3734.81i | 0.649319 | + | 0.374884i | 0.788195 | − | 0.615425i | \(-0.211016\pi\) |
−0.138876 | + | 0.990310i | \(0.544349\pi\) | |||||||
\(464\) | 22920.3 | 2.29320 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 16597.6i | − | 1.64993i | ||||||
\(467\) | 17196.4 | 1.70398 | 0.851988 | − | 0.523562i | \(-0.175397\pi\) | ||||
0.851988 | + | 0.523562i | \(0.175397\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13955.9 | −1.37403 | ||||||||
\(470\) | 17631.0i | 1.73033i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2354.03 | −0.229561 | ||||||||
\(473\) | −278.156 | − | 160.594i | −0.0270394 | − | 0.0156112i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3970.23 | + | 2292.21i | 0.383509 | + | 0.221419i | ||||
\(476\) | − | 668.421i | − | 0.0643635i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1306.74 | + | 2263.33i | −0.125039 | + | 0.216574i | ||||
\(479\) | − | 985.534i | − | 0.0940087i | −0.998895 | − | 0.0470044i | \(-0.985033\pi\) | ||
0.998895 | − | 0.0470044i | \(-0.0149675\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10162.4 | − | 14614.0i | 0.963342 | − | 1.38532i | ||||
\(482\) | 1220.11 | − | 2113.29i | 0.115299 | − | 0.199704i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7132.72 | −0.669865 | ||||||||
\(485\) | 124.440 | + | 215.536i | 0.0116505 | + | 0.0201793i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9271.86 | + | 5353.11i | −0.862727 | + | 0.498096i | −0.864925 | − | 0.501902i | \(-0.832634\pi\) |
0.00219755 | + | 0.999998i | \(0.499300\pi\) | |||||||
\(488\) | −2827.53 | − | 1632.48i | −0.262287 | − | 0.151432i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 41888.1 | 3.86186 | ||||||||
\(491\) | −705.204 | − | 1221.45i | −0.0648176 | − | 0.112267i | 0.831795 | − | 0.555082i | \(-0.187313\pi\) |
−0.896613 | + | 0.442815i | \(0.853980\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −576.320 | − | 998.216i | −0.0526494 | − | 0.0911915i | ||||
\(494\) | −3519.07 | + | 1654.87i | −0.320507 | + | 0.150720i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11718.5 | + | 6765.67i | 1.06084 | + | 0.612475i | ||||
\(497\) | 9394.33 | 0.847874 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4911.34 | − | 2835.56i | −0.440605 | − | 0.254383i | 0.263249 | − | 0.964728i | \(-0.415206\pi\) |
−0.703854 | + | 0.710345i | \(0.748539\pi\) | |||||||
\(500\) | 7715.24i | 0.690072i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22587.3 | + | 13040.8i | −2.00821 | + | 1.15944i | ||||
\(503\) | −1271.73 | − | 2202.70i | −0.112731 | − | 0.195255i | 0.804140 | − | 0.594441i | \(-0.202626\pi\) |
−0.916870 | + | 0.399185i | \(0.869293\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14191.9 | + | 8193.69i | 1.25056 | + | 0.722009i | ||||
\(506\) | 544.099 | + | 942.407i | 0.0478026 | + | 0.0827966i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4828.35 | + | 8362.94i | −0.421699 | + | 0.730405i | ||||
\(509\) | −3751.14 | + | 2165.72i | −0.326653 | + | 0.188593i | −0.654354 | − | 0.756188i | \(-0.727059\pi\) |
0.327701 | + | 0.944781i | \(0.393726\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1355.63 | + | 2348.02i | −0.117357 | + | 0.203269i | ||||
\(512\) | 10689.4i | 0.922673i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22618.7 | + | 13058.9i | −1.94099 | + | 1.12063i | ||||
\(515\) | −24612.6 | + | 14210.1i | −2.10595 | + | 1.21587i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 702.986 | + | 1217.61i | 0.0598014 | + | 0.103579i | ||||
\(518\) | 37662.0 | − | 21744.2i | 3.19455 | − | 1.84437i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6459.51 | + | 4491.89i | 0.544747 | + | 0.378813i | ||||
\(521\) | −8320.00 | −0.699627 | −0.349814 | − | 0.936819i | \(-0.613755\pi\) | ||||
−0.349814 | + | 0.936819i | \(0.613755\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −994.860 | + | 1723.15i | −0.0831781 | + | 0.144069i | −0.904613 | − | 0.426233i | \(-0.859840\pi\) |
0.821435 | + | 0.570302i | \(0.193174\pi\) | |||||||
\(524\) | 2540.63 | − | 4400.50i | 0.211809 | − | 0.366864i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19939.1i | 1.65282i | ||||||||
\(527\) | − | 680.479i | − | 0.0562469i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4519.26 | − | 7827.58i | 0.371435 | − | 0.643345i | ||||
\(530\) | 14832.6 | − | 25690.9i | 1.21564 | − | 2.10555i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3860.04 | −0.314575 | ||||||||
\(533\) | −2645.84 | − | 5626.39i | −0.215017 | − | 0.457234i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13694.9 | − | 7906.74i | 1.10669 | − | 0.638950i | ||||
\(536\) | −2073.61 | − | 3591.60i | −0.167101 | − | 0.289428i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13027.7 | − | 7521.52i | 1.04398 | − | 0.602743i | ||||
\(539\) | 2892.82 | − | 1670.17i | 0.231174 | − | 0.133468i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5180.38i | 0.411686i | 0.978585 | + | 0.205843i | \(0.0659936\pi\) | ||||
−0.978585 | + | 0.205843i | \(0.934006\pi\) | |||||||
\(542\) | 4312.66 | − | 7469.74i | 0.341780 | − | 0.591980i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 716.920 | − | 413.914i | 0.0565031 | − | 0.0326221i | ||||
\(545\) | 17634.4 | − | 30543.7i | 1.38601 | − | 2.40064i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3793.38 | + | 6570.33i | 0.296514 | + | 0.513577i | 0.975336 | − | 0.220725i | \(-0.0708425\pi\) |
−0.678822 | + | 0.734303i | \(0.737509\pi\) | |||||||
\(548\) | −4325.38 | − | 2497.26i | −0.337173 | − | 0.194667i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1973.13 | + | 3417.56i | 0.152972 | + | 0.264955i | ||||
\(551\) | −5764.56 | + | 3328.17i | −0.445696 | + | 0.257323i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15219.7i | − | 1.17036i | ||||||
\(554\) | 10271.7 | + | 5930.34i | 0.787727 | + | 0.454794i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13278.3 | 1.01282 | ||||||||
\(557\) | −11208.0 | − | 6470.93i | −0.852599 | − | 0.492248i | 0.00892808 | − | 0.999960i | \(-0.497158\pi\) |
−0.861527 | + | 0.507712i | \(0.830491\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2332.03 | + | 1621.68i | 0.176448 | + | 0.122701i | ||||
\(560\) | 21980.3 | + | 38070.9i | 1.65864 | + | 2.87284i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1400.25 | − | 2425.30i | −0.105100 | − | 0.182038i | ||||
\(563\) | −860.355 | −0.0644043 | −0.0322022 | − | 0.999481i | \(-0.510252\pi\) | ||||
−0.0322022 | + | 0.999481i | \(0.510252\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20788.6 | − | 12002.3i | −1.54793 | − | 0.893698i | ||||
\(566\) | 13693.9 | − | 7906.18i | 1.01696 | − | 0.587141i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1395.84 | + | 2417.67i | 0.103113 | + | 0.178597i | ||||
\(569\) | −175.472 | −0.0129283 | −0.00646413 | − | 0.999979i | \(-0.502058\pi\) | ||||
−0.00646413 | + | 0.999979i | \(0.502058\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5355.41 | + | 9275.84i | −0.392499 | + | 0.679828i | −0.992778 | − | 0.119962i | \(-0.961723\pi\) |
0.600280 | + | 0.799790i | \(0.295056\pi\) | |||||||
\(572\) | −1355.21 | − | 114.144i | −0.0990631 | − | 0.00834374i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 15190.2i | − | 1.10458i | ||||||
\(575\) | −5672.60 | + | 9825.23i | −0.411415 | + | 0.712592i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4210.54i | 0.303790i | 0.988397 | + | 0.151895i | \(0.0485376\pi\) | ||||
−0.988397 | + | 0.151895i | \(0.951462\pi\) | |||||||
\(578\) | 15569.6 | + | 8989.10i | 1.12043 | + | 0.646881i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −25281.1 | − | 14596.0i | −1.80989 | − | 1.04494i | ||||
\(581\) | −30346.0 | −2.16689 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2365.64i | − | 0.168053i | ||||||
\(584\) | −805.697 | −0.0570890 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7167.33 | −0.505255 | ||||||||
\(587\) | − | 26112.5i | − | 1.83608i | −0.396488 | − | 0.918040i | \(-0.629771\pi\) | ||
0.396488 | − | 0.918040i | \(-0.370229\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3929.67 | −0.274906 | ||||||||
\(590\) | 14615.6 | + | 8438.31i | 1.01985 | + | 0.588813i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 25595.4 | + | 14777.5i | 1.77697 | + | 1.02593i | ||||
\(593\) | 18330.1i | 1.26935i | 0.772779 | + | 0.634676i | \(0.218866\pi\) | ||||
−0.772779 | + | 0.634676i | \(0.781134\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1105.37 | − | 1914.56i | 0.0761609 | − | 0.131914i | ||||
\(596\) | 3251.76i | 0.223486i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4095.34 | − | 8708.74i | −0.280051 | − | 0.595530i | ||||
\(599\) | −3567.25 | + | 6178.66i | −0.243329 | + | 0.421458i | −0.961660 | − | 0.274243i | \(-0.911573\pi\) |
0.718332 | + | 0.695701i | \(0.244906\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8910.23 | −0.604752 | −0.302376 | − | 0.953189i | \(-0.597780\pi\) | ||||
−0.302376 | + | 0.953189i | \(0.597780\pi\) | |||||||
\(602\) | 3469.84 | + | 6009.94i | 0.234917 | + | 0.406889i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7723.72 | − | 4459.29i | 0.520321 | − | 0.300407i | ||||
\(605\) | −20430.2 | − | 11795.4i | −1.37290 | − | 0.792646i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24487.8 | −1.63744 | −0.818722 | − | 0.574191i | \(-0.805317\pi\) | ||||
−0.818722 | + | 0.574191i | \(0.805317\pi\) | |||||||
\(608\) | −2390.30 | − | 4140.11i | −0.159440 | − | 0.276158i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11703.6 | + | 20271.3i | 0.776829 | + | 1.34551i | ||||
\(611\) | −5291.25 | − | 11251.9i | −0.350346 | − | 0.745011i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1218.37 | − | 703.428i | −0.0802767 | − | 0.0463478i | 0.459324 | − | 0.888269i | \(-0.348092\pi\) |
−0.539601 | + | 0.841921i | \(0.681425\pi\) | |||||||
\(614\) | 16823.4 | 1.10576 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1327.50 | + | 766.435i | 0.0868290 | + | 0.0501308i | ||||
\(617\) | 10833.8i | 0.706889i | 0.935455 | + | 0.353445i | \(0.114990\pi\) | ||||
−0.935455 | + | 0.353445i | \(0.885010\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18673.7 | + | 10781.3i | −1.21254 | + | 0.700059i | −0.963311 | − | 0.268386i | \(-0.913510\pi\) |
−0.249226 | + | 0.968445i | \(0.580176\pi\) | |||||||
\(620\) | −8616.99 | − | 14925.1i | −0.558172 | − | 0.966782i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17283.8 | + | 9978.79i | 1.11417 | + | 0.643269i | ||||
\(623\) | 14227.8 | + | 24643.2i | 0.914965 | + | 1.58477i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −81.4616 | + | 141.096i | −0.00521354 | + | 0.00903012i | ||||
\(626\) | 9082.12 | − | 5243.57i | 0.579864 | − | 0.334784i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7629.99 | − | 13215.5i | 0.484824 | − | 0.839740i | ||||
\(629\) | − | 1486.30i | − | 0.0942172i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12316.3 | − | 7110.82i | 0.777027 | − | 0.448617i | −0.0583487 | − | 0.998296i | \(-0.518584\pi\) |
0.835376 | + | 0.549680i | \(0.185250\pi\) | |||||||
\(632\) | 3916.85 | − | 2261.40i | 0.246525 | − | 0.142332i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −447.414 | − | 774.943i | −0.0280269 | − | 0.0485441i | ||||
\(635\) | −27659.6 | + | 15969.3i | −1.72857 | + | 0.997988i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26732.5 | + | 12571.1i | −1.66276 | + | 0.781923i | ||||
\(638\) | −5729.75 | −0.355553 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10207.5 | + | 17679.9i | −0.630448 | + | 1.09197i | ||||
\(641\) | −14814.9 | + | 25660.2i | −0.912877 | + | 1.58115i | −0.102897 | + | 0.994692i | \(0.532811\pi\) |
−0.809980 | + | 0.586457i | \(0.800522\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21519.2i | 1.31980i | 0.751352 | + | 0.659902i | \(0.229402\pi\) | ||||
−0.751352 | + | 0.659902i | \(0.770598\pi\) | |||||||
\(644\) | − | 9552.53i | − | 0.584507i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −162.355 | + | 281.207i | −0.00988817 | + | 0.0171268i | ||||
\(647\) | −15501.1 | + | 26848.6i | −0.941901 | + | 1.63142i | −0.180061 | + | 0.983655i | \(0.557629\pi\) |
−0.761840 | + | 0.647765i | \(0.775704\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1345.82 | 0.0813991 | ||||||||
\(650\) | −14851.4 | − | 31581.5i | −0.896184 | − | 1.90574i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3607.20 | − | 2082.62i | 0.216670 | − | 0.125095i | ||||
\(653\) | −2890.04 | − | 5005.69i | −0.173194 | − | 0.299982i | 0.766341 | − | 0.642435i | \(-0.222076\pi\) |
−0.939535 | + | 0.342453i | \(0.888742\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14554.2 | − | 8402.88i | 0.868214 | − | 0.501264i | ||||
\(656\) | 8940.31 | − | 5161.69i | 0.532104 | − | 0.307211i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 30377.9i | − | 1.79978i | ||||||
\(659\) | 9660.89 | − | 16733.2i | 0.571070 | − | 0.989122i | −0.425387 | − | 0.905012i | \(-0.639862\pi\) |
0.996456 | − | 0.0841102i | \(-0.0268048\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10613.2 | − | 6127.56i | 0.624519 | − | 0.360566i | −0.154107 | − | 0.988054i | \(-0.549250\pi\) |
0.778626 | + | 0.627488i | \(0.215917\pi\) | |||||||
\(662\) | −16290.7 | + | 28216.4i | −0.956430 | + | 1.65659i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4508.90 | − | 7809.65i | −0.263523 | − | 0.456436i | ||||
\(665\) | −11056.3 | − | 6383.35i | −0.644729 | − | 0.372234i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8236.31 | − | 14265.7i | −0.478127 | − | 0.828141i | ||||
\(668\) | 4801.41 | − | 2772.09i | 0.278102 | − | 0.160562i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 29732.4i | 1.71442i | ||||||||
\(671\) | 1616.52 | + | 933.300i | 0.0930032 | + | 0.0536954i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24278.7 | 1.39060 | 0.695301 | − | 0.718719i | \(-0.255271\pi\) | ||||
0.695301 | + | 0.718719i | \(0.255271\pi\) | |||||||
\(674\) | −16006.5 | − | 9241.35i | −0.914758 | − | 0.528136i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11857.9 | + | 2011.78i | 0.674666 | + | 0.114462i | ||||
\(677\) | −1040.37 | − | 1801.98i | −0.0590618 | − | 0.102298i | 0.834983 | − | 0.550276i | \(-0.185478\pi\) |
−0.894044 | + | 0.447978i | \(0.852144\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −214.408 | − | 371.365i | −0.0121181 | − | 0.0209892i | ||||
\(680\) | 656.958 | 0.0370488 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2929.46 | − | 1691.32i | −0.164479 | − | 0.0949620i | ||||
\(683\) | −1724.70 | + | 995.758i | −0.0966236 | + | 0.0557857i | −0.547533 | − | 0.836784i | \(-0.684433\pi\) |
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8259.44 | − | 14305.8i | −0.460696 | − | 0.797950i | ||||
\(686\) | −32893.7 | −1.83074 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2358.13 | + | 4084.41i | −0.130673 | + | 0.226332i | ||||
\(689\) | −1755.87 | + | 20847.0i | −0.0970877 | + | 1.15270i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 6214.52i | − | 0.342129i | −0.985260 | − | 0.171065i | \(-0.945279\pi\) | ||
0.985260 | − | 0.171065i | \(-0.0547207\pi\) | |||||||
\(692\) | −4817.59 | + | 8344.31i | −0.264649 | + | 0.458386i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3844.36i | 0.210274i | ||||||||
\(695\) | 38033.0 | + | 21958.4i | 2.07579 | + | 1.19846i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −449.601 | − | 259.577i | −0.0244331 | − | 0.0141064i | ||||
\(698\) | −13637.0 | −0.739497 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 34641.5i | − | 1.87046i | ||||||
\(701\) | 28692.5 | 1.54594 | 0.772969 | − | 0.634444i | \(-0.218771\pi\) | ||||
0.772969 | + | 0.634444i | \(0.218771\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8583.17 | −0.460484 | ||||||||
\(704\) | − | 815.223i | − | 0.0436433i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11804.0 | −0.629251 | ||||||||
\(707\) | −24452.4 | − | 14117.6i | −1.30075 | − | 0.750987i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12389.9 | − | 7153.33i | −0.656295 | − | 0.378912i | 0.134569 | − | 0.990904i | \(-0.457035\pi\) |
−0.790864 | + | 0.611992i | \(0.790368\pi\) | |||||||
\(710\) | − | 20014.3i | − | 1.05792i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4228.02 | + | 7323.14i | −0.222544 | + | 0.385458i | ||||
\(713\) | − | 9724.86i | − | 0.510798i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3692.95 | − | 2568.05i | −0.193159 | − | 0.134321i | ||||
\(716\) | −6328.49 | + | 10961.3i | −0.330317 | + | 0.572125i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9016.89 | −0.468673 | ||||||||
\(719\) | −7489.59 | − | 12972.3i | −0.388476 | − | 0.672861i | 0.603768 | − | 0.797160i | \(-0.293665\pi\) |
−0.992245 | + | 0.124299i | \(0.960332\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42407.2 | − | 24483.8i | 2.19047 | − | 1.26467i | ||||
\(722\) | −20180.6 | − | 11651.3i | −1.04023 | − | 0.600576i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3233.18 | 0.165967 | ||||||||
\(725\) | −29868.3 | − | 51733.4i | −1.53004 | − | 2.65011i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14255.9 | − | 24691.9i | −0.727264 | − | 1.25966i | −0.958035 | − | 0.286651i | \(-0.907458\pi\) |
0.230771 | − | 0.973008i | \(-0.425875\pi\) | |||||||
\(728\) | −11129.6 | − | 7739.47i | −0.566610 | − | 0.394016i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5002.37 | + | 2888.12i | 0.253625 | + | 0.146430i | ||||
\(731\) | 237.177 | 0.0120004 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1279.08 | − | 738.479i | −0.0644530 | − | 0.0372119i | 0.467427 | − | 0.884032i | \(-0.345181\pi\) |
−0.531880 | + | 0.846820i | \(0.678514\pi\) | |||||||
\(734\) | 26457.5i | 1.33047i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10245.6 | − | 5915.32i | 0.513124 | − | 0.296252i | ||||
\(737\) | 1185.50 | + | 2053.35i | 0.0592516 | + | 0.102627i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5378.35 | + | 3105.19i | 0.267721 | + | 0.154569i | 0.627851 | − | 0.778333i | \(-0.283935\pi\) |
−0.360131 | + | 0.932902i | \(0.617268\pi\) | |||||||
\(740\) | −18821.2 | − | 32599.2i | −0.934973 | − | 1.61942i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −25556.4 | + | 44265.0i | −1.26443 | + | 2.19006i | ||||
\(743\) | −21362.4 | + | 12333.6i | −1.05479 | + | 0.608986i | −0.923988 | − | 0.382422i | \(-0.875090\pi\) |
−0.130807 | + | 0.991408i | \(0.541757\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5377.45 | + | 9314.01i | −0.264449 | + | 0.458039i | ||||
\(746\) | 13280.9i | 0.651807i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −98.3457 | + | 56.7799i | −0.00480732 | + | 0.00277551i | ||||
\(749\) | −23596.1 | + | 13623.2i | −1.15111 | + | 0.664595i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7372.23 | + | 12769.1i | 0.358211 | + | 0.620440i | 0.987662 | − | 0.156601i | \(-0.0500535\pi\) |
−0.629451 | + | 0.777040i | \(0.716720\pi\) | |||||||
\(752\) | 17879.2 | − | 10322.5i | 0.867003 | − | 0.500564i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 50493.0 | + | 4252.84i | 2.43879 | + | 0.205410i | ||||
\(755\) | 29497.4 | 1.42188 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14902.9 | + | 25812.6i | −0.715530 | + | 1.23933i | 0.247224 | + | 0.968958i | \(0.420482\pi\) |
−0.962755 | + | 0.270376i | \(0.912852\pi\) | |||||||
\(758\) | −7827.80 | + | 13558.1i | −0.375090 | + | 0.649675i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 3793.84i | − | 0.181075i | ||||||
\(761\) | 23987.0i | 1.14261i | 0.820737 | + | 0.571306i | \(0.193563\pi\) | ||||
−0.820737 | + | 0.571306i | \(0.806437\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30383.9 | + | 52626.4i | −1.44164 | + | 2.49699i | ||||
\(764\) | −7710.03 | + | 13354.2i | −0.365103 | + | 0.632378i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8071.52 | −0.380726 | ||||||||
\(767\) | −11859.9 | − | 998.919i | −0.558327 | − | 0.0470259i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8670.15 | − | 5005.71i | 0.406572 | − | 0.234734i | −0.282744 | − | 0.959195i | \(-0.591245\pi\) |
0.689316 | + | 0.724461i | \(0.257911\pi\) | |||||||
\(770\) | −5494.76 | − | 9517.21i | −0.257166 | − | 0.445424i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17015.0 | + | 9823.61i | −0.793242 | + | 0.457978i | ||||
\(773\) | −26216.7 | + | 15136.2i | −1.21986 | + | 0.704285i | −0.964887 | − | 0.262664i | \(-0.915399\pi\) |
−0.254970 | + | 0.966949i | \(0.582066\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 35266.4i | − | 1.63459i | ||||||
\(776\) | 63.7148 | − | 110.357i | 0.00294746 | − | 0.00510515i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30060.8 | − | 17355.6i | 1.38526 | − | 0.799779i | ||||
\(779\) | −1499.02 | + | 2596.38i | −0.0689448 | + | 0.119416i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −798.014 | − | 1382.20i | −0.0365623 | − | 0.0633278i | ||||
\(782\) | −695.909 | − | 401.783i | −0.0318231 | − | 0.0183731i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −24524.6 | − | 42477.8i | −1.11719 | − | 1.93503i | ||||
\(785\) | 43709.1 | − | 25235.4i | 1.98732 | − | 1.14738i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19094.1i | 0.864842i | 0.901672 | + | 0.432421i | \(0.142341\pi\) | ||||
−0.901672 | + | 0.432421i | \(0.857659\pi\) | |||||||
\(788\) | −17665.6 | − | 10199.2i | −0.798619 | − | 0.461083i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32425.0 | −1.46029 | ||||||||
\(791\) | 35818.4 | + | 20679.8i | 1.61006 | + | 0.929567i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13552.7 | − | 9424.48i | −0.606900 | − | 0.422034i | ||||
\(794\) | 748.545 | + | 1296.52i | 0.0334570 | + | 0.0579492i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4480.32 | − | 7760.13i | −0.199498 | − | 0.345541i | ||||
\(797\) | 23412.4 | 1.04054 | 0.520269 | − | 0.854002i | \(-0.325832\pi\) | ||||
0.520269 | + | 0.854002i | \(0.325832\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −899.128 | − | 519.112i | −0.0398108 | − | 0.0229848i | ||||
\(800\) | 37155.0 | − | 21451.4i | 1.64203 | − | 0.948028i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20348.9 | − | 35245.3i | −0.895940 | − | 1.55181i | ||||
\(803\) | 460.624 | 0.0202429 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15797.0 | − | 27361.3i | 0.691643 | − | 1.19796i | ||||
\(806\) | 24560.2 | + | 17079.0i | 1.07332 | + | 0.746380i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 8390.57i | − | 0.365321i | ||||||
\(809\) | 125.058 | − | 216.607i | 0.00543486 | − | 0.00941345i | −0.863295 | − | 0.504699i | \(-0.831603\pi\) |
0.868730 | + | 0.495286i | \(0.164937\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2544.87i | 0.110188i | 0.998481 | + | 0.0550941i | \(0.0175459\pi\) | ||||
−0.998481 | + | 0.0550941i | \(0.982454\pi\) | |||||||
\(812\) | 43558.9 | + | 25148.8i | 1.88253 | + | 1.08688i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6398.50 | − | 3694.18i | −0.275513 | − | 0.159067i | ||||
\(815\) | 13776.1 | 0.592094 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1369.66i | − | 0.0586518i | ||||||
\(818\) | −16721.9 | −0.714752 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13148.2 | −0.559946 | ||||||||
\(821\) | − | 17444.1i | − | 0.741538i | −0.928725 | − | 0.370769i | \(-0.879094\pi\) | ||
0.928725 | − | 0.370769i | \(-0.120906\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21736.6 | −0.920645 | −0.460322 | − | 0.887752i | \(-0.652266\pi\) | ||||
−0.460322 | + | 0.887752i | \(0.652266\pi\) | |||||||
\(824\) | 12602.0 | + | 7275.78i | 0.532782 | + | 0.307602i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −25182.5 | − | 14539.1i | −1.06079 | − | 0.612446i | ||||
\(827\) | − | 31700.0i | − | 1.33291i | −0.745544 | − | 0.666456i | \(-0.767810\pi\) | ||
0.745544 | − | 0.666456i | \(-0.232190\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17175.2 | − | 29748.3i | 0.719565 | − | 1.24632i | −0.241608 | − | 0.970374i | \(-0.577675\pi\) |
0.961172 | − | 0.275949i | \(-0.0889920\pi\) | |||||||
\(830\) | 64650.9i | 2.70369i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −605.090 | + | 7184.09i | −0.0252136 | + | 0.299355i | ||||
\(833\) | −1233.32 | + | 2136.17i | −0.0512989 | + | 0.0888523i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18336.9 | 0.759968 | ||||||||
\(836\) | 327.896 | + | 567.933i | 0.0135652 | + | 0.0234956i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16656.7 | − | 9616.76i | 0.686631 | − | 0.396427i | ||||
\(839\) | −34912.6 | − | 20156.8i | −1.43661 | − | 0.829427i | −0.438998 | − | 0.898488i | \(-0.644666\pi\) |
−0.997612 | + | 0.0690608i | \(0.978000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 62345.2 | 2.55628 | ||||||||
\(842\) | −4974.86 | − | 8616.71i | −0.203616 | − | 0.352674i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10213.8 | − | 17690.9i | −0.416557 | − | 0.721498i | ||||
\(845\) | 30637.8 | + | 25371.8i | 1.24730 | + | 1.03292i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35201.0 | + | 20323.3i | 1.42801 | + | 0.824459i | ||||
\(848\) | −34736.7 | −1.40668 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2523.66 | − | 1457.03i | −0.101836 | − | 0.0587951i | ||||
\(851\) | − | 21241.0i | − | 0.855618i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9517.24 | − | 5494.78i | 0.382021 | − | 0.220560i | −0.296676 | − | 0.954978i | \(-0.595878\pi\) |
0.678697 | + | 0.734418i | \(0.262545\pi\) | |||||||
\(854\) | −20165.2 | − | 34927.1i | −0.808007 | − | 1.39951i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7011.97 | − | 4048.37i | −0.279982 | − | 0.161648i | ||||
\(857\) | 4133.04 | + | 7158.63i | 0.164740 | + | 0.285338i | 0.936563 | − | 0.350500i | \(-0.113988\pi\) |
−0.771823 | + | 0.635837i | \(0.780655\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16811.7 | − | 29118.8i | 0.667764 | − | 1.15660i | −0.310765 | − | 0.950487i | \(-0.600585\pi\) |
0.978528 | − | 0.206113i | \(-0.0660816\pi\) | |||||||
\(860\) | 5202.04 | − | 3003.40i | 0.206265 | − | 0.119087i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14743.9 | + | 25537.1i | −0.582573 | + | 1.00905i | ||||
\(863\) | − | 23570.2i | − | 0.929709i | −0.885387 | − | 0.464855i | \(-0.846107\pi\) | ||
0.885387 | − | 0.464855i | \(-0.153893\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27598.0 | + | 15933.7i | −1.08481 | + | 0.626315i | ||||
\(866\) | 38644.8 | − | 22311.6i | 1.51640 | − | 0.875495i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14847.0 | + | 25715.7i | 0.580574 | + | 1.00558i | ||||
\(869\) | −2239.30 | + | 1292.86i | −0.0874142 | + | 0.0504686i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8923.05 | − | 18974.9i | −0.347125 | − | 0.738162i | ||||
\(872\) | −18058.1 | −0.701291 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2320.24 | + | 4018.78i | −0.0897979 | + | 0.155535i | ||||
\(875\) | 21983.1 | − | 38075.8i | 0.849330 | − | 1.47108i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39291.0i | 1.51284i | 0.654085 | + | 0.756421i | \(0.273054\pi\) | ||||
−0.654085 | + | 0.756421i | \(0.726946\pi\) | |||||||
\(878\) | 33673.0i | 1.29431i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3734.29 | − | 6467.97i | 0.143049 | − | 0.247767i | ||||
\(881\) | −8048.55 | + | 13940.5i | −0.307789 | + | 0.533107i | −0.977878 | − | 0.209174i | \(-0.932923\pi\) |
0.670089 | + | 0.742281i | \(0.266256\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50307.6 | 1.91731 | 0.958656 | − | 0.284567i | \(-0.0918500\pi\) | ||||
0.958656 | + | 0.284567i | \(0.0918500\pi\) | |||||||
\(884\) | 908.808 | − | 427.372i | 0.0345775 | − | 0.0162603i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15974.4 | − | 9222.82i | 0.605723 | − | 0.349714i | ||||
\(887\) | −10617.0 | − | 18389.2i | −0.401899 | − | 0.696109i | 0.592056 | − | 0.805897i | \(-0.298316\pi\) |
−0.993955 | + | 0.109788i | \(0.964983\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 47657.2 | − | 27514.9i | 1.79794 | − | 1.03804i | ||||
\(890\) | 52501.4 | − | 30311.7i | 1.97736 | − | 1.14163i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 12261.0i | − | 0.460235i | ||||||
\(893\) | −2997.80 | + | 5192.34i | −0.112338 | + | 0.194574i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36253.3 | + | 20930.9i | −1.35398 | + | 0.781722i | ||||
\(896\) | 17587.4 | − | 30462.3i | 0.655752 | − | 1.13580i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4144.43 | − | 7178.37i | −0.154011 | − | 0.266754i | ||||
\(899\) | 44344.7 | + | 25602.4i | 1.64514 | + | 0.949821i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 873.440 | + | 1512.84i | 0.0322958 | + | 0.0559380i | ||||
\(902\) | −2234.95 | + | 1290.35i | −0.0825009 | + | 0.0476319i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12290.7i | 0.452192i | ||||||||
\(905\) | 9260.77 | + | 5346.71i | 0.340153 | + | 0.196387i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18513.6 | −0.677768 | −0.338884 | − | 0.940828i | \(-0.610049\pi\) | ||||
−0.338884 | + | 0.940828i | \(0.610049\pi\) | |||||||
\(908\) | −7178.85 | − | 4144.71i | −0.262377 | − | 0.151484i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 41358.1 | + | 87948.1i | 1.50660 | + | 3.20379i | ||||
\(911\) | −1537.30 | − | 2662.68i | −0.0559088 | − | 0.0968369i | 0.836716 | − | 0.547636i | \(-0.184472\pi\) |
−0.892625 | + | 0.450799i | \(0.851139\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2577.78 | + | 4464.84i | 0.0934414 | + | 0.161845i | ||||
\(914\) | −51412.7 | −1.86059 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15140.5 | − | 8741.35i | −0.546130 | − | 0.315308i | ||||
\(917\) | −25076.7 | + | 14478.1i | −0.903060 | + | 0.521382i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1520.38 | + | 2633.38i | 0.0545733 | + | 0.0945237i | 0.892021 | − | 0.451993i | \(-0.149287\pi\) |
−0.837448 | + | 0.546517i | \(0.815953\pi\) | |||||||
\(920\) | 9388.71 | 0.336453 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14229.7 | − | 24646.5i | 0.508275 | − | 0.880359i | ||||
\(923\) | 6006.51 | + | 12772.8i | 0.214200 | + | 0.455497i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 77028.6i | − | 2.73804i | ||||||
\(926\) | −13709.6 | + | 23745.7i | −0.486528 | + | 0.842691i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 62292.6i | 2.20351i | ||||||||
\(929\) | −29546.3 | − | 17058.6i | −1.04347 | − | 0.602447i | −0.122655 | − | 0.992449i | \(-0.539141\pi\) |
−0.920814 | + | 0.390002i | \(0.872474\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12336.1 | + | 7122.25i | 0.434263 | + | 0.250722i | ||||
\(932\) | 24753.2 | 0.869975 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 63124.0i | 2.21143i | ||||||||
\(935\) | −375.588 | −0.0131369 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5165.26 | −0.180087 | −0.0900436 | − | 0.995938i | \(-0.528701\pi\) | ||||
−0.0900436 | + | 0.995938i | \(0.528701\pi\) | |||||||
\(938\) | − | 51228.6i | − | 1.78323i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −26294.3 | −0.912367 | ||||||||
\(941\) | 22962.4 | + | 13257.3i | 0.795485 | + | 0.459274i | 0.841890 | − | 0.539649i | \(-0.181443\pi\) |
−0.0464048 | + | 0.998923i | \(0.514776\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6425.33 | − | 3709.66i | −0.221885 | − | 0.128105i | ||||
\(944\) | − | 19761.8i | − | 0.681347i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 589.500 | − | 1021.04i | 0.0202604 | − | 0.0350920i | ||||
\(947\) | 17080.6i | 0.586107i | 0.956096 | + | 0.293054i | \(0.0946715\pi\) | ||||
−0.956096 | + | 0.293054i | \(0.905329\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4059.21 | − | 341.893i | −0.138849 | − | 0.0116947i | ||||
\(950\) | −8414.16 | + | 14573.8i | −0.287359 | + | 0.497721i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1131.93 | −0.0385358 | ||||||||
\(953\) | −2582.09 | − | 4472.31i | −0.0877671 | − | 0.152017i | 0.818800 | − | 0.574079i | \(-0.194640\pi\) |
−0.906567 | + | 0.422062i | \(0.861306\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −44167.6 | + | 25500.2i | −1.49658 | + | 0.864048i | ||||
\(956\) | −3375.47 | − | 1948.83i | −0.114195 | − | 0.0659305i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3617.65 | 0.122005 | ||||||||
\(959\) | 14230.9 | + | 24648.7i | 0.479187 | + | 0.829976i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 219.286 | + | 379.815i | 0.00736082 | + | 0.0127493i | ||||
\(962\) | 53644.3 | + | 37303.9i | 1.79788 | + | 1.25023i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3151.69 | + | 1819.63i | 0.105300 | + | 0.0607950i | ||||
\(965\) | −64981.3 | −2.16769 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20692.4 | − | 11946.7i | −0.688129 | − | 0.397292i | 0.114781 | − | 0.993391i | \(-0.463383\pi\) |
−0.802911 | + | 0.596099i | \(0.796717\pi\) | |||||||
\(968\) | 12078.8i | 0.401062i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −791.179 | + | 456.787i | −0.0261889 | + | 0.0151202i | ||||
\(971\) | −1767.00 | − | 3060.54i | −0.0583994 | − | 0.101151i | 0.835348 | − | 0.549722i | \(-0.185266\pi\) |
−0.893747 | + | 0.448571i | \(0.851933\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −65530.3 | − | 37833.9i | −2.15910 | − | 1.24656i | ||||
\(974\) | −19650.0 | − | 34034.7i | −0.646433 | − | 1.11965i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13704.4 | − | 23736.8i | 0.449455 | − | 0.778479i | ||||
\(977\) | 21527.2 | − | 12428.7i | 0.704929 | − | 0.406991i | −0.104252 | − | 0.994551i | \(-0.533245\pi\) |
0.809181 | + | 0.587560i | \(0.199911\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2417.19 | − | 4186.70i | 0.0789109 | − | 0.136678i | ||||
\(980\) | 62470.7i | 2.03628i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4483.64 | − | 2588.63i | 0.145701 | − | 0.0841208i | ||||
\(983\) | 16346.0 | − | 9437.38i | 0.530373 | − | 0.306211i | −0.210795 | − | 0.977530i | \(-0.567605\pi\) |
0.741168 | + | 0.671319i | \(0.234272\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33733.0 | − | 58427.3i | −1.09119 | − | 1.89000i | ||||
\(986\) | 3664.21 | − | 2115.53i | 0.118349 | − | 0.0683289i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2468.02 | − | 5248.24i | −0.0794717 | − | 0.168997i | ||||
\(989\) | 3389.54 | 0.108980 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6486.71 | + | 11235.3i | −0.207928 | + | 0.360143i | −0.951062 | − | 0.309001i | \(-0.900005\pi\) |
0.743133 | + | 0.669143i | \(0.233339\pi\) | |||||||
\(992\) | −18387.7 | + | 31848.4i | −0.588518 | + | 1.01934i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 34484.3i | 1.10038i | ||||||||
\(995\) | − | 29636.4i | − | 0.944259i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30380.5 | + | 52620.6i | −0.965056 | + | 1.67153i | −0.255591 | + | 0.966785i | \(0.582270\pi\) |
−0.709465 | + | 0.704741i | \(0.751063\pi\) | |||||||
\(998\) | 10408.7 | − | 18028.3i | 0.330141 | − | 0.571821i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 351.4.l.a.199.31 | 80 | ||
3.2 | odd | 2 | 117.4.l.a.4.10 | ✓ | 80 | ||
9.2 | odd | 6 | 117.4.r.a.43.10 | yes | 80 | ||
9.7 | even | 3 | 351.4.r.a.316.31 | 80 | |||
13.10 | even | 6 | 351.4.r.a.10.31 | 80 | |||
39.23 | odd | 6 | 117.4.r.a.49.10 | yes | 80 | ||
117.88 | even | 6 | inner | 351.4.l.a.127.10 | 80 | ||
117.101 | odd | 6 | 117.4.l.a.88.31 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.l.a.4.10 | ✓ | 80 | 3.2 | odd | 2 | ||
117.4.l.a.88.31 | yes | 80 | 117.101 | odd | 6 | ||
117.4.r.a.43.10 | yes | 80 | 9.2 | odd | 6 | ||
117.4.r.a.49.10 | yes | 80 | 39.23 | odd | 6 | ||
351.4.l.a.127.10 | 80 | 117.88 | even | 6 | inner | ||
351.4.l.a.199.31 | 80 | 1.1 | even | 1 | trivial | ||
351.4.r.a.10.31 | 80 | 13.10 | even | 6 | |||
351.4.r.a.316.31 | 80 | 9.7 | even | 3 |