Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,3,Mod(161,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.l (of order \(2\), degree \(1\), 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: | \(6.53952634465\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.681615360000.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 2x^{6} + 20x^{5} + 49x^{4} - 136x^{3} + 168x^{2} - 96x + 864 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.3 | ||
Root | \(-2.22255 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.161 |
Dual form | 240.3.l.d.161.4 |
$q$-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 \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(181\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.291610 | − | 2.98579i | −0.0972033 | − | 0.995265i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.46268 | −0.637525 | −0.318763 | − | 0.947835i | \(-0.603267\pi\) | ||||
−0.318763 | + | 0.947835i | \(0.603267\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.82993 | + | 1.74137i | −0.981103 | + | 0.193486i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 17.8696i | − | 1.62451i | −0.583305 | − | 0.812253i | \(-0.698241\pi\) | ||
0.583305 | − | 0.812253i | \(-0.301759\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11.0107 | −0.846980 | −0.423490 | − | 0.905901i | \(-0.639195\pi\) | ||||
−0.423490 | + | 0.905901i | \(0.639195\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.67644 | − | 0.652060i | 0.445096 | − | 0.0434707i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.794055i | − | 0.0467091i | −0.999727 | − | 0.0233546i | \(-0.992565\pi\) | ||
0.999727 | − | 0.0233546i | \(-0.00743466\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −26.5852 | −1.39922 | −0.699611 | − | 0.714524i | \(-0.746643\pi\) | ||||
−0.699611 | + | 0.714524i | \(0.746643\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.30136 | + | 13.3246i | 0.0619696 | + | 0.634506i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 14.9276i | 0.649027i | 0.945881 | + | 0.324514i | \(0.105201\pi\) | ||||
−0.945881 | + | 0.324514i | \(0.894799\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.77428 | + | 25.8565i | 0.287936 | + | 0.957650i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.58545i | − | 0.192602i | −0.995352 | − | 0.0963008i | \(-0.969299\pi\) | ||
0.995352 | − | 0.0963008i | \(-0.0307011\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −53.1074 | −1.71314 | −0.856571 | − | 0.516030i | \(-0.827409\pi\) | ||||
−0.856571 | + | 0.516030i | \(0.827409\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −53.3549 | + | 5.21095i | −1.61681 | + | 0.157907i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 9.97885i | − | 0.285110i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 51.7565 | 1.39882 | 0.699412 | − | 0.714719i | \(-0.253445\pi\) | ||||
0.699412 | + | 0.714719i | \(0.253445\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.21084 | + | 32.8758i | 0.0823293 | + | 0.842969i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 67.8236i | − | 1.65423i | −0.562030 | − | 0.827117i | \(-0.689980\pi\) | ||
0.562030 | − | 0.827117i | \(-0.310020\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 40.8243 | 0.949403 | 0.474701 | − | 0.880147i | \(-0.342556\pi\) | ||||
0.474701 | + | 0.880147i | \(0.342556\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.89383 | − | 19.7443i | −0.0865296 | − | 0.438763i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.3483i | 0.262729i | 0.991334 | + | 0.131365i | \(0.0419359\pi\) | ||||
−0.991334 | + | 0.131365i | \(0.958064\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −29.0845 | −0.593562 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.37088 | + | 0.231554i | −0.0464879 | + | 0.00454028i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 37.0351i | − | 0.698775i | −0.936978 | − | 0.349387i | \(-0.886390\pi\) | ||
0.936978 | − | 0.349387i | \(-0.113610\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 39.9576 | 0.726502 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.75251 | + | 79.3779i | 0.136009 | + | 1.39260i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 61.0932i | − | 1.03548i | −0.855539 | − | 0.517739i | \(-0.826774\pi\) | ||
0.855539 | − | 0.517739i | \(-0.173226\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 97.8289 | 1.60375 | 0.801876 | − | 0.597490i | \(-0.203835\pi\) | ||||
0.801876 | + | 0.597490i | \(0.203835\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 39.4051 | − | 7.77119i | 0.625478 | − | 0.123352i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 24.6208i | − | 0.378781i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.02541 | −0.0451553 | −0.0225777 | − | 0.999745i | \(-0.507187\pi\) | ||||
−0.0225777 | + | 0.999745i | \(0.507187\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 44.5708 | − | 4.35305i | 0.645954 | − | 0.0630876i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 57.0787i | − | 0.803926i | −0.915656 | − | 0.401963i | \(-0.868328\pi\) | ||
0.915656 | − | 0.401963i | \(-0.131672\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −31.4690 | −0.431082 | −0.215541 | − | 0.976495i | \(-0.569152\pi\) | ||||
−0.215541 | + | 0.976495i | \(0.569152\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.45805 | + | 14.9290i | 0.0194407 | + | 0.199053i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 79.7461i | 1.03566i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.16053 | 0.0273485 | 0.0136743 | − | 0.999907i | \(-0.495647\pi\) | ||||
0.0136743 | + | 0.999907i | \(0.495647\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 74.9352 | − | 30.7524i | 0.925126 | − | 0.379660i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 13.0710i | − | 0.157482i | −0.996895 | − | 0.0787411i | \(-0.974910\pi\) | ||
0.996895 | − | 0.0787411i | \(-0.0250900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.77556 | 0.0208890 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16.6770 | + | 1.62877i | −0.191690 | + | 0.0187215i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 173.692i | 1.95160i | 0.218667 | + | 0.975800i | \(0.429829\pi\) | ||||
−0.218667 | + | 0.975800i | \(0.570171\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 49.1374 | 0.539971 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.4866 | + | 158.568i | 0.166523 | + | 1.70503i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 59.4463i | − | 0.625751i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −91.6381 | −0.944722 | −0.472361 | − | 0.881405i | \(-0.656598\pi\) | ||||
−0.472361 | + | 0.881405i | \(0.656598\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 31.1176 | + | 157.787i | 0.314319 | + | 1.59381i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 116.353i | − | 1.15201i | −0.817446 | − | 0.576005i | \(-0.804611\pi\) | ||
0.817446 | − | 0.576005i | \(-0.195389\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 182.071 | 1.76768 | 0.883842 | − | 0.467786i | \(-0.154948\pi\) | ||||
0.883842 | + | 0.467786i | \(0.154948\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −29.7948 | + | 2.90993i | −0.283760 | + | 0.0277136i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 102.828i | 0.961013i | 0.876991 | + | 0.480506i | \(0.159547\pi\) | ||||
−0.876991 | + | 0.480506i | \(0.840453\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 75.4257 | 0.691979 | 0.345990 | − | 0.938238i | \(-0.387543\pi\) | ||||
0.345990 | + | 0.938238i | \(0.387543\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.0927 | − | 154.534i | −0.135970 | − | 1.39220i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 141.923i | − | 1.25596i | −0.778230 | − | 0.627980i | \(-0.783882\pi\) | ||
0.778230 | − | 0.627980i | \(-0.216118\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −33.3792 | −0.290254 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 97.2241 | − | 19.1738i | 0.830975 | − | 0.163879i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.54361i | 0.0297782i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −198.322 | −1.63902 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −202.507 | + | 19.7780i | −1.64640 | + | 0.160797i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −112.920 | −0.889132 | −0.444566 | − | 0.895746i | \(-0.646642\pi\) | ||||
−0.444566 | + | 0.895746i | \(0.646642\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.9048 | − | 121.893i | −0.0922851 | − | 0.944907i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 107.233i | − | 0.818570i | −0.912407 | − | 0.409285i | \(-0.865778\pi\) | ||
0.912407 | − | 0.409285i | \(-0.134222\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 118.641 | 0.892039 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −57.8170 | + | 17.3838i | −0.428274 | + | 0.128769i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 67.7434i | − | 0.494477i | −0.968955 | − | 0.247239i | \(-0.920477\pi\) | ||
0.968955 | − | 0.247239i | \(-0.0795232\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 141.204 | 1.01586 | 0.507928 | − | 0.861399i | \(-0.330411\pi\) | ||||
0.507928 | + | 0.861399i | \(0.330411\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 36.8694 | − | 3.60088i | 0.261485 | − | 0.0255382i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 196.757i | 1.37593i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.4894 | 0.0861341 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.48134 | + | 86.8404i | 0.0576962 | + | 0.590751i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 55.0831i | − | 0.369685i | −0.982768 | − | 0.184843i | \(-0.940822\pi\) | ||
0.982768 | − | 0.184843i | \(-0.0591775\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −56.1302 | −0.371723 | −0.185862 | − | 0.982576i | \(-0.559508\pi\) | ||||
−0.185862 | + | 0.982576i | \(0.559508\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.38275 | + | 7.01145i | 0.00903756 | + | 0.0458265i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 118.752i | − | 0.766140i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −274.266 | −1.74692 | −0.873460 | − | 0.486896i | \(-0.838129\pi\) | ||||
−0.873460 | + | 0.486896i | \(0.838129\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −110.579 | + | 10.7998i | −0.695466 | + | 0.0679232i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 66.6172i | − | 0.413771i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −260.316 | −1.59703 | −0.798516 | − | 0.601974i | \(-0.794381\pi\) | ||||
−0.798516 | + | 0.601974i | \(0.794381\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.6520 | − | 119.305i | −0.0706184 | − | 0.723061i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 179.949i | 1.07754i | 0.842453 | + | 0.538769i | \(0.181111\pi\) | ||||
−0.842453 | + | 0.538769i | \(0.818889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −47.7635 | −0.282624 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 234.745 | − | 46.2948i | 1.37278 | − | 0.270730i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 111.265i | 0.643148i | 0.946884 | + | 0.321574i | \(0.104212\pi\) | ||||
−0.946884 | + | 0.321574i | \(0.895788\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.3134 | 0.127505 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −182.412 | + | 17.8154i | −1.03057 | + | 0.100652i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 77.8475i | − | 0.434902i | −0.976071 | − | 0.217451i | \(-0.930226\pi\) | ||
0.976071 | − | 0.217451i | \(-0.0697743\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −238.852 | −1.31963 | −0.659813 | − | 0.751430i | \(-0.729364\pi\) | ||||
−0.659813 | + | 0.751430i | \(0.729364\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −28.5279 | − | 292.097i | −0.155890 | − | 1.59616i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 115.731i | 0.625573i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.1894 | −0.0758793 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −34.6941 | − | 115.389i | −0.183567 | − | 0.610526i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 177.248i | 0.928002i | 0.885835 | + | 0.464001i | \(0.153587\pi\) | ||||
−0.885835 | + | 0.464001i | \(0.846413\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 284.254 | 1.47282 | 0.736409 | − | 0.676536i | \(-0.236520\pi\) | ||||
0.736409 | + | 0.676536i | \(0.236520\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −73.5125 | + | 7.17966i | −0.376987 | + | 0.0368188i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 244.341i | 1.24031i | 0.784479 | + | 0.620156i | \(0.212931\pi\) | ||||
−0.784479 | + | 0.620156i | \(0.787069\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −74.0122 | −0.371921 | −0.185960 | − | 0.982557i | \(-0.559540\pi\) | ||||
−0.185960 | + | 0.982557i | \(0.559540\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.882239 | + | 9.03324i | 0.00438925 | + | 0.0449415i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.9260i | 0.122788i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 151.658 | 0.739796 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −25.9946 | − | 131.810i | −0.125578 | − | 0.636763i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 475.066i | 2.27304i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 31.0682 | 0.147243 | 0.0736214 | − | 0.997286i | \(-0.476544\pi\) | ||||
0.0736214 | + | 0.997286i | \(0.476544\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −170.425 | + | 16.6447i | −0.800119 | + | 0.0781443i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 91.2859i | 0.424586i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 237.001 | 1.09217 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.17668 | + | 93.9600i | 0.0419026 | + | 0.429041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.74314i | 0.0395617i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −100.432 | −0.450366 | −0.225183 | − | 0.974316i | \(-0.572298\pi\) | ||||
−0.225183 | + | 0.974316i | \(0.572298\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 44.1496 | − | 8.70687i | 0.196221 | − | 0.0386972i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 349.117i | − | 1.53796i | −0.639273 | − | 0.768980i | \(-0.720764\pi\) | ||
0.639273 | − | 0.768980i | \(-0.279236\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −165.007 | −0.720555 | −0.360278 | − | 0.932845i | \(-0.617318\pi\) | ||||
−0.360278 | + | 0.932845i | \(0.617318\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 238.105 | − | 23.2548i | 1.03076 | − | 0.100670i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 124.800i | − | 0.535620i | −0.963472 | − | 0.267810i | \(-0.913700\pi\) | ||
0.963472 | − | 0.267810i | \(-0.0863000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −27.6116 | −0.117496 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.630033 | − | 6.45091i | −0.00265837 | − | 0.0272190i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 61.8321i | − | 0.258712i | −0.991598 | − | 0.129356i | \(-0.958709\pi\) | ||
0.991598 | − | 0.129356i | \(-0.0412910\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.25555 | 0.00935913 | 0.00467956 | − | 0.999989i | \(-0.498510\pi\) | ||||
0.00467956 | + | 0.999989i | \(0.498510\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −113.672 | − | 214.773i | −0.467787 | − | 0.883841i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 65.0350i | − | 0.265449i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 292.723 | 1.18511 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −39.0274 | + | 3.81164i | −0.156736 | + | 0.0153078i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 108.993i | 0.434234i | 0.976146 | + | 0.217117i | \(0.0696654\pi\) | ||||
−0.976146 | + | 0.217117i | \(0.930335\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 266.750 | 1.05435 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.517771 | − | 5.30146i | −0.00203048 | − | 0.0207900i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 31.4664i | − | 0.122437i | −0.998124 | − | 0.0612187i | \(-0.980501\pi\) | ||
0.998124 | − | 0.0612187i | \(-0.0194987\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −230.972 | −0.891785 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.72636 | + | 49.3191i | 0.0372657 | + | 0.188962i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 235.190i | 0.894260i | 0.894469 | + | 0.447130i | \(0.147554\pi\) | ||||
−0.894469 | + | 0.447130i | \(0.852446\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 82.8129 | 0.312502 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 518.609 | − | 50.6504i | 1.94236 | − | 0.189702i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 221.066i | − | 0.821808i | −0.911679 | − | 0.410904i | \(-0.865213\pi\) | ||
0.911679 | − | 0.410904i | \(-0.134787\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −268.830 | −0.991991 | −0.495995 | − | 0.868325i | \(-0.665197\pi\) | ||||
−0.495995 | + | 0.868325i | \(0.665197\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.3290 | − | 146.714i | −0.0524870 | − | 0.537414i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 89.3479i | 0.324901i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 144.697 | 0.522370 | 0.261185 | − | 0.965289i | \(-0.415887\pi\) | ||||
0.261185 | + | 0.965289i | \(0.415887\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 468.934 | − | 92.4798i | 1.68077 | − | 0.331469i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 189.426i | − | 0.674112i | −0.941485 | − | 0.337056i | \(-0.890569\pi\) | ||
0.941485 | − | 0.337056i | \(-0.109431\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 420.621 | 1.48629 | 0.743146 | − | 0.669129i | \(-0.233333\pi\) | ||||
0.743146 | + | 0.669129i | \(0.233333\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −177.494 | + | 17.3351i | −0.622788 | + | 0.0608251i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 302.675i | 1.05462i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 288.369 | 0.997818 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 26.7226 | + | 273.612i | 0.0918302 | + | 0.940249i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 283.828i | 0.968696i | 0.874875 | + | 0.484348i | \(0.160943\pi\) | ||||
−0.874875 | + | 0.484348i | \(0.839057\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 136.609 | 0.463080 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 462.045 | − | 138.923i | 1.55571 | − | 0.467754i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 164.364i | − | 0.549713i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −182.186 | −0.605268 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −347.406 | + | 33.9297i | −1.14656 | + | 0.111979i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 218.752i | 0.717220i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −167.979 | −0.547162 | −0.273581 | − | 0.961849i | \(-0.588208\pi\) | ||||
−0.273581 | + | 0.961849i | \(0.588208\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −53.0938 | − | 543.628i | −0.171825 | − | 1.75931i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 192.970i | 0.620482i | 0.950658 | + | 0.310241i | \(0.100410\pi\) | ||||
−0.950658 | + | 0.310241i | \(0.899590\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 161.056 | 0.514555 | 0.257278 | − | 0.966338i | \(-0.417175\pi\) | ||||
0.257278 | + | 0.966338i | \(0.417175\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 17.3769 | + | 88.1125i | 0.0551648 | + | 0.279722i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 514.761i | − | 1.62385i | −0.583761 | − | 0.811926i | \(-0.698419\pi\) | ||
0.583761 | − | 0.811926i | \(-0.301581\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −99.8096 | −0.312883 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 307.024 | − | 29.9858i | 0.956462 | − | 0.0934136i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.1101i | 0.0653564i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 55.0537 | 0.169396 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.9949 | − | 225.206i | −0.0672627 | − | 0.688702i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 55.1064i | − | 0.167497i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −63.7466 | −0.192588 | −0.0962939 | − | 0.995353i | \(-0.530699\pi\) | ||||
−0.0962939 | + | 0.995353i | \(0.530699\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −457.006 | + | 90.1274i | −1.37239 | + | 0.270653i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 6.76502i | − | 0.0201941i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −64.2444 | −0.190636 | −0.0953181 | − | 0.995447i | \(-0.530387\pi\) | ||||
−0.0953181 | + | 0.995447i | \(0.530387\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −423.754 | + | 41.3863i | −1.25001 | + | 0.122083i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 949.006i | 2.78301i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 348.466 | 1.01594 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.73371 | + | 99.6634i | 0.0282136 | + | 0.288879i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 66.1416i | 0.190610i | 0.995448 | + | 0.0953049i | \(0.0303826\pi\) | ||||
−0.995448 | + | 0.0953049i | \(0.969617\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −188.752 | −0.540837 | −0.270419 | − | 0.962743i | \(-0.587162\pi\) | ||||
−0.270419 | + | 0.962743i | \(0.587162\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −85.6006 | − | 284.700i | −0.243876 | − | 0.811110i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 435.927i | − | 1.23492i | −0.786602 | − | 0.617461i | \(-0.788161\pi\) | ||
0.786602 | − | 0.617461i | \(-0.211839\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 127.632 | 0.359527 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.5805 | − | 1.03335i | 0.0296372 | − | 0.00289454i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 188.255i | 0.524386i | 0.965015 | + | 0.262193i | \(0.0844457\pi\) | ||||
−0.965015 | + | 0.262193i | \(0.915554\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 345.773 | 0.957820 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 57.8326 | + | 592.148i | 0.159318 | + | 1.63126i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 70.3668i | − | 0.192786i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −276.868 | −0.754409 | −0.377205 | − | 0.926130i | \(-0.623115\pi\) | ||||
−0.377205 | + | 0.926130i | \(0.623115\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 118.106 | + | 598.877i | 0.320071 | + | 1.62297i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 165.275i | 0.445486i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −510.098 | −1.36756 | −0.683778 | − | 0.729691i | \(-0.739664\pi\) | ||||
−0.683778 | + | 0.729691i | \(0.739664\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −33.3822 | + | 3.26030i | −0.0890192 | + | 0.00869413i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 61.4999i | 0.163130i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 298.461 | 0.787497 | 0.393748 | − | 0.919218i | \(-0.371178\pi\) | ||||
0.393748 | + | 0.919218i | \(0.371178\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 32.9285 | + | 337.155i | 0.0864266 | + | 0.884922i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 500.548i | − | 1.30691i | −0.756963 | − | 0.653457i | \(-0.773318\pi\) | ||
0.756963 | − | 0.653457i | \(-0.226682\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −178.318 | −0.463163 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −360.476 | + | 71.0904i | −0.931462 | + | 0.183696i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 465.726i | − | 1.19724i | −0.801033 | − | 0.598620i | \(-0.795716\pi\) | ||
0.801033 | − | 0.598620i | \(-0.204284\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.8534 | 0.0303155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −320.175 | + | 31.2701i | −0.814694 | + | 0.0795678i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.83110i | 0.0122306i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −344.998 | −0.869013 | −0.434507 | − | 0.900669i | \(-0.643077\pi\) | ||||
−0.434507 | + | 0.900669i | \(0.643077\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −34.5969 | − | 354.238i | −0.0867091 | − | 0.887815i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 428.755i | 1.06922i | 0.845100 | + | 0.534608i | \(0.179541\pi\) | ||||
−0.845100 | + | 0.534608i | \(0.820459\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 584.752 | 1.45100 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 68.7645 | + | 167.560i | 0.169789 | + | 0.413729i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 924.866i | − | 2.27240i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −349.445 | −0.854389 | −0.427194 | − | 0.904160i | \(-0.640498\pi\) | ||||
−0.427194 | + | 0.904160i | \(0.640498\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −202.268 | + | 19.7547i | −0.492136 | + | 0.0480648i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 272.639i | 0.660143i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.2277 | 0.0704281 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −41.1765 | − | 421.606i | −0.0987447 | − | 1.01105i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 225.745i | − | 0.538770i | −0.963033 | − | 0.269385i | \(-0.913180\pi\) | ||
0.963033 | − | 0.269385i | \(-0.0868205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −138.931 | −0.330003 | −0.165002 | − | 0.986293i | \(-0.552763\pi\) | ||||
−0.165002 | + | 0.986293i | \(0.552763\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.5030 | − | 109.034i | −0.0508345 | − | 0.257765i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.97027i | 0.00934182i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −436.579 | −1.02243 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 587.477 | − | 57.3764i | 1.36941 | − | 0.133745i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 289.802i | 0.672394i | 0.941792 | + | 0.336197i | \(0.109141\pi\) | ||||
−0.941792 | + | 0.336197i | \(0.890859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 53.8425 | 0.124348 | 0.0621738 | − | 0.998065i | \(-0.480197\pi\) | ||||
0.0621738 | + | 0.998065i | \(0.480197\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.64205 | − | 37.2909i | −0.00837252 | − | 0.0857262i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 396.854i | − | 0.908133i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −333.179 | −0.758949 | −0.379474 | − | 0.925202i | \(-0.623895\pi\) | ||||
−0.379474 | + | 0.925202i | \(0.623895\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 256.814 | − | 50.6471i | 0.582345 | − | 0.114846i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 652.015i | − | 1.47182i | −0.677081 | − | 0.735909i | \(-0.736755\pi\) | ||
0.677081 | − | 0.735909i | \(-0.263245\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −388.388 | −0.872782 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −164.467 | + | 16.0628i | −0.367935 | + | 0.0359346i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 115.054i | 0.256245i | 0.991758 | + | 0.128122i | \(0.0408950\pi\) | ||||
−0.991758 | + | 0.128122i | \(0.959105\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1211.98 | −2.68731 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.3681 | + | 167.593i | 0.0361327 | + | 0.369963i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 109.875i | 0.241482i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −138.318 | −0.302666 | −0.151333 | − | 0.988483i | \(-0.548357\pi\) | ||||
−0.151333 | + | 0.988483i | \(0.548357\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.5315 | − | 6.17321i | 0.0447310 | − | 0.0134493i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 300.475i | − | 0.651789i | −0.945406 | − | 0.325894i | \(-0.894335\pi\) | ||
0.945406 | − | 0.325894i | \(-0.105665\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 91.5721 | 0.197780 | 0.0988899 | − | 0.995098i | \(-0.468471\pi\) | ||||
0.0988899 | + | 0.995098i | \(0.468471\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −354.568 | + | 34.6292i | −0.762512 | + | 0.0744714i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 308.136i | − | 0.659821i | −0.944012 | − | 0.329910i | \(-0.892981\pi\) | ||
0.944012 | − | 0.329910i | \(-0.107019\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.5014 | 0.0287877 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 79.9788 | + | 818.903i | 0.169806 | + | 1.73865i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 729.513i | − | 1.54231i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 132.926 | 0.279844 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 64.4919 | + | 327.017i | 0.135203 | + | 0.685570i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 218.332i | 0.455808i | 0.973684 | + | 0.227904i | \(0.0731873\pi\) | ||||
−0.973684 | + | 0.227904i | \(0.926813\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −569.877 | −1.18478 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −198.905 | + | 19.4262i | −0.411812 | + | 0.0402200i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 204.909i | − | 0.422493i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 538.368 | 1.10548 | 0.552739 | − | 0.833354i | \(-0.313583\pi\) | ||||
0.552739 | + | 0.833354i | \(0.313583\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 75.9108 | + | 777.250i | 0.155237 | + | 1.58947i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 418.223i | − | 0.851777i | −0.904776 | − | 0.425889i | \(-0.859962\pi\) | ||
0.904776 | − | 0.425889i | \(-0.140038\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.43515 | −0.00899625 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −352.823 | + | 69.5811i | −0.712773 | + | 0.140568i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 254.724i | 0.512523i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 732.199 | 1.46733 | 0.733667 | − | 0.679510i | \(-0.237807\pi\) | ||||
0.733667 | + | 0.679510i | \(0.237807\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 537.291 | − | 52.4749i | 1.07244 | − | 0.104740i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 338.339i | 0.672641i | 0.941748 | + | 0.336321i | \(0.109183\pi\) | ||||
−0.941748 | + | 0.336321i | \(0.890817\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 260.173 | 0.515195 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.9283 | + | 142.612i | 0.0274720 | + | 0.281286i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 864.760i | − | 1.69894i | −0.527637 | − | 0.849470i | \(-0.676922\pi\) | ||
0.527637 | − | 0.849470i | \(-0.323078\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 140.436 | 0.274826 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −206.681 | − | 687.401i | −0.402887 | − | 1.33996i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 407.124i | 0.790532i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 220.659 | 0.426806 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 332.213 | − | 32.4459i | 0.640103 | − | 0.0625162i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 294.647i | − | 0.565541i | −0.959188 | − | 0.282770i | \(-0.908747\pi\) | ||
0.959188 | − | 0.282770i | \(-0.0912534\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 613.850 | 1.17371 | 0.586855 | − | 0.809692i | \(-0.300366\pi\) | ||||
0.586855 | + | 0.809692i | \(0.300366\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.50680 | − | 66.6231i | −0.0123939 | − | 0.126901i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 42.1702i | 0.0800193i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 306.166 | 0.578763 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 106.386 | + | 539.448i | 0.200351 | + | 1.01591i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 746.788i | 1.40110i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −229.931 | −0.429778 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −232.437 | + | 22.7011i | −0.432843 | + | 0.0422740i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 519.728i | 0.964245i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 188.436 | 0.348311 | 0.174156 | − | 0.984718i | \(-0.444280\pi\) | ||||
0.174156 | + | 0.984718i | \(0.444280\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 69.6517 | + | 713.163i | 0.128272 | + | 1.31338i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 168.657i | 0.309462i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −637.744 | −1.16589 | −0.582947 | − | 0.812510i | \(-0.698101\pi\) | ||||
−0.582947 | + | 0.812510i | \(0.698101\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −863.822 | + | 170.357i | −1.57345 | + | 0.310304i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 148.490i | 0.269492i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.64176 | −0.0174354 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 345.549 | − | 33.7483i | 0.622611 | − | 0.0608078i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 77.2307i | − | 0.138655i | −0.997594 | − | 0.0693274i | \(-0.977915\pi\) | ||
0.997594 | − | 0.0693274i | \(-0.0220853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −449.506 | −0.804125 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.13778 | + | 42.3667i | 0.00737572 | + | 0.0755200i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 257.584i | 0.457521i | 0.973483 | + | 0.228760i | \(0.0734672\pi\) | ||||
−0.973483 | + | 0.228760i | \(0.926533\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 317.351 | 0.561682 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −334.412 | + | 137.238i | −0.589791 | + | 0.242042i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 307.483i | − | 0.540392i | −0.962805 | − | 0.270196i | \(-0.912911\pi\) | ||
0.962805 | − | 0.270196i | \(-0.0870886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 384.100 | 0.672679 | 0.336340 | − | 0.941741i | \(-0.390811\pi\) | ||||
0.336340 | + | 0.941741i | \(0.390811\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 529.227 | − | 51.6874i | 0.923608 | − | 0.0902049i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 74.6382i | − | 0.129805i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −235.337 | −0.407863 | −0.203932 | − | 0.978985i | \(-0.565372\pi\) | ||||
−0.203932 | + | 0.978985i | \(0.565372\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −82.8913 | − | 848.724i | −0.143163 | − | 1.46584i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 58.3317i | 0.100399i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −661.801 | −1.13516 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 42.8740 | + | 217.400i | 0.0732889 | + | 0.371623i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 230.275i | − | 0.392292i | −0.980575 | − | 0.196146i | \(-0.937157\pi\) | ||
0.980575 | − | 0.196146i | \(-0.0628426\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1411.87 | 2.39706 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 729.553 | − | 71.2524i | 1.23444 | − | 0.120562i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1042.09i | 1.75731i | 0.477455 | + | 0.878656i | \(0.341559\pi\) | ||||
−0.477455 | + | 0.878656i | \(0.658441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.92375 | −0.0133172 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.5827 | + | 220.985i | 0.0361519 | + | 0.370160i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 136.181i | − | 0.227348i | −0.993518 | − | 0.113674i | \(-0.963738\pi\) | ||
0.993518 | − | 0.113674i | \(-0.0362619\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 136.625 | 0.227329 | 0.113665 | − | 0.993519i | \(-0.463741\pi\) | ||||
0.113665 | + | 0.993519i | \(0.463741\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.7141 | − | 5.26837i | 0.0443020 | − | 0.00873693i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 443.461i | − | 0.732993i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 426.666 | 0.702910 | 0.351455 | − | 0.936205i | \(-0.385687\pi\) | ||||
0.351455 | + | 0.936205i | \(0.385687\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 74.4240 | − | 7.26868i | 0.122207 | − | 0.0119354i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 135.964i | − | 0.222527i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 665.317 | 1.08535 | 0.542673 | − | 0.839944i | \(-0.317412\pi\) | ||||
0.542673 | + | 0.839944i | \(0.317412\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −44.2250 | − | 452.820i | −0.0719106 | − | 0.736292i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 826.628i | − | 1.33975i | −0.742473 | − | 0.669877i | \(-0.766347\pi\) | ||
0.742473 | − | 0.669877i | \(-0.233653\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.8176 | −0.0320155 | −0.0160078 | − | 0.999872i | \(-0.505096\pi\) | ||||
−0.0160078 | + | 0.999872i | \(0.505096\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −385.977 | + | 116.052i | −0.621541 | + | 0.186879i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 775.133i | − | 1.24419i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1418.45 | − | 138.534i | 2.26228 | − | 0.220948i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 41.0975i | − | 0.0653378i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 728.156 | 1.15397 | 0.576986 | − | 0.816754i | \(-0.304229\pi\) | ||||
0.576986 | + | 0.816754i | \(0.304229\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.05981 | − | 92.7633i | −0.0143125 | − | 0.146546i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 252.496i | − | 0.397632i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 320.242 | 0.502735 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 99.3955 | + | 504.001i | 0.155548 | + | 0.788734i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 438.969i | − | 0.684819i | −0.939551 | − | 0.342410i | \(-0.888757\pi\) | ||
0.939551 | − | 0.342410i | \(-0.111243\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −483.535 | −0.751998 | −0.375999 | − | 0.926620i | \(-0.622700\pi\) | ||||
−0.375999 | + | 0.926620i | \(0.622700\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 272.561 | − | 26.6199i | 0.422575 | − | 0.0412711i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 575.687i | 0.889780i | 0.895585 | + | 0.444890i | \(0.146757\pi\) | ||||
−0.895585 | + | 0.444890i | \(0.853243\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1091.71 | −1.68214 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −69.1119 | − | 707.636i | −0.106163 | − | 1.08700i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 407.885i | 0.624633i | 0.949978 | + | 0.312317i | \(0.101105\pi\) | ||||
−0.949978 | + | 0.312317i | \(0.898895\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 239.780 | 0.366076 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 277.869 | − | 54.7993i | 0.422936 | − | 0.0834084i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 187.060i | − | 0.283854i | −0.989877 | − | 0.141927i | \(-0.954670\pi\) | ||
0.989877 | − | 0.141927i | \(-0.0453298\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 483.965 | 0.732171 | 0.366085 | − | 0.930581i | \(-0.380698\pi\) | ||||
0.366085 | + | 0.930581i | \(0.380698\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.1052 | − | 2.54959i | 0.0393744 | − | 0.00384553i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 265.290i | 0.398932i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 83.3775 | 0.125004 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 29.2869 | + | 299.868i | 0.0437771 | + | 0.448233i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1748.16i | − | 2.60531i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 480.449 | 0.713891 | 0.356945 | − | 0.934125i | \(-0.383818\pi\) | ||||
0.356945 | + | 0.934125i | \(0.383818\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −38.8714 | − | 129.283i | −0.0575873 | − | 0.191530i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1245.12i | 1.83918i | 0.392881 | + | 0.919589i | \(0.371478\pi\) | ||||
−0.392881 | + | 0.919589i | \(0.628522\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 408.951 | 0.602284 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1042.39 | + | 101.806i | −1.53068 | + | 0.149495i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 118.409i | − | 0.173366i | −0.996236 | − | 0.0866832i | \(-0.972373\pi\) | ||
0.996236 | − | 0.0866832i | \(-0.0276268\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 151.479 | 0.221137 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 48.1177 | + | 492.677i | 0.0700404 | + | 0.717143i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 407.784i | 0.591848i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 481.257 | 0.696465 | 0.348232 | − | 0.937408i | \(-0.386782\pi\) | ||||
0.348232 | + | 0.937408i | \(0.386782\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −138.868 | − | 704.152i | −0.200387 | − | 1.01609i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 315.742i | 0.454305i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −53.8556 | −0.0772678 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −372.626 | + | 36.3928i | −0.533084 | + | 0.0520641i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 644.879i | 0.919941i | 0.887934 | + | 0.459971i | \(0.152140\pi\) | ||||
−0.887934 | + | 0.459971i | \(0.847860\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1375.96 | −1.95726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.05182 | + | 82.4425i | 0.0114210 | + | 0.116940i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 519.246i | 0.734436i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −534.801 | −0.754303 | −0.377151 | − | 0.926152i | \(-0.623096\pi\) | ||||
−0.377151 | + | 0.926152i | \(0.623096\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.0774 | + | 3.76230i | −0.0268317 | + | 0.00529156i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 792.767i | − | 1.11188i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −439.963 | −0.615332 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −184.618 | + | 18.0309i | −0.257487 | + | 0.0251476i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 891.507i | 1.23993i | 0.784631 | + | 0.619963i | \(0.212852\pi\) | ||||
−0.784631 | + | 0.619963i | \(0.787148\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −812.526 | −1.12694 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.657741 | − | 6.73461i | −0.000909739 | − | 0.00931481i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 27.9272i | 0.0385203i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 720.024 | 0.990405 | 0.495202 | − | 0.868778i | \(-0.335094\pi\) | ||||
0.495202 | + | 0.868778i | \(0.335094\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −608.121 | + | 402.032i | −0.834185 | + | 0.551484i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 32.4167i | − | 0.0443458i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 953.335 | 1.30059 | 0.650296 | − | 0.759681i | \(-0.274645\pi\) | ||||
0.650296 | + | 0.759681i | \(0.274645\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −194.181 | + | 18.9649i | −0.264192 | + | 0.0258025i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 54.0627i | 0.0733552i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −615.723 | −0.833185 | −0.416592 | − | 0.909093i | \(-0.636776\pi\) | ||||
−0.416592 | + | 0.909093i | \(0.636776\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −85.3609 | − | 874.010i | −0.115197 | − | 1.17950i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 377.743i | − | 0.508403i | −0.967151 | − | 0.254201i | \(-0.918187\pi\) | ||
0.967151 | − | 0.254201i | \(-0.0818126\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 123.170 | 0.165328 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.7615 | + | 115.416i | 0.0304706 | + | 0.154506i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 458.890i | − | 0.612670i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −735.578 | −0.979465 | −0.489733 | − | 0.871873i | \(-0.662906\pi\) | ||||
−0.489733 | + | 0.871873i | \(0.662906\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 325.430 | − | 31.7834i | 0.432178 | − | 0.0422090i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 125.511i | − | 0.166240i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 921.601 | 1.21744 | 0.608719 | − | 0.793386i | \(-0.291684\pi\) | ||||
0.608719 | + | 0.793386i | \(0.291684\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −77.7871 | − | 796.462i | −0.102486 | − | 1.04936i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 240.158i | 0.315582i | 0.987473 | + | 0.157791i | \(0.0504372\pi\) | ||||
−0.987473 | + | 0.157791i | \(0.949563\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −336.601 | −0.441154 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.6781 | + | 3.09192i | −0.0204942 | + | 0.00404172i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 672.682i | 0.877029i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.79672 | −0.00623760 | −0.00311880 | − | 0.999995i | \(-0.500993\pi\) | ||||
−0.00311880 | + | 0.999995i | \(0.500993\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −93.9522 | + | 9.17592i | −0.121858 | + | 0.0119013i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 140.044i | 0.181170i | 0.995889 | + | 0.0905850i | \(0.0288737\pi\) | ||||
−0.995889 | + | 0.0905850i | \(0.971126\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 265.537 | 0.342628 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 67.3539 | + | 689.636i | 0.0866845 | + | 0.887562i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1803.10i | 2.31464i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1019.97 | −1.30598 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 144.420 | − | 43.4228i | 0.184445 | − | 0.0554570i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 613.278i | − | 0.781246i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −649.685 | −0.825520 | −0.412760 | − | 0.910840i | \(-0.635435\pi\) | ||||
−0.412760 | + | 0.910840i | \(0.635435\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 702.230 | − | 68.5838i | 0.890025 | − | 0.0869250i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 633.358i | 0.800706i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1077.17 | −1.35835 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.1491 | − | 247.262i | −0.0303762 | − | 0.311022i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 547.802i | 0.687329i | 0.939092 | + | 0.343665i | \(0.111668\pi\) | ||||
−0.939092 | + | 0.343665i | \(0.888332\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.80522 | 0.0122719 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −302.463 | − | 1533.69i | −0.377607 | − | 1.91472i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 562.338i | 0.700296i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 148.961 | 0.185044 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −660.059 | + | 64.4652i | −0.817916 | + | 0.0798825i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 719.685i | 0.889598i | 0.895630 | + | 0.444799i | \(0.146725\pi\) | ||||
−0.895630 | + | 0.444799i | \(0.853275\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 775.519 | 0.956251 | 0.478125 | − | 0.878292i | \(-0.341316\pi\) | ||||
0.478125 | + | 0.878292i | \(0.341316\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 78.3934 | + | 802.669i | 0.0964248 | + | 0.987293i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 582.085i | − | 0.714214i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1085.32 | −1.32842 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −433.879 | + | 85.5666i | −0.529767 | + | 0.104477i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1383.11i | − | 1.68466i | −0.538960 | − | 0.842331i | \(-0.681183\pi\) | ||
0.538960 | − | 0.842331i | \(-0.318817\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −536.474 | −0.651852 | −0.325926 | − | 0.945395i | \(-0.605676\pi\) | ||||
−0.325926 | + | 0.945395i | \(0.605676\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 266.774 | − | 26.0547i | 0.323363 | − | 0.0315815i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1652.28i | 1.99792i | 0.0455686 | + | 0.998961i | \(0.485490\pi\) | ||||
−0.0455686 | + | 0.998961i | \(0.514510\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −999.416 | −1.20557 | −0.602784 | − | 0.797904i | \(-0.705942\pi\) | ||||
−0.602784 | + | 0.797904i | \(0.705942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −42.1950 | − | 432.034i | −0.0507761 | − | 0.519897i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.0947i | 0.0277247i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −402.378 | −0.481890 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −412.872 | − | 1373.17i | −0.493276 | − | 1.64059i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1394.04i | − | 1.66155i | −0.556611 | − | 0.830773i | \(-0.687899\pi\) | ||
0.556611 | − | 0.830773i | \(-0.312101\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 809.803 | 0.962905 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −565.586 | + | 55.2384i | −0.670920 | + | 0.0655260i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 106.802i | − | 0.126393i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 885.045 | 1.04492 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −122.657 | − | 1255.89i | −0.144473 | − | 1.47925i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 772.602i | 0.907875i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1293.04 | −1.51587 | −0.757935 | − | 0.652330i | \(-0.773792\pi\) | ||||
−0.757935 | + | 0.652330i | \(0.773792\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 103.518 | + | 524.907i | 0.121074 | + | 0.613926i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1513.48i | 1.76602i | 0.469357 | + | 0.883008i | \(0.344486\pi\) | ||||
−0.469357 | + | 0.883008i | \(0.655514\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −767.814 | −0.893846 | −0.446923 | − | 0.894572i | \(-0.647480\pi\) | ||||
−0.446923 | + | 0.894572i | \(0.647480\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 903.724 | − | 88.2629i | 1.04962 | − | 0.102512i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 29.2279i | − | 0.0338677i | −0.999857 | − | 0.0169339i | \(-0.994610\pi\) | ||
0.999857 | − | 0.0169339i | \(-0.00539048\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −248.795 | −0.287625 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −84.0914 | − | 861.012i | −0.0969913 | − | 0.993093i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 38.6078i | − | 0.0444279i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.3120 | 0.0382457 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 809.157 | − | 159.576i | 0.926870 | − | 0.182791i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 49.8942i | 0.0570220i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1070.98 | −1.22119 | −0.610595 | − | 0.791943i | \(-0.709070\pi\) | ||||
−0.610595 | + | 0.791943i | \(0.709070\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 847.452 | − | 82.7671i | 0.964109 | − | 0.0941605i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 489.535i | − | 0.555659i | −0.960630 | − | 0.277829i | \(-0.910385\pi\) | ||
0.960630 | − | 0.277829i | \(-0.0896150\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 742.175 | 0.840515 | 0.420257 | − | 0.907405i | \(-0.361940\pi\) | ||||
0.420257 | + | 0.907405i | \(0.361940\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −39.8364 | − | 407.885i | −0.0450129 | − | 0.460887i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1441.82i | − | 1.62550i | −0.582612 | − | 0.812751i | \(-0.697969\pi\) | ||
0.582612 | − | 0.812751i | \(-0.302031\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 503.924 | 0.566844 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −549.533 | − | 1339.06i | −0.616759 | − | 1.50287i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 328.282i | − | 0.367617i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 174.072 | 0.194494 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −490.758 | + | 47.9303i | −0.547110 | + | 0.0534340i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 296.629i | 0.329954i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.4079 | −0.0326392 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 53.1272 | + | 543.969i | 0.0588341 | + | 0.602402i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 534.090i | − | 0.590154i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 352.397 | 0.388531 | 0.194265 | − | 0.980949i | \(-0.437768\pi\) | ||||
0.194265 | + | 0.980949i | \(0.437768\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 202.614 | + | 1027.39i | 0.222898 | + | 1.13024i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 184.505i | − | 0.202531i | −0.994859 | − | 0.101265i | \(-0.967711\pi\) | ||
0.994859 | − | 0.101265i | \(-0.0322891\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −233.574 | −0.255831 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 653.149 | − | 63.7903i | 0.713824 | − | 0.0697162i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 478.545i | 0.521859i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −666.062 | −0.724769 | −0.362384 | − | 0.932029i | \(-0.618037\pi\) | ||||
−0.362384 | + | 0.932029i | \(0.618037\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 48.9843 | + | 501.550i | 0.0531860 | + | 0.544571i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 628.479i | 0.680909i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −258.782 | −0.279765 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1607.68 | + | 317.055i | −1.73428 | + | 0.342022i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 957.310i | 1.03047i | 0.857048 | + | 0.515237i | \(0.172296\pi\) | ||||
−0.857048 | + | 0.515237i | \(0.827704\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 773.218 | 0.830524 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 576.169 | − | 56.2720i | 0.617544 | − | 0.0603130i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 31.7285i | − | 0.0339342i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1108.63 | 1.18317 | 0.591585 | − | 0.806243i | \(-0.298502\pi\) | ||||
0.591585 | + | 0.806243i | \(0.298502\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −46.9655 | − | 480.879i | −0.0500165 | − | 0.512119i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.4523i | 0.0536157i | 0.999641 | + | 0.0268078i | \(0.00853422\pi\) | ||||
−0.999641 | + | 0.0268078i | \(0.991466\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1012.45 | 1.07364 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 258.018 | − | 77.5783i | 0.273035 | − | 0.0820935i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 883.676i | − | 0.933132i | −0.884486 | − | 0.466566i | \(-0.845491\pi\) | ||
0.884486 | − | 0.466566i | \(-0.154509\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 346.497 | 0.365118 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1536.97 | + | 150.109i | −1.61616 | + | 0.157844i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1238.78i | 1.29988i | 0.759987 | + | 0.649938i | \(0.225205\pi\) | ||||
−0.759987 | + | 0.649938i | \(0.774795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −396.340 | −0.415015 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29.1055 | + | 298.011i | 0.0304132 | + | 0.311401i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 302.317i | 0.315242i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1859.39 | 1.93485 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −179.063 | − | 907.967i | −0.185943 | − | 0.942852i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 635.611i | 0.658665i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1221.47 | −1.26315 | −0.631575 | − | 0.775314i | \(-0.717591\pi\) | ||||
−0.631575 | + | 0.775314i | \(0.717591\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 63.0304 | − | 6.15592i | 0.0650469 | − | 0.00635286i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1142.08i | − | 1.17619i | −0.808792 | − | 0.588095i | \(-0.799878\pi\) | ||
0.808792 | − | 0.588095i | \(-0.200122\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −630.148 | −0.647634 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.0542 | − | 164.379i | −0.0164659 | − | 0.168594i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 364.738i | − | 0.373324i | −0.982424 | − | 0.186662i | \(-0.940233\pi\) | ||
0.982424 | − | 0.186662i | \(-0.0597669\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3103.81 | 3.17039 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −666.004 | + | 131.344i | −0.678903 | + | 0.133888i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.0459i | 0.0407384i | 0.999793 | + | 0.0203692i | \(0.00648417\pi\) | ||||
−0.999793 | + | 0.0203692i | \(0.993516\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −546.364 | −0.554684 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −164.536 | + | 16.0696i | −0.166703 | + | 0.0162812i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 609.410i | 0.616188i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 910.307 | 0.918574 | 0.459287 | − | 0.888288i | \(-0.348105\pi\) | ||||
0.459287 | + | 0.888288i | \(0.348105\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.5891 | + | 190.334i | 0.0187202 | + | 0.191676i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 165.496i | − | 0.166328i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 358.437 | 0.359516 | 0.179758 | − | 0.983711i | \(-0.442469\pi\) | ||||
0.179758 | + | 0.983711i | \(0.442469\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 402.369 | + | 1338.24i | 0.402772 | + | 1.33958i |
(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 | 240.3.l.d.161.3 | 8 | ||
3.2 | odd | 2 | inner | 240.3.l.d.161.4 | 8 | ||
4.3 | odd | 2 | 120.3.l.a.41.6 | yes | 8 | ||
5.2 | odd | 4 | 1200.3.c.m.449.2 | 16 | |||
5.3 | odd | 4 | 1200.3.c.m.449.15 | 16 | |||
5.4 | even | 2 | 1200.3.l.x.401.6 | 8 | |||
8.3 | odd | 2 | 960.3.l.h.641.3 | 8 | |||
8.5 | even | 2 | 960.3.l.g.641.6 | 8 | |||
12.11 | even | 2 | 120.3.l.a.41.5 | ✓ | 8 | ||
15.2 | even | 4 | 1200.3.c.m.449.16 | 16 | |||
15.8 | even | 4 | 1200.3.c.m.449.1 | 16 | |||
15.14 | odd | 2 | 1200.3.l.x.401.5 | 8 | |||
20.3 | even | 4 | 600.3.c.d.449.2 | 16 | |||
20.7 | even | 4 | 600.3.c.d.449.15 | 16 | |||
20.19 | odd | 2 | 600.3.l.f.401.3 | 8 | |||
24.5 | odd | 2 | 960.3.l.g.641.5 | 8 | |||
24.11 | even | 2 | 960.3.l.h.641.4 | 8 | |||
60.23 | odd | 4 | 600.3.c.d.449.16 | 16 | |||
60.47 | odd | 4 | 600.3.c.d.449.1 | 16 | |||
60.59 | even | 2 | 600.3.l.f.401.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.l.a.41.5 | ✓ | 8 | 12.11 | even | 2 | ||
120.3.l.a.41.6 | yes | 8 | 4.3 | odd | 2 | ||
240.3.l.d.161.3 | 8 | 1.1 | even | 1 | trivial | ||
240.3.l.d.161.4 | 8 | 3.2 | odd | 2 | inner | ||
600.3.c.d.449.1 | 16 | 60.47 | odd | 4 | |||
600.3.c.d.449.2 | 16 | 20.3 | even | 4 | |||
600.3.c.d.449.15 | 16 | 20.7 | even | 4 | |||
600.3.c.d.449.16 | 16 | 60.23 | odd | 4 | |||
600.3.l.f.401.3 | 8 | 20.19 | odd | 2 | |||
600.3.l.f.401.4 | 8 | 60.59 | even | 2 | |||
960.3.l.g.641.5 | 8 | 24.5 | odd | 2 | |||
960.3.l.g.641.6 | 8 | 8.5 | even | 2 | |||
960.3.l.h.641.3 | 8 | 8.3 | odd | 2 | |||
960.3.l.h.641.4 | 8 | 24.11 | even | 2 | |||
1200.3.c.m.449.1 | 16 | 15.8 | even | 4 | |||
1200.3.c.m.449.2 | 16 | 5.2 | odd | 4 | |||
1200.3.c.m.449.15 | 16 | 5.3 | odd | 4 | |||
1200.3.c.m.449.16 | 16 | 15.2 | even | 4 | |||
1200.3.l.x.401.5 | 8 | 15.14 | odd | 2 | |||
1200.3.l.x.401.6 | 8 | 5.4 | even | 2 |