Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(865,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.865");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.d (of order \(2\), degree \(1\), 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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 170x^{12} + 7609x^{8} + 59868x^{4} + 104976 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{40}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 865.7 | ||
Root | \(0.890014 + 0.890014i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.865 |
Dual form | 1728.4.d.i.865.9 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.31976i | − 0.118043i | −0.998257 | − | 0.0590215i | \(-0.981202\pi\) | ||||
0.998257 | − | 0.0590215i | \(-0.0187980\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.47210 | −0.133481 | −0.0667404 | − | 0.997770i | \(-0.521260\pi\) | ||||
−0.0667404 | + | 0.997770i | \(0.521260\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 35.9931i | − 0.986575i | −0.869866 | − | 0.493288i | \(-0.835795\pi\) | ||||
0.869866 | − | 0.493288i | \(-0.164205\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 65.5540i | − 1.39857i | −0.714843 | − | 0.699285i | \(-0.753502\pi\) | ||||
0.714843 | − | 0.699285i | \(-0.246498\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 87.1175 | 1.24289 | 0.621444 | − | 0.783459i | \(-0.286546\pi\) | ||||
0.621444 | + | 0.783459i | \(0.286546\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 9.13947i | − 0.110355i | −0.998477 | − | 0.0551773i | \(-0.982428\pi\) | ||||
0.998477 | − | 0.0551773i | \(-0.0175724\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 49.3929 | 0.447789 | 0.223894 | − | 0.974613i | \(-0.428123\pi\) | ||||
0.223894 | + | 0.974613i | \(0.428123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 123.258 | 0.986066 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 122.355i | 0.783471i | 0.920078 | + | 0.391736i | \(0.128125\pi\) | ||||
−0.920078 | + | 0.391736i | \(0.871875\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 138.042 | 0.799775 | 0.399887 | − | 0.916564i | \(-0.369049\pi\) | ||||
0.399887 | + | 0.916564i | \(0.369049\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.26258i | 0.0157565i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 90.2859i | 0.401160i | 0.979677 | + | 0.200580i | \(0.0642826\pi\) | ||||
−0.979677 | + | 0.200580i | \(0.935717\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −93.1282 | −0.354736 | −0.177368 | − | 0.984145i | \(-0.556758\pi\) | ||||
−0.177368 | + | 0.984145i | \(0.556758\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 191.655i | 0.679701i | 0.940480 | + | 0.339850i | \(0.110376\pi\) | ||||
−0.940480 | + | 0.339850i | \(0.889624\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −275.910 | −0.856289 | −0.428145 | − | 0.903710i | \(-0.640833\pi\) | ||||
−0.428145 | + | 0.903710i | \(0.640833\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −336.889 | −0.982183 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 648.331i | − 1.68029i | −0.542366 | − | 0.840143i | \(-0.682471\pi\) | ||||
0.542366 | − | 0.840143i | \(-0.317529\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −47.5023 | −0.116458 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 173.633i | 0.383137i | 0.981479 | + | 0.191569i | \(0.0613575\pi\) | ||||
−0.981479 | + | 0.191569i | \(0.938643\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 297.865i | 0.625208i | 0.949884 | + | 0.312604i | \(0.101201\pi\) | ||||
−0.949884 | + | 0.312604i | \(0.898799\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −86.5156 | −0.165091 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 658.458i | − 1.20065i | −0.799757 | − | 0.600324i | \(-0.795038\pi\) | ||||
0.799757 | − | 0.600324i | \(-0.204962\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −558.113 | −0.932899 | −0.466450 | − | 0.884548i | \(-0.654467\pi\) | ||||
−0.466450 | + | 0.884548i | \(0.654467\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 275.325 | 0.441429 | 0.220715 | − | 0.975338i | \(-0.429161\pi\) | ||||
0.220715 | + | 0.975338i | \(0.429161\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 88.9784i | 0.131689i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −625.878 | −0.891351 | −0.445676 | − | 0.895195i | \(-0.647036\pi\) | ||||
−0.445676 | + | 0.895195i | \(0.647036\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 119.135i | − 0.157551i | −0.996892 | − | 0.0787755i | \(-0.974899\pi\) | ||||
0.996892 | − | 0.0787755i | \(-0.0251010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 114.974i | − 0.146714i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 551.721 | 0.657104 | 0.328552 | − | 0.944486i | \(-0.393439\pi\) | ||||
0.328552 | + | 0.944486i | \(0.393439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 162.056i | 0.186682i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.0619 | −0.0130266 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 74.6796 | 0.0781708 | 0.0390854 | − | 0.999236i | \(-0.487556\pi\) | ||||
0.0390854 | + | 0.999236i | \(0.487556\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 855.709i | − 0.843032i | −0.906821 | − | 0.421516i | \(-0.861498\pi\) | ||||
0.906821 | − | 0.421516i | \(-0.138502\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −183.007 | −0.175070 | −0.0875349 | − | 0.996161i | \(-0.527899\pi\) | ||||
−0.0875349 | + | 0.996161i | \(0.527899\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1395.85i | − 1.26114i | −0.776133 | − | 0.630569i | \(-0.782821\pi\) | ||||
0.776133 | − | 0.630569i | \(-0.217179\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 590.120i | − 0.518562i | −0.965802 | − | 0.259281i | \(-0.916514\pi\) | ||||
0.965802 | − | 0.259281i | \(-0.0834856\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 606.251 | 0.504702 | 0.252351 | − | 0.967636i | \(-0.418796\pi\) | ||||
0.252351 | + | 0.967636i | \(0.418796\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 65.1868i | − 0.0528583i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −215.363 | −0.165902 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 35.4971 | 0.0266695 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 327.641i | − 0.234441i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1258.67 | 0.879440 | 0.439720 | − | 0.898135i | \(-0.355078\pi\) | ||||
0.439720 | + | 0.898135i | \(0.355078\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1933.54i | − 1.28958i | −0.764361 | − | 0.644788i | \(-0.776946\pi\) | ||||
0.764361 | − | 0.644788i | \(-0.223054\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 22.5937i | 0.0147302i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2156.67 | 1.34494 | 0.672469 | − | 0.740125i | \(-0.265234\pi\) | ||||
0.672469 | + | 0.740125i | \(0.265234\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2153.75i | 1.31424i | 0.753787 | + | 0.657119i | \(0.228225\pi\) | ||||
−0.753787 | + | 0.657119i | \(0.771775\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2359.49 | −1.37979 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 161.479 | 0.0924832 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 2268.88i | − 1.24748i | −0.781633 | − | 0.623738i | \(-0.785613\pi\) | ||||
0.781633 | − | 0.623738i | \(-0.214387\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1519.19 | 0.818743 | 0.409372 | − | 0.912368i | \(-0.365748\pi\) | ||||
0.409372 | + | 0.912368i | \(0.365748\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 182.182i | − 0.0944078i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 66.6451i | 0.0338781i | 0.999857 | + | 0.0169390i | \(0.00539212\pi\) | ||||
−0.999857 | + | 0.0169390i | \(0.994608\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −122.104 | −0.0597712 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 220.564i | − 0.105987i | −0.998595 | − | 0.0529937i | \(-0.983124\pi\) | ||||
0.998595 | − | 0.0529937i | \(-0.0168763\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3322.97 | −1.53976 | −0.769878 | − | 0.638191i | \(-0.779683\pi\) | ||||
−0.769878 | + | 0.638191i | \(0.779683\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2100.33 | −0.955998 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 3687.70i | − 1.62064i | −0.585988 | − | 0.810320i | \(-0.699293\pi\) | ||||
0.585988 | − | 0.810320i | \(-0.300707\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −304.706 | −0.131621 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1344.27i | 0.561315i | 0.959808 | + | 0.280658i | \(0.0905525\pi\) | ||||
−0.959808 | + | 0.280658i | \(0.909447\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 168.428i | − 0.0691665i | −0.999402 | − | 0.0345832i | \(-0.988990\pi\) | ||||
0.999402 | − | 0.0345832i | \(-0.0110104\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 119.156 | 0.0473541 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3135.63i | − 1.22620i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2866.99 | −1.08611 | −0.543057 | − | 0.839696i | \(-0.682733\pi\) | ||||
−0.543057 | + | 0.839696i | \(0.682733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3021.80 | 1.12701 | 0.563507 | − | 0.826111i | \(-0.309452\pi\) | ||||
0.563507 | + | 0.826111i | \(0.309452\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 782.353i | − 0.282946i | −0.989942 | − | 0.141473i | \(-0.954816\pi\) | ||||
0.989942 | − | 0.141473i | \(-0.0451838\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1925.31 | −0.685836 | −0.342918 | − | 0.939365i | \(-0.611415\pi\) | ||||
−0.342918 | + | 0.939365i | \(0.611415\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 302.472i | − 0.104578i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 122.907i | 0.0418741i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −328.958 | −0.108873 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1361.40i | 0.444183i | 0.975026 | + | 0.222092i | \(0.0712884\pi\) | ||||
−0.975026 | + | 0.222092i | \(0.928712\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 252.939 | 0.0802339 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −341.252 | −0.106755 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 5710.90i | − 1.73827i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5314.09 | −1.59577 | −0.797887 | − | 0.602806i | \(-0.794049\pi\) | ||||
−0.797887 | + | 0.602806i | \(0.794049\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 3437.08i | − 1.00496i | −0.864587 | − | 0.502482i | \(-0.832420\pi\) | ||||
0.864587 | − | 0.502482i | \(-0.167580\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 880.344i | 0.254038i | 0.991900 | + | 0.127019i | \(0.0405409\pi\) | ||||
−0.991900 | + | 0.127019i | \(0.959459\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2858.44 | 0.803701 | 0.401850 | − | 0.915705i | \(-0.368367\pi\) | ||||
0.401850 | + | 0.915705i | \(0.368367\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 364.135i | 0.101079i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5350.87 | −1.44820 | −0.724098 | − | 0.689697i | \(-0.757744\pi\) | ||||
−0.724098 | + | 0.689697i | \(0.757744\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2790.27 | −0.745798 | −0.372899 | − | 0.927872i | \(-0.621636\pi\) | ||||
−0.372899 | + | 0.927872i | \(0.621636\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 444.612i | 0.115940i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −599.129 | −0.154339 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 3752.93i | − 0.943757i | −0.881664 | − | 0.471878i | \(-0.843576\pi\) | ||||
0.881664 | − | 0.471878i | \(-0.156424\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1777.80i | − 0.441777i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6299.43 | 1.52898 | 0.764490 | − | 0.644636i | \(-0.222991\pi\) | ||||
0.764490 | + | 0.644636i | \(0.222991\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 223.196i | − 0.0535471i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7614.33 | −1.78525 | −0.892623 | − | 0.450805i | \(-0.851137\pi\) | ||||
−0.892623 | + | 0.450805i | \(0.851137\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −855.642 | −0.198346 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 6081.62i | − 1.37845i | −0.724547 | − | 0.689225i | \(-0.757951\pi\) | ||||
0.724547 | − | 0.689225i | \(-0.242049\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7989.97 | 1.79098 | 0.895491 | − | 0.445080i | \(-0.146825\pi\) | ||||
0.895491 | + | 0.445080i | \(0.146825\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 4436.45i | − 0.972828i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6087.60i | 1.32046i | 0.751061 | + | 0.660232i | \(0.229542\pi\) | ||||
−0.751061 | + | 0.660232i | \(0.770458\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6106.28 | 1.29633 | 0.648167 | − | 0.761498i | \(-0.275536\pi\) | ||||
0.648167 | + | 0.761498i | \(0.275536\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 5424.68i | − 1.13945i | −0.821836 | − | 0.569724i | \(-0.807050\pi\) | ||||
0.821836 | − | 0.569724i | \(-0.192950\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 230.222 | 0.0473504 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2676.45 | 0.544770 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1513.45i | − 0.301763i | −0.988552 | − | 0.150882i | \(-0.951789\pi\) | ||||
0.988552 | − | 0.150882i | \(-0.0482113\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 229.154 | 0.0452267 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 3237.90i | − 0.626264i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 473.790i | − 0.0907269i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 393.110 | 0.0738014 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6543.54i | 1.21648i | 0.793753 | + | 0.608241i | \(0.208124\pi\) | ||||
−0.793753 | + | 0.608241i | \(0.791876\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1284.46 | 0.234196 | 0.117098 | − | 0.993120i | \(-0.462641\pi\) | ||||
0.117098 | + | 0.993120i | \(0.462641\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4013.86 | 0.724847 | 0.362423 | − | 0.932014i | \(-0.381949\pi\) | ||||
0.362423 | + | 0.932014i | \(0.381949\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2203.61i | − 0.390433i | −0.980760 | − | 0.195216i | \(-0.937459\pi\) | ||||
0.980760 | − | 0.195216i | \(-0.0625409\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4403.92 | 0.772953 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 796.208i | − 0.137159i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 8080.07i | − 1.37908i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 682.076 | 0.114298 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2467.37i | 0.409725i | 0.978791 | + | 0.204862i | \(0.0656747\pi\) | ||||
−0.978791 | + | 0.204862i | \(0.934325\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −869.007 | −0.141728 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7160.82 | −1.15749 | −0.578746 | − | 0.815508i | \(-0.696458\pi\) | ||||
−0.578746 | + | 0.815508i | \(0.696458\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 4968.55i | − 0.789038i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1680.75 | 0.264583 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1843.40i | − 0.285184i | −0.989782 | − | 0.142592i | \(-0.954456\pi\) | ||||
0.989782 | − | 0.142592i | \(-0.0455436\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5209.52i | 0.799023i | 0.916728 | + | 0.399512i | \(0.130820\pi\) | ||||
−0.916728 | + | 0.399512i | \(0.869180\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8650.90 | −1.30437 | −0.652183 | − | 0.758062i | \(-0.726146\pi\) | ||||
−0.652183 | + | 0.758062i | \(0.726146\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 736.576i | 0.110122i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12565.4 | −1.84728 | −0.923641 | − | 0.383260i | \(-0.874801\pi\) | ||||
−0.923641 | + | 0.383260i | \(0.874801\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6775.47 | 0.987822 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 363.363i | − 0.0521076i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10796.9 | −1.53567 | −0.767837 | − | 0.640646i | \(-0.778667\pi\) | ||||
−0.767837 | + | 0.640646i | \(0.778667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1602.74i | 0.224286i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 8397.99i | − 1.16577i | −0.812555 | − | 0.582884i | \(-0.801924\pi\) | ||||
0.812555 | − | 0.582884i | \(-0.198076\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8020.83 | 1.09574 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 242.519i | − 0.0328690i | −0.999865 | − | 0.0164345i | \(-0.994768\pi\) | ||||
0.999865 | − | 0.0164345i | \(-0.00523150\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3601.64 | −0.480510 | −0.240255 | − | 0.970710i | \(-0.577231\pi\) | ||||
−0.240255 | + | 0.970710i | \(0.577231\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 117.430 | 0.0155449 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 13291.8i | − 1.73245i | −0.499656 | − | 0.866224i | \(-0.666540\pi\) | ||||
0.499656 | − | 0.866224i | \(-0.333460\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4302.99 | 0.556551 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 826.008i | 0.105218i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3255.27i | − 0.411530i | −0.978601 | − | 0.205765i | \(-0.934032\pi\) | ||||
0.978601 | − | 0.205765i | \(-0.0659682\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8209.13 | −1.02231 | −0.511153 | − | 0.859490i | \(-0.670781\pi\) | ||||
−0.511153 | + | 0.859490i | \(0.670781\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 9049.19i | − 1.11854i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3249.67 | 0.395774 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4554.98 | 0.550683 | 0.275342 | − | 0.961346i | \(-0.411209\pi\) | ||||
0.275342 | + | 0.961346i | \(0.411209\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 429.238i | − 0.0511414i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −157.229 | −0.0185978 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7550.04i | 0.880295i | 0.897925 | + | 0.440148i | \(0.145074\pi\) | ||||
−0.897925 | + | 0.440148i | \(0.854926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11044.7i | 1.27859i | 0.768961 | + | 0.639296i | \(0.220774\pi\) | ||||
−0.768961 | + | 0.639296i | \(0.779226\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10737.9 | 1.22557 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 736.351i | − 0.0834532i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9156.47 | −1.02332 | −0.511661 | − | 0.859187i | \(-0.670970\pi\) | ||||
−0.511661 | + | 0.859187i | \(0.670970\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2250.45 | −0.249768 | −0.124884 | − | 0.992171i | \(-0.539856\pi\) | ||||
−0.124884 | + | 0.992171i | \(0.539856\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 451.425i | − 0.0494156i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11848.2 | −1.28812 | −0.644061 | − | 0.764974i | \(-0.722752\pi\) | ||||
−0.644061 | + | 0.764974i | \(0.722752\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1274.32i | 0.136670i | 0.997662 | + | 0.0683348i | \(0.0217686\pi\) | ||||
−0.997662 | + | 0.0683348i | \(0.978231\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 728.139i | − 0.0775665i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8201.95 | −0.862080 | −0.431040 | − | 0.902333i | \(-0.641853\pi\) | ||||
−0.431040 | + | 0.902333i | \(0.641853\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3351.97i | 0.349974i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 213.875 | 0.0220365 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16627.3 | −1.70195 | −0.850976 | − | 0.525205i | \(-0.823989\pi\) | ||||
−0.850976 | + | 0.525205i | \(0.823989\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8128.27i | 0.821196i | 0.911816 | + | 0.410598i | \(0.134680\pi\) | ||||
−0.911816 | + | 0.410598i | \(0.865320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1415.26 | −0.142057 | −0.0710286 | − | 0.997474i | \(-0.522628\pi\) | ||||
−0.0710286 | + | 0.997474i | \(0.522628\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 17479.2i | − 1.73200i | −0.500048 | − | 0.865998i | \(-0.666684\pi\) | ||||
0.500048 | − | 0.865998i | \(-0.333316\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1627.77i | 0.160263i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6898.26 | 0.670576 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1126.52i | − 0.108817i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6370.47 | 0.607670 | 0.303835 | − | 0.952725i | \(-0.401733\pi\) | ||||
0.303835 | + | 0.952725i | \(0.401733\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5918.60 | 0.561050 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 98.5592i | − 0.00922751i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13658.3 | 1.27088 | 0.635440 | − | 0.772150i | \(-0.280819\pi\) | ||||
0.635440 | + | 0.772150i | \(0.280819\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 3242.02i | − 0.297984i | −0.988838 | − | 0.148992i | \(-0.952397\pi\) | ||||
0.988838 | − | 0.148992i | \(-0.0476029\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10659.2i | 0.973767i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1379.71 | 0.124524 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 388.342i | − 0.0348388i | −0.999848 | − | 0.0174194i | \(-0.994455\pi\) | ||||
0.999848 | − | 0.0174194i | \(-0.00554506\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12450.6 | 1.10367 | 0.551834 | − | 0.833954i | \(-0.313928\pi\) | ||||
0.551834 | + | 0.833954i | \(0.313928\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1129.33 | −0.0995140 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12529.1i | 1.09104i | 0.838097 | + | 0.545521i | \(0.183668\pi\) | ||||
−0.838097 | + | 0.545521i | \(0.816332\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −680.630 | −0.0589223 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 241.525i | 0.0206658i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9930.85i | 0.844794i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5185.14 | 0.436017 | 0.218009 | − | 0.975947i | \(-0.430044\pi\) | ||||
0.218009 | + | 0.975947i | \(0.430044\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10344.4i | 0.864877i | 0.901663 | + | 0.432438i | \(0.142347\pi\) | ||||
−0.901663 | + | 0.432438i | \(0.857653\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12025.8 | 0.994030 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9727.34 | −0.799485 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6104.93i | 0.496123i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1842.19 | −0.148869 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12125.7i | 0.968997i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 21105.5i | − 1.67726i | −0.544705 | − | 0.838628i | \(-0.683358\pi\) | ||||
0.544705 | − | 0.838628i | \(-0.316642\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −778.817 | −0.0612126 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 12491.4i | − 0.976409i | −0.872729 | − | 0.488204i | \(-0.837652\pi\) | ||||
0.872729 | − | 0.488204i | \(-0.162348\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1118.26 | 0.0864597 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1547.23 | 0.118978 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8317.90i | 0.632748i | 0.948635 | + | 0.316374i | \(0.102465\pi\) | ||||
−0.948635 | + | 0.316374i | \(0.897535\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12563.8 | 0.950609 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8298.80i | 0.621231i | 0.950536 | + | 0.310615i | \(0.100535\pi\) | ||||
−0.950536 | + | 0.310615i | \(0.899465\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 800.106i | − 0.0595765i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6133.13 | −0.451870 | −0.225935 | − | 0.974142i | \(-0.572544\pi\) | ||||
−0.225935 | + | 0.974142i | \(0.572544\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26180.9i | 1.91880i | 0.282043 | + | 0.959402i | \(0.408988\pi\) | ||||
−0.282043 | + | 0.959402i | \(0.591012\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6088.09 | 0.441549 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22659.7 | 1.63489 | 0.817447 | − | 0.576004i | \(-0.195389\pi\) | ||||
0.817447 | + | 0.576004i | \(0.195389\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 294.513i | 0.0210300i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23335.4 | −1.65773 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 4163.23i | − 0.292734i | −0.989230 | − | 0.146367i | \(-0.953242\pi\) | ||||
0.989230 | − | 0.146367i | \(-0.0467580\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1261.63i | − 0.0882589i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11485.2 | −0.795350 | −0.397675 | − | 0.917526i | \(-0.630183\pi\) | ||||
−0.397675 | + | 0.917526i | \(0.630183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 284.227i | 0.0195835i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10138.6 | −0.691571 | −0.345785 | − | 0.938314i | \(-0.612387\pi\) | ||||
−0.345785 | + | 0.938314i | \(0.612387\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5983.08 | −0.406082 | −0.203041 | − | 0.979170i | \(-0.565082\pi\) | ||||
−0.203041 | + | 0.979170i | \(0.565082\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 46.8477i | − 0.00314815i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2579.69 | −0.172498 | −0.0862492 | − | 0.996274i | \(-0.527488\pi\) | ||||
−0.0862492 | + | 0.996274i | \(0.527488\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18087.0i | 1.19758i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 28274.9i | − 1.86299i | −0.363759 | − | 0.931493i | \(-0.618507\pi\) | ||||
0.363759 | − | 0.931493i | \(-0.381493\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8007.60 | 0.522486 | 0.261243 | − | 0.965273i | \(-0.415868\pi\) | ||||
0.261243 | + | 0.965273i | \(0.415868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 27366.1i | − 1.77696i | −0.458915 | − | 0.888480i | \(-0.651762\pi\) | ||||
0.458915 | − | 0.888480i | \(-0.348238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1363.91 | −0.0877107 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14974.9 | 0.958392 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7865.48i | 0.498596i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27939.7 | 1.76270 | 0.881349 | − | 0.472466i | \(-0.156636\pi\) | ||||
0.881349 | + | 0.472466i | \(0.156636\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1661.14i | − 0.103812i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22084.4i | 1.37365i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28620.9 | −1.76358 | −0.881792 | − | 0.471639i | \(-0.843663\pi\) | ||||
−0.881792 | + | 0.471639i | \(0.843663\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 4650.43i | − 0.285218i | −0.989779 | − | 0.142609i | \(-0.954451\pi\) | ||||
0.989779 | − | 0.142609i | \(-0.0455491\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22838.1 | 1.38772 | 0.693862 | − | 0.720108i | \(-0.255908\pi\) | ||||
0.693862 | + | 0.720108i | \(0.255908\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6249.59 | 0.377994 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 8551.87i | − 0.512497i | −0.966611 | − | 0.256248i | \(-0.917513\pi\) | ||||
0.966611 | − | 0.256248i | \(-0.0824865\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2551.81 | −0.152225 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10145.1i | 0.599689i | 0.953988 | + | 0.299845i | \(0.0969348\pi\) | ||||
−0.953988 | + | 0.299845i | \(0.903065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 17372.6i | − 1.02226i | −0.859503 | − | 0.511131i | \(-0.829227\pi\) | ||||
0.859503 | − | 0.511131i | \(-0.170773\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 29.8182 | 0.00173880 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6043.45i | 0.350829i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10721.1 | 0.616815 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19271.9 | −1.10383 | −0.551914 | − | 0.833901i | \(-0.686102\pi\) | ||||
−0.551914 | + | 0.833901i | \(0.686102\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30042.8i | 1.70552i | 0.522300 | + | 0.852762i | \(0.325074\pi\) | ||||
−0.522300 | + | 0.852762i | \(0.674926\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −184.615 | −0.0104343 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17811.9i | 0.997880i | 0.866636 | + | 0.498940i | \(0.166277\pi\) | ||||
−0.866636 | + | 0.498940i | \(0.833723\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 2846.28i | − 0.158760i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −42500.7 | −2.35000 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 2461.63i | − 0.135521i | −0.997702 | − | 0.0677604i | \(-0.978415\pi\) | ||||
0.997702 | − | 0.0677604i | \(-0.0215854\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2842.44 | 0.155137 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8113.10 | −0.440897 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13292.5i | 0.716190i | 0.933685 | + | 0.358095i | \(0.116574\pi\) | ||||
−0.933685 | + | 0.358095i | \(0.883426\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 825.165 | 0.0442699 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2115.40i | 0.112529i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27124.4i | 1.43678i | 0.695640 | + | 0.718390i | \(0.255121\pi\) | ||||
−0.695640 | + | 0.718390i | \(0.744879\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6818.28 | 0.358130 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3113.96i | 0.162875i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30827.3 | 1.59898 | 0.799489 | − | 0.600680i | \(-0.205103\pi\) | ||||
0.799489 | + | 0.600680i | \(0.205103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 452.411 | 0.0233684 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15081.2i | 0.772554i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29322.3 | −1.49588 | −0.747939 | − | 0.663767i | \(-0.768957\pi\) | ||||
−0.747939 | + | 0.663767i | \(0.768957\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16696.5i | 0.844791i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5700.95i | 0.287271i | 0.989631 | + | 0.143635i | \(0.0458792\pi\) | ||||
−0.989631 | + | 0.143635i | \(0.954121\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23699.9 | −1.18453 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26824.2i | 1.33524i | 0.744502 | + | 0.667621i | \(0.232687\pi\) | ||||
−0.744502 | + | 0.667621i | \(0.767313\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25329.2 | 1.25066 | 0.625328 | − | 0.780362i | \(-0.284965\pi\) | ||||
0.625328 | + | 0.780362i | \(0.284965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2994.38 | −0.147256 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3450.68i | 0.168338i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9862.86 | 0.479229 | 0.239614 | − | 0.970868i | \(-0.422979\pi\) | ||||
0.239614 | + | 0.970868i | \(0.422979\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 2004.97i | − 0.0966469i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12425.8i | 0.596595i | 0.954473 | + | 0.298298i | \(0.0964188\pi\) | ||||
−0.954473 | + | 0.298298i | \(0.903581\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38708.2 | 1.84385 | 0.921926 | − | 0.387365i | \(-0.126615\pi\) | ||||
0.921926 | + | 0.387365i | \(0.126615\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1458.83i | 0.0692180i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11382.3 | 0.535844 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17734.4 | −0.831626 | −0.415813 | − | 0.909450i | \(-0.636503\pi\) | ||||
−0.415813 | + | 0.909450i | \(0.636503\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32273.9i | 1.50170i | 0.660475 | + | 0.750848i | \(0.270355\pi\) | ||||
−0.660475 | + | 0.750848i | \(0.729645\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17014.8 | 0.788631 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 851.143i | 0.0391468i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20088.2i | 0.920375i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 87.9556 | 0.00399907 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 24819.5i | − 1.12417i | −0.827080 | − | 0.562084i | \(-0.810000\pi\) | ||||
0.827080 | − | 0.562084i | \(-0.190000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1498.71 | −0.0673679 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19526.2 | 0.874397 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15582.6i | 0.692553i | 0.938132 | + | 0.346277i | \(0.112554\pi\) | ||||
−0.938132 | + | 0.346277i | \(0.887446\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24036.6 | −1.06427 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 9909.80i | − 0.435503i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 161.148i | 0.00705556i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13815.9 | 0.600422 | 0.300211 | − | 0.953873i | \(-0.402943\pi\) | ||||
0.300211 | + | 0.953873i | \(0.402943\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 26934.2i | − 1.16620i | −0.812400 | − | 0.583100i | \(-0.801839\pi\) | ||||
0.812400 | − | 0.583100i | \(-0.198161\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −291.092 | −0.0125111 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1751.63 | 0.0750081 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8300.96i | 0.352869i | 0.984312 | + | 0.176434i | \(0.0564564\pi\) | ||||
−0.984312 | + | 0.176434i | \(0.943544\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27975.6 | 1.18489 | 0.592447 | − | 0.805609i | \(-0.298162\pi\) | ||||
0.592447 | + | 0.805609i | \(0.298162\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 11664.8i | − 0.490476i | −0.969463 | − | 0.245238i | \(-0.921134\pi\) | ||||
0.969463 | − | 0.245238i | \(-0.0788662\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 22133.6i | − 0.927298i | −0.886019 | − | 0.463649i | \(-0.846540\pi\) | ||||
0.886019 | − | 0.463649i | \(-0.153460\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29348.9 | −1.22074 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4385.53i | 0.181757i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44278.9 | 1.82202 | 0.911012 | − | 0.412380i | \(-0.135302\pi\) | ||||
0.911012 | + | 0.412380i | \(0.135302\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9418.38 | 0.386173 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2771.93i | 0.112849i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −87.7524 | −0.00355987 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4459.48i | 0.179635i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32745.5i | 1.31440i | 0.753715 | + | 0.657202i | \(0.228260\pi\) | ||||
−0.753715 | + | 0.657202i | \(0.771740\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11799.2 | 0.470305 | 0.235153 | − | 0.971958i | \(-0.424441\pi\) | ||||
0.235153 | + | 0.971958i | \(0.424441\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 6975.49i | − 0.277067i | −0.990358 | − | 0.138534i | \(-0.955761\pi\) | ||||
0.990358 | − | 0.138534i | \(-0.0442389\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8615.25 | −0.339822 | −0.169911 | − | 0.985459i | \(-0.554348\pi\) | ||||
−0.169911 | + | 0.985459i | \(0.554348\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4866.88 | −0.191305 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22527.3i | 0.879385i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43164.6 | −1.67919 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 809.961i | 0.0312934i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 32197.0i | − 1.23970i | −0.784720 | − | 0.619850i | \(-0.787193\pi\) | ||||
0.784720 | − | 0.619850i | \(-0.212807\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30615.2 | −1.17077 | −0.585387 | − | 0.810754i | \(-0.699057\pi\) | ||||
−0.585387 | + | 0.810754i | \(0.699057\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37640.3i | 1.43454i | 0.696796 | + | 0.717269i | \(0.254608\pi\) | ||||
−0.696796 | + | 0.717269i | \(0.745392\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21465.3 | 0.812553 | 0.406276 | − | 0.913750i | \(-0.366827\pi\) | ||||
0.406276 | + | 0.913750i | \(0.366827\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3111.55 | −0.117388 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2521.67i | 0.0944955i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1774.11 | 0.0662593 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16890.0i | 0.626600i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 56481.0i | − 2.08841i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −222.284 | −0.00816462 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 8317.31i | − 0.304489i | −0.988343 | − | 0.152245i | \(-0.951350\pi\) | ||||
0.988343 | − | 0.152245i | \(-0.0486502\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28334.9 | 1.03049 | 0.515246 | − | 0.857043i | \(-0.327701\pi\) | ||||
0.515246 | + | 0.857043i | \(0.327701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4288.03 | −0.155436 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4779.91i | 0.172134i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18433.3 | 0.661652 | 0.330826 | − | 0.943692i | \(-0.392673\pi\) | ||||
0.330826 | + | 0.943692i | \(0.392673\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36586.6i | 1.30473i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11128.5i | 0.395570i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20036.0 | −0.707600 | −0.353800 | − | 0.935321i | \(-0.615111\pi\) | ||||
−0.353800 | + | 0.935321i | \(0.615111\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3078.99i | 0.108388i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4138.28 | −0.144745 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24844.2 | 0.866196 | 0.433098 | − | 0.901347i | \(-0.357420\pi\) | ||||
0.433098 | + | 0.901347i | \(0.357420\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12898.8i | 0.446853i | 0.974721 | + | 0.223426i | \(0.0717243\pi\) | ||||
−0.974721 | + | 0.223426i | \(0.928276\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4599.88 | −0.158847 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45388.5i | 1.55747i | 0.627350 | + | 0.778737i | \(0.284139\pi\) | ||||
−0.627350 | + | 0.778737i | \(0.715861\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 18048.7i | − 0.617370i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13191.2 | 0.448378 | 0.224189 | − | 0.974546i | \(-0.428027\pi\) | ||||
0.224189 | + | 0.974546i | \(0.428027\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3783.74i | 0.128208i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5331.49 | −0.179523 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10735.5 | −0.360360 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 3988.05i | − 0.133036i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3495.31 | 0.116237 | 0.0581186 | − | 0.998310i | \(-0.481490\pi\) | ||||
0.0581186 | + | 0.998310i | \(0.481490\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 21176.9i | − 0.699896i | −0.936769 | − | 0.349948i | \(-0.886199\pi\) | ||||
0.936769 | − | 0.349948i | \(-0.113801\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 5324.29i | − 0.175425i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −58221.0 | −1.90650 | −0.953252 | − | 0.302178i | \(-0.902286\pi\) | ||||
−0.953252 | + | 0.302178i | \(0.902286\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 19858.1i | − 0.648283i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32317.8 | −1.04860 | −0.524302 | − | 0.851533i | \(-0.675674\pi\) | ||||
−0.524302 | + | 0.851533i | \(0.675674\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1032.52 | −0.0333998 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9466.41i | 0.304362i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43887.8 | 1.40680 | 0.703401 | − | 0.710793i | \(-0.251664\pi\) | ||||
0.703401 | + | 0.710793i | \(0.251664\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2540.94i | 0.0809581i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19646.1i | 0.624071i | 0.950070 | + | 0.312036i | \(0.101011\pi\) | ||||
−0.950070 | + | 0.312036i | \(0.898989\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1728.4.d.i.865.7 | ✓ | 16 | |
3.2 | odd | 2 | 1728.4.d.k.865.9 | yes | 16 | ||
4.3 | odd | 2 | inner | 1728.4.d.i.865.8 | yes | 16 | |
8.3 | odd | 2 | inner | 1728.4.d.i.865.10 | yes | 16 | |
8.5 | even | 2 | inner | 1728.4.d.i.865.9 | yes | 16 | |
12.11 | even | 2 | 1728.4.d.k.865.10 | yes | 16 | ||
24.5 | odd | 2 | 1728.4.d.k.865.7 | yes | 16 | ||
24.11 | even | 2 | 1728.4.d.k.865.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.4.d.i.865.7 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1728.4.d.i.865.8 | yes | 16 | 4.3 | odd | 2 | inner | |
1728.4.d.i.865.9 | yes | 16 | 8.5 | even | 2 | inner | |
1728.4.d.i.865.10 | yes | 16 | 8.3 | odd | 2 | inner | |
1728.4.d.k.865.7 | yes | 16 | 24.5 | odd | 2 | ||
1728.4.d.k.865.8 | yes | 16 | 24.11 | even | 2 | ||
1728.4.d.k.865.9 | yes | 16 | 3.2 | odd | 2 | ||
1728.4.d.k.865.10 | yes | 16 | 12.11 | even | 2 |