Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(161,1728)]
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, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.h (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.2 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.161 |
Dual form | 1728.3.h.g.161.1 |
$q$-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 | ||||||||
\(5\) | −4.89898 | −0.979796 | −0.489898 | − | 0.871780i | \(-0.662966\pi\) | ||||
−0.489898 | + | 0.871780i | \(0.662966\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.73205 | −0.247436 | −0.123718 | − | 0.992317i | \(-0.539482\pi\) | ||||
−0.123718 | + | 0.992317i | \(0.539482\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.48528 | 0.771389 | 0.385695 | − | 0.922627i | \(-0.373962\pi\) | ||||
0.385695 | + | 0.922627i | \(0.373962\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.19615i | 0.399704i | 0.979826 | + | 0.199852i | \(0.0640461\pi\) | ||||
−0.979826 | + | 0.199852i | \(0.935954\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 25.4558i | − 1.49740i | −0.662908 | − | 0.748701i | \(-0.730678\pi\) | ||||
0.662908 | − | 0.748701i | \(-0.269322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 5.00000i | − 0.263158i | −0.991306 | − | 0.131579i | \(-0.957995\pi\) | ||||
0.991306 | − | 0.131579i | \(-0.0420047\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24.4949i | 1.06500i | 0.846431 | + | 0.532498i | \(0.178747\pi\) | ||||
−0.846431 | + | 0.532498i | \(0.821253\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.0400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 39.1918 | 1.35144 | 0.675721 | − | 0.737157i | \(-0.263832\pi\) | ||||
0.675721 | + | 0.737157i | \(0.263832\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −13.8564 | −0.446981 | −0.223490 | − | 0.974706i | \(-0.571745\pi\) | ||||
−0.223490 | + | 0.974706i | \(0.571745\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.48528 | 0.242437 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 32.9090i | 0.889431i | 0.895672 | + | 0.444716i | \(0.146695\pi\) | ||||
−0.895672 | + | 0.444716i | \(0.853305\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16.9706i | 0.413916i | 0.978350 | + | 0.206958i | \(0.0663564\pi\) | ||||
−0.978350 | + | 0.206958i | \(0.933644\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 34.0000i | − 0.790698i | −0.918531 | − | 0.395349i | \(-0.870624\pi\) | ||||
0.918531 | − | 0.395349i | \(-0.129376\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 4.89898i | − 0.104234i | −0.998641 | − | 0.0521168i | \(-0.983403\pi\) | ||||
0.998641 | − | 0.0521168i | \(-0.0165968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −46.0000 | −0.938776 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.79796 | −0.184867 | −0.0924336 | − | 0.995719i | \(-0.529465\pi\) | ||||
−0.0924336 | + | 0.995719i | \(0.529465\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −41.5692 | −0.755804 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 76.3675 | 1.29436 | 0.647182 | − | 0.762335i | \(-0.275947\pi\) | ||||
0.647182 | + | 0.762335i | \(0.275947\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 22.5167i | 0.369126i | 0.982821 | + | 0.184563i | \(0.0590869\pi\) | ||||
−0.982821 | + | 0.184563i | \(0.940913\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 25.4558i | − 0.391628i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 19.0000i | − 0.283582i | −0.989897 | − | 0.141791i | \(-0.954714\pi\) | ||||
0.989897 | − | 0.141791i | \(-0.0452861\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 68.5857i | − 0.965996i | −0.875621 | − | 0.482998i | \(-0.839548\pi\) | ||||
0.875621 | − | 0.482998i | \(-0.160452\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −25.0000 | −0.342466 | −0.171233 | − | 0.985231i | \(-0.554775\pi\) | ||||
−0.171233 | + | 0.985231i | \(0.554775\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.6969 | −0.190869 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −140.296 | −1.77590 | −0.887950 | − | 0.459940i | \(-0.847871\pi\) | ||||
−0.887950 | + | 0.459940i | \(0.847871\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −101.823 | −1.22679 | −0.613394 | − | 0.789777i | \(-0.710196\pi\) | ||||
−0.613394 | + | 0.789777i | \(0.710196\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 124.708i | 1.46715i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 8.48528i | − 0.0953402i | −0.998863 | − | 0.0476701i | \(-0.984820\pi\) | ||||
0.998863 | − | 0.0476701i | \(-0.0151796\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 9.00000i | − 0.0989011i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 24.4949i | 0.257841i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −71.0000 | −0.731959 | −0.365979 | − | 0.930623i | \(-0.619266\pi\) | ||||
−0.365979 | + | 0.930623i | \(0.619266\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −127.373 | −1.26112 | −0.630562 | − | 0.776139i | \(-0.717175\pi\) | ||||
−0.630562 | + | 0.776139i | \(0.717175\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −53.6936 | −0.521297 | −0.260648 | − | 0.965434i | \(-0.583936\pi\) | ||||
−0.260648 | + | 0.965434i | \(0.583936\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −178.191 | −1.66534 | −0.832668 | − | 0.553773i | \(-0.813188\pi\) | ||||
−0.832668 | + | 0.553773i | \(0.813188\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 152.420i | 1.39835i | 0.714949 | + | 0.699176i | \(0.246450\pi\) | ||||
−0.714949 | + | 0.699176i | \(0.753550\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 212.132i | 1.87727i | 0.344906 | + | 0.938637i | \(0.387911\pi\) | ||||
−0.344906 | + | 0.938637i | \(0.612089\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 120.000i | − 1.04348i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 44.0908i | 0.370511i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −49.0000 | −0.404959 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 127.373 | 1.01899 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −110.851 | −0.872845 | −0.436422 | − | 0.899742i | \(-0.643755\pi\) | ||||
−0.436422 | + | 0.899742i | \(0.643755\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 33.9411 | 0.259093 | 0.129546 | − | 0.991573i | \(-0.458648\pi\) | ||||
0.129546 | + | 0.991573i | \(0.458648\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.66025i | 0.0651147i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 8.48528i | − 0.0619364i | −0.999520 | − | 0.0309682i | \(-0.990141\pi\) | ||||
0.999520 | − | 0.0309682i | \(-0.00985905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 77.0000i | − 0.553957i | −0.960876 | − | 0.276978i | \(-0.910667\pi\) | ||||
0.960876 | − | 0.276978i | \(-0.0893331\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 44.0908i | 0.308327i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −192.000 | −1.32414 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −146.969 | −0.986372 | −0.493186 | − | 0.869924i | \(-0.664168\pi\) | ||||
−0.493186 | + | 0.869924i | \(0.664168\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −261.540 | −1.73205 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 67.8823 | 0.437950 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 263.272i | 1.67689i | 0.544986 | + | 0.838445i | \(0.316535\pi\) | ||||
−0.544986 | + | 0.838445i | \(0.683465\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 42.4264i | − 0.263518i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 101.000i | − 0.619632i | −0.950797 | − | 0.309816i | \(-0.899733\pi\) | ||||
0.950797 | − | 0.309816i | \(-0.100267\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 112.677i | − 0.674710i | −0.941378 | − | 0.337355i | \(-0.890468\pi\) | ||||
0.941378 | − | 0.337355i | \(-0.109532\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 142.000 | 0.840237 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 127.373 | 0.736263 | 0.368131 | − | 0.929774i | \(-0.379998\pi\) | ||||
0.368131 | + | 0.929774i | \(0.379998\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.73205 | 0.00989743 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 118.794 | 0.663653 | 0.331827 | − | 0.943340i | \(-0.392335\pi\) | ||||
0.331827 | + | 0.943340i | \(0.392335\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 174.937i | 0.966503i | 0.875481 | + | 0.483252i | \(0.160544\pi\) | ||||
−0.875481 | + | 0.483252i | \(0.839456\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 161.220i | − 0.871461i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 216.000i | − 1.15508i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 318.434i | − 1.66719i | −0.552375 | − | 0.833596i | \(-0.686278\pi\) | ||||
0.552375 | − | 0.833596i | \(-0.313722\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −265.000 | −1.37306 | −0.686528 | − | 0.727103i | \(-0.740866\pi\) | ||||
−0.686528 | + | 0.727103i | \(0.740866\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −44.0908 | −0.223811 | −0.111906 | − | 0.993719i | \(-0.535695\pi\) | ||||
−0.111906 | + | 0.993719i | \(0.535695\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.9808 | −0.130557 | −0.0652783 | − | 0.997867i | \(-0.520794\pi\) | ||||
−0.0652783 | + | 0.997867i | \(0.520794\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −67.8823 | −0.334395 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 83.1384i | − 0.405553i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 42.4264i | − 0.202997i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 53.0000i | 0.251185i | 0.992082 | + | 0.125592i | \(0.0400832\pi\) | ||||
−0.992082 | + | 0.125592i | \(0.959917\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 166.565i | 0.774722i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.0000 | 0.110599 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 132.272 | 0.598518 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −401.836 | −1.80195 | −0.900977 | − | 0.433867i | \(-0.857149\pi\) | ||||
−0.900977 | + | 0.433867i | \(0.857149\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 186.676 | 0.822362 | 0.411181 | − | 0.911554i | \(-0.365116\pi\) | ||||
0.411181 | + | 0.911554i | \(0.365116\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 304.841i | 1.33118i | 0.746316 | + | 0.665592i | \(0.231821\pi\) | ||||
−0.746316 | + | 0.665592i | \(0.768179\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 118.794i | 0.509845i | 0.966961 | + | 0.254923i | \(0.0820500\pi\) | ||||
−0.966961 | + | 0.254923i | \(0.917950\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.0000i | 0.102128i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 372.322i | 1.55783i | 0.627127 | + | 0.778917i | \(0.284231\pi\) | ||||
−0.627127 | + | 0.778917i | \(0.715769\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.0000 | −0.103734 | −0.0518672 | − | 0.998654i | \(-0.516517\pi\) | ||||
−0.0518672 | + | 0.998654i | \(0.516517\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 225.353 | 0.919808 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 25.9808 | 0.105185 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 186.676 | 0.743730 | 0.371865 | − | 0.928287i | \(-0.378718\pi\) | ||||
0.371865 | + | 0.928287i | \(0.378718\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 207.846i | 0.821526i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 390.323i | − 1.51877i | −0.650644 | − | 0.759383i | \(-0.725501\pi\) | ||||
0.650644 | − | 0.759383i | \(-0.274499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 57.0000i | − 0.220077i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 411.514i | 1.56469i | 0.622843 | + | 0.782347i | \(0.285977\pi\) | ||||
−0.622843 | + | 0.782347i | \(0.714023\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 48.0000 | 0.181132 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −161.666 | −0.600990 | −0.300495 | − | 0.953783i | \(-0.597152\pi\) | ||||
−0.300495 | + | 0.953783i | \(0.597152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 154.153 | 0.568828 | 0.284414 | − | 0.958701i | \(-0.408201\pi\) | ||||
0.284414 | + | 0.958701i | \(0.408201\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.48528 | −0.0308556 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 318.697i | − 1.15053i | −0.817966 | − | 0.575266i | \(-0.804899\pi\) | ||||
0.817966 | − | 0.575266i | \(-0.195101\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 135.765i | 0.483148i | 0.970382 | + | 0.241574i | \(0.0776636\pi\) | ||||
−0.970382 | + | 0.241574i | \(0.922336\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 226.000i | 0.798587i | 0.916823 | + | 0.399293i | \(0.130744\pi\) | ||||
−0.916823 | + | 0.399293i | \(0.869256\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 29.3939i | − 0.102418i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −359.000 | −1.24221 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 240.050 | 0.819283 | 0.409642 | − | 0.912247i | \(-0.365654\pi\) | ||||
0.409642 | + | 0.912247i | \(0.365654\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −374.123 | −1.26821 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −127.279 | −0.425683 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 58.8897i | 0.195647i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 110.309i | − 0.361668i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 130.000i | − 0.423453i | −0.977329 | − | 0.211726i | \(-0.932091\pi\) | ||||
0.977329 | − | 0.211726i | \(-0.0679086\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 465.403i | − 1.49647i | −0.663432 | − | 0.748236i | \(-0.730901\pi\) | ||||
0.663432 | − | 0.748236i | \(-0.269099\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 481.000 | 1.53674 | 0.768371 | − | 0.640005i | \(-0.221068\pi\) | ||||
0.768371 | + | 0.640005i | \(0.221068\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −529.090 | −1.66905 | −0.834526 | − | 0.550968i | \(-0.814259\pi\) | ||||
−0.834526 | + | 0.550968i | \(0.814259\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 332.554 | 1.04249 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −127.279 | −0.394053 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 5.19615i | − 0.0159882i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.48528i | 0.0257911i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 413.000i | − 1.24773i | −0.781530 | − | 0.623867i | \(-0.785561\pi\) | ||||
0.781530 | − | 0.623867i | \(-0.214439\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 93.0806i | 0.277853i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −503.000 | −1.49258 | −0.746291 | − | 0.665620i | \(-0.768167\pi\) | ||||
−0.746291 | + | 0.665620i | \(0.768167\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −117.576 | −0.344796 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 164.545 | 0.479723 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −305.470 | −0.880317 | −0.440159 | − | 0.897920i | \(-0.645078\pi\) | ||||
−0.440159 | + | 0.897920i | \(0.645078\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 507.491i | − 1.45413i | −0.686569 | − | 0.727064i | \(-0.740884\pi\) | ||||
0.686569 | − | 0.727064i | \(-0.259116\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 101.823i | 0.288451i | 0.989545 | + | 0.144226i | \(0.0460691\pi\) | ||||
−0.989545 | + | 0.144226i | \(0.953931\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 336.000i | 0.946479i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 494.797i | − 1.37826i | −0.724636 | − | 0.689132i | \(-0.757992\pi\) | ||||
0.724636 | − | 0.689132i | \(-0.242008\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 336.000 | 0.930748 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 122.474 | 0.335547 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −219.970 | −0.599375 | −0.299687 | − | 0.954037i | \(-0.596882\pi\) | ||||
−0.299687 | + | 0.954037i | \(0.596882\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.9706 | 0.0457428 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 254.611i | 0.682604i | 0.939954 | + | 0.341302i | \(0.110868\pi\) | ||||
−0.939954 | + | 0.341302i | \(0.889132\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 203.647i | 0.540177i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 533.000i | 1.40633i | 0.711025 | + | 0.703166i | \(0.248231\pi\) | ||||
−0.711025 | + | 0.703166i | \(0.751769\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 362.524i | − 0.946539i | −0.880918 | − | 0.473270i | \(-0.843074\pi\) | ||||
0.880918 | − | 0.473270i | \(-0.156926\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 72.0000 | 0.187013 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 93.0806 | 0.239282 | 0.119641 | − | 0.992817i | \(-0.461826\pi\) | ||||
0.119641 | + | 0.992817i | \(0.461826\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 623.538 | 1.59473 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 687.308 | 1.74002 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 69.2820i | − 0.174514i | −0.996186 | − | 0.0872570i | \(-0.972190\pi\) | ||||
0.996186 | − | 0.0872570i | \(-0.0278101\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 407.294i | 1.01569i | 0.861447 | + | 0.507847i | \(0.169559\pi\) | ||||
−0.861447 | + | 0.507847i | \(0.830441\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 72.0000i | − 0.178660i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 279.242i | 0.686098i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 431.000 | 1.05379 | 0.526895 | − | 0.849930i | \(-0.323356\pi\) | ||||
0.526895 | + | 0.849930i | \(0.323356\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −132.272 | −0.320272 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 498.831 | 1.20200 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −551.543 | −1.31633 | −0.658166 | − | 0.752873i | \(-0.728668\pi\) | ||||
−0.658166 | + | 0.752873i | \(0.728668\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 715.337i | − 1.69914i | −0.527478 | − | 0.849569i | \(-0.676862\pi\) | ||||
0.527478 | − | 0.849569i | \(-0.323138\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.4558i | 0.0598961i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 39.0000i | − 0.0913349i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 475.201i | 1.10255i | 0.834322 | + | 0.551277i | \(0.185859\pi\) | ||||
−0.834322 | + | 0.551277i | \(0.814141\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −218.000 | −0.503464 | −0.251732 | − | 0.967797i | \(-0.581000\pi\) | ||||
−0.251732 | + | 0.967797i | \(0.581000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 122.474 | 0.280262 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −290.985 | −0.662835 | −0.331417 | − | 0.943484i | \(-0.607527\pi\) | ||||
−0.331417 | + | 0.943484i | \(0.607527\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −322.441 | −0.727857 | −0.363929 | − | 0.931427i | \(-0.618565\pi\) | ||||
−0.363929 | + | 0.931427i | \(0.618565\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 41.5692i | 0.0934140i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 721.249i | 1.60635i | 0.595747 | + | 0.803173i | \(0.296856\pi\) | ||||
−0.595747 | + | 0.803173i | \(0.703144\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 144.000i | 0.319290i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 44.0908i | 0.0969029i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 794.000 | 1.73742 | 0.868709 | − | 0.495323i | \(-0.164950\pi\) | ||||
0.868709 | + | 0.495323i | \(0.164950\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 132.272 | 0.286925 | 0.143463 | − | 0.989656i | \(-0.454176\pi\) | ||||
0.143463 | + | 0.989656i | \(0.454176\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 524.811 | 1.13350 | 0.566751 | − | 0.823889i | \(-0.308200\pi\) | ||||
0.566751 | + | 0.823889i | \(0.308200\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −500.632 | −1.07202 | −0.536008 | − | 0.844213i | \(-0.680068\pi\) | ||||
−0.536008 | + | 0.844213i | \(0.680068\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.9090i | 0.0701684i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 288.500i | − 0.609936i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.00000i | 0.0105263i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 734.847i | − 1.53413i | −0.641571 | − | 0.767064i | \(-0.721717\pi\) | ||||
0.641571 | − | 0.767064i | \(-0.278283\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −171.000 | −0.355509 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 347.828 | 0.717170 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 400.104 | 0.821568 | 0.410784 | − | 0.911733i | \(-0.365255\pi\) | ||||
0.410784 | + | 0.911733i | \(0.365255\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.4264 | 0.0864082 | 0.0432041 | − | 0.999066i | \(-0.486243\pi\) | ||||
0.0432041 | + | 0.999066i | \(0.486243\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 997.661i | − 2.02365i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 118.794i | 0.239022i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 326.000i | 0.653307i | 0.945144 | + | 0.326653i | \(0.105921\pi\) | ||||
−0.945144 | + | 0.326653i | \(0.894079\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 318.434i | 0.633069i | 0.948581 | + | 0.316534i | \(0.102519\pi\) | ||||
−0.948581 | + | 0.316534i | \(0.897481\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 624.000 | 1.23564 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −700.554 | −1.37633 | −0.688167 | − | 0.725552i | \(-0.741584\pi\) | ||||
−0.688167 | + | 0.725552i | \(0.741584\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.3013 | 0.0847383 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 263.044 | 0.510765 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 41.5692i | − 0.0804047i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 602.455i | − 1.15634i | −0.815915 | − | 0.578172i | \(-0.803766\pi\) | ||||
0.815915 | − | 0.578172i | \(-0.196234\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 605.000i | 1.15679i | 0.815758 | + | 0.578394i | \(0.196320\pi\) | ||||
−0.815758 | + | 0.578394i | \(0.803680\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 352.727i | 0.669310i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −71.0000 | −0.134216 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −88.1816 | −0.165444 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 872.954 | 1.63169 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −390.323 | −0.724161 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 174.937i | − 0.323359i | −0.986843 | − | 0.161679i | \(-0.948309\pi\) | ||||
0.986843 | − | 0.161679i | \(-0.0516911\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 746.705i | − 1.37010i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 67.0000i | 0.122486i | 0.998123 | + | 0.0612431i | \(0.0195065\pi\) | ||||
−0.998123 | + | 0.0612431i | \(0.980493\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 195.959i | − 0.355643i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 243.000 | 0.439421 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −455.605 | −0.817962 | −0.408981 | − | 0.912543i | \(-0.634116\pi\) | ||||
−0.408981 | + | 0.912543i | \(0.634116\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 176.669 | 0.316045 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 967.322 | 1.71816 | 0.859078 | − | 0.511844i | \(-0.171038\pi\) | ||||
0.859078 | + | 0.511844i | \(0.171038\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1039.23i | − 1.83935i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 432.749i | − 0.760544i | −0.924875 | − | 0.380272i | \(-0.875830\pi\) | ||||
0.924875 | − | 0.380272i | \(-0.124170\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 451.000i | 0.789842i | 0.918715 | + | 0.394921i | \(0.129228\pi\) | ||||
−0.918715 | + | 0.394921i | \(0.870772\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 24.4949i | − 0.0425998i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −623.000 | −1.07972 | −0.539861 | − | 0.841754i | \(-0.681523\pi\) | ||||
−0.539861 | + | 0.841754i | \(0.681523\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 176.363 | 0.303551 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −83.1384 | −0.142605 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 857.013 | 1.45999 | 0.729994 | − | 0.683453i | \(-0.239523\pi\) | ||||
0.729994 | + | 0.683453i | \(0.239523\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 69.2820i | 0.117627i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 576.999i | − 0.973017i | −0.873676 | − | 0.486509i | \(-0.838270\pi\) | ||||
0.873676 | − | 0.486509i | \(-0.161730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 216.000i | − 0.363025i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 685.857i | 1.14500i | 0.819903 | + | 0.572502i | \(0.194027\pi\) | ||||
−0.819903 | + | 0.572502i | \(0.805973\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 986.000 | 1.64060 | 0.820300 | − | 0.571934i | \(-0.193807\pi\) | ||||
0.820300 | + | 0.571934i | \(0.193807\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 240.050 | 0.396777 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 538.668 | 0.887426 | 0.443713 | − | 0.896169i | \(-0.353661\pi\) | ||||
0.443713 | + | 0.896169i | \(0.353661\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.4558 | 0.0416626 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 476.314i | − 0.777021i | −0.921444 | − | 0.388511i | \(-0.872990\pi\) | ||||
0.921444 | − | 0.388511i | \(-0.127010\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 958.837i | 1.55403i | 0.629482 | + | 0.777015i | \(0.283267\pi\) | ||||
−0.629482 | + | 0.777015i | \(0.716733\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 821.000i | − 1.32633i | −0.748472 | − | 0.663166i | \(-0.769212\pi\) | ||||
0.748472 | − | 0.663166i | \(-0.230788\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.6969i | 0.0235906i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −599.000 | −0.958400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 837.725 | 1.33184 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 957.824 | 1.51795 | 0.758973 | − | 0.651122i | \(-0.225701\pi\) | ||||
0.758973 | + | 0.651122i | \(0.225701\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 543.058 | 0.855209 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 239.023i | − 0.375232i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 220.617i | 0.344177i | 0.985082 | + | 0.172088i | \(0.0550515\pi\) | ||||
−0.985082 | + | 0.172088i | \(0.944949\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 898.000i | 1.39658i | 0.715816 | + | 0.698289i | \(0.246055\pi\) | ||||
−0.715816 | + | 0.698289i | \(0.753945\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 303.737i | − 0.469454i | −0.972061 | − | 0.234727i | \(-0.924580\pi\) | ||||
0.972061 | − | 0.234727i | \(-0.0754196\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 648.000 | 0.998459 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −176.363 | −0.270082 | −0.135041 | − | 0.990840i | \(-0.543117\pi\) | ||||
−0.135041 | + | 0.990840i | \(0.543117\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −166.277 | −0.253858 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −424.264 | −0.643800 | −0.321900 | − | 0.946774i | \(-0.604321\pi\) | ||||
−0.321900 | + | 0.946774i | \(0.604321\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 310.037i | − 0.469043i | −0.972111 | − | 0.234521i | \(-0.924648\pi\) | ||||
0.972111 | − | 0.234521i | \(-0.0753522\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 42.4264i | − 0.0637991i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 960.000i | 1.43928i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 191.060i | 0.284739i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −215.000 | −0.319465 | −0.159733 | − | 0.987160i | \(-0.551063\pi\) | ||||
−0.159733 | + | 0.987160i | \(0.551063\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 171.464 | 0.253271 | 0.126635 | − | 0.991949i | \(-0.459582\pi\) | ||||
0.126635 | + | 0.991949i | \(0.459582\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 122.976 | 0.181113 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −695.793 | −1.01873 | −0.509365 | − | 0.860550i | \(-0.670120\pi\) | ||||
−0.509365 | + | 0.860550i | \(0.670120\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41.5692i | 0.0606850i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 50.9117i | − 0.0738921i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 562.000i | 0.813314i | 0.913581 | + | 0.406657i | \(0.133306\pi\) | ||||
−0.913581 | + | 0.406657i | \(0.866694\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 377.221i | 0.542765i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 432.000 | 0.619799 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1131.66 | 1.61436 | 0.807179 | − | 0.590307i | \(-0.200993\pi\) | ||||
0.807179 | + | 0.590307i | \(0.200993\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 164.545 | 0.234061 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 220.617 | 0.312047 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 368.927i | − 0.520348i | −0.965562 | − | 0.260174i | \(-0.916220\pi\) | ||||
0.965562 | − | 0.260174i | \(-0.0837799\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 339.411i | − 0.476033i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 216.000i | − 0.302098i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 93.0000 | 0.128988 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −39.1918 | −0.0540577 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −457.261 | −0.628970 | −0.314485 | − | 0.949262i | \(-0.601832\pi\) | ||||
−0.314485 | + | 0.949262i | \(0.601832\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −865.499 | −1.18399 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 96.9948i | − 0.132326i | −0.997809 | − | 0.0661629i | \(-0.978924\pi\) | ||||
0.997809 | − | 0.0661629i | \(-0.0210757\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 161.220i | − 0.218752i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 514.000i | − 0.695535i | −0.937581 | − | 0.347767i | \(-0.886940\pi\) | ||||
0.937581 | − | 0.347767i | \(-0.113060\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1053.28i | − 1.41761i | −0.705407 | − | 0.708803i | \(-0.749236\pi\) | ||||
0.705407 | − | 0.708803i | \(-0.250764\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 720.000 | 0.966443 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 308.636 | 0.412064 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 289.252 | 0.385156 | 0.192578 | − | 0.981282i | \(-0.438315\pi\) | ||||
0.192578 | + | 0.981282i | \(0.438315\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1281.28 | 1.69706 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 434.745i | 0.574300i | 0.957886 | + | 0.287150i | \(0.0927077\pi\) | ||||
−0.957886 | + | 0.287150i | \(0.907292\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1094.60i | 1.43837i | 0.694817 | + | 0.719186i | \(0.255485\pi\) | ||||
−0.694817 | + | 0.719186i | \(0.744515\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 264.000i | − 0.346003i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 396.817i | 0.517363i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −529.000 | −0.687906 | −0.343953 | − | 0.938987i | \(-0.611766\pi\) | ||||
−0.343953 | + | 0.938987i | \(0.611766\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1332.52 | −1.72383 | −0.861916 | − | 0.507051i | \(-0.830736\pi\) | ||||
−0.861916 | + | 0.507051i | \(0.830736\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.8564 | 0.0178792 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 84.8528 | 0.108925 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 581.969i | − 0.745159i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 1289.76i | − 1.64301i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 197.000i | − 0.250318i | −0.992137 | − | 0.125159i | \(-0.960056\pi\) | ||||
0.992137 | − | 0.125159i | \(-0.0399440\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 367.423i | − 0.464505i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −117.000 | −0.147541 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 421.312 | 0.528623 | 0.264311 | − | 0.964437i | \(-0.414855\pi\) | ||||
0.264311 | + | 0.964437i | \(0.414855\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −124.708 | −0.156080 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −212.132 | −0.264174 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 207.846i | 0.258194i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 220.617i | − 0.272704i | −0.990660 | − | 0.136352i | \(-0.956462\pi\) | ||||
0.990660 | − | 0.136352i | \(-0.0435378\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 110.000i | 0.135635i | 0.997698 | + | 0.0678175i | \(0.0216036\pi\) | ||||
−0.997698 | + | 0.0678175i | \(0.978396\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 494.797i | 0.607113i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −170.000 | −0.208078 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1268.84 | −1.54548 | −0.772738 | − | 0.634725i | \(-0.781113\pi\) | ||||
−0.772738 | + | 0.634725i | \(0.781113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 389.711 | 0.473525 | 0.236763 | − | 0.971568i | \(-0.423914\pi\) | ||||
0.236763 | + | 0.971568i | \(0.423914\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −415.779 | −0.502755 | −0.251378 | − | 0.967889i | \(-0.580884\pi\) | ||||
−0.251378 | + | 0.967889i | \(0.580884\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 213.042i | − 0.256987i | −0.991710 | − | 0.128494i | \(-0.958986\pi\) | ||||
0.991710 | − | 0.128494i | \(-0.0410142\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1170.97i | 1.40572i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 552.000i | 0.661078i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 107.778i | − 0.128460i | −0.997935 | − | 0.0642298i | \(-0.979541\pi\) | ||||
0.997935 | − | 0.0642298i | \(-0.0204591\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 695.000 | 0.826397 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −695.655 | −0.823260 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 84.8705 | 0.100201 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −806.102 | −0.947241 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 684.160i | 0.802063i | 0.916064 | + | 0.401032i | \(0.131348\pi\) | ||||
−0.916064 | + | 0.401032i | \(0.868652\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1035.20i | 1.20794i | 0.797007 | + | 0.603970i | \(0.206415\pi\) | ||||
−0.797007 | + | 0.603970i | \(0.793585\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 341.000i | 0.396973i | 0.980104 | + | 0.198487i | \(0.0636026\pi\) | ||||
−0.980104 | + | 0.198487i | \(0.936397\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1376.61i | − 1.59515i | −0.603221 | − | 0.797574i | \(-0.706116\pi\) | ||||
0.603221 | − | 0.797574i | \(-0.293884\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −624.000 | −0.721387 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1190.45 | −1.36991 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 98.7269 | 0.113349 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −220.617 | −0.252134 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1030.57i | 1.17511i | 0.809185 | + | 0.587554i | \(0.199909\pi\) | ||||
−0.809185 | + | 0.587554i | \(0.800091\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 347.897i | 0.394888i | 0.980314 | + | 0.197444i | \(0.0632641\pi\) | ||||
−0.980314 | + | 0.197444i | \(0.936736\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1613.00i | − 1.82673i | −0.407145 | − | 0.913364i | \(-0.633476\pi\) | ||||
0.407145 | − | 0.913364i | \(-0.366524\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 117.576i | 0.132554i | 0.997801 | + | 0.0662771i | \(0.0211121\pi\) | ||||
−0.997801 | + | 0.0662771i | \(0.978888\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 192.000 | 0.215973 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.4949 | −0.0274299 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −581.969 | −0.650245 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −543.058 | −0.604069 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 249.415i | 0.276821i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 857.013i | − 0.946976i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1171.00i | − 1.29107i | −0.763731 | − | 0.645535i | \(-0.776635\pi\) | ||||
0.763731 | − | 0.645535i | \(-0.223365\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 186.161i | 0.204348i | 0.994767 | + | 0.102174i | \(0.0325799\pi\) | ||||
−0.994767 | + | 0.102174i | \(0.967420\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −864.000 | −0.946331 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −58.7878 | −0.0641088 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −706.677 | −0.768963 | −0.384481 | − | 0.923133i | \(-0.625620\pi\) | ||||
−0.384481 | + | 0.923133i | \(0.625620\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 356.382 | 0.386112 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 32.9090i | − 0.0355773i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1086.12i | 1.16912i | 0.811349 | + | 0.584562i | \(0.198734\pi\) | ||||
−0.811349 | + | 0.584562i | \(0.801266\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 230.000i | 0.247046i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1058.18i | 1.13174i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.00000 | 0.00106724 | 0.000533618 | − | 1.00000i | \(-0.499830\pi\) | ||||
0.000533618 | 1.00000i | \(0.499830\pi\) | ||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 759.342 | 0.806952 | 0.403476 | − | 0.914990i | \(-0.367802\pi\) | ||||
0.403476 | + | 0.914990i | \(0.367802\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −415.692 | −0.440819 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1077.63 | −1.13794 | −0.568971 | − | 0.822358i | \(-0.692658\pi\) | ||||
−0.568971 | + | 0.822358i | \(0.692658\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 129.904i | − 0.136885i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 93.3381i | − 0.0979413i | −0.998800 | − | 0.0489707i | \(-0.984406\pi\) | ||||
0.998800 | − | 0.0489707i | \(-0.0155941\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1560.00i | 1.63351i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.6969i | 0.0153253i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −769.000 | −0.800208 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1298.23 | 1.34532 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1151.81 | −1.19112 | −0.595560 | − | 0.803311i | \(-0.703070\pi\) | ||||
−0.595560 | + | 0.803311i | \(0.703070\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1077.63 | −1.10982 | −0.554908 | − | 0.831912i | \(-0.687246\pi\) | ||||
−0.554908 | + | 0.831912i | \(0.687246\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 133.368i | 0.137069i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 373.352i | − 0.382142i | −0.981576 | − | 0.191071i | \(-0.938804\pi\) | ||||
0.981576 | − | 0.191071i | \(-0.0611960\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 72.0000i | − 0.0735444i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 631.968i | − 0.642898i | −0.946927 | − | 0.321449i | \(-0.895830\pi\) | ||||
0.946927 | − | 0.321449i | \(-0.104170\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 216.000 | 0.219289 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 832.827 | 0.842089 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −219.970 | −0.221968 | −0.110984 | − | 0.993822i | \(-0.535400\pi\) | ||||
−0.110984 | + | 0.993822i | \(0.535400\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 127.279 | 0.127919 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1039.23i | 1.04236i | 0.853448 | + | 0.521179i | \(0.174508\pi\) | ||||
−0.853448 | + | 0.521179i | \(0.825492\pi\) | |||||||
\(998\) | 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 | 1728.3.h.g.161.2 | yes | 8 | |
3.2 | odd | 2 | inner | 1728.3.h.g.161.6 | yes | 8 | |
4.3 | odd | 2 | inner | 1728.3.h.g.161.4 | yes | 8 | |
8.3 | odd | 2 | inner | 1728.3.h.g.161.7 | yes | 8 | |
8.5 | even | 2 | inner | 1728.3.h.g.161.5 | yes | 8 | |
12.11 | even | 2 | inner | 1728.3.h.g.161.8 | yes | 8 | |
24.5 | odd | 2 | inner | 1728.3.h.g.161.1 | ✓ | 8 | |
24.11 | even | 2 | inner | 1728.3.h.g.161.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.3.h.g.161.1 | ✓ | 8 | 24.5 | odd | 2 | inner | |
1728.3.h.g.161.2 | yes | 8 | 1.1 | even | 1 | trivial | |
1728.3.h.g.161.3 | yes | 8 | 24.11 | even | 2 | inner | |
1728.3.h.g.161.4 | yes | 8 | 4.3 | odd | 2 | inner | |
1728.3.h.g.161.5 | yes | 8 | 8.5 | even | 2 | inner | |
1728.3.h.g.161.6 | yes | 8 | 3.2 | odd | 2 | inner | |
1728.3.h.g.161.7 | yes | 8 | 8.3 | odd | 2 | inner | |
1728.3.h.g.161.8 | yes | 8 | 12.11 | even | 2 | inner |