Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2400,2,Mod(49,2400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2400.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2400.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.1640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.214798336.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 600) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.5 | ||
Root | \(1.23291 - 0.692769i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2400.49 |
Dual form | 2400.2.d.h.49.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2400\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1601\) | \(1951\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0802864i | 0.0303454i | 0.999885 | + | 0.0151727i | \(0.00482980\pi\) | ||||
−0.999885 | + | 0.0151727i | \(0.995170\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.41649i | 0.728599i | 0.931282 | + | 0.364300i | \(0.118692\pi\) | ||||
−0.931282 | + | 0.364300i | \(0.881308\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.26785 | −1.46104 | −0.730520 | − | 0.682892i | \(-0.760722\pi\) | ||||
−0.730520 | + | 0.682892i | \(0.760722\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.255918i | 0.0620692i | 0.999518 | + | 0.0310346i | \(0.00988021\pi\) | ||||
−0.999518 | + | 0.0310346i | \(0.990120\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.95864i | 1.59642i | 0.602378 | + | 0.798211i | \(0.294220\pi\) | ||||
−0.602378 | + | 0.798211i | \(0.705780\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0802864i | 0.0175199i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.64542i | 0.343093i | 0.985176 | + | 0.171546i | \(0.0548764\pi\) | ||||
−0.985176 | + | 0.171546i | \(0.945124\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 4.51516i | − 0.838444i | −0.907884 | − | 0.419222i | \(-0.862303\pi\) | ||||
0.907884 | − | 0.419222i | \(-0.137697\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.29484 | −1.48980 | −0.744899 | − | 0.667177i | \(-0.767502\pi\) | ||||
−0.744899 | + | 0.667177i | \(0.767502\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.41649i | 0.420657i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.67241 | 0.439341 | 0.219671 | − | 0.975574i | \(-0.429502\pi\) | ||||
0.219671 | + | 0.975574i | \(0.429502\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.26785 | −0.843531 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.11921 | −1.26801 | −0.634004 | − | 0.773330i | \(-0.718590\pi\) | ||||
−0.634004 | + | 0.773330i | \(0.718590\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.08890 | −0.623551 | −0.311776 | − | 0.950156i | \(-0.600924\pi\) | ||||
−0.311776 | + | 0.950156i | \(0.600924\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.70272i | 0.831827i | 0.909404 | + | 0.415914i | \(0.136538\pi\) | ||||
−0.909404 | + | 0.415914i | \(0.863462\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99355 | 0.999079 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.255918i | 0.0358357i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.5627 | −1.58826 | −0.794129 | − | 0.607749i | \(-0.792073\pi\) | ||||
−0.794129 | + | 0.607749i | \(0.792073\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.95864i | 0.921694i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.6963i | 1.65291i | 0.563000 | + | 0.826457i | \(0.309647\pi\) | ||||
−0.563000 | + | 0.826457i | \(0.690353\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.9403i | 1.52879i | 0.644746 | + | 0.764397i | \(0.276963\pi\) | ||||
−0.644746 | + | 0.764397i | \(0.723037\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0802864i | 0.0101151i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.27979 | 0.889367 | 0.444684 | − | 0.895688i | \(-0.353316\pi\) | ||||
0.444684 | + | 0.895688i | \(0.353316\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.64542i | 0.198085i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3481 | 1.34678 | 0.673388 | − | 0.739289i | \(-0.264838\pi\) | ||||
0.673388 | + | 0.739289i | \(0.264838\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 12.0779i | − 1.41361i | −0.707411 | − | 0.706803i | \(-0.750137\pi\) | ||||
0.707411 | − | 0.706803i | \(-0.249863\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.194011 | −0.0221096 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.50539 | 0.619405 | 0.309702 | − | 0.950834i | \(-0.399771\pi\) | ||||
0.309702 | + | 0.950834i | \(0.399771\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.20811 | −1.01072 | −0.505361 | − | 0.862908i | \(-0.668641\pi\) | ||||
−0.505361 | + | 0.862908i | \(0.668641\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 4.51516i | − 0.484076i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.9173 | −1.26323 | −0.631615 | − | 0.775283i | \(-0.717607\pi\) | ||||
−0.631615 | + | 0.775283i | \(0.717607\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 0.422937i | − 0.0443358i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.29484 | −0.860135 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 8.50539i | − 0.863592i | −0.901971 | − | 0.431796i | \(-0.857880\pi\) | ||||
0.901971 | − | 0.431796i | \(-0.142120\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.41649i | 0.242866i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.56270i | 0.752516i | 0.926515 | + | 0.376258i | \(0.122789\pi\) | ||||
−0.926515 | + | 0.376258i | \(0.877211\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.78544i | 0.175925i | 0.996124 | + | 0.0879624i | \(0.0280355\pi\) | ||||
−0.996124 | + | 0.0879624i | \(0.971964\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.4705 | 1.01222 | 0.506110 | − | 0.862469i | \(-0.331083\pi\) | ||||
0.506110 | + | 0.862469i | \(0.331083\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.64298i | 0.348934i | 0.984663 | + | 0.174467i | \(0.0558203\pi\) | ||||
−0.984663 | + | 0.174467i | \(0.944180\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.67241 | 0.253654 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.83298i | 0.830937i | 0.909608 | + | 0.415468i | \(0.136382\pi\) | ||||
−0.909608 | + | 0.415468i | \(0.863618\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.26785 | −0.487013 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.0205467 | −0.00188351 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.16057 | 0.469143 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.11921 | −0.732085 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 8.69628i | − 0.771670i | −0.922568 | − | 0.385835i | \(-0.873913\pi\) | ||||
0.922568 | − | 0.385835i | \(-0.126087\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.08890 | −0.360008 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7916i | 0.942868i | 0.881901 | + | 0.471434i | \(0.156264\pi\) | ||||
−0.881901 | + | 0.471434i | \(0.843736\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.558684 | −0.0484440 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 11.5421i | − 0.986112i | −0.869997 | − | 0.493056i | \(-0.835880\pi\) | ||||
0.869997 | − | 0.493056i | \(-0.164120\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.214558i | 0.0181986i | 0.999959 | + | 0.00909928i | \(0.00289643\pi\) | ||||
−0.999959 | + | 0.00909928i | \(0.997104\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.70272i | 0.480256i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 12.7297i | − 1.06451i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.99355 | 0.576819 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.0475i | 1.88813i | 0.329762 | + | 0.944064i | \(0.393031\pi\) | ||||
−0.329762 | + | 0.944064i | \(0.606969\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.48573 | −0.771938 | −0.385969 | − | 0.922512i | \(-0.626133\pi\) | ||||
−0.385969 | + | 0.922512i | \(0.626133\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.255918i | 0.0206897i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.34413 | −0.506316 | −0.253158 | − | 0.967425i | \(-0.581469\pi\) | ||||
−0.253158 | + | 0.967425i | \(0.581469\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.5627 | −0.916981 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.132104 | −0.0104113 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.4100 | −0.972030 | −0.486015 | − | 0.873951i | \(-0.661550\pi\) | ||||
−0.486015 | + | 0.873951i | \(0.661550\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.2654i | 1.80033i | 0.435547 | + | 0.900166i | \(0.356555\pi\) | ||||
−0.435547 | + | 0.900166i | \(0.643445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.7503 | 1.13464 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.95864i | 0.532140i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.63897 | −0.656809 | −0.328404 | − | 0.944537i | \(-0.606511\pi\) | ||||
−0.328404 | + | 0.944537i | \(0.606511\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.6963i | 0.954311i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 9.40544i | − 0.702996i | −0.936189 | − | 0.351498i | \(-0.885672\pi\) | ||||
0.936189 | − | 0.351498i | \(-0.114328\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 6.43487i | − 0.478300i | −0.970983 | − | 0.239150i | \(-0.923131\pi\) | ||||
0.970983 | − | 0.239150i | \(-0.0768688\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.9403i | 0.882649i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.618423 | −0.0452236 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.0802864i | 0.00583997i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.56270 | 0.402503 | 0.201251 | − | 0.979540i | \(-0.435499\pi\) | ||||
0.201251 | + | 0.979540i | \(0.435499\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 18.4227i | − 1.32609i | −0.748578 | − | 0.663046i | \(-0.769263\pi\) | ||||
0.748578 | − | 0.663046i | \(-0.230737\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0239 | 1.28415 | 0.642074 | − | 0.766643i | \(-0.278074\pi\) | ||||
0.642074 | + | 0.766643i | \(0.278074\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.1214 | 1.42637 | 0.713183 | − | 0.700977i | \(-0.247253\pi\) | ||||
0.713183 | + | 0.700977i | \(0.247253\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.27979 | 0.513476 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.362505 | 0.0254429 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.64542i | 0.114364i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.8155 | −1.16315 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.25592i | 0.224147i | 0.993700 | + | 0.112073i | \(0.0357492\pi\) | ||||
−0.993700 | + | 0.112073i | \(0.964251\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.3481 | 0.777562 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 0.665963i | − 0.0452085i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 12.0779i | − 0.816146i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1.34814i | − 0.0906856i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 26.9911i | − 1.80746i | −0.428104 | − | 0.903730i | \(-0.640818\pi\) | ||||
0.428104 | − | 0.903730i | \(-0.359182\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.8219 | −1.31563 | −0.657814 | − | 0.753180i | \(-0.728519\pi\) | ||||
−0.657814 | + | 0.753180i | \(0.728519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.6797i | 1.43264i | 0.697773 | + | 0.716319i | \(0.254174\pi\) | ||||
−0.697773 | + | 0.716319i | \(0.745826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.194011 | −0.0127650 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.2733i | 1.13161i | 0.824538 | + | 0.565807i | \(0.191435\pi\) | ||||
−0.824538 | + | 0.565807i | \(0.808565\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.50539 | 0.357614 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.3718 | −1.05900 | −0.529502 | − | 0.848309i | \(-0.677621\pi\) | ||||
−0.529502 | + | 0.848309i | \(0.677621\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.82654 | −0.439736 | −0.219868 | − | 0.975530i | \(-0.570563\pi\) | ||||
−0.219868 | + | 0.975530i | \(0.570563\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 36.6571i | − 2.33243i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.20811 | −0.583540 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.96969i | − 0.187445i | −0.995598 | − | 0.0937225i | \(-0.970123\pi\) | ||||
0.995598 | − | 0.0937225i | \(-0.0298766\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.97613 | −0.249977 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 5.03031i | − 0.313782i | −0.987616 | − | 0.156891i | \(-0.949853\pi\) | ||||
0.987616 | − | 0.156891i | \(-0.0501472\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.214558i | 0.0133320i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 4.51516i | − 0.279481i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.70585i | 0.166850i | 0.996514 | + | 0.0834248i | \(0.0265859\pi\) | ||||
−0.996514 | + | 0.0834248i | \(0.973414\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.9173 | −0.729326 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 22.3718i | − 1.36403i | −0.731337 | − | 0.682017i | \(-0.761103\pi\) | ||||
0.731337 | − | 0.682017i | \(-0.238897\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.869741 | 0.0528330 | 0.0264165 | − | 0.999651i | \(-0.491590\pi\) | ||||
0.0264165 | + | 0.999651i | \(0.491590\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 0.422937i | − 0.0255973i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.6733 | 1.72281 | 0.861406 | − | 0.507918i | \(-0.169585\pi\) | ||||
0.861406 | + | 0.507918i | \(0.169585\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.29484 | −0.496599 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.1429 | 0.903349 | 0.451674 | − | 0.892183i | \(-0.350827\pi\) | ||||
0.451674 | + | 0.892183i | \(0.350827\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.23225 | −0.370469 | −0.185234 | − | 0.982694i | \(-0.559304\pi\) | ||||
−0.185234 | + | 0.982694i | \(0.559304\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 0.651862i | − 0.0384782i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9345 | 0.996147 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 8.50539i | − 0.498595i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.5054 | 1.25636 | 0.628179 | − | 0.778069i | \(-0.283800\pi\) | ||||
0.628179 | + | 0.778069i | \(0.283800\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.41649i | 0.140219i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 8.66781i | − 0.501272i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 0.328283i | − 0.0189219i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.56270i | 0.434466i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.57706 | −0.204154 | −0.102077 | − | 0.994777i | \(-0.532549\pi\) | ||||
−0.102077 | + | 0.994777i | \(0.532549\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.78544i | 0.101570i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.49461 | 0.141456 | 0.0707282 | − | 0.997496i | \(-0.477468\pi\) | ||||
0.0707282 | + | 0.997496i | \(0.477468\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.57246i | 0.541068i | 0.962710 | + | 0.270534i | \(0.0872002\pi\) | ||||
−0.962710 | + | 0.270534i | \(0.912800\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.16702 | −0.177877 | −0.0889387 | − | 0.996037i | \(-0.528348\pi\) | ||||
−0.0889387 | + | 0.996037i | \(0.528348\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.9108 | 0.610889 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.4705 | 0.584405 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.78084 | −0.0990887 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.64298i | 0.201457i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.457851 | −0.0252421 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.5118i | 0.907573i | 0.891111 | + | 0.453786i | \(0.149927\pi\) | ||||
−0.891111 | + | 0.453786i | \(0.850073\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.67241 | 0.146447 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.8330i | 0.644584i | 0.946640 | + | 0.322292i | \(0.104453\pi\) | ||||
−0.946640 | + | 0.322292i | \(0.895547\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.83298i | 0.479742i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 20.0444i | − 1.08547i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.12349i | 0.0606628i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.9713 | −1.28684 | −0.643422 | − | 0.765511i | \(-0.722486\pi\) | ||||
−0.643422 | + | 0.765511i | \(0.722486\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 8.91570i | − 0.477247i | −0.971112 | − | 0.238623i | \(-0.923304\pi\) | ||||
0.971112 | − | 0.238623i | \(-0.0766961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.26785 | −0.281177 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 7.35606i | − 0.391524i | −0.980651 | − | 0.195762i | \(-0.937282\pi\) | ||||
0.980651 | − | 0.195762i | \(-0.0627179\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0205467 | −0.00108745 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.2114 | 1.33061 | 0.665304 | − | 0.746572i | \(-0.268302\pi\) | ||||
0.665304 | + | 0.746572i | \(0.268302\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −29.4227 | −1.54856 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.16057 | 0.270860 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.86573i | 0.306189i | 0.988212 | + | 0.153094i | \(0.0489238\pi\) | ||||
−0.988212 | + | 0.153094i | \(0.951076\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.11921 | −0.422669 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 0.928327i | − 0.0481963i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.5063 | 1.42422 | 0.712111 | − | 0.702067i | \(-0.247739\pi\) | ||||
0.712111 | + | 0.702067i | \(0.247739\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.7852i | 1.22500i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 11.7549i | − 0.603807i | −0.953339 | − | 0.301903i | \(-0.902378\pi\) | ||||
0.953339 | − | 0.301903i | \(-0.0976220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 8.69628i | − 0.445524i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.3335i | 1.75436i | 0.480162 | + | 0.877180i | \(0.340578\pi\) | ||||
−0.480162 | + | 0.877180i | \(0.659422\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.08890 | −0.207850 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.89515i | 0.146790i | 0.997303 | + | 0.0733951i | \(0.0233834\pi\) | ||||
−0.997303 | + | 0.0733951i | \(0.976617\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.421092 | −0.0212955 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.7916i | 0.544365i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.9099 | −1.14982 | −0.574909 | − | 0.818218i | \(-0.694962\pi\) | ||||
−0.574909 | + | 0.818218i | \(0.694962\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.558684 | −0.0279692 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.4337 | −0.620910 | −0.310455 | − | 0.950588i | \(-0.600481\pi\) | ||||
−0.310455 | + | 0.950588i | \(0.600481\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 43.6960 | 2.17665 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.45785i | 0.320104i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.0886 | 1.58668 | 0.793340 | − | 0.608778i | \(-0.208340\pi\) | ||||
0.793340 | + | 0.608778i | \(0.208340\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 11.5421i | − 0.569332i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.01934 | −0.0501583 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.214558i | 0.0105069i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 16.1364i | − 0.788317i | −0.919043 | − | 0.394158i | \(-0.871036\pi\) | ||||
0.919043 | − | 0.394158i | \(-0.128964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 28.7675i | − 1.40204i | −0.713141 | − | 0.701021i | \(-0.752728\pi\) | ||||
0.713141 | − | 0.701021i | \(-0.247272\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.70272i | 0.277276i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.958640 | −0.0463918 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 12.7297i | − 0.614596i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.7297 | −1.19119 | −0.595594 | − | 0.803285i | \(-0.703083\pi\) | ||||
−0.595594 | + | 0.803285i | \(0.703083\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 4.48816i | − 0.215687i | −0.994168 | − | 0.107844i | \(-0.965605\pi\) | ||||
0.994168 | − | 0.107844i | \(-0.0343946\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.4499 | −0.547721 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.96081 | 0.284494 | 0.142247 | − | 0.989831i | \(-0.454567\pi\) | ||||
0.142247 | + | 0.989831i | \(0.454567\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.99355 | 0.333026 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.2924 | 0.679053 | 0.339526 | − | 0.940597i | \(-0.389733\pi\) | ||||
0.339526 | + | 0.940597i | \(0.389733\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23.0475i | 1.09011i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.5529 | −1.15872 | −0.579362 | − | 0.815070i | \(-0.696698\pi\) | ||||
−0.579362 | + | 0.815070i | \(0.696698\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 19.6200i | − 0.923870i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.48573 | −0.445678 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 28.9108i | − 1.35239i | −0.736722 | − | 0.676196i | \(-0.763627\pi\) | ||||
0.736722 | − | 0.676196i | \(-0.236373\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.255918i | 0.0119452i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.35458i | 0.202813i | 0.994845 | + | 0.101407i | \(0.0323343\pi\) | ||||
−0.994845 | + | 0.101407i | \(0.967666\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 11.1303i | − 0.517267i | −0.965976 | − | 0.258634i | \(-0.916728\pi\) | ||||
0.965976 | − | 0.258634i | \(-0.0832722\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.1257 | 0.885030 | 0.442515 | − | 0.896761i | \(-0.354086\pi\) | ||||
0.442515 | + | 0.896761i | \(0.354086\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.584467i | 0.0269882i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.34413 | −0.292322 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 9.88079i | − 0.454319i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.5627 | −0.529419 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.6358 | −1.17133 | −0.585666 | − | 0.810553i | \(-0.699167\pi\) | ||||
−0.585666 | + | 0.810553i | \(0.699167\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.0779 | −0.641895 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.132104 | −0.00601096 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 12.8434i | − 0.581992i | −0.956724 | − | 0.290996i | \(-0.906013\pi\) | ||||
0.956724 | − | 0.290996i | \(-0.0939866\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.4100 | −0.561202 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 16.9887i | − 0.766689i | −0.923605 | − | 0.383344i | \(-0.874772\pi\) | ||||
0.923605 | − | 0.383344i | \(-0.125228\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.15551 | 0.0520415 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.911101i | 0.0408684i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 14.0521i | − 0.629060i | −0.949248 | − | 0.314530i | \(-0.898153\pi\) | ||||
0.949248 | − | 0.314530i | \(-0.101847\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.2654i | 1.03942i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.53258i | 0.425037i | 0.977157 | + | 0.212518i | \(0.0681665\pi\) | ||||
−0.977157 | + | 0.212518i | \(0.931833\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.7503 | 0.655082 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 30.3450i | − 1.34502i | −0.740088 | − | 0.672510i | \(-0.765216\pi\) | ||||
0.740088 | − | 0.672510i | \(-0.234784\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.969687 | 0.0428964 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.95864i | 0.307231i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.7806 | −0.606069 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.63897 | −0.379209 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.4245 | 0.631949 | 0.315975 | − | 0.948768i | \(-0.397669\pi\) | ||||
0.315975 | + | 0.948768i | \(0.397669\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.2207 | 1.23401 | 0.617003 | − | 0.786961i | \(-0.288346\pi\) | ||||
0.617003 | + | 0.786961i | \(0.288346\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 2.12280i | − 0.0924706i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.2926 | 0.882287 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.6963i | 0.550971i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.7708 | 1.85261 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 9.40544i | − 0.405875i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.8999i | 0.727928i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 13.4695i | − 0.579100i | −0.957163 | − | 0.289550i | \(-0.906494\pi\) | ||||
0.957163 | − | 0.289550i | \(-0.0935056\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 6.43487i | − 0.276147i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.42773 | −0.189316 | −0.0946581 | − | 0.995510i | \(-0.530176\pi\) | ||||
−0.0946581 | + | 0.995510i | \(0.530176\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.9403i | 0.509598i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.4193 | 1.33851 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.442008i | 0.0187961i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −40.2017 | −1.70340 | −0.851700 | − | 0.524030i | \(-0.824428\pi\) | ||||
−0.851700 | + | 0.524030i | \(0.824428\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.5397 | 0.911033 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.618423 | −0.0261099 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.1128 | 0.552637 | 0.276319 | − | 0.961066i | \(-0.410885\pi\) | ||||
0.276319 | + | 0.961066i | \(0.410885\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.0802864i | 0.00337171i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.0257 | 0.462222 | 0.231111 | − | 0.972927i | \(-0.425764\pi\) | ||||
0.231111 | + | 0.972927i | \(0.425764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 45.6960i | − 1.91232i | −0.292847 | − | 0.956159i | \(-0.594603\pi\) | ||||
0.292847 | − | 0.956159i | \(-0.405397\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.56270 | 0.232385 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 17.2685i | − 0.718899i | −0.933165 | − | 0.359449i | \(-0.882965\pi\) | ||||
0.933165 | − | 0.359449i | \(-0.117035\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 18.4227i | − 0.765620i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 0.739286i | − 0.0306707i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 27.9411i | − 1.15720i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.7155 | 1.43286 | 0.716432 | − | 0.697657i | \(-0.245774\pi\) | ||||
0.716432 | + | 0.697657i | \(0.245774\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 57.7208i | − 2.37835i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.0239 | 0.741403 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.34022i | 0.383557i | 0.981438 | + | 0.191778i | \(0.0614255\pi\) | ||||
−0.981438 | + | 0.191778i | \(0.938575\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.1214 | 0.823513 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.9110 | −0.568389 | −0.284195 | − | 0.958767i | \(-0.591726\pi\) | ||||
−0.284195 | + | 0.958767i | \(0.591726\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.7330 | 0.478600 | 0.239300 | − | 0.970946i | \(-0.423082\pi\) | ||||
0.239300 | + | 0.970946i | \(0.423082\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.27979 | 0.296456 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.8158i | 0.438998i | 0.975613 | + | 0.219499i | \(0.0704423\pi\) | ||||
−0.975613 | + | 0.219499i | \(0.929558\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.362505 | 0.0146895 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 30.0411i | − 1.21533i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.9632 | 0.725528 | 0.362764 | − | 0.931881i | \(-0.381833\pi\) | ||||
0.362764 | + | 0.931881i | \(0.381833\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.3576i | 0.497500i | 0.968568 | + | 0.248750i | \(0.0800197\pi\) | ||||
−0.968568 | + | 0.248750i | \(0.919980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.99540i | 0.200782i | 0.994948 | + | 0.100391i | \(0.0320094\pi\) | ||||
−0.994948 | + | 0.100391i | \(0.967991\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.64542i | 0.0660283i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 0.956795i | − 0.0383332i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.8155 | −0.671546 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.683917i | 0.0272696i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.9674 | 0.715273 | 0.357636 | − | 0.933861i | \(-0.383583\pi\) | ||||
0.357636 | + | 0.933861i | \(0.383583\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.25592i | 0.129411i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −36.8410 | −1.45969 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.3481 | 0.448925 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.3638 | 1.08081 | 0.540403 | − | 0.841406i | \(-0.318272\pi\) | ||||
0.540403 | + | 0.841406i | \(0.318272\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.27518 | 0.0897245 | 0.0448623 | − | 0.998993i | \(-0.485715\pi\) | ||||
0.0448623 | + | 0.998993i | \(0.485715\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 12.4769i | − 0.490516i | −0.969458 | − | 0.245258i | \(-0.921127\pi\) | ||||
0.969458 | − | 0.245258i | \(-0.0788726\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.6804 | −1.20431 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 0.665963i | − 0.0261011i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.3055 | −1.14681 | −0.573406 | − | 0.819271i | \(-0.694378\pi\) | ||||
−0.573406 | + | 0.819271i | \(0.694378\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 12.0779i | − 0.471202i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.6009i | 0.724589i | 0.932064 | + | 0.362295i | \(0.118007\pi\) | ||||
−0.932064 | + | 0.362295i | \(0.881993\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.1318i | 0.627456i | 0.949513 | + | 0.313728i | \(0.101578\pi\) | ||||
−0.949513 | + | 0.313728i | \(0.898422\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 1.34814i | − 0.0523573i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.42931 | 0.287664 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 26.9911i | − 1.04354i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.8535 | −1.11388 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.1385i | 1.31594i | 0.753043 | + | 0.657971i | \(0.228585\pi\) | ||||
−0.753043 | + | 0.657971i | \(0.771415\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.1940 | 0.468654 | 0.234327 | − | 0.972158i | \(-0.424711\pi\) | ||||
0.234327 | + | 0.972158i | \(0.424711\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.682867 | 0.0262060 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.8219 | −0.759578 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.8567 | 0.836322 | 0.418161 | − | 0.908373i | \(-0.362675\pi\) | ||||
0.418161 | + | 0.908373i | \(0.362675\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.6797i | 0.827134i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 60.9106 | 2.32051 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 6.17780i | − 0.235015i | −0.993072 | − | 0.117507i | \(-0.962510\pi\) | ||||
0.993072 | − | 0.117507i | \(-0.0374903\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.194011 | −0.00736988 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 2.07785i | − 0.0787043i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.2733i | 0.653338i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.9746i | 1.28320i | 0.767038 | + | 0.641601i | \(0.221730\pi\) | ||||
−0.767038 | + | 0.641601i | \(0.778270\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.5963i | 0.701374i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.607181 | −0.0228354 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.3441i | 0.839151i | 0.907720 | + | 0.419576i | \(0.137821\pi\) | ||||
−0.907720 | + | 0.419576i | \(0.862179\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.50539 | 0.206468 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 13.6485i | − 0.511139i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.3718 | −0.611416 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.8427 | −0.665422 | −0.332711 | − | 0.943029i | \(-0.607963\pi\) | ||||
−0.332711 | + | 0.943029i | \(0.607963\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.143347 | −0.00533851 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.82654 | −0.253882 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.9148i | 0.886953i | 0.896286 | + | 0.443476i | \(0.146255\pi\) | ||||
−0.896286 | + | 0.443476i | \(0.853745\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.04642i | − 0.0387034i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.6789 | −0.579112 | −0.289556 | − | 0.957161i | \(-0.593508\pi\) | ||||
−0.289556 | + | 0.957161i | \(0.593508\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.5915i | 0.647992i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.3083i | 0.820622i | 0.911946 | + | 0.410311i | \(0.134580\pi\) | ||||
−0.911946 | + | 0.410311i | \(0.865420\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 36.6571i | − 1.34663i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.78057i | 0.358814i | 0.983775 | + | 0.179407i | \(0.0574180\pi\) | ||||
−0.983775 | + | 0.179407i | \(0.942582\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.20811 | −0.336907 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.840636i | 0.0307162i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.05399 | 0.293894 | 0.146947 | − | 0.989144i | \(-0.453055\pi\) | ||||
0.146947 | + | 0.989144i | \(0.453055\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 2.96969i | − 0.108221i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.4889 | 1.03545 | 0.517723 | − | 0.855549i | \(-0.326780\pi\) | ||||
0.517723 | + | 0.855549i | \(0.326780\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.97613 | −0.144324 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.5005 | −0.779393 | −0.389697 | − | 0.920943i | \(-0.627420\pi\) | ||||
−0.389697 | + | 0.920943i | \(0.627420\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.292482 | −0.0105886 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 66.8821i | − 2.41497i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.5596 | −0.849580 | −0.424790 | − | 0.905292i | \(-0.639652\pi\) | ||||
−0.424790 | + | 0.905292i | \(0.639652\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 5.03031i | − 0.181162i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.1655 | 1.12094 | 0.560472 | − | 0.828173i | \(-0.310620\pi\) | ||||
0.560472 | + | 0.828173i | \(0.310620\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.214558i | 0.00769722i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 56.4987i | − 2.02428i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.4227i | 0.981260i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 4.51516i | − 0.161359i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.07812 | 0.181015 | 0.0905077 | − | 0.995896i | \(-0.471151\pi\) | ||||
0.0905077 | + | 0.995896i | \(0.471151\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.70585i | 0.0963307i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.709168 | −0.0252151 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 62.8995i | − 2.23363i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.43418 | −0.0508012 | −0.0254006 | − | 0.999677i | \(-0.508086\pi\) | ||||
−0.0254006 | + | 0.999677i | \(0.508086\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.45943 | −0.0516309 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.9173 | −0.421076 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.1860 | 1.02995 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 22.3718i | − 0.787525i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.7153 | −0.833787 | −0.416894 | − | 0.908955i | \(-0.636881\pi\) | ||||
−0.416894 | + | 0.908955i | \(0.636881\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.8394i | 1.67987i | 0.542689 | + | 0.839933i | \(0.317406\pi\) | ||||
−0.542689 | + | 0.839933i | \(0.682594\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.869741 | 0.0305031 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 28.4532i | − 0.995451i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 0.422937i | − 0.0147786i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 51.9216i | − 1.81208i | −0.423195 | − | 0.906038i | \(-0.639092\pi\) | ||||
0.423195 | − | 0.906038i | \(-0.360908\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.8542i | 0.970937i | 0.874254 | + | 0.485469i | \(0.161351\pi\) | ||||
−0.874254 | + | 0.485469i | \(0.838649\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.9365 | −1.52782 | −0.763912 | − | 0.645321i | \(-0.776724\pi\) | ||||
−0.763912 | + | 0.645321i | \(0.776724\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 41.6898i | − 1.44795i | −0.689827 | − | 0.723974i | \(-0.742314\pi\) | ||||
0.689827 | − | 0.723974i | \(-0.257686\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.6733 | 0.994666 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.78978i | 0.0620121i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.29484 | −0.286712 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.4733 | −0.879437 | −0.439719 | − | 0.898136i | \(-0.644922\pi\) | ||||
−0.439719 | + | 0.898136i | \(0.644922\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.61336 | 0.297012 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.1429 | 0.521549 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.414324i | 0.0142363i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.23225 | −0.213890 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.39722i | 0.150735i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.5366 | −0.429245 | −0.214622 | − | 0.976697i | \(-0.568852\pi\) | ||||
−0.214622 | + | 0.976697i | \(0.568852\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.61409i | 0.0892956i | 0.999003 | + | 0.0446478i | \(0.0142166\pi\) | ||||
−0.999003 | + | 0.0446478i | \(0.985783\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.8438i | 1.08650i | 0.839573 | + | 0.543248i | \(0.182805\pi\) | ||||
−0.839573 | + | 0.543248i | \(0.817195\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 0.651862i | − 0.0222154i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 22.3335i | − 0.760241i | −0.924937 | − | 0.380121i | \(-0.875882\pi\) | ||||
0.924937 | − | 0.380121i | \(-0.124118\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.9345 | 0.575126 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.3037i | 0.451298i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.3488 | −1.29940 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 8.50539i | − 0.287864i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.4408 | 1.26429 | 0.632143 | − | 0.774852i | \(-0.282176\pi\) | ||||
0.632143 | + | 0.774852i | \(0.282176\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.5054 | 0.725359 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.1952 | 1.79219 | 0.896096 | − | 0.443860i | \(-0.146391\pi\) | ||||
0.896096 | + | 0.443860i | \(0.146391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.0907 | −1.21455 | −0.607274 | − | 0.794493i | \(-0.707737\pi\) | ||||
−0.607274 | + | 0.794493i | \(0.707737\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 43.3018i | 1.45393i | 0.686673 | + | 0.726966i | \(0.259070\pi\) | ||||
−0.686673 | + | 0.726966i | \(0.740930\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.698192 | 0.0234166 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.41649i | 0.0809555i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −39.6832 | −1.32795 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 8.66781i | − 0.289410i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.4525i | 1.24911i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2.95910i | − 0.0985820i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 0.328283i | − 0.0109246i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.75026 | −0.290548 | −0.145274 | − | 0.989391i | \(-0.546406\pi\) | ||||
−0.145274 | + | 0.989391i | \(0.546406\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.56270i | 0.250839i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.7438 | 0.455353 | 0.227676 | − | 0.973737i | \(-0.426887\pi\) | ||||
0.227676 | + | 0.973737i | \(0.426887\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 22.2513i | − 0.736411i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.866420 | −0.0286117 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.989347 | −0.0326355 | −0.0163178 | − | 0.999867i | \(-0.505194\pi\) | ||||
−0.0163178 | + | 0.999867i | \(0.505194\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.57706 | −0.117868 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −59.7803 | −1.96769 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.78544i | 0.0586416i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.49434 | 0.278690 | 0.139345 | − | 0.990244i | \(-0.455500\pi\) | ||||
0.139345 | + | 0.990244i | \(0.455500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 48.6656i | 1.59495i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.49461 | 0.0816699 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.6912i | 0.610615i | 0.952254 | + | 0.305308i | \(0.0987593\pi\) | ||||
−0.952254 | + | 0.305308i | \(0.901241\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.57246i | 0.312386i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 3.03170i | − 0.0988305i | −0.998778 | − | 0.0494152i | \(-0.984264\pi\) | ||||
0.998778 | − | 0.0494152i | \(-0.0157358\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 13.3595i | − 0.435045i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.8327 | 0.546990 | 0.273495 | − | 0.961873i | \(-0.411820\pi\) | ||||
0.273495 | + | 0.961873i | \(0.411820\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 63.6243i | 2.06533i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.16702 | −0.102698 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 1.73948i | − 0.0563473i | −0.999603 | − | 0.0281737i | \(-0.991031\pi\) | ||||
0.999603 | − | 0.0281737i | \(-0.00896914\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.9108 | 0.352697 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.926677 | 0.0299240 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.8044 | 1.21950 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.4705 | 0.337406 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.3399i | 0.557615i | 0.960347 | + | 0.278808i | \(0.0899392\pi\) | ||||
−0.960347 | + | 0.278808i | \(0.910061\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.78084 | −0.0572089 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.4054i | 1.45713i | 0.684977 | + | 0.728565i | \(0.259812\pi\) | ||||
−0.684977 | + | 0.728565i | \(0.740188\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.0172261 | −0.000552243 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.4336i | 1.38957i | 0.719220 | + | 0.694783i | \(0.244499\pi\) | ||||
−0.719220 | + | 0.694783i | \(0.755501\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 28.7980i | − 0.920388i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.64298i | 0.116311i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 47.4465i | − 1.51331i | −0.653815 | − | 0.756655i | \(-0.726832\pi\) | ||||
0.653815 | − | 0.756655i | \(-0.273168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.457851 | −0.0145735 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 6.72794i | − 0.213936i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.8434 | 0.916242 | 0.458121 | − | 0.888890i | \(-0.348523\pi\) | ||||
0.458121 | + | 0.888890i | \(0.348523\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.5118i | 0.523987i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.1449 | 1.04971 | 0.524855 | − | 0.851192i | \(-0.324119\pi\) | ||||
0.524855 | + | 0.851192i | \(0.324119\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.67241 | 0.0845513 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))