Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(769,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1280.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.c (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: | \(10.2208514587\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 640) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.1 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.769 |
Dual form | 1280.2.c.m.769.4 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 2.44949i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | − | 2.00000i | 0.447214 | − | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44949i | 0.925820i | 0.886405 | + | 0.462910i | \(0.153195\pi\) | ||||
−0.886405 | + | 0.462910i | \(0.846805\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.89898 | 1.47710 | 0.738549 | − | 0.674200i | \(-0.235511\pi\) | ||||
0.738549 | + | 0.674200i | \(0.235511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.89898 | − | 2.44949i | −1.26491 | − | 0.632456i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.00000i | − | 0.970143i | −0.874475 | − | 0.485071i | \(-0.838794\pi\) | ||
0.874475 | − | 0.485071i | \(-0.161206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.89898 | 1.12390 | 0.561951 | − | 0.827170i | \(-0.310051\pi\) | ||||
0.561951 | + | 0.827170i | \(0.310051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.00000 | 1.30931 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.44949i | − | 0.510754i | −0.966842 | − | 0.255377i | \(-0.917800\pi\) | ||
0.966842 | − | 0.255377i | \(-0.0821996\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.00000 | −1.48556 | −0.742781 | − | 0.669534i | \(-0.766494\pi\) | ||||
−0.742781 | + | 0.669534i | \(0.766494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.79796 | 1.75977 | 0.879883 | − | 0.475191i | \(-0.157621\pi\) | ||||
0.879883 | + | 0.475191i | \(0.157621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 12.0000i | − | 2.08893i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.89898 | + | 2.44949i | 0.828079 | + | 0.414039i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.00000 | −1.24939 | −0.624695 | − | 0.780869i | \(-0.714777\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.34847i | − | 1.12063i | −0.828279 | − | 0.560316i | \(-0.810680\pi\) | ||
0.828279 | − | 0.560316i | \(-0.189320\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | + | 6.00000i | −0.447214 | + | 0.894427i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.2474i | 1.78647i | 0.449586 | + | 0.893237i | \(0.351571\pi\) | ||||
−0.449586 | + | 0.893237i | \(0.648429\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.79796 | −1.37199 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.00000i | 1.09888i | 0.835532 | + | 0.549442i | \(0.185160\pi\) | ||||
−0.835532 | + | 0.549442i | \(0.814840\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.89898 | − | 9.79796i | 0.660578 | − | 1.32116i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 12.0000i | − | 1.58944i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.89898 | −0.637793 | −0.318896 | − | 0.947790i | \(-0.603312\pi\) | ||||
−0.318896 | + | 0.947790i | \(0.603312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 7.34847i | − | 0.925820i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.44949i | 0.299253i | 0.988743 | + | 0.149626i | \(0.0478071\pi\) | ||||
−0.988743 | + | 0.149626i | \(0.952193\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.79796 | −1.16280 | −0.581402 | − | 0.813617i | \(-0.697496\pi\) | ||||
−0.581402 | + | 0.813617i | \(0.697496\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.79796 | + | 7.34847i | −1.13137 | + | 0.848528i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.0000i | 1.36753i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.79796 | −1.10236 | −0.551178 | − | 0.834388i | \(-0.685822\pi\) | ||||
−0.551178 | + | 0.834388i | \(0.685822\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.44949i | 0.268866i | 0.990923 | + | 0.134433i | \(0.0429214\pi\) | ||||
−0.990923 | + | 0.134433i | \(0.957079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | − | 4.00000i | −0.867722 | − | 0.433861i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19.5959i | 2.10090i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 24.0000i | − | 2.48868i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.89898 | − | 9.79796i | 0.502625 | − | 1.00525i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.00000i | 0.406138i | 0.979164 | + | 0.203069i | \(0.0650917\pi\) | ||||
−0.979164 | + | 0.203069i | \(0.934908\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.6969 | −1.47710 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.00000 | 0.796030 | 0.398015 | − | 0.917379i | \(-0.369699\pi\) | ||||
0.398015 | + | 0.917379i | \(0.369699\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.44949i | − | 0.241355i | −0.992692 | − | 0.120678i | \(-0.961493\pi\) | ||
0.992692 | − | 0.120678i | \(-0.0385068\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.00000 | − | 12.0000i | 0.585540 | − | 1.17108i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.34847i | 0.710403i | 0.934790 | + | 0.355202i | \(0.115588\pi\) | ||||
−0.934790 | + | 0.355202i | \(0.884412\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.79796 | −0.929981 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 16.0000i | − | 1.50515i | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||
0.658505 | − | 0.752577i | \(-0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.89898 | − | 2.44949i | −0.456832 | − | 0.228416i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.79796 | 0.898177 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 19.5959i | 1.76690i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0000 | + | 2.00000i | −0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.34847i | 0.652071i | 0.945357 | + | 0.326036i | \(0.105713\pi\) | ||||
−0.945357 | + | 0.326036i | \(0.894287\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.0000 | −1.58481 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.89898 | 0.428026 | 0.214013 | − | 0.976831i | \(-0.431347\pi\) | ||||
0.214013 | + | 0.976831i | \(0.431347\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000i | 1.04053i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.00000i | − | 0.683486i | −0.939793 | − | 0.341743i | \(-0.888983\pi\) | ||
0.939793 | − | 0.341743i | \(-0.111017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.89898 | 0.415526 | 0.207763 | − | 0.978179i | \(-0.433382\pi\) | ||||
0.207763 | + | 0.978179i | \(0.433382\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 30.0000 | 2.52646 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.00000 | + | 16.0000i | −0.664364 | + | 1.32873i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 2.44949i | − | 0.202031i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.00000 | −0.163846 | −0.0819232 | − | 0.996639i | \(-0.526106\pi\) | ||||
−0.0819232 | + | 0.996639i | \(0.526106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.0000i | 0.970143i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.79796 | − | 19.5959i | 0.786991 | − | 1.57398i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 20.0000i | − | 1.59617i | −0.602542 | − | 0.798087i | \(-0.705846\pi\) | ||
0.602542 | − | 0.798087i | \(-0.294154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.5959 | 1.55406 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.44949i | − | 0.191859i | −0.995388 | − | 0.0959294i | \(-0.969418\pi\) | ||
0.995388 | − | 0.0959294i | \(-0.0305823\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −24.0000 | − | 12.0000i | −1.86840 | − | 0.934199i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.44949i | − | 0.189547i | −0.995499 | − | 0.0947736i | \(-0.969787\pi\) | ||
0.995499 | − | 0.0947736i | \(-0.0302127\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.6969 | −1.12390 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.00000i | 0.304114i | 0.988372 | + | 0.152057i | \(0.0485898\pi\) | ||||
−0.988372 | + | 0.152057i | \(0.951410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.79796 | − | 7.34847i | 0.740656 | − | 0.555492i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0000i | 0.901975i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.6969 | 1.09850 | 0.549250 | − | 0.835658i | \(-0.314913\pi\) | ||||
0.549250 | + | 0.835658i | \(0.314913\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 14.6969i | − | 1.08643i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.00000 | − | 4.00000i | −0.588172 | − | 0.294086i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 19.5959i | − | 1.43300i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.5959 | −1.41791 | −0.708955 | − | 0.705253i | \(-0.750833\pi\) | ||||
−0.708955 | + | 0.705253i | \(0.750833\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.0000i | 0.863779i | 0.901927 | + | 0.431889i | \(0.142153\pi\) | ||||
−0.901927 | + | 0.431889i | \(0.857847\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.00000i | − | 0.569976i | −0.958531 | − | 0.284988i | \(-0.908010\pi\) | ||
0.958531 | − | 0.284988i | \(-0.0919897\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.79796 | −0.694559 | −0.347279 | − | 0.937762i | \(-0.612894\pi\) | ||||
−0.347279 | + | 0.937762i | \(0.612894\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.00000 | 0.423207 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 19.5959i | − | 1.37536i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.00000 | + | 16.0000i | −0.558744 | + | 1.11749i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.34847i | 0.510754i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.0000 | 1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.4949 | 1.68630 | 0.843149 | − | 0.537680i | \(-0.180699\pi\) | ||||
0.843149 | + | 0.537680i | \(0.180699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.0000i | 1.64445i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.6969 | − | 7.34847i | −1.00232 | − | 0.501161i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.0000i | 1.62923i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.79796 | 0.662085 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.34847i | 0.492090i | 0.969258 | + | 0.246045i | \(0.0791311\pi\) | ||||
−0.969258 | + | 0.246045i | \(0.920869\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.00000 | + | 12.0000i | 0.600000 | + | 0.800000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 2.44949i | − | 0.162578i | −0.996691 | − | 0.0812892i | \(-0.974096\pi\) | ||
0.996691 | − | 0.0812892i | \(-0.0259037\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.00000 | −0.528655 | −0.264327 | − | 0.964433i | \(-0.585150\pi\) | ||||
−0.264327 | + | 0.964433i | \(0.585150\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 29.3939 | 1.93398 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.0000i | 1.31024i | 0.755523 | + | 0.655122i | \(0.227383\pi\) | ||||
−0.755523 | + | 0.655122i | \(0.772617\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.4949 | + | 12.2474i | 1.59787 | + | 0.798935i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 24.0000i | 1.55897i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.79796 | 0.633777 | 0.316889 | − | 0.948463i | \(-0.397362\pi\) | ||||
0.316889 | + | 0.948463i | \(0.397362\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.0454i | 1.41421i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | − | 2.00000i | 0.0638877 | − | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.89898 | 0.309221 | 0.154610 | − | 0.987976i | \(-0.450588\pi\) | ||||
0.154610 | + | 0.987976i | \(0.450588\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 12.0000i | − | 0.754434i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.79796 | + | 19.5959i | −0.613572 | + | 1.22714i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.00000i | 0.499026i | 0.968371 | + | 0.249513i | \(0.0802706\pi\) | ||||
−0.968371 | + | 0.249513i | \(0.919729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.79796 | 0.608816 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24.0000 | 1.48556 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.0454i | 1.35938i | 0.733500 | + | 0.679689i | \(0.237885\pi\) | ||||
−0.733500 | + | 0.679689i | \(0.762115\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.0000 | + | 8.00000i | 0.982872 | + | 0.491436i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.89898i | 0.299813i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.0000 | −1.58525 | −0.792624 | − | 0.609711i | \(-0.791286\pi\) | ||||
−0.792624 | + | 0.609711i | \(0.791286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.79796 | 0.595184 | 0.297592 | − | 0.954693i | \(-0.403817\pi\) | ||||
0.297592 | + | 0.954693i | \(0.403817\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.6969 | − | 19.5959i | −0.886259 | − | 1.18168i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0000i | 0.721010i | 0.932757 | + | 0.360505i | \(0.117396\pi\) | ||||
−0.932757 | + | 0.360505i | \(0.882604\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −29.3939 | −1.75977 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.0000 | −0.954480 | −0.477240 | − | 0.878773i | \(-0.658363\pi\) | ||||
−0.477240 | + | 0.878773i | \(0.658363\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.9444i | 1.60168i | 0.598880 | + | 0.800839i | \(0.295613\pi\) | ||||
−0.598880 | + | 0.800839i | \(0.704387\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −24.0000 | − | 12.0000i | −1.42164 | − | 0.710819i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 19.5959i | − | 1.15671i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.79796 | 0.574367 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 20.0000i | − | 1.16841i | −0.811605 | − | 0.584206i | \(-0.801406\pi\) | ||
0.811605 | − | 0.584206i | \(-0.198594\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.89898 | + | 9.79796i | −0.285230 | + | 0.570459i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.0000 | 1.03750 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 19.5959i | − | 1.12576i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00000 | − | 12.0000i | 0.343559 | − | 0.687118i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.1464i | − | 0.978598i | −0.872116 | − | 0.489299i | \(-0.837253\pi\) | ||
0.872116 | − | 0.489299i | \(-0.162747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.00000 | −0.341328 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.5959 | 1.11118 | 0.555591 | − | 0.831456i | \(-0.312492\pi\) | ||||
0.555591 | + | 0.831456i | \(0.312492\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.0000i | 1.35656i | 0.734803 | + | 0.678280i | \(0.237274\pi\) | ||||
−0.734803 | + | 0.678280i | \(0.762726\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.6969 | − | 7.34847i | −0.828079 | − | 0.414039i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.00000i | 0.449325i | 0.974437 | + | 0.224662i | \(0.0721279\pi\) | ||||
−0.974437 | + | 0.224662i | \(0.927872\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −39.1918 | −2.19432 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0000 | 1.00466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 19.5959i | − | 1.09035i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 24.4949i | − | 1.35457i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −30.0000 | −1.65395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.89898 | −0.269272 | −0.134636 | − | 0.990895i | \(-0.542987\pi\) | ||||
−0.134636 | + | 0.990895i | \(0.542987\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.0000i | 0.657596i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.89898 | + | 2.44949i | 0.267660 | + | 0.133830i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0000i | 0.871576i | 0.900049 | + | 0.435788i | \(0.143530\pi\) | ||||
−0.900049 | + | 0.435788i | \(0.856470\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −39.1918 | −2.12861 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 48.0000 | 2.59935 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5959i | 1.05808i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.00000 | + | 12.0000i | −0.323029 | + | 0.646058i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.2474i | 0.657477i | 0.944421 | + | 0.328739i | \(0.106624\pi\) | ||||
−0.944421 | + | 0.328739i | \(0.893376\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.0000 | −1.28469 | −0.642345 | − | 0.766415i | \(-0.722038\pi\) | ||||
−0.642345 | + | 0.766415i | \(0.722038\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 8.00000i | − | 0.425797i | −0.977074 | − | 0.212899i | \(-0.931710\pi\) | ||
0.977074 | − | 0.212899i | \(-0.0682904\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.79796 | + | 19.5959i | −0.520022 | + | 1.04004i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 24.0000i | − | 1.27021i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.5959 | 1.03423 | 0.517116 | − | 0.855915i | \(-0.327005\pi\) | ||||
0.517116 | + | 0.855915i | \(0.327005\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.00000 | 0.263158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 31.8434i | − | 1.67134i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.00000 | + | 4.00000i | 0.418739 | + | 0.209370i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 31.8434i | − | 1.66221i | −0.556115 | − | 0.831105i | \(-0.687709\pi\) | ||
0.556115 | − | 0.831105i | \(-0.312291\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 24.0000 | 1.24939 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.5959 | −1.01737 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 20.0000i | − | 1.03556i | −0.855514 | − | 0.517780i | \(-0.826758\pi\) | ||
0.855514 | − | 0.517780i | \(-0.173242\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.89898 | + | 26.9444i | 0.252982 | + | 1.39140i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.6969 | −0.754931 | −0.377466 | − | 0.926024i | \(-0.623204\pi\) | ||||
−0.377466 | + | 0.926024i | \(0.623204\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.0000 | 0.922168 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.9444i | 1.37679i | 0.725334 | + | 0.688397i | \(0.241685\pi\) | ||||
−0.725334 | + | 0.688397i | \(0.758315\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 24.0000 | + | 12.0000i | 1.22315 | + | 0.611577i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.0454i | 1.12063i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.00000 | −0.101404 | −0.0507020 | − | 0.998714i | \(-0.516146\pi\) | ||||
−0.0507020 | + | 0.998714i | \(0.516146\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.79796 | −0.495504 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 12.0000i | − | 0.605320i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.79796 | + | 19.5959i | −0.492989 | + | 0.985978i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 8.00000i | − | 0.401508i | −0.979642 | − | 0.200754i | \(-0.935661\pi\) | ||
0.979642 | − | 0.200754i | \(-0.0643393\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 29.3939 | 1.47153 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.0000 | 0.499376 | 0.249688 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249688 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.00000 | + | 18.0000i | −0.447214 | + | 0.894427i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 19.5959i | − | 0.971334i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.0000 | 1.18672 | 0.593362 | − | 0.804936i | \(-0.297800\pi\) | ||||
0.593362 | + | 0.804936i | \(0.297800\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.5959 | −0.966595 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 12.0000i | − | 0.590481i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.89898 | + | 2.44949i | 0.240481 | + | 0.120241i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 12.0000i | − | 0.587643i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.6969 | 0.717992 | 0.358996 | − | 0.933339i | \(-0.383119\pi\) | ||||
0.358996 | + | 0.933339i | \(0.383119\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 36.7423i | − | 1.78647i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.0000 | + | 12.0000i | −0.776114 | + | 0.582086i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.6969i | 0.711235i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.3939 | 1.41585 | 0.707927 | − | 0.706286i | \(-0.249631\pi\) | ||||
0.707927 | + | 0.706286i | \(0.249631\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.0000i | 1.73005i | 0.501729 | + | 0.865025i | \(0.332697\pi\) | ||||
−0.501729 | + | 0.865025i | \(0.667303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 39.1918 | + | 19.5959i | 1.87910 | + | 0.939552i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 12.0000i | − | 0.574038i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.5959 | 0.935262 | 0.467631 | − | 0.883924i | \(-0.345108\pi\) | ||||
0.467631 | + | 0.883924i | \(0.345108\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.9444i | 1.28017i | 0.768306 | + | 0.640083i | \(0.221100\pi\) | ||||
−0.768306 | + | 0.640083i | \(0.778900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.00000 | + | 4.00000i | −0.0948091 | + | 0.189618i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.89898i | 0.231714i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.0000 | −1.51017 | −0.755087 | − | 0.655625i | \(-0.772405\pi\) | ||||
−0.755087 | + | 0.655625i | \(0.772405\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −39.1918 | −1.84547 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.0000i | 1.49690i | 0.663193 | + | 0.748448i | \(0.269201\pi\) | ||||
−0.663193 | + | 0.748448i | \(0.730799\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.00000 | 0.372597 | 0.186299 | − | 0.982493i | \(-0.440351\pi\) | ||||
0.186299 | + | 0.982493i | \(0.440351\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.8434i | 1.47989i | 0.672669 | + | 0.739943i | \(0.265148\pi\) | ||||
−0.672669 | + | 0.739943i | \(0.734852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −48.0000 | − | 24.0000i | −2.22595 | − | 1.11297i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.7423i | 1.70023i | 0.526595 | + | 0.850117i | \(0.323469\pi\) | ||||
−0.526595 | + | 0.850117i | \(0.676531\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.00000 | −0.277054 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −48.9898 | −2.25733 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 36.0000i | − | 1.65528i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.6969 | − | 19.5959i | −0.674342 | − | 0.899122i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 24.0000i | − | 1.09888i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.5959 | −0.895360 | −0.447680 | − | 0.894194i | \(-0.647750\pi\) | ||||
−0.447680 | + | 0.894194i | \(0.647750\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 14.6969i | − | 0.668734i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.00000 | + | 4.00000i | 0.363261 | + | 0.181631i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17.1464i | − | 0.776979i | −0.921453 | − | 0.388489i | \(-0.872997\pi\) | ||
0.921453 | − | 0.388489i | \(-0.127003\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.00000 | −0.271329 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.6969 | 0.663264 | 0.331632 | − | 0.943409i | \(-0.392401\pi\) | ||||
0.331632 | + | 0.943409i | \(0.392401\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.0000i | 1.44121i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.6969 | + | 29.3939i | −0.660578 | + | 1.32116i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 24.0000i | − | 1.07655i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.89898 | −0.219308 | −0.109654 | − | 0.993970i | \(-0.534974\pi\) | ||||
−0.109654 | + | 0.993970i | \(0.534974\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | −0.268060 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.1464i | 0.764521i | 0.924055 | + | 0.382261i | \(0.124854\pi\) | ||||
−0.924055 | + | 0.382261i | \(0.875146\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.00000 | − | 16.0000i | 0.355995 | − | 0.711991i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 31.8434i | − | 1.41421i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.00000 | −0.354594 | −0.177297 | − | 0.984157i | \(-0.556735\pi\) | ||||
−0.177297 | + | 0.984157i | \(0.556735\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.79796 | −0.433436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.89898 | − | 2.44949i | −0.215875 | − | 0.107937i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 60.0000i | 2.63880i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.79796 | 0.430083 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.0000 | 0.963837 | 0.481919 | − | 0.876216i | \(-0.339940\pi\) | ||||
0.481919 | + | 0.876216i | \(0.339940\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 31.8434i | − | 1.39241i | −0.717841 | − | 0.696207i | \(-0.754870\pi\) | ||
0.717841 | − | 0.696207i | \(-0.245130\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.0000 | − | 24.0000i | −0.785584 | − | 1.04745i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 39.1918i | − | 1.70722i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.0000 | 0.739130 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.6969 | 0.637793 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.6969 | + | 7.34847i | 0.635404 | + | 0.317702i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 36.0000i | − | 1.55351i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.89898 | 0.211014 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | 0.343947 | 0.171973 | − | 0.985102i | \(-0.444986\pi\) | ||||
0.171973 | + | 0.985102i | \(0.444986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 19.5959i | − | 0.840941i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.0000 | − | 20.0000i | 0.428353 | − | 0.856706i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 22.0454i | − | 0.942594i | −0.881975 | − | 0.471297i | \(-0.843786\pi\) | ||
0.881975 | − | 0.471297i | \(-0.156214\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.0000 | −0.768221 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.1918 | −1.66963 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 24.0000i | − | 1.02058i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.79796 | + | 19.5959i | −0.415900 | + | 0.831800i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 4.00000i | − | 0.169485i | −0.996403 | − | 0.0847427i | \(-0.972993\pi\) | ||
0.996403 | − | 0.0847427i | \(-0.0270068\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −48.0000 | −2.02656 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 2.44949i | − | 0.103234i | −0.998667 | − | 0.0516168i | \(-0.983563\pi\) | ||
0.998667 | − | 0.0516168i | \(-0.0164375\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.0000 | − | 16.0000i | −1.34625 | − | 0.673125i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 22.0454i | − | 0.925820i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.00000 | 0.335377 | 0.167689 | − | 0.985840i | \(-0.446370\pi\) | ||||
0.167689 | + | 0.985840i | \(0.446370\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.0908 | 1.84514 | 0.922572 | − | 0.385826i | \(-0.126083\pi\) | ||||
0.922572 | + | 0.385826i | \(0.126083\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 48.0000i | 2.00523i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.79796 | + | 7.34847i | −0.408603 | + | 0.306452i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 24.0000i | − | 0.999133i | −0.866276 | − | 0.499567i | \(-0.833493\pi\) | ||
0.866276 | − | 0.499567i | \(-0.166507\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.3939 | 1.22157 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00000 | −0.248922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 39.1918i | 1.62316i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.2474i | 0.505506i | 0.967531 | + | 0.252753i | \(0.0813361\pi\) | ||||
−0.967531 | + | 0.252753i | \(0.918664\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 48.0000 | 1.97781 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.5959 | −0.806068 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 8.00000i | − | 0.328521i | −0.986417 | − | 0.164260i | \(-0.947476\pi\) | ||
0.986417 | − | 0.164260i | \(-0.0525237\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.79796 | − | 19.5959i | 0.401677 | − | 0.803354i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.0000i | 0.982255i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.79796 | 0.400334 | 0.200167 | − | 0.979762i | \(-0.435852\pi\) | ||||
0.200167 | + | 0.979762i | \(0.435852\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.0000 | −0.652654 | −0.326327 | − | 0.945257i | \(-0.605811\pi\) | ||||
−0.326327 | + | 0.945257i | \(0.605811\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 7.34847i | − | 0.299253i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.0000 | − | 26.0000i | 0.528525 | − | 1.05705i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.34847i | − | 0.298265i | −0.988817 | − | 0.149133i | \(-0.952352\pi\) | ||
0.988817 | − | 0.149133i | \(-0.0476481\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −48.0000 | −1.94506 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 16.0000i | − | 0.646234i | −0.946359 | − | 0.323117i | \(-0.895269\pi\) | ||
0.946359 | − | 0.323117i | \(-0.104731\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 39.1918 | + | 19.5959i | 1.58037 | + | 0.790184i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 28.0000i | − | 1.12724i | −0.826035 | − | 0.563619i | \(-0.809409\pi\) | ||
0.826035 | − | 0.563619i | \(-0.190591\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.4949 | −0.984533 | −0.492267 | − | 0.870445i | \(-0.663831\pi\) | ||||
−0.492267 | + | 0.870445i | \(0.663831\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 4.89898i | − | 0.196273i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 58.7878i | − | 2.34776i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 60.0000i | − | 2.38479i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.6969 | + | 7.34847i | 0.583230 | + | 0.291615i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.3939 | 1.16280 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.0000 | −0.631962 | −0.315981 | − | 0.948766i | \(-0.602334\pi\) | ||||
−0.315981 | + | 0.948766i | \(0.602334\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.44949i | 0.0965984i | 0.998833 | + | 0.0482992i | \(0.0153801\pi\) | ||||
−0.998833 | + | 0.0482992i | \(0.984620\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.0000 | + | 36.0000i | −0.708749 | + | 1.41750i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.0454i | 0.866694i | 0.901227 | + | 0.433347i | \(0.142668\pi\) | ||||
−0.901227 | + | 0.433347i | \(0.857332\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 58.7878 | 2.30407 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 16.0000i | − | 0.626128i | −0.949732 | − | 0.313064i | \(-0.898644\pi\) | ||
0.949732 | − | 0.313064i | \(-0.101356\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.89898 | − | 9.79796i | 0.191419 | − | 0.382838i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 12.0000i | − | 0.468165i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.6969 | 0.572511 | 0.286256 | − | 0.958153i | \(-0.407589\pi\) | ||||
0.286256 | + | 0.958153i | \(0.407589\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.0000 | −1.16686 | −0.583432 | − | 0.812162i | \(-0.698291\pi\) | ||||
−0.583432 | + | 0.812162i | \(0.698291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.0000 | + | 12.0000i | 0.930680 | + | 0.465340i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.5959i | 0.758757i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.0000 | 0.695920 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.3939 | 1.13474 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.0000i | 1.38770i | 0.720121 | + | 0.693849i | \(0.244086\pi\) | ||||
−0.720121 | + | 0.693849i | \(0.755914\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 32.0000i | − | 1.22986i | −0.788582 | − | 0.614930i | \(-0.789184\pi\) | ||
0.788582 | − | 0.614930i | \(-0.210816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.79796 | −0.376011 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.00000 | −0.229920 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 7.34847i | − | 0.281181i | −0.990068 | − | 0.140591i | \(-0.955100\pi\) | ||
0.990068 | − | 0.140591i | \(-0.0449002\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.0000 | − | 8.00000i | −0.611329 | − | 0.305664i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.5959i | 0.747631i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.6969 | −0.559098 | −0.279549 | − | 0.960131i | \(-0.590185\pi\) | ||||
−0.279549 | + | 0.960131i | \(0.590185\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 36.0000i | − | 1.36753i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.89898 | − | 9.79796i | 0.185829 | − | 0.371658i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.0000i | 1.21209i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 48.9898 | 1.85296 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0000 | 0.982006 | 0.491003 | − | 0.871158i | \(-0.336630\pi\) | ||||
0.491003 | + | 0.871158i | \(0.336630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 19.5959i | − | 0.739074i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 30.0000 | − | 60.0000i | 1.12987 | − | 2.25973i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.5959i | 0.736980i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.0000 | 1.50223 | 0.751116 | − | 0.660171i | \(-0.229516\pi\) | ||||
0.751116 | + | 0.660171i | \(0.229516\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.3939 | 1.10236 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 24.0000i | − | 0.898807i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 24.0000i | − | 0.896296i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −48.9898 | −1.82701 | −0.913506 | − | 0.406826i | \(-0.866635\pi\) | ||||
−0.913506 | + | 0.406826i | \(0.866635\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | 0.223452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.0000 | + | 32.0000i | 0.891338 | + | 1.18845i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 36.7423i | − | 1.36270i | −0.731959 | − | 0.681349i | \(-0.761394\pi\) | ||
0.731959 | − | 0.681349i | \(-0.238606\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.3939 | −1.08717 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0000i | 0.443230i | 0.975134 | + | 0.221615i | \(0.0711328\pi\) | ||||
−0.975134 | + | 0.221615i | \(0.928867\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.89898 | − | 2.44949i | −0.180702 | − | 0.0903508i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.0000i | 0.442026i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.6969 | 0.540636 | 0.270318 | − | 0.962771i | \(-0.412871\pi\) | ||||
0.270318 | + | 0.962771i | \(0.412871\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 17.1464i | − | 0.629041i | −0.949251 | − | 0.314521i | \(-0.898156\pi\) | ||
0.949251 | − | 0.314521i | \(-0.101844\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00000 | + | 4.00000i | −0.0732743 | + | 0.146549i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 7.34847i | − | 0.268866i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.0000 | −0.657706 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 12.0000i | − | 0.437304i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 12.0000i | − | 0.436147i | −0.975932 | − | 0.218074i | \(-0.930023\pi\) | ||
0.975932 | − | 0.218074i | \(-0.0699773\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −29.3939 | −1.06693 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.0000 | −0.797499 | −0.398750 | − | 0.917060i | \(-0.630556\pi\) | ||||
−0.398750 | + | 0.917060i | \(0.630556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.4949i | 0.886775i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 24.0000 | + | 12.0000i | 0.867722 | + | 0.433861i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.0000 | −0.937584 | −0.468792 | − | 0.883309i | \(-0.655311\pi\) | ||||
−0.468792 | + | 0.883309i | \(0.655311\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.5959 | 0.705730 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.00000i | 0.287740i | 0.989597 | + | 0.143870i | \(0.0459547\pi\) | ||||
−0.989597 | + | 0.143870i | \(0.954045\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.3939 | − | 39.1918i | −1.05586 | − | 1.40781i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 24.0000i | − | 0.860995i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −39.1918 | −1.40419 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −48.0000 | −1.71758 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −40.0000 | − | 20.0000i | −1.42766 | − | 0.713831i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.6413i | 1.48435i | 0.670205 | + | 0.742176i | \(0.266206\pi\) | ||||
−0.670205 | + | 0.742176i | \(0.733794\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 54.0000 | 1.92245 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.1918 | 1.39350 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.5959 | − | 39.1918i | 0.694996 | − | 1.38999i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.00000i | 0.283375i | 0.989911 | + | 0.141687i | \(0.0452527\pi\) | ||||
−0.989911 | + | 0.141687i | \(0.954747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.9898 | 1.73313 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.5959i | 0.691525i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.00000 | − | 12.0000i | 0.211472 | − | 0.422944i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 63.6867i | 2.24188i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.0000 | −0.351581 | −0.175791 | − | 0.984428i | \(-0.556248\pi\) | ||||
−0.175791 | + | 0.984428i | \(0.556248\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −53.8888 | −1.89229 | −0.946145 | − | 0.323742i | \(-0.895059\pi\) | ||||
−0.946145 | + | 0.323742i | \(0.895059\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 24.0000i | − | 0.841717i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.89898 | − | 2.44949i | −0.171604 | − | 0.0858019i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 36.0000i | − | 1.25948i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.0000 | −0.488603 | −0.244302 | − | 0.969699i | \(-0.578559\pi\) | ||||
−0.244302 | + | 0.969699i | \(0.578559\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 22.0454i | − | 0.768455i | −0.923239 | − | 0.384227i | \(-0.874468\pi\) | ||
0.923239 | − | 0.384227i | \(-0.125532\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −48.0000 | + | 36.0000i | −1.67115 | + | 1.25336i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 46.5403i | − | 1.61836i | −0.587557 | − | 0.809182i | \(-0.699910\pi\) | ||
0.587557 | − | 0.809182i | \(-0.300090\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.0000 | 0.764092 | 0.382046 | − | 0.924143i | \(-0.375220\pi\) | ||||
0.382046 | + | 0.924143i | \(0.375220\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.3939 | 1.01966 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 4.00000i | − | 0.138592i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.89898 | − | 2.44949i | −0.169536 | − | 0.0847681i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.1918 | −1.35305 | −0.676526 | − | 0.736419i | \(-0.736515\pi\) | ||||
−0.676526 | + | 0.736419i | \(0.736515\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 39.1918i | 1.34984i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.0000 | − | 26.0000i | 0.447214 | − | 0.894427i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.8434i | 1.09415i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 66.0000 | 2.26511 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.79796 | −0.335870 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 32.0000i | − | 1.09566i | −0.836590 | − | 0.547830i | \(-0.815454\pi\) | ||
0.836590 | − | 0.547830i | \(-0.184546\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.6969 | + | 29.3939i | −0.502625 | + | 1.00525i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 32.0000i | − | 1.09310i | −0.837427 | − | 0.546550i | \(-0.815941\pi\) | ||
0.837427 | − | 0.546550i | \(-0.184059\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.4949 | −0.835755 | −0.417878 | − | 0.908503i | \(-0.637226\pi\) | ||||
−0.417878 | + | 0.908503i | \(0.637226\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −48.0000 | −1.63584 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 51.4393i | 1.75101i | 0.483206 | + | 0.875507i | \(0.339472\pi\) | ||||
−0.483206 | + | 0.875507i | \(0.660528\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.00000 | + | 4.00000i | 0.272008 | + | 0.136004i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 2.44949i | − | 0.0831890i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.0000 | −1.62829 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 12.0000i | − | 0.406138i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.89898 | − | 26.9444i | −0.165616 | − | 0.910887i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 28.0000i | − | 0.945493i | −0.881199 | − | 0.472746i | \(-0.843263\pi\) | ||
0.881199 | − | 0.472746i | \(-0.156737\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −48.9898 | −1.65238 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.00000 | −0.269527 | −0.134763 | − | 0.990878i | \(-0.543027\pi\) | ||||
−0.134763 | + | 0.990878i | \(0.543027\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.7423i | 1.23648i | 0.785990 | + | 0.618239i | \(0.212154\pi\) | ||||
−0.785990 | + | 0.618239i | \(0.787846\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24.0000 | + | 12.0000i | 0.806751 | + | 0.403376i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.44949i | 0.0822458i | 0.999154 | + | 0.0411229i | \(0.0130935\pi\) | ||||
−0.999154 | + | 0.0411229i | \(0.986906\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.0000 | −0.603701 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −44.0908 | −1.47710 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 60.0000i | 2.00782i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.6969 | − | 29.3939i | 0.491264 | − | 0.982529i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −78.3837 | −2.61424 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.0000 | 1.06607 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 44.0908i | − | 1.46725i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.00000 | − | 16.0000i | 0.265929 | − | 0.531858i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 12.2474i | − | 0.406670i | −0.979109 | − | 0.203335i | \(-0.934822\pi\) | ||
0.979109 | − | 0.203335i | \(-0.0651780\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.0000 | −0.796030 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.3939 | −0.973863 | −0.486931 | − | 0.873440i | \(-0.661884\pi\) | ||||
−0.486931 | + | 0.873440i | \(0.661884\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000i | 0.397142i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −29.3939 | − | 14.6969i | −0.971732 | − | 0.485866i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.0000i | 0.396275i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.9898 | 1.61602 | 0.808012 | − | 0.589166i | \(-0.200544\pi\) | ||||
0.808012 | + | 0.589166i | \(0.200544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −42.0000 | −1.38395 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.0000 | + | 12.0000i | −0.526077 | + | 0.394558i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.34847i | 0.241355i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.0000 | −0.524943 | −0.262471 | − | 0.964940i | \(-0.584538\pi\) | ||||
−0.262471 | + | 0.964940i | \(0.584538\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.89898 | 0.160558 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 48.0000i | − | 1.57145i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −39.1918 | − | 19.5959i | −1.28171 | − | 0.640855i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 60.0000i | 1.96011i | 0.198715 | + | 0.980057i | \(0.436323\pi\) | ||||
−0.198715 | + | 0.980057i | \(0.563677\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 58.7878 | 1.91847 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.00000 | 0.260793 | 0.130396 | − | 0.991462i | \(-0.458375\pi\) | ||||
0.130396 | + | 0.991462i | \(0.458375\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.5959i | 0.638131i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 17.1464i | − | 0.557184i | −0.960410 | − | 0.278592i | \(-0.910132\pi\) | ||
0.960410 | − | 0.278592i | \(-0.0898677\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.5959 | 0.635441 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.0000i | 1.03658i | 0.855204 | + | 0.518291i | \(0.173432\pi\) | ||||
−0.855204 | + | 0.518291i | \(0.826568\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.5959 | + | 39.1918i | −0.634109 | + | 1.26822i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 96.0000i | 3.10324i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.5959 | 0.632785 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 65.0000 | 2.09677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 22.0454i | − | 0.710403i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.0000 | + | 12.0000i | 0.772587 | + | 0.386294i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.1464i | 0.551392i | 0.961245 | + | 0.275696i | \(0.0889083\pi\) | ||||
−0.961245 | + | 0.275696i | \(0.911092\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −48.0000 | −1.54198 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.4949 | −0.786079 | −0.393039 | − | 0.919522i | \(-0.628576\pi\) | ||||
−0.393039 | + | 0.919522i | \(0.628576\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0000i | 0.384702i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.00000i | 0.127971i | 0.997951 | + | 0.0639857i | \(0.0203812\pi\) | ||||
−0.997951 | + | 0.0639857i | \(0.979619\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.79796 | −0.313144 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.0000 | −0.957826 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.0454i | 0.703139i | 0.936162 | + | 0.351570i | \(0.114352\pi\) | ||||
−0.936162 | + | 0.351570i | \(0.885648\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.0000 | − | 8.00000i | −0.509802 | − | 0.254901i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 73.4847i | 2.33904i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.0000 | −0.572367 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.1918 | −1.24497 | −0.622485 | − | 0.782632i | \(-0.713877\pi\) | ||||
−0.622485 | + | 0.782632i | \(0.713877\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.0000i | 0.380808i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.79796 | + | 19.5959i | −0.310616 | + | 0.621232i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.0000i | 1.77354i | 0.462213 | + | 0.886769i | \(0.347056\pi\) | ||||
−0.462213 | + | 0.886769i | \(0.652944\pi\) | |||||||
\(998\) | 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 \(a_p\))