Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [640,2,Mod(449,640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("640.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 640 = 2^{7} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 640.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.11042572936\) |
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: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 640.449 |
Dual form | 640.2.f.c.449.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −2.44949 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | + | 1.00000i | −0.894427 | + | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.44949i | − | 0.925820i | −0.886405 | − | 0.462910i | \(-0.846805\pi\) | ||
0.886405 | − | 0.462910i | \(-0.153195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.89898i | − | 1.47710i | −0.674200 | − | 0.738549i | \(-0.735511\pi\) | ||
0.674200 | − | 0.738549i | \(-0.264489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.89898 | − | 2.44949i | 1.26491 | − | 0.632456i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00000i | 0.970143i | 0.874475 | + | 0.485071i | \(0.161206\pi\) | ||||
−0.874475 | + | 0.485071i | \(0.838794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.89898i | 1.12390i | 0.827170 | + | 0.561951i | \(0.189949\pi\) | ||||
−0.827170 | + | 0.561951i | \(0.810051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.00000i | 1.30931i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.44949i | 0.510754i | 0.966842 | + | 0.255377i | \(0.0821996\pi\) | ||||
−0.966842 | + | 0.255377i | \(0.917800\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.00000i | 1.48556i | 0.669534 | + | 0.742781i | \(0.266494\pi\) | ||||
−0.669534 | + | 0.742781i | \(0.733506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.79796 | −1.75977 | −0.879883 | − | 0.475191i | \(-0.842379\pi\) | ||||
−0.879883 | + | 0.475191i | \(0.842379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.0000i | 2.08893i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.44949 | + | 4.89898i | 0.414039 | + | 0.828079i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.00000 | 1.24939 | 0.624695 | − | 0.780869i | \(-0.285223\pi\) | ||||
0.624695 | + | 0.780869i | \(0.285223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.34847 | 1.12063 | 0.560316 | − | 0.828279i | \(-0.310680\pi\) | ||||
0.560316 | + | 0.828279i | \(0.310680\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.00000 | + | 3.00000i | −0.894427 | + | 0.447214i | ||||
\(46\) | 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 | ||||||||
\(51\) | − | 9.79796i | − | 1.37199i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.00000 | 1.09888 | 0.549442 | − | 0.835532i | \(-0.314840\pi\) | ||||
0.549442 | + | 0.835532i | \(0.314840\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.89898 | + | 9.79796i | 0.660578 | + | 1.32116i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 12.0000i | − | 1.58944i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.89898i | 0.637793i | 0.947790 | + | 0.318896i | \(0.103312\pi\) | ||||
−0.947790 | + | 0.318896i | \(0.896688\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.00000i | − | 0.768221i | −0.923287 | − | 0.384111i | \(-0.874508\pi\) | ||
0.923287 | − | 0.384111i | \(-0.125492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 7.34847i | − | 0.925820i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.44949 | 0.299253 | 0.149626 | − | 0.988743i | \(-0.452193\pi\) | ||||
0.149626 | + | 0.988743i | \(0.452193\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.00000i | − | 0.722315i | ||||||
\(70\) | 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 | ||||||||
\(75\) | −7.34847 | + | 9.79796i | −0.848528 | + | 1.13137i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.0000 | −1.36753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.79796 | 1.10236 | 0.551178 | − | 0.834388i | \(-0.314178\pi\) | ||||
0.551178 | + | 0.834388i | \(0.314178\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.44949 | 0.268866 | 0.134433 | − | 0.990923i | \(-0.457079\pi\) | ||||
0.134433 | + | 0.990923i | \(0.457079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | − | 8.00000i | −0.433861 | − | 0.867722i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 19.5959i | − | 2.10090i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 24.0000 | 2.48868 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.89898 | − | 9.79796i | −0.502625 | − | 1.00525i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.00000i | − | 0.406138i | −0.979164 | − | 0.203069i | \(-0.934908\pi\) | ||
0.979164 | − | 0.203069i | \(-0.0650917\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 14.6969i | − | 1.47710i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.00000i | 0.796030i | 0.917379 | + | 0.398015i | \(0.130301\pi\) | ||||
−0.917379 | + | 0.398015i | \(0.869699\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.44949i | 0.241355i | 0.992692 | + | 0.120678i | \(0.0385068\pi\) | ||||
−0.992692 | + | 0.120678i | \(0.961493\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.00000 | − | 12.0000i | −0.585540 | − | 1.17108i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.34847 | −0.710403 | −0.355202 | − | 0.934790i | \(-0.615588\pi\) | ||||
−0.355202 | + | 0.934790i | \(0.615588\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.0000i | − | 0.957826i | −0.877862 | − | 0.478913i | \(-0.841031\pi\) | ||
0.877862 | − | 0.478913i | \(-0.158969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.79796 | 0.929981 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.0000i | 1.50515i | 0.658505 | + | 0.752577i | \(0.271189\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.44949 | − | 4.89898i | −0.228416 | − | 0.456832i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.79796 | 0.898177 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.0000 | −1.18182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.5959 | −1.76690 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.00000 | + | 11.0000i | −0.178885 | + | 0.983870i | ||||
\(126\) | 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 | ||||||||
\(131\) | 4.89898i | 0.428026i | 0.976831 | + | 0.214013i | \(0.0686535\pi\) | ||||
−0.976831 | + | 0.214013i | \(0.931347\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000 | 1.04053 | ||||||||
\(134\) | 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 | ||||||||
\(139\) | − | 4.89898i | − | 0.415526i | −0.978179 | − | 0.207763i | \(-0.933382\pi\) | ||
0.978179 | − | 0.207763i | \(-0.0666183\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 30.0000i | − | 2.52646i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.00000 | − | 16.0000i | −0.664364 | − | 1.32873i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.44949 | −0.202031 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2.00000i | − | 0.163846i | −0.996639 | − | 0.0819232i | \(-0.973894\pi\) | ||
0.996639 | − | 0.0819232i | \(-0.0261062\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 19.5959 | − | 9.79796i | 1.57398 | − | 0.786991i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.0000 | 1.59617 | 0.798087 | − | 0.602542i | \(-0.205846\pi\) | ||||
0.798087 | + | 0.602542i | \(0.205846\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.5959 | −1.55406 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.44949 | −0.191859 | −0.0959294 | − | 0.995388i | \(-0.530582\pi\) | ||||
−0.0959294 | + | 0.995388i | \(0.530582\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.0000 | − | 24.0000i | −0.934199 | − | 1.86840i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.44949i | 0.189547i | 0.995499 | + | 0.0947736i | \(0.0302127\pi\) | ||||
−0.995499 | + | 0.0947736i | \(0.969787\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.6969i | 1.12390i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.00000 | −0.304114 | −0.152057 | − | 0.988372i | \(-0.548590\pi\) | ||||
−0.152057 | + | 0.988372i | \(0.548590\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.79796 | − | 7.34847i | −0.740656 | − | 0.555492i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.0000i | − | 0.901975i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.6969i | 1.09850i | 0.835658 | + | 0.549250i | \(0.185087\pi\) | ||||
−0.835658 | + | 0.549250i | \(0.814913\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000i | 0.594635i | 0.954779 | + | 0.297318i | \(0.0960920\pi\) | ||||
−0.954779 | + | 0.297318i | \(0.903908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.6969i | 1.08643i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.00000 | − | 4.00000i | 0.588172 | − | 0.294086i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.5959 | 1.43300 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.5959 | 1.41791 | 0.708955 | − | 0.705253i | \(-0.249167\pi\) | ||||
0.708955 | + | 0.705253i | \(0.249167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 12.0000i | − | 0.863779i | −0.901927 | − | 0.431889i | \(-0.857847\pi\) | ||
0.901927 | − | 0.431889i | \(-0.142153\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.00000 | −0.569976 | −0.284988 | − | 0.958531i | \(-0.591990\pi\) | ||||
−0.284988 | + | 0.958531i | \(0.591990\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 19.5959 | 1.37536 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.0000 | + | 8.00000i | −1.11749 | + | 0.558744i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.34847i | 0.510754i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.0000 | 1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.4949i | 1.68630i | 0.537680 | + | 0.843149i | \(0.319301\pi\) | ||||
−0.537680 | + | 0.843149i | \(0.680699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.0000 | 1.64445 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.6969 | + | 7.34847i | −1.00232 | + | 0.501161i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.0000i | 1.62923i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 9.79796i | − | 0.662085i | ||||||
\(220\) | 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 | ||||||||
\(227\) | −2.44949 | −0.162578 | −0.0812892 | − | 0.996691i | \(-0.525904\pi\) | ||||
−0.0812892 | + | 0.996691i | \(0.525904\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 8.00000i | − | 0.528655i | −0.964433 | − | 0.264327i | \(-0.914850\pi\) | ||
0.964433 | − | 0.264327i | \(-0.0851500\pi\) | |||||||
\(230\) | 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 | ||||||||
\(235\) | −12.2474 | − | 24.4949i | −0.798935 | − | 1.59787i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −24.0000 | −1.55897 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.79796 | −0.633777 | −0.316889 | − | 0.948463i | \(-0.602638\pi\) | ||||
−0.316889 | + | 0.948463i | \(0.602638\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.0454 | 1.41421 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.00000 | + | 1.00000i | −0.127775 | + | 0.0638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4.89898i | − | 0.309221i | −0.987976 | − | 0.154610i | \(-0.950588\pi\) | ||
0.987976 | − | 0.154610i | \(-0.0494122\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.79796 | + | 19.5959i | 0.613572 | + | 1.22714i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 8.00000i | − | 0.499026i | −0.968371 | − | 0.249513i | \(-0.919729\pi\) | ||
0.968371 | − | 0.249513i | \(-0.0802706\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.79796i | 0.608816i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24.0000i | 1.48556i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 22.0454i | − | 1.35938i | −0.733500 | − | 0.679689i | \(-0.762115\pi\) | ||
0.733500 | − | 0.679689i | \(-0.237885\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.0000 | + | 8.00000i | −0.982872 | + | 0.491436i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.89898 | −0.299813 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.0000i | 1.58525i | 0.609711 | + | 0.792624i | \(0.291286\pi\) | ||||
−0.609711 | + | 0.792624i | \(0.708714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.79796 | −0.595184 | −0.297592 | − | 0.954693i | \(-0.596183\pi\) | ||||
−0.297592 | + | 0.954693i | \(0.596183\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.5959 | − | 14.6969i | −1.18168 | − | 0.886259i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0000 | 0.721010 | 0.360505 | − | 0.932757i | \(-0.382604\pi\) | ||||
0.360505 | + | 0.932757i | \(0.382604\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −29.3939 | −1.75977 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0000 | 0.954480 | 0.477240 | − | 0.878773i | \(-0.341637\pi\) | ||||
0.477240 | + | 0.878773i | \(0.341637\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.9444 | −1.60168 | −0.800839 | − | 0.598880i | \(-0.795613\pi\) | ||||
−0.800839 | + | 0.598880i | \(0.795613\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.0000 | + | 24.0000i | 0.710819 | + | 1.42164i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 19.5959i | − | 1.15671i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.79796i | 0.574367i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.0000 | −1.16841 | −0.584206 | − | 0.811605i | \(-0.698594\pi\) | ||||
−0.584206 | + | 0.811605i | \(0.698594\pi\) | |||||||
\(294\) | 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 | ||||||||
\(301\) | − | 18.0000i | − | 1.03750i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 19.5959i | − | 1.12576i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00000 | + | 12.0000i | 0.343559 | + | 0.687118i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.1464 | −0.978598 | −0.489299 | − | 0.872116i | \(-0.662747\pi\) | ||||
−0.489299 | + | 0.872116i | \(0.662747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 6.00000i | − | 0.341328i | ||||||
\(310\) | 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 | ||||||||
\(315\) | 7.34847 | + | 14.6969i | 0.414039 | + | 0.828079i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.00000 | −0.449325 | −0.224662 | − | 0.974437i | \(-0.572128\pi\) | ||||
−0.224662 | + | 0.974437i | \(0.572128\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39.1918 | 2.19432 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0000 | 1.00466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.5959 | −1.09035 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.4949i | 1.35457i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.0000 | 1.65395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.89898i | 0.269272i | 0.990895 | + | 0.134636i | \(0.0429866\pi\) | ||||
−0.990895 | + | 0.134636i | \(0.957013\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.0000 | −0.657596 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.89898 | + | 2.44949i | −0.267660 | + | 0.133830i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.0000i | − | 0.871576i | −0.900049 | − | 0.435788i | \(-0.856470\pi\) | ||
0.900049 | − | 0.435788i | \(-0.143530\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 39.1918i | − | 2.12861i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 48.0000i | 2.59935i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.5959i | − | 1.05808i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.00000 | + | 12.0000i | 0.323029 | + | 0.646058i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.2474 | −0.657477 | −0.328739 | − | 0.944421i | \(-0.606624\pi\) | ||||
−0.328739 | + | 0.944421i | \(0.606624\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.0000i | 1.28469i | 0.766415 | + | 0.642345i | \(0.222038\pi\) | ||||
−0.766415 | + | 0.642345i | \(0.777962\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.00000i | 0.425797i | 0.977074 | + | 0.212899i | \(0.0682904\pi\) | ||||
−0.977074 | + | 0.212899i | \(0.931710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.5959 | − | 9.79796i | 1.04004 | − | 0.520022i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −24.0000 | −1.27021 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 31.8434 | 1.67134 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.00000 | − | 8.00000i | −0.209370 | − | 0.418739i | ||||
\(366\) | 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 | ||||||||
\(371\) | − | 19.5959i | − | 1.01737i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.0000 | −1.03556 | −0.517780 | − | 0.855514i | \(-0.673242\pi\) | ||||
−0.517780 | + | 0.855514i | \(0.673242\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.89898 | − | 26.9444i | 0.252982 | − | 1.39140i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.6969i | 0.754931i | 0.926024 | + | 0.377466i | \(0.123204\pi\) | ||||
−0.926024 | + | 0.377466i | \(0.876796\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 18.0000i | − | 0.922168i | ||||||
\(382\) | 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 | ||||||||
\(387\) | 22.0454 | 1.12063 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 2.00000i | − | 0.101404i | −0.998714 | − | 0.0507020i | \(-0.983854\pi\) | ||
0.998714 | − | 0.0507020i | \(-0.0161459\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.79796 | −0.495504 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 12.0000i | − | 0.605320i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.5959 | + | 9.79796i | −0.985978 | + | 0.492989i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.00000 | 0.401508 | 0.200754 | − | 0.979642i | \(-0.435661\pi\) | ||||
0.200754 | + | 0.979642i | \(0.435661\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | 18.0000 | − | 9.00000i | 0.894427 | − | 0.447214i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.5959i | 0.971334i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.0000 | −1.18672 | −0.593362 | − | 0.804936i | \(-0.702200\pi\) | ||||
−0.593362 | + | 0.804936i | \(0.702200\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.5959i | 0.966595i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.0000 | 0.590481 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.89898 | + | 2.44949i | −0.240481 | + | 0.120241i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0000i | 0.587643i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.6969i | 0.717992i | 0.933339 | + | 0.358996i | \(0.116881\pi\) | ||||
−0.933339 | + | 0.358996i | \(0.883119\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.00000i | − | 0.0974740i | −0.998812 | − | 0.0487370i | \(-0.984480\pi\) | ||
0.998812 | − | 0.0487370i | \(-0.0155196\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 36.7423i | 1.78647i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.0000 | + | 12.0000i | 0.776114 | + | 0.582086i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.6969 | −0.711235 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.3939 | −1.41585 | −0.707927 | − | 0.706286i | \(-0.750369\pi\) | ||||
−0.707927 | + | 0.706286i | \(0.750369\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 36.0000i | − | 1.73005i | −0.501729 | − | 0.865025i | \(-0.667303\pi\) | ||
0.501729 | − | 0.865025i | \(-0.332697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.5959 | + | 39.1918i | 0.939552 | + | 1.87910i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.0000 | −0.574038 | ||||||||
\(438\) | 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 | ||||||||
\(443\) | −26.9444 | −1.28017 | −0.640083 | − | 0.768306i | \(-0.721100\pi\) | ||||
−0.640083 | + | 0.768306i | \(0.721100\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.00000 | + | 2.00000i | −0.189618 | + | 0.0948091i | ||||
\(446\) | 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 | ||||||||
\(451\) | − | 39.1918i | − | 1.84547i | ||||||
\(452\) | 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 | ||||||||
\(461\) | − | 8.00000i | − | 0.372597i | −0.982493 | − | 0.186299i | \(-0.940351\pi\) | ||
0.982493 | − | 0.186299i | \(-0.0596492\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | 36.7423 | 1.70023 | 0.850117 | − | 0.526595i | \(-0.176531\pi\) | ||||
0.850117 | + | 0.526595i | \(0.176531\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.00000i | − | 0.277054i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −48.9898 | −2.25733 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 36.0000i | − | 1.65528i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.5959 | + | 14.6969i | 0.899122 | + | 0.674342i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.0000 | 1.09888 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.5959 | 0.895360 | 0.447680 | − | 0.894194i | \(-0.352250\pi\) | ||||
0.447680 | + | 0.894194i | \(0.352250\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.6969 | −0.668734 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.00000 | + | 8.00000i | 0.181631 | + | 0.363261i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.1464i | 0.776979i | 0.921453 | + | 0.388489i | \(0.127003\pi\) | ||||
−0.921453 | + | 0.388489i | \(0.872997\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.00000 | 0.271329 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.6969i | − | 0.663264i | −0.943409 | − | 0.331632i | \(-0.892401\pi\) | ||
0.943409 | − | 0.331632i | \(-0.107599\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.0000 | −1.44121 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.6969 | + | 29.3939i | 0.660578 | + | 1.32116i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.0000i | 1.07655i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 4.89898i | − | 0.219308i | −0.993970 | − | 0.109654i | \(-0.965026\pi\) | ||
0.993970 | − | 0.109654i | \(-0.0349744\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 6.00000i | − | 0.268060i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 17.1464i | − | 0.764521i | −0.924055 | − | 0.382261i | \(-0.875146\pi\) | ||
0.924055 | − | 0.382261i | \(-0.124854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.00000 | − | 16.0000i | −0.355995 | − | 0.711991i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 31.8434 | 1.41421 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.00000i | 0.354594i | 0.984157 | + | 0.177297i | \(0.0567353\pi\) | ||||
−0.984157 | + | 0.177297i | \(0.943265\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.79796 | 0.433436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.44949 | − | 4.89898i | −0.107937 | − | 0.215875i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 60.0000 | 2.63880 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.79796 | 0.430083 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.0000 | −0.963837 | −0.481919 | − | 0.876216i | \(-0.660060\pi\) | ||||
−0.481919 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.8434 | 1.39241 | 0.696207 | − | 0.717841i | \(-0.254870\pi\) | ||||
0.696207 | + | 0.717841i | \(0.254870\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24.0000 | + | 18.0000i | 1.04745 | + | 0.785584i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 39.1918i | − | 1.70722i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.0000 | 0.739130 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.6969i | 0.637793i | ||||||||
\(532\) | 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 | ||||||||
\(539\) | − | 4.89898i | − | 0.211014i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 8.00000i | − | 0.343947i | −0.985102 | − | 0.171973i | \(-0.944986\pi\) | ||
0.985102 | − | 0.171973i | \(-0.0550143\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 19.5959i | − | 0.840941i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.0000 | + | 20.0000i | 0.428353 | + | 0.856706i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.0454 | −0.942594 | −0.471297 | − | 0.881975i | \(-0.656214\pi\) | ||||
−0.471297 | + | 0.881975i | \(0.656214\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 18.0000i | − | 0.768221i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.1918 | −1.66963 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 24.0000i | − | 1.02058i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.5959 | + | 9.79796i | −0.831800 | + | 0.415900i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.00000 | 0.169485 | 0.0847427 | − | 0.996403i | \(-0.472993\pi\) | ||||
0.0847427 | + | 0.996403i | \(0.472993\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −48.0000 | −2.02656 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.44949 | −0.103234 | −0.0516168 | − | 0.998667i | \(-0.516437\pi\) | ||||
−0.0516168 | + | 0.998667i | \(0.516437\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.0000 | − | 32.0000i | −0.673125 | − | 1.34625i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.0454i | 0.925820i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.00000 | −0.335377 | −0.167689 | − | 0.985840i | \(-0.553630\pi\) | ||||
−0.167689 | + | 0.985840i | \(0.553630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 44.0908i | − | 1.84514i | −0.385826 | − | 0.922572i | \(-0.626083\pi\) | ||
0.385826 | − | 0.922572i | \(-0.373917\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −48.0000 | −2.00523 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.79796 | + | 7.34847i | 0.408603 | + | 0.306452i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.0000i | 0.999133i | 0.866276 | + | 0.499567i | \(0.166507\pi\) | ||||
−0.866276 | + | 0.499567i | \(0.833493\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.3939i | 1.22157i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 6.00000i | − | 0.248922i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 39.1918i | − | 1.62316i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.2474 | −0.505506 | −0.252753 | − | 0.967531i | \(-0.581336\pi\) | ||||
−0.252753 | + | 0.967531i | \(0.581336\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 48.0000i | − | 1.97781i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.5959 | 0.806068 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.00000i | 0.328521i | 0.986417 | + | 0.164260i | \(0.0525237\pi\) | ||||
−0.986417 | + | 0.164260i | \(0.947476\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.5959 | + | 9.79796i | −0.803354 | + | 0.401677i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.0000 | 0.982255 | ||||||||
\(598\) | 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 | \(-0.394189\pi\) | ||||
0.326327 | + | 0.945257i | \(0.394189\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.34847 | 0.299253 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 26.0000 | − | 13.0000i | 1.05705 | − | 0.528525i | ||||
\(606\) | 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 | ||||||||
\(613\) | −16.0000 | −0.646234 | −0.323117 | − | 0.946359i | \(-0.604731\pi\) | ||||
−0.323117 | + | 0.946359i | \(0.604731\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | 24.4949i | 0.984533i | 0.870445 | + | 0.492267i | \(0.163831\pi\) | ||||
−0.870445 | + | 0.492267i | \(0.836169\pi\) | |||||||
\(620\) | 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 | ||||||||
\(627\) | −58.7878 | −2.34776 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 16.0000i | − | 0.637962i | ||||||
\(630\) | 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 | ||||||||
\(635\) | −7.34847 | − | 14.6969i | −0.291615 | − | 0.583230i | ||||
\(636\) | 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 | ||||||||
\(643\) | 2.44949 | 0.0965984 | 0.0482992 | − | 0.998833i | \(-0.484620\pi\) | ||||
0.0482992 | + | 0.998833i | \(0.484620\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 36.0000 | − | 18.0000i | 1.41750 | − | 0.708749i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 22.0454i | − | 0.866694i | −0.901227 | − | 0.433347i | \(-0.857332\pi\) | ||
0.901227 | − | 0.433347i | \(-0.142668\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | 0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 58.7878i | − | 2.30407i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.0000 | 0.626128 | 0.313064 | − | 0.949732i | \(-0.398644\pi\) | ||||
0.313064 | + | 0.949732i | \(0.398644\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.89898 | − | 9.79796i | −0.191419 | − | 0.382838i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.0000i | 0.468165i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.6969i | 0.572511i | 0.958153 | + | 0.286256i | \(0.0924107\pi\) | ||||
−0.958153 | + | 0.286256i | \(0.907589\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 30.0000i | − | 1.16686i | −0.812162 | − | 0.583432i | \(-0.801709\pi\) | ||
0.812162 | − | 0.583432i | \(-0.198291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −24.0000 | + | 12.0000i | −0.930680 | + | 0.465340i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.5959 | −0.758757 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 18.0000i | − | 0.695920i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.3939 | −1.13474 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.0000i | − | 1.38770i | −0.720121 | − | 0.693849i | \(-0.755914\pi\) | ||
0.720121 | − | 0.693849i | \(-0.244086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.0000 | −1.22986 | −0.614930 | − | 0.788582i | \(-0.710816\pi\) | ||||
−0.614930 | + | 0.788582i | \(0.710816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.79796 | −0.376011 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | 0.229920 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.34847 | 0.281181 | 0.140591 | − | 0.990068i | \(-0.455100\pi\) | ||||
0.140591 | + | 0.990068i | \(0.455100\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.00000 | + | 16.0000i | 0.305664 | + | 0.611329i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.5959i | 0.747631i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 14.6969i | − | 0.559098i | −0.960131 | − | 0.279549i | \(-0.909815\pi\) | ||
0.960131 | − | 0.279549i | \(-0.0901849\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −36.0000 | −1.36753 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.89898 | + | 9.79796i | 0.185829 | + | 0.371658i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.0000i | 1.21209i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 48.9898i | − | 1.85296i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 26.0000i | − | 0.982006i | −0.871158 | − | 0.491003i | \(-0.836630\pi\) | ||
0.871158 | − | 0.491003i | \(-0.163370\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 19.5959i | − | 0.739074i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 30.0000 | + | 60.0000i | 1.12987 | + | 2.25973i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.5959 | 0.736980 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.0000i | 1.50223i | 0.660171 | + | 0.751116i | \(0.270484\pi\) | ||||
−0.660171 | + | 0.751116i | \(0.729516\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.3939 | 1.10236 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 24.0000i | − | 0.898807i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.0000 | 0.896296 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 48.9898 | 1.82701 | 0.913506 | − | 0.406826i | \(-0.133365\pi\) | ||||
0.913506 | + | 0.406826i | \(0.133365\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | 0.223452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.0000 | + | 24.0000i | 1.18845 | + | 0.891338i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.7423i | 1.36270i | 0.731959 | + | 0.681349i | \(0.238606\pi\) | ||||
−0.731959 | + | 0.681349i | \(0.761394\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.3939i | 1.08717i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.0000 | −0.443230 | −0.221615 | − | 0.975134i | \(-0.571133\pi\) | ||||
−0.221615 | + | 0.975134i | \(0.571133\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.89898 | − | 2.44949i | 0.180702 | − | 0.0903508i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 12.0000i | − | 0.442026i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.6969i | 0.540636i | 0.962771 | + | 0.270318i | \(0.0871288\pi\) | ||||
−0.962771 | + | 0.270318i | \(0.912871\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.1464i | 0.629041i | 0.949251 | + | 0.314521i | \(0.101844\pi\) | ||||
−0.949251 | + | 0.314521i | \(0.898156\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.00000 | + | 4.00000i | 0.0732743 | + | 0.146549i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.34847 | 0.268866 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0000i | 0.657706i | ||||||||
\(750\) | 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 | ||||||||
\(757\) | −12.0000 | −0.436147 | −0.218074 | − | 0.975932i | \(-0.569977\pi\) | ||||
−0.218074 | + | 0.975932i | \(0.569977\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −29.3939 | −1.06693 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.0000 | 0.797499 | 0.398750 | − | 0.917060i | \(-0.369444\pi\) | ||||
0.398750 | + | 0.917060i | \(0.369444\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.4949 | −0.886775 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.0000 | − | 24.0000i | −0.433861 | − | 0.867722i | ||||
\(766\) | 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 | ||||||||
\(771\) | 19.5959i | 0.705730i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.00000 | 0.287740 | 0.143870 | − | 0.989597i | \(-0.454045\pi\) | ||||
0.143870 | + | 0.989597i | \(0.454045\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.3939 | + | 39.1918i | −1.05586 | + | 1.40781i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 24.0000i | − | 0.860995i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 39.1918i | 1.40419i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48.0000i | 1.71758i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −40.0000 | + | 20.0000i | −1.42766 | + | 0.713831i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.6413 | 1.48435 | 0.742176 | − | 0.670205i | \(-0.233794\pi\) | ||||
0.742176 | + | 0.670205i | \(0.233794\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 54.0000i | 1.92245i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.1918 | 1.39350 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 39.1918 | − | 19.5959i | 1.38999 | − | 0.694996i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.00000 | −0.283375 | −0.141687 | − | 0.989911i | \(-0.545253\pi\) | ||||
−0.141687 | + | 0.989911i | \(0.545253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.9898 | −1.73313 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.5959 | 0.691525 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.0000 | + | 6.00000i | −0.422944 | + | 0.211472i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 63.6867i | − | 2.24188i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.0000 | 0.351581 | 0.175791 | − | 0.984428i | \(-0.443752\pi\) | ||||
0.175791 | + | 0.984428i | \(0.443752\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53.8888i | 1.89229i | 0.323742 | + | 0.946145i | \(0.395059\pi\) | ||||
−0.323742 | + | 0.946145i | \(0.604941\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.0000 | 0.841717 | ||||||||
\(814\) | 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 | ||||||||
\(821\) | − | 14.0000i | − | 0.488603i | −0.969699 | − | 0.244302i | \(-0.921441\pi\) | ||
0.969699 | − | 0.244302i | \(-0.0785587\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.0454i | 0.768455i | 0.923239 | + | 0.384227i | \(0.125532\pi\) | ||||
−0.923239 | + | 0.384227i | \(0.874468\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 48.0000 | + | 36.0000i | 1.67115 | + | 1.25336i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.5403 | 1.61836 | 0.809182 | − | 0.587557i | \(-0.199910\pi\) | ||||
0.809182 | + | 0.587557i | \(0.199910\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 22.0000i | − | 0.764092i | −0.924143 | − | 0.382046i | \(-0.875220\pi\) | ||
0.924143 | − | 0.382046i | \(-0.124780\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.3939 | −1.01966 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.00000i | 0.138592i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.44949 | − | 4.89898i | −0.0847681 | − | 0.169536i | ||||
\(836\) | 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 | ||||||||
\(843\) | −39.1918 | −1.34984 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.0000 | − | 13.0000i | 0.894427 | − | 0.447214i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.8434i | 1.09415i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 66.0000 | 2.26511 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 9.79796i | − | 0.335870i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.0000 | −1.09566 | −0.547830 | − | 0.836590i | \(-0.684546\pi\) | ||||
−0.547830 | + | 0.836590i | \(0.684546\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | 24.4949i | 0.835755i | 0.908503 | + | 0.417878i | \(0.137226\pi\) | ||||
−0.908503 | + | 0.417878i | \(0.862774\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 48.0000i | 1.63584i | ||||||||
\(862\) | 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 | ||||||||
\(867\) | −2.44949 | −0.0831890 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 48.0000i | − | 1.62829i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 12.0000i | − | 0.406138i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.9444 | + | 4.89898i | 0.910887 | + | 0.165616i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.0000 | 0.945493 | 0.472746 | − | 0.881199i | \(-0.343263\pi\) | ||||
0.472746 | + | 0.881199i | \(0.343263\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 36.7423 | 1.23648 | 0.618239 | − | 0.785990i | \(-0.287846\pi\) | ||||
0.618239 | + | 0.785990i | \(0.287846\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.0000 | + | 24.0000i | 0.403376 | + | 0.806751i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 2.44949i | − | 0.0822458i | −0.999154 | − | 0.0411229i | \(-0.986906\pi\) | ||
0.999154 | − | 0.0411229i | \(-0.0130935\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000 | 0.603701 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 44.0908i | 1.47710i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −60.0000 | −2.00782 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.6969 | − | 29.3939i | −0.491264 | − | 0.982529i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 78.3837i | − | 2.61424i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.0000i | 1.06607i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 44.0908i | 1.46725i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.00000 | − | 16.0000i | −0.265929 | − | 0.531858i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.2474 | 0.406670 | 0.203335 | − | 0.979109i | \(-0.434822\pi\) | ||||
0.203335 | + | 0.979109i | \(0.434822\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24.0000i | 0.796030i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.3939 | 0.973863 | 0.486931 | − | 0.873440i | \(-0.338116\pi\) | ||||
0.486931 | + | 0.873440i | \(0.338116\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12.0000i | − | 0.397142i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.6969 | − | 29.3939i | −0.485866 | − | 0.971732i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.0000 | 0.396275 | ||||||||
\(918\) | 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 | ||||||||
\(925\) | −12.0000 | + | 16.0000i | −0.394558 | + | 0.526077i | ||||
\(926\) | 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 | ||||||||
\(931\) | 4.89898i | 0.160558i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −48.0000 | −1.57145 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | − | 58.7878i | − | 1.91847i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 8.00000i | − | 0.260793i | −0.991462 | − | 0.130396i | \(-0.958375\pi\) | ||
0.991462 | − | 0.130396i | \(-0.0416250\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.5959i | 0.638131i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.1464 | −0.557184 | −0.278592 | − | 0.960410i | \(-0.589868\pi\) | ||||
−0.278592 | + | 0.960410i | \(0.589868\pi\) | |||||||
\(948\) | 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 | ||||||||
\(955\) | −39.1918 | + | 19.5959i | −1.26822 | + | 0.634109i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −96.0000 | −3.10324 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.5959 | −0.632785 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 65.0000 | 2.09677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.0454 | −0.710403 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.0000 | + | 24.0000i | 0.386294 | + | 0.772587i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17.1464i | − | 0.551392i | −0.961245 | − | 0.275696i | \(-0.911092\pi\) | ||
0.961245 | − | 0.275696i | \(-0.0889083\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 48.0000 | 1.54198 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.4949i | 0.786079i | 0.919522 | + | 0.393039i | \(0.128576\pi\) | ||||
−0.919522 | + | 0.393039i | \(0.871424\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0000 | −0.384702 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 4.00000i | − | 0.127971i | −0.997951 | − | 0.0639857i | \(-0.979619\pi\) | ||
0.997951 | − | 0.0639857i | \(-0.0203812\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 9.79796i | − | 0.313144i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 30.0000i | − | 0.957826i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 22.0454i | − | 0.703139i | −0.936162 | − | 0.351570i | \(-0.885648\pi\) | ||
0.936162 | − | 0.351570i | \(-0.114352\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0000 | − | 8.00000i | 0.509802 | − | 0.254901i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −73.4847 | −2.33904 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.0000i | 0.572367i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.1918 | 1.24497 | 0.622485 | − | 0.782632i | \(-0.286123\pi\) | ||||
0.622485 | + | 0.782632i | \(0.286123\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 12.0000i | − | 0.380808i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.5959 | − | 9.79796i | 0.621232 | − | 0.310616i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.0000 | 1.77354 | 0.886769 | − | 0.462213i | \(-0.152944\pi\) | ||||
0.886769 | + | 0.462213i | \(0.152944\pi\) | |||||||
\(998\) | 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 \(a_p\))