Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(209,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cc (of order \(6\), degree \(2\), 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 209.1 | ||
Root | \(-1.69547 - 0.354107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.209 |
Dual form | 1008.2.cc.b.545.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.69547 | + | 0.354107i | −0.978878 | + | 0.204444i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.895175 | − | 1.55049i | −0.400334 | − | 0.693399i | 0.593432 | − | 0.804884i | \(-0.297773\pi\) |
−0.993766 | + | 0.111485i | \(0.964439\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.30191 | − | 1.30430i | 0.870040 | − | 0.492981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.74922 | − | 1.20075i | 0.916406 | − | 0.400251i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.07976 | + | 1.20075i | 0.627072 | + | 0.362040i | 0.779617 | − | 0.626256i | \(-0.215414\pi\) |
−0.152545 | + | 0.988297i | \(0.548747\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.23601 | + | 2.44566i | −1.17486 | + | 0.678305i | −0.954820 | − | 0.297186i | \(-0.903952\pi\) |
−0.220039 | + | 0.975491i | \(0.570618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.06678 | + | 2.31181i | 0.533640 | + | 0.596908i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.66466 | 0.888812 | 0.444406 | − | 0.895826i | \(-0.353415\pi\) | ||||
0.444406 | + | 0.895826i | \(0.353415\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.01701i | − | 0.692150i | −0.938207 | − | 0.346075i | \(-0.887514\pi\) | ||
0.938207 | − | 0.346075i | \(-0.112486\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.44095 | + | 3.02653i | −0.750877 | + | 0.660442i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.26178 | + | 1.88319i | −0.680129 | + | 0.392673i | −0.799904 | − | 0.600128i | \(-0.795116\pi\) |
0.119775 | + | 0.992801i | \(0.461783\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.897324 | − | 1.55421i | 0.179465 | − | 0.310842i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.23601 | + | 3.00935i | −0.815221 | + | 0.579150i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.68202 | − | 3.28052i | −1.05512 | − | 0.609176i | −0.131045 | − | 0.991376i | \(-0.541833\pi\) |
−0.924080 | + | 0.382200i | \(0.875167\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.02408 | − | 2.32330i | 0.722746 | − | 0.417278i | −0.0930163 | − | 0.995665i | \(-0.529651\pi\) |
0.815763 | + | 0.578387i | \(0.196318\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.95136 | − | 1.29938i | −0.687844 | − | 0.226193i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.08292 | − | 2.40150i | −0.690140 | − | 0.405928i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.36404 | 1.53944 | 0.769719 | − | 0.638382i | \(-0.220396\pi\) | ||||
0.769719 | + | 0.638382i | \(0.220396\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.31599 | − | 5.64654i | 1.01137 | − | 0.904170i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.04094 | − | 6.99911i | −0.631088 | − | 1.09308i | −0.987330 | − | 0.158683i | \(-0.949275\pi\) |
0.356241 | − | 0.934394i | \(-0.384058\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.48127 | − | 6.02973i | 0.530888 | − | 0.919526i | −0.468462 | − | 0.883484i | \(-0.655192\pi\) |
0.999350 | − | 0.0360419i | \(-0.0114750\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.32278 | − | 3.18775i | −0.644402 | − | 0.475201i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.56802 | + | 4.44794i | −0.374584 | + | 0.648799i | −0.990265 | − | 0.139197i | \(-0.955548\pi\) |
0.615680 | + | 0.787996i | \(0.288881\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.59758 | − | 6.00478i | 0.513940 | − | 0.857826i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.21332 | + | 1.29768i | −0.870039 | + | 0.181712i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.29953i | − | 0.579749i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.06834 | + | 5.11524i | 0.141506 | + | 0.677530i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.29501 | − | 12.6353i | −0.949729 | − | 1.64498i | −0.745994 | − | 0.665953i | \(-0.768025\pi\) |
−0.203735 | − | 0.979026i | \(-0.565308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.81058 | + | 5.66414i | 1.25612 | + | 0.725219i | 0.972317 | − | 0.233665i | \(-0.0750718\pi\) |
0.283799 | + | 0.958884i | \(0.408405\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.76230 | − | 6.34984i | 0.599994 | − | 0.800005i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.58394 | + | 4.37859i | 0.940672 | + | 0.543097i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.285115 | + | 0.493834i | 0.0348324 | + | 0.0603315i | 0.882916 | − | 0.469531i | \(-0.155577\pi\) |
−0.848084 | + | 0.529862i | \(0.822244\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.86340 | − | 4.34791i | 0.585484 | − | 0.523427i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.96254i | − | 0.707623i | −0.935317 | − | 0.353811i | \(-0.884885\pi\) | ||
0.935317 | − | 0.353811i | \(-0.115115\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.3814i | − | 1.44913i | −0.689204 | − | 0.724567i | \(-0.742040\pi\) | ||
0.689204 | − | 0.724567i | \(-0.257960\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.971027 | + | 2.95286i | −0.112125 | + | 0.340967i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.35358 | + | 0.0513786i | 0.724057 | + | 0.00585514i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.51831 | − | 2.62979i | 0.170824 | − | 0.295875i | −0.767884 | − | 0.640588i | \(-0.778691\pi\) |
0.938708 | + | 0.344713i | \(0.112024\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.11639 | − | 6.60226i | 0.679599 | − | 0.733584i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.00270 | − | 12.1290i | 0.768646 | − | 1.33133i | −0.169651 | − | 0.985504i | \(-0.554264\pi\) |
0.938297 | − | 0.345830i | \(-0.112403\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.28052 | − | 5.68202i | −0.355822 | − | 0.616302i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.7953 | + | 3.54997i | 1.15738 | + | 0.380596i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.74863 | −0.397354 | −0.198677 | − | 0.980065i | \(-0.563664\pi\) | ||||
−0.198677 | + | 0.980065i | \(0.563664\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.56103 | + | 11.1547i | −0.687783 | + | 1.16934i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.00000 | + | 5.36404i | −0.622171 | + | 0.556225i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.67784 | + | 2.70075i | −0.479936 | + | 0.277091i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.77256 | + | 2.75544i | 0.484580 | + | 0.279772i | 0.722323 | − | 0.691556i | \(-0.243074\pi\) |
−0.237743 | + | 0.971328i | \(0.576408\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.15953 | + | 0.803848i | 0.719560 | + | 0.0807897i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.125162 | + | 0.216787i | −0.0124541 | + | 0.0215711i | −0.872185 | − | 0.489176i | \(-0.837298\pi\) |
0.859731 | + | 0.510747i | \(0.170631\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.145433 | + | 0.0839657i | −0.0143299 | + | 0.00827339i | −0.507148 | − | 0.861859i | \(-0.669300\pi\) |
0.492818 | + | 0.870132i | \(0.335967\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.77285 | + | 2.62588i | 0.758552 | + | 0.256260i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.99080i | 0.772500i | 0.922394 | + | 0.386250i | \(0.126230\pi\) | ||||
−0.922394 | + | 0.386250i | \(0.873770\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.9533 | −1.81540 | −0.907700 | − | 0.419619i | \(-0.862164\pi\) | ||||
−0.907700 | + | 0.419619i | \(0.862164\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.8764 | + | 3.31587i | −1.50692 | + | 0.314728i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.00418 | + | 0.579764i | −0.0944653 | + | 0.0545396i | −0.546488 | − | 0.837467i | \(-0.684036\pi\) |
0.452023 | + | 0.892006i | \(0.350702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.83973 | + | 3.37157i | 0.544558 | + | 0.314401i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.70908 | + | 11.8101i | −0.805155 | + | 1.09184i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.43573 | − | 4.77984i | 0.773302 | − | 0.438167i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.61639 | − | 4.53172i | −0.237854 | − | 0.411974i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.32971 | + | 10.4358i | 0.841231 | + | 0.940968i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1648 | −1.08805 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.40150 | −0.124363 | −0.0621817 | − | 0.998065i | \(-0.519806\pi\) | ||||
−0.0621817 | + | 0.998065i | \(0.519806\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.76721 | + | 11.4560i | −0.331684 | + | 1.00864i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.24589 | + | 9.08614i | 0.458335 | + | 0.793860i | 0.998873 | − | 0.0474597i | \(-0.0151126\pi\) |
−0.540538 | + | 0.841320i | \(0.681779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.93510 | − | 6.94489i | −0.341216 | − | 0.602198i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.45794 | + | 3.87399i | 0.727943 | + | 0.333420i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.08812 | − | 2.36028i | −0.349272 | − | 0.201652i | 0.315093 | − | 0.949061i | \(-0.397964\pi\) |
−0.664365 | + | 0.747409i | \(0.731298\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.04707 | − | 1.18187i | 0.173630 | − | 0.100245i | −0.410666 | − | 0.911786i | \(-0.634704\pi\) |
0.584296 | + | 0.811540i | \(0.301371\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.77895 | − | 8.45070i | 0.234030 | − | 0.711677i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.7465 | −0.982295 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.7465i | 0.975497i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.97325 | + | 11.4548i | −0.327708 | + | 0.944779i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.0377 | + | 8.68202i | −1.23194 | + | 0.711259i | −0.967433 | − | 0.253126i | \(-0.918541\pi\) |
−0.264503 | + | 0.964385i | \(0.585208\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.61639 | + | 9.72787i | −0.457055 | + | 0.791643i | −0.998804 | − | 0.0488977i | \(-0.984429\pi\) |
0.541749 | + | 0.840541i | \(0.317762\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.0750 | − | 4.40035i | 0.814512 | − | 0.355748i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.20451 | − | 4.15953i | −0.578680 | − | 0.334101i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.9885 | − | 6.92154i | 0.956783 | − | 0.552399i | 0.0616014 | − | 0.998101i | \(-0.480379\pi\) |
0.895181 | + | 0.445702i | \(0.147046\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.05208 | + | 8.58930i | −0.398159 | + | 0.676931i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.33577 | 0.339604 | 0.169802 | − | 0.985478i | \(-0.445687\pi\) | ||||
0.169802 | + | 0.985478i | \(0.445687\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.52249 | + | 7.28972i | 0.118526 | + | 0.567504i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.20756 | + | 10.7518i | 0.480355 | + | 0.832000i | 0.999746 | − | 0.0225370i | \(-0.00717435\pi\) |
−0.519391 | + | 0.854537i | \(0.673841\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.46254 | − | 9.46139i | 0.420195 | − | 0.727799i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.62268 | − | 8.29442i | −0.277033 | − | 0.634290i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.70908 | − | 15.0846i | 0.662139 | − | 1.14686i | −0.317913 | − | 0.948120i | \(-0.602982\pi\) |
0.980052 | − | 0.198739i | \(-0.0636846\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0383954 | − | 4.74804i | 0.00290242 | − | 0.358918i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.8427 | + | 18.8396i | 1.26597 | + | 1.41607i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 13.1221i | − | 0.980789i | −0.871501 | − | 0.490395i | \(-0.836853\pi\) | ||
0.871501 | − | 0.490395i | \(-0.163147\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3577i | 0.992873i | 0.868073 | + | 0.496437i | \(0.165359\pi\) | ||||
−0.868073 | + | 0.496437i | \(0.834641\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.6392 | − | 6.12937i | −1.37785 | − | 0.453096i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.38245 | − | 14.5188i | −0.616290 | − | 1.06745i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.62164 | + | 4.40035i | 0.557349 | + | 0.321786i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.82581 | + | 12.4523i | −0.423765 | + | 0.905772i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.01361 | + | 4.62666i | 0.579845 | + | 0.334774i | 0.761072 | − | 0.648668i | \(-0.224674\pi\) |
−0.181227 | + | 0.983441i | \(0.558007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.2801 | + | 21.2698i | 0.883941 | + | 1.53103i | 0.846923 | + | 0.531716i | \(0.178452\pi\) |
0.0370176 | + | 0.999315i | \(0.488214\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.4088 | − | 4.73823i | −1.03184 | − | 0.339312i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 12.4861i | − | 0.889598i | −0.895630 | − | 0.444799i | \(-0.853275\pi\) | ||
0.895630 | − | 0.444799i | \(-0.146725\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 0.179145i | − | 0.0126993i | −0.999980 | − | 0.00634964i | \(-0.997979\pi\) | ||
0.999980 | − | 0.00634964i | \(-0.00202117\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.658274 | − | 0.736319i | −0.0464311 | − | 0.0519359i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.3583 | − | 0.140369i | −1.21831 | − | 0.00985198i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.23469 | + | 12.5309i | −0.505293 | + | 0.875193i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.70610 | + | 9.09390i | −0.466107 | + | 0.632069i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.62268 | − | 6.27467i | 0.250586 | − | 0.434028i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.56103 | − | 13.0961i | −0.520523 | − | 0.901572i | −0.999715 | − | 0.0238622i | \(-0.992404\pi\) |
0.479192 | − | 0.877710i | \(-0.340930\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.11137 | + | 10.1093i | 0.144669 | + | 0.692677i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.4654 | −0.850131 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.23278 | − | 10.5967i | 0.423109 | − | 0.719348i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.38434 | + | 20.9923i | 0.296266 | + | 1.41853i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.5236 | + | 8.96254i | −1.04423 | + | 0.602885i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.27049 | + | 4.19762i | 0.486868 | + | 0.281093i | 0.723274 | − | 0.690561i | \(-0.242636\pi\) |
−0.236406 | + | 0.971654i | \(0.575970\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.600717 | − | 5.35033i | 0.0400478 | − | 0.356688i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.21261 | + | 2.10030i | −0.0804836 | + | 0.139402i | −0.903458 | − | 0.428677i | \(-0.858980\pi\) |
0.822974 | + | 0.568079i | \(0.192313\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.74915 | − | 1.00987i | 0.115587 | − | 0.0667344i | −0.441092 | − | 0.897462i | \(-0.645409\pi\) |
0.556679 | + | 0.830728i | \(0.312075\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.7905 | + | 2.16273i | −0.709961 | + | 0.142297i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.7289i | 0.833899i | 0.908930 | + | 0.416950i | \(0.136901\pi\) | ||||
−0.908930 | + | 0.416950i | \(0.863099\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.19531 | 0.599836 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.64302 | + | 4.99637i | −0.106726 | + | 0.324549i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.1117 | + | 8.72474i | −0.977494 | + | 0.564356i | −0.901513 | − | 0.432753i | \(-0.857542\pi\) |
−0.0759814 | + | 0.997109i | \(0.524209\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.90142 | + | 5.71659i | 0.637807 | + | 0.368238i | 0.783769 | − | 0.621052i | \(-0.213295\pi\) |
−0.145963 | + | 0.989290i | \(0.546628\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.03223 | + | 13.3598i | −0.515268 | + | 0.857029i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.5308 | − | 0.202676i | −0.800564 | − | 0.0129485i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.37859 | + | 12.7801i | 0.469489 | + | 0.813178i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.57788 | + | 23.0441i | −0.480228 | + | 1.46036i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.3560 | 1.72669 | 0.863347 | − | 0.504611i | \(-0.168364\pi\) | ||||
0.863347 | + | 0.504611i | \(0.168364\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.04499 | −0.568653 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.57405 | + | 8.47203i | 0.474305 | + | 0.530539i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.74837 | + | 3.02826i | 0.109060 | + | 0.188898i | 0.915390 | − | 0.402569i | \(-0.131883\pi\) |
−0.806330 | + | 0.591466i | \(0.798549\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.5552 | − | 12.2136i | 1.33937 | − | 0.758914i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.5602 | − | 2.19615i | −1.21075 | − | 0.135938i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.35150 | + | 4.82174i | 0.514976 | + | 0.297321i | 0.734877 | − | 0.678201i | \(-0.237240\pi\) |
−0.219901 | + | 0.975522i | \(0.570573\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.35568 | − | 1.32741i | 0.388961 | − | 0.0812365i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.91107 | −0.421376 | −0.210688 | − | 0.977553i | \(-0.567570\pi\) | ||||
−0.210688 | + | 0.977553i | \(0.567570\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 20.6312i | − | 1.25326i | −0.779318 | − | 0.626629i | \(-0.784434\pi\) | ||
0.779318 | − | 0.626629i | \(-0.215566\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.17404 | − | 21.2358i | 0.434193 | − | 1.28525i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.73244 | − | 2.15493i | 0.225075 | − | 0.129947i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.75718 | − | 13.4358i | 0.466084 | − | 0.807281i | −0.533166 | − | 0.846011i | \(-0.678998\pi\) |
0.999250 | + | 0.0387296i | \(0.0123311\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.27336 | − | 11.2192i | 0.495313 | − | 0.671675i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.7759 | + | 6.79883i | 0.702492 | + | 0.405584i | 0.808275 | − | 0.588805i | \(-0.200401\pi\) |
−0.105783 | + | 0.994389i | \(0.533735\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.71796 | − | 2.72392i | 0.280454 | − | 0.161920i | −0.353175 | − | 0.935557i | \(-0.614898\pi\) |
0.633629 | + | 0.773637i | \(0.281565\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.97477 | − | 6.23549i | 0.413150 | − | 0.369359i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.4308 | − | 10.8407i | −1.08794 | − | 0.639907i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.57023 | −0.210014 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.06743 | − | 2.98176i | −0.531542 | − | 0.174794i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.2311 | + | 21.1849i | 0.714550 | + | 1.23764i | 0.963133 | + | 0.269026i | \(0.0867017\pi\) |
−0.248583 | + | 0.968610i | \(0.579965\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.0606 | + | 22.6216i | −0.760418 | + | 1.31708i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.4234 | + | 1.17234i | −0.720878 | + | 0.0680260i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.21130 | − | 15.9544i | 0.532703 | − | 0.922670i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.148959 | − | 18.4205i | 0.00858585 | − | 1.06174i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.135442 | − | 0.411876i | 0.00778097 | − | 0.0236617i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 20.2816i | − | 1.16132i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.2223i | 1.78195i | 0.454053 | + | 0.890975i | \(0.349978\pi\) | ||||
−0.454053 | + | 0.890975i | \(0.650022\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.216844 | − | 0.193860i | 0.0123358 | − | 0.0110283i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.45501 | + | 9.44836i | 0.309325 | + | 0.535767i | 0.978215 | − | 0.207594i | \(-0.0665634\pi\) |
−0.668889 | + | 0.743362i | \(0.733230\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.96532 | + | 1.71203i | 0.167610 | + | 0.0967694i | 0.581458 | − | 0.813576i | \(-0.302482\pi\) |
−0.413849 | + | 0.910346i | \(0.635816\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.1084 | − | 1.69968i | −0.794921 | − | 0.0957662i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.4953 | + | 9.52357i | 0.926468 | + | 0.534897i | 0.885693 | − | 0.464272i | \(-0.153684\pi\) |
0.0407755 | + | 0.999168i | \(0.487017\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.87817 | − | 13.6454i | −0.441093 | − | 0.763995i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.82960 | − | 13.5481i | −0.157933 | − | 0.756183i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11.0563i | − | 0.615191i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.77821i | 0.486927i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 32.1348 | − | 6.71150i | 1.77706 | − | 0.371147i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.109882 | + | 13.5882i | −0.00605801 | + | 0.749144i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.0366251 | − | 0.0634366i | 0.00201310 | − | 0.00348679i | −0.865017 | − | 0.501742i | \(-0.832693\pi\) |
0.867030 | + | 0.498256i | \(0.166026\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.7438 | − | 11.2439i | 1.41075 | − | 0.616161i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.510456 | − | 0.884136i | 0.0278892 | − | 0.0483055i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.11639 | + | 1.93364i | 0.0608136 | + | 0.105332i | 0.894829 | − | 0.446408i | \(-0.147297\pi\) |
−0.834016 | + | 0.551741i | \(0.813964\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.49726 | − | 1.33856i | 0.0813198 | − | 0.0727004i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.1589 | 0.604286 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.449242 | − | 18.5148i | 0.0242568 | − | 0.999706i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.0950 | − | 3.64850i | −0.597333 | − | 0.196429i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.5751 | + | 15.9205i | −1.48031 | + | 0.854656i | −0.999751 | − | 0.0223084i | \(-0.992898\pi\) |
−0.480556 | + | 0.876964i | \(0.659565\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7613 | − | 7.36772i | −0.683095 | − | 0.394385i | 0.117925 | − | 0.993022i | \(-0.462376\pi\) |
−0.801020 | + | 0.598637i | \(0.795709\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.5839 | − | 23.1075i | 0.564929 | − | 1.23339i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.07979 | + | 1.87025i | −0.0574713 | + | 0.0995431i | −0.893330 | − | 0.449402i | \(-0.851637\pi\) |
0.835858 | + | 0.548945i | \(0.184970\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.24484 | + | 5.33751i | −0.490665 | + | 0.283286i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.6099 | + | 11.0912i | −0.667388 | + | 0.587009i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.6448i | 1.72293i | 0.507820 | + | 0.861463i | \(0.330451\pi\) | ||||
−0.507820 | + | 0.861463i | \(0.669549\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.89765 | 0.520929 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.04071 | + | 6.75690i | 0.317055 | + | 0.354645i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.1972 | + | 11.0835i | −1.00483 | + | 0.580138i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.7212 | − | 14.8501i | −1.34264 | − | 0.775171i | −0.355442 | − | 0.934698i | \(-0.615670\pi\) |
−0.987194 | + | 0.159527i | \(0.949003\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.5136 | − | 14.3899i | −1.01584 | − | 0.749109i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.00836 | + | 1.74653i | 0.0522109 | + | 0.0904320i | 0.890950 | − | 0.454102i | \(-0.150040\pi\) |
−0.838739 | + | 0.544534i | \(0.816707\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.6250 | − | 4.30763i | 1.06507 | − | 0.222445i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.0921 | 1.65283 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8709 | 0.969332 | 0.484666 | − | 0.874699i | \(-0.338941\pi\) | ||||
0.484666 | + | 0.874699i | \(0.338941\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.37620 | − | 0.496282i | 0.121737 | − | 0.0254253i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.418256 | + | 0.724440i | 0.0213719 | + | 0.0370172i | 0.876514 | − | 0.481377i | \(-0.159863\pi\) |
−0.855142 | + | 0.518394i | \(0.826530\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.60790 | − | 9.89714i | −0.285805 | − | 0.504405i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.33055 | − | 20.7572i | 0.118468 | − | 1.05515i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.4964 | + | 12.4109i | 1.08991 | + | 0.629260i | 0.933552 | − | 0.358441i | \(-0.116692\pi\) |
0.156357 | + | 0.987701i | \(0.450025\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.9533 | + | 6.90127i | −0.604507 | + | 0.349012i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.1117 | − | 13.5477i | −0.610954 | − | 0.683389i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.43662 | −0.273546 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.03390i | − | 0.152267i | −0.997098 | − | 0.0761336i | \(-0.975742\pi\) | ||
0.997098 | − | 0.0761336i | \(-0.0242575\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.13106 | + | 10.3814i | 0.457125 | + | 0.519719i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.3251 | − | 6.53854i | 0.565548 | − | 0.326519i | −0.189822 | − | 0.981819i | \(-0.560791\pi\) |
0.755369 | + | 0.655300i | \(0.227458\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.3640 | + | 19.6831i | −0.566083 | + | 0.980485i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.7120 | − | 3.57322i | −0.780733 | − | 0.177555i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.4750 | + | 11.2439i | 0.965339 | + | 0.557339i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.82124 | − | 2.78354i | 0.238395 | − | 0.137637i | −0.376044 | − | 0.926602i | \(-0.622716\pi\) |
0.614439 | + | 0.788965i | \(0.289382\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.76707 | + | 2.55414i | 0.383121 | + | 0.125987i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −33.2728 | − | 19.5705i | −1.63725 | − | 0.963000i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.0746 | −1.23086 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.05223 | + | 2.72871i | −0.149468 | + | 0.133625i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.19938 | − | 14.2017i | −0.400566 | − | 0.693800i | 0.593228 | − | 0.805034i | \(-0.297853\pi\) |
−0.993794 | + | 0.111234i | \(0.964520\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.72892 | + | 13.3869i | −0.376684 | + | 0.652437i | −0.990578 | − | 0.136952i | \(-0.956269\pi\) |
0.613893 | + | 0.789389i | \(0.289603\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.71917 | + | 15.3119i | −0.0835889 | + | 0.744491i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.28839 | − | 5.69566i | 0.159510 | − | 0.276280i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.9708 | + | 0.242361i | 1.45039 | + | 0.0117287i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 19.9159 | − | 4.15953i | 0.961547 | − | 0.200824i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 25.0266i | − | 1.20549i | −0.797935 | − | 0.602744i | \(-0.794074\pi\) | ||
0.797935 | − | 0.602744i | \(-0.205926\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.25168i | − | 0.108209i | −0.998535 | − | 0.0541044i | \(-0.982770\pi\) | ||
0.998535 | − | 0.0541044i | \(-0.0172304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.15953 | − | 19.9159i | −0.199434 | − | 0.954893i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.68161 | + | 9.84084i | 0.271788 | + | 0.470751i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.2293 | − | 9.37000i | −0.774583 | − | 0.447206i | 0.0599239 | − | 0.998203i | \(-0.480914\pi\) |
−0.834507 | + | 0.550997i | \(0.814248\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.68027 | − | 20.8283i | 0.127632 | − | 0.991822i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.04314 | + | 0.602256i | 0.0495610 | + | 0.0286141i | 0.524576 | − | 0.851364i | \(-0.324224\pi\) |
−0.475015 | + | 0.879978i | \(0.657557\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.35568 | + | 5.81221i | 0.159074 | + | 0.275525i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.4216 | − | 20.0450i | 1.06050 | − | 0.948097i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 26.8022i | − | 1.26487i | −0.774612 | − | 0.632436i | \(-0.782055\pi\) | ||
0.774612 | − | 0.632436i | \(-0.217945\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 19.4087i | − | 0.913918i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.07770 | − | 18.4821i | 0.285555 | − | 0.868364i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.1686 | + | 0.187354i | 1.08616 | + | 0.00878331i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.92442 | + | 11.9934i | −0.323911 | + | 0.561030i | −0.981291 | − | 0.192529i | \(-0.938331\pi\) |
0.657381 | + | 0.753559i | \(0.271664\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.5236 | + | 11.0283i | −0.724578 | + | 0.514755i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.40241 | − | 4.16110i | 0.111892 | − | 0.193802i | −0.804641 | − | 0.593761i | \(-0.797642\pi\) |
0.916533 | + | 0.399959i | \(0.130976\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.5194 | − | 18.2201i | −0.488877 | − | 0.846760i | 0.511041 | − | 0.859556i | \(-0.329260\pi\) |
−0.999918 | + | 0.0127960i | \(0.995927\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.6879 | + | 4.50118i | 0.634763 | + | 0.208737i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.82302 | −0.269457 | −0.134729 | − | 0.990883i | \(-0.543016\pi\) | ||||
−0.134729 | + | 0.990883i | \(0.543016\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.30042 | + | 0.764885i | 0.0600478 | + | 0.0353191i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.8751 | + | 15.9804i | −0.823640 | + | 0.736339i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.4804 | − | 8.36028i | 0.665811 | − | 0.384406i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.68907 | − | 2.70724i | −0.215149 | − | 0.124217i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.4781 | + | 23.3447i | −0.615828 | + | 1.06665i | 0.374411 | + | 0.927263i | \(0.377845\pi\) |
−0.990239 | + | 0.139382i | \(0.955488\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −39.6662 | + | 22.9013i | −1.80862 | + | 1.04421i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.52410 | − | 16.3518i | 0.251355 | − | 0.744035i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 9.86639i | − | 0.448010i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.6268 | 0.617487 | 0.308744 | − | 0.951145i | \(-0.400091\pi\) | ||||
0.308744 | + | 0.951145i | \(0.400091\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.35116 | + | 1.53533i | −0.332431 | + | 0.0694299i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.7430 | − | 19.4815i | 1.52280 | − | 0.879188i | 0.523162 | − | 0.852234i | \(-0.324752\pi\) |
0.999637 | − | 0.0269544i | \(-0.00858088\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.8227 | − | 12.0220i | −0.937807 | − | 0.541443i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.16267 | − | 11.8203i | −0.232045 | − | 0.531285i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.77696 | − | 13.7252i | −0.348844 | − | 0.615660i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.0048 | + | 22.5250i | 0.582176 | + | 1.00836i | 0.995221 | + | 0.0976483i | \(0.0311320\pi\) |
−0.413045 | + | 0.910711i | \(0.635535\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.3320 | − | 16.0312i | −0.640307 | − | 0.716221i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.5271 | −0.469378 | −0.234689 | − | 0.972070i | \(-0.575407\pi\) | ||||
−0.234689 | + | 0.972070i | \(0.575407\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.448168 | 0.0199432 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.91121 | + | 17.9758i | −0.262526 | + | 0.798333i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.469435 | + | 0.813086i | 0.0208074 | + | 0.0360394i | 0.876242 | − | 0.481872i | \(-0.160043\pi\) |
−0.855434 | + | 0.517911i | \(0.826710\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.1491 | − | 28.5009i | −0.714395 | − | 1.26081i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.07925 | + | 12.7801i | 0.400859 | + | 0.564255i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.260376 | + | 0.150328i | 0.0114735 | + | 0.00662424i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.6818 | + | 6.16711i | −0.469783 | + | 0.271229i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.42442 | + | 28.6593i | −0.413686 | + | 1.25801i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.5054 | −1.73076 | −0.865382 | − | 0.501112i | \(-0.832924\pi\) | ||||
−0.865382 | + | 0.501112i | \(0.832924\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.3292i | 1.06384i | 0.846794 | + | 0.531922i | \(0.178530\pi\) | ||||
−0.846794 | + | 0.531922i | \(0.821470\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.61621 | + | 8.06374i | 0.0705373 | + | 0.351930i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.7469 | − | 8.51413i | 0.642385 | − | 0.370881i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.40718 | + | 7.63346i | −0.191616 | + | 0.331889i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.2274 | − | 25.9777i | −1.52874 | − | 1.12734i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.2349 | + | 19.7655i | 1.48288 | + | 0.856141i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.3896 | − | 7.15316i | 0.535651 | − | 0.309258i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.64661 | + | 22.2480i | 0.200516 | + | 0.960073i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.6924 | − | 8.16873i | 0.632845 | − | 0.351852i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.7281 | 1.83702 | 0.918512 | − | 0.395394i | \(-0.129392\pi\) | ||||
0.918512 | + | 0.395394i | \(0.129392\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.73007 | − | 22.6476i | −0.202987 | − | 0.971902i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.9665 | + | 29.3869i | 0.726767 | + | 1.25880i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.2477 | − | 21.2136i | 0.523672 | − | 0.907026i | −0.475949 | − | 0.879473i | \(-0.657895\pi\) |
0.999620 | − | 0.0275530i | \(-0.00877149\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 33.7727 | + | 3.79188i | 1.44138 | + | 0.161833i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.89735 | + | 17.1427i | −0.421641 | + | 0.730304i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.0649667 | − | 8.03389i | 0.00276266 | − | 0.341636i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.3534 | + | 21.6479i | 0.821506 | + | 0.918903i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.54431i | 0.107806i | 0.998546 | + | 0.0539030i | \(0.0171662\pi\) | ||||
−0.998546 | + | 0.0539030i | \(0.982834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.0560i | 1.44042i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.4804 | − | 4.76178i | −0.611364 | − | 0.201043i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.90707 | + | 13.6954i | 0.333243 | + | 0.577194i | 0.983146 | − | 0.182823i | \(-0.0585236\pi\) |
−0.649902 | + | 0.760018i | \(0.725190\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.79783 | + | 1.03798i | 0.0756354 | + | 0.0436681i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.46803 | − | 23.1754i | 0.229635 | − | 0.973277i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.52793 | − | 3.19155i | −0.231743 | − | 0.133797i | 0.379633 | − | 0.925137i | \(-0.376050\pi\) |
−0.611376 | + | 0.791340i | \(0.709384\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.91188 | − | 6.77557i | −0.163707 | − | 0.283549i | 0.772488 | − | 0.635029i | \(-0.219012\pi\) |
−0.936195 | + | 0.351480i | \(0.885678\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.2252 | − | 5.00668i | −0.636040 | − | 0.209157i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.75933i | 0.281884i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.3197i | 0.596138i | 0.954544 | + | 0.298069i | \(0.0963425\pi\) | ||||
−0.954544 | + | 0.298069i | \(0.903657\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.3523 | − | 31.7137i | −1.17828 | − | 1.31798i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.299637 | − | 37.0536i | 0.0124310 | − | 1.53724i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 26.1075 | + | 2.93126i | 1.07941 | + | 0.121193i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.37575 | − | 4.11492i | 0.0980577 | − | 0.169841i | −0.812823 | − | 0.582511i | \(-0.802070\pi\) |
0.910881 | + | 0.412670i | \(0.135404\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.00943 | − | 12.1407i | −0.288819 | − | 0.500249i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.42141 | + | 21.1698i | 0.181873 | + | 0.870808i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.58070 | 0.147042 | 0.0735208 | − | 0.997294i | \(-0.476576\pi\) | ||||
0.0735208 | + | 0.997294i | \(0.476576\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.9625 | − | 8.80071i | −0.613404 | − | 0.360794i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.0634366 | + | 0.303735i | 0.00259629 | + | 0.0124311i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.0471 | − | 7.53277i | 0.533091 | − | 0.307780i | −0.209183 | − | 0.977877i | \(-0.567080\pi\) |
0.742274 | + | 0.670096i | \(0.233747\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.8704 | − | 11.4722i | −0.810530 | − | 0.467960i | 0.0366096 | − | 0.999330i | \(-0.488344\pi\) |
−0.847140 | + | 0.531370i | \(0.821678\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.37682 | + | 1.01531i | 0.0560683 | + | 0.0413464i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.68425 | + | 8.11336i | −0.190442 | + | 0.329855i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.2030 | + | 12.2416i | −0.860605 | + | 0.496870i | −0.864215 | − | 0.503123i | \(-0.832184\pi\) |
0.00360990 | + | 0.999993i | \(0.498851\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.4801 | − | 5.90869i | 1.19459 | − | 0.239432i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 25.1221i | − | 1.01633i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.880086 | −0.0355463 | −0.0177732 | − | 0.999842i | \(-0.505658\pi\) | ||||
−0.0177732 | + | 0.999842i | \(0.505658\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.82892 | − | 23.8075i | 0.315693 | − | 0.960011i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.7607 | + | 6.79005i | −0.473468 | + | 0.273357i | −0.717690 | − | 0.696362i | \(-0.754801\pi\) |
0.244222 | + | 0.969719i | \(0.421467\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.7325 | + | 17.7434i | 1.23524 | + | 0.713169i | 0.968118 | − | 0.250493i | \(-0.0805926\pi\) |
0.267126 | + | 0.963662i | \(0.413926\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.14977 | − | 17.7931i | 0.327039 | − | 0.714012i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.62901 | + | 4.88936i | −0.345714 | + | 0.195888i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.40300 | + | 11.0903i | 0.256120 | + | 0.443613i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.92024 | + | 11.9213i | −0.156559 | + | 0.476091i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.3161 | 1.36827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.9822 | −1.07415 | −0.537073 | − | 0.843536i | \(-0.680470\pi\) | ||||
−0.537073 | + | 0.843536i | \(0.680470\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.4569 | + | 19.5266i | 0.693849 | + | 0.776112i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.25459 | + | 2.17302i | 0.0497869 | + | 0.0862335i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.553721 | + | 34.2348i | −0.0219392 | + | 1.35643i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.15953 | − | 16.3923i | −0.283227 | − | 0.648470i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.932777 | + | 0.538539i | 0.0368425 | + | 0.0212710i | 0.518308 | − | 0.855194i | \(-0.326562\pi\) |
−0.481466 | + | 0.876465i | \(0.659895\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.3126 | + | 19.2330i | −1.31372 | + | 0.758477i | −0.982710 | − | 0.185150i | \(-0.940723\pi\) |
−0.331010 | + | 0.943627i | \(0.607389\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.1346 | − | 4.41407i | 0.832175 | − | 0.173804i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.95210 | 0.351943 | 0.175972 | − | 0.984395i | \(-0.443693\pi\) | ||||
0.175972 | + | 0.984395i | \(0.443693\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 35.0380i | − | 1.37536i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.81512 | + | 20.1734i | −0.267106 | + | 0.790656i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.85934 | + | 5.69229i | −0.385826 | + | 0.222757i | −0.680350 | − | 0.732887i | \(-0.738172\pi\) |
0.294524 | + | 0.955644i | \(0.404839\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.39197 | − | 16.2674i | 0.366975 | − | 0.635619i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.8670 | − | 34.0392i | −0.580017 | − | 1.32799i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.4373 | − | 18.1503i | −1.22462 | − | 0.707036i | −0.258723 | − | 0.965952i | \(-0.583302\pi\) |
−0.965900 | + | 0.258915i | \(0.916635\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.2425 | + | 18.0379i | −1.21519 | + | 0.701593i | −0.963886 | − | 0.266315i | \(-0.914194\pi\) |
−0.251308 | + | 0.967907i | \(0.580861\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.1460 | − | 20.6927i | 0.898916 | − | 0.803637i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.24536 | + | 12.3182i | −0.280963 | + | 0.477680i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.7114 | 0.956828 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.8133 | − | 4.54240i | −0.534052 | − | 0.175619i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.6025 | + | 23.5602i | 0.525117 | + | 0.909530i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.78512 | − | 8.28806i | 0.184453 | − | 0.319481i | −0.758939 | − | 0.651161i | \(-0.774282\pi\) |
0.943392 | + | 0.331680i | \(0.107615\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.876091 | + | 9.28402i | 0.0337207 | + | 0.357342i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.81408 | − | 13.5344i | 0.300320 | − | 0.520169i | −0.675889 | − | 0.737004i | \(-0.736240\pi\) |
0.976208 | + | 0.216835i | \(0.0695733\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.5799 | + | 0.117902i | 0.559526 | + | 0.00452465i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.31221 | − | 3.99038i | 0.0502839 | − | 0.152912i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.1313i | 0.425926i | 0.977060 | + | 0.212963i | \(0.0683114\pi\) | ||||
−0.977060 | + | 0.212963i | \(0.931689\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.45145i | 0.322913i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.60803 | + | 2.33159i | −0.0995025 | + | 0.0889559i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.61903 | − | 1.51210i | −0.0996324 | − | 0.0575228i | 0.449356 | − | 0.893353i | \(-0.351654\pi\) |
−0.548988 | + | 0.835830i | \(0.684987\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.5291 | − | 7.48782i | 0.665874 | − | 0.284439i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.66497 | − | 2.11597i | −0.139020 | − | 0.0802633i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.8087 | − | 25.6494i | −0.560919 | − | 0.971540i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.50739 | − | 21.5815i | −0.170485 | − | 0.816286i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 50.1486i | − | 1.89409i | −0.321103 | − | 0.947044i | \(-0.604054\pi\) | ||
0.321103 | − | 0.947044i | \(-0.395946\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 28.2514i | − | 1.06552i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.5904 | + | 3.25612i | −0.587167 | + | 0.122633i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.00535553 | + | 0.662274i | −0.000201415 | + | 0.0249074i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.80385 | − | 3.12436i | 0.0677449 | − | 0.117338i | −0.830163 | − | 0.557520i | \(-0.811753\pi\) |
0.897908 | + | 0.440183i | \(0.145086\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.01644 | − | 9.05299i | 0.0381195 | − | 0.339514i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.75046 | + | 15.1562i | −0.327707 | + | 0.567605i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.5152 | + | 18.2129i | 0.393246 | + | 0.681123i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.5319 | − | 20.1437i | 0.841469 | − | 0.752279i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.3161 | 1.27977 | 0.639887 | − | 0.768469i | \(-0.278981\pi\) | ||||
0.639887 | + | 0.768469i | \(0.278981\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.225257 | + | 0.382970i | −0.00838899 | + | 0.0142626i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.8118 | − | 6.18613i | −0.699619 | − | 0.230065i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.1972 | + | 5.88737i | −0.378716 | + | 0.218651i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.4757 | − | 11.2443i | −0.722315 | − | 0.417029i | 0.0932892 | − | 0.995639i | \(-0.470262\pi\) |
−0.815604 | + | 0.578610i | \(0.803595\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.88761 | − | 25.4953i | 0.329171 | − | 0.944270i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.7577 | − | 22.0970i | 0.471860 | − | 0.817285i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.0065 | − | 15.5922i | 0.997509 | − | 0.575912i | 0.0899987 | − | 0.995942i | \(-0.471314\pi\) |
0.907510 | + | 0.420030i | \(0.137980\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.3173 | − | 4.09361i | 0.786302 | − | 0.150995i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.36941i | 0.0504429i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.08628 | −0.150316 | −0.0751581 | − | 0.997172i | \(-0.523946\pi\) | ||||
−0.0751581 | + | 0.997172i | \(0.523946\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.0357 | − | 19.0554i | −0.625821 | − | 0.700018i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.78246 | − | 1.02910i | 0.0653921 | − | 0.0377542i | −0.466947 | − | 0.884285i | \(-0.654646\pi\) |
0.532340 | + | 0.846531i | \(0.321313\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.9227 | + | 15.5439i | 0.986373 | + | 0.569483i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.68798 | − | 41.7538i | 0.171524 | − | 1.52769i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.4224 | + | 18.3941i | 0.380828 | + | 0.672106i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.9053 | + | 20.6205i | 0.434429 | + | 0.752454i | 0.997249 | − | 0.0741262i | \(-0.0236168\pi\) |
−0.562820 | + | 0.826580i | \(0.690283\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −46.3811 | + | 9.68693i | −1.69022 | + | 0.353011i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.1106 | 0.731900 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0754 | 0.366197 | 0.183098 | − | 0.983095i | \(-0.441387\pi\) | ||||
0.183098 | + | 0.983095i | \(0.441387\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.3355 | − | 3.20289i | 0.556642 | − | 0.116258i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.9368 | + | 24.1392i | 0.505207 | + | 0.875044i | 0.999982 | + | 0.00602283i | \(0.00191714\pi\) |
−0.494775 | + | 0.869021i | \(0.664750\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.6289 | + | 24.7209i | −1.57947 | + | 0.894957i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.8415 | − | 11.6820i | −0.572752 | − | 0.422364i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 61.8035 | + | 35.6823i | 2.23159 | + | 1.28841i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.21166 | + | 3.58631i | −0.223998 | + | 0.129326i | −0.607800 | − | 0.794090i | \(-0.707948\pi\) |
0.383802 | + | 0.923415i | \(0.374615\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.03663 | − | 4.51521i | −0.145376 | − | 0.162611i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.14153 | −0.0770255 | −0.0385128 | − | 0.999258i | \(-0.512262\pi\) | ||||
−0.0385128 | + | 0.999258i | \(0.512262\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 8.33903i | − | 0.299547i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −32.2212 | + | 28.3405i | −1.15593 | + | 1.01671i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.1164 | + | 12.1916i | −0.756573 | + | 0.436808i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.15953 | − | 12.4007i | 0.256188 | − | 0.443731i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33.9413 | − | 3.20289i | 1.21296 | − | 0.114462i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.4635 | − | 12.3920i | −0.766066 | − | 0.442288i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.8961 | + | 9.17759i | −0.566633 | + | 0.327146i | −0.755804 | − | 0.654798i | \(-0.772753\pi\) |
0.189170 | + | 0.981944i | \(0.439420\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.8671 | − | 5.21778i | −0.564884 | − | 0.185758i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.55534 | + | 2.64432i | −0.0553017 | + | 0.0940212i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −55.4103 | −1.96768 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.4226 | + | 21.5166i | 0.440031 | + | 0.762156i | 0.997691 | − | 0.0679130i | \(-0.0216340\pi\) |
−0.557660 | + | 0.830069i | \(0.688301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.41094 | + | 16.3002i | −0.332935 | + | 0.576660i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.3058 | + | 4.50118i | −0.364138 | + | 0.159041i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.8670 | − | 25.7504i | 0.524645 | − | 0.908712i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.8401 | + | 0.144265i | 0.628781 | + | 0.00508468i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.7175 | − | 2.44726i | 0.412475 | − | 0.0861475i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.7861i | 1.32849i | 0.747516 | + | 0.664244i | \(0.231246\pi\) | ||||
−0.747516 | + | 0.664244i | \(0.768754\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.5165i | 1.28227i | 0.767429 | + | 0.641134i | \(0.221536\pi\) | ||||
−0.767429 | + | 0.641134i | \(0.778464\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.30565 | + | 34.9795i | 0.256220 | + | 1.22679i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.88128 | − | 6.72257i | −0.135955 | − | 0.235481i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.1918 | − | 10.5030i | −0.636449 | − | 0.367454i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.64361 | + | 38.5450i | −0.162261 | + | 1.34687i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.52142 | − | 3.18779i | −0.192699 | − | 0.111255i | 0.400547 | − | 0.916276i | \(-0.368820\pi\) |
−0.593245 | + | 0.805022i | \(0.702154\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.0293 | + | 24.2995i | 0.489032 | + | 0.847028i | 0.999920 | − | 0.0126187i | \(-0.00401678\pi\) |
−0.510888 | + | 0.859647i | \(0.670683\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.56516 | + | 4.97529i | −0.193754 | + | 0.173217i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 0.581579i | − | 0.0202235i | −0.999949 | − | 0.0101117i | \(-0.996781\pi\) | ||
0.999949 | − | 0.0101117i | \(-0.00321872\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 51.9246i | − | 1.80342i | −0.432346 | − | 0.901708i | \(-0.642314\pi\) | ||
0.432346 | − | 0.901708i | \(-0.357686\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.39433 | + | 25.5269i | −0.291196 | + | 0.885518i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.1839 | − | 22.0055i | 0.456796 | − | 0.762446i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.1137 | − | 19.2495i | 0.384606 | − | 0.666156i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.0544 | + | 21.9514i | −0.347532 | + | 0.758752i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.33038 | − | 5.76838i | 0.114977 | − | 0.199147i | −0.802793 | − | 0.596257i | \(-0.796654\pi\) |
0.917771 | + | 0.397111i | \(0.129987\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.02357 | + | 12.1652i | 0.242192 | + | 0.419489i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.3732 | − | 7.35726i | −0.770574 | − | 0.253397i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.5597 | −0.672874 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.9334 | − | 7.01904i | −0.410038 | − | 0.241177i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.03459 | + | 6.28897i | −0.241427 | + | 0.215837i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.5435 | + | 17.6343i | −1.04702 | + | 0.604495i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.2287 | − | 11.1017i | −0.658378 | − | 0.380115i | 0.133281 | − | 0.991078i | \(-0.457449\pi\) |
−0.791659 | + | 0.610964i | \(0.790782\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.61746 | + | 13.0419i | −0.328910 | + | 0.446023i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.64830 | + | 13.2472i | −0.261261 | + | 0.452517i | −0.966577 | − | 0.256375i | \(-0.917472\pi\) |
0.705316 | + | 0.708893i | \(0.250805\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.68620 | + | 2.12823i | −0.125772 | + | 0.0726143i | −0.561566 | − | 0.827432i | \(-0.689801\pi\) |
0.435794 | + | 0.900046i | \(0.356468\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.0877 | + | 11.8536i | 1.19578 | + | 0.403969i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 23.6624i | − | 0.805476i | −0.915315 | − | 0.402738i | \(-0.868059\pi\) | ||
0.915315 | − | 0.402738i | \(-0.131941\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.1846 | −1.06031 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.05321 | − | 1.26424i | 0.205578 | − | 0.0429359i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.31546 | − | 3.64623i | 0.214237 | − | 0.123690i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.41551 | − | 1.39459i | −0.0818463 | − | 0.0472540i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.4294 | + | 1.84464i | 0.556051 | + | 0.0624315i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28.0023 | + | 15.8666i | −0.946649 | + | 0.536389i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.1962 | + | 17.6603i | 0.344300 | + | 0.596344i | 0.985226 | − | 0.171258i | \(-0.0547831\pi\) |
−0.640927 | + | 0.767602i | \(0.721450\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.2392 | − | 31.5872i | −0.952484 | − | 1.06541i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.4586 | 1.09356 | 0.546780 | − | 0.837276i | \(-0.315853\pi\) | ||||
0.546780 | + | 0.837276i | \(0.315853\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.8311 | 0.835632 | 0.417816 | − | 0.908532i | \(-0.362796\pi\) | ||||
0.417816 | + | 0.908532i | \(0.362796\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.1334 | − | 42.9791i | 0.475088 | − | 1.44473i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.86059 | + | 8.41879i | 0.163203 | + | 0.282675i | 0.936016 | − | 0.351959i | \(-0.114484\pi\) |
−0.772813 | + | 0.634634i | \(0.781151\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.22614 | + | 1.82799i | −0.108201 | + | 0.0613088i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.6483 | − | 6.38687i | 0.691745 | − | 0.213968i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.4195 | + | 7.74775i | 0.449066 | + | 0.259269i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.3456 | + | 11.7465i | −0.680079 | + | 0.392644i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.96789 | + | 30.3120i | −0.332818 | + | 1.01209i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.4865 | −1.01678 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.27028 | + | 31.2842i | 0.208662 | + | 1.04107i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.7110 | − | 11.9575i | 0.688458 | − | 0.397481i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.04314 | + | 13.9311i | −0.267068 | + | 0.462575i | −0.968103 | − | 0.250551i | \(-0.919388\pi\) |
0.701035 | + | 0.713127i | \(0.252722\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.0837902 | + | 0.746284i | −0.00277915 | + | 0.0247527i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.0087 | − | 15.5935i | −0.894838 | − | 0.516635i | −0.0193161 | − | 0.999813i | \(-0.506149\pi\) |
−0.875522 | + | 0.483179i | \(0.839482\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.1279 | − | 16.8170i | 0.963993 | − | 0.556562i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.18184 | + | 34.3868i | 0.237424 | + | 1.13679i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.9267 | + | 14.0733i | 0.790128 | + | 0.464740i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.7664 | −0.849955 | −0.424977 | − | 0.905204i | \(-0.639718\pi\) | ||||
−0.424977 | + | 0.905204i | \(0.639718\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.0560 | − | 52.9363i | −0.364308 | − | 1.74431i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.5824 | + | 25.2574i | 0.479984 | + | 0.831357i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.40258 | − | 14.5537i | 0.276275 | − | 0.478522i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.299004 | + | 0.405469i | −0.00982060 | + | 0.0133173i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.3744 | + | 47.4138i | −0.898124 | + | 1.55560i | −0.0682329 | + | 0.997669i | \(0.521736\pi\) |
−0.829891 | + | 0.557926i | \(0.811597\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.1165 | − | 10.8539i | −0.593744 | − | 0.355723i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.5945 | − | 14.0877i | −0.412326 | − | 0.461212i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 15.7563i | − | 0.515288i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 58.2065i | 1.90152i | 0.309924 | + | 0.950761i | \(0.399696\pi\) | ||||
−0.309924 | + | 0.950761i | \(0.600304\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.63384 | − | 1.85265i | −0.183853 | − | 0.0604588i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.6658 | + | 28.8660i | 0.543289 | + | 0.941005i | 0.998712 | + | 0.0507297i | \(0.0161547\pi\) |
−0.455423 | + | 0.890275i | \(0.650512\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.3613 | + | 15.2197i | 0.858443 | + | 0.495622i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 24.5223 | − | 2.11414i | 0.797710 | − | 0.0687730i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.59497 | + | 3.80761i | 0.214308 | + | 0.123731i | 0.603312 | − | 0.797505i | \(-0.293847\pi\) |
−0.389004 | + | 0.921236i | \(0.627181\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.2808 | + | 52.4478i | 0.982955 | + | 1.70253i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.3396 | − | 10.3058i | −1.01626 | − | 0.334188i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.7861i | 1.80709i | 0.428495 | + | 0.903544i | \(0.359044\pi\) | ||||
−0.428495 | + | 0.903544i | \(0.640956\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 16.5667i | − | 0.536085i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.1891 | + | 20.3456i | 0.587970 | + | 0.657680i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.4890 | − | 0.100993i | −0.403291 | − | 0.00326125i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.70451 | + | 8.14845i | −0.151758 | + | 0.262853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.59497 | + | 21.9684i | 0.309194 | + | 0.707923i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.9857 | − | 38.0803i | 0.707744 | − | 1.22585i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.3369 | + | 23.1003i | 0.428887 | + | 0.742855i | 0.996775 | − | 0.0802517i | \(-0.0255724\pi\) |
−0.567887 | + | 0.823106i | \(0.692239\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.91512 | + | 18.7456i | 0.125772 | + | 0.602197i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.59942 | 0.275968 | 0.137984 | − | 0.990434i | \(-0.455938\pi\) | ||||
0.137984 | + | 0.990434i | \(0.455938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.17064 | − | 5.39057i | 0.101646 | − | 0.172814i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.10842 | − | 14.8832i | −0.0995492 | − | 0.476643i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.7973 | + | 7.38854i | −0.409423 | + | 0.236380i | −0.690542 | − | 0.723293i | \(-0.742628\pi\) |
0.281119 | + | 0.959673i | \(0.409295\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.79627 | − | 4.50118i | −0.249170 | − | 0.143858i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −52.1068 | + | 22.7583i | −1.66364 | + | 0.726615i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.2568 | + | 17.7652i | −0.327140 | + | 0.566623i | −0.981943 | − | 0.189176i | \(-0.939418\pi\) |
0.654803 | + | 0.755800i | \(0.272752\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.3596 | + | 11.1772i | −0.616847 | + | 0.356137i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.62539 | − | 23.0773i | −0.147228 | − | 0.734560i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.2236i | 0.833861i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.29294 | 0.295200 | 0.147600 | − | 0.989047i | \(-0.452845\pi\) | ||||
0.147600 | + | 0.989047i | \(0.452845\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.0396334 | + | 0.120524i | −0.00125773 | + | 0.00382471i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.277763 | + | 0.160366i | −0.00880567 | + | 0.00508396i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.0172917 | − | 0.00998339i | −0.000547635 | − | 0.000316177i | 0.499726 | − | 0.866183i | \(-0.333434\pi\) |
−0.500274 | + | 0.865867i | \(0.666767\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −39.6662 | + | 28.1797i | −1.25498 | + | 0.891566i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))