Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(949,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.949");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.l (of order \(3\), 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{5} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.5 | ||
Root | \(-0.674693 + 1.59524i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.961 |
Dual form | 1764.2.l.i.949.5 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0.674693 | − | 1.59524i | 0.389534 | − | 0.921012i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.14520 | −1.85379 | −0.926894 | − | 0.375322i | \(-0.877532\pi\) | ||||
−0.926894 | + | 0.375322i | \(0.877532\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.08958 | − | 2.15260i | −0.696526 | − | 0.717532i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.868858 | 0.261971 | 0.130985 | − | 0.991384i | \(-0.458186\pi\) | ||||
0.130985 | + | 0.991384i | \(0.458186\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.86231 | − | 4.95766i | −0.793861 | − | 1.37501i | −0.923560 | − | 0.383455i | \(-0.874734\pi\) |
0.129698 | − | 0.991554i | \(-0.458599\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.79674 | + | 6.61258i | −0.722115 | + | 1.70736i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.44613 | + | 2.50478i | 0.350739 | + | 0.607498i | 0.986379 | − | 0.164488i | \(-0.0525971\pi\) |
−0.635640 | + | 0.771986i | \(0.719264\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00703 | − | 3.47627i | 0.460444 | − | 0.797512i | −0.538539 | − | 0.842600i | \(-0.681024\pi\) |
0.998983 | + | 0.0450884i | \(0.0143570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.82977 | −1.21559 | −0.607795 | − | 0.794094i | \(-0.707946\pi\) | ||||
−0.607795 | + | 0.794094i | \(0.707946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.1827 | 2.43653 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.84373 | + | 1.88104i | −0.932176 | + | 0.362005i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.900417 | + | 1.55957i | −0.167203 | + | 0.289604i | −0.937435 | − | 0.348159i | \(-0.886807\pi\) |
0.770232 | + | 0.637763i | \(0.220140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.48046 | + | 2.56422i | −0.265898 | + | 0.460548i | −0.967798 | − | 0.251727i | \(-0.919002\pi\) |
0.701901 | + | 0.712275i | \(0.252335\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.586213 | − | 1.38604i | 0.102047 | − | 0.241278i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.64925 | + | 4.58864i | −0.435535 | + | 0.754368i | −0.997339 | − | 0.0729017i | \(-0.976774\pi\) |
0.561804 | + | 0.827270i | \(0.310107\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.83984 | + | 1.22116i | −1.57564 | + | 0.195543i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.89325 | + | 10.2074i | 0.920371 | + | 1.59413i | 0.798842 | + | 0.601541i | \(0.205446\pi\) |
0.121528 | + | 0.992588i | \(0.461220\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00703 | + | 3.47627i | −0.306069 | + | 0.530127i | −0.977499 | − | 0.210941i | \(-0.932347\pi\) |
0.671430 | + | 0.741068i | \(0.265680\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.66171 | + | 8.92293i | 1.29121 | + | 1.33015i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.17218 | + | 2.03028i | 0.170980 | + | 0.296147i | 0.938763 | − | 0.344564i | \(-0.111973\pi\) |
−0.767783 | + | 0.640711i | \(0.778640\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.97142 | − | 0.616973i | 0.696138 | − | 0.0863935i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.09116 | − | 1.88995i | −0.149883 | − | 0.259605i | 0.781301 | − | 0.624154i | \(-0.214556\pi\) |
−0.931184 | + | 0.364549i | \(0.881223\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.60159 | −0.485638 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.19136 | − | 5.54711i | −0.555159 | − | 0.734733i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.52715 | + | 2.64510i | −0.198818 | + | 0.344363i | −0.948146 | − | 0.317837i | \(-0.897044\pi\) |
0.749327 | + | 0.662200i | \(0.230377\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.81659 | + | 4.87848i | 0.360628 | + | 0.624625i | 0.988064 | − | 0.154042i | \(-0.0492292\pi\) |
−0.627437 | + | 0.778668i | \(0.715896\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.8648 | + | 20.5505i | 1.47165 | + | 2.54898i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.25539 | − | 2.17440i | 0.153370 | − | 0.265645i | −0.779094 | − | 0.626907i | \(-0.784321\pi\) |
0.932464 | + | 0.361262i | \(0.117654\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.93331 | + | 9.29988i | −0.473514 | + | 1.11957i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.09143 | −0.129529 | −0.0647647 | − | 0.997901i | \(-0.520630\pi\) | ||||
−0.0647647 | + | 0.997901i | \(0.520630\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.723285 | − | 1.25277i | −0.0846541 | − | 0.146625i | 0.820590 | − | 0.571518i | \(-0.193645\pi\) |
−0.905244 | + | 0.424893i | \(0.860312\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.21956 | − | 19.4343i | 0.949113 | − | 2.24408i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.06464 | + | 1.84401i | 0.119781 | + | 0.207468i | 0.919681 | − | 0.392666i | \(-0.128447\pi\) |
−0.799900 | + | 0.600134i | \(0.795114\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.267330 | + | 8.99603i | −0.0297034 | + | 0.999559i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.18784 | + | 3.78946i | −0.240147 | + | 0.415947i | −0.960756 | − | 0.277395i | \(-0.910529\pi\) |
0.720609 | + | 0.693342i | \(0.243862\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.99451 | − | 10.3828i | −0.650196 | − | 1.12617i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.88038 | + | 2.48861i | 0.201598 | + | 0.266807i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.83373 | + | 10.1043i | −0.618374 | + | 1.07105i | 0.371409 | + | 0.928469i | \(0.378875\pi\) |
−0.989783 | + | 0.142585i | \(0.954459\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.09170 | + | 4.09174i | 0.320594 | + | 0.424294i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.31953 | + | 14.4098i | −0.853566 | + | 1.47842i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.98779 | − | 6.90706i | 0.404899 | − | 0.701306i | −0.589411 | − | 0.807834i | \(-0.700640\pi\) |
0.994310 | + | 0.106528i | \(0.0339733\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.81555 | − | 1.87030i | −0.182469 | − | 0.187972i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.76370 | 0.374502 | 0.187251 | − | 0.982312i | \(-0.440042\pi\) | ||||
0.187251 | + | 0.982312i | \(0.440042\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8556 | −1.06963 | −0.534815 | − | 0.844969i | \(-0.679619\pi\) | ||||
−0.534815 | + | 0.844969i | \(0.679619\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.82343 | + | 8.35442i | −0.466298 | + | 0.807653i | −0.999259 | − | 0.0384875i | \(-0.987746\pi\) |
0.532961 | + | 0.846140i | \(0.321079\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.86131 | − | 10.1521i | −0.561412 | − | 0.972394i | −0.997374 | − | 0.0724288i | \(-0.976925\pi\) |
0.435962 | − | 0.899965i | \(-0.356408\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.53255 | + | 7.32212i | 0.525127 | + | 0.694985i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.88981 | + | 5.00530i | 0.271851 | + | 0.470859i | 0.969336 | − | 0.245740i | \(-0.0790310\pi\) |
−0.697485 | + | 0.716599i | \(0.745698\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.1655 | 2.25345 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.69083 | + | 16.5208i | −0.433667 | + | 1.52735i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2451 | −0.931371 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.2594 | − | 2.51427i | 1.82673 | − | 0.226704i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −29.7736 | −2.66303 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.47468 | 0.574535 | 0.287268 | − | 0.957850i | \(-0.407253\pi\) | ||||
0.287268 | + | 0.957850i | \(0.407253\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.19136 | + | 5.54711i | 0.369029 | + | 0.488396i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.7303 | 1.54910 | 0.774551 | − | 0.632511i | \(-0.217976\pi\) | ||||
0.774551 | + | 0.632511i | \(0.217976\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20.0782 | − | 7.79726i | 1.72806 | − | 0.671081i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.72232 | 0.232583 | 0.116292 | − | 0.993215i | \(-0.462899\pi\) | ||||
0.116292 | + | 0.993215i | \(0.462899\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.65431 | − | 14.9897i | −0.734049 | − | 1.27141i | −0.955139 | − | 0.296157i | \(-0.904295\pi\) |
0.221090 | − | 0.975253i | \(-0.429038\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.02964 | − | 0.500095i | 0.339357 | − | 0.0421156i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.48694 | − | 4.30751i | −0.207968 | − | 0.360212i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.73241 | − | 6.46472i | 0.309959 | − | 0.536865i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.84685 | −0.560916 | −0.280458 | − | 0.959866i | \(-0.590486\pi\) | ||||
−0.280458 | + | 0.959866i | \(0.590486\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.28166 | 0.755331 | 0.377666 | − | 0.925942i | \(-0.376727\pi\) | ||||
0.377666 | + | 0.925942i | \(0.376727\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.36996 | − | 8.34687i | 0.191600 | − | 0.674804i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.13678 | − | 10.6292i | 0.492918 | − | 0.853759i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.83840 | − | 11.8445i | 0.545764 | − | 0.945291i | −0.452795 | − | 0.891615i | \(-0.649573\pi\) |
0.998558 | − | 0.0536759i | \(-0.0170938\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.75113 | + | 0.465530i | −0.297484 | + | 0.0369189i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.65003 | + | 2.85793i | −0.129240 | + | 0.223850i | −0.923382 | − | 0.383882i | \(-0.874587\pi\) |
0.794142 | + | 0.607732i | \(0.207920\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.42997 | + | 5.74540i | −0.189173 | + | 0.447279i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.96228 | − | 10.3270i | −0.461375 | − | 0.799125i | 0.537655 | − | 0.843165i | \(-0.319310\pi\) |
−0.999030 | + | 0.0440399i | \(0.985977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.88562 | + | 17.1224i | −0.760432 | + | 1.31711i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.6769 | + | 2.94363i | −0.892951 | + | 0.225105i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.81694 | − | 8.34319i | −0.366225 | − | 0.634321i | 0.622747 | − | 0.782424i | \(-0.286017\pi\) |
−0.988972 | + | 0.148103i | \(0.952683\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.18922 | + | 4.22081i | 0.239716 | + | 0.317255i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.5285 | − | 19.9680i | −0.861682 | − | 1.49248i | −0.870304 | − | 0.492515i | \(-0.836078\pi\) |
0.00862183 | − | 0.999963i | \(-0.497256\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.8325 | 0.879504 | 0.439752 | − | 0.898119i | \(-0.355066\pi\) | ||||
0.439752 | + | 0.898119i | \(0.355066\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.68268 | − | 1.20166i | 0.715764 | − | 0.0888292i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.9817 | − | 19.0208i | 0.807390 | − | 1.39844i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.25649 | + | 2.17630i | 0.0918833 | + | 0.159147i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.14254 | + | 5.44303i | 0.227386 | + | 0.393844i | 0.957033 | − | 0.289980i | \(-0.0936487\pi\) |
−0.729647 | + | 0.683824i | \(0.760315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.86559 | + | 11.8915i | −0.494196 | + | 0.855972i | −0.999978 | − | 0.00668919i | \(-0.997871\pi\) |
0.505782 | + | 0.862661i | \(0.331204\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 40.7881 | − | 5.06197i | 2.92090 | − | 0.362495i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.161495 | −0.0115061 | −0.00575303 | − | 0.999983i | \(-0.501831\pi\) | ||||
−0.00575303 | + | 0.999983i | \(0.501831\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.4140 | + | 21.5016i | 0.880003 | + | 1.52421i | 0.851336 | + | 0.524621i | \(0.175793\pi\) |
0.0286672 | + | 0.999589i | \(0.490874\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.62168 | − | 3.46970i | −0.184919 | − | 0.244733i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.4287 | − | 42.3117i | −1.70617 | − | 2.95518i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.1818 | + | 12.5491i | 0.846690 | + | 0.872225i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.74382 | − | 3.02039i | 0.120623 | − | 0.208925i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.44607 | + | 16.3611i | 0.650295 | + | 1.12634i | 0.983051 | + | 0.183331i | \(0.0586879\pi\) |
−0.332757 | + | 0.943013i | \(0.607979\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.736384 | + | 1.74110i | −0.0504562 | + | 0.119298i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.31953 | − | 14.4098i | 0.567387 | − | 0.982743i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.48646 | + | 0.308580i | −0.168019 | + | 0.0208519i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.27856 | − | 14.3389i | 0.556876 | − | 0.964538i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.04717 | + | 12.2061i | −0.471914 | + | 0.817378i | −0.999484 | − | 0.0321333i | \(-0.989770\pi\) |
0.527570 | + | 0.849512i | \(0.323103\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.4566 | − | 26.2243i | −1.69711 | − | 1.74829i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.9782 | −1.72424 | −0.862118 | − | 0.506708i | \(-0.830862\pi\) | ||||
−0.862118 | + | 0.506708i | \(0.830862\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.9157 | −1.64648 | −0.823239 | − | 0.567695i | \(-0.807835\pi\) | ||||
−0.823239 | + | 0.567695i | \(0.807835\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.05923 | + | 5.29874i | −0.200417 | + | 0.347132i | −0.948663 | − | 0.316289i | \(-0.897563\pi\) |
0.748246 | + | 0.663421i | \(0.230896\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.85893 | − | 8.41591i | −0.316961 | − | 0.548993i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.65995 | − | 0.454214i | 0.237739 | − | 0.0295044i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.71988 | − | 13.3712i | −0.499357 | − | 0.864912i | 0.500643 | − | 0.865654i | \(-0.333097\pi\) |
−1.00000 | 0.000742080i | \(0.999764\pi\) | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.84518 | −0.634183 | −0.317092 | − | 0.948395i | \(-0.602706\pi\) | ||||
−0.317092 | + | 0.948395i | \(0.602706\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.1705 | + | 6.49602i | 0.909035 | + | 0.416720i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.9789 | −1.46211 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.56897 | + | 6.04685i | 0.289546 | + | 0.383204i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.8843 | −1.69692 | −0.848461 | − | 0.529258i | \(-0.822470\pi\) | ||||
−0.848461 | + | 0.529258i | \(0.822470\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.06524 | −0.318449 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20.6075 | + | 2.55748i | −1.29049 | + | 0.160155i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.0127 | −0.686954 | −0.343477 | − | 0.939161i | \(-0.611605\pi\) | ||||
−0.343477 | + | 0.939161i | \(0.611605\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.23861 | − | 1.32060i | 0.324262 | − | 0.0817434i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.31095 | −0.450812 | −0.225406 | − | 0.974265i | \(-0.572371\pi\) | ||||
−0.225406 | + | 0.974265i | \(0.572371\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.52309 | + | 7.83423i | 0.277851 | + | 0.481253i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1828 | + | 16.1235i | 0.745576 | + | 0.986742i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.08048 | + | 3.60349i | 0.126849 | + | 0.219709i | 0.922454 | − | 0.386107i | \(-0.126180\pi\) |
−0.795605 | + | 0.605815i | \(0.792847\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.18300 | − | 7.24516i | 0.254099 | − | 0.440112i | −0.710551 | − | 0.703645i | \(-0.751554\pi\) |
0.964650 | + | 0.263533i | \(0.0848878\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.5850 | 0.638300 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.79856 | −0.168149 | −0.0840745 | − | 0.996459i | \(-0.526793\pi\) | ||||
−0.0840745 | + | 0.996459i | \(0.526793\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.61326 | − | 2.17132i | 0.515662 | − | 0.129994i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.44314 | + | 9.42779i | −0.324710 | + | 0.562415i | −0.981454 | − | 0.191699i | \(-0.938600\pi\) |
0.656743 | + | 0.754114i | \(0.271933\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.01212 | + | 1.75304i | −0.0601642 | + | 0.104207i | −0.894539 | − | 0.446990i | \(-0.852496\pi\) |
0.834374 | + | 0.551198i | \(0.185829\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.3740 | + | 22.9939i | 1.02915 | + | 1.36204i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.31739 | − | 7.47794i | 0.253964 | − | 0.439879i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.32788 | − | 11.0216i | −0.488189 | − | 0.646100i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.65448 | + | 16.7220i | 0.564021 | + | 0.976912i | 0.997140 | + | 0.0755757i | \(0.0240795\pi\) |
−0.433120 | + | 0.901336i | \(0.642587\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.33035 | − | 10.9645i | 0.368567 | − | 0.638377i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.20851 | + | 1.63435i | −0.244203 | + | 0.0948348i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.6866 | + | 28.9020i | 0.965011 | + | 1.67145i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.53935 | − | 6.00401i | 0.145882 | − | 0.344921i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.6753 | − | 20.2223i | −0.668527 | − | 1.15792i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.1378 | 0.749813 | 0.374907 | − | 0.927063i | \(-0.377675\pi\) | ||||
0.374907 | + | 0.927063i | \(0.377675\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.32417 | + | 17.3172i | −0.416658 | + | 0.985142i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.76606 | + | 11.7192i | −0.383668 | + | 0.664533i | −0.991583 | − | 0.129469i | \(-0.958673\pi\) |
0.607915 | + | 0.794002i | \(0.292006\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.6000 | − | 21.8238i | −0.712194 | − | 1.23356i | −0.964032 | − | 0.265787i | \(-0.914368\pi\) |
0.251838 | − | 0.967770i | \(-0.418965\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.14888 | + | 10.6502i | 0.345356 | + | 0.598173i | 0.985418 | − | 0.170149i | \(-0.0544250\pi\) |
−0.640063 | + | 0.768323i | \(0.721092\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.782335 | + | 1.35504i | −0.0438023 | + | 0.0758679i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.0730 | + | 13.3312i | 0.562218 | + | 0.744075i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.6097 | 0.645982 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −34.8705 | − | 60.3975i | −1.93427 | − | 3.35025i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.1496 | + | 2.50065i | −1.11428 | + | 0.138286i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.96285 | + | 17.2562i | 0.547608 | + | 0.948484i | 0.998438 | + | 0.0558745i | \(0.0177947\pi\) |
−0.450830 | + | 0.892610i | \(0.648872\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.4133 | − | 3.88556i | 0.844645 | − | 0.212927i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.20383 | + | 9.01330i | −0.284316 | + | 0.492449i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.966380 | − | 1.67382i | −0.0526421 | − | 0.0911788i | 0.838504 | − | 0.544896i | \(-0.183431\pi\) |
−0.891146 | + | 0.453717i | \(0.850098\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.93439 | − | 1.23290i | 0.539562 | − | 0.0669618i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.28631 | + | 2.22795i | −0.0696574 | + | 0.120650i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.3043 | − | 38.5498i | 0.877796 | − | 2.07545i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.48241 | + | 14.6920i | −0.455360 | + | 0.788706i | −0.998709 | − | 0.0508006i | \(-0.983823\pi\) |
0.543349 | + | 0.839507i | \(0.317156\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.25767 | − | 10.8386i | 0.334966 | − | 0.580177i | −0.648513 | − | 0.761204i | \(-0.724609\pi\) |
0.983478 | + | 0.181027i | \(0.0579420\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.1898 | + | 18.6295i | 1.23778 | + | 0.994368i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.3857 | −1.72372 | −0.861859 | − | 0.507149i | \(-0.830700\pi\) | ||||
−0.861859 | + | 0.507149i | \(0.830700\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.52421 | 0.240120 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.98559 | − | 15.5635i | 0.474242 | − | 0.821410i | −0.525323 | − | 0.850903i | \(-0.676056\pi\) |
0.999565 | + | 0.0294922i | \(0.00938902\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.44368 | + | 2.50052i | 0.0759830 | + | 0.131606i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.91229 | + | 16.3434i | −0.362801 | + | 0.857804i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.99816 | + | 5.19297i | 0.156931 | + | 0.271812i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.16840 | −0.426387 | −0.213194 | − | 0.977010i | \(-0.568386\pi\) | ||||
−0.213194 | + | 0.977010i | \(0.568386\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.65801 | − | 34.0149i | 0.502776 | − | 1.77075i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.16161 | −0.267258 | −0.133629 | − | 0.991031i | \(-0.542663\pi\) | ||||
−0.133629 | + | 0.991031i | \(0.542663\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −20.0880 | + | 47.4960i | −1.03734 | + | 2.45268i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.3091 | 0.530945 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.0017 | 1.07878 | 0.539392 | − | 0.842055i | \(-0.318654\pi\) | ||||
0.539392 | + | 0.842055i | \(0.318654\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.36843 | − | 10.3287i | 0.223801 | − | 0.529154i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.5589 | −1.51039 | −0.755194 | − | 0.655501i | \(-0.772458\pi\) | ||||
−0.755194 | + | 0.655501i | \(0.772458\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.6769 | − | 2.94363i | 0.593568 | − | 0.149633i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.5379 | −0.838505 | −0.419252 | − | 0.907870i | \(-0.637708\pi\) | ||||
−0.419252 | + | 0.907870i | \(0.637708\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.43063 | − | 14.6023i | −0.426355 | − | 0.738469i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.9625 | − | 28.2840i | 0.603429 | − | 1.42674i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.41315 | − | 7.64379i | −0.222049 | − | 0.384601i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.4394 | + | 26.7418i | −0.774881 | + | 1.34213i | 0.159980 | + | 0.987120i | \(0.448857\pi\) |
−0.934861 | + | 0.355014i | \(0.884476\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.6323 | 0.530951 | 0.265475 | − | 0.964118i | \(-0.414471\pi\) | ||||
0.265475 | + | 0.964118i | \(0.414471\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.9501 | 0.844343 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.10814 | − | 37.2903i | 0.0550638 | − | 1.85297i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.30183 | + | 3.98688i | −0.114097 | + | 0.197622i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.39782 | + | 12.8134i | −0.365799 | + | 0.633582i | −0.988904 | − | 0.148556i | \(-0.952538\pi\) |
0.623105 | + | 0.782138i | \(0.285871\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.83673 | − | 4.34275i | 0.0905993 | − | 0.214212i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.06904 | − | 15.7080i | 0.445182 | − | 0.771078i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.7512 | + | 3.69224i | −1.45692 | + | 0.180810i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.56134 | + | 2.70432i | 0.0762765 | + | 0.132115i | 0.901641 | − | 0.432486i | \(-0.142363\pi\) |
−0.825364 | + | 0.564601i | \(0.809030\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.644580 | + | 1.11645i | −0.0314149 | + | 0.0544122i | −0.881305 | − | 0.472547i | \(-0.843335\pi\) |
0.849891 | + | 0.526959i | \(0.176668\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.92100 | − | 6.76566i | 0.0934023 | − | 0.328958i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.6178 | + | 30.5149i | 0.854587 | + | 1.48019i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.54943 | + | 1.06102i | −0.412770 | + | 0.0512265i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.5916 | − | 20.0773i | −0.558350 | − | 0.967090i | −0.997634 | − | 0.0687421i | \(-0.978101\pi\) |
0.439285 | − | 0.898348i | \(-0.355232\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.6437 | −1.71293 | −0.856464 | − | 0.516207i | \(-0.827343\pi\) | ||||
−0.856464 | + | 0.516207i | \(0.827343\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.79454 | − | 10.3158i | −0.373720 | − | 0.494604i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.7005 | + | 20.2659i | −0.559711 | + | 0.969448i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00620 | + | 13.8671i | 0.382115 | + | 0.661843i | 0.991364 | − | 0.131136i | \(-0.0418625\pi\) |
−0.609249 | + | 0.792979i | \(0.708529\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.17778 | − | 12.4323i | −0.341027 | − | 0.590676i | 0.643597 | − | 0.765365i | \(-0.277441\pi\) |
−0.984624 | + | 0.174689i | \(0.944108\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.1819 | − | 41.8844i | 1.14633 | − | 1.98551i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.61953 | + | 10.9224i | −0.218496 | + | 0.516610i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.72475 | 0.270168 | 0.135084 | − | 0.990834i | \(-0.456870\pi\) | ||||
0.135084 | + | 0.990834i | \(0.456870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.12040 | + | 8.86879i | 0.241110 | + | 0.417615i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.26228 | − | 14.8065i | 0.294227 | − | 0.695669i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.33175 | − | 12.6990i | −0.342965 | − | 0.594033i | 0.642017 | − | 0.766690i | \(-0.278098\pi\) |
−0.984982 | + | 0.172658i | \(0.944765\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.7163 | − | 9.41223i | −0.546868 | − | 0.439325i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.9720 | − | 22.4681i | 0.604164 | − | 1.04644i | −0.388018 | − | 0.921652i | \(-0.626840\pi\) |
0.992183 | − | 0.124792i | \(-0.0398263\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.46277 | − | 11.1939i | −0.300351 | − | 0.520223i | 0.675865 | − | 0.737026i | \(-0.263770\pi\) |
−0.976215 | + | 0.216803i | \(0.930437\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.8157 | − | 16.9611i | −0.594314 | − | 0.786552i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.3104 | − | 28.2504i | 0.754755 | − | 1.30727i | −0.190741 | − | 0.981640i | \(-0.561089\pi\) |
0.945496 | − | 0.325633i | \(-0.105577\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.2809 | − | 18.9003i | −0.658030 | − | 0.870878i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.74382 | + | 3.02039i | −0.0801811 | + | 0.138878i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.4509 | − | 42.3503i | 1.12189 | − | 1.94316i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.78823 | + | 6.29804i | −0.0818774 | + | 0.288367i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.3478 | 1.15817 | 0.579084 | − | 0.815268i | \(-0.303410\pi\) | ||||
0.579084 | + | 0.815268i | \(0.303410\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.3319 | 1.38302 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.5302 | + | 28.6311i | −0.750597 | + | 1.30007i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.7383 | + | 30.7236i | 0.803799 | + | 1.39222i | 0.917099 | + | 0.398660i | \(0.130525\pi\) |
−0.113299 | + | 0.993561i | \(0.536142\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.44582 | + | 4.56041i | 0.155825 | + | 0.206229i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.2554 | + | 22.9590i | 0.598208 | + | 1.03613i | 0.993085 | + | 0.117393i | \(0.0374538\pi\) |
−0.394877 | + | 0.918734i | \(0.629213\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.20849 | −0.234579 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.52580 | + | 7.75276i | 0.338260 | + | 0.348461i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.00261 | −0.268714 | −0.134357 | − | 0.990933i | \(-0.542897\pi\) | ||||
−0.134357 | + | 0.990933i | \(0.542897\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.4967 | + | 2.54373i | −0.915725 | + | 0.113645i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.9460 | 1.02311 | 0.511556 | − | 0.859250i | \(-0.329069\pi\) | ||||
0.511556 | + | 0.859250i | \(0.329069\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.6013 | −0.694248 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.6446 | + | 27.3223i | 0.916857 | + | 1.21343i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.8697 | −1.32395 | −0.661975 | − | 0.749526i | \(-0.730281\pi\) | ||||
−0.661975 | + | 0.749526i | \(0.730281\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.18250 | + | 20.6134i | −0.140511 | + | 0.910105i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 44.9984 | 1.98287 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.01846 | + | 1.76402i | 0.0447918 | + | 0.0775817i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.5593 | + | 2.05508i | −0.726875 | + | 0.0902081i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.5980 | − | 27.0166i | −0.683362 | − | 1.18362i | −0.973949 | − | 0.226769i | \(-0.927184\pi\) |
0.290587 | − | 0.956849i | \(-0.406149\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.07911 | − | 5.33318i | 0.134640 | − | 0.233203i | −0.790820 | − | 0.612049i | \(-0.790346\pi\) |
0.925460 | + | 0.378846i | \(0.123679\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.56375 | −0.373043 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.9862 | 0.477661 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.88494 | − | 2.23981i | 0.385574 | − | 0.0971995i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.7366 | − | 58.4335i | 1.46129 | − | 2.53103i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.9941 | − | 34.6307i | 0.864419 | − | 1.49722i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −39.6319 | + | 4.91849i | −1.71024 | + | 0.212248i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.5137 | + | 23.4064i | −0.580999 | + | 1.00632i | 0.414362 | + | 0.910112i | \(0.364005\pi\) |
−0.995361 | + | 0.0962083i | \(0.969329\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.98332 | − | 18.8757i | 0.342597 | − | 0.810033i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.2963 | + | 42.0824i | 1.04074 | + | 1.80261i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.9426 | − | 25.8814i | 0.638900 | − | 1.10661i | −0.346775 | − | 0.937948i | \(-0.612723\pi\) |
0.985675 | − | 0.168658i | \(-0.0539434\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.61590 | − | 16.2569i | 0.197002 | − | 0.693829i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.61432 | + | 6.26019i | 0.153975 | + | 0.266693i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −22.9335 | − | 30.3517i | −0.973474 | − | 1.28836i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.6650 | + | 18.4722i | 0.451889 | + | 0.782694i | 0.998503 | − | 0.0546900i | \(-0.0174171\pi\) |
−0.546615 | + | 0.837384i | \(0.684084\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.9789 | 0.971905 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.31946 | − | 0.536062i | 0.182368 | − | 0.0226326i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.7317 | − | 27.2482i | 0.663014 | − | 1.14837i | −0.316805 | − | 0.948491i | \(-0.602610\pi\) |
0.979820 | − | 0.199884i | \(-0.0640564\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.9788 | − | 20.7480i | −0.503954 | − | 0.872873i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.6696 | − | 25.4084i | −0.614980 | − | 1.06518i | −0.990388 | − | 0.138317i | \(-0.955831\pi\) |
0.375408 | − | 0.926860i | \(-0.377503\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.7473 | − | 23.8111i | 0.575308 | − | 0.996463i | −0.420700 | − | 0.907200i | \(-0.638215\pi\) |
0.996008 | − | 0.0892631i | \(-0.0284512\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.8032 | − | 1.34072i | 0.451310 | − | 0.0560094i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −71.0221 | −2.96183 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.2293 | + | 35.0381i | 0.842156 | + | 1.45866i | 0.888068 | + | 0.459712i | \(0.152047\pi\) |
−0.0459122 | + | 0.998945i | \(0.514619\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.3377 | + | 18.9754i | 0.595854 | + | 0.788591i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.948067 | − | 1.64210i | −0.0392649 | − | 0.0680089i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.4444 | − | 68.4820i | 0.803927 | − | 2.83138i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.6559 | − | 23.6528i | 0.563641 | − | 0.976255i | −0.433533 | − | 0.901137i | \(-0.642733\pi\) |
0.997175 | − | 0.0751177i | \(-0.0239333\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.94263 | + | 10.2929i | 0.244862 | + | 0.424113i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.108960 | + | 0.257624i | −0.00448201 | + | 0.0105972i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.2898 | + | 24.7507i | −0.586813 | + | 1.01639i | 0.407833 | + | 0.913056i | \(0.366284\pi\) |
−0.994647 | + | 0.103334i | \(0.967049\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 42.6759 | − | 5.29625i | 1.74661 | − | 0.216761i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.9919 | + | 34.6270i | −0.816848 | + | 1.41482i | 0.0911461 | + | 0.995838i | \(0.470947\pi\) |
−0.907994 | + | 0.418984i | \(0.862386\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.6948 | − | 21.9880i | 0.517831 | − | 0.896910i | −0.481954 | − | 0.876196i | \(-0.660073\pi\) |
0.999785 | − | 0.0207133i | \(-0.00659372\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.30383 | + | 1.84123i | −0.297435 | + | 0.0749806i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 42.4679 | 1.72657 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.2939 | 1.51371 | 0.756856 | − | 0.653581i | \(-0.226734\pi\) | ||||
0.756856 | + | 0.653581i | \(0.226734\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.71029 | − | 11.6226i | 0.271469 | − | 0.470199i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.7319 | − | 20.3203i | −0.473848 | − | 0.820729i | 0.525704 | − | 0.850668i | \(-0.323802\pi\) |
−0.999552 | + | 0.0299390i | \(0.990469\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −83.9792 | + | 10.4222i | −3.38637 | + | 0.420262i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.56888 | + | 11.3776i | 0.264453 | + | 0.458047i | 0.967420 | − | 0.253176i | \(-0.0814752\pi\) |
−0.702967 | + | 0.711223i | \(0.748142\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.5553 | −0.866380 | −0.433190 | − | 0.901303i | \(-0.642612\pi\) | ||||
−0.433190 | + | 0.901303i | \(0.642612\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.2378 | − | 10.9660i | 1.13314 | − | 0.440050i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 62.5040 | 2.50016 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.64170 | − | 4.81965i | −0.145435 | − | 0.192478i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.3247 | −0.611036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.15223 | −0.244916 | −0.122458 | − | 0.992474i | \(-0.539078\pi\) | ||||
−0.122458 | + | 0.992474i | \(0.539078\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.4730 | − | 4.03004i | 1.29069 | − | 0.160180i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26.8388 | −1.06507 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.28064 | + | 2.34942i | 0.0902206 | + | 0.0929415i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.47364 | −0.176698 | −0.0883491 | − | 0.996090i | \(-0.528159\pi\) | ||||
−0.0883491 | + | 0.996090i | \(0.528159\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.98009 | − | 15.5540i | −0.354140 | − | 0.613389i | 0.632830 | − | 0.774291i | \(-0.281893\pi\) |
−0.986970 | + | 0.160902i | \(0.948560\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.3740 | − | 22.9939i | −0.684101 | − | 0.905383i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.02992 | − | 10.4441i | −0.237061 | − | 0.410601i | 0.722809 | − | 0.691048i | \(-0.242851\pi\) |
−0.959870 | + | 0.280447i | \(0.909517\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.32688 | + | 2.29822i | −0.0520845 | + | 0.0902131i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −48.2733 | −1.88908 | −0.944540 | − | 0.328397i | \(-0.893492\pi\) | ||||
−0.944540 | + | 0.328397i | \(0.893492\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −73.4955 | −2.87171 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.18534 | + | 4.17469i | −0.0462445 | + | 0.162870i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.5795 | − | 25.2525i | 0.567937 | − | 0.983696i | −0.428832 | − | 0.903384i | \(-0.641075\pi\) |
0.996770 | − | 0.0803122i | \(-0.0255917\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.27428 | + | 12.5994i | −0.282937 | + | 0.490061i | −0.972107 | − | 0.234539i | \(-0.924642\pi\) |
0.689170 | + | 0.724600i | \(0.257975\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.2885 | − | 22.8806i | −0.671429 | − | 0.888611i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.24922 | − | 9.09192i | 0.203251 | − | 0.352040i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.7169 | + | 19.4773i | 0.568989 | + | 0.753035i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.44722 | + | 4.23871i | 0.0944738 | + | 0.163633i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6825 | − | 20.2348i | 0.450329 | − | 0.779993i | −0.548077 | − | 0.836428i | \(-0.684640\pi\) |
0.998406 | + | 0.0564349i | \(0.0179733\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −59.0095 | + | 22.9160i | −2.27128 | + | 0.882038i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.85875 | − | 15.3438i | −0.340469 | − | 0.589710i | 0.644051 | − | 0.764983i | \(-0.277253\pi\) |
−0.984520 | + | 0.175273i | \(0.943919\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.5273 | + | 41.4415i | −0.671649 | + | 1.58804i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.7769 | + | 37.7186i | 0.833269 | + | 1.44326i | 0.895432 | + | 0.445198i | \(0.146867\pi\) |
−0.0621637 | + | 0.998066i | \(0.519800\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.2846 | −0.431161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.8105 | + | 39.7466i | −0.641360 | + | 1.51643i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.24650 | + | 10.8193i | −0.237973 | + | 0.412181i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.7672 | + | 20.3814i | 0.447645 | + | 0.775345i | 0.998232 | − | 0.0594333i | \(-0.0189294\pi\) |
−0.550587 | + | 0.834778i | \(0.685596\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35.8738 | + | 62.1353i | 1.36077 | + | 2.35693i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.0449 | + | 29.5225i | −0.645620 | + | 1.11825i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.38872 | + | 8.45523i | 0.241644 | + | 0.319806i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.1804 | 1.70644 | 0.853219 | − | 0.521552i | \(-0.174647\pi\) | ||||
0.853219 | + | 0.521552i | \(0.174647\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.6343 | + | 18.4191i | 0.401079 | + | 0.694689i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.7037 | + | 2.07299i | −0.629097 | + | 0.0780735i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5064 | + | 23.3937i | 0.507242 | + | 0.878568i | 0.999965 | + | 0.00838223i | \(0.00266818\pi\) |
−0.492723 | + | 0.870186i | \(0.663998\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.74476 | − | 6.14495i | 0.0654337 | − | 0.230453i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.63071 | − | 14.9488i | 0.323223 | − | 0.559838i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.3089 | + | 17.8555i | 0.385529 | + | 0.667757i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.5388 | + | 3.29358i | −0.991111 | + | 0.123001i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.2096 | − | 19.4156i | 0.418048 | − | 0.724080i | −0.577695 | − | 0.816253i | \(-0.696048\pi\) |
0.995743 | + | 0.0921724i | \(0.0293811\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.64247 | + | 15.7054i | −0.247036 | + | 0.584091i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.9695 | + | 18.9997i | −0.407396 | + | 0.705631i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.9820 | + | 38.0740i | −0.815268 | + | 1.41208i | 0.0938680 | + | 0.995585i | \(0.470077\pi\) |
−0.909136 | + | 0.416500i | \(0.863256\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.9234 | − | 18.2224i | 0.737904 | − | 0.674905i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.6097 | −0.429401 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.866772 | −0.0320149 | −0.0160075 | − | 0.999872i | \(-0.505096\pi\) | ||||
−0.0160075 | + | 0.999872i | \(0.505096\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.09075 | − | 1.88924i | 0.0401785 | − | 0.0695911i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.0442 | + | 22.5932i | 0.479838 | + | 0.831103i | 0.999733 | − | 0.0231270i | \(-0.00736222\pi\) |
−0.519895 | + | 0.854230i | \(0.674029\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.5037 | + | 36.6569i | −0.569544 | + | 1.34662i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.5842 | + | 39.1170i | 0.828533 | + | 1.43506i | 0.899189 | + | 0.437561i | \(0.144158\pi\) |
−0.0706551 | + | 0.997501i | \(0.522509\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.3816 | 1.03982 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.7288 | − | 3.20882i | 0.465724 | − | 0.117405i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.5988 | −0.751662 | −0.375831 | − | 0.926688i | \(-0.622643\pi\) | ||||
−0.375831 | + | 0.926688i | \(0.622643\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.1387 | + | 42.8869i | −0.661009 | + | 1.56288i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.4743 | −1.40022 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.0856 | −1.42059 | −0.710294 | − | 0.703905i | \(-0.751438\pi\) | ||||
−0.710294 | + | 0.703905i | \(0.751438\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.41749 | + | 8.08028i | −0.124047 | + | 0.293295i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.8872 | 1.04716 | 0.523581 | − | 0.851976i | \(-0.324596\pi\) | ||||
0.523581 | + | 0.851976i | \(0.324596\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.82396 | + | 34.5994i | −0.355186 | + | 1.25094i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.4847 | 0.631336 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.1407 | + | 19.2962i | 0.401742 | + | 0.695838i | 0.993936 | − | 0.109957i | \(-0.0350714\pi\) |
−0.592194 | + | 0.805796i | \(0.701738\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.43021 | + | 17.5679i | −0.267592 | + | 0.632693i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.3593 | + | 36.9955i | 0.768242 | + | 1.33063i | 0.938515 | + | 0.345238i | \(0.112202\pi\) |
−0.170273 | + | 0.985397i | \(0.554465\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.0359 | + | 31.2391i | −0.647868 | + | 1.12214i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 47.3116 | 1.69512 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.948302 | −0.0339329 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.42777 | − | 9.24784i | 0.0510245 | − | 0.330491i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.3465 | + | 49.0976i | −1.01173 | + | 1.75237i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.143384 | + | 0.248349i | −0.00511110 | + | 0.00885268i | −0.868570 | − | 0.495567i | \(-0.834960\pi\) |
0.863459 | + | 0.504420i | \(0.168294\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.93265 | + | 11.6627i | −0.175607 | + | 0.415203i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.1239 | − | 27.9274i | 0.572577 | − | 0.991732i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.5492 | − | 1.92971i | 0.551472 | − | 0.0684399i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.457746 | + | 0.792840i | 0.0162142 | + | 0.0280838i | 0.874019 | − | 0.485892i | \(-0.161505\pi\) |
−0.857804 | + | 0.513976i | \(0.828172\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.39026 | + | 5.87211i | −0.119939 | + | 0.207740i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 33.9405 | − | 8.55609i | 1.19923 | − | 0.302315i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.628433 | − | 1.08848i | −0.0221769 | − | 0.0384115i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.15211 | − | 0.887606i | 0.251766 | − | 0.0312452i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.3721 | − | 24.8932i | −0.505297 | − | 0.875199i | −0.999981 | − | 0.00612685i | \(-0.998050\pi\) |
0.494685 | − | 0.869073i | \(-0.335284\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.3005 | −0.502157 | −0.251079 | − | 0.967967i | \(-0.580785\pi\) | ||||
−0.251079 | + | 0.967967i | \(0.580785\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.73553 | − | 11.5611i | −0.306368 | − | 0.405467i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.83969 | − | 11.8467i | 0.239584 | − | 0.414971i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.05632 | + | 13.9540i | 0.281855 | + | 0.488187i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.8125 | − | 30.8521i | −0.621660 | − | 1.07675i | −0.989177 | − | 0.146730i | \(-0.953125\pi\) |
0.367516 | − | 0.930017i | \(-0.380208\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.2157 | − | 19.4261i | 0.390953 | − | 0.677151i | −0.601622 | − | 0.798781i | \(-0.705479\pi\) |
0.992576 | + | 0.121630i | \(0.0388121\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.14164 | − | 16.8856i | 0.248640 | − | 0.587882i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.6728 | −0.927505 | −0.463753 | − | 0.885965i | \(-0.653497\pi\) | ||||
−0.463753 | + | 0.885965i | \(0.653497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.0078 | + | 27.7263i | 0.555973 | + | 0.962973i | 0.997827 | + | 0.0658866i | \(0.0209875\pi\) |
−0.441854 | + | 0.897087i | \(0.645679\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.88817 | + | 4.46437i | −0.0654998 | + | 0.154867i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.7148 | + | 42.8074i | 0.855292 | + | 1.48141i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.34753 | − | 15.2052i | 0.0811425 | − | 0.525568i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.10375 | + | 15.7682i | −0.314296 | + | 0.544377i | −0.979288 | − | 0.202474i | \(-0.935102\pi\) |
0.664991 | + | 0.746851i | \(0.268435\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8785 | + | 22.3062i | 0.444086 | + | 0.769180i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.3671 | + | 15.0440i | 0.391505 | + | 0.518142i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 40.9778 | − | 70.9757i | 1.40968 | − | 2.44164i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.11365 | + | 2.79734i | 0.0725403 | + | 0.0960044i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.4445 | − | 26.7507i | 0.529432 | − | 0.917003i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.9242 | + | 36.2419i | −0.716432 | + | 1.24090i | 0.245972 | + | 0.969277i | \(0.420893\pi\) |
−0.962404 | + | 0.271621i | \(0.912440\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 48.4029 | − | 12.2019i | 1.65534 | − | 0.417297i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.7141 | −0.536783 | −0.268391 | − | 0.963310i | \(-0.586492\pi\) | ||||
−0.268391 | + | 0.963310i | \(0.586492\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.2046 | −0.825849 | −0.412924 | − | 0.910765i | \(-0.635493\pi\) | ||||
−0.412924 | + | 0.910765i | \(0.635493\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.0542 | − | 45.1272i | 0.886896 | − | 1.53615i | 0.0433714 | − | 0.999059i | \(-0.486190\pi\) |
0.843525 | − | 0.537090i | \(-0.180477\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.9672 | + | 34.5842i | 0.678904 | + | 1.17590i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.01619 | − | 11.9326i | −0.306206 | − | 0.405252i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.925022 | + | 1.60219i | 0.0313792 | + | 0.0543504i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.3732 | −0.487018 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23.2009 | + | 5.84874i | −0.785232 | + | 0.197950i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.9768 | −0.471964 | −0.235982 | − | 0.971757i | \(-0.575831\pi\) | ||||
−0.235982 | + | 0.971757i | \(0.575831\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 33.1895 | − | 4.11895i | 1.11945 | − | 0.138929i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.1210 | −0.947421 | −0.473710 | − | 0.880681i | \(-0.657086\pi\) | ||||
−0.473710 | + | 0.880681i | \(0.657086\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.1633 | −1.18334 | −0.591670 | − | 0.806180i | \(-0.701531\pi\) | ||||
−0.591670 | + | 0.806180i | \(0.701531\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.2199 | − | 17.4961i | −0.444383 | − | 0.588124i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.9219 | 0.903950 | 0.451975 | − | 0.892031i | \(-0.350720\pi\) | ||||
0.451975 | + | 0.892031i | \(0.350720\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.232272 | + | 7.81627i | −0.00778142 | + | 0.261855i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.41041 | 0.314907 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 47.7880 | + | 82.7713i | 1.59738 | + | 2.76674i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 57.3640 | − | 7.11911i | 1.91533 | − | 0.237700i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.66605 | − | 4.61774i | −0.0889179 | − | 0.154010i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.15594 | − | 5.46625i | 0.105140 | − | 0.182107i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −49.0481 | −1.63041 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.7142 | −1.48471 | −0.742355 | − | 0.670007i | \(-0.766291\pi\) | ||||
−0.742355 | + | 0.670007i | \(0.766291\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.86455 | − | 8.10173i | −0.260851 | − | 0.268717i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.7822 | + | 23.8715i | −0.456626 | + | 0.790899i | −0.998780 | − | 0.0493800i | \(-0.984275\pi\) |
0.542154 | + | 0.840279i | \(0.317609\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.90093 | + | 3.29250i | −0.0629115 | + | 0.108966i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −40.1366 | + | 4.98112i | −1.32688 | + | 0.164671i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.3836 | + | 37.0376i | −0.705381 | + | 1.22176i | 0.261173 | + | 0.965292i | \(0.415891\pi\) |
−0.966554 | + | 0.256464i | \(0.917442\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.86398 | − | 20.9579i | 0.292078 | − | 0.690587i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.12402 | + | 5.41096i | 0.102828 | + | 0.178104i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.2750 | + | 55.9019i | −1.06119 | + | 1.83804i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.6835 | + | 23.3676i | 0.745025 | + | 0.767493i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.9748 | + | 41.5256i | 0.786589 | + | 1.36241i | 0.928045 | + | 0.372468i | \(0.121488\pi\) |
−0.141456 | + | 0.989945i | \(0.545178\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.1299 | + | 18.7003i | 0.462591 | + | 0.612221i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.20838 | − | 9.02118i | −0.170332 | − | 0.295024i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.9136 | −1.10791 | −0.553955 | − | 0.832547i | \(-0.686882\pi\) | ||||
−0.553955 | + | 0.832547i | \(0.686882\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −43.3154 | + | 5.37562i | −1.41354 | + | 0.175427i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.27395 | + | 7.40270i | −0.139327 | + | 0.241321i | −0.927242 | − | 0.374463i | \(-0.877827\pi\) |
0.787915 | + | 0.615784i | \(0.211161\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.3563 | − | 59.5068i | −1.11879 | − | 1.93781i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.411563 | − | 0.712848i | −0.0133740 | − | 0.0231645i | 0.859261 | − | 0.511538i | \(-0.170924\pi\) |
−0.872635 | + | 0.488373i | \(0.837591\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.14053 | + | 7.17161i | −0.134407 | + | 0.232800i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.1382 | − | 2.62334i | 0.685453 | − | 0.0850675i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.6726 | −1.44709 | −0.723544 | − | 0.690278i | \(-0.757488\pi\) | ||||
−0.723544 | + | 0.690278i | \(0.757488\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.0264 | − | 22.5625i | −0.421526 | − | 0.730104i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.63378 | + | 2.16225i | 0.0528127 | + | 0.0698956i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.1165 | + | 19.2544i | 0.358597 | + | 0.621108i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 28.0626 | − | 7.07433i | 0.904305 | − | 0.227967i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28.4592 | − | 49.2928i | 0.916135 | − | 1.58679i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.2289 | − | 31.5735i | −0.586203 | − | 1.01533i | −0.994724 | − | 0.102585i | \(-0.967289\pi\) |
0.408521 | − | 0.912749i | \(-0.366045\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.83301 | − | 18.5203i | 0.251632 | − | 0.594957i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.63674 | + | 14.9593i | −0.277166 | + | 0.480066i | −0.970679 | − | 0.240378i | \(-0.922729\pi\) |
0.693513 | + | 0.720444i | \(0.256062\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −119.875 | + | 14.8770i | −3.83909 | + | 0.476446i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.51775 | + | 7.82497i | −0.144536 | + | 0.250343i | −0.929200 | − | 0.369578i | \(-0.879502\pi\) |
0.784664 | + | 0.619921i | \(0.212835\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.06868 | + | 8.77921i | −0.161996 | + | 0.280585i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.60567 | + | 33.8306i | −0.306686 | + | 1.08013i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.8573 | 0.729034 | 0.364517 | − | 0.931197i | \(-0.381234\pi\) | ||||
0.364517 | + | 0.931197i | \(0.381234\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.669430 | 0.0213298 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.7005 | − | 20.2659i | 0.372055 | − | 0.644417i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.37884 | − | 7.58437i | −0.139098 | − | 0.240925i | 0.788057 | − | 0.615602i | \(-0.211087\pi\) |
−0.927156 | + | 0.374677i | \(0.877754\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34.2496 | − | 4.25051i | 1.08688 | − | 0.134886i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −51.4584 | − | 89.1285i | −1.63134 | − | 2.82556i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.93070 | −0.219498 | −0.109749 | − | 0.993959i | \(-0.535005\pi\) | ||||
−0.109749 | + | 0.993959i | \(0.535005\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.20087 | − | 27.2095i | 0.132910 | − | 0.860870i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))