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: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 949.2 | ||
Root | \(0.500000 + 2.05195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.949 |
Dual form | 1764.2.l.e.961.2 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −0.796790 | − | 1.53790i | −0.460027 | − | 0.887905i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.46050 | 1.10037 | 0.550186 | − | 0.835042i | \(-0.314557\pi\) | ||||
0.550186 | + | 0.835042i | \(0.314557\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.73025 | + | 2.45076i | −0.576751 | + | 0.816920i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.64766 | 1.40132 | 0.700662 | − | 0.713494i | \(-0.252888\pi\) | ||||
0.700662 | + | 0.713494i | \(0.252888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.55408 | + | 6.15585i | −0.985726 | + | 1.70733i | −0.347059 | + | 0.937843i | \(0.612820\pi\) |
−0.638667 | + | 0.769484i | \(0.720514\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.96050 | − | 3.78400i | −0.506200 | − | 0.977025i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.25729 | − | 3.90975i | 0.547474 | − | 0.948253i | −0.450972 | − | 0.892538i | \(-0.648923\pi\) |
0.998447 | − | 0.0557155i | \(-0.0177440\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.16372 | − | 3.74766i | −0.496390 | − | 0.859773i | 0.503601 | − | 0.863936i | \(-0.332008\pi\) |
−0.999991 | + | 0.00416311i | \(0.998675\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.86693 | 1.22334 | 0.611669 | − | 0.791114i | \(-0.290498\pi\) | ||||
0.611669 | + | 0.791114i | \(0.290498\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.05408 | 0.210817 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.14766 | + | 0.708209i | 0.990668 | + | 0.136295i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.48755 | + | 6.04061i | 0.647621 | + | 1.12171i | 0.983689 | + | 0.179875i | \(0.0575694\pi\) |
−0.336068 | + | 0.941838i | \(0.609097\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.69076 | + | 6.39258i | 0.662880 | + | 1.14814i | 0.979856 | + | 0.199708i | \(0.0639992\pi\) |
−0.316976 | + | 0.948434i | \(0.602667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.70321 | − | 7.14763i | −0.644646 | − | 1.24424i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.363327 | + | 0.629301i | 0.0597306 | + | 0.103456i | 0.894344 | − | 0.447379i | \(-0.147643\pi\) |
−0.834614 | + | 0.550835i | \(0.814309\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.2989 | + | 0.560893i | 1.96940 | + | 0.0898148i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.136673 | + | 0.236725i | −0.0213448 | + | 0.0369702i | −0.876500 | − | 0.481401i | \(-0.840128\pi\) |
0.855156 | + | 0.518371i | \(0.173461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.41741 | + | 4.18708i | 0.368652 | + | 0.638524i | 0.989355 | − | 0.145522i | \(-0.0464862\pi\) |
−0.620703 | + | 0.784046i | \(0.713153\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.25729 | + | 6.03011i | −0.634640 | + | 0.898915i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.83628 | + | 3.18054i | −0.267850 | + | 0.463929i | −0.968306 | − | 0.249766i | \(-0.919646\pi\) |
0.700457 | + | 0.713695i | \(0.252980\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.81138 | − | 0.356238i | −1.09381 | − | 0.0498833i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.52704 | + | 4.37697i | −0.347116 | + | 0.601222i | −0.985736 | − | 0.168300i | \(-0.946172\pi\) |
0.638620 | + | 0.769522i | \(0.279506\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.4356 | 1.54198 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.03950 | + | 6.31367i | −0.535044 | + | 0.836266i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.56654 | − | 7.90947i | −0.594513 | − | 1.02973i | −0.993615 | − | 0.112820i | \(-0.964012\pi\) |
0.399103 | − | 0.916906i | \(-0.369322\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.90856 | − | 11.9660i | 0.884550 | − | 1.53209i | 0.0383215 | − | 0.999265i | \(-0.487799\pi\) |
0.846228 | − | 0.532820i | \(-0.178868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.74484 | + | 15.1465i | −1.08466 | + | 1.87869i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.663715 | + | 1.14959i | 0.0810857 | + | 0.140445i | 0.903717 | − | 0.428131i | \(-0.140828\pi\) |
−0.822631 | + | 0.568576i | \(0.807495\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.67471 | − | 9.02273i | −0.562768 | − | 1.08621i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5218 | 1.60474 | 0.802370 | − | 0.596826i | \(-0.203572\pi\) | ||||
0.802370 | + | 0.596826i | \(0.203572\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.16372 | − | 3.74766i | 0.253244 | − | 0.438631i | −0.711173 | − | 0.703017i | \(-0.751836\pi\) |
0.964417 | + | 0.264386i | \(0.0851692\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.839883 | − | 1.62107i | −0.0969814 | − | 0.187185i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.21780 | + | 5.57339i | −0.362031 | + | 0.627056i | −0.988295 | − | 0.152555i | \(-0.951250\pi\) |
0.626264 | + | 0.779611i | \(0.284583\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.01245 | − | 8.48087i | −0.334717 | − | 0.942319i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.742705 | − | 1.28640i | −0.0815225 | − | 0.141201i | 0.822382 | − | 0.568936i | \(-0.192645\pi\) |
−0.903904 | + | 0.427735i | \(0.859312\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.55408 | − | 9.61996i | 0.602425 | − | 1.04343i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.51099 | − | 10.1766i | 0.698051 | − | 1.09104i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.91741 | − | 8.51721i | −0.521245 | − | 0.902822i | −0.999695 | − | 0.0247073i | \(-0.992135\pi\) |
0.478450 | − | 0.878115i | \(-0.341199\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.89037 | − | 10.7695i | 0.714498 | − | 1.11675i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.32383 | − | 9.22115i | −0.546214 | − | 0.946070i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.246304 | + | 0.426611i | 0.0250084 | + | 0.0433158i | 0.878259 | − | 0.478186i | \(-0.158705\pi\) |
−0.853250 | + | 0.521502i | \(0.825372\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.04163 | + | 11.3903i | −0.808214 | + | 1.14477i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.40642 | 0.338952 | 0.169476 | − | 0.985534i | \(-0.445793\pi\) | ||||
0.169476 | + | 0.985534i | \(0.445793\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.16225 | 0.508652 | 0.254326 | − | 0.967119i | \(-0.418146\pi\) | ||||
0.254326 | + | 0.967119i | \(0.418146\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.88151 | + | 4.99093i | 0.278567 | + | 0.482491i | 0.971029 | − | 0.238963i | \(-0.0768074\pi\) |
−0.692462 | + | 0.721454i | \(0.743474\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.49115 | − | 7.77889i | 0.430174 | − | 0.745083i | −0.566714 | − | 0.823914i | \(-0.691786\pi\) |
0.996888 | + | 0.0788317i | \(0.0251190\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.678304 | − | 1.06018i | 0.0643818 | − | 0.100628i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.679767 | − | 1.17739i | 0.0639471 | − | 0.110760i | −0.832279 | − | 0.554356i | \(-0.812964\pi\) |
0.896226 | + | 0.443597i | \(0.146298\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.4356 | 1.34613 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.93706 | − | 19.3614i | −0.826232 | − | 1.78996i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6008 | 0.963707 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.472958 | + | 0.0215693i | 0.0426452 | + | 0.00194484i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.70895 | −0.868394 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.820039 | −0.0727667 | −0.0363833 | − | 0.999338i | \(-0.511584\pi\) | ||||
−0.0363833 | + | 0.999338i | \(0.511584\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.51313 | − | 7.05395i | 0.397359 | − | 0.621066i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.78794 | 0.680435 | 0.340218 | − | 0.940347i | \(-0.389499\pi\) | ||||
0.340218 | + | 0.940347i | \(0.389499\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12.6659 | + | 1.74255i | 1.09010 | + | 0.149975i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.99280 | −0.255692 | −0.127846 | − | 0.991794i | \(-0.540806\pi\) | ||||
−0.127846 | + | 0.991794i | \(0.540806\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.16372 | + | 5.47972i | −0.268343 | + | 0.464783i | −0.968434 | − | 0.249270i | \(-0.919809\pi\) |
0.700091 | + | 0.714053i | \(0.253143\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.35447 | + | 0.289796i | 0.535143 | + | 0.0244052i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.5182 | + | 28.6103i | −1.38132 | + | 2.39252i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.58113 | + | 14.8629i | 0.712624 | + | 1.23430i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.38151 | −0.358948 | −0.179474 | − | 0.983763i | \(-0.557440\pi\) | ||||
−0.179474 | + | 0.983763i | \(0.557440\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.60078 | 0.537164 | 0.268582 | − | 0.963257i | \(-0.413445\pi\) | ||||
0.268582 | + | 0.963257i | \(0.413445\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.67617 | + | 12.2969i | 0.458891 | + | 0.994149i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.08113 | + | 15.7290i | 0.729414 | + | 1.26338i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.89037 | + | 5.00627i | 0.230677 | + | 0.399544i | 0.958007 | − | 0.286743i | \(-0.0925727\pi\) |
−0.727331 | + | 0.686287i | \(0.759239\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.74484 | + | 0.398809i | 0.693511 | + | 0.0316276i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.66372 | − | 6.34574i | −0.286964 | − | 0.497037i | 0.686119 | − | 0.727489i | \(-0.259313\pi\) |
−0.973084 | + | 0.230452i | \(0.925979\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.11177 | − | 17.5868i | −0.709350 | − | 1.36913i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.01459 | − | 10.4176i | 0.465423 | − | 0.806136i | −0.533798 | − | 0.845612i | \(-0.679236\pi\) |
0.999221 | + | 0.0394762i | \(0.0125689\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.7630 | − | 32.4985i | −1.44331 | − | 2.49989i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.9284 | + | 1.18166i | 0.988660 | + | 0.0903637i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.44951 | + | 4.24268i | −0.186233 | + | 0.322565i | −0.943991 | − | 0.329970i | \(-0.892961\pi\) |
0.757758 | + | 0.652535i | \(0.226295\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.52538 | + | 13.3251i | −0.640807 | + | 1.00157i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.890369 | − | 1.54216i | 0.0665493 | − | 0.115267i | −0.830831 | − | 0.556525i | \(-0.812134\pi\) |
0.897380 | + | 0.441258i | \(0.145468\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.9430 | −1.25936 | −0.629681 | − | 0.776854i | \(-0.716815\pi\) | ||||
−0.629681 | + | 0.776854i | \(0.716815\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.9071 | − | 1.09028i | −1.76726 | − | 0.0805961i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.893968 | + | 1.54840i | 0.0657258 | + | 0.113840i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.4911 | − | 18.1712i | 0.767189 | − | 1.32881i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.74484 | − | 4.75420i | 0.198610 | − | 0.344002i | −0.749468 | − | 0.662040i | \(-0.769691\pi\) |
0.948078 | + | 0.318038i | \(0.103024\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.75370 | + | 4.76954i | 0.198215 | + | 0.343319i | 0.947950 | − | 0.318420i | \(-0.103152\pi\) |
−0.749734 | + | 0.661739i | \(0.769819\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 30.2616 | + | 1.38008i | 2.16708 | + | 0.0988296i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6300 | 0.828600 | 0.414300 | − | 0.910140i | \(-0.364026\pi\) | ||||
0.414300 | + | 0.910140i | \(0.364026\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.07373 | − | 3.59181i | 0.147003 | − | 0.254617i | −0.783115 | − | 0.621876i | \(-0.786371\pi\) |
0.930118 | + | 0.367260i | \(0.119704\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.23911 | − | 1.93671i | 0.0873999 | − | 0.136605i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.336285 | + | 0.582462i | −0.0234871 | + | 0.0406809i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.1513 | + | 14.3784i | −0.705561 | + | 0.999370i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.0562 | − | 17.4179i | −0.695603 | − | 1.20482i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.6082 | − | 23.5700i | 0.936825 | − | 1.62263i | 0.165478 | − | 0.986213i | \(-0.447083\pi\) |
0.771347 | − | 0.636415i | \(-0.219583\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.7740 | − | 20.7951i | −0.738224 | − | 1.42486i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.94805 | + | 10.3023i | 0.405654 | + | 0.702613i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.48755 | − | 0.341470i | −0.505962 | − | 0.0230744i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.0452 | + | 27.7912i | 1.07932 | + | 1.86944i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.60817 | + | 2.78543i | 0.107691 | + | 0.186526i | 0.914834 | − | 0.403829i | \(-0.132321\pi\) |
−0.807144 | + | 0.590355i | \(0.798988\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.82383 | + | 2.58331i | −0.121589 | + | 0.172221i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.9459 | 1.05837 | 0.529184 | − | 0.848507i | \(-0.322498\pi\) | ||||
0.529184 | + | 0.848507i | \(0.322498\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.21634 | −0.0803778 | −0.0401889 | − | 0.999192i | \(-0.512796\pi\) | ||||
−0.0401889 | + | 0.999192i | \(0.512796\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.98608 | − | 17.2964i | −0.654210 | − | 1.13313i | −0.982091 | − | 0.188406i | \(-0.939668\pi\) |
0.327881 | − | 0.944719i | \(-0.393665\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.51819 | + | 7.82573i | −0.294734 | + | 0.510494i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.1352 | + | 0.507822i | 0.723310 | + | 0.0329866i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.00739 | + | 5.20896i | −0.194532 | + | 0.336939i | −0.946747 | − | 0.321978i | \(-0.895652\pi\) |
0.752215 | + | 0.658918i | \(0.228985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.6156 | −1.19913 | −0.599567 | − | 0.800325i | \(-0.704660\pi\) | ||||
−0.599567 | + | 0.800325i | \(0.704660\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.6424 | + | 11.3903i | −0.682711 | + | 0.730689i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.7601 | 1.95722 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.38658 | + | 2.16720i | −0.0878707 | + | 0.137341i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.99707 | 0.441651 | 0.220826 | − | 0.975313i | \(-0.429125\pi\) | ||||
0.220826 | + | 0.975313i | \(0.429125\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.2675 | 1.71429 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19.2199 | − | 0.876526i | −1.20360 | − | 0.0548902i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.7778 | −1.10895 | −0.554475 | − | 0.832201i | \(-0.687081\pi\) | ||||
−0.554475 | + | 0.832201i | \(0.687081\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.8384 | − | 1.90464i | −1.28987 | − | 0.117894i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.1986 | −1.67714 | −0.838570 | − | 0.544794i | \(-0.816608\pi\) | ||||
−0.838570 | + | 0.544794i | \(0.816608\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.21780 | + | 10.7695i | −0.381956 | + | 0.661568i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.18044 | + | 14.3489i | −0.561834 | + | 0.878138i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.9481 | + | 20.6946i | −0.728486 | + | 1.26177i | 0.229038 | + | 0.973418i | \(0.426442\pi\) |
−0.957523 | + | 0.288356i | \(0.906891\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.13667 | − | 10.6290i | −0.372776 | − | 0.645668i | 0.617215 | − | 0.786794i | \(-0.288261\pi\) |
−0.989992 | + | 0.141127i | \(0.954927\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.89903 | 0.295423 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.7807 | 0.767920 | 0.383960 | − | 0.923350i | \(-0.374560\pi\) | ||||
0.383960 | + | 0.923350i | \(0.374560\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −22.0526 | − | 2.01561i | −1.32026 | − | 0.120672i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.2573 | + | 24.6944i | 0.850519 | + | 1.47314i | 0.880741 | + | 0.473599i | \(0.157045\pi\) |
−0.0302219 | + | 0.999543i | \(0.509621\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.363327 | − | 0.629301i | −0.0215975 | − | 0.0374080i | 0.855025 | − | 0.518587i | \(-0.173542\pi\) |
−0.876622 | + | 0.481179i | \(0.840209\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.93920 | + | 15.5348i | −0.588747 | + | 0.920203i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.69076 | − | 2.92848i | −0.0994563 | − | 0.172263i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.459831 | − | 0.718710i | 0.0269558 | − | 0.0421315i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.7901 | + | 22.1531i | −0.747204 | + | 1.29420i | 0.201954 | + | 0.979395i | \(0.435271\pi\) |
−0.949158 | + | 0.314800i | \(0.898062\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.2360 | − | 19.4613i | −0.654184 | − | 1.13308i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 23.9246 | + | 3.29152i | 1.38825 | + | 0.190993i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.8515 | + | 36.1159i | −1.20588 | + | 2.08864i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.71420 | − | 5.23872i | −0.155927 | − | 0.300957i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.9985 | − | 29.4423i | 0.973333 | − | 1.68586i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.23405 | −0.355796 | −0.177898 | − | 0.984049i | \(-0.556930\pi\) | ||||
−0.177898 | + | 0.984049i | \(0.556930\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.11323 | − | 7.93901i | −0.233993 | − | 0.451635i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.6192 | − | 25.3211i | −0.828976 | − | 1.43583i | −0.898842 | − | 0.438273i | \(-0.855590\pi\) |
0.0698655 | − | 0.997556i | \(-0.477743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.2434 | + | 24.6703i | −0.805083 | + | 1.39445i | 0.111151 | + | 0.993803i | \(0.464546\pi\) |
−0.916235 | + | 0.400642i | \(0.868787\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.809243 | + | 1.40165i | −0.0454516 | + | 0.0787245i | −0.887856 | − | 0.460121i | \(-0.847806\pi\) |
0.842405 | + | 0.538846i | \(0.181139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.2089 | + | 28.0747i | 0.907527 | + | 1.57188i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.37957 | − | 8.40819i | 0.300258 | − | 0.469300i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.5366 | −1.08704 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.74630 | + | 6.48879i | −0.207808 | + | 0.359933i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.5416 | − | 0.708777i | −0.859454 | − | 0.0391954i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.99115 | − | 12.1090i | 0.384268 | − | 0.665572i | −0.607399 | − | 0.794397i | \(-0.707787\pi\) |
0.991667 | + | 0.128825i | \(0.0411205\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.17091 | − | 0.198422i | −0.118965 | − | 0.0108734i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.63307 | + | 2.82857i | 0.0892244 | + | 0.154541i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.8619 | + | 24.0095i | −0.755104 | + | 1.30788i | 0.190219 | + | 0.981742i | \(0.439080\pi\) |
−0.945323 | + | 0.326137i | \(0.894253\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.35234 | − | 0.107278i | −0.127761 | − | 0.00582656i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.1534 | + | 29.7106i | 0.928909 | + | 1.60892i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.5021 | − | 22.2005i | −0.619254 | − | 1.19523i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.76449 | − | 6.52029i | −0.202089 | − | 0.350028i | 0.747113 | − | 0.664697i | \(-0.231440\pi\) |
−0.949201 | + | 0.314670i | \(0.898106\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.0541 | + | 26.0744i | 0.805827 | + | 1.39573i | 0.915732 | + | 0.401791i | \(0.131612\pi\) |
−0.109905 | + | 0.993942i | \(0.535055\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.6549 | + | 29.1712i | −1.20923 | + | 1.55705i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.3638 | −1.08386 | −0.541928 | − | 0.840425i | \(-0.682305\pi\) | ||||
−0.541928 | + | 0.840425i | \(0.682305\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.2704 | 1.76581 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.01313 | + | 13.8791i | 0.422917 | + | 0.732513i | 0.996223 | − | 0.0868277i | \(-0.0276730\pi\) |
−0.573307 | + | 0.819341i | \(0.694340\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.136673 | − | 0.236725i | 0.00719332 | − | 0.0124592i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.44659 | − | 16.3029i | −0.443331 | − | 0.855680i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.32383 | − | 9.22115i | 0.278662 | − | 0.482657i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5979 | −0.709802 | −0.354901 | − | 0.934904i | \(-0.615485\pi\) | ||||
−0.354901 | + | 0.934904i | \(0.615485\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.343677 | − | 0.744547i | −0.0178911 | − | 0.0387595i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.9282 | −1.13540 | −0.567700 | − | 0.823236i | \(-0.692167\pi\) | ||||
−0.567700 | + | 0.823236i | \(0.692167\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.73599 | + | 14.9314i | 0.399485 | + | 0.771052i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −49.5801 | −2.55351 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.7965 | −1.53054 | −0.765271 | − | 0.643708i | \(-0.777395\pi\) | ||||
−0.765271 | + | 0.643708i | \(0.777395\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.653398 | + | 1.26113i | 0.0334746 | + | 0.0646099i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.0219809 | −0.00112317 | −0.000561587 | − | 1.00000i | \(-0.500179\pi\) | ||||
−0.000561587 | 1.00000i | \(0.500179\pi\) | ||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14.4443 | − | 1.32021i | −0.734243 | − | 0.0671099i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.3566 | −1.79265 | −0.896326 | − | 0.443396i | \(-0.853773\pi\) | ||||
−0.896326 | + | 0.443396i | \(0.853773\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.2434 | − | 22.9382i | 0.669746 | − | 1.16003i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.20535 | − | 11.9770i | −0.313018 | − | 0.604162i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.91741 | + | 13.7134i | −0.398368 | + | 0.689994i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.47150 | + | 14.6731i | 0.425172 | + | 0.736420i | 0.996436 | − | 0.0843464i | \(-0.0268802\pi\) |
−0.571264 | + | 0.820766i | \(0.693547\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.96362 | −0.147996 | −0.0739982 | − | 0.997258i | \(-0.523576\pi\) | ||||
−0.0739982 | + | 0.997258i | \(0.523576\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −52.4690 | −2.61367 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.41216 | − | 20.8672i | −0.368313 | − | 1.03690i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.68862 | + | 2.92478i | 0.0837018 | + | 0.144976i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.32743 | + | 12.6915i | 0.362318 | + | 0.627553i | 0.988342 | − | 0.152251i | \(-0.0486521\pi\) |
−0.626024 | + | 0.779804i | \(0.715319\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.38463 | + | 4.60262i | 0.117625 | + | 0.227031i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.82743 | − | 3.16520i | −0.0897050 | − | 0.155374i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.9481 | + | 0.499286i | 0.536128 | + | 0.0244502i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.6352 | − | 21.8848i | 0.617270 | − | 1.06914i | −0.372711 | − | 0.927947i | \(-0.621572\pi\) |
0.989982 | − | 0.141196i | \(-0.0450949\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.99854 | + | 13.8539i | 0.389825 | + | 0.675196i | 0.992426 | − | 0.122846i | \(-0.0392022\pi\) |
−0.602601 | + | 0.798043i | \(0.705869\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.61750 | − | 10.0034i | −0.224511 | − | 0.486383i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.37938 | − | 4.12120i | 0.115417 | − | 0.199908i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 57.1613 | + | 2.60684i | 2.75977 | + | 0.125860i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.51673 | + | 11.2873i | −0.313900 | + | 0.543690i | −0.979203 | − | 0.202883i | \(-0.934969\pi\) |
0.665303 | + | 0.746573i | \(0.268302\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.5467 | 1.13158 | 0.565791 | − | 0.824549i | \(-0.308571\pi\) | ||||
0.565791 | + | 0.824549i | \(0.308571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.0203 | − | 25.0395i | 0.768116 | − | 1.20055i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.6944 | − | 21.9873i | −0.607253 | − | 1.05179i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.35447 | + | 5.81012i | −0.160100 | + | 0.277302i | −0.934904 | − | 0.354900i | \(-0.884515\pi\) |
0.774804 | + | 0.632201i | \(0.217848\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.6228 | + | 30.5235i | −0.837282 | + | 1.45022i | 0.0548760 | + | 0.998493i | \(0.482524\pi\) |
−0.892158 | + | 0.451723i | \(0.850810\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0993 | − | 20.9566i | −0.573562 | − | 0.993439i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.49115 | + | 6.73832i | 0.165126 | + | 0.318711i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.9387 | −0.610616 | −0.305308 | − | 0.952254i | \(-0.598759\pi\) | ||||
−0.305308 | + | 0.952254i | \(0.598759\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.635211 | + | 1.10022i | −0.0299109 | + | 0.0518072i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.25943 | − | 10.1513i | −0.247110 | − | 0.476950i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5993 | − | 25.2868i | 0.682927 | − | 1.18286i | −0.291156 | − | 0.956675i | \(-0.594040\pi\) |
0.974083 | − | 0.226189i | \(-0.0726267\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.3887 | − | 18.5274i | 0.671608 | − | 0.864787i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.34348 | + | 16.1834i | 0.435169 | + | 0.753735i | 0.997309 | − | 0.0733066i | \(-0.0233552\pi\) |
−0.562140 | + | 0.827042i | \(0.690022\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.1249 | − | 33.1253i | 0.888809 | − | 1.53946i | 0.0475247 | − | 0.998870i | \(-0.484867\pi\) |
0.841285 | − | 0.540593i | \(-0.181800\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.9538 | − | 26.4985i | 0.786213 | − | 1.22884i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.64387 | + | 13.2396i | 0.353716 | + | 0.612654i | 0.986897 | − | 0.161349i | \(-0.0515846\pi\) |
−0.633181 | + | 0.774004i | \(0.718251\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.39610 | − | 8.43403i | 0.248639 | − | 0.388620i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.2353 | + | 19.4601i | 0.516600 | + | 0.894778i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.28074 | − | 3.95035i | −0.104647 | − | 0.181255i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.35447 | − | 13.7664i | −0.290951 | − | 0.630322i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.0321 | 0.504070 | 0.252035 | − | 0.967718i | \(-0.418900\pi\) | ||||
0.252035 | + | 0.967718i | \(0.418900\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.16518 | −0.235512 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.606032 | + | 1.04968i | 0.0275185 | + | 0.0476635i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.30039 | + | 14.3767i | −0.376126 | + | 0.651470i | −0.990495 | − | 0.137549i | \(-0.956078\pi\) |
0.614368 | + | 0.789019i | \(0.289411\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.83988 | + | 10.6906i | −0.309310 | + | 0.483447i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.3633 | − | 23.1460i | 0.603079 | − | 1.04456i | −0.389273 | − | 0.921122i | \(-0.627274\pi\) |
0.992352 | − | 0.123440i | \(-0.0393928\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.4897 | 1.41822 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.7865 | + | 28.0259i | −0.889336 | + | 1.25967i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.23697 | 0.0553744 | 0.0276872 | − | 0.999617i | \(-0.491186\pi\) | ||||
0.0276872 | + | 0.999617i | \(0.491186\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.8135 | − | 0.949201i | −0.929879 | − | 0.0424072i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.07179 | −0.0477889 | −0.0238944 | − | 0.999714i | \(-0.507607\pi\) | ||||
−0.0238944 | + | 0.999714i | \(0.507607\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.38151 | 0.372973 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −35.0292 | + | 54.7501i | −1.55570 | + | 2.43154i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.0689 | 0.889537 | 0.444768 | − | 0.895646i | \(-0.353286\pi\) | ||||
0.444768 | + | 0.895646i | \(0.353286\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.48395 | − | 20.8241i | −0.374575 | − | 0.919406i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.7017 | 0.559706 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.53443 | + | 14.7821i | −0.375344 | + | 0.650115i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.47656 | + | 0.386574i | 0.372080 | + | 0.0169687i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.4430 | − | 26.7480i | 0.676570 | − | 1.17185i | −0.299438 | − | 0.954116i | \(-0.596799\pi\) |
0.976007 | − | 0.217737i | \(-0.0698676\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.69961 | + | 6.40792i | 0.161773 | + | 0.280199i | 0.935505 | − | 0.353315i | \(-0.114946\pi\) |
−0.773732 | + | 0.633513i | \(0.781612\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.3245 | 1.45164 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4208 | 0.496557 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.2855 | + | 2.49390i | 1.18409 | + | 0.108226i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.971495 | − | 1.68268i | −0.0420801 | − | 0.0728849i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.08998 | + | 12.2802i | 0.306527 | + | 0.530920i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.08113 | − | 0.140515i | −0.132960 | − | 0.00606367i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.3348 | − | 19.6325i | −0.487322 | − | 0.844067i | 0.512572 | − | 0.858644i | \(-0.328693\pi\) |
−0.999894 | + | 0.0145779i | \(0.995360\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.5000 | + | 26.0566i | 0.579340 | + | 1.11819i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.0505 | − | 19.1400i | 0.473351 | − | 0.819868i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.07373 | + | 5.32386i | 0.131423 | + | 0.227632i | 0.924225 | − | 0.381847i | \(-0.124712\pi\) |
−0.792802 | + | 0.609479i | \(0.791379\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.3722 | + | 37.6354i | 0.741427 | + | 1.60624i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.0921 | − | 26.1403i | 0.642946 | − | 1.11361i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.66897 | − | 2.60858i | 0.0708439 | − | 0.110728i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.8370 | + | 25.6984i | −0.628662 | + | 1.08887i | 0.359158 | + | 0.933277i | \(0.383064\pi\) |
−0.987820 | + | 0.155598i | \(0.950270\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −34.3667 | −1.45356 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −36.3047 | − | 1.65568i | −1.53278 | − | 0.0699027i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.6555 | + | 25.3841i | 0.617657 | + | 1.06981i | 0.989912 | + | 0.141683i | \(0.0452514\pi\) |
−0.372255 | + | 0.928131i | \(0.621415\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.67257 | − | 2.89698i | 0.0703655 | − | 0.121877i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.4430 | − | 31.9442i | 0.773170 | − | 1.33917i | −0.162647 | − | 0.986684i | \(-0.552003\pi\) |
0.935817 | − | 0.352486i | \(-0.114664\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.1893 | − | 28.0407i | −0.677501 | − | 1.17347i | −0.975731 | − | 0.218972i | \(-0.929730\pi\) |
0.298230 | − | 0.954494i | \(-0.403604\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.49854 | − | 0.433181i | −0.396807 | − | 0.0180964i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.18423 | 0.257900 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.5093 | + | 19.9348i | −0.479140 | + | 0.829895i | −0.999714 | − | 0.0239220i | \(-0.992385\pi\) |
0.520574 | + | 0.853817i | \(0.325718\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.14095 | − | 8.03522i | 0.213650 | − | 0.333932i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.7448 | + | 20.3427i | −0.486422 | + | 0.842507i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −21.9897 | − | 47.6388i | −0.909161 | − | 1.96962i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.87052 | − | 4.97189i | −0.118479 | − | 0.205212i | 0.800686 | − | 0.599084i | \(-0.204469\pi\) |
−0.919165 | + | 0.393872i | \(0.871135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.9715 | − | 27.6634i | 0.658094 | − | 1.13985i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.26663 | − | 17.8857i | −0.381178 | − | 0.735718i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.8727 | − | 24.0282i | −0.569682 | − | 0.986718i | −0.996597 | − | 0.0824263i | \(-0.973733\pi\) |
0.426915 | − | 0.904292i | \(-0.359600\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.17617 | − | 0.327269i | −0.293701 | − | 0.0133942i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.05408 | − | 3.55778i | −0.0839276 | − | 0.145367i | 0.821006 | − | 0.570919i | \(-0.193413\pi\) |
−0.904934 | + | 0.425552i | \(0.860080\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.80924 | − | 13.5260i | −0.318546 | − | 0.551737i | 0.661639 | − | 0.749822i | \(-0.269861\pi\) |
−0.980185 | + | 0.198085i | \(0.936528\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.96576 | − | 0.362471i | −0.161498 | − | 0.0147610i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 26.0833 | 1.06044 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.561476 | −0.0227896 | −0.0113948 | − | 0.999935i | \(-0.503627\pi\) | ||||
−0.0113948 | + | 0.999935i | \(0.503627\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.0526 | − | 22.6078i | −0.528053 | − | 0.914614i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.1008 | − | 17.4951i | 0.407967 | − | 0.706619i | −0.586695 | − | 0.809808i | \(-0.699571\pi\) |
0.994662 | + | 0.103189i | \(0.0329047\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.16372 | + | 0.0530713i | 0.0469255 | + | 0.00214004i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.4569 | − | 19.8439i | 0.461238 | − | 0.798887i | −0.537785 | − | 0.843082i | \(-0.680739\pi\) |
0.999023 | + | 0.0441948i | \(0.0140722\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.7031 | 1.59580 | 0.797901 | − | 0.602788i | \(-0.205944\pi\) | ||||
0.797901 | + | 0.602788i | \(0.205944\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30.2010 | + | 4.15501i | 1.21192 | + | 0.166735i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.1593 | −1.16637 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.7742 | + | 29.3438i | −0.749770 | + | 1.17188i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.28054 | 0.130804 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.0364 | −1.23554 | −0.617769 | − | 0.786359i | \(-0.711963\pi\) | ||||
−0.617769 | + | 0.786359i | \(0.711963\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −47.0911 | − | 2.14759i | −1.87170 | − | 0.0853592i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.01771 | −0.0800703 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.3961 | + | 33.1387i | −0.925536 | + | 1.31095i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.5864 | −1.16859 | −0.584296 | − | 0.811541i | \(-0.698629\pi\) | ||||
−0.584296 | + | 0.811541i | \(0.698629\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.8442 | + | 22.2467i | −0.506524 | + | 0.877325i | 0.493447 | + | 0.869776i | \(0.335737\pi\) |
−0.999972 | + | 0.00754978i | \(0.997597\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.1046 | − | 17.3563i | 0.437242 | − | 0.683403i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.50885 | + | 14.7378i | −0.334518 | + | 0.579401i | −0.983392 | − | 0.181494i | \(-0.941907\pi\) |
0.648874 | + | 0.760895i | \(0.275240\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.2237 | − | 36.7606i | −0.833104 | − | 1.44298i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.47102 | 0.0575653 | 0.0287827 | − | 0.999586i | \(-0.490837\pi\) | ||||
0.0287827 | + | 0.999586i | \(0.490837\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.1623 | 0.748731 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.44085 | + | 11.7872i | 0.212268 | + | 0.459861i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.7003 | + | 35.8539i | 0.806369 | + | 1.39667i | 0.915363 | + | 0.402629i | \(0.131904\pi\) |
−0.108995 | + | 0.994042i | \(0.534763\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.1352 | − | 33.1432i | −0.744273 | − | 1.28912i | −0.950533 | − | 0.310622i | \(-0.899463\pi\) |
0.206260 | − | 0.978497i | \(-0.433871\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 29.9552 | − | 46.8196i | 1.16337 | − | 1.81832i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.4612 | + | 35.4398i | 0.792260 | + | 1.37223i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.00233 | − | 4.69260i | 0.116077 | − | 0.181426i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.1086 | − | 55.6138i | 1.23954 | − | 2.14695i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.2448 | + | 26.4048i | 0.587645 | + | 1.01783i | 0.994540 | + | 0.104357i | \(0.0332783\pi\) |
−0.406894 | + | 0.913475i | \(0.633388\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.42607 | + | 0.746512i | 0.208850 | + | 0.0287333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.4626 | + | 38.9064i | −0.863309 | + | 1.49530i | 0.00540665 | + | 0.999985i | \(0.498279\pi\) |
−0.868716 | + | 0.495310i | \(0.835054\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.7055 | − | 24.5232i | −0.486877 | − | 0.939730i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.1986 | − | 41.9133i | 0.925935 | − | 1.60377i | 0.135884 | − | 0.990725i | \(-0.456613\pi\) |
0.790051 | − | 0.613041i | \(-0.210054\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.36381 | −0.281357 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.969165 | + | 1.87060i | 0.0369759 | + | 0.0713679i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.9626 | − | 31.1122i | −0.684322 | − | 1.18528i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.19076 | + | 15.9189i | −0.349633 | + | 0.605582i | −0.986184 | − | 0.165652i | \(-0.947027\pi\) |
0.636551 | + | 0.771234i | \(0.280360\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.78434 | + | 13.4829i | −0.295277 | + | 0.511434i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.617023 | + | 1.06871i | 0.0233714 | + | 0.0404805i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.6433 | + | 29.1392i | −0.705153 | + | 1.10214i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.0292 | −1.02088 | −0.510439 | − | 0.859914i | \(-0.670517\pi\) | ||||
−0.510439 | + | 0.859914i | \(0.670517\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.57227 | − | 2.72325i | 0.0592994 | − | 0.102710i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.6352 | + | 0.713045i | 0.588856 | + | 0.0268548i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.49261 | + | 4.31732i | −0.0936119 | + | 0.162141i | −0.909028 | − | 0.416734i | \(-0.863175\pi\) |
0.815417 | + | 0.578875i | \(0.196508\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.09144 | − | 17.5294i | −0.303453 | − | 0.657405i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.6534 | + | 37.5048i | 0.810926 | + | 1.40457i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −40.6431 | + | 70.3959i | −1.51997 | + | 2.63266i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.4071 | + | 0.474616i | 0.388660 | + | 0.0177249i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.84708 | − | 13.5915i | −0.292647 | − | 0.506879i | 0.681788 | − | 0.731550i | \(-0.261203\pi\) |
−0.974435 | + | 0.224671i | \(0.927869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.8327 | + | 28.6288i | 0.551634 | + | 1.06472i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.67617 | + | 6.36731i | 0.136529 | + | 0.236476i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.9071 | − | 18.8916i | −0.404522 | − | 0.700652i | 0.589744 | − | 0.807590i | \(-0.299229\pi\) |
−0.994266 | + | 0.106938i | \(0.965895\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.9969 | + | 7.29124i | 0.962847 | + | 0.270046i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.8272 | 0.807309 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.0148 | −0.887006 | −0.443503 | − | 0.896273i | \(-0.646264\pi\) | ||||
−0.443503 | + | 0.896273i | \(0.646264\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.08472 | + | 5.34290i | 0.113627 | + | 0.196808i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.35447 | + | 16.2024i | −0.344110 | + | 0.596016i | −0.985192 | − | 0.171457i | \(-0.945153\pi\) |
0.641082 | + | 0.767473i | \(0.278486\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.5093 | − | 47.3059i | −0.900373 | − | 1.73782i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.1534 | − | 34.9067i | 0.739356 | − | 1.28060i | −0.213429 | − | 0.976959i | \(-0.568463\pi\) |
0.952785 | − | 0.303644i | \(-0.0982035\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.7807 | −0.394976 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.43773 | + | 0.405610i | 0.162368 | + | 0.0148405i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.1259 | −0.770894 | −0.385447 | − | 0.922730i | \(-0.625953\pi\) | ||||
−0.385447 | + | 0.922730i | \(0.625953\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.57520 | − | 10.7608i | −0.203171 | − | 0.392145i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.2412 | 0.591079 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.85934 | 0.321998 | 0.160999 | − | 0.986955i | \(-0.448528\pi\) | ||||
0.160999 | + | 0.986955i | \(0.448528\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21.7265 | − | 41.9346i | −0.788621 | − | 1.52213i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.38910 | 0.0503549 | 0.0251774 | − | 0.999683i | \(-0.491985\pi\) | ||||
0.0251774 | + | 0.999683i | \(0.491985\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.9662 | + | 30.2567i | 0.504950 | + | 1.09393i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 64.9194 | 2.34410 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.9626 | − | 32.8443i | 0.683810 | − | 1.18439i | −0.289999 | − | 0.957027i | \(-0.593655\pi\) |
0.973809 | − | 0.227367i | \(-0.0730118\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.1652 | + | 27.3404i | 0.510146 | + | 0.984642i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.657981 | + | 1.13966i | −0.0236659 | + | 0.0409906i | −0.877616 | − | 0.479365i | \(-0.840867\pi\) |
0.853950 | + | 0.520355i | \(0.174200\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.89037 | + | 6.73832i | 0.139746 | + | 0.242047i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.18289 | 0.0423813 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 62.8447 | 2.24876 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.6747 | + | 33.5649i | 0.488694 | + | 1.19951i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.11177 | + | 12.3179i | 0.253830 | + | 0.439646i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.12928 | − | 10.6162i | −0.218485 | − | 0.378428i | 0.735860 | − | 0.677134i | \(-0.236778\pi\) |
−0.954345 | + | 0.298706i | \(0.903445\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.6716 | + | 41.8287i | 0.771529 | + | 1.48914i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.1072 | + | 85.0561i | 1.74385 | + | 3.02043i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 21.5167 | + | 0.981271i | 0.763120 | + | 0.0348021i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.7178 | + | 18.5638i | −0.379644 | + | 0.657563i | −0.991010 | − | 0.133785i | \(-0.957287\pi\) |
0.611366 | + | 0.791348i | \(0.290620\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.29007 | + | 14.3588i | 0.293282 | + | 0.507979i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.3820 | + | 2.68552i | 1.03816 | + | 0.0948882i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.0562 | − | 17.4179i | 0.354876 | − | 0.614664i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 41.3463 | + | 1.88560i | 1.45546 | + | 0.0663762i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.3478 | + | 23.1190i | −0.469282 | + | 0.812820i | −0.999383 | − | 0.0351140i | \(-0.988821\pi\) |
0.530101 | + | 0.847934i | \(0.322154\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.2852 | 1.34438 | 0.672188 | − | 0.740381i | \(-0.265355\pi\) | ||||
0.672188 | + | 0.740381i | \(0.265355\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.4567 | + | 17.9067i | −0.401804 | + | 0.628014i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.01459 | − | 15.6137i | −0.315767 | − | 0.546925i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4612 | − | 18.1193i | 0.365990 | − | 0.633914i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.24990 | − | 9.09310i | 0.183223 | − | 0.317351i | −0.759753 | − | 0.650211i | \(-0.774680\pi\) |
0.942976 | + | 0.332860i | \(0.108014\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | − | 13.8564i | −0.278862 | − | 0.483004i | 0.692240 | − | 0.721668i | \(-0.256624\pi\) |
−0.971102 | + | 0.238664i | \(0.923291\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.90350 | − | 7.53420i | −0.135902 | − | 0.262307i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.7817 | −1.69631 | −0.848153 | − | 0.529752i | \(-0.822285\pi\) | ||||
−0.848153 | + | 0.529752i | \(0.822285\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.10963 | − | 5.38604i | 0.108002 | − | 0.187065i | −0.806959 | − | 0.590608i | \(-0.798888\pi\) |
0.914961 | + | 0.403543i | \(0.132221\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.1836 | − | 19.6555i | −0.353264 | − | 0.681840i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.7989 | − | 25.6325i | 0.512138 | − | 0.887049i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.4715 | + | 35.5207i | 0.500208 | + | 1.22777i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.0366 | + | 36.4364i | 0.726263 | + | 1.25792i | 0.958452 | + | 0.285254i | \(0.0920779\pi\) |
−0.232189 | + | 0.972671i | \(0.574589\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.82597 | + | 17.0191i | −0.338826 | + | 0.586865i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26.6173 | − | 41.6025i | 0.916749 | − | 1.43286i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −46.1665 | − | 79.9628i | −1.58818 | − | 2.75080i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.678304 | + | 1.06018i | −0.0232793 | + | 0.0363853i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.13161 | + | 3.69206i | 0.0730707 | + | 0.126562i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.72519 | + | 11.6484i | 0.230266 | + | 0.398833i | 0.957886 | − | 0.287147i | \(-0.0927070\pi\) |
−0.727620 | + | 0.685980i | \(0.759374\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31.8104 | + | 2.90748i | 1.08789 | + | 0.0994336i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.3786 | 1.41347 | 0.706733 | − | 0.707481i | \(-0.250168\pi\) | ||||
0.706733 | + | 0.707481i | \(0.250168\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.7630 | −1.35670 | −0.678349 | − | 0.734740i | \(-0.737304\pi\) | ||||
−0.678349 | + | 0.734740i | \(0.737304\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.6929 | − | 46.2334i | −0.908637 | − | 1.57380i | −0.815960 | − | 0.578109i | \(-0.803791\pi\) |
−0.0926768 | − | 0.995696i | \(-0.529542\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.02704 | + | 10.4391i | −0.204926 | + | 0.354942i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.15652 | + | 4.93359i | −0.107201 | + | 0.167554i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.9552 | + | 25.9033i | −0.507322 | + | 0.878708i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.43560 | −0.319713 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.47169 | − | 0.134513i | −0.0498092 | − | 0.00455257i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.85349 | −0.231426 | −0.115713 | − | 0.993283i | \(-0.536915\pi\) | ||||
−0.115713 | + | 0.993283i | \(0.536915\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 44.2601 | + | 2.01848i | 1.49286 | + | 0.0680818i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.5103 | −0.421483 | −0.210742 | − | 0.977542i | \(-0.567588\pi\) | ||||
−0.210742 | + | 0.977542i | \(0.567588\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.69124 | 0.225178 | 0.112589 | − | 0.993642i | \(-0.464086\pi\) | ||||
0.112589 | + | 0.993642i | \(0.464086\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.9768 | + | 32.7864i | −0.705126 | + | 1.10210i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.1416 | 1.07921 | 0.539605 | − | 0.841918i | \(-0.318574\pi\) | ||||
0.539605 | + | 0.841918i | \(0.318574\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.0009 | − | 39.4162i | −0.469047 | − | 1.32049i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.8928 | 0.531832 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.19076 | − | 3.79450i | 0.0732289 | − | 0.126836i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 72.1569 | + | 3.29072i | 2.40925 | + | 0.109874i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.7434 | + | 44.5888i | −0.858590 | + | 1.48712i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.4086 | + | 19.7602i | 0.380074 | + | 0.658308i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −41.6883 | −1.38577 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.4031 | −1.04272 | −0.521362 | − | 0.853336i | \(-0.674576\pi\) | ||||
−0.521362 | + | 0.853336i | \(0.674576\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.89397 | + | 8.34832i | −0.195491 | + | 0.276896i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.8982 | − | 39.6609i | −0.758653 | − | 1.31402i | −0.943538 | − | 0.331265i | \(-0.892525\pi\) |
0.184885 | − | 0.982760i | \(-0.440809\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.45185 | − | 5.97877i | −0.114239 | − | 0.197868i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −58.8235 | − | 2.68265i | −1.94465 | − | 0.0886857i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.5900 | − | 23.5385i | −0.448292 | − | 0.776465i | 0.549983 | − | 0.835176i | \(-0.314634\pi\) |
−0.998275 | + | 0.0587112i | \(0.981301\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.96722 | + | 9.58732i | 0.163676 | + | 0.315913i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −48.0576 | + | 83.2381i | −1.58183 | + | 2.73982i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.382977 | + | 0.663336i | 0.0125922 | + | 0.0218104i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.93200 | + | 12.6514i | −0.293365 | + | 0.415528i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.3338 | − | 35.2192i | 0.667132 | − | 1.15551i | −0.311571 | − | 0.950223i | \(-0.600855\pi\) |
0.978703 | − | 0.205283i | \(-0.0658115\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.2929 | + | 42.6584i | −0.893529 | + | 1.39657i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.8135 | − | 44.7103i | 0.844192 | − | 1.46218i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.4150 | 0.536254 | 0.268127 | − | 0.963384i | \(-0.413595\pi\) | ||||
0.268127 | + | 0.963384i | \(0.413595\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 49.2893 | + | 2.24784i | 1.60849 | + | 0.0733555i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.66878 | − | 6.35451i | −0.119599 | − | 0.207151i | 0.800010 | − | 0.599987i | \(-0.204827\pi\) |
−0.919609 | + | 0.392836i | \(0.871494\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.801851 | + | 1.38885i | −0.0261119 | + | 0.0452271i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.5562 | + | 51.1929i | −0.960448 | + | 1.66354i | −0.239071 | + | 0.971002i | \(0.576843\pi\) |
−0.721377 | + | 0.692543i | \(0.756490\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.3801 | + | 26.6390i | 0.499258 | + | 0.864740i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.80039 | + | 0.127712i | 0.0908088 | + | 0.00414134i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.9354 | −0.548592 | −0.274296 | − | 0.961645i | \(-0.588445\pi\) | ||||
−0.274296 | + | 0.961645i | \(0.588445\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.75370 | − | 11.6977i | 0.218544 | − | 0.378530i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 30.2609 | − | 47.2973i | 0.978196 | − | 1.52891i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.7434 | + | 20.3401i | −0.378819 | + | 0.656133i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.2173 | − | 1.57367i | −0.554820 | − | 0.0507107i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.77548 | + | 11.7355i | 0.218110 | + | 0.377778i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.55555 | − | 6.15839i | 0.114339 | − | 0.198040i | −0.803177 | − | 0.595741i | \(-0.796858\pi\) |
0.917515 | + | 0.397701i | \(0.130192\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.5665 | + | 30.0452i | 0.500069 | + | 0.965192i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.735508 | + | 1.27394i | 0.0236036 | + | 0.0408826i | 0.877586 | − | 0.479419i | \(-0.159153\pi\) |
−0.853982 | + | 0.520302i | \(0.825819\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.9641 | + | 0.591229i | 0.415184 | + | 0.0189345i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.71634 | + | 16.8292i | 0.310853 | + | 0.538413i | 0.978547 | − | 0.206022i | \(-0.0660519\pi\) |
−0.667694 | + | 0.744436i | \(0.732719\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.8545 | − | 39.5851i | −0.730432 | − | 1.26515i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.2934 | + | 24.4662i | 0.360570 | + | 0.781145i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.74436 | 0.247007 | 0.123503 | − | 0.992344i | \(-0.460587\pi\) | ||||
0.123503 | + | 0.992344i | \(0.460587\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.6156 | 0.911768 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.1828 | + | 24.5653i | 0.450986 | + | 0.781130i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.23551 | − | 12.5323i | 0.229843 | − | 0.398101i | −0.727918 | − | 0.685664i | \(-0.759512\pi\) |
0.957762 | + | 0.287563i | \(0.0928452\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.1929 | − | 1.10332i | −0.767738 | − | 0.0350127i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.10243 | − | 8.83767i | 0.161758 | − | 0.280173i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55.3097 | −1.75168 | −0.875838 | − | 0.482605i | \(-0.839691\pi\) | ||||
−0.875838 | + | 0.482605i | \(0.839691\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.42461 | + | 3.49674i | 0.0450726 | + | 0.110632i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))