Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (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: | \(8.04892052375\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(0.500000 + 2.05195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.337 |
Dual form | 1008.2.r.j.673.2 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0.933463 | − | 1.45899i | 0.538935 | − | 0.842347i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.23025 | + | 2.13086i | −0.550186 | + | 0.952949i | 0.448075 | + | 0.893996i | \(0.352110\pi\) |
−0.998261 | + | 0.0589535i | \(0.981224\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.25729 | − | 2.72382i | −0.419098 | − | 0.907941i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.32383 | + | 4.02499i | 0.700662 | + | 1.21358i | 0.968234 | + | 0.250044i | \(0.0804451\pi\) |
−0.267573 | + | 0.963538i | \(0.586222\pi\) | |||||||
\(12\) | 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 | ||||||||
\(17\) | −4.51459 | −1.09495 | −0.547474 | − | 0.836822i | \(-0.684411\pi\) | ||||
−0.547474 | + | 0.836822i | \(0.684411\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.32743 | −0.992781 | −0.496390 | − | 0.868099i | \(-0.665342\pi\) | ||||
−0.496390 | + | 0.868099i | \(0.665342\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.73025 | − | 0.0789082i | −0.377572 | − | 0.0172192i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.93346 | − | 5.08091i | 0.611669 | − | 1.05944i | −0.379290 | − | 0.925278i | \(-0.623832\pi\) |
0.990959 | − | 0.134164i | \(-0.0428350\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.527042 | − | 0.912864i | −0.105408 | − | 0.182573i | ||||
\(26\) | 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 | 0.316976 | + | 0.948434i | \(0.397333\pi\) |
−0.979856 | + | 0.199708i | \(0.936001\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.04163 | + | 0.366739i | 1.39987 | + | 0.0638411i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.46050 | 0.415901 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.726654 | −0.119461 | −0.0597306 | − | 0.998215i | \(-0.519024\pi\) | ||||
−0.0597306 | + | 0.998215i | \(0.519024\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.66372 | + | 10.9316i | 0.906920 | + | 1.75046i | ||||
\(40\) | 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 | 0.620703 | − | 0.784046i | \(-0.286847\pi\) |
−0.989355 | + | 0.145522i | \(0.953514\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.35087 | + | 0.671871i | 1.09580 | + | 0.100157i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.83628 | + | 3.18054i | 0.267850 | + | 0.463929i | 0.968306 | − | 0.249766i | \(-0.0803536\pi\) |
−0.700457 | + | 0.713695i | \(0.747020\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.21420 | + | 6.58673i | −0.590106 | + | 0.922327i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.05408 | 0.694232 | 0.347116 | − | 0.937822i | \(-0.387161\pi\) | ||||
0.347116 | + | 0.937822i | \(0.387161\pi\) | |||||||
\(54\) | 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 | −0.399103 | − | 0.916906i | \(-0.630678\pi\) |
0.993615 | − | 0.112820i | \(-0.0359883\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.90856 | + | 11.9660i | 0.884550 | + | 1.53209i | 0.846228 | + | 0.532820i | \(0.178868\pi\) |
0.0383215 | + | 0.999265i | \(0.487799\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.73025 | + | 2.45076i | −0.217991 | + | 0.308767i | ||||
\(64\) | 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 | \(-0.859172\pi\) |
0.822631 | + | 0.568576i | \(0.192505\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.67471 | − | 9.02273i | −0.562768 | − | 1.08621i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.5218 | −1.60474 | −0.802370 | − | 0.596826i | \(-0.796428\pi\) | ||||
−0.802370 | + | 0.596826i | \(0.796428\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.32743 | −0.506487 | −0.253244 | − | 0.967403i | \(-0.581497\pi\) | ||||
−0.253244 | + | 0.967403i | \(0.581497\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.82383 | − | 0.0831759i | −0.210598 | − | 0.00960433i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.32383 | − | 4.02499i | 0.264825 | − | 0.458691i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.21780 | + | 5.57339i | 0.362031 | + | 0.627056i | 0.988295 | − | 0.152555i | \(-0.0487502\pi\) |
−0.626264 | + | 0.779611i | \(0.715417\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.83842 | + | 6.84929i | −0.648713 | + | 0.761033i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.742705 | + | 1.28640i | 0.0815225 | + | 0.141201i | 0.903904 | − | 0.427735i | \(-0.140688\pi\) |
−0.822382 | + | 0.568936i | \(0.807355\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.55408 | − | 9.61996i | 0.602425 | − | 1.04343i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.0687 | + | 0.550392i | 1.29390 | + | 0.0590083i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.83482 | 1.04249 | 0.521245 | − | 0.853407i | \(-0.325468\pi\) | ||||
0.521245 | + | 0.853407i | \(0.325468\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.10817 | 0.745139 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.88151 | + | 11.3520i | 0.609885 | + | 1.17715i | ||||
\(94\) | 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 | ||||||||
\(101\) | −1.70321 | − | 2.95005i | −0.169476 | − | 0.293541i | 0.768760 | − | 0.639537i | \(-0.220874\pi\) |
−0.938236 | + | 0.345997i | \(0.887541\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.58113 | − | 4.47064i | 0.254326 | − | 0.440505i | −0.710386 | − | 0.703812i | \(-0.751480\pi\) |
0.964712 | + | 0.263307i | \(0.0848131\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.29679 | − | 3.58985i | 0.224144 | − | 0.350333i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.76303 | 0.557133 | 0.278567 | − | 0.960417i | \(-0.410141\pi\) | ||||
0.278567 | + | 0.960417i | \(0.410141\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.98229 | −0.860347 | −0.430174 | − | 0.902746i | \(-0.641548\pi\) | ||||
−0.430174 | + | 0.902746i | \(0.641548\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 7.21780 | + | 12.5016i | 0.673063 | + | 1.16578i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 21.2360 | + | 1.94097i | 1.96327 | + | 0.179443i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.25729 | + | 3.90975i | 0.206926 | + | 0.358406i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.30039 | + | 9.18054i | −0.481853 | + | 0.834595i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.217799 | + | 0.420378i | 0.0196383 | + | 0.0379042i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.70895 | −0.868394 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.820039 | 0.0727667 | 0.0363833 | − | 0.999338i | \(-0.488416\pi\) | ||||
0.0363833 | + | 0.999338i | \(0.488416\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.36546 | − | 0.381507i | −0.736538 | − | 0.0335898i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.89397 | − | 6.74455i | 0.340218 | − | 0.589274i | −0.644255 | − | 0.764810i | \(-0.722833\pi\) |
0.984473 | + | 0.175536i | \(0.0561660\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.16372 | + | 3.74766i | 0.187618 | + | 0.324964i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.84202 | − | 10.0977i | 0.674934 | − | 0.869069i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.49640 | + | 2.59184i | 0.127846 | + | 0.221436i | 0.922842 | − | 0.385179i | \(-0.125860\pi\) |
−0.794996 | + | 0.606615i | \(0.792527\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.16372 | − | 5.47972i | 0.268343 | − | 0.464783i | −0.700091 | − | 0.714053i | \(-0.746857\pi\) |
0.968434 | + | 0.249270i | \(0.0801907\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.35447 | + | 0.289796i | 0.535143 | + | 0.0244052i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −33.0364 | −2.76264 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.1623 | −1.42525 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.796790 | + | 1.53790i | 0.0657181 | + | 0.126844i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.19076 | − | 3.79450i | 0.179474 | − | 0.310858i | −0.762227 | − | 0.647310i | \(-0.775894\pi\) |
0.941700 | + | 0.336452i | \(0.109227\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.30039 | + | 5.71644i | 0.268582 | + | 0.465197i | 0.968496 | − | 0.249030i | \(-0.0801117\pi\) |
−0.699914 | + | 0.714227i | \(0.746778\pi\) | |||||||
\(152\) | 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 | −0.727331 | − | 0.686287i | \(-0.759239\pi\) |
0.958007 | + | 0.286743i | \(0.0925727\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.71780 | − | 7.37385i | 0.374146 | − | 0.584784i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.86693 | −0.462379 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.32743 | −0.573929 | −0.286964 | − | 0.957941i | \(-0.592646\pi\) | ||||
−0.286964 | + | 0.957941i | \(0.592646\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.6747 | + | 16.6844i | −0.831025 | + | 1.29888i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.01459 | + | 10.4176i | −0.465423 | + | 0.806136i | −0.999221 | − | 0.0394762i | \(-0.987431\pi\) |
0.533798 | + | 0.845612i | \(0.320764\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.7630 | − | 32.4985i | −1.44331 | − | 2.49989i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.44085 | + | 11.7872i | 0.416073 | + | 0.901386i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.44951 | − | 4.24268i | −0.186233 | − | 0.322565i | 0.757758 | − | 0.652535i | \(-0.226295\pi\) |
−0.943991 | + | 0.329970i | \(0.892961\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.527042 | + | 0.912864i | −0.0398406 | + | 0.0690060i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.27714 | − | 14.0457i | −0.546983 | − | 1.05574i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.78074 | 0.133099 | 0.0665493 | − | 0.997783i | \(-0.478801\pi\) | ||||
0.0665493 | + | 0.997783i | \(0.478801\pi\) | |||||||
\(180\) | 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 | ||||||||
\(189\) | 1.96050 | + | 4.81211i | 0.142606 | + | 0.350030i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.74484 | − | 4.75420i | −0.198610 | − | 0.344002i | 0.749468 | − | 0.662040i | \(-0.230309\pi\) |
−0.948078 | + | 0.318038i | \(0.896976\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.75370 | − | 4.76954i | 0.198215 | − | 0.343319i | −0.749734 | − | 0.661739i | \(-0.769819\pi\) |
0.947950 | + | 0.318420i | \(0.103152\pi\) | |||||||
\(194\) | 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 | ||||||||
\(199\) | 4.14747 | 0.294006 | 0.147003 | − | 0.989136i | \(-0.453037\pi\) | ||||
0.147003 | + | 0.989136i | \(0.453037\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.05768 | + | 2.04145i | 0.0746032 | + | 0.143993i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.48755 | − | 6.04061i | 0.244778 | − | 0.423968i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.336285 | − | 0.582462i | −0.0234871 | − | 0.0406809i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −17.5277 | − | 1.60204i | −1.21826 | − | 0.111349i | ||||
\(208\) | 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 | \(0.552917\pi\) |
−0.771347 | + | 0.636415i | \(0.780417\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.6221 | + | 19.7281i | −0.864851 | + | 1.35175i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.8961 | 0.811308 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.38151 | 0.501090 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.03950 | + | 6.31367i | −0.272964 | + | 0.426638i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.0452 | − | 27.7912i | 1.07932 | − | 1.86944i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.60817 | − | 2.78543i | −0.107691 | − | 0.186526i | 0.807144 | − | 0.590355i | \(-0.201012\pi\) |
−0.914834 | + | 0.403829i | \(0.867679\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.82383 | + | 2.58331i | −0.121589 | + | 0.172221i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.97296 | + | 13.8096i | 0.529184 | + | 0.916573i | 0.999421 | + | 0.0340330i | \(0.0108351\pi\) |
−0.470237 | + | 0.882540i | \(0.655832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.608168 | − | 1.05338i | 0.0401889 | − | 0.0696092i | −0.845231 | − | 0.534401i | \(-0.820537\pi\) |
0.885420 | + | 0.464791i | \(0.153871\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.70321 | − | 7.14763i | −0.243653 | − | 0.470279i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.9722 | 1.30842 | 0.654210 | − | 0.756313i | \(-0.273001\pi\) | ||||
0.654210 | + | 0.756313i | \(0.273001\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.03638 | −0.589468 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.1352 | + | 0.507822i | 0.723310 | + | 0.0329866i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.00739 | − | 5.20896i | 0.194532 | − | 0.336939i | −0.752215 | − | 0.658918i | \(-0.771015\pi\) |
0.946747 | + | 0.321978i | \(0.104348\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.30778 | + | 16.1215i | 0.599567 | + | 1.03848i | 0.992885 | + | 0.119078i | \(0.0379938\pi\) |
−0.393318 | + | 0.919402i | \(0.628673\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.54309 | + | 14.9118i | 0.291440 | + | 0.956589i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.23025 | − | 2.13086i | −0.0785979 | − | 0.136136i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.3801 | − | 26.6390i | 0.978609 | − | 1.69500i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.57014 | + | 0.117211i | 0.162876 | + | 0.00742796i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.99707 | −0.441651 | −0.220826 | − | 0.975313i | \(-0.570875\pi\) | ||||
−0.220826 | + | 0.975313i | \(0.570875\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.2675 | 1.71429 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.85087 | − | 17.0832i | −0.554263 | − | 1.06979i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.88891 | − | 15.3960i | 0.554475 | − | 0.960378i | −0.443469 | − | 0.896289i | \(-0.646253\pi\) |
0.997944 | − | 0.0640889i | \(-0.0204141\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.363327 | + | 0.629301i | 0.0225760 | + | 0.0391028i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.0687 | − | 17.0943i | 0.747032 | − | 1.05811i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.5993 | − | 23.5547i | −0.838570 | − | 1.45245i | −0.891091 | − | 0.453825i | \(-0.850059\pi\) |
0.0525210 | − | 0.998620i | \(-0.483274\pi\) | |||||||
\(264\) | 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 | ||||||||
\(269\) | 23.8961 | 1.45697 | 0.728486 | − | 0.685061i | \(-0.240225\pi\) | ||||
0.728486 | + | 0.685061i | \(0.240225\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.2733 | −0.745553 | −0.372776 | − | 0.927921i | \(-0.621594\pi\) | ||||
−0.372776 | + | 0.927921i | \(0.621594\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.63521 | − | 10.3707i | 0.401581 | − | 0.627665i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.44951 | − | 4.24268i | 0.147711 | − | 0.255843i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.39037 | − | 11.0684i | −0.383960 | − | 0.665038i | 0.607664 | − | 0.794194i | \(-0.292107\pi\) |
−0.991624 | + | 0.129156i | \(0.958773\pi\) | |||||||
\(278\) | 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 | \(-0.826458\pi\) |
0.876622 | + | 0.481179i | \(0.159791\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.48395 | − | 16.3750i | −0.502546 | − | 0.969972i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.273346 | 0.0161351 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.38151 | 0.198913 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.852336 | + | 0.0388708i | 0.0499648 | + | 0.00227865i | ||||
\(292\) | 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 | ||||||||
\(297\) | −9.11177 | − | 22.3651i | −0.528718 | − | 1.29775i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.8515 | + | 36.1159i | 1.20588 | + | 2.08864i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.41741 | + | 4.18708i | −0.139337 | + | 0.241339i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.89397 | − | 0.268795i | −0.338600 | − | 0.0154419i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.9971 | −1.94667 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.23405 | 0.355796 | 0.177898 | − | 0.984049i | \(-0.443070\pi\) | ||||
0.177898 | + | 0.984049i | \(0.443070\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.11323 | − | 7.93901i | −0.233993 | − | 0.451635i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.6192 | − | 25.3211i | 0.828976 | − | 1.43583i | −0.0698655 | − | 0.997556i | \(-0.522257\pi\) |
0.898842 | − | 0.438273i | \(-0.144410\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.2434 | − | 24.6703i | −0.805083 | − | 1.39445i | −0.916235 | − | 0.400642i | \(-0.868787\pi\) |
0.111151 | − | 0.993803i | \(-0.464546\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.09358 | − | 6.70198i | −0.174303 | − | 0.377614i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.809243 | − | 1.40165i | −0.0454516 | − | 0.0787245i | 0.842405 | − | 0.538846i | \(-0.181139\pi\) |
−0.887856 | + | 0.460121i | \(0.847806\pi\) | |||||||
\(318\) | 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 | ||||||||
\(325\) | 7.49261 | 0.415615 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.38463 | + | 13.1051i | −0.463671 | + | 0.724711i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.83628 | − | 3.18054i | 0.101238 | − | 0.175349i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.99115 | − | 12.1090i | −0.384268 | − | 0.665572i | 0.607399 | − | 0.794397i | \(-0.292213\pi\) |
−0.991667 | + | 0.128825i | \(0.958880\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.913618 | + | 1.97928i | 0.0500660 | + | 0.108464i | ||||
\(334\) | 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 | ||||||||
\(339\) | −1.08326 | − | 2.09082i | −0.0588347 | − | 0.113558i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −34.3068 | −1.85782 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.9772 | + | 1.13909i | 1.34473 | + | 0.0613264i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.76449 | − | 6.52029i | 0.202089 | − | 0.350028i | −0.747113 | − | 0.664697i | \(-0.768560\pi\) |
0.949201 | + | 0.314670i | \(0.101894\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | 10.1819 | + | 17.6356i | 0.541928 | + | 0.938647i | 0.998793 | + | 0.0491110i | \(0.0156388\pi\) |
−0.456865 | + | 0.889536i | \(0.651028\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.6352 | − | 28.8130i | 0.882905 | − | 1.52924i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.81138 | + | 0.356238i | 0.413422 | + | 0.0188541i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.0263 | 0.845833 | 0.422917 | − | 0.906169i | \(-0.361006\pi\) | ||||
0.422917 | + | 0.906169i | \(0.361006\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.273346 | −0.0143866 | ||||||||
\(362\) | 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 | ||||||||
\(367\) | −6.79893 | − | 11.7761i | −0.354901 | − | 0.614707i | 0.632200 | − | 0.774805i | \(-0.282152\pi\) |
−0.987101 | + | 0.160099i | \(0.948819\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.816635 | + | 0.0746406i | 0.0425123 | + | 0.00388563i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.52704 | − | 4.37697i | −0.131197 | − | 0.227241i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.9641 | − | 18.9904i | 0.567700 | − | 0.983285i | −0.429093 | − | 0.903260i | \(-0.641167\pi\) |
0.996793 | − | 0.0800246i | \(-0.0254999\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.06294 | + | 14.1652i | −0.468008 | + | 0.731490i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −49.5801 | −2.55351 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.7965 | 1.53054 | 0.765271 | − | 0.643708i | \(-0.222605\pi\) | ||||
0.765271 | + | 0.643708i | \(0.222605\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.765475 | − | 1.19643i | 0.0392165 | − | 0.0612948i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.0109905 | + | 0.0190361i | −0.000561587 | + | 0.000972697i | −0.866306 | − | 0.499514i | \(-0.833512\pi\) |
0.865744 | + | 0.500486i | \(0.166845\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.71780 | + | 9.90352i | 0.291406 | + | 0.504730i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.36546 | + | 11.8490i | −0.425240 | + | 0.602318i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.6783 | + | 30.6197i | 0.896326 | + | 1.55248i | 0.832155 | + | 0.554543i | \(0.187107\pi\) |
0.0641702 | + | 0.997939i | \(0.479560\pi\) | |||||||
\(390\) | 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 | ||||||||
\(395\) | −15.8348 | −0.796736 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.9430 | −0.850344 | −0.425172 | − | 0.905112i | \(-0.639786\pi\) | ||||
−0.425172 | + | 0.905112i | \(0.639786\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.48755 | + | 0.341470i | 0.374846 | + | 0.0170949i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.48181 | − | 2.56657i | 0.0739982 | − | 0.128169i | −0.826652 | − | 0.562713i | \(-0.809757\pi\) |
0.900650 | + | 0.434545i | \(0.143091\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.2345 | − | 45.4395i | −1.30683 | − | 2.26350i | ||||
\(404\) | 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 | −0.626024 | − | 0.779804i | \(-0.715319\pi\) |
0.988342 | + | 0.152251i | \(0.0486521\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.17830 | + | 0.236157i | 0.255427 | + | 0.0116488i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.13307 | −0.449409 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.65486 | −0.179410 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.04163 | − | 9.73093i | −0.246890 | − | 0.476526i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.6352 | + | 21.8848i | −0.617270 | + | 1.06914i | 0.372711 | + | 0.927947i | \(0.378428\pi\) |
−0.989982 | + | 0.141196i | \(0.954905\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 6.35447 | − | 9.00059i | 0.308965 | − | 0.437624i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.37938 | + | 4.12120i | 0.115417 | + | 0.199908i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.90856 | − | 11.9660i | 0.334328 | − | 0.579074i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −30.8382 | + | 48.1997i | −1.48888 | + | 2.32710i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.0335 | −0.627799 | −0.313900 | − | 0.949456i | \(-0.601636\pi\) | ||||
−0.313900 | + | 0.949456i | \(0.601636\pi\) | |||||||
\(432\) | 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 | \(-0.115485\pi\) |
−0.774804 | + | 0.632201i | \(0.782152\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.98755 | + | 0.273062i | 0.142264 | + | 0.0130030i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.6228 | + | 30.5235i | 0.837282 | + | 1.45022i | 0.892158 | + | 0.451723i | \(0.149190\pi\) |
−0.0548760 | + | 0.998493i | \(0.517476\pi\) | |||||||
\(444\) | 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 | ||||||||
\(451\) | −1.27042 | −0.0598218 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.4210 | + | 0.520856i | 0.536606 | + | 0.0244719i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.74484 | + | 15.1465i | −0.409964 | + | 0.710079i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5993 | + | 25.2868i | 0.682927 | + | 1.18286i | 0.974083 | + | 0.226189i | \(0.0726267\pi\) |
−0.291156 | + | 0.956675i | \(0.594040\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23.2396 | + | 3.19727i | 1.08473 | + | 0.149236i | ||||
\(460\) | 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 | \(0.515133\pi\) |
−0.841285 | + | 0.540593i | \(0.818200\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −31.4253 | − | 1.43315i | −1.45731 | − | 0.0664608i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.2877 | 0.707432 | 0.353716 | − | 0.935353i | \(-0.384918\pi\) | ||||
0.353716 | + | 0.935353i | \(0.384918\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.32743 | 0.0612950 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.60603 | − | 8.89018i | −0.212235 | − | 0.409638i | ||||
\(472\) | 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 | ||||||||
\(479\) | 5.51605 | + | 9.55408i | 0.252035 | + | 0.436537i | 0.964086 | − | 0.265591i | \(-0.0855669\pi\) |
−0.712051 | + | 0.702128i | \(0.752234\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.58259 | − | 4.47318i | 0.117756 | − | 0.203959i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.47656 | + | 8.55978i | −0.249192 | + | 0.389483i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.21206 | −0.0550370 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.6008 | −0.752253 | −0.376126 | − | 0.926568i | \(-0.622744\pi\) | ||||
−0.376126 | + | 0.926568i | \(0.622744\pi\) | |||||||
\(488\) | 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 | \(0.372726\pi\) |
−0.992352 | + | 0.123440i | \(0.960607\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.7448 | − | 27.2709i | −0.709112 | − | 1.22822i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.3779 | + | 31.1485i | 0.646239 | + | 1.40002i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.76089 | + | 11.7102i | 0.303268 | + | 0.525275i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.618485 | − | 1.07125i | 0.0276872 | − | 0.0479557i | −0.851850 | − | 0.523786i | \(-0.824519\pi\) |
0.879537 | + | 0.475830i | \(0.157852\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.58472 | + | 18.4996i | 0.428214 | + | 0.826503i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.07179 | 0.0477889 | 0.0238944 | − | 0.999714i | \(-0.492393\pi\) | ||||
0.0238944 | + | 0.999714i | \(0.492393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.38151 | 0.372973 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −64.9296 | − | 2.96112i | −2.88362 | − | 0.131508i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.0344 | + | 17.3801i | −0.444768 | + | 0.770362i | −0.998036 | − | 0.0626420i | \(-0.980047\pi\) |
0.553268 | + | 0.833004i | \(0.313381\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.16372 | + | 3.74766i | 0.0957171 | + | 0.165787i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.2762 | + | 3.06472i | 0.983516 | + | 0.135311i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.35087 | + | 11.0000i | 0.279853 | + | 0.484720i | ||||
\(516\) | 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 | ||||||||
\(521\) | −30.8860 | −1.35314 | −0.676570 | − | 0.736379i | \(-0.736534\pi\) | ||||
−0.676570 | + | 0.736379i | \(0.736534\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.39922 | 0.323545 | 0.161773 | − | 0.986828i | \(-0.448279\pi\) | ||||
0.161773 | + | 0.986828i | \(0.448279\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.839883 | + | 1.62107i | 0.0366555 | + | 0.0707494i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.6623 | − | 28.8599i | 0.725819 | − | 1.25716i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.71041 | − | 9.89072i | −0.248279 | − | 0.430031i | ||||
\(530\) | 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 | ||||||||
\(537\) | 1.66225 | − | 2.59808i | 0.0717315 | − | 0.112115i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.64766 | −0.200189 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.6696 | 0.974644 | 0.487322 | − | 0.873222i | \(-0.337974\pi\) | ||||
0.487322 | + | 0.873222i | \(0.337974\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.8157 | + | 24.7196i | −0.678715 | + | 1.06082i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.0505 | − | 19.1400i | 0.473351 | − | 0.819868i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.07373 | − | 5.32386i | −0.131423 | − | 0.227632i | 0.792802 | − | 0.609479i | \(-0.208621\pi\) |
−0.924225 | + | 0.381847i | \(0.875288\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.9071 | − | 33.8624i | 1.02033 | − | 1.44521i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.0921 | − | 26.1403i | −0.642946 | − | 1.11361i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.21780 | − | 5.57339i | 0.136835 | − | 0.237005i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.42461 | − | 2.74966i | −0.0604713 | − | 0.116717i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.6739 | 1.25732 | 0.628662 | − | 0.777679i | \(-0.283603\pi\) | ||||
0.628662 | + | 0.777679i | \(0.283603\pi\) | |||||||
\(558\) | 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 | 0.372255 | + | 0.928131i | \(0.378585\pi\) |
−0.989912 | + | 0.141683i | \(0.954749\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.67257 | + | 2.89698i | 0.0703655 | + | 0.121877i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.85087 | + | 1.63157i | 0.371702 | + | 0.0685196i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.4430 | + | 31.9442i | 0.773170 | + | 1.33917i | 0.935817 | + | 0.352486i | \(0.114664\pi\) |
−0.162647 | + | 0.986684i | \(0.552003\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.1893 | − | 28.0407i | 0.677501 | − | 1.17347i | −0.298230 | − | 0.954494i | \(-0.596396\pi\) |
0.975731 | − | 0.218972i | \(-0.0702703\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.49854 | − | 0.433181i | −0.396807 | − | 0.0180964i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.18423 | −0.257900 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.0187 | 0.958280 | 0.479140 | − | 0.877739i | \(-0.340949\pi\) | ||||
0.479140 | + | 0.877739i | \(0.340949\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.38823 | − | 8.46980i | −0.182369 | − | 0.351993i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.742705 | − | 1.28640i | 0.0308126 | − | 0.0533690i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.7448 | + | 20.3427i | 0.486422 | + | 0.842507i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −30.2616 | + | 42.8630i | −1.25116 | + | 1.77217i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.87052 | + | 4.97189i | 0.118479 | + | 0.205212i | 0.919165 | − | 0.393872i | \(-0.128865\pi\) |
−0.800686 | + | 0.599084i | \(0.795531\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.9715 | − | 27.6634i | 0.658094 | − | 1.13985i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.8561 | − | 16.9680i | 0.446562 | − | 0.697969i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.7453 | 1.13936 | 0.569682 | − | 0.821865i | \(-0.307066\pi\) | ||||
0.569682 | + | 0.821865i | \(0.307066\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.1082 | −0.455391 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.87151 | − | 6.05111i | 0.158450 | − | 0.247655i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.05408 | − | 3.55778i | 0.0839276 | − | 0.145367i | −0.821006 | − | 0.570919i | \(-0.806587\pi\) |
0.904934 | + | 0.425552i | \(0.139920\pi\) | |||||||
\(600\) | 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 | ||||||||
\(605\) | −13.0416 | − | 22.5888i | −0.530218 | − | 0.918364i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.280738 | + | 0.486253i | −0.0113948 | + | 0.0197364i | −0.871667 | − | 0.490099i | \(-0.836960\pi\) |
0.860272 | + | 0.509836i | \(0.170294\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.55768 | − | 10.7270i | −0.225209 | − | 0.434679i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.1052 | −1.05611 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.2016 | −0.815933 | −0.407967 | − | 0.912997i | \(-0.633762\pi\) | ||||
−0.407967 | + | 0.912997i | \(0.633762\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | 19.8515 | + | 34.3839i | 0.797901 | + | 1.38201i | 0.920981 | + | 0.389608i | \(0.127390\pi\) |
−0.123080 | + | 0.992397i | \(0.539277\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.6988 | + | 24.0773i | −0.750358 | + | 0.966188i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.91741 | − | 8.51721i | −0.197012 | − | 0.341235i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5797 | − | 25.2527i | 0.583187 | − | 1.01011i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −34.7996 | − | 1.58704i | −1.38976 | − | 0.0633802i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.28054 | 0.130804 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.0364 | 1.23554 | 0.617769 | − | 0.786359i | \(-0.288037\pi\) | ||||
0.617769 | + | 0.786359i | \(0.288037\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.6857 | + | 41.8559i | 0.861929 | + | 1.66362i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.00885 | + | 1.74739i | −0.0400352 | + | 0.0693429i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.55408 | − | 6.15585i | −0.140818 | − | 0.243904i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.0009 | + | 36.8309i | 0.672544 | + | 1.45701i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.7932 | + | 25.6226i | 0.584296 | + | 1.01203i | 0.994963 | + | 0.100245i | \(0.0319626\pi\) |
−0.410667 | + | 0.911785i | \(0.634704\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.8442 | − | 22.2467i | 0.506524 | − | 0.877325i | −0.493447 | − | 0.869776i | \(-0.664263\pi\) |
0.999972 | − | 0.00754978i | \(-0.00240319\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.1046 | − | 17.3563i | 0.437242 | − | 0.683403i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.0177 | −0.669035 | −0.334518 | − | 0.942390i | \(-0.608573\pi\) | ||||
−0.334518 | + | 0.942390i | \(0.608573\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 42.4475 | 1.66621 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.89037 | − | 10.7695i | 0.270055 | − | 0.422092i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.735508 | + | 1.27394i | −0.0287827 | + | 0.0498530i | −0.880058 | − | 0.474866i | \(-0.842496\pi\) |
0.851275 | + | 0.524719i | \(0.175830\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.58113 | + | 16.5950i | 0.374366 | + | 0.648420i | ||||
\(656\) | 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 | \(-0.868096\pi\) |
0.108995 | − | 0.994042i | \(-0.465237\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.1352 | + | 33.1432i | −0.744273 | + | 1.28912i | 0.206260 | + | 0.978497i | \(0.433871\pi\) |
−0.950533 | + | 0.310622i | \(0.899463\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −25.5693 | − | 49.3518i | −0.993031 | − | 1.91667i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.6477 | −0.412899 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40.9224 | 1.58452 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.56507 | − | 0.253795i | −0.215158 | − | 0.00981230i | ||||
\(670\) | 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 | ||||||||
\(675\) | 2.06654 | + | 5.07237i | 0.0795411 | + | 0.195236i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.4626 | − | 38.9064i | −0.863309 | − | 1.49530i | −0.868716 | − | 0.495310i | \(-0.835054\pi\) |
0.00540665 | − | 0.999985i | \(-0.498279\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.246304 | − | 0.426611i | 0.00945228 | − | 0.0163718i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.5905 | + | 1.25826i | 1.05727 | + | 0.0482168i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.3973 | 1.85187 | 0.925935 | − | 0.377683i | \(-0.123279\pi\) | ||||
0.925935 | + | 0.377683i | \(0.123279\pi\) | |||||||
\(684\) | 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 | \(-0.0529730\pi\) |
−0.636551 | + | 0.771234i | \(0.719640\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.8851 | − | 1.26910i | −0.527452 | − | 0.0482092i | ||||
\(694\) | 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 | ||||||||
\(703\) | 3.14454 | 0.118599 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.43512 | + | 13.1840i | −0.317685 | + | 0.496537i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.70321 | + | 2.95005i | −0.0640558 | + | 0.110948i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.49261 | − | 4.31732i | −0.0936119 | − | 0.162141i | 0.815417 | − | 0.578875i | \(-0.196508\pi\) |
−0.909028 | + | 0.416734i | \(0.863175\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.1352 | − | 15.7721i | 0.417603 | − | 0.591500i | ||||
\(712\) | 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 | ||||||||
\(717\) | −4.79252 | − | 9.25012i | −0.178980 | − | 0.345452i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.6942 | −0.585293 | −0.292647 | − | 0.956221i | \(-0.594536\pi\) | ||||
−0.292647 | + | 0.956221i | \(0.594536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.16225 | −0.192252 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.2096 | + | 1.46892i | 1.19789 | + | 0.0546298i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.67617 | − | 6.36731i | 0.136529 | − | 0.236476i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.9071 | + | 18.8916i | 0.404522 | + | 0.700652i | 0.994266 | − | 0.106938i | \(-0.0341047\pi\) |
−0.589744 | + | 0.807590i | \(0.700771\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.9969 | + | 7.29124i | 0.962847 | + | 0.270046i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.9136 | + | 18.9029i | 0.403655 | + | 0.699151i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0074 | − | 20.7974i | 0.443503 | − | 0.768170i | −0.554443 | − | 0.832221i | \(-0.687069\pi\) |
0.997947 | + | 0.0640514i | \(0.0204022\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.25729 | − | 0.194154i | −0.157033 | − | 0.00716148i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.16945 | −0.227255 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.7089 | −0.688220 | −0.344110 | − | 0.938929i | \(-0.611819\pi\) | ||||
−0.344110 | + | 0.938929i | \(0.611819\pi\) | |||||||
\(740\) | 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 | \(0.431537\pi\) |
−0.952785 | + | 0.303644i | \(0.901797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.39037 | + | 9.33639i | 0.197488 | + | 0.342059i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.57014 | − | 3.64039i | 0.0940364 | − | 0.133195i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.88151 | − | 4.99093i | −0.105288 | − | 0.182365i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.5629 | + | 18.2955i | −0.385447 | + | 0.667614i | −0.991831 | − | 0.127558i | \(-0.959286\pi\) |
0.606384 | + | 0.795172i | \(0.292619\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.53151 | + | 10.2087i | −0.238021 | + | 0.372024i | ||||
\(754\) | 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 | ||||||||
\(759\) | 25.4532 | − | 39.7830i | 0.923892 | − | 1.44403i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.694551 | + | 1.20300i | −0.0251774 | + | 0.0436086i | −0.878340 | − | 0.478037i | \(-0.841348\pi\) |
0.853162 | + | 0.521646i | \(0.174682\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.49115 | + | 7.77889i | 0.162590 | + | 0.281615i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −33.1862 | − | 3.03322i | −1.19985 | − | 0.109666i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 32.4597 | + | 56.2219i | 1.17205 | + | 2.03005i | ||||
\(768\) | 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 | ||||||||
\(773\) | 1.31596 | 0.0473318 | 0.0236659 | − | 0.999720i | \(-0.492466\pi\) | ||||
0.0236659 | + | 0.999720i | \(0.492466\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.78074 | 0.279492 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.25729 | + | 0.0573390i | 0.0451052 | + | 0.00205702i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.591443 | − | 1.02441i | 0.0211907 | − | 0.0367033i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.4224 | − | 54.4251i | −1.12438 | − | 1.94748i | ||||
\(782\) | 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 | \(-0.763222\pi\) |
0.954345 | + | 0.298706i | \(0.0965551\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −47.0605 | − | 2.14620i | −1.67540 | − | 0.0764066i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.35953 | −0.0483395 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −98.2144 | −3.48769 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.90856 | + | 19.1247i | 0.351420 | + | 0.678282i | ||||
\(796\) | 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 | ||||||||
\(801\) | −12.3653 | − | 26.7883i | −0.436905 | − | 0.946518i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.0562 | − | 17.4179i | −0.354876 | − | 0.614664i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.21780 | − | 12.5016i | 0.254394 | − | 0.440623i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.3061 | − | 34.8641i | 0.785213 | − | 1.22728i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.6955 | 0.938564 | 0.469282 | − | 0.883048i | \(-0.344513\pi\) | ||||
0.469282 | + | 0.883048i | \(0.344513\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.2852 | −1.34438 | −0.672188 | − | 0.740381i | \(-0.734645\pi\) | ||||
−0.672188 | + | 0.740381i | \(0.734645\pi\) | |||||||
\(812\) | 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 | ||||||||
\(819\) | −8.93706 | − | 19.3614i | −0.312286 | − | 0.676542i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.24990 | + | 9.09310i | 0.183223 | + | 0.317351i | 0.942976 | − | 0.332860i | \(-0.108014\pi\) |
−0.759753 | + | 0.650211i | \(0.774680\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | − | 13.8564i | 0.278862 | − | 0.483004i | −0.692240 | − | 0.721668i | \(-0.743376\pi\) |
0.971102 | + | 0.238664i | \(0.0767093\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.90350 | − | 7.53420i | −0.135902 | − | 0.262307i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.7817 | 1.69631 | 0.848153 | − | 0.529752i | \(-0.177715\pi\) | ||||
0.848153 | + | 0.529752i | \(0.177715\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.21926 | −0.216004 | −0.108002 | − | 0.994151i | \(-0.534445\pi\) | ||||
−0.108002 | + | 0.994151i | \(0.534445\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.1139 | − | 1.00851i | −0.767123 | − | 0.0349847i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.25729 | − | 3.90975i | 0.0782106 | − | 0.135465i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.7989 | − | 25.6325i | −0.512138 | − | 0.887049i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23.5261 | − | 30.2930i | 0.813180 | − | 1.04708i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.0366 | − | 36.4364i | −0.726263 | − | 1.25792i | −0.958452 | − | 0.285254i | \(-0.907922\pi\) |
0.232189 | − | 0.972671i | \(-0.425411\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.82597 | + | 17.0191i | −0.338826 | + | 0.586865i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 49.3374 | + | 2.25004i | 1.69927 | + | 0.0774954i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 92.3330 | 3.17635 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.6008 | 0.364247 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.578990 | − | 1.11752i | −0.0198709 | − | 0.0383531i | ||||
\(850\) | 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 | ||||||||
\(857\) | −20.6893 | − | 35.8349i | −0.706733 | − | 1.22410i | −0.966063 | − | 0.258308i | \(-0.916835\pi\) |
0.259330 | − | 0.965789i | \(-0.416498\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.8815 | + | 34.4358i | −0.678349 | + | 1.17493i | 0.297129 | + | 0.954837i | \(0.403971\pi\) |
−0.975478 | + | 0.220097i | \(0.929363\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.255158 | − | 0.398809i | 0.00869578 | − | 0.0135914i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −53.3858 | −1.81727 | −0.908637 | − | 0.417588i | \(-0.862876\pi\) | ||||
−0.908637 | + | 0.417588i | \(0.862876\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0541 | 0.409851 | ||||||||
\(866\) | 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 | ||||||||
\(871\) | −4.71780 | − | 8.17147i | −0.159857 | − | 0.276880i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.852336 | − | 1.20726i | 0.0288472 | − | 0.0408597i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.85447 | + | 8.40819i | 0.164111 | + | 0.284249i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.42674 | − | 5.93530i | 0.115713 | − | 0.200421i | −0.802352 | − | 0.596852i | \(-0.796418\pi\) |
0.918065 | + | 0.396431i | \(0.129751\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.3820 | + | 39.3396i | 0.687468 | + | 1.32689i | ||||
\(880\) | 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 | \(-0.535914\pi\) | ||||
−0.112589 | + | 0.993642i | \(0.535914\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 38.8822 | + | 1.77322i | 1.30701 | + | 0.0596063i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.0708 | − | 27.8355i | 0.539605 | − | 0.934623i | −0.459320 | − | 0.888271i | \(-0.651907\pi\) |
0.998925 | − | 0.0463524i | \(-0.0147597\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.410019 | − | 0.710174i | −0.0137516 | − | 0.0238185i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −41.1359 | − | 7.58300i | −1.37810 | − | 0.254040i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.94639 | − | 13.7636i | −0.265916 | − | 0.460580i | ||||
\(894\) | 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 | ||||||||
\(899\) | −51.4868 | −1.71718 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.8171 | −0.760148 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.85234 | + | 7.43546i | 0.128198 | + | 0.247437i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.8442 | − | 36.1031i | 0.692883 | − | 1.20011i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.7016 | − | 27.1959i | −0.521362 | − | 0.903025i | −0.999691 | − | 0.0248444i | \(-0.992091\pi\) |
0.478330 | − | 0.878180i | \(-0.341242\pi\) | |||||||
\(908\) | 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 | \(0.107475\pi\) |
−0.184885 | + | 0.982760i | \(0.559191\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.45185 | + | 5.97877i | −0.114239 | + | 0.197868i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −31.7350 | + | 49.6013i | −1.04913 | + | 1.63977i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.78794 | −0.257180 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.1800 | −0.896584 | −0.448292 | − | 0.893887i | \(-0.647968\pi\) | ||||
−0.448292 | + | 0.893887i | \(0.647968\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.81925 | − | 9.09540i | 0.191751 | − | 0.299704i | ||||
\(922\) | 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 | ||||||||
\(927\) | −15.4225 | − | 1.40962i | −0.506540 | − | 0.0462979i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.3338 | + | 35.2192i | 0.667132 | + | 1.15551i | 0.978703 | + | 0.205283i | \(0.0658115\pi\) |
−0.311571 | + | 0.950223i | \(0.600855\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.16372 | − | 3.74766i | 0.0709129 | − | 0.122825i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.2968 | − | 44.9655i | −0.762703 | − | 1.47210i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 51.6270 | 1.68838 | ||||||||
\(936\) | 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 | −0.919609 | − | 0.392836i | \(-0.871494\pi\) |
0.800010 | + | 0.599987i | \(0.204827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.801851 | + | 1.38885i | 0.0261119 | + | 0.0452271i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.6659 | − | 1.74255i | −0.412020 | − | 0.0566852i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.5562 | + | 51.1929i | 0.960448 | + | 1.66354i | 0.721377 | + | 0.692543i | \(0.243510\pi\) |
0.239071 | + | 0.971002i | \(0.423157\pi\) | |||||||
\(948\) | 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 | ||||||||
\(955\) | 13.5074 | 0.437089 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.8302 | + | 49.8554i | 0.834973 | + | 1.61160i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.49640 | − | 2.59184i | 0.0483213 | − | 0.0836950i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.7434 | − | 20.3401i | −0.378819 | − | 0.656133i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.24583 | − | 15.6975i | −0.233493 | − | 0.505844i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.77548 | + | 11.7355i | 0.218110 | + | 0.377778i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.55555 | + | 6.15839i | −0.114339 | + | 0.198040i | −0.917515 | − | 0.397701i | \(-0.869808\pi\) |
0.803177 | + | 0.595741i | \(0.203142\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.2367 | − | 28.5036i | 0.585846 | − | 0.915669i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.47102 | 0.0472072 | 0.0236036 | − | 0.999721i | \(-0.492486\pi\) | ||||
0.0236036 | + | 0.999721i | \(0.492486\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.32743 | −0.202848 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.99407 | − | 10.9316i | 0.223990 | − | 0.350092i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.71634 | − | 16.8292i | 0.310853 | − | 0.538413i | −0.667694 | − | 0.744436i | \(-0.732719\pi\) |
0.978547 | + | 0.206022i | \(0.0660519\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | 3.87218 | + | 6.70681i | 0.123503 | + | 0.213914i | 0.921147 | − | 0.389215i | \(-0.127254\pi\) |
−0.797644 | + | 0.603129i | \(0.793920\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.3078 | + | 24.7818i | −0.455884 | + | 0.789614i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.92627 | − | 5.64803i | −0.0931441 | − | 0.179779i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.3655 | −0.901972 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.4710 | 0.459687 | 0.229843 | − | 0.973228i | \(-0.426179\pi\) | ||||
0.229843 | + | 0.973228i | \(0.426179\pi\) | |||||||
\(992\) | 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 | ||||||||
\(997\) | 27.6549 | + | 47.8996i | 0.875838 | + | 1.51700i | 0.855867 | + | 0.517196i | \(0.173024\pi\) |
0.0199711 | + | 0.999801i | \(0.493643\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.74057 | + | 0.514623i | 0.118346 | + | 0.0162819i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))