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: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 673.1 | ||
Root | \(-0.766044 - 0.642788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.673 |
Dual form | 1008.2.r.h.337.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −1.70574 | − | 0.300767i | −0.984808 | − | 0.173648i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.26604 | − | 2.19285i | −0.566192 | − | 0.980674i | −0.996938 | − | 0.0782003i | \(-0.975083\pi\) |
0.430745 | − | 0.902473i | \(-0.358251\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.81908 | + | 1.02606i | 0.939693 | + | 0.342020i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.233956 | − | 0.405223i | 0.0705403 | − | 0.122179i | −0.828598 | − | 0.559844i | \(-0.810861\pi\) |
0.899138 | + | 0.437665i | \(0.144194\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.91147 | − | 5.04282i | −0.807498 | − | 1.39863i | −0.914592 | − | 0.404378i | \(-0.867488\pi\) |
0.107094 | − | 0.994249i | \(-0.465845\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | + | 4.12122i | 0.387298 | + | 1.06409i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.87939 | 0.940889 | 0.470445 | − | 0.882430i | \(-0.344094\pi\) | ||||
0.470445 | + | 0.882430i | \(0.344094\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.18479 | 0.501226 | 0.250613 | − | 0.968087i | \(-0.419368\pi\) | ||||
0.250613 | + | 0.968087i | \(0.419368\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.11334 | + | 1.32683i | −0.242951 | + | 0.289538i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0530334 | − | 0.0918566i | −0.0110582 | − | 0.0191534i | 0.860443 | − | 0.509546i | \(-0.170187\pi\) |
−0.871502 | + | 0.490393i | \(0.836853\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.705737 | + | 1.22237i | −0.141147 | + | 0.244474i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.50000 | − | 2.59808i | −0.866025 | − | 0.500000i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.39053 | + | 7.60462i | −0.815301 | + | 1.41214i | 0.0938108 | + | 0.995590i | \(0.470095\pi\) |
−0.909112 | + | 0.416552i | \(0.863238\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.84002 | − | 6.65111i | −0.689688 | − | 1.19458i | −0.971939 | − | 0.235235i | \(-0.924414\pi\) |
0.282250 | − | 0.959341i | \(-0.408919\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.520945 | + | 0.620838i | −0.0906848 | + | 0.108074i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.53209 | −0.428001 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.68004 | −1.26259 | −0.631296 | − | 0.775542i | \(-0.717477\pi\) | ||||
−0.631296 | + | 0.775542i | \(0.717477\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.44949 | + | 9.47740i | 0.552361 | + | 1.51760i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.11334 | + | 1.92836i | 0.173875 | + | 0.301160i | 0.939771 | − | 0.341804i | \(-0.111038\pi\) |
−0.765897 | + | 0.642964i | \(0.777705\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.613341 | − | 1.06234i | 0.0935336 | − | 0.162005i | −0.815462 | − | 0.578811i | \(-0.803517\pi\) |
0.908996 | + | 0.416806i | \(0.136850\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.31908 | − | 7.48086i | −0.196637 | − | 1.11518i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.66637 | + | 4.61830i | −0.388931 | + | 0.673648i | −0.992306 | − | 0.123810i | \(-0.960489\pi\) |
0.603375 | + | 0.797457i | \(0.293822\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.61721 | − | 1.16679i | −0.926595 | − | 0.163384i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.716881 | −0.0984712 | −0.0492356 | − | 0.998787i | \(-0.515679\pi\) | ||||
−0.0492356 | + | 0.998787i | \(0.515679\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.18479 | −0.159757 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.72668 | − | 0.657115i | −0.493611 | − | 0.0870369i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.368241 | + | 0.637812i | 0.0479409 | + | 0.0830360i | 0.889000 | − | 0.457907i | \(-0.151401\pi\) |
−0.841059 | + | 0.540943i | \(0.818067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.479055 | + | 0.829748i | −0.0613368 | + | 0.106238i | −0.895063 | − | 0.445939i | \(-0.852870\pi\) |
0.833726 | + | 0.552178i | \(0.186203\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.29813 | − | 1.92836i | 0.289538 | − | 0.242951i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.37211 | + | 12.7689i | −0.914398 | + | 1.58378i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.81908 | − | 8.34689i | −0.588744 | − | 1.01973i | −0.994397 | − | 0.105708i | \(-0.966289\pi\) |
0.405653 | − | 0.914027i | \(-0.367044\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0628336 | + | 0.172634i | 0.00756428 | + | 0.0207827i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.2344 | −1.57064 | −0.785318 | − | 0.619092i | \(-0.787501\pi\) | ||||
−0.785318 | + | 0.619092i | \(0.787501\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2686 | −1.20185 | −0.600923 | − | 0.799307i | \(-0.705200\pi\) | ||||
−0.600923 | + | 0.799307i | \(0.705200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.57145 | − | 1.87278i | 0.181456 | − | 0.216250i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.233956 | − | 0.405223i | −0.0266617 | − | 0.0461794i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.31908 | + | 10.9450i | −0.710952 | + | 1.23140i | 0.253548 | + | 0.967323i | \(0.418402\pi\) |
−0.964500 | + | 0.264082i | \(0.914931\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.89440 | + | 5.78509i | 0.766044 | + | 0.642788i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.36571 | + | 2.36549i | −0.149907 | + | 0.259646i | −0.931193 | − | 0.364527i | \(-0.881231\pi\) |
0.781286 | + | 0.624173i | \(0.214564\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.91147 | − | 8.50692i | −0.532724 | − | 0.922705i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.77631 | − | 11.6510i | 1.04813 | − | 1.24911i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.11381 | −0.860062 | −0.430031 | − | 0.902814i | \(-0.641497\pi\) | ||||
−0.430031 | + | 0.902814i | \(0.641497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.82295 | −0.610411 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.54963 | + | 12.5000i | 0.471775 | + | 1.29619i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.76604 | − | 4.79093i | −0.283790 | − | 0.491539i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.80200 | − | 11.7814i | 0.690639 | − | 1.19622i | −0.280990 | − | 0.959711i | \(-0.590663\pi\) |
0.971629 | − | 0.236511i | \(-0.0760039\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.07532 | − | 0.902302i | 0.108074 | − | 0.0906848i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.78699 | − | 8.29131i | 0.476323 | − | 0.825016i | −0.523309 | − | 0.852143i | \(-0.675303\pi\) |
0.999632 | + | 0.0271271i | \(0.00863590\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.52094 | + | 2.63435i | 0.149863 | + | 0.259571i | 0.931177 | − | 0.364568i | \(-0.118783\pi\) |
−0.781314 | + | 0.624139i | \(0.785450\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.31908 | + | 0.761570i | 0.421499 | + | 0.0743216i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.51754 | 0.630074 | 0.315037 | − | 0.949079i | \(-0.397983\pi\) | ||||
0.315037 | + | 0.949079i | \(0.397983\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.6382 | 1.01895 | 0.509475 | − | 0.860485i | \(-0.329840\pi\) | ||||
0.509475 | + | 0.860485i | \(0.329840\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.1001 | + | 2.30991i | 1.24341 | + | 0.219247i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.58853 | − | 4.48346i | −0.243508 | − | 0.421768i | 0.718203 | − | 0.695834i | \(-0.244965\pi\) |
−0.961711 | + | 0.274065i | \(0.911632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.134285 | + | 0.232589i | −0.0125222 | + | 0.0216890i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.03343 | − | 17.2035i | −0.280441 | − | 1.59046i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.93969 | − | 3.35965i | 0.177811 | − | 0.307978i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.39053 | + | 9.33667i | 0.490048 | + | 0.848788i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.31908 | − | 3.62414i | −0.118937 | − | 0.326777i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.08647 | −0.812718 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.88207 | 0.788157 | 0.394078 | − | 0.919077i | \(-0.371064\pi\) | ||||
0.394078 | + | 0.919077i | \(0.371064\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.36571 | + | 1.62760i | −0.120244 | + | 0.143302i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.68139 | + | 9.84045i | 0.496385 | + | 0.859764i | 0.999991 | − | 0.00416893i | \(-0.00132701\pi\) |
−0.503606 | + | 0.863933i | \(0.667994\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.09240 | − | 1.89209i | 0.0947228 | − | 0.164065i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.1571i | 1.13238i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.86231 | − | 4.95767i | 0.244544 | − | 0.423562i | −0.717459 | − | 0.696600i | \(-0.754695\pi\) |
0.962003 | + | 0.273038i | \(0.0880285\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.461981 | − | 0.800175i | −0.0391847 | − | 0.0678700i | 0.845768 | − | 0.533551i | \(-0.179143\pi\) |
−0.884953 | + | 0.465681i | \(0.845809\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.93717 | − | 7.07564i | 0.500000 | − | 0.595876i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.72462 | −0.227844 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.2344 | 1.84647 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.592396 | + | 1.62760i | 0.0488600 | + | 0.134242i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.36231 | − | 7.55574i | −0.357374 | − | 0.618991i | 0.630147 | − | 0.776476i | \(-0.282995\pi\) |
−0.987521 | + | 0.157485i | \(0.949661\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.21348 | − | 15.9582i | 0.749782 | − | 1.29866i | −0.198145 | − | 0.980173i | \(-0.563492\pi\) |
0.947927 | − | 0.318488i | \(-0.103175\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.9363 | + | 3.98048i | 0.884147 | + | 0.321803i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.72328 | + | 16.8412i | −0.780992 | + | 1.35272i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.46198 | − | 4.26428i | −0.196488 | − | 0.340326i | 0.750900 | − | 0.660416i | \(-0.229620\pi\) |
−0.947387 | + | 0.320090i | \(0.896287\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.22281 | + | 0.215615i | 0.0969752 | + | 0.0170994i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.106067 | −0.00835924 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.63816 | −0.598267 | −0.299133 | − | 0.954211i | \(-0.596698\pi\) | ||||
−0.299133 | + | 0.954211i | \(0.596698\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.02094 | + | 0.356347i | 0.157330 | + | 0.0277416i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.82770 | − | 4.89771i | −0.218814 | − | 0.378996i | 0.735632 | − | 0.677382i | \(-0.236885\pi\) |
−0.954446 | + | 0.298385i | \(0.903552\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4534 | + | 18.1058i | −0.804105 | + | 1.39275i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.15910 | + | 2.24173i | 0.470998 | + | 0.171429i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.5346 | + | 18.2465i | −0.800932 | + | 1.38725i | 0.118071 | + | 0.993005i | \(0.462329\pi\) |
−0.919003 | + | 0.394250i | \(0.871005\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.705737 | + | 1.22237i | 0.0533487 | + | 0.0924027i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.436289 | − | 1.19869i | −0.0327935 | − | 0.0900994i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.12061 | 0.382733 | 0.191366 | − | 0.981519i | \(-0.438708\pi\) | ||||
0.191366 | + | 0.981519i | \(0.438708\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.319955 | −0.0237821 | −0.0118910 | − | 0.999929i | \(-0.503785\pi\) | ||||
−0.0118910 | + | 0.999929i | \(0.503785\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.06670 | − | 1.27125i | 0.0788530 | − | 0.0939734i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.72328 | + | 16.8412i | 0.714870 | + | 1.23819i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.907604 | − | 1.57202i | 0.0663706 | − | 0.114957i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.50000 | + | 2.59808i | −0.327327 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.78359 | + | 13.4816i | −0.563200 | + | 0.975492i | 0.434014 | + | 0.900906i | \(0.357097\pi\) |
−0.997215 | + | 0.0745858i | \(0.976237\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.02094 | − | 5.23243i | −0.217452 | − | 0.376639i | 0.736576 | − | 0.676355i | \(-0.236441\pi\) |
−0.954028 | + | 0.299716i | \(0.903108\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.4153 | − | 19.5630i | 1.17553 | − | 1.40094i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.2344 | 1.79788 | 0.898939 | − | 0.438074i | \(-0.144339\pi\) | ||||
0.898939 | + | 0.438074i | \(0.144339\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.04189 | −0.215634 | −0.107817 | − | 0.994171i | \(-0.534386\pi\) | ||||
−0.107817 | + | 0.994171i | \(0.534386\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.70961 | + | 15.6870i | 0.402725 | + | 1.10648i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.39053 | + | 7.60462i | 0.308155 | + | 0.533740i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.81908 | − | 4.88279i | 0.196893 | − | 0.341029i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.0552549 | − | 0.313366i | −0.00384048 | − | 0.0217805i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.511144 | − | 0.885328i | 0.0353566 | − | 0.0612394i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.72668 | − | 4.72275i | −0.187713 | − | 0.325128i | 0.756775 | − | 0.653676i | \(-0.226774\pi\) |
−0.944487 | + | 0.328548i | \(0.893441\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.5744 | + | 3.98048i | 1.54678 | + | 0.272738i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.10607 | −0.211832 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.68004 | −0.521355 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.5155 | + | 3.08845i | 1.18359 | + | 0.208698i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.2947 | − | 19.5630i | −0.759766 | − | 1.31595i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.09627 | − | 12.2911i | 0.475201 | − | 0.823073i | −0.524395 | − | 0.851475i | \(-0.675709\pi\) |
0.999597 | + | 0.0284023i | \(0.00904195\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.24376 | + | 2.72183i | −0.216250 | + | 0.181456i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.44697 | + | 2.50622i | −0.0960385 | + | 0.166344i | −0.910042 | − | 0.414517i | \(-0.863951\pi\) |
0.814003 | + | 0.580861i | \(0.197284\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.58378 | − | 7.93934i | −0.302905 | − | 0.524646i | 0.673888 | − | 0.738834i | \(-0.264623\pi\) |
−0.976793 | + | 0.214187i | \(0.931290\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.277189 | + | 0.761570i | 0.0182377 | + | 0.0501076i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.2713 | 0.869429 | 0.434715 | − | 0.900568i | \(-0.356849\pi\) | ||||
0.434715 | + | 0.900568i | \(0.356849\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.5030 | 0.880838 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.0706 | − | 16.7687i | 0.913982 | − | 1.08924i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.76857 | + | 8.25941i | 0.308453 | + | 0.534257i | 0.978024 | − | 0.208491i | \(-0.0668553\pi\) |
−0.669571 | + | 0.742748i | \(0.733522\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.47906 | − | 7.75795i | 0.288521 | − | 0.499734i | −0.684936 | − | 0.728604i | \(-0.740170\pi\) |
0.973457 | + | 0.228870i | \(0.0735031\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.0201 | − | 11.9415i | −0.642788 | − | 0.766044i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.26604 | + | 2.19285i | −0.0808846 | + | 0.140096i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.36097 | − | 11.0175i | −0.404739 | − | 0.701028i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.04101 | − | 3.62414i | 0.192716 | − | 0.229670i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.9982 | 1.57788 | 0.788938 | − | 0.614473i | \(-0.210631\pi\) | ||||
0.788938 | + | 0.614473i | \(0.210631\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.0496299 | −0.00312020 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.81908 | + | 15.9878i | 0.364405 | + | 1.00119i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.42602 | − | 9.39815i | −0.338466 | − | 0.586240i | 0.645678 | − | 0.763609i | \(-0.276575\pi\) |
−0.984144 | + | 0.177369i | \(0.943241\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.84002 | + | 6.65111i | −0.238607 | + | 0.413280i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.1800 | + | 16.9331i | −1.24911 | + | 1.04813i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.0437 | − | 22.5924i | 0.804309 | − | 1.39310i | −0.112448 | − | 0.993658i | \(-0.535869\pi\) |
0.916757 | − | 0.399446i | \(-0.130798\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.907604 | + | 1.57202i | 0.0557537 | + | 0.0965682i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.8400 | + | 2.44037i | 0.846996 | + | 0.149348i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.63310 | −0.465399 | −0.232699 | − | 0.972549i | \(-0.574756\pi\) | ||||
−0.232699 | + | 0.972549i | \(0.574756\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.40373 | −0.206762 | −0.103381 | − | 0.994642i | \(-0.532966\pi\) | ||||
−0.103381 | + | 0.994642i | \(0.532966\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.93242 | + | 1.75135i | 0.601137 | + | 0.105997i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.330222 | + | 0.571962i | 0.0199131 | + | 0.0344906i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.86097 | − | 4.95534i | 0.171899 | − | 0.297738i | −0.767185 | − | 0.641426i | \(-0.778343\pi\) |
0.939084 | + | 0.343689i | \(0.111676\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00088 | − | 22.6901i | −0.239526 | − | 1.35842i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.1887 | + | 24.5755i | −0.846425 | + | 1.46605i | 0.0379535 | + | 0.999280i | \(0.487916\pi\) |
−0.884378 | + | 0.466771i | \(0.845417\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.28564 | + | 3.95885i | 0.135867 | + | 0.235329i | 0.925929 | − | 0.377699i | \(-0.123285\pi\) |
−0.790061 | + | 0.613028i | \(0.789951\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.27719 | + | 9.00400i | 0.194124 | + | 0.533351i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.22668 | 0.131437 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.95037 | −0.114728 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.1459 | + | 18.0502i | −0.887868 | + | 1.05812i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.16385 | − | 3.74789i | −0.126413 | − | 0.218954i | 0.795871 | − | 0.605466i | \(-0.207013\pi\) |
−0.922285 | + | 0.386512i | \(0.873680\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.932419 | − | 1.61500i | 0.0542875 | − | 0.0940287i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.10560 | + | 1.21567i | −0.122179 | + | 0.0705403i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.308811 | + | 0.534876i | −0.0178590 | + | 0.0309327i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.613341 | − | 1.06234i | −0.0353524 | − | 0.0612321i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.6591 | + | 12.7030i | −0.612349 | + | 0.729769i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.42602 | 0.138914 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.3773 | −0.706411 | −0.353206 | − | 0.935546i | \(-0.614908\pi\) | ||||
−0.353206 | + | 0.935546i | \(0.614908\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.80200 | − | 4.95096i | −0.102512 | − | 0.281651i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.9927 | − | 19.0400i | −0.623340 | − | 1.07966i | −0.988859 | − | 0.148853i | \(-0.952442\pi\) |
0.365519 | − | 0.930804i | \(-0.380892\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.94491 | − | 12.0289i | 0.392549 | − | 0.679915i | −0.600236 | − | 0.799823i | \(-0.704927\pi\) |
0.992785 | + | 0.119908i | \(0.0382599\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.13816 | − | 2.59808i | −0.402190 | − | 0.146385i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.09105 | − | 5.35386i | 0.173611 | − | 0.300703i | −0.766069 | − | 0.642759i | \(-0.777790\pi\) |
0.939680 | + | 0.342056i | \(0.111123\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.05438 | + | 3.55829i | 0.115023 | + | 0.199226i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.1172 | − | 1.96026i | −0.620502 | − | 0.109411i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.47565 | 0.471598 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.21894 | 0.455905 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.1459 | − | 3.19961i | −1.00347 | − | 0.176939i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.66637 | + | 4.61830i | 0.147002 | + | 0.254615i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.36571 | − | 9.29369i | 0.294926 | − | 0.510827i | −0.680041 | − | 0.733174i | \(-0.738038\pi\) |
0.974968 | + | 0.222346i | \(0.0713715\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.6506 | − | 7.88019i | −1.18645 | − | 0.431832i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.2023 | + | 21.1351i | −0.666685 | + | 1.15473i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.29726 | + | 16.1033i | 0.506454 | + | 0.877204i | 0.999972 | + | 0.00746831i | \(0.00237726\pi\) |
−0.493518 | + | 0.869735i | \(0.664289\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.06687 | + | 8.42615i | 0.166569 | + | 0.457645i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.59358 | −0.194603 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.299011 | − | 0.356347i | 0.0160982 | − | 0.0191851i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.2062 | − | 17.6777i | −0.547898 | − | 0.948987i | −0.998418 | − | 0.0562207i | \(-0.982095\pi\) |
0.450521 | − | 0.892766i | \(-0.351238\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.78106 | − | 3.08489i | 0.0953379 | − | 0.165130i | −0.814412 | − | 0.580288i | \(-0.802940\pi\) |
0.909750 | + | 0.415157i | \(0.136274\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 30.2569i | 1.61500i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.01114 | + | 8.67956i | −0.266716 | + | 0.461966i | −0.968012 | − | 0.250904i | \(-0.919272\pi\) |
0.701296 | + | 0.712871i | \(0.252605\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.7554 | + | 29.0211i | 0.889283 | + | 1.54028i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.31908 | + | 5.14728i | −0.228590 | + | 0.272423i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.48070 | −0.500372 | −0.250186 | − | 0.968198i | \(-0.580492\pi\) | ||||
−0.250186 | + | 0.968198i | \(0.580492\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.2267 | −0.748773 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.38666 | − | 17.5472i | −0.335213 | − | 0.920989i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.0005 | + | 22.5175i | 0.680476 | + | 1.17862i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.06670 | − | 13.9719i | 0.421079 | − | 0.729329i | −0.574967 | − | 0.818177i | \(-0.694985\pi\) |
0.996045 | + | 0.0888474i | \(0.0283183\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.15998 | + | 6.57856i | 0.0603860 | + | 0.342466i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.358441 | + | 0.620838i | −0.0186093 | + | 0.0322323i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.02481 | − | 12.1673i | −0.363731 | − | 0.630001i | 0.624841 | − | 0.780752i | \(-0.285164\pi\) |
−0.988572 | + | 0.150752i | \(0.951831\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.4991 | + | 2.73291i | 0.800371 | + | 0.141127i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 51.1317 | 2.63341 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0574 | −0.824812 | −0.412406 | − | 0.911000i | \(-0.635311\pi\) | ||||
−0.412406 | + | 0.911000i | \(0.635311\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.1505 | − | 2.67144i | −0.776183 | − | 0.136862i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.0103 | − | 27.7306i | −0.818086 | − | 1.41697i | −0.907090 | − | 0.420936i | \(-0.861702\pi\) |
0.0890039 | − | 0.996031i | \(-0.471632\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.592396 | + | 1.02606i | −0.0301913 | + | 0.0522929i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.81908 | − | 2.36549i | 0.143302 | − | 0.120244i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0214 | − | 26.0178i | 0.761616 | − | 1.31916i | −0.180402 | − | 0.983593i | \(-0.557740\pi\) |
0.942017 | − | 0.335564i | \(-0.108927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.205737 | − | 0.356347i | −0.0104046 | − | 0.0180212i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.73127 | − | 18.4940i | −0.339548 | − | 0.932899i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 32.0009 | 1.61014 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.3200 | −0.618321 | −0.309160 | − | 0.951010i | \(-0.600048\pi\) | ||||
−0.309160 | + | 0.951010i | \(0.600048\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.43242 | + | 2.89884i | −0.121773 | + | 0.145124i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.4880 | − | 18.1657i | −0.523745 | − | 0.907152i | −0.999618 | − | 0.0276385i | \(-0.991201\pi\) |
0.475873 | − | 0.879514i | \(-0.342132\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.3603 | + | 38.7291i | −1.11384 | + | 1.92923i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.95723 | − | 22.4426i | 0.196637 | − | 1.11518i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.79679 | + | 3.11213i | −0.0890635 | + | 0.154263i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.8307 | − | 22.2234i | −0.634437 | − | 1.09888i | −0.986634 | − | 0.162951i | \(-0.947899\pi\) |
0.352197 | − | 0.935926i | \(-0.385435\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.37346 | + | 7.59559i | −0.314379 | + | 0.374663i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.736482 | 0.0362399 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.91622 | 0.339504 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.547352 | + | 1.50384i | 0.0268039 | + | 0.0736432i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.739885 | − | 1.28152i | −0.0361458 | − | 0.0626063i | 0.847387 | − | 0.530976i | \(-0.178175\pi\) |
−0.883532 | + | 0.468370i | \(0.844841\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.55350 | + | 11.3510i | −0.319398 | + | 0.553214i | −0.980363 | − | 0.197203i | \(-0.936814\pi\) |
0.660965 | + | 0.750417i | \(0.270147\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.2554 | + | 10.2835i | −0.595876 | + | 0.500000i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.73783 | + | 4.74205i | −0.132804 | + | 0.230023i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.479055 | + | 0.829748i | 0.0231831 | + | 0.0401543i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.64749 | + | 0.819478i | 0.224383 | + | 0.0395648i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.7270 | −0.853879 | −0.426939 | − | 0.904280i | \(-0.640408\pi\) | ||||
−0.426939 | + | 0.904280i | \(0.640408\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.83843 | −0.280577 | −0.140289 | − | 0.990111i | \(-0.544803\pi\) | ||||
−0.140289 | + | 0.990111i | \(0.544803\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −37.9261 | − | 6.68739i | −1.81842 | − | 0.320636i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.115867 | − | 0.200688i | −0.00554267 | − | 0.00960019i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.9277 | − | 25.8555i | 0.712459 | − | 1.23401i | −0.251473 | − | 0.967864i | \(-0.580915\pi\) |
0.963931 | − | 0.266151i | \(-0.0857518\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.520945 | − | 2.95442i | −0.0248069 | − | 0.140687i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.33275 | − | 9.23659i | 0.253367 | − | 0.438844i | −0.711084 | − | 0.703107i | \(-0.751795\pi\) |
0.964451 | + | 0.264263i | \(0.0851288\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.2724 | + | 17.7924i | 0.486960 | + | 0.843440i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.16843 | + | 14.2002i | 0.244459 | + | 0.671644i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.55438 | 0.167741 | 0.0838707 | − | 0.996477i | \(-0.473272\pi\) | ||||
0.0838707 | + | 0.996477i | \(0.473272\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.04189 | 0.0490606 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.5155 | + | 24.4494i | −0.963901 | + | 1.14873i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.37211 | + | 12.7689i | 0.345610 | + | 0.598614i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.51161 | + | 4.35024i | −0.117488 | + | 0.203496i | −0.918772 | − | 0.394789i | \(-0.870818\pi\) |
0.801283 | + | 0.598285i | \(0.204151\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.4572 | − | 10.0789i | −0.814834 | − | 0.470445i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.23055 | + | 15.9878i | −0.429910 | + | 0.744625i | −0.996865 | − | 0.0791233i | \(-0.974788\pi\) |
0.566955 | + | 0.823749i | \(0.308121\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.11721 | − | 12.3274i | −0.330765 | − | 0.572902i | 0.651897 | − | 0.758307i | \(-0.273973\pi\) |
−0.982662 | + | 0.185406i | \(0.940640\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 21.6506 | − | 25.8022i | 1.00402 | − | 1.19655i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.36865 | 0.155883 | 0.0779413 | − | 0.996958i | \(-0.475165\pi\) | ||||
0.0779413 | + | 0.996958i | \(0.475165\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.63816 | −0.445049 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.91694 | + | 8.01422i | 0.134405 | + | 0.369276i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.286989 | − | 0.497079i | −0.0131958 | − | 0.0228557i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.54189 | + | 2.67063i | −0.0707467 | + | 0.122537i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.02094 | − | 0.735564i | −0.0925327 | − | 0.0336791i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.3833 | + | 31.8407i | −0.839952 | + | 1.45484i | 0.0499812 | + | 0.998750i | \(0.484084\pi\) |
−0.889934 | + | 0.456090i | \(0.849249\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.3603 | + | 38.7291i | 1.01954 | + | 1.76589i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.180922 | + | 0.0319015i | 0.00823224 | + | 0.00145157i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.4466 | −1.56414 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.4175 | 1.69555 | 0.847773 | − | 0.530358i | \(-0.177943\pi\) | ||||
0.847773 | + | 0.530358i | \(0.177943\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.0287 | + | 2.29731i | 0.589178 | + | 0.103888i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.3353 | − | 23.0974i | −0.601813 | − | 1.04237i | −0.992547 | − | 0.121866i | \(-0.961112\pi\) |
0.390734 | − | 0.920504i | \(-0.372221\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.0326 | + | 29.5013i | −0.767108 | + | 1.32867i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.34002 | − | 1.21567i | −0.150123 | − | 0.0546402i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.61721 | + | 11.4613i | −0.296822 | + | 0.514112i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.8726 | + | 29.2242i | 0.755320 | + | 1.30825i | 0.945215 | + | 0.326449i | \(0.105852\pi\) |
−0.189895 | + | 0.981804i | \(0.560815\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.35023 | + | 9.20469i | 0.149677 | + | 0.411235i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.0401 | 1.42860 | 0.714299 | − | 0.699840i | \(-0.246745\pi\) | ||||
0.714299 | + | 0.699840i | \(0.246745\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.2422 | −1.07876 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.2763 | − | 27.7396i | 1.03374 | − | 1.23196i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.96926 | + | 6.87495i | 0.175934 | + | 0.304727i | 0.940484 | − | 0.339838i | \(-0.110372\pi\) |
−0.764550 | + | 0.644564i | \(0.777039\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.13429 | + | 8.89284i | −0.227127 | + | 0.393396i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.83157 | − | 5.67626i | −0.434074 | − | 0.250613i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.85117 | − | 6.67042i | 0.169703 | − | 0.293934i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.24763 | + | 2.16095i | 0.0548705 | + | 0.0950386i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.4572 | − | 27.9552i | 1.02966 | − | 1.22710i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.6750 | −0.642923 | −0.321462 | − | 0.946923i | \(-0.604174\pi\) | ||||
−0.321462 | + | 0.946923i | \(0.604174\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.3432 | −1.23936 | −0.619680 | − | 0.784854i | \(-0.712738\pi\) | ||||
−0.619680 | + | 0.784854i | \(0.712738\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.836152 | − | 2.29731i | −0.0364927 | − | 0.100263i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.8969 | − | 25.8022i | −0.648920 | − | 1.12396i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4944 | − | 19.9088i | 0.499755 | − | 0.865602i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.383666 | + | 2.17588i | 0.0166497 | + | 0.0944251i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.48293 | − | 11.2288i | 0.280807 | − | 0.486371i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.25150 | − | 14.2920i | −0.356743 | − | 0.617898i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.73442 | − | 1.54011i | −0.376918 | − | 0.0664608i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.467911 | −0.0201544 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.2858 | 0.485215 | 0.242607 | − | 0.970125i | \(-0.421997\pi\) | ||||
0.242607 | + | 0.970125i | \(0.421997\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.545759 | + | 0.0962321i | 0.0234208 | + | 0.00412972i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.4684 | − | 23.3279i | −0.576922 | − | 0.999258i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.6202 | + | 25.3229i | −0.625115 | + | 1.08273i | 0.363404 | + | 0.931632i | \(0.381615\pi\) |
−0.988519 | + | 0.151099i | \(0.951719\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.20187 | + | 1.84759i | −0.0939734 | + | 0.0788530i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.59240 | + | 16.6145i | −0.408650 | + | 0.707802i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.31908 | + | 10.9450i | 0.268715 | + | 0.465427i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.5201 | − | 31.6511i | −0.489000 | − | 1.34352i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.775682 | −0.0328667 | −0.0164334 | − | 0.999865i | \(-0.505231\pi\) | ||||
−0.0164334 | + | 0.999865i | \(0.505231\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.14290 | −0.302113 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.02094 | + | 2.40847i | −0.0853243 | + | 0.101686i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.4761 | + | 21.6093i | 0.525806 | + | 0.910722i | 0.999548 | + | 0.0300588i | \(0.00956944\pi\) |
−0.473742 | + | 0.880663i | \(0.657097\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.55438 | + | 11.3525i | −0.275745 | + | 0.477604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.45723 | − | 3.07818i | 0.355170 | − | 0.129271i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.4017 | − | 21.4803i | 0.519905 | − | 0.900502i | −0.479827 | − | 0.877363i | \(-0.659301\pi\) |
0.999732 | − | 0.0231391i | \(-0.00736608\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.39827 | + | 7.61803i | 0.184062 | + | 0.318805i | 0.943260 | − | 0.332055i | \(-0.107742\pi\) |
−0.759198 | + | 0.650860i | \(0.774409\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.3316 | − | 20.6550i | 0.724037 | − | 0.862873i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.149711 | 0.00624336 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.8743 | −0.535965 | −0.267983 | − | 0.963424i | \(-0.586357\pi\) | ||||
−0.267983 | + | 0.963424i | \(0.586357\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.57919 | + | 9.83375i | 0.148746 | + | 0.408677i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.36571 | + | 2.36549i | 0.0566594 | + | 0.0981369i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.167718 | + | 0.290497i | −0.00694619 | + | 0.0120311i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −33.8842 | + | 28.4322i | −1.40094 | + | 1.17553i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.4315 | − | 38.8526i | 0.925849 | − | 1.60362i | 0.135658 | − | 0.990756i | \(-0.456685\pi\) |
0.790190 | − | 0.612861i | \(-0.209982\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.38965 | − | 14.5313i | −0.345690 | − | 0.598752i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −43.0433 | − | 7.58969i | −1.77056 | − | 0.312198i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.76053 | 0.154426 | 0.0772131 | − | 0.997015i | \(-0.475398\pi\) | ||||
0.0772131 | + | 0.997015i | \(0.475398\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.82295 | −0.402702 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.18866 | + | 0.914901i | 0.212358 | + | 0.0374444i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.84524 | − | 3.19604i | −0.0753943 | − | 0.130587i | 0.825863 | − | 0.563870i | \(-0.190688\pi\) |
−0.901258 | + | 0.433283i | \(0.857355\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.9285 | − | 18.9288i | 0.445785 | − | 0.772122i | −0.552322 | − | 0.833631i | \(-0.686258\pi\) |
0.998107 | + | 0.0615091i | \(0.0195913\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.02094 | − | 28.4752i | −0.204469 | − | 1.15960i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.6493 | − | 23.6413i | 0.554923 | − | 0.961155i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.1973 | + | 21.1263i | 0.495072 | + | 0.857490i | 0.999984 | − | 0.00568063i | \(-0.00180821\pi\) |
−0.504911 | + | 0.863171i | \(0.668475\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.20187 | − | 14.2920i | −0.210790 | − | 0.579142i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.0523 | 1.25624 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.0215 | 1.69723 | 0.848616 | − | 0.529010i | \(-0.177437\pi\) | ||||
0.848616 | + | 0.529010i | \(0.177437\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.27719 | + | 7.48086i | −0.253121 | + | 0.301657i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.2049 | − | 40.1920i | −0.934192 | − | 1.61807i | −0.776068 | − | 0.630650i | \(-0.782788\pi\) |
−0.158125 | − | 0.987419i | \(-0.550545\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.6047 | + | 23.5641i | −0.546820 | + | 0.947120i | 0.451670 | + | 0.892185i | \(0.350828\pi\) |
−0.998490 | + | 0.0549349i | \(0.982505\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.551139i | 0.0221165i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.05690 | + | 7.02676i | −0.162536 | + | 0.281521i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.0326 | + | 26.0372i | 0.601302 | + | 1.04149i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.13816 | + | 1.35640i | −0.0454536 | + | 0.0541694i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.7939 | −1.18796 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.6023 | 1.17845 | 0.589224 | − | 0.807970i | \(-0.299434\pi\) | ||||
0.589224 | + | 0.807970i | \(0.299434\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.23055 | + | 8.87587i | 0.128403 | + | 0.352784i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.2451 | − | 19.4771i | −0.446248 | − | 0.772925i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.91147 | + | 5.04282i | −0.115357 | + | 0.199804i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −37.3089 | − | 13.5793i | −1.47592 | − | 0.537189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.139500 | − | 0.241621i | 0.00550991 | − | 0.00954345i | −0.863257 | − | 0.504764i | \(-0.831579\pi\) |
0.868767 | + | 0.495221i | \(0.164913\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.12196 | − | 15.7997i | −0.359735 | − | 0.623079i | 0.628181 | − | 0.778067i | \(-0.283800\pi\) |
−0.987916 | + | 0.154988i | \(0.950466\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.29813 | + | 0.934204i | 0.208614 | + | 0.0367842i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.4570 | −0.882875 | −0.441438 | − | 0.897292i | \(-0.645531\pi\) | ||||
−0.441438 | + | 0.897292i | \(0.645531\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.344608 | 0.0135270 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.1001 | + | 2.30991i | 0.513435 | + | 0.0905324i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.2656 | + | 43.7614i | 0.988721 | + | 1.71251i | 0.624066 | + | 0.781372i | \(0.285480\pi\) |
0.364655 | + | 0.931143i | \(0.381187\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.3858 | − | 24.9169i | 0.562099 | − | 0.973584i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.9479 | − | 10.5362i | −1.12937 | − | 0.411055i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.33631 | + | 2.31456i | −0.0520554 | + | 0.0901626i | −0.890879 | − | 0.454241i | \(-0.849911\pi\) |
0.838824 | + | 0.544403i | \(0.183244\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.3050 | + | 29.9731i | 0.673086 | + | 1.16582i | 0.977024 | + | 0.213128i | \(0.0683651\pi\) |
−0.303938 | + | 0.952692i | \(0.598302\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.3819 | + | 36.7665i | 0.519710 | + | 1.42789i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.53209 | −0.214525 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.931379 | 0.0360631 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.8011 | + | 18.8310i | −0.610907 | + | 0.728050i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.224155 | + | 0.388249i | 0.00865342 | + | 0.0149882i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.25624 | + | 14.3002i | −0.318255 | + | 0.551234i | −0.980124 | − | 0.198386i | \(-0.936430\pi\) |
0.661869 | + | 0.749619i | \(0.269763\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.35163 | − | 3.66712i | 0.244474 | − | 0.141147i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.8790 | − | 37.8955i | 0.840877 | − | 1.45644i | −0.0482766 | − | 0.998834i | \(-0.515373\pi\) |
0.889154 | − | 0.457608i | \(-0.151294\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.80200 | − | 11.7814i | −0.261037 | − | 0.452129i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.22193 | − | 3.83975i | 0.123465 | − | 0.147140i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.2412 | −1.08062 | −0.540310 | − | 0.841466i | \(-0.681693\pi\) | ||||
−0.540310 | + | 0.841466i | \(0.681693\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.4953 | −0.553835 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.43083 | + | 14.9211i | 0.207199 | + | 0.569274i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.08718 | + | 3.61510i | 0.0795153 | + | 0.137725i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.5326 | + | 25.1711i | −0.552844 | + | 0.957555i | 0.445223 | + | 0.895420i | \(0.353124\pi\) |
−0.998068 | + | 0.0621351i | \(0.980209\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.243756 | − | 1.38241i | −0.00925951 | − | 0.0525133i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.16978 | + | 2.02611i | −0.0443722 | + | 0.0768549i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.31908 | + | 7.48086i | 0.163597 | + | 0.283358i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.6373 | − | 3.99156i | −0.856221 | − | 0.150975i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.10876 | −0.0418771 | −0.0209386 | − | 0.999781i | \(-0.506665\pi\) | ||||
−0.0209386 | + | 0.999781i | \(0.506665\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.7793 | −0.632843 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23.0326 | − | 4.06126i | −0.867456 | − | 0.152956i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.78699 | − | 8.29131i | −0.180033 | − | 0.311827i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.23442 | − | 15.9945i | 0.346806 | − | 0.600686i | −0.638874 | − | 0.769311i | \(-0.720600\pi\) |
0.985680 | + | 0.168626i | \(0.0539329\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.0442 | + | 24.3709i | −1.08924 | + | 0.913982i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.407299 | + | 0.705463i | −0.0152535 | + | 0.0264198i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.44949 | + | 5.97470i | 0.129004 | + | 0.223441i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.64977 | − | 15.5226i | −0.210994 | − | 0.579702i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.7769 | 1.25967 | 0.629834 | − | 0.776730i | \(-0.283123\pi\) | ||||
0.629834 | + | 0.776730i | \(0.283123\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.04189 | 0.113286 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.97343 | + | 11.8859i | −0.370916 | + | 0.442040i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.19712 | − | 10.7337i | −0.230155 | − | 0.398641i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.40214 | − | 14.5529i | 0.311618 | − | 0.539738i | −0.667095 | − | 0.744973i | \(-0.732462\pi\) |
0.978713 | + | 0.205234i | \(0.0657957\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5000 | + | 23.3827i | 0.500000 | + | 0.866025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.37939 | − | 4.12122i | 0.0880047 | − | 0.152429i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.81820 | + | 11.8095i | 0.251836 | + | 0.436193i | 0.964031 | − | 0.265789i | \(-0.0856323\pi\) |
−0.712195 | + | 0.701981i | \(0.752299\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.81908 | − | 3.35965i | 0.103983 | − | 0.123922i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.50980 | −0.166121 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.0419 | 1.17868 | 0.589340 | − | 0.807885i | \(-0.299388\pi\) | ||||
0.589340 | + | 0.807885i | \(0.299388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.53643 | + | 20.7062i | 0.276858 | + | 0.760660i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.8764 | + | 29.2309i | 0.619137 | + | 1.07238i | 0.989644 | + | 0.143547i | \(0.0458507\pi\) |
−0.370507 | + | 0.928830i | \(0.620816\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.0458 | + | 19.1318i | −0.404685 | + | 0.700936i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.27719 | + | 5.26719i | −0.229670 | + | 0.192716i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.25877 | − | 5.64436i | 0.119073 | − | 0.206240i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0582 | + | 22.6175i | 0.476502 | + | 0.825326i | 0.999637 | − | 0.0269236i | \(-0.00857108\pi\) |
−0.523135 | + | 0.852250i | \(0.675238\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −42.6404 | − | 7.51866i | −1.55390 | − | 0.273995i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −46.6587 | −1.69808 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.6536 | 1.29585 | 0.647927 | − | 0.761703i | \(-0.275636\pi\) | ||||
0.647927 | + | 0.761703i | \(0.275636\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0846555 | + | 0.0149270i | 0.00307280 | + | 0.000541817i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.3824 | − | 35.3033i | −0.738861 | − | 1.27974i | −0.953009 | − | 0.302943i | \(-0.902031\pi\) |
0.214148 | − | 0.976801i | \(-0.431302\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.31908 | − | 9.21291i | 0.192564 | − | 0.333530i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.11721 | − | 29.0211i | −0.185013 | − | 1.04926i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.14425 | − | 3.71395i | 0.0774243 | − | 0.134103i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.7135 | − | 34.1447i | −0.710886 | − | 1.23129i | −0.964525 | − | 0.263992i | \(-0.914961\pi\) |
0.253639 | − | 0.967299i | \(-0.418373\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.42871 | + | 17.6627i | 0.231524 | + | 0.636108i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.9026 | 0.895685 | 0.447842 | − | 0.894113i | \(-0.352193\pi\) | ||||
0.447842 | + | 0.894113i | \(0.352193\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.8402 | 0.389391 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.55051 | − | 10.1901i | 0.306748 | − | 0.365568i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.43242 | + | 4.21307i | 0.0871504 | + | 0.150949i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.09627 | + | 5.36289i | −0.110793 | + | 0.191899i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 39.5148 | − | 22.8139i | 1.41214 | − | 0.815301i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.23396 | + | 10.7975i | −0.222499 | + | 0.385380i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.3525 | − | 26.5913i | −0.547258 | − | 0.947879i | −0.998461 | − | 0.0554572i | \(-0.982338\pi\) |
0.451203 | − | 0.892421i | \(-0.350995\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.0442 | + | 34.6135i | −1.03400 | + | 1.23227i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.17705 | −0.184075 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.57903 | 0.198117 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.07532 | − | 2.95442i | −0.0381377 | − | 0.104783i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.50686 | + | 9.53817i | 0.195063 | + | 0.337859i | 0.946921 | − | 0.321466i | \(-0.104175\pi\) |
−0.751858 | + | 0.659325i | \(0.770842\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.3439 | + | 17.9161i | −0.365941 | + | 0.633828i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.8735 | − | 8.32526i | −0.808194 | − | 0.294158i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.40239 | + | 4.16106i | −0.0847785 | + | 0.146841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.134285 | + | 0.232589i | 0.00473294 | + | 0.00819769i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.0201 | + | 2.29579i | 0.458328 | + | 0.0808156i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.9881 | 0.597271 | 0.298636 | − | 0.954367i | \(-0.403468\pi\) | ||||
0.298636 | + | 0.954367i | \(0.403468\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.9796 | −1.33364 | −0.666822 | − | 0.745217i | \(-0.732346\pi\) | ||||
−0.666822 | + | 0.745217i | \(0.732346\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.80587 | + | 1.02373i | 0.203621 | + | 0.0359039i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.67024 | + | 16.7494i | 0.338734 | + | 0.586704i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.34002 | − | 2.32099i | 0.0468814 | − | 0.0812011i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.4153 | − | 5.97470i | −0.573599 | − | 0.208773i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.13934 | + | 7.16954i | −0.144464 | + | 0.250219i | −0.929173 | − | 0.369646i | \(-0.879479\pi\) |
0.784709 | + | 0.619864i | \(0.212812\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.2763 | + | 47.2440i | 0.950792 | + | 1.64682i | 0.743716 | + | 0.668496i | \(0.233062\pi\) |
0.207077 | + | 0.978325i | \(0.433605\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.391245 | − | 1.07494i | −0.0136214 | − | 0.0374245i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.8708 | 1.10826 | 0.554129 | − | 0.832431i | \(-0.313052\pi\) | ||||
0.554129 | + | 0.832431i | \(0.313052\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.352349 | −0.0122376 | −0.00611879 | − | 0.999981i | \(-0.501948\pi\) | ||||
−0.00611879 | + | 0.999981i | \(0.501948\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.37046 | + | 7.59202i | −0.220989 | + | 0.263364i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.93969 | − | 3.35965i | −0.0672064 | − | 0.116405i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.15998 | + | 12.4014i | −0.247781 | + | 0.429170i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 39.9067i | 1.37938i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.5077 | − | 21.6640i | 0.431815 | − | 0.747926i | −0.565215 | − | 0.824944i | \(-0.691207\pi\) |
0.997030 | + | 0.0770182i | \(0.0245399\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0535 | − | 41.6619i | −0.829431 | − | 1.43662i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.5936 | − | 37.6518i | 1.08814 | − | 1.29680i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 52.9377 | 1.82111 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.7811 | 0.370442 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.70801 | − | 7.44021i | −0.0929388 | − | 0.255347i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.407299 | + | 0.705463i | 0.0139620 | + | 0.0241829i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.5954 | + | 33.9402i | −0.670933 | + | 1.16209i | 0.306706 | + | 0.951804i | \(0.400773\pi\) |
−0.977640 | + | 0.210286i | \(0.932560\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.88191 | − | 16.3441i | −0.0985593 | − | 0.558958i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.20368 | + | 14.2092i | −0.280232 | + | 0.485377i | −0.971442 | − | 0.237278i | \(-0.923745\pi\) |
0.691210 | + | 0.722654i | \(0.257078\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.4162 | − | 23.2376i | −0.457756 | − | 0.792856i | 0.541086 | − | 0.840967i | \(-0.318013\pi\) |
−0.998842 | + | 0.0481111i | \(0.984680\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.79813 | − | 0.669713i | −0.129440 | − | 0.0228238i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.5057 | −0.493779 | −0.246890 | − | 0.969044i | \(-0.579408\pi\) | ||||
−0.246890 | + | 0.969044i | \(0.579408\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 53.3492 | 1.81393 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.32682 | + | 0.586608i | 0.112985 | + | 0.0199222i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.95677 | + | 5.12127i | 0.100301 | + | 0.173727i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.0612 | + | 48.6035i | −0.950819 | + | 1.64687i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.2638 | − | 26.2335i | 1.05812 | − | 0.887868i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.54323 | + | 7.86911i | −0.153589 | + | 0.266024i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.45723 | − | 16.3804i | −0.319348 | − | 0.553127i | 0.661004 | − | 0.750382i | \(-0.270131\pi\) |
−0.980352 | + | 0.197255i | \(0.936797\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.56371 | + | 7.04374i | 0.0864718 | + | 0.237579i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.8976 | 1.81585 | 0.907927 | − | 0.419128i | \(-0.137664\pi\) | ||||
0.907927 | + | 0.419128i | \(0.137664\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.4252 | −1.46137 | −0.730687 | − | 0.682712i | \(-0.760800\pi\) | ||||
−0.730687 | + | 0.682712i | \(0.760800\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.07620 | + | 2.47432i | −0.0697907 | + | 0.0831733i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.4800 | − | 33.7403i | −0.654074 | − | 1.13289i | −0.982125 | − | 0.188229i | \(-0.939725\pi\) |
0.328051 | − | 0.944660i | \(-0.393608\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.44104 | − | 7.69210i | 0.148948 | − | 0.257985i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.95723 | − | 1.44032i | 0.132572 | − | 0.0482524i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.82547 | + | 10.0900i | −0.194942 | + | 0.337650i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.48293 | − | 11.2288i | −0.216700 | − | 0.375336i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.687623 | − | 0.819478i | 0.0229591 | − | 0.0273616i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 67.4389 | 2.24921 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.78106 | −0.0926505 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.726682 | + | 1.99654i | 0.0241824 | + | 0.0664407i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.405078 | + | 0.701615i | 0.0134652 | + | 0.0233225i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.2638 | − | 29.9018i | 0.573236 | − | 0.992874i | −0.422995 | − | 0.906132i | \(-0.639021\pi\) |
0.996231 | − | 0.0867416i | \(-0.0276454\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.0023 | − | 18.4621i | 0.729769 | − | 0.612349i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.2631 | − | 40.2929i | 0.770741 | − | 1.33496i | −0.166416 | − | 0.986056i | \(-0.553220\pi\) |
0.937157 | − | 0.348907i | \(-0.113447\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.639033 | + | 1.10684i | 0.0211489 | + | 0.0366310i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.13816 | − | 0.729669i | −0.136803 | − | 0.0241221i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.3628 | 0.375232 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.95636 | 0.328430 | 0.164215 | − | 0.986425i | \(-0.447491\pi\) | ||||
0.164215 | + | 0.986425i | \(0.447491\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.1125 | + | 3.72270i | 0.695679 | + | 0.122667i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 38.5317 | + | 66.7388i | 1.26829 | + | 2.19674i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.42009 | − | 9.38788i | 0.178212 | − | 0.308671i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.58466 | + | 8.98703i | 0.0520469 | + | 0.295173i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.52300 | + | 7.83407i | −0.148395 | + | 0.257028i | −0.930634 | − | 0.365950i | \(-0.880744\pi\) |
0.782239 | + | 0.622978i | \(0.214077\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.09240 | − | 1.89209i | −0.0358018 | − | 0.0620106i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.0241 | + | 35.7834i | 0.426390 | + | 1.17150i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.59627 | −0.150314 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.3928 | −0.796878 | −0.398439 | − | 0.917195i | \(-0.630448\pi\) | ||||
−0.398439 | + | 0.917195i | \(0.630448\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.4641 | + | 18.4294i | −0.504652 | + | 0.601421i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.7690 | + | 51.5615i | 0.970443 | + | 1.68086i | 0.694220 | + | 0.719763i | \(0.255749\pi\) |
0.276223 | + | 0.961094i | \(0.410917\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.118089 | − | 0.204535i | 0.00384549 | − | 0.00666059i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.3944 | + | 6.57856i | 0.370660 | + | 0.214001i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.32429 | − | 7.48989i | 0.140521 | − | 0.243389i | −0.787172 | − | 0.616733i | \(-0.788456\pi\) |
0.927693 | + | 0.373344i | \(0.121789\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.8967 | + | 51.7826i | 0.970487 | + | 1.68093i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.88279 | + | 8.20259i | −0.223190 | + | 0.265987i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.78249 | 0.122527 | 0.0612634 | − | 0.998122i | \(-0.480487\pi\) | ||||
0.0612634 | + | 0.998122i | \(0.480487\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.4175 | 1.27552 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.43401 | − | 6.68739i | −0.0786804 | − | 0.216173i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.86231 | − | 4.95767i | −0.0924288 | − | 0.160091i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.9915 | + | 24.2341i | −0.451340 | + | 0.781744i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.3735 | + | 6.68739i | 0.592076 | + | 0.215498i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.64930 | + | 13.2490i | −0.246240 | + | 0.426500i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.4745 | − | 28.5346i | −0.529783 | − | 0.917611i | −0.999396 | − | 0.0347392i | \(-0.988940\pi\) |
0.469613 | − | 0.882872i | \(-0.344393\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.4572 | − | 2.54920i | −0.464433 | − | 0.0818921i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55.4570 | 1.77970 | 0.889850 | − | 0.456254i | \(-0.150809\pi\) | ||||
0.889850 | + | 0.456254i | \(0.150809\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.923963 | −0.0296209 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.0194 | − | 2.47199i | −0.448979 | − | 0.0791670i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.2743 | − | 48.9724i | −0.904573 | − | 1.56677i | −0.821489 | − | 0.570225i | \(-0.806856\pi\) |
−0.0830847 | − | 0.996542i | \(-0.526477\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.89827 | + | 3.28790i | −0.0606690 | + | 0.105082i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.9898 | + | 10.9154i | 0.957500 | + | 0.348502i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.4987 | − | 25.1124i | 0.462435 | − | 0.800961i | −0.536646 | − | 0.843807i | \(-0.680309\pi\) |
0.999082 | + | 0.0428458i | \(0.0136424\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.9479 | − | 55.3354i | −1.01794 | − | 1.76313i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.15910 | − | 8.67956i | −0.100555 | − | 0.276273i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.130110 | −0.00413726 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.80922 | −0.216302 | −0.108151 | − | 0.994134i | \(-0.534493\pi\) | ||||
−0.108151 | + | 0.994134i | \(0.534493\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.9477 | + | 14.2388i | −0.379150 | + | 0.451853i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.85117 | + | 6.67042i | 0.122090 | + | 0.211466i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.4688 | − | 33.7210i | 0.616585 | − | 1.06796i | −0.373520 | − | 0.927622i | \(-0.621849\pi\) |
0.990104 | − | 0.140333i | \(-0.0448175\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 34.5602 | + | 19.9533i | 1.09344 | + | 0.631296i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))