Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(293,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.293");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.x (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 293.3 | ||
Root | \(-0.544978 + 1.64408i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.293 |
Dual form | 1764.2.x.a.1469.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.09400 | + | 1.34282i | −0.631619 | + | 0.775279i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.95741 | + | 3.39033i | −0.875381 | + | 1.51620i | −0.0190238 | + | 0.999819i | \(0.506056\pi\) |
−0.856357 | + | 0.516385i | \(0.827278\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.606348 | − | 2.93808i | −0.202116 | − | 0.979362i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.19958 | − | 1.84728i | 0.964710 | − | 0.556976i | 0.0670908 | − | 0.997747i | \(-0.478628\pi\) |
0.897620 | + | 0.440771i | \(0.145295\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.480242 | + | 0.277268i | 0.133195 | + | 0.0769002i | 0.565117 | − | 0.825011i | \(-0.308831\pi\) |
−0.431922 | + | 0.901911i | \(0.642164\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.41122 | − | 6.33747i | −0.622575 | − | 1.63633i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.83832 | −1.41600 | −0.708000 | − | 0.706213i | \(-0.750402\pi\) | ||||
−0.708000 | + | 0.706213i | \(0.750402\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.33973i | − | 1.22502i | −0.790464 | − | 0.612509i | \(-0.790160\pi\) | ||
0.790464 | − | 0.612509i | \(-0.209840\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.96965 | + | 1.13718i | 0.410700 | + | 0.237118i | 0.691090 | − | 0.722768i | \(-0.257131\pi\) |
−0.280390 | + | 0.959886i | \(0.590464\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.16291 | − | 8.94242i | −1.03258 | − | 1.78848i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.60867 | + | 2.40003i | 0.886939 | + | 0.461887i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.53638 | − | 2.04173i | 0.656690 | − | 0.379140i | −0.134325 | − | 0.990937i | \(-0.542887\pi\) |
0.791014 | + | 0.611797i | \(0.209553\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.00132 | − | 4.04222i | −1.25748 | − | 0.726004i | −0.284892 | − | 0.958560i | \(-0.591958\pi\) |
−0.972583 | + | 0.232556i | \(0.925291\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.01976 | + | 6.31739i | −0.177517 | + | 1.09972i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.79699 | −1.28182 | −0.640909 | − | 0.767617i | \(-0.721442\pi\) | ||||
−0.640909 | + | 0.767617i | \(0.721442\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.897704 | + | 0.341550i | −0.143748 | + | 0.0546918i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.59234 | − | 6.22212i | 0.561030 | − | 0.971732i | −0.436377 | − | 0.899764i | \(-0.643739\pi\) |
0.997407 | − | 0.0719684i | \(-0.0229281\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.754009 | − | 1.30598i | −0.114985 | − | 0.199160i | 0.802789 | − | 0.596264i | \(-0.203349\pi\) |
−0.917774 | + | 0.397103i | \(0.870015\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.1480 | + | 3.69531i | 1.66184 | + | 0.550865i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.41416 | + | 2.44940i | 0.206277 | + | 0.357282i | 0.950539 | − | 0.310606i | \(-0.100532\pi\) |
−0.744262 | + | 0.667888i | \(0.767199\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.38709 | − | 7.83983i | 0.894372 | − | 1.09780i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 0.0479960i | − | 0.00659276i | −0.999995 | − | 0.00329638i | \(-0.998951\pi\) | ||
0.999995 | − | 0.00329638i | \(-0.00104927\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.4635i | 1.95026i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.17031 | + | 5.84164i | 0.949731 | + | 0.773744i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.45656 | − | 7.71900i | 0.580195 | − | 1.00493i | −0.415261 | − | 0.909703i | \(-0.636310\pi\) |
0.995456 | − | 0.0952251i | \(-0.0303571\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.03343 | − | 3.48340i | 0.772501 | − | 0.446004i | −0.0612648 | − | 0.998122i | \(-0.519513\pi\) |
0.833766 | + | 0.552118i | \(0.186180\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.88006 | + | 1.08545i | −0.233193 | + | 0.134634i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.587402 | + | 1.01741i | −0.0717626 | + | 0.124296i | −0.899674 | − | 0.436563i | \(-0.856196\pi\) |
0.827911 | + | 0.560859i | \(0.189529\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.68181 | + | 1.40082i | −0.443238 | + | 0.168639i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.71061i | 0.796403i | 0.917298 | + | 0.398202i | \(0.130366\pi\) | ||||
−0.917298 | + | 0.398202i | \(0.869634\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.07253i | − | 0.476654i | −0.971185 | − | 0.238327i | \(-0.923401\pi\) | ||
0.971185 | − | 0.238327i | \(-0.0765990\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.6563 | + | 2.85009i | 2.03877 | + | 0.329101i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.97374 | + | 3.41861i | 0.222063 | + | 0.384624i | 0.955434 | − | 0.295204i | \(-0.0953877\pi\) |
−0.733371 | + | 0.679828i | \(0.762054\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.26468 | + | 3.56300i | −0.918298 | + | 0.395889i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.84674 | + | 6.66275i | 0.422235 | + | 0.731332i | 0.996158 | − | 0.0875774i | \(-0.0279125\pi\) |
−0.573923 | + | 0.818909i | \(0.694579\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.4280 | − | 19.7938i | 1.23954 | − | 2.14694i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.12710 | + | 6.98238i | −0.120838 | + | 0.748590i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.42600 | 0.575155 | 0.287577 | − | 0.957757i | \(-0.407150\pi\) | ||||
0.287577 | + | 0.957757i | \(0.407150\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.0874 | − | 4.97937i | 1.35710 | − | 0.516337i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.1035 | + | 10.4520i | 1.85738 | + | 1.07236i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.9874 | − | 8.07563i | 1.42021 | − | 0.819956i | 0.423890 | − | 0.905714i | \(-0.360664\pi\) |
0.996316 | + | 0.0857571i | \(0.0273309\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.36753 | − | 8.28055i | −0.740464 | − | 0.832227i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.811750 | + | 1.40599i | 0.0807722 | + | 0.139901i | 0.903582 | − | 0.428416i | \(-0.140928\pi\) |
−0.822810 | + | 0.568317i | \(0.807595\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.342653 | + | 0.197831i | 0.0337626 | + | 0.0194929i | 0.516786 | − | 0.856114i | \(-0.327128\pi\) |
−0.483024 | + | 0.875607i | \(0.660461\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.66700i | 0.547850i | 0.961751 | + | 0.273925i | \(0.0883219\pi\) | ||||
−0.961751 | + | 0.273925i | \(0.911678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.5133 | 1.29434 | 0.647171 | − | 0.762345i | \(-0.275952\pi\) | ||||
0.647171 | + | 0.762345i | \(0.275952\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.52987 | − | 10.4700i | 0.809619 | − | 0.993766i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.13651 | + | 0.656162i | 0.106913 | + | 0.0617265i | 0.552503 | − | 0.833511i | \(-0.313673\pi\) |
−0.445590 | + | 0.895237i | \(0.647006\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.71082 | + | 4.45184i | −0.719038 | + | 0.415137i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.523442 | − | 1.57911i | 0.0483922 | − | 0.145989i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.32489 | − | 2.29477i | 0.120444 | − | 0.208615i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.42520 | + | 11.6309i | 0.399007 | + | 1.04872i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 20.8496 | 1.86485 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.3935 | −1.54342 | −0.771710 | − | 0.635975i | \(-0.780598\pi\) | ||||
−0.771710 | + | 0.635975i | \(0.780598\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.57858 | + | 0.416237i | 0.227032 | + | 0.0366476i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.45361 | − | 9.44593i | 0.476484 | − | 0.825295i | −0.523153 | − | 0.852239i | \(-0.675244\pi\) |
0.999637 | + | 0.0269442i | \(0.00857764\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.1580 | + | 10.9271i | −1.47672 | + | 0.940454i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.62547 | + | 4.40257i | −0.651488 | + | 0.376137i | −0.789026 | − | 0.614360i | \(-0.789414\pi\) |
0.137538 | + | 0.990496i | \(0.456081\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.2352 | − | 8.21869i | −1.20741 | − | 0.697100i | −0.245220 | − | 0.969468i | \(-0.578860\pi\) |
−0.962193 | + | 0.272367i | \(0.912193\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.83621 | − | 0.780664i | −0.407282 | − | 0.0657438i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.04876 | 0.171326 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.9860i | 1.32757i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.5814 | − | 7.26390i | −1.03071 | − | 0.595082i | −0.113523 | − | 0.993535i | \(-0.536214\pi\) |
−0.917188 | + | 0.398454i | \(0.869547\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.80307 | − | 4.85505i | −0.228110 | − | 0.395099i | 0.729138 | − | 0.684367i | \(-0.239921\pi\) |
−0.957248 | + | 0.289268i | \(0.906588\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.54005 | + | 17.1535i | 0.286196 | + | 1.38678i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.4089 | − | 15.8246i | 2.20154 | − | 1.27106i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.4411 | − | 8.91493i | −1.23233 | − | 0.711489i | −0.264819 | − | 0.964298i | \(-0.585312\pi\) |
−0.967516 | + | 0.252809i | \(0.918645\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.0644502 | + | 0.0525074i | 0.00511123 | + | 0.00416411i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.15399 | 0.0903874 | 0.0451937 | − | 0.998978i | \(-0.485610\pi\) | ||||
0.0451937 | + | 0.998978i | \(0.485610\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −19.4220 | − | 15.8230i | −1.51200 | − | 1.23182i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.95550 | + | 15.5114i | −0.692997 | + | 1.20031i | 0.277854 | + | 0.960623i | \(0.410377\pi\) |
−0.970851 | + | 0.239683i | \(0.922957\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.34625 | − | 10.9920i | −0.488173 | − | 0.845540i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.6886 | + | 3.23773i | −1.19974 | + | 0.247596i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.74814 | − | 6.49197i | −0.284966 | − | 0.493576i | 0.687635 | − | 0.726057i | \(-0.258649\pi\) |
−0.972601 | + | 0.232481i | \(0.925316\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.48979 | + | 14.4289i | 0.412638 | + | 1.08454i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.720974i | 0.0538881i | 0.999637 | + | 0.0269441i | \(0.00857760\pi\) | ||||
−0.999637 | + | 0.0269441i | \(0.991422\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.07121i | − | 0.376940i | −0.982079 | − | 0.188470i | \(-0.939647\pi\) | ||
0.982079 | − | 0.188470i | \(-0.0603529\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.92295 | + | 11.9127i | −0.142149 | + | 0.880609i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.2619 | − | 26.4344i | 1.12208 | − | 1.94350i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.6802 | + | 10.7850i | −1.36603 | + | 0.788678i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.0005 | − | 6.35111i | 0.795965 | − | 0.459551i | −0.0460934 | − | 0.998937i | \(-0.514677\pi\) |
0.842058 | + | 0.539387i | \(0.181344\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.4076 | − | 19.7586i | 0.821140 | − | 1.42226i | −0.0836931 | − | 0.996492i | \(-0.526672\pi\) |
0.904834 | − | 0.425765i | \(-0.139995\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.599205 | − | 3.71207i | 0.0429100 | − | 0.265827i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.0311360i | 0.00221835i | 0.999999 | + | 0.00110918i | \(0.000353062\pi\) | ||||
−0.999999 | + | 0.00110918i | \(0.999647\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.9952i | 1.63008i | 0.579402 | + | 0.815042i | \(0.303286\pi\) | ||||
−0.579402 | + | 0.815042i | \(0.696714\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.723587 | − | 1.90182i | −0.0510379 | − | 0.134144i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.0634 | + | 24.3585i | 0.982229 | + | 1.70127i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.14683 | − | 6.47652i | 0.149215 | − | 0.450149i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.86397 | − | 17.0849i | −0.682305 | − | 1.18179i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.55841 | − | 14.8236i | 0.589185 | − | 1.02050i | −0.405154 | − | 0.914248i | \(-0.632782\pi\) |
0.994339 | − | 0.106250i | \(-0.0338845\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.01117 | − | 7.34138i | −0.617435 | − | 0.503023i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.90362 | 0.402623 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.46869 | + | 4.45533i | 0.369540 | + | 0.301064i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.80380 | − | 1.61878i | −0.188604 | − | 0.108891i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.25230 | − | 0.723016i | 0.0838602 | − | 0.0484167i | −0.457484 | − | 0.889218i | \(-0.651249\pi\) |
0.541344 | + | 0.840801i | \(0.317916\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −23.1431 | + | 20.5913i | −1.54287 | + | 1.37275i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.23596 | − | 3.87280i | −0.148406 | − | 0.257047i | 0.782232 | − | 0.622987i | \(-0.214081\pi\) |
−0.930639 | + | 0.365940i | \(0.880748\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.24072 | − | 1.29368i | −0.148071 | − | 0.0854888i | 0.424134 | − | 0.905599i | \(-0.360579\pi\) |
−0.572205 | + | 0.820111i | \(0.693912\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 17.4078i | − | 1.14042i | −0.821498 | − | 0.570211i | \(-0.806862\pi\) | ||
0.821498 | − | 0.570211i | \(-0.193138\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.0724 | −0.722284 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.74985 | − | 1.08957i | −0.438450 | − | 0.0707750i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.23642 | + | 2.44590i | 0.274031 | + | 0.158212i | 0.630718 | − | 0.776012i | \(-0.282760\pi\) |
−0.356687 | + | 0.934224i | \(0.616094\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.04282 | + | 4.06618i | −0.453668 | + | 0.261925i | −0.709378 | − | 0.704828i | \(-0.751024\pi\) |
0.255710 | + | 0.966754i | \(0.417691\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.25704 | − | 14.9959i | 0.273089 | − | 0.961989i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.48053 | − | 2.56436i | 0.0942041 | − | 0.163166i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.1552 | − | 2.12353i | −0.833678 | − | 0.134573i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.9341 | −1.63694 | −0.818472 | − | 0.574546i | \(-0.805179\pi\) | ||||
−0.818472 | + | 0.574546i | \(0.805179\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.40274 | 0.528276 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.0775 | + | 37.0001i | 0.881566 | + | 2.31704i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.4115 | − | 26.6935i | 0.961344 | − | 1.66510i | 0.242213 | − | 0.970223i | \(-0.422127\pi\) |
0.719131 | − | 0.694874i | \(-0.244540\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.14306 | − | 9.15219i | −0.504043 | − | 0.566506i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.6625 | − | 9.04276i | 0.965792 | − | 0.557600i | 0.0678413 | − | 0.997696i | \(-0.478389\pi\) |
0.897951 | + | 0.440096i | \(0.145056\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.162723 | + | 0.0939479i | 0.00999597 | + | 0.00577117i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.93602 | + | 7.28616i | −0.363278 | + | 0.445906i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.6406 | 1.31945 | 0.659725 | − | 0.751507i | \(-0.270673\pi\) | ||||
0.659725 | + | 0.751507i | \(0.270673\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.2551i | 0.865937i | 0.901409 | + | 0.432968i | \(0.142534\pi\) | ||||
−0.901409 | + | 0.432968i | \(0.857466\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −33.0383 | − | 19.0747i | −1.99229 | − | 1.15025i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.40164 | − | 7.62386i | −0.264469 | − | 0.458073i | 0.702956 | − | 0.711234i | \(-0.251863\pi\) |
−0.967424 | + | 0.253160i | \(0.918530\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.63113 | + | 23.0215i | −0.456864 | + | 1.37826i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.6889 | + | 9.63537i | −0.995579 | + | 0.574798i | −0.906937 | − | 0.421266i | \(-0.861586\pi\) |
−0.0886417 | + | 0.996064i | \(0.528253\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.32822 | − | 4.80830i | −0.495061 | − | 0.285824i | 0.231611 | − | 0.972809i | \(-0.425601\pi\) |
−0.726672 | + | 0.686985i | \(0.758934\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −33.8403 | + | 12.8753i | −2.00453 | + | 0.762665i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0859 | 1.00506 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.45801 | + | 27.6173i | −0.261333 | + | 1.61896i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.22598 | − | 2.12346i | 0.0716225 | − | 0.124054i | −0.827990 | − | 0.560743i | \(-0.810516\pi\) |
0.899613 | + | 0.436689i | \(0.143849\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.4467 | + | 30.2185i | 1.01578 | + | 1.75939i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 19.1794 | − | 0.834401i | 1.11290 | − | 0.0484168i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.630605 | + | 1.09224i | 0.0364688 | + | 0.0631658i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.77605 | − | 0.448112i | −0.159480 | − | 0.0257434i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 27.2738i | 1.56169i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.6839i | − | 0.609760i | −0.952391 | − | 0.304880i | \(-0.901384\pi\) | ||
0.952391 | − | 0.304880i | \(-0.0986163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.640513 | + | 0.243697i | −0.0364375 | + | 0.0138634i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.3833 | − | 17.9843i | 0.588780 | − | 1.01980i | −0.405612 | − | 0.914045i | \(-0.632942\pi\) |
0.994393 | − | 0.105752i | \(-0.0337250\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.40449 | − | 1.96558i | 0.192433 | − | 0.111101i | −0.400688 | − | 0.916215i | \(-0.631229\pi\) |
0.593121 | + | 0.805113i | \(0.297896\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.98369 | + | 1.14528i | −0.111415 | + | 0.0643256i | −0.554672 | − | 0.832069i | \(-0.687156\pi\) |
0.443257 | + | 0.896395i | \(0.353823\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.54330 | − | 13.0654i | 0.422344 | − | 0.731521i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.60978 | − | 6.19967i | −0.424736 | − | 0.346032i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.1750i | 1.73462i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.72603i | − | 0.317623i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.7835 | + | 18.1460i | −0.817531 | + | 1.00348i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.46788 | − | 6.00655i | −0.190612 | − | 0.330150i | 0.754841 | − | 0.655908i | \(-0.227714\pi\) |
−0.945453 | + | 0.325758i | \(0.894381\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.72769 | + | 22.9082i | 0.259076 | + | 1.25536i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.29957 | − | 3.98298i | −0.125639 | − | 0.217613i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.59771 | + | 16.6237i | −0.522821 | + | 0.905552i | 0.476827 | + | 0.878997i | \(0.341787\pi\) |
−0.999647 | + | 0.0265545i | \(0.991546\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.12444 | + | 0.808288i | −0.115384 | + | 0.0439002i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.8684 | −1.61747 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.45756 | − | 15.2246i | 0.132311 | − | 0.819663i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.35287 | + | 4.24518i | 0.394723 | + | 0.227893i | 0.684204 | − | 0.729290i | \(-0.260150\pi\) |
−0.289482 | + | 0.957184i | \(0.593483\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.5478 | + | 9.55386i | −0.885782 | + | 0.511407i | −0.872560 | − | 0.488506i | \(-0.837542\pi\) |
−0.0132216 | + | 0.999913i | \(0.504209\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.54782 | + | 2.43043i | 0.0826167 | + | 0.129727i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.82951 | + | 11.8291i | 0.363498 | + | 0.629597i | 0.988534 | − | 0.150999i | \(-0.0482490\pi\) |
−0.625036 | + | 0.780596i | \(0.714916\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.7512 | − | 13.1354i | −1.20751 | − | 0.697156i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.1945i | 0.907490i | 0.891132 | + | 0.453745i | \(0.149912\pi\) | ||||
−0.891132 | + | 0.453745i | \(0.850088\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.51270 | −0.500668 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.63205 | + | 4.28955i | 0.0856604 | + | 0.225143i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.8073 | + | 7.97162i | 0.722705 | + | 0.417254i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.6001 | + | 8.42936i | −0.762118 | + | 0.440009i | −0.830056 | − | 0.557680i | \(-0.811691\pi\) |
0.0679376 | + | 0.997690i | \(0.478358\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.4593 | − | 6.78184i | −1.06507 | − | 0.353048i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.704288 | − | 1.21986i | 0.0364667 | − | 0.0631621i | −0.847216 | − | 0.531248i | \(-0.821723\pi\) |
0.883683 | + | 0.468086i | \(0.155056\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −22.8094 | + | 27.9974i | −1.17787 | + | 1.44578i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.26442 | 0.116624 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.598572 | −0.0307466 | −0.0153733 | − | 0.999882i | \(-0.504894\pi\) | ||||
−0.0153733 | + | 0.999882i | \(0.504894\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.0284 | − | 23.3563i | 0.974853 | − | 1.19658i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.26039 | + | 7.37921i | −0.217696 | + | 0.377060i | −0.954103 | − | 0.299478i | \(-0.903187\pi\) |
0.736407 | + | 0.676538i | \(0.236521\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.37989 | + | 3.00722i | −0.171810 | + | 0.152866i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.9624 | − | 17.2988i | 1.51915 | − | 0.877084i | 0.519409 | − | 0.854526i | \(-0.326152\pi\) |
0.999746 | − | 0.0225587i | \(-0.00718126\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.4994 | − | 6.63920i | −0.581551 | − | 0.335759i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.71799 | + | 17.6570i | 0.338878 | + | 0.890680i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.4537 | −0.777558 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 32.2821i | − | 1.62019i | −0.586296 | − | 0.810097i | \(-0.699414\pi\) | ||
0.586296 | − | 0.810097i | \(-0.300586\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.3473 | − | 6.55139i | −0.566659 | − | 0.327161i | 0.189155 | − | 0.981947i | \(-0.439425\pi\) |
−0.755814 | + | 0.654787i | \(0.772758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.24155 | − | 3.88248i | −0.111660 | − | 0.193400i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.09760 | − | 34.9943i | 0.203611 | − | 1.73888i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.9471 | + | 14.4032i | −1.23658 | + | 0.713941i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.3493 | + | 18.6769i | 1.59957 | + | 0.923513i | 0.991569 | + | 0.129577i | \(0.0413620\pi\) |
0.608002 | + | 0.793936i | \(0.291971\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.43036 | − | 15.0561i | 0.119881 | − | 0.742660i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −30.1186 | −1.47846 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 26.6095 | − | 10.1241i | 1.30307 | − | 0.495781i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.1954 | − | 24.5871i | 0.693490 | − | 1.20116i | −0.277198 | − | 0.960813i | \(-0.589406\pi\) |
0.970687 | − | 0.240346i | \(-0.0772610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.3359 | − | 30.0267i | −0.844901 | − | 1.46341i | −0.885707 | − | 0.464245i | \(-0.846326\pi\) |
0.0408054 | − | 0.999167i | \(-0.487008\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.33908 | − | 5.64013i | 0.308217 | − | 0.274232i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 30.1427 | + | 52.2087i | 1.46214 | + | 2.53249i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.24134 | + | 2.75113i | −0.108213 | + | 0.132826i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.2240i | 0.733315i | 0.930356 | + | 0.366657i | \(0.119498\pi\) | ||||
−0.930356 | + | 0.366657i | \(0.880502\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.97041i | 0.190806i | 0.995439 | + | 0.0954028i | \(0.0304139\pi\) | ||||
−0.995439 | + | 0.0954028i | \(0.969586\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.4664 | − | 17.4886i | −1.02924 | − | 0.838516i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.07222 | − | 10.5174i | 0.290474 | − | 0.503115i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.21910 | − | 4.74530i | 0.392276 | − | 0.226481i | −0.290870 | − | 0.956763i | \(-0.593945\pi\) |
0.683146 | + | 0.730282i | \(0.260611\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.3955 | − | 16.3942i | 1.34911 | − | 0.778910i | 0.360989 | − | 0.932570i | \(-0.382439\pi\) |
0.988124 | + | 0.153660i | \(0.0491060\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.6209 | + | 18.3960i | −0.503479 | + | 0.872052i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23.5182 | − | 8.94798i | 1.11237 | − | 0.423225i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 0.658896i | − | 0.0310952i | −0.999879 | − | 0.0155476i | \(-0.995051\pi\) | ||
0.999879 | − | 0.0155476i | \(-0.00494916\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 26.5443i | − | 1.24992i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.58602 | + | 1.54738i | 0.450390 | + | 0.0727024i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.94514 | − | 13.7614i | −0.371658 | − | 0.643730i | 0.618163 | − | 0.786050i | \(-0.287877\pi\) |
−0.989821 | + | 0.142320i | \(0.954544\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −26.9069 | − | 14.0122i | −1.25591 | − | 0.654031i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.81626 | − | 17.0023i | −0.457189 | − | 0.791874i | 0.541622 | − | 0.840622i | \(-0.317810\pi\) |
−0.998811 | + | 0.0487477i | \(0.984477\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.600159 | − | 1.03951i | 0.0278918 | − | 0.0483099i | −0.851743 | − | 0.523960i | \(-0.824454\pi\) |
0.879634 | + | 0.475651i | \(0.157787\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.73567 | + | 54.1173i | −0.405107 | + | 2.50963i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −38.5618 | −1.78443 | −0.892213 | − | 0.451614i | \(-0.850848\pi\) | ||||
−0.892213 | + | 0.451614i | \(0.850848\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28.8637 | − | 10.9818i | 1.32997 | − | 0.506014i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.82503 | − | 2.78573i | −0.221855 | − | 0.128088i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −47.7501 | + | 27.5685i | −2.19093 | + | 1.26493i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.141016 | + | 0.0291023i | −0.00645670 | + | 0.00133250i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.61289 | − | 6.25771i | −0.165077 | − | 0.285922i | 0.771606 | − | 0.636101i | \(-0.219454\pi\) |
−0.936683 | + | 0.350179i | \(0.886121\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.74444 | − | 2.16185i | −0.170732 | − | 0.0985720i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 63.2293i | 2.87110i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.71539 | −0.440247 | −0.220123 | − | 0.975472i | \(-0.570646\pi\) | ||||
−0.220123 | + | 0.975472i | \(0.570646\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.26246 | + | 1.54960i | −0.0570903 | + | 0.0700754i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.2480 | + | 9.95814i | 0.778392 | + | 0.449405i | 0.835860 | − | 0.548943i | \(-0.184969\pi\) |
−0.0574682 | + | 0.998347i | \(0.518303\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.6465 | + | 11.9203i | −0.929872 | + | 0.536862i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 42.4951 | − | 8.76994i | 1.91001 | − | 0.394179i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.1920 | + | 29.7774i | −0.769619 | + | 1.33302i | 0.168150 | + | 0.985761i | \(0.446221\pi\) |
−0.937770 | + | 0.347258i | \(0.887113\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.0318 | − | 28.9950i | −0.492863 | − | 1.29540i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.22542 | 0.0546388 | 0.0273194 | − | 0.999627i | \(-0.491303\pi\) | ||||
0.0273194 | + | 0.999627i | \(0.491303\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.35571 | −0.282826 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.7031 | + | 3.50333i | 0.963869 | + | 0.155588i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.05078 | − | 8.74820i | 0.223872 | − | 0.387757i | −0.732109 | − | 0.681188i | \(-0.761464\pi\) |
0.955980 | + | 0.293431i | \(0.0947970\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.8155 | − | 24.6090i | 0.565819 | − | 1.08652i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.34143 | + | 0.774473i | −0.0591103 | + | 0.0341274i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.04947 | + | 5.22471i | 0.397995 | + | 0.229783i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.8180 | + | 2.06910i | 0.562649 | + | 0.0908233i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.0781 | −0.923446 | −0.461723 | − | 0.887024i | \(-0.652769\pi\) | ||||
−0.461723 | + | 0.887024i | \(0.652769\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 19.7145i | − | 0.862057i | −0.902338 | − | 0.431028i | \(-0.858151\pi\) | ||
0.902338 | − | 0.431028i | \(-0.141849\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 40.8760 | + | 23.5997i | 1.78058 | + | 1.02802i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.91366 | − | 15.4389i | −0.387550 | − | 0.671257i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −25.3813 | − | 8.41336i | −1.10145 | − | 0.365109i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.45039 | − | 1.99208i | 0.149453 | − | 0.0862866i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.2130 | − | 11.0926i | −0.830652 | − | 0.479577i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.968140 | − | 0.788742i | −0.0417783 | − | 0.0340367i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.44950 | 0.363272 | 0.181636 | − | 0.983366i | \(-0.441861\pi\) | ||||
0.181636 | + | 0.983366i | \(0.441861\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.80974 | + | 5.54788i | 0.292234 | + | 0.238082i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.4511 | + | 45.8147i | −1.13304 | + | 1.96249i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.02889 | − | 6.97824i | −0.172263 | − | 0.298368i | 0.766948 | − | 0.641709i | \(-0.221774\pi\) |
−0.939211 | + | 0.343342i | \(0.888441\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.8929 | − | 15.6146i | −0.592934 | − | 0.666414i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.9023 | − | 18.8833i | −0.464453 | − | 0.804456i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.8003 | + | 49.4132i | 0.798027 | + | 2.09747i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 21.0495i | − | 0.891895i | −0.895059 | − | 0.445947i | \(-0.852867\pi\) | ||
0.895059 | − | 0.445947i | \(-0.147133\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.836249i | − | 0.0353696i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.95367 | − | 36.8829i | 0.251364 | − | 1.55720i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.6410 | + | 35.7513i | −0.869916 | + | 1.50674i | −0.00783378 | + | 0.999969i | \(0.502494\pi\) |
−0.862082 | + | 0.506769i | \(0.830840\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.44922 | + | 2.56876i | −0.187180 | + | 0.108068i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.2691 | + | 18.0532i | −1.31087 | + | 0.756829i | −0.982240 | − | 0.187630i | \(-0.939919\pi\) |
−0.328627 | + | 0.944460i | \(0.606586\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.62111 | − | 16.6642i | 0.402631 | − | 0.697377i | −0.591412 | − | 0.806370i | \(-0.701429\pi\) |
0.994043 | + | 0.108993i | \(0.0347625\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.50602 | + | 21.7198i | −0.146466 | + | 0.907356i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 23.4846i | − | 0.979375i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 29.8031i | − | 1.24072i | −0.784318 | − | 0.620359i | \(-0.786987\pi\) | ||
0.784318 | − | 0.620359i | \(-0.213013\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.0524 | + | 36.9343i | 0.583999 | + | 1.53494i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.0886621 | − | 0.153567i | −0.00367201 | − | 0.00636010i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.32912 | + | 4.86561i | 0.178987 | + | 0.201168i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.72218 | + | 8.17905i | 0.194905 | + | 0.337586i | 0.946869 | − | 0.321618i | \(-0.104227\pi\) |
−0.751964 | + | 0.659204i | \(0.770893\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.5843 | + | 37.3852i | −0.889367 | + | 1.54043i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0418102 | − | 0.0340627i | −0.00171984 | − | 0.00140115i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.8352 | −1.01986 | −0.509929 | − | 0.860216i | \(-0.670328\pi\) | ||||
−0.509929 | + | 0.860216i | \(0.670328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −30.8784 | − | 25.1566i | −1.26377 | − | 1.02959i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.3052 | + | 5.94974i | 0.421061 | + | 0.243100i | 0.695531 | − | 0.718496i | \(-0.255169\pi\) |
−0.274470 | + | 0.961596i | \(0.588502\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.1276 | − | 12.7754i | 0.902604 | − | 0.521118i | 0.0245596 | − | 0.999698i | \(-0.492182\pi\) |
0.878044 | + | 0.478580i | \(0.158848\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.34541 | + | 1.10893i | 0.136236 | + | 0.0451592i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.18669 | + | 8.98361i | 0.210869 | + | 0.365236i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.5544 | + | 11.2897i | 0.793687 | + | 0.458235i | 0.841259 | − | 0.540632i | \(-0.181815\pi\) |
−0.0475718 | + | 0.998868i | \(0.515148\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.56841i | 0.0634510i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.8588 | 0.923257 | 0.461628 | − | 0.887073i | \(-0.347265\pi\) | ||||
0.461628 | + | 0.887073i | \(0.347265\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −48.0944 | − | 7.76344i | −1.93935 | − | 0.313052i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.78792 | + | 1.03226i | 0.0719791 | + | 0.0415572i | 0.535558 | − | 0.844499i | \(-0.320101\pi\) |
−0.463578 | + | 0.886056i | \(0.653435\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.2233 | − | 16.2947i | 1.13439 | − | 0.654940i | 0.189354 | − | 0.981909i | \(-0.439361\pi\) |
0.945035 | + | 0.326969i | \(0.106027\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.34820 | + | 9.96809i | 0.254744 | + | 0.400006i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.9967 | + | 25.9751i | −0.599870 | + | 1.03901i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 33.7331 | + | 5.44523i | 1.34717 | + | 0.217462i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 45.5213 | 1.81505 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.4706 | 1.53149 | 0.765744 | − | 0.643145i | \(-0.222371\pi\) | ||||
0.765744 | + | 0.643145i | \(0.222371\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.5426 | + | 27.7094i | 0.419031 | + | 1.10135i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 34.0461 | − | 58.9696i | 1.35108 | − | 2.34014i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.7163 | − | 4.06897i | 0.779967 | − | 0.160966i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.3645 | + | 23.8818i | −1.63380 | + | 0.943274i | −0.650892 | + | 0.759170i | \(0.725605\pi\) |
−0.982907 | + | 0.184104i | \(0.941062\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.2346 | + | 16.8786i | 1.15290 | + | 0.665626i | 0.949592 | − | 0.313489i | \(-0.101498\pi\) |
0.203306 | + | 0.979115i | \(0.434831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.45853 | + | 7.92752i | −0.254304 | + | 0.312146i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.07202 | −0.0421453 | −0.0210727 | − | 0.999778i | \(-0.506708\pi\) | ||||
−0.0210727 | + | 0.999778i | \(0.506708\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 32.9301i | − | 1.29262i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.8503 | − | 16.6567i | −1.12900 | − | 0.651828i | −0.185317 | − | 0.982679i | \(-0.559331\pi\) |
−0.943683 | + | 0.330851i | \(0.892664\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.3499 | + | 36.9791i | 0.834210 | + | 1.44489i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.9654 | + | 2.46937i | −0.466817 | + | 0.0963394i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.41890 | + | 4.86065i | −0.327954 | + | 0.189344i | −0.654932 | − | 0.755688i | \(-0.727303\pi\) |
0.326979 | + | 0.945032i | \(0.393969\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.7856 | − | 8.53647i | −0.575093 | − | 0.332030i | 0.184088 | − | 0.982910i | \(-0.441067\pi\) |
−0.759181 | + | 0.650880i | \(0.774400\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.24108 | − | 1.99408i | 0.203547 | − | 0.0774436i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.28724 | 0.359603 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.399128 | + | 2.47259i | −0.0154312 | + | 0.0955960i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.8696 | − | 22.2909i | 0.496827 | − | 0.860529i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.3359 | − | 31.7588i | −0.706798 | − | 1.22421i | −0.966039 | − | 0.258398i | \(-0.916805\pi\) |
0.259240 | − | 0.965813i | \(-0.416528\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.33204 | − | 53.6038i | −0.0897604 | − | 2.06321i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.1769 | + | 34.9474i | 0.775461 | + | 1.34314i | 0.934535 | + | 0.355872i | \(0.115816\pi\) |
−0.159073 | + | 0.987267i | \(0.550851\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.64663 | + | 1.23432i | 0.293019 | + | 0.0472994i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.51083i | 0.363922i | 0.983306 | + | 0.181961i | \(0.0582444\pi\) | ||||
−0.983306 | + | 0.181961i | \(0.941756\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 34.4705i | − | 1.31705i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.18852 | − | 1.59361i | 0.159802 | − | 0.0608000i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0133077 | − | 0.0230497i | 0.000506985 | − | 0.000878123i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.67519 | + | 3.85392i | −0.253936 | + | 0.146610i | −0.621565 | − | 0.783362i | \(-0.713503\pi\) |
0.367629 | + | 0.929972i | \(0.380170\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 55.7282 | − | 32.1747i | 2.11389 | − | 1.22046i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.9732 | + | 36.3267i | −0.794418 | + | 1.37597i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.3756 | + | 19.0440i | 0.884145 | + | 0.720311i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15.6388i | − | 0.590671i | −0.955394 | − | 0.295336i | \(-0.904569\pi\) | ||
0.955394 | − | 0.295336i | \(-0.0954314\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.6338i | 1.57025i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.1132 | − | 14.8683i | 0.456208 | − | 0.559972i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.72025 | − | 11.6398i | −0.252384 | − | 0.437142i | 0.711797 | − | 0.702385i | \(-0.247881\pi\) |
−0.964182 | + | 0.265242i | \(0.914548\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.84740 | − | 7.87187i | 0.331803 | − | 0.295218i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.19343 | − | 15.9235i | −0.344297 | − | 0.596339i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.01027 | + | 6.94599i | −0.149976 | + | 0.259765i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.91903 | + | 3.01296i | −0.295742 | + | 0.112521i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.0619 | −1.49405 | −0.747027 | − | 0.664793i | \(-0.768520\pi\) | ||||
−0.747027 | + | 0.664793i | \(0.768520\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.24466 | − | 13.9056i | 0.0834798 | − | 0.517156i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −36.5161 | − | 21.0826i | −1.35617 | − | 0.782986i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.2091 | − | 24.9468i | 1.60254 | − | 0.925225i | 0.611560 | − | 0.791198i | \(-0.290542\pi\) |
0.990978 | − | 0.134027i | \(-0.0427910\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.4797 | + | 22.1219i | 0.573322 | + | 0.819330i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.40214 | + | 7.62473i | 0.162819 | + | 0.282011i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.91430 | + | 5.72402i | 0.366193 | + | 0.211422i | 0.671794 | − | 0.740738i | \(-0.265524\pi\) |
−0.305601 | + | 0.952160i | \(0.598857\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.34038i | 0.159880i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.92607 | −0.328351 | −0.164175 | − | 0.986431i | \(-0.552496\pi\) | ||||
−0.164175 | + | 0.986431i | \(0.552496\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.82378 | + | 4.79349i | 0.0669984 | + | 0.176093i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.8621 | − | 26.4785i | −1.68252 | − | 0.971403i | −0.959979 | − | 0.280074i | \(-0.909641\pi\) |
−0.722540 | − | 0.691329i | \(-0.757026\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 49.2541 | − | 28.4369i | 1.80453 | − | 1.04185i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.2433 | − | 15.3420i | 0.630898 | − | 0.561334i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.2326 | − | 22.9195i | 0.482865 | − | 0.836346i | −0.516942 | − | 0.856021i | \(-0.672930\pi\) |
0.999806 | + | 0.0196744i | \(0.00626295\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.3718 | − | 34.8249i | 1.03392 | − | 1.26909i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.9470 | 0.798733 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.46749 | 0.307756 | 0.153878 | − | 0.988090i | \(-0.450824\pi\) | ||||
0.153878 | + | 0.988090i | \(0.450824\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.19256 | + | 11.2834i | −0.333669 | + | 0.409561i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.9968 | + | 46.7599i | −0.978635 | + | 1.69505i | −0.311258 | + | 0.950325i | \(0.600750\pi\) |
−0.667377 | + | 0.744720i | \(0.732583\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −65.0853 | − | 21.5744i | −2.35317 | − | 0.780025i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.28046 | − | 2.47132i | 0.154558 | − | 0.0892343i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.1912 | + | 17.4309i | 1.08872 | + | 0.628575i | 0.933236 | − | 0.359263i | \(-0.116972\pi\) |
0.155487 | + | 0.987838i | \(0.450305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.9846 | + | 49.8976i | 0.683713 | + | 1.79702i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.12749 | 0.0765207 | 0.0382603 | − | 0.999268i | \(-0.487818\pi\) | ||||
0.0382603 | + | 0.999268i | \(0.487818\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 83.4784i | 2.99863i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33.2244 | − | 19.1821i | −1.19039 | − | 0.687272i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.3964 | + | 21.4712i | 0.443577 | + | 0.768298i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.1982 | − | 0.922233i | 0.757563 | − | 0.0329579i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 60.4492 | − | 34.9004i | 2.15752 | − | 1.24565i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.5457 | + | 14.1715i | 0.874959 | + | 0.505158i | 0.868993 | − | 0.494824i | \(-0.164768\pi\) |
0.00596615 | + | 0.999982i | \(0.498101\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.99190 | + | 30.9247i | −0.177716 | + | 1.10095i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.86334 | 0.137191 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.304173 | + | 0.115729i | −0.0107879 | + | 0.00410449i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.9123 | + | 32.7570i | −0.669907 | + | 1.16031i | 0.308022 | + | 0.951379i | \(0.400333\pi\) |
−0.977930 | + | 0.208935i | \(0.933000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.25634 | − | 14.3004i | −0.292088 | − | 0.505912i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.29005 | − | 15.9420i | −0.116248 | − | 0.563285i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.52311 | − | 13.0304i | −0.265485 | − | 0.459833i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.6747 | + | 29.0595i | −0.833389 | + | 1.02294i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.3191i | 1.59333i | 0.604419 | + | 0.796667i | \(0.293405\pi\) | ||||
−0.604419 | + | 0.796667i | \(0.706595\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.45145i | − | 0.191426i | −0.995409 | − | 0.0957132i | \(-0.969487\pi\) | ||
0.995409 | − | 0.0957132i | \(-0.0305132\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.1421 | − | 15.5950i | −0.671343 | − | 0.546942i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.25883 | + | 3.91241i | −0.0791233 | + | 0.137046i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.97359 | + | 4.02620i | −0.243975 | + | 0.140859i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.7121 | − | 24.6598i | 1.49066 | − | 0.860634i | 0.490718 | − | 0.871318i | \(-0.336734\pi\) |
0.999943 | + | 0.0106847i | \(0.00340111\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.8496 | − | 20.5241i | 0.413050 | − | 0.715424i | −0.582171 | − | 0.813066i | \(-0.697797\pi\) |
0.995222 | + | 0.0976419i | \(0.0311300\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 61.7577 | − | 23.4970i | 2.15013 | − | 0.818061i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.9706i | 0.694445i | 0.937783 | + | 0.347222i | \(0.112875\pi\) | ||||
−0.937783 | + | 0.347222i | \(0.887125\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 15.4431i | − | 0.536361i | −0.963369 | − | 0.268181i | \(-0.913578\pi\) | ||
0.963369 | − | 0.268181i | \(-0.0864224\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.0529 | + | 2.42985i | 0.522178 | + | 0.0842904i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.0592 | − | 60.7242i | −1.21327 | − | 2.10145i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.5653 | − | 35.4327i | −0.779972 | − | 1.22473i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.53910 | − | 9.59401i | −0.191231 | − | 0.331222i | 0.754427 | − | 0.656383i | \(-0.227915\pi\) |
−0.945658 | + | 0.325162i | \(0.894581\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.16267 | + | 10.6741i | −0.212506 | + | 0.368071i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.31903 | − | 32.9513i | 0.183197 | − | 1.13490i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 49.6888 | 1.70935 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.5677 | − | 5.92307i | 0.534283 | − | 0.203279i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.3573 | − | 8.86656i | −0.526442 | − | 0.303942i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.1706 | + | 24.3472i | −1.44389 | + | 0.833633i | −0.998107 | − | 0.0615058i | \(-0.980410\pi\) |
−0.445788 | + | 0.895139i | \(0.647076\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.7320 | − | 59.5271i | 0.674819 | − | 2.03578i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.39130 | + | 14.5342i | 0.286641 | + | 0.496477i | 0.973006 | − | 0.230780i | \(-0.0741279\pi\) |
−0.686365 | + | 0.727258i | \(0.740795\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.7682 | + | 12.5679i | 0.742722 | + | 0.428811i | 0.823058 | − | 0.567957i | \(-0.192266\pi\) |
−0.0803361 | + | 0.996768i | \(0.525599\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 6.78244i | − | 0.230877i | −0.993315 | − | 0.115438i | \(-0.963173\pi\) | ||
0.993315 | − | 0.115438i | \(-0.0368273\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.3466 | 0.997815 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.6919 | + | 22.9434i | −0.634812 | + | 0.779199i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.6303 | + | 7.29209i | 0.428452 | + | 0.247367i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.564190 | + | 0.325735i | −0.0191168 | + | 0.0110371i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −32.2081 | − | 36.1995i | −1.09008 | − | 1.22517i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.8630 | − | 37.8678i | 0.738260 | − | 1.27870i | −0.215019 | − | 0.976610i | \(-0.568981\pi\) |
0.953278 | − | 0.302093i | \(-0.0976854\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.51021 | + | 3.96933i | 0.0509382 | + | 0.133882i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.5307 | −0.927531 | −0.463766 | − | 0.885958i | \(-0.653502\pi\) | ||||
−0.463766 | + | 0.885958i | \(0.653502\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.56040 | 0.187122 | 0.0935612 | − | 0.995614i | \(-0.470175\pi\) | ||||
0.0935612 | + | 0.995614i | \(0.470175\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −59.6646 | − | 9.63112i | −2.00560 | − | 0.323746i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.3092 | − | 21.3202i | 0.413303 | − | 0.715862i | −0.581945 | − | 0.813228i | \(-0.697708\pi\) |
0.995249 | + | 0.0973655i | \(0.0310416\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.8617 | + | 26.6673i | −0.665391 | + | 0.893388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.0792 | − | 7.55125i | 0.437677 | − | 0.252693i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.44434 | − | 1.41124i | −0.0817054 | − | 0.0471726i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.15656 | − | 0.348114i | −0.0720056 | − | 0.0116232i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −33.0125 | −1.10103 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.280216i | 0.00933535i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.1931 | + | 9.92644i | 0.571518 | + | 0.329966i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.04337 | + | 8.73537i | 0.167462 | + | 0.290053i | 0.937527 | − | 0.347913i | \(-0.113109\pi\) |
−0.770065 | + | 0.637966i | \(0.779776\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.63872 | − | 3.23751i | 0.120689 | − | 0.107381i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.5808 | − | 13.6144i | 0.781267 | − | 0.451065i | −0.0556121 | − | 0.998452i | \(-0.517711\pi\) |
0.836879 | + | 0.547388i | \(0.184378\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.6159 | + | 14.2120i | 0.814668 | + | 0.470349i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −36.6239 | − | 29.8374i | −1.21075 | − | 0.986394i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.6986 | 1.30954 | 0.654769 | − | 0.755829i | \(-0.272766\pi\) | ||||
0.654769 | + | 0.755829i | \(0.272766\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.3465 | + | 11.6881i | 0.472734 | + | 0.385136i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.86064 | + | 3.22272i | −0.0612436 | + | 0.106077i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40.2552 | + | 69.7240i | 1.32358 | + | 2.29251i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.373477 | − | 1.12670i | 0.0122666 | − | 0.0370057i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.142283 | + | 0.246442i | 0.00466816 | + | 0.00808550i | 0.868350 | − | 0.495952i | \(-0.165181\pi\) |
−0.863682 | + | 0.504037i | \(0.831847\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.7905 | + | 33.6176i | 0.418743 | + | 1.10059i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 84.4427i | − | 2.76157i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.7298i | 0.709881i | 0.934889 | + | 0.354940i | \(0.115499\pi\) | ||||
−0.934889 | + | 0.354940i | \(0.884501\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.08507 | + | 6.72197i | −0.0354098 | + | 0.219363i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.64242 | − | 9.77295i | 0.183938 | − | 0.318589i | −0.759280 | − | 0.650764i | \(-0.774449\pi\) |
0.943218 | + | 0.332174i | \(0.107782\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.1513 | − | 8.17026i | 0.460830 | − | 0.266060i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.6701 | + | 11.3566i | −0.639194 | + | 0.369039i | −0.784304 | − | 0.620377i | \(-0.786980\pi\) |
0.145110 | + | 0.989416i | \(0.453646\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.12918 | − | 1.95580i | 0.0366548 | − | 0.0634880i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.632234 | − | 3.91668i | 0.0205016 | − | 0.127007i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.5638i | − | 0.536554i | −0.963342 | − | 0.268277i | \(-0.913546\pi\) | ||
0.963342 | − | 0.268277i | \(-0.0864543\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 49.7270i | 1.60913i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.29215 | + | 24.4228i | 0.300373 | + | 0.789476i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.1790 | + | 29.7550i | 0.554162 | + | 0.959837i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.6501 | − | 3.43618i | 0.536543 | − | 0.110729i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 44.6589 | + | 77.3515i | 1.43762 | + | 2.49003i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.38867 | − | 14.5296i | 0.269762 | − | 0.467241i | −0.699039 | − | 0.715084i | \(-0.746388\pi\) |
0.968800 | + | 0.247843i | \(0.0797218\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −41.8625 | − | 34.1053i | −1.34482 | − | 1.09562i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.3640 | 1.00652 | 0.503259 | − | 0.864136i | \(-0.332134\pi\) | ||||
0.503259 | + | 0.864136i | \(0.332134\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.68905 | + | 6.26425i | 0.246247 | + | 0.200617i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49.0953 | − | 28.3452i | −1.57070 | − | 0.906843i | −0.996083 | − | 0.0884183i | \(-0.971819\pi\) |
−0.574614 | − | 0.818424i | \(-0.694848\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.3609 | − | 10.0233i | 0.554858 | − | 0.320347i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.19378 | − | 39.7033i | −0.261607 | − | 1.26763i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.9204 | + | 34.5032i | 0.635362 | + | 1.10048i | 0.986438 | + | 0.164133i | \(0.0524825\pi\) |
−0.351076 | + | 0.936347i | \(0.614184\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.105562 | − | 0.0609460i | −0.00336347 | − | 0.00194190i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 3.42977i | − | 0.109060i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −62.5951 | −1.98840 | −0.994199 | − | 0.107558i | \(-0.965697\pi\) | ||||
−0.994199 | + | 0.107558i | \(0.965697\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.8596 | + | 1.91438i | 0.376352 | + | 0.0607511i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −77.9613 | − | 45.0110i | −2.47154 | − | 1.42694i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.0613 | + | 22.5520i | −1.23708 | + | 0.714230i | −0.968497 | − | 0.249025i | \(-0.919890\pi\) |
−0.268586 | + | 0.963256i | \(0.586556\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −35.9338 | − | 18.7130i | −1.13689 | − | 0.592054i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))