Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(901,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.k (of order \(2\), degree \(1\), 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: | \(14.3730723638\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.180227832610816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + x^{10} - 8x^{6} + 16x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 901.12 | ||
Root | \(1.37729 - 0.321037i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.901 |
Dual form | 1800.2.k.u.901.11 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.37729 | + | 0.321037i | 0.973893 | + | 0.227007i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.79387 | + | 0.884323i | 0.896935 | + | 0.442162i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.05705 | −1.53342 | −0.766710 | − | 0.641994i | \(-0.778107\pi\) | ||||
−0.766710 | + | 0.641994i | \(0.778107\pi\) | |||||||
\(8\) | 2.18678 | + | 1.79387i | 0.773145 | + | 0.634229i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.985939i | 0.297272i | 0.988892 | + | 0.148636i | \(0.0474882\pi\) | ||||
−0.988892 | + | 0.148636i | \(0.952512\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.94567i | 1.37168i | 0.727752 | + | 0.685841i | \(0.240565\pi\) | ||||
−0.727752 | + | 0.685841i | \(0.759435\pi\) | |||||||
\(14\) | −5.58774 | − | 1.30246i | −1.49339 | − | 0.348097i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.43594 | + | 3.17272i | 0.608986 | + | 0.793181i | ||||
\(17\) | −4.52323 | −1.09704 | −0.548522 | − | 0.836136i | \(-0.684809\pi\) | ||||
−0.548522 | + | 0.836136i | \(0.684809\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.60492i | 0.597610i | 0.954314 | + | 0.298805i | \(0.0965881\pi\) | ||||
−0.954314 | + | 0.298805i | \(0.903412\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.316523 | + | 1.35793i | −0.0674829 | + | 0.289511i | ||||
\(23\) | −3.53729 | −0.737577 | −0.368788 | − | 0.929513i | \(-0.620227\pi\) | ||||
−0.368788 | + | 0.929513i | \(0.620227\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.58774 | + | 6.81163i | −0.311382 | + | 1.33587i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −7.27782 | − | 3.58774i | −1.37538 | − | 0.678019i | ||||
\(29\) | − | 7.59434i | − | 1.41023i | −0.709091 | − | 0.705117i | \(-0.750895\pi\) | ||
0.709091 | − | 0.705117i | \(-0.249105\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.28415 | −0.589850 | −0.294925 | − | 0.955520i | \(-0.595295\pi\) | ||||
−0.294925 | + | 0.955520i | \(0.595295\pi\) | |||||||
\(32\) | 2.33645 | + | 5.15180i | 0.413029 | + | 0.910718i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.22982 | − | 1.45212i | −1.06840 | − | 0.249037i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.945668i | 0.155467i | 0.996974 | + | 0.0777334i | \(0.0247683\pi\) | ||||
−0.996974 | + | 0.0777334i | \(0.975232\pi\) | |||||||
\(38\) | −0.836276 | + | 3.58774i | −0.135662 | + | 0.582009i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.568295 | −0.0887527 | −0.0443763 | − | 0.999015i | \(-0.514130\pi\) | ||||
−0.0443763 | + | 0.999015i | \(0.514130\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.45963i | 1.29008i | 0.764148 | + | 0.645041i | \(0.223160\pi\) | ||||
−0.764148 | + | 0.645041i | \(0.776840\pi\) | |||||||
\(44\) | −0.871889 | + | 1.76865i | −0.131442 | + | 0.266634i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.87189 | − | 1.13560i | −0.718321 | − | 0.167435i | ||||
\(47\) | −2.60492 | −0.379967 | −0.189984 | − | 0.981787i | \(-0.560843\pi\) | ||||
−0.189984 | + | 0.981787i | \(0.560843\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.45963 | 1.35138 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.37357 | + | 8.87189i | −0.606505 | + | 1.23031i | ||||
\(53\) | − | 0.229815i | − | 0.0315675i | −0.999875 | − | 0.0157838i | \(-0.994976\pi\) | ||
0.999875 | − | 0.0157838i | \(-0.00502434\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.87189 | − | 7.27782i | −1.18556 | − | 0.972539i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.43806 | − | 10.4596i | 0.320133 | − | 1.37342i | ||||
\(59\) | 9.10003i | 1.18472i | 0.805672 | + | 0.592362i | \(0.201804\pi\) | ||||
−0.805672 | + | 0.592362i | \(0.798196\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.0183i | 1.41075i | 0.708832 | + | 0.705377i | \(0.249222\pi\) | ||||
−0.708832 | + | 0.705377i | \(0.750778\pi\) | |||||||
\(62\) | −4.52323 | − | 1.05433i | −0.574451 | − | 0.133900i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.56406 | + | 7.84562i | 0.195507 | + | 0.980702i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.45963i | 1.03351i | 0.856134 | + | 0.516754i | \(0.172860\pi\) | ||||
−0.856134 | + | 0.516754i | \(0.827140\pi\) | |||||||
\(68\) | −8.11409 | − | 4.00000i | −0.983978 | − | 0.485071i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.43171 | −0.169912 | −0.0849561 | − | 0.996385i | \(-0.527075\pi\) | ||||
−0.0849561 | + | 0.996385i | \(0.527075\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.9507 | 1.39873 | 0.699363 | − | 0.714767i | \(-0.253467\pi\) | ||||
0.699363 | + | 0.714767i | \(0.253467\pi\) | |||||||
\(74\) | −0.303594 | + | 1.30246i | −0.0352921 | + | 0.151408i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.30359 | + | 4.67289i | −0.264240 | + | 0.536018i | ||||
\(77\) | − | 4.00000i | − | 0.455842i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.28415 | −0.369495 | −0.184748 | − | 0.982786i | \(-0.559147\pi\) | ||||
−0.184748 | + | 0.982786i | \(0.559147\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.782708 | − | 0.182443i | −0.0864356 | − | 0.0201475i | ||||
\(83\) | − | 9.89134i | − | 1.08572i | −0.839825 | − | 0.542858i | \(-0.817342\pi\) | ||
0.839825 | − | 0.542858i | \(-0.182658\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.71585 | + | 11.6514i | −0.292858 | + | 1.25640i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.76865 | + | 2.15604i | −0.188538 | + | 0.229834i | ||||
\(89\) | 12.3510 | 1.30920 | 0.654600 | − | 0.755976i | \(-0.272837\pi\) | ||||
0.654600 | + | 0.755976i | \(0.272837\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 20.0648i | − | 2.10336i | ||||||
\(92\) | −6.34545 | − | 3.12811i | −0.661559 | − | 0.326128i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.58774 | − | 0.836276i | −0.370047 | − | 0.0862553i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.23797 | −0.328766 | −0.164383 | − | 0.986397i | \(-0.552563\pi\) | ||||
−0.164383 | + | 0.986397i | \(0.552563\pi\) | |||||||
\(98\) | 13.0287 | + | 3.03689i | 1.31610 | + | 0.306772i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 4.35637i | − | 0.433475i | −0.976230 | − | 0.216738i | \(-0.930458\pi\) | ||
0.976230 | − | 0.216738i | \(-0.0695416\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.0754 | −1.48542 | −0.742711 | − | 0.669612i | \(-0.766460\pi\) | ||||
−0.742711 | + | 0.669612i | \(0.766460\pi\) | |||||||
\(104\) | −8.87189 | + | 10.8151i | −0.869960 | + | 1.06051i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0737791 | − | 0.316523i | 0.00716606 | − | 0.0307434i | ||||
\(107\) | 4.00000i | 0.386695i | 0.981130 | + | 0.193347i | \(0.0619344\pi\) | ||||
−0.981130 | + | 0.193347i | \(0.938066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.17034i | − | 0.399446i | −0.979852 | − | 0.199723i | \(-0.935996\pi\) | ||
0.979852 | − | 0.199723i | \(-0.0640042\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.88274 | − | 12.8719i | −0.933831 | − | 1.21628i | ||||
\(113\) | 1.28526 | 0.120907 | 0.0604537 | − | 0.998171i | \(-0.480745\pi\) | ||||
0.0604537 | + | 0.998171i | \(0.480745\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.71585 | − | 13.6233i | 0.623551 | − | 1.26489i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.92145 | + | 12.5334i | −0.268941 | + | 1.15379i | ||||
\(119\) | 18.3510 | 1.68223 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0279 | 0.911630 | ||||||||
\(122\) | −3.53729 | + | 15.1755i | −0.320252 | + | 1.37392i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.89134 | − | 2.90425i | −0.529058 | − | 0.260809i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.15280 | −0.102294 | −0.0511472 | − | 0.998691i | \(-0.516288\pi\) | ||||
−0.0511472 | + | 0.998691i | \(0.516288\pi\) | |||||||
\(128\) | −0.364570 | + | 11.3078i | −0.0322237 | + | 0.999481i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.89019i | 0.339887i | 0.985454 | + | 0.169944i | \(0.0543586\pi\) | ||||
−0.985454 | + | 0.169944i | \(0.945641\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 10.5683i | − | 0.916387i | ||||||
\(134\) | −2.71585 | + | 11.6514i | −0.234614 | + | 1.00653i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.89134 | − | 8.11409i | −0.848175 | − | 0.695778i | ||||
\(137\) | 17.5135 | 1.49628 | 0.748138 | − | 0.663544i | \(-0.230948\pi\) | ||||
0.748138 | + | 0.663544i | \(0.230948\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.8612i | − | 1.43015i | −0.699047 | − | 0.715076i | \(-0.746392\pi\) | ||
0.699047 | − | 0.715076i | \(-0.253608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.97188 | − | 0.459630i | −0.165476 | − | 0.0385713i | ||||
\(143\) | −4.87613 | −0.407762 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.4596 | + | 3.83662i | 1.36221 | + | 0.317521i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.836276 | + | 1.69641i | −0.0687415 | + | 0.139444i | ||||
\(149\) | − | 10.4986i | − | 0.860078i | −0.902810 | − | 0.430039i | \(-0.858500\pi\) | ||
0.902810 | − | 0.430039i | \(-0.141500\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.71585 | 0.383771 | 0.191885 | − | 0.981417i | \(-0.438540\pi\) | ||||
0.191885 | + | 0.981417i | \(0.438540\pi\) | |||||||
\(152\) | −4.67289 | + | 5.69641i | −0.379022 | + | 0.462040i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.28415 | − | 5.50917i | 0.103480 | − | 0.443942i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.94567i | 0.713942i | 0.934115 | + | 0.356971i | \(0.116191\pi\) | ||||
−0.934115 | + | 0.356971i | \(0.883809\pi\) | |||||||
\(158\) | −4.52323 | − | 1.05433i | −0.359849 | − | 0.0838782i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.3510 | 1.13101 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.7827i | − | 1.23619i | −0.786102 | − | 0.618097i | \(-0.787904\pi\) | ||
0.786102 | − | 0.618097i | \(-0.212096\pi\) | |||||||
\(164\) | −1.01945 | − | 0.502556i | −0.0796054 | − | 0.0392430i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.17548 | − | 13.6233i | 0.246465 | − | 1.05737i | ||||
\(167\) | −5.50917 | −0.426312 | −0.213156 | − | 0.977018i | \(-0.568374\pi\) | ||||
−0.213156 | + | 0.977018i | \(0.568374\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4596 | −0.881510 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.48105 | + | 15.1755i | −0.570425 | + | 1.15712i | ||||
\(173\) | − | 10.3385i | − | 0.786020i | −0.919534 | − | 0.393010i | \(-0.871434\pi\) | ||
0.919534 | − | 0.393010i | \(-0.128566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.12811 | + | 2.40169i | −0.235790 | + | 0.181034i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.0109 | + | 3.96511i | 1.27502 | + | 0.297198i | ||||
\(179\) | − | 16.1746i | − | 1.20895i | −0.796625 | − | 0.604474i | \(-0.793383\pi\) | ||
0.796625 | − | 0.604474i | \(-0.206617\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.11409i | 0.603116i | 0.953448 | + | 0.301558i | \(0.0975067\pi\) | ||||
−0.953448 | + | 0.301558i | \(0.902493\pi\) | |||||||
\(182\) | 6.44154 | − | 27.6351i | 0.477479 | − | 2.04845i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.73530 | − | 6.34545i | −0.570254 | − | 0.467793i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.45963i | − | 0.326120i | ||||||
\(188\) | −4.67289 | − | 2.30359i | −0.340806 | − | 0.168007i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.9193 | 1.80309 | 0.901547 | − | 0.432681i | \(-0.142432\pi\) | ||||
0.901547 | + | 0.432681i | \(0.142432\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.03951 | 0.0748254 | 0.0374127 | − | 0.999300i | \(-0.488088\pi\) | ||||
0.0374127 | + | 0.999300i | \(0.488088\pi\) | |||||||
\(194\) | −4.45963 | − | 1.03951i | −0.320183 | − | 0.0746323i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 16.9694 | + | 8.36537i | 1.21210 | + | 0.597527i | ||||
\(197\) | 9.66152i | 0.688355i | 0.938905 | + | 0.344177i | \(0.111842\pi\) | ||||
−0.938905 | + | 0.344177i | \(0.888158\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.0668 | 1.63516 | 0.817582 | − | 0.575813i | \(-0.195314\pi\) | ||||
0.817582 | + | 0.575813i | \(0.195314\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.39856 | − | 6.00000i | 0.0984020 | − | 0.422159i | ||||
\(203\) | 30.8106i | 2.16248i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −20.7632 | − | 4.83975i | −1.44664 | − | 0.337202i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −15.6912 | + | 12.0474i | −1.08799 | + | 0.835335i | ||||
\(209\) | −2.56829 | −0.177653 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.44154i | 0.443454i | 0.975109 | + | 0.221727i | \(0.0711694\pi\) | ||||
−0.975109 | + | 0.221727i | \(0.928831\pi\) | |||||||
\(212\) | 0.203231 | − | 0.412259i | 0.0139580 | − | 0.0283140i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.28415 | + | 5.50917i | −0.0877825 | + | 0.376599i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.3239 | 0.904488 | ||||||||
\(218\) | 1.33883 | − | 5.74378i | 0.0906772 | − | 0.389018i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 22.3704i | − | 1.50480i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.9796 | −1.20401 | −0.602003 | − | 0.798494i | \(-0.705630\pi\) | ||||
−0.602003 | + | 0.798494i | \(0.705630\pi\) | |||||||
\(224\) | −9.47908 | − | 20.9011i | −0.633347 | − | 1.39651i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.77018 | + | 0.412617i | 0.117751 | + | 0.0274469i | ||||
\(227\) | 7.02792i | 0.466460i | 0.972422 | + | 0.233230i | \(0.0749295\pi\) | ||||
−0.972422 | + | 0.233230i | \(0.925071\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.17034i | 0.275584i | 0.990461 | + | 0.137792i | \(0.0440005\pi\) | ||||
−0.990461 | + | 0.137792i | \(0.955999\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.6233 | − | 16.6072i | 0.894411 | − | 1.09032i | ||||
\(233\) | 23.9894 | 1.57160 | 0.785799 | − | 0.618483i | \(-0.212252\pi\) | ||||
0.785799 | + | 0.618483i | \(0.212252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.04737 | + | 16.3243i | −0.523839 | + | 1.06262i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 25.2747 | + | 5.89134i | 1.63831 | + | 0.381879i | ||||
\(239\) | 8.91926 | 0.576939 | 0.288469 | − | 0.957489i | \(-0.406854\pi\) | ||||
0.288469 | + | 0.957489i | \(0.406854\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.3510 | −1.05326 | −0.526629 | − | 0.850095i | \(-0.676544\pi\) | ||||
−0.526629 | + | 0.850095i | \(0.676544\pi\) | |||||||
\(242\) | 13.8114 | + | 3.21933i | 0.887830 | + | 0.206947i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.74378 | + | 19.7655i | −0.623781 | + | 1.26536i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.8831 | −0.819731 | ||||||||
\(248\) | −7.18172 | − | 5.89134i | −0.456040 | − | 0.374100i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.22391i | 0.266611i | 0.991075 | + | 0.133305i | \(0.0425591\pi\) | ||||
−0.991075 | + | 0.133305i | \(0.957441\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.48755i | − | 0.219261i | ||||||
\(254\) | −1.58774 | − | 0.370091i | −0.0996238 | − | 0.0232216i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.13235 | + | 15.4572i | −0.258272 | + | 0.966072i | ||||
\(257\) | −24.6952 | −1.54044 | −0.770221 | − | 0.637777i | \(-0.779854\pi\) | ||||
−0.770221 | + | 0.637777i | \(0.779854\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.83662i | − | 0.238396i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.24889 | + | 5.35793i | −0.0771569 | + | 0.331014i | ||||
\(263\) | −14.6628 | −0.904145 | −0.452073 | − | 0.891981i | \(-0.649315\pi\) | ||||
−0.452073 | + | 0.891981i | \(0.649315\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.39281 | − | 14.5556i | 0.208027 | − | 0.892463i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.48105 | + | 15.1755i | −0.456978 | + | 0.926990i | ||||
\(269\) | 11.5381i | 0.703490i | 0.936096 | + | 0.351745i | \(0.114412\pi\) | ||||
−0.936096 | + | 0.351745i | \(0.885588\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.63511 | 0.342309 | 0.171154 | − | 0.985244i | \(-0.445250\pi\) | ||||
0.171154 | + | 0.985244i | \(0.445250\pi\) | |||||||
\(272\) | −11.0183 | − | 14.3510i | −0.668085 | − | 0.870155i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 24.1212 | + | 5.62246i | 1.45721 | + | 0.339665i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 17.4053i | − | 1.04578i | −0.852399 | − | 0.522892i | \(-0.824853\pi\) | ||
0.852399 | − | 0.522892i | \(-0.175147\pi\) | |||||||
\(278\) | 5.41308 | − | 23.2229i | 0.324655 | − | 1.39281i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.7827 | −1.29945 | −0.649723 | − | 0.760171i | \(-0.725115\pi\) | ||||
−0.649723 | + | 0.760171i | \(0.725115\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.5962i | 1.28376i | 0.766804 | + | 0.641881i | \(0.221846\pi\) | ||||
−0.766804 | + | 0.641881i | \(0.778154\pi\) | |||||||
\(284\) | −2.56829 | − | 1.26609i | −0.152400 | − | 0.0751287i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.71585 | − | 1.56542i | −0.397117 | − | 0.0925650i | ||||
\(287\) | 2.30560 | 0.136095 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.45963 | 0.203508 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 21.4380 | + | 10.5683i | 1.25457 | + | 0.618463i | ||||
\(293\) | 32.0125i | 1.87019i | 0.354398 | + | 0.935095i | \(0.384686\pi\) | ||||
−0.354398 | + | 0.935095i | \(0.615314\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.69641 | + | 2.06797i | −0.0986016 | + | 0.120198i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.37043 | − | 14.4596i | 0.195244 | − | 0.837624i | ||||
\(299\) | − | 17.4943i | − | 1.01172i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 34.3211i | − | 1.97824i | ||||||
\(302\) | 6.49511 | + | 1.51396i | 0.373752 | + | 0.0871187i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.26470 | + | 6.34545i | −0.474013 | + | 0.363936i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.13659i | 0.0648686i | 0.999474 | + | 0.0324343i | \(0.0103260\pi\) | ||||
−0.999474 | + | 0.0324343i | \(0.989674\pi\) | |||||||
\(308\) | 3.53729 | − | 7.17548i | 0.201556 | − | 0.408861i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.13659 | −0.291269 | −0.145635 | − | 0.989338i | \(-0.546522\pi\) | ||||
−0.145635 | + | 0.989338i | \(0.546522\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.0762 | 1.30434 | 0.652172 | − | 0.758071i | \(-0.273858\pi\) | ||||
0.652172 | + | 0.758071i | \(0.273858\pi\) | |||||||
\(314\) | −2.87189 | + | 12.3208i | −0.162070 | + | 0.695303i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.89134 | − | 2.90425i | −0.331414 | − | 0.163377i | ||||
\(317\) | 1.66152i | 0.0933203i | 0.998911 | + | 0.0466601i | \(0.0148578\pi\) | ||||
−0.998911 | + | 0.0466601i | \(0.985142\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.48755 | 0.419223 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 19.7655 | + | 4.60719i | 1.10149 | + | 0.256749i | ||||
\(323\) | − | 11.7827i | − | 0.655605i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.06682 | − | 21.7374i | 0.280625 | − | 1.20392i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.24274 | − | 1.01945i | −0.0686187 | − | 0.0562895i | ||||
\(329\) | 10.5683 | 0.582649 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.9077i | 1.42402i | 0.702171 | + | 0.712008i | \(0.252214\pi\) | ||||
−0.702171 | + | 0.712008i | \(0.747786\pi\) | |||||||
\(332\) | 8.74714 | − | 17.7438i | 0.480062 | − | 0.973816i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.58774 | − | 1.76865i | −0.415183 | − | 0.0967760i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00696 | 0.436167 | 0.218083 | − | 0.975930i | \(-0.430020\pi\) | ||||
0.218083 | + | 0.975930i | \(0.430020\pi\) | |||||||
\(338\) | −15.7833 | − | 3.67896i | −0.858496 | − | 0.200109i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 3.23797i | − | 0.175346i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.97884 | −0.538806 | ||||||||
\(344\) | −15.1755 | + | 18.4994i | −0.818207 | + | 0.997420i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.31903 | − | 14.2391i | 0.178432 | − | 0.765499i | ||||
\(347\) | − | 23.0279i | − | 1.23620i | −0.786098 | − | 0.618102i | \(-0.787902\pi\) | ||
0.786098 | − | 0.618102i | \(-0.212098\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.4380i | 1.14755i | 0.819012 | + | 0.573776i | \(0.194522\pi\) | ||||
−0.819012 | + | 0.573776i | \(0.805478\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.07936 | + | 2.30359i | −0.270731 | + | 0.122782i | ||||
\(353\) | 4.52323 | 0.240747 | 0.120374 | − | 0.992729i | \(-0.461591\pi\) | ||||
0.120374 | + | 0.992729i | \(0.461591\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 22.1560 | + | 10.9222i | 1.17427 | + | 0.578878i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.19265 | − | 22.2772i | 0.274440 | − | 1.17739i | ||||
\(359\) | −10.3510 | −0.546303 | −0.273152 | − | 0.961971i | \(-0.588066\pi\) | ||||
−0.273152 | + | 0.961971i | \(0.588066\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.2144 | 0.642862 | ||||||||
\(362\) | −2.60492 | + | 11.1755i | −0.136912 | + | 0.587370i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 17.7438 | − | 35.9937i | 0.930027 | − | 1.88658i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.485359 | −0.0253355 | −0.0126678 | − | 0.999920i | \(-0.504032\pi\) | ||||
−0.0126678 | + | 0.999920i | \(0.504032\pi\) | |||||||
\(368\) | −8.61665 | − | 11.2229i | −0.449174 | − | 0.585032i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.932371i | 0.0484063i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 30.0823i | − | 1.55760i | −0.627272 | − | 0.778800i | \(-0.715829\pi\) | ||
0.627272 | − | 0.778800i | \(-0.284171\pi\) | |||||||
\(374\) | 1.43171 | − | 6.14222i | 0.0740317 | − | 0.317606i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.69641 | − | 4.67289i | −0.293770 | − | 0.240986i | ||||
\(377\) | 37.5591 | 1.93439 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.6881i | 1.73044i | 0.501392 | + | 0.865220i | \(0.332821\pi\) | ||||
−0.501392 | + | 0.865220i | \(0.667179\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 34.3211 | + | 8.00000i | 1.75602 | + | 0.409316i | ||||
\(383\) | 5.17545 | 0.264453 | 0.132227 | − | 0.991220i | \(-0.457787\pi\) | ||||
0.132227 | + | 0.991220i | \(0.457787\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.43171 | + | 0.333720i | 0.0728719 | + | 0.0169859i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.80850 | − | 2.86341i | −0.294882 | − | 0.145368i | ||||
\(389\) | 16.6408i | 0.843722i | 0.906660 | + | 0.421861i | \(0.138623\pi\) | ||||
−0.906660 | + | 0.421861i | \(0.861377\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | 20.6862 | + | 16.9694i | 1.04481 | + | 0.857082i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.10170 | + | 13.3067i | −0.156262 | + | 0.670384i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 20.4332i | − | 1.02551i | −0.858534 | − | 0.512757i | \(-0.828624\pi\) | ||
0.858534 | − | 0.512757i | \(-0.171376\pi\) | |||||||
\(398\) | 31.7698 | + | 7.40530i | 1.59247 | + | 0.371194i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.56829 | 0.228130 | 0.114065 | − | 0.993473i | \(-0.463613\pi\) | ||||
0.114065 | + | 0.993473i | \(0.463613\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 16.2423i | − | 0.809087i | ||||||
\(404\) | 3.85244 | − | 7.81477i | 0.191666 | − | 0.388799i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.89134 | + | 42.4352i | −0.490899 | + | 2.10602i | ||||
\(407\) | −0.932371 | −0.0462159 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.8913 | 0.983563 | 0.491782 | − | 0.870719i | \(-0.336346\pi\) | ||||
0.491782 | + | 0.870719i | \(0.336346\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −27.0433 | − | 13.3315i | −1.33233 | − | 0.656797i | ||||
\(413\) | − | 36.9193i | − | 1.81668i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −25.4791 | + | 11.5553i | −1.24921 | + | 0.566545i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.53729 | − | 0.824517i | −0.173015 | − | 0.0403284i | ||||
\(419\) | 0.387288i | 0.0189203i | 0.999955 | + | 0.00946013i | \(0.00301130\pi\) | ||||
−0.999955 | + | 0.00946013i | \(0.996989\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.0578i | − | 0.587664i | −0.955857 | − | 0.293832i | \(-0.905069\pi\) | ||
0.955857 | − | 0.293832i | \(-0.0949306\pi\) | |||||||
\(422\) | −2.06797 | + | 8.87189i | −0.100667 | + | 0.431877i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.412259 | − | 0.502556i | 0.0200210 | − | 0.0244063i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 44.7019i | − | 2.16328i | ||||||
\(428\) | −3.53729 | + | 7.17548i | −0.170982 | + | 0.346840i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −40.4068 | −1.94633 | −0.973164 | − | 0.230113i | \(-0.926090\pi\) | ||||
−0.973164 | + | 0.230113i | \(0.926090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.1859 | 1.73898 | 0.869491 | − | 0.493949i | \(-0.164447\pi\) | ||||
0.869491 | + | 0.493949i | \(0.164447\pi\) | |||||||
\(434\) | 18.3510 | + | 4.27748i | 0.880875 | + | 0.205325i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.68793 | − | 7.48105i | 0.176620 | − | 0.358277i | ||||
\(437\) | − | 9.21438i | − | 0.440783i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.4178 | −1.21312 | −0.606562 | − | 0.795036i | \(-0.707452\pi\) | ||||
−0.606562 | + | 0.795036i | \(0.707452\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.18172 | − | 30.8106i | 0.341600 | − | 1.46551i | ||||
\(443\) | 7.02792i | 0.333907i | 0.985965 | + | 0.166953i | \(0.0533929\pi\) | ||||
−0.985965 | + | 0.166953i | \(0.946607\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −24.7632 | − | 5.77213i | −1.17257 | − | 0.273318i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.34545 | − | 31.8300i | −0.299794 | − | 1.50383i | ||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 0.560304i | − | 0.0263837i | ||||||
\(452\) | 2.30560 | + | 1.13659i | 0.108446 | + | 0.0534607i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.25622 | + | 9.67951i | −0.105890 | + | 0.454282i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.2747 | 1.18230 | 0.591149 | − | 0.806562i | \(-0.298674\pi\) | ||||
0.591149 | + | 0.806562i | \(0.298674\pi\) | |||||||
\(458\) | −1.33883 | + | 5.74378i | −0.0625595 | + | 0.268389i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.0902i | 1.91376i | 0.290479 | + | 0.956881i | \(0.406185\pi\) | ||||
−0.290479 | + | 0.956881i | \(0.593815\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.2106 | −0.613951 | −0.306975 | − | 0.951717i | \(-0.599317\pi\) | ||||
−0.306975 | + | 0.951717i | \(0.599317\pi\) | |||||||
\(464\) | 24.0947 | − | 18.4994i | 1.11857 | − | 0.858813i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 33.0404 | + | 7.70148i | 1.53057 | + | 0.356764i | ||||
\(467\) | − | 1.89134i | − | 0.0875206i | −0.999042 | − | 0.0437603i | \(-0.986066\pi\) | ||
0.999042 | − | 0.0437603i | \(-0.0139338\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 34.3211i | − | 1.58480i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16.3243 | + | 19.8998i | −0.751386 | + | 0.915963i | ||||
\(473\) | −8.34068 | −0.383505 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 32.9193 | + | 16.2282i | 1.50885 | + | 0.743818i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.2844 | + | 2.86341i | 0.561877 | + | 0.130969i | ||||
\(479\) | −31.4876 | −1.43870 | −0.719352 | − | 0.694646i | \(-0.755561\pi\) | ||||
−0.719352 | + | 0.694646i | \(0.755561\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.67696 | −0.213251 | ||||||||
\(482\) | −22.5201 | − | 5.24926i | −1.02576 | − | 0.239097i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.9888 | + | 8.86793i | 0.817673 | + | 0.403088i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.9964 | 0.588922 | 0.294461 | − | 0.955664i | \(-0.404860\pi\) | ||||
0.294461 | + | 0.955664i | \(0.404860\pi\) | |||||||
\(488\) | −19.7655 | + | 24.0947i | −0.894741 | + | 1.09072i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.9085i | − | 0.672812i | −0.941717 | − | 0.336406i | \(-0.890788\pi\) | ||
0.941717 | − | 0.336406i | \(-0.109212\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.3510i | 1.54709i | ||||||||
\(494\) | −17.7438 | − | 4.13594i | −0.798330 | − | 0.186085i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.00000 | − | 10.4197i | −0.359211 | − | 0.467858i | ||||
\(497\) | 5.80850 | 0.260547 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 35.6599i | − | 1.59636i | −0.602420 | − | 0.798179i | \(-0.705797\pi\) | ||
0.602420 | − | 0.798179i | \(-0.294203\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.35603 | + | 5.81756i | −0.0605226 | + | 0.259650i | ||||
\(503\) | 25.3090 | 1.12847 | 0.564237 | − | 0.825613i | \(-0.309170\pi\) | ||||
0.564237 | + | 0.825613i | \(0.309170\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.11963 | − | 4.80338i | 0.0497738 | − | 0.213536i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.06797 | − | 1.01945i | −0.0917514 | − | 0.0452306i | ||||
\(509\) | 13.7366i | 0.608862i | 0.952534 | + | 0.304431i | \(0.0984663\pi\) | ||||
−0.952534 | + | 0.304431i | \(0.901534\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −48.4846 | −2.14483 | ||||||||
\(512\) | −10.6538 | + | 19.9624i | −0.470835 | + | 0.882221i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −34.0125 | − | 7.92806i | −1.50023 | − | 0.349692i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.56829i | − | 0.112953i | ||||||
\(518\) | 1.23170 | − | 5.28415i | 0.0541176 | − | 0.232172i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.9193 | 1.35460 | 0.677299 | − | 0.735708i | \(-0.263150\pi\) | ||||
0.677299 | + | 0.735708i | \(0.263150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.8385i | 0.954932i | 0.878650 | + | 0.477466i | \(0.158445\pi\) | ||||
−0.878650 | + | 0.477466i | \(0.841555\pi\) | |||||||
\(524\) | −3.44018 | + | 6.97849i | −0.150285 | + | 0.304857i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.1949 | − | 4.70729i | −0.880541 | − | 0.205248i | ||||
\(527\) | 14.8550 | 0.647092 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.4876 | −0.455981 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.34579 | − | 18.9582i | 0.405191 | − | 0.821940i | ||||
\(533\) | − | 2.81060i | − | 0.121740i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −15.1755 | + | 18.4994i | −0.655481 | + | 0.799052i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.70415 | + | 15.8913i | −0.159697 | + | 0.685124i | ||||
\(539\) | 9.32662i | 0.401726i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.3423i | 1.04656i | 0.852162 | + | 0.523278i | \(0.175291\pi\) | ||||
−0.852162 | + | 0.523278i | \(0.824709\pi\) | |||||||
\(542\) | 7.76120 | + | 1.80908i | 0.333372 | + | 0.0777066i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.5683 | − | 23.3028i | −0.453112 | − | 0.999098i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.3789i | 1.42718i | 0.700564 | + | 0.713589i | \(0.252932\pi\) | ||||
−0.700564 | + | 0.713589i | \(0.747068\pi\) | |||||||
\(548\) | 31.4169 | + | 15.4876i | 1.34206 | + | 0.661596i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.7827 | 0.842770 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.3239 | 0.566592 | ||||||||
\(554\) | 5.58774 | − | 23.9722i | 0.237400 | − | 1.01848i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.9108 | − | 30.2469i | 0.632358 | − | 1.28275i | ||||
\(557\) | − | 30.5808i | − | 1.29575i | −0.761747 | − | 0.647875i | \(-0.775658\pi\) | ||
0.761747 | − | 0.647875i | \(-0.224342\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.8385 | −1.76958 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −30.0011 | − | 6.99304i | −1.26552 | − | 0.294984i | ||||
\(563\) | − | 7.02792i | − | 0.296192i | −0.988973 | − | 0.148096i | \(-0.952686\pi\) | ||
0.988973 | − | 0.148096i | \(-0.0473144\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.93318 | + | 29.7443i | −0.291423 | + | 1.25025i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.13083 | − | 2.56829i | −0.131367 | − | 0.107763i | ||||
\(569\) | −24.3510 | −1.02085 | −0.510423 | − | 0.859924i | \(-0.670511\pi\) | ||||
−0.510423 | + | 0.859924i | \(0.670511\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0992i | 0.841125i | 0.907263 | + | 0.420563i | \(0.138167\pi\) | ||||
−0.907263 | + | 0.420563i | \(0.861833\pi\) | |||||||
\(572\) | −8.74714 | − | 4.31207i | −0.365736 | − | 0.180297i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.17548 | + | 0.740182i | 0.132542 | + | 0.0308946i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.76899 | −0.198536 | −0.0992678 | − | 0.995061i | \(-0.531650\pi\) | ||||
−0.0992678 | + | 0.995061i | \(0.531650\pi\) | |||||||
\(578\) | 4.76492 | + | 1.11067i | 0.198195 | + | 0.0461977i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.1296i | 1.66486i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.226584 | 0.00938413 | ||||||||
\(584\) | 26.1336 | + | 21.4380i | 1.08142 | + | 0.887112i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.2772 | + | 44.0906i | −0.424547 | + | 1.82136i | ||||
\(587\) | 8.21733i | 0.339165i | 0.985516 | + | 0.169583i | \(0.0542420\pi\) | ||||
−0.985516 | + | 0.169583i | \(0.945758\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 8.55495i | − | 0.352501i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.00034 | + | 2.30359i | −0.123313 | + | 0.0946771i | ||||
\(593\) | 7.76120 | 0.318714 | 0.159357 | − | 0.987221i | \(-0.449058\pi\) | ||||
0.159357 | + | 0.987221i | \(0.449058\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.28415 | − | 18.8331i | 0.380293 | − | 0.771434i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.61631 | − | 24.0947i | 0.229668 | − | 0.985307i | ||||
\(599\) | 5.64903 | 0.230813 | 0.115407 | − | 0.993318i | \(-0.463183\pi\) | ||||
0.115407 | + | 0.993318i | \(0.463183\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.7299 | −1.53903 | −0.769516 | − | 0.638627i | \(-0.779503\pi\) | ||||
−0.769516 | + | 0.638627i | \(0.779503\pi\) | |||||||
\(602\) | 11.0183 | − | 47.2702i | 0.449074 | − | 1.92659i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.45963 | + | 4.17034i | 0.344217 | + | 0.169689i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.113292 | −0.00459837 | −0.00229919 | − | 0.999997i | \(-0.500732\pi\) | ||||
−0.00229919 | + | 0.999997i | \(0.500732\pi\) | |||||||
\(608\) | −13.4200 | + | 6.08627i | −0.544254 | + | 0.246831i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 12.8831i | − | 0.521194i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 0.703366i | − | 0.0284087i | −0.999899 | − | 0.0142044i | \(-0.995478\pi\) | ||
0.999899 | − | 0.0142044i | \(-0.00452154\pi\) | |||||||
\(614\) | −0.364887 | + | 1.56542i | −0.0147256 | + | 0.0631750i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.17548 | − | 8.74714i | 0.289108 | − | 0.352432i | ||||
\(617\) | −24.4809 | −0.985564 | −0.492782 | − | 0.870153i | \(-0.664020\pi\) | ||||
−0.492782 | + | 0.870153i | \(0.664020\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.4966i | 1.58750i | 0.608243 | + | 0.793751i | \(0.291874\pi\) | ||||
−0.608243 | + | 0.793751i | \(0.708126\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.07459 | − | 1.64903i | −0.283665 | − | 0.0661202i | ||||
\(623\) | −50.1084 | −2.00755 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 31.7827 | + | 7.40831i | 1.27029 | + | 0.296095i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.91086 | + | 16.0474i | −0.315678 | + | 0.640360i | ||||
\(629\) | − | 4.27748i | − | 0.170554i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.3400 | 0.690294 | 0.345147 | − | 0.938549i | \(-0.387829\pi\) | ||||
0.345147 | + | 0.938549i | \(0.387829\pi\) | |||||||
\(632\) | −7.18172 | − | 5.89134i | −0.285674 | − | 0.234345i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.533409 | + | 2.28840i | −0.0211844 | + | 0.0908840i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46.7842i | 1.85366i | ||||||||
\(638\) | 10.3126 | + | 2.40378i | 0.408278 | + | 0.0951666i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.7019 | −1.52863 | −0.764317 | − | 0.644840i | \(-0.776924\pi\) | ||||
−0.764317 | + | 0.644840i | \(0.776924\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.13659i | − | 0.0448227i | −0.999749 | − | 0.0224113i | \(-0.992866\pi\) | ||
0.999749 | − | 0.0224113i | \(-0.00713435\pi\) | |||||||
\(644\) | 25.7438 | + | 12.6909i | 1.01445 | + | 0.500091i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.78267 | − | 16.2282i | 0.148827 | − | 0.638490i | ||||
\(647\) | −6.54868 | −0.257455 | −0.128728 | − | 0.991680i | \(-0.541089\pi\) | ||||
−0.128728 | + | 0.991680i | \(0.541089\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.97208 | −0.352185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.9570 | − | 28.3121i | 0.546598 | − | 1.10879i | ||||
\(653\) | − | 8.74226i | − | 0.342111i | −0.985261 | − | 0.171056i | \(-0.945282\pi\) | ||
0.985261 | − | 0.171056i | \(-0.0547178\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.38433 | − | 1.80304i | −0.0540492 | − | 0.0703969i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.5556 | + | 3.39281i | 0.567438 | + | 0.132266i | ||||
\(659\) | 35.5336i | 1.38419i | 0.721804 | + | 0.692097i | \(0.243313\pi\) | ||||
−0.721804 | + | 0.692097i | \(0.756687\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 23.3028i | − | 0.906373i | −0.891416 | − | 0.453186i | \(-0.850287\pi\) | ||
0.891416 | − | 0.453186i | \(-0.149713\pi\) | |||||||
\(662\) | −8.31732 | + | 35.6825i | −0.323262 | + | 1.38684i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.7438 | − | 21.6302i | 0.688592 | − | 0.839415i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.8634i | 1.04016i | ||||||||
\(668\) | −9.88274 | − | 4.87189i | −0.382375 | − | 0.188499i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.8634 | −0.419377 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.3634 | −0.553670 | −0.276835 | − | 0.960917i | \(-0.589286\pi\) | ||||
−0.276835 | + | 0.960917i | \(0.589286\pi\) | |||||||
\(674\) | 11.0279 | + | 2.57053i | 0.424780 | + | 0.0990130i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.5571 | − | 10.1340i | −0.790658 | − | 0.389770i | ||||
\(677\) | 24.3076i | 0.934217i | 0.884200 | + | 0.467109i | \(0.154704\pi\) | ||||
−0.884200 | + | 0.467109i | \(0.845296\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.1366 | 0.504136 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.03951 | − | 4.45963i | 0.0398048 | − | 0.170768i | ||||
\(683\) | − | 38.5933i | − | 1.47673i | −0.674401 | − | 0.738365i | \(-0.735598\pi\) | ||
0.674401 | − | 0.738365i | \(-0.264402\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13.7438 | − | 3.20357i | −0.524740 | − | 0.122313i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26.8401 | + | 20.6072i | −1.02327 | + | 0.785642i | ||||
\(689\) | 1.13659 | 0.0433006 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4090i | 0.510102i | 0.966928 | + | 0.255051i | \(0.0820923\pi\) | ||||
−0.966928 | + | 0.255051i | \(0.917908\pi\) | |||||||
\(692\) | 9.14256 | − | 18.5459i | 0.347548 | − | 0.705009i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.39281 | − | 31.7162i | 0.280627 | − | 1.20393i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.57053 | 0.0973657 | ||||||||
\(698\) | −6.88240 | + | 29.5264i | −0.260503 | + | 1.11759i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.6013i | 0.589253i | 0.955613 | + | 0.294626i | \(0.0951952\pi\) | ||||
−0.955613 | + | 0.294626i | \(0.904805\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.46339 | −0.0929086 | ||||||||
\(704\) | −7.73530 | + | 1.54206i | −0.291535 | + | 0.0581187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.22982 | + | 1.45212i | 0.234462 | + | 0.0546514i | ||||
\(707\) | 17.6740i | 0.664699i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.7873i | 0.592906i | 0.955047 | + | 0.296453i | \(0.0958038\pi\) | ||||
−0.955047 | + | 0.296453i | \(0.904196\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27.0089 | + | 22.1560i | 1.01220 | + | 0.830333i | ||||
\(713\) | 11.6170 | 0.435060 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.3036 | − | 29.0152i | 0.534550 | − | 1.08435i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.2563 | − | 3.32304i | −0.532041 | − | 0.124015i | ||||
\(719\) | −22.5683 | −0.841655 | −0.420828 | − | 0.907141i | \(-0.638260\pi\) | ||||
−0.420828 | + | 0.907141i | \(0.638260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 61.1616 | 2.27778 | ||||||||
\(722\) | 16.8228 | + | 3.92126i | 0.626079 | + | 0.145934i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.17548 | + | 14.5556i | −0.266675 | + | 0.540956i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.79096 | 0.103511 | 0.0517554 | − | 0.998660i | \(-0.483518\pi\) | ||||
0.0517554 | + | 0.998660i | \(0.483518\pi\) | |||||||
\(728\) | 35.9937 | − | 43.8774i | 1.33401 | − | 1.62621i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 38.2649i | − | 1.41528i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.4860i | 0.608926i | 0.952524 | + | 0.304463i | \(0.0984769\pi\) | ||||
−0.952524 | + | 0.304463i | \(0.901523\pi\) | |||||||
\(734\) | −0.668481 | − | 0.155818i | −0.0246741 | − | 0.00575135i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.26470 | − | 18.2234i | −0.304641 | − | 0.671724i | ||||
\(737\) | −8.34068 | −0.307233 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.8894i | 0.547714i | 0.961770 | + | 0.273857i | \(0.0882995\pi\) | ||||
−0.961770 | + | 0.273857i | \(0.911701\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.299325 | + | 1.28415i | −0.0109886 | + | 0.0471425i | ||||
\(743\) | −41.4301 | −1.51992 | −0.759961 | − | 0.649968i | \(-0.774782\pi\) | ||||
−0.759961 | + | 0.649968i | \(0.774782\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.65751 | − | 41.4321i | 0.353587 | − | 1.51694i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.94376 | − | 8.00000i | 0.144198 | − | 0.292509i | ||||
\(749\) | − | 16.2282i | − | 0.592965i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.5544 | 1.11494 | 0.557472 | − | 0.830195i | \(-0.311771\pi\) | ||||
0.557472 | + | 0.830195i | \(0.311771\pi\) | |||||||
\(752\) | −6.34545 | − | 8.26470i | −0.231395 | − | 0.301383i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 51.7299 | + | 12.0578i | 1.88389 | + | 0.439121i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.433223i | 0.0157457i | 0.999969 | + | 0.00787287i | \(0.00250604\pi\) | ||||
−0.999969 | + | 0.00787287i | \(0.997494\pi\) | |||||||
\(758\) | −10.8151 | + | 46.3983i | −0.392823 | + | 1.68526i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.9193 | 0.540823 | 0.270411 | − | 0.962745i | \(-0.412840\pi\) | ||||
0.270411 | + | 0.962745i | \(0.412840\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.9193i | 0.612518i | ||||||||
\(764\) | 44.7019 | + | 22.0367i | 1.61726 | + | 0.797259i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.12811 | + | 1.66151i | 0.257549 | + | 0.0600328i | ||||
\(767\) | −45.0057 | −1.62506 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.3789 | −1.13155 | −0.565776 | − | 0.824559i | \(-0.691423\pi\) | ||||
−0.565776 | + | 0.824559i | \(0.691423\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.86474 | + | 0.919260i | 0.0671135 | + | 0.0330849i | ||||
\(773\) | 13.4192i | 0.482656i | 0.970444 | + | 0.241328i | \(0.0775829\pi\) | ||||
−0.970444 | + | 0.241328i | \(0.922417\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.08074 | − | 5.80850i | −0.254184 | − | 0.208513i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.34231 | + | 22.9193i | −0.191531 | + | 0.821695i | ||||
\(779\) | − | 1.48036i | − | 0.0530395i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1.41157i | − | 0.0505101i | ||||||
\(782\) | 22.0367 | + | 5.13659i | 0.788030 | + | 0.183684i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 23.0431 | + | 30.0128i | 0.822969 | + | 1.07189i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.4846i | 1.30054i | 0.759705 | + | 0.650268i | \(0.225343\pi\) | ||||
−0.759705 | + | 0.650268i | \(0.774657\pi\) | |||||||
\(788\) | −8.54391 | + | 17.3315i | −0.304364 | + | 0.617410i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.21438 | −0.185402 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −54.4931 | −1.93511 | ||||||||
\(794\) | 6.55982 | − | 28.1425i | 0.232799 | − | 0.998741i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 41.3789 | + | 20.3985i | 1.46664 | + | 0.723007i | ||||
\(797\) | 26.0683i | 0.923388i | 0.887039 | + | 0.461694i | \(0.152758\pi\) | ||||
−0.887039 | + | 0.461694i | \(0.847242\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.7827 | 0.416841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.29188 | + | 1.46659i | 0.222174 | + | 0.0517871i | ||||
\(803\) | 11.7827i | 0.415801i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.21438 | − | 22.3704i | 0.183669 | − | 0.787964i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.81477 | − | 9.52645i | 0.274923 | − | 0.335139i | ||||
\(809\) | −35.6212 | −1.25237 | −0.626187 | − | 0.779673i | \(-0.715385\pi\) | ||||
−0.626187 | + | 0.779673i | \(0.715385\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 43.8935i | − | 1.54131i | −0.637253 | − | 0.770654i | \(-0.719929\pi\) | ||
0.637253 | − | 0.770654i | \(-0.280071\pi\) | |||||||
\(812\) | −27.2465 | + | 55.2702i | −0.956166 | + | 1.93960i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.28415 | − | 0.299325i | −0.0450093 | − | 0.0104913i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.0367 | −0.770966 | ||||||||
\(818\) | 27.3962 | + | 6.38585i | 0.957885 | + | 0.223276i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 28.8058i | − | 1.00533i | −0.864482 | − | 0.502665i | \(-0.832353\pi\) | ||
0.864482 | − | 0.502665i | \(-0.167647\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.9585 | 0.974571 | 0.487286 | − | 0.873243i | \(-0.337987\pi\) | ||||
0.487286 | + | 0.873243i | \(0.337987\pi\) | |||||||
\(824\) | −32.9666 | − | 27.0433i | −1.14845 | − | 0.942098i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.8524 | − | 50.8486i | 0.412399 | − | 1.76925i | ||||
\(827\) | − | 14.8634i | − | 0.516851i | −0.966031 | − | 0.258426i | \(-0.916796\pi\) | ||
0.966031 | − | 0.258426i | \(-0.0832037\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 41.7678i | − | 1.45065i | −0.688404 | − | 0.725327i | \(-0.741688\pi\) | ||
0.688404 | − | 0.725327i | \(-0.258312\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −38.8018 | + | 7.73530i | −1.34521 | + | 0.268173i | ||||
\(833\) | −42.7881 | −1.48252 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.60719 | − | 2.27120i | −0.159343 | − | 0.0785512i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.124334 | + | 0.533409i | −0.00429504 | + | 0.0184263i | ||||
\(839\) | 21.6490 | 0.747408 | 0.373704 | − | 0.927548i | \(-0.378088\pi\) | ||||
0.373704 | + | 0.927548i | \(0.378088\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6740 | −0.988759 | ||||||||
\(842\) | 3.87101 | − | 16.6072i | 0.133404 | − | 0.572322i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.69641 | + | 11.5553i | −0.196078 | + | 0.397750i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −40.6838 | −1.39791 | ||||||||
\(848\) | 0.729140 | − | 0.559817i | 0.0250388 | − | 0.0192242i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.34510i | − | 0.114669i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 49.1880i | − | 1.68416i | −0.539350 | − | 0.842082i | \(-0.681330\pi\) | ||
0.539350 | − | 0.842082i | \(-0.318670\pi\) | |||||||
\(854\) | 14.3510 | − | 61.5676i | 0.491080 | − | 2.10680i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.17548 | + | 8.74714i | −0.245253 | + | 0.298971i | ||||
\(857\) | 2.65849 | 0.0908123 | 0.0454062 | − | 0.998969i | \(-0.485542\pi\) | ||||
0.0454062 | + | 0.998969i | \(0.485542\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 4.57680i | − | 0.156158i | −0.996947 | − | 0.0780792i | \(-0.975121\pi\) | ||
0.996947 | − | 0.0780792i | \(-0.0248787\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −55.6520 | − | 12.9721i | −1.89552 | − | 0.441831i | ||||
\(863\) | 34.0218 | 1.15812 | 0.579058 | − | 0.815287i | \(-0.303421\pi\) | ||||
0.579058 | + | 0.815287i | \(0.303421\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 49.8385 | + | 11.6170i | 1.69358 | + | 0.394761i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 23.9014 | + | 11.7827i | 0.811267 | + | 0.399930i | ||||
\(869\) | − | 3.23797i | − | 0.109841i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.8385 | −1.41764 | ||||||||
\(872\) | 7.48105 | − | 9.11963i | 0.253340 | − | 0.308830i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.95815 | − | 12.6909i | 0.100061 | − | 0.429276i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 11.7563i | − | 0.396981i | −0.980103 | − | 0.198490i | \(-0.936396\pi\) | ||
0.980103 | − | 0.198490i | \(-0.0636039\pi\) | |||||||
\(878\) | −35.0077 | − | 8.16004i | −1.18145 | − | 0.275388i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.2702 | −0.447085 | −0.223543 | − | 0.974694i | \(-0.571762\pi\) | ||||
−0.223543 | + | 0.974694i | \(0.571762\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 17.1366i | − | 0.576692i | −0.957526 | − | 0.288346i | \(-0.906895\pi\) | ||
0.957526 | − | 0.288346i | \(-0.0931054\pi\) | |||||||
\(884\) | 19.7827 | − | 40.1296i | 0.665363 | − | 1.34970i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.25622 | + | 9.67951i | −0.0757993 | + | 0.325189i | ||||
\(887\) | 32.0883 | 1.07742 | 0.538709 | − | 0.842492i | \(-0.318912\pi\) | ||||
0.538709 | + | 0.842492i | \(0.318912\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.67696 | 0.156860 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −32.2531 | − | 15.8998i | −1.07992 | − | 0.532365i | ||||
\(893\) | − | 6.78562i | − | 0.227072i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.47908 | − | 45.8764i | 0.0494125 | − | 1.53262i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.75459 | + | 0.642074i | 0.0919217 | + | 0.0214263i | ||||
\(899\) | 24.9409i | 0.831827i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.03951i | 0.0346310i | ||||||||
\(902\) | 0.179878 | − | 0.771702i | 0.00598929 | − | 0.0256949i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.81060 | + | 2.30560i | 0.0934790 | + | 0.0766830i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 40.4596i | − | 1.34344i | −0.740805 | − | 0.671720i | \(-0.765556\pi\) | ||
0.740805 | − | 0.671720i | \(-0.234444\pi\) | |||||||
\(908\) | −6.21496 | + | 12.6072i | −0.206251 | + | 0.418384i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0000 | −0.530104 | −0.265052 | − | 0.964234i | \(-0.585389\pi\) | ||||
−0.265052 | + | 0.964234i | \(0.585389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.75225 | 0.322752 | ||||||||
\(914\) | 34.8106 | + | 8.11409i | 1.15143 | + | 0.268390i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.68793 | + | 7.48105i | −0.121853 | + | 0.247181i | ||||
\(917\) | − | 15.7827i | − | 0.521190i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.8495 | 1.67737 | 0.838685 | − | 0.544617i | \(-0.183325\pi\) | ||||
0.838685 | + | 0.544617i | \(0.183325\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13.1915 | + | 56.5933i | −0.434438 | + | 1.86380i | ||||
\(923\) | − | 7.08074i | − | 0.233065i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.1949 | − | 4.24110i | −0.597922 | − | 0.139371i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 39.1245 | − | 17.7438i | 1.28432 | − | 0.582468i | ||||
\(929\) | −12.6461 | −0.414904 | −0.207452 | − | 0.978245i | \(-0.566517\pi\) | ||||
−0.207452 | + | 0.978245i | \(0.566517\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.6416i | 0.807596i | ||||||||
\(932\) | 43.0339 | + | 21.2144i | 1.40962 | + | 0.694900i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.607188 | − | 2.60492i | 0.0198678 | − | 0.0852357i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.7971 | −1.33278 | −0.666391 | − | 0.745603i | \(-0.732162\pi\) | ||||
−0.666391 | + | 0.745603i | \(0.732162\pi\) | |||||||
\(938\) | 11.0183 | − | 47.2702i | 0.359762 | − | 1.54343i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 14.1086i | − | 0.459928i | −0.973199 | − | 0.229964i | \(-0.926139\pi\) | ||
0.973199 | − | 0.229964i | \(-0.0738608\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.01022 | 0.0654619 | ||||||||
\(944\) | −28.8719 | + | 22.1672i | −0.939700 | + | 0.721480i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.4876 | − | 2.67766i | −0.373493 | − | 0.0870584i | ||||
\(947\) | 45.8385i | 1.48955i | 0.667315 | + | 0.744776i | \(0.267444\pi\) | ||||
−0.667315 | + | 0.744776i | \(0.732556\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 59.1043i | 1.91861i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 40.1296 | + | 32.9193i | 1.30061 | + | 1.06692i | ||||
\(953\) | 21.9104 | 0.709747 | 0.354873 | − | 0.934914i | \(-0.384524\pi\) | ||||
0.354873 | + | 0.934914i | \(0.384524\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.0000 | + | 7.88751i | 0.517477 | + | 0.255100i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −43.3676 | − | 10.1087i | −1.40114 | − | 0.326596i | ||||
\(959\) | −71.0529 | −2.29442 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.2144 | −0.652077 | ||||||||
\(962\) | −6.44154 | − | 1.50148i | −0.207684 | − | 0.0484095i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −29.3315 | − | 14.4595i | −0.944705 | − | 0.465710i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.0359 | 0.451364 | 0.225682 | − | 0.974201i | \(-0.427539\pi\) | ||||
0.225682 | + | 0.974201i | \(0.427539\pi\) | |||||||
\(968\) | 21.9289 | + | 17.9888i | 0.704822 | + | 0.578182i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.6494i | 0.694762i | 0.937724 | + | 0.347381i | \(0.112929\pi\) | ||||
−0.937724 | + | 0.347381i | \(0.887071\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 68.4068i | 2.19302i | ||||||||
\(974\) | 17.8998 | + | 4.17231i | 0.573547 | + | 0.133690i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.9582 | + | 26.8401i | −1.11898 | + | 0.859130i | ||||
\(977\) | −6.60225 | −0.211225 | −0.105612 | − | 0.994407i | \(-0.533680\pi\) | ||||
−0.105612 | + | 0.994407i | \(0.533680\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.1773i | 0.389188i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.78619 | − | 20.5334i | 0.152733 | − | 0.655247i | ||||
\(983\) | 53.8600 | 1.71787 | 0.858934 | − | 0.512087i | \(-0.171127\pi\) | ||||
0.858934 | + | 0.512087i | \(0.171127\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −11.0279 | + | 47.3113i | −0.351201 | + | 1.50670i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −23.1106 | − | 11.3928i | −0.735246 | − | 0.362454i | ||||
\(989\) | − | 29.9242i | − | 0.951534i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.7129 | 0.943861 | 0.471931 | − | 0.881636i | \(-0.343557\pi\) | ||||
0.471931 | + | 0.881636i | \(0.343557\pi\) | |||||||
\(992\) | −7.67324 | − | 16.9193i | −0.243626 | − | 0.537187i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.00000 | + | 1.86474i | 0.253745 | + | 0.0591460i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 16.6506i | − | 0.527328i | −0.964615 | − | 0.263664i | \(-0.915069\pi\) | ||
0.964615 | − | 0.263664i | \(-0.0849311\pi\) | |||||||
\(998\) | 11.4482 | − | 49.1142i | 0.362385 | − | 1.55468i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))