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: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
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 | 293.1 | ||
Root | \(-0.268067 + 1.71118i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.293 |
Dual form | 1764.2.x.b.1469.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.56269 | − | 0.746985i | −0.902222 | − | 0.431272i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.842869 | − | 1.45989i | 0.376942 | − | 0.652883i | −0.613673 | − | 0.789560i | \(-0.710309\pi\) |
0.990616 | + | 0.136677i | \(0.0436422\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.88403 | + | 2.33462i | 0.628009 | + | 0.778206i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.38216 | + | 1.95269i | −1.01976 | + | 0.588758i | −0.914034 | − | 0.405637i | \(-0.867050\pi\) |
−0.105725 | + | 0.994395i | \(0.533716\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.24391 | + | 3.02757i | 1.45440 | + | 0.839698i | 0.998727 | − | 0.0504496i | \(-0.0160654\pi\) |
0.455673 | + | 0.890147i | \(0.349399\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.40766 | + | 1.65175i | −0.621656 | + | 0.426481i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.402488 | −0.0976176 | −0.0488088 | − | 0.998808i | \(-0.515542\pi\) | ||||
−0.0488088 | + | 0.998808i | \(0.515542\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.168144i | − | 0.0385748i | −0.999814 | − | 0.0192874i | \(-0.993860\pi\) | ||
0.999814 | − | 0.0192874i | \(-0.00613975\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.69373 | − | 4.44198i | −1.60425 | − | 0.926216i | −0.990623 | − | 0.136623i | \(-0.956375\pi\) |
−0.613630 | − | 0.789593i | \(-0.710291\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.07914 | + | 1.86913i | 0.215829 | + | 0.373827i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.20023 | − | 5.05563i | −0.230985 | − | 0.972957i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.15380 | + | 3.55290i | −1.14273 | + | 0.659757i | −0.947106 | − | 0.320921i | \(-0.896007\pi\) |
−0.195627 | + | 0.980678i | \(0.562674\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.44527 | − | 3.14383i | −0.978000 | − | 0.564649i | −0.0763342 | − | 0.997082i | \(-0.524322\pi\) |
−0.901666 | + | 0.432434i | \(0.857655\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.74391 | − | 0.525036i | 1.17396 | − | 0.0913971i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.26515 | −1.02998 | −0.514992 | − | 0.857195i | \(-0.672205\pi\) | ||||
−0.514992 | + | 0.857195i | \(0.672205\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.93308 | − | 8.64829i | −0.950053 | − | 1.38484i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.64707 | + | 2.85281i | −0.257229 | + | 0.445534i | −0.965499 | − | 0.260408i | \(-0.916143\pi\) |
0.708269 | + | 0.705942i | \(0.249476\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.80474 | + | 3.12590i | 0.275220 | + | 0.476695i | 0.970191 | − | 0.242343i | \(-0.0779161\pi\) |
−0.694971 | + | 0.719038i | \(0.744583\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.99628 | − | 0.782698i | 0.744801 | − | 0.116678i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.38482 | + | 7.59474i | 0.639592 | + | 1.10781i | 0.985522 | + | 0.169546i | \(0.0542301\pi\) |
−0.345930 | + | 0.938260i | \(0.612437\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.628965 | + | 0.300652i | 0.0880727 | + | 0.0420997i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.71148i | 0.784532i | 0.919852 | + | 0.392266i | \(0.128309\pi\) | ||||
−0.919852 | + | 0.392266i | \(0.871691\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.58345i | 0.887712i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.125601 | + | 0.262757i | −0.0166362 | + | 0.0348030i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.25163 | − | 3.89994i | 0.293138 | − | 0.507729i | −0.681412 | − | 0.731900i | \(-0.738634\pi\) |
0.974550 | + | 0.224171i | \(0.0719673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.43678 | + | 2.56157i | −0.568071 | + | 0.327976i | −0.756379 | − | 0.654134i | \(-0.773033\pi\) |
0.188308 | + | 0.982110i | \(0.439700\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.83986 | − | 5.10369i | 1.09645 | − | 0.633035i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.95521 | − | 5.11857i | 0.361036 | − | 0.625332i | −0.627096 | − | 0.778942i | \(-0.715757\pi\) |
0.988132 | + | 0.153610i | \(0.0490899\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.70486 | + | 12.6886i | 1.04794 | + | 1.52752i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4308i | 1.35658i | 0.734792 | + | 0.678292i | \(0.237280\pi\) | ||||
−0.734792 | + | 0.678292i | \(0.762720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.99239i | 0.818397i | 0.912445 | + | 0.409199i | \(0.134192\pi\) | ||||
−0.912445 | + | 0.409199i | \(0.865808\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.290159 | − | 3.72699i | −0.0335046 | − | 0.430356i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.603968 | − | 1.04610i | −0.0679517 | − | 0.117696i | 0.830048 | − | 0.557692i | \(-0.188313\pi\) |
−0.898000 | + | 0.439996i | \(0.854980\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.90088 | + | 8.79697i | −0.211209 | + | 0.977441i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.181350 | − | 0.314108i | −0.0199058 | − | 0.0344779i | 0.855901 | − | 0.517140i | \(-0.173003\pi\) |
−0.875807 | + | 0.482662i | \(0.839670\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.339244 | + | 0.587588i | −0.0367962 | + | 0.0637329i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.2705 | − | 0.955298i | 1.31553 | − | 0.102419i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.77052 | −0.293674 | −0.146837 | − | 0.989161i | \(-0.546909\pi\) | ||||
−0.146837 | + | 0.989161i | \(0.546909\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.16090 | + | 8.98038i | 0.638856 | + | 0.931222i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.245471 | − | 0.141723i | −0.0251848 | − | 0.0145405i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.508914 | − | 0.293821i | 0.0516723 | − | 0.0298330i | −0.473941 | − | 0.880556i | \(-0.657169\pi\) |
0.525614 | + | 0.850723i | \(0.323836\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.9309 | − | 4.21713i | −1.09859 | − | 0.423837i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.92329 | − | 11.9915i | −0.688893 | − | 1.19320i | −0.972196 | − | 0.234167i | \(-0.924764\pi\) |
0.283303 | − | 0.959030i | \(-0.408570\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.4610 | + | 6.03967i | 1.03075 | + | 0.595106i | 0.917201 | − | 0.398425i | \(-0.130443\pi\) |
0.113554 | + | 0.993532i | \(0.463777\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.3942i | 1.77824i | 0.457678 | + | 0.889118i | \(0.348681\pi\) | ||||
−0.457678 | + | 0.889118i | \(0.651319\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0207 | 1.05559 | 0.527796 | − | 0.849371i | \(-0.323018\pi\) | ||||
0.527796 | + | 0.849371i | \(0.323018\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.79051 | + | 4.67997i | 0.929274 | + | 0.444203i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.36811 | − | 4.25398i | −0.693133 | − | 0.400181i | 0.111652 | − | 0.993747i | \(-0.464386\pi\) |
−0.804785 | + | 0.593567i | \(0.797719\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.9696 | + | 7.48801i | −1.20942 | + | 0.698260i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.81144 | + | 17.9466i | 0.259918 | + | 1.65916i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.12600 | − | 3.68234i | 0.193273 | − | 0.334758i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.70487 | − | 3.22773i | 0.424224 | − | 0.291035i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0670 | 1.07930 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6312 | −0.943365 | −0.471682 | − | 0.881769i | \(-0.656353\pi\) | ||||
−0.471682 | + | 0.881769i | \(0.656353\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.485255 | − | 6.23293i | −0.0427243 | − | 0.548779i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.16740 | + | 5.48610i | −0.276737 | + | 0.479322i | −0.970572 | − | 0.240812i | \(-0.922586\pi\) |
0.693835 | + | 0.720134i | \(0.255920\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.39232 | − | 2.50903i | −0.722296 | − | 0.215942i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.4158 | + | 8.32296i | −1.23162 | + | 0.711078i | −0.967368 | − | 0.253375i | \(-0.918459\pi\) |
−0.264255 | + | 0.964453i | \(0.585126\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.24007 | − | 2.44800i | −0.359638 | − | 0.207637i | 0.309284 | − | 0.950970i | \(-0.399911\pi\) |
−0.668922 | + | 0.743333i | \(0.733244\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.17898 | − | 15.1437i | −0.0992884 | − | 1.27533i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.6477 | −1.97752 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.9785i | 0.994761i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.57864 | + | 2.64348i | 0.375097 | + | 0.216562i | 0.675683 | − | 0.737192i | \(-0.263849\pi\) |
−0.300586 | + | 0.953755i | \(0.597182\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.29163 | + | 12.6295i | 0.593385 | + | 1.02777i | 0.993773 | + | 0.111427i | \(0.0355421\pi\) |
−0.400388 | + | 0.916346i | \(0.631125\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.758298 | − | 0.939655i | −0.0613047 | − | 0.0759666i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.17930 | + | 5.29967i | −0.737299 | + | 0.425680i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.4160 | + | 8.90044i | 1.23033 | + | 0.710332i | 0.967099 | − | 0.254400i | \(-0.0818781\pi\) |
0.263232 | + | 0.964732i | \(0.415211\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.26639 | − | 8.92529i | 0.338346 | − | 0.707822i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.0964456 | −0.00755420 | −0.00377710 | − | 0.999993i | \(-0.501202\pi\) | ||||
−0.00377710 | + | 0.999993i | \(0.501202\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.91774 | − | 10.2879i | 0.382845 | − | 0.800913i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.47872 | + | 4.29327i | −0.191809 | + | 0.332224i | −0.945850 | − | 0.324604i | \(-0.894769\pi\) |
0.754041 | + | 0.656828i | \(0.228102\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8324 | + | 20.4943i | 0.910185 | + | 1.57649i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.392551 | − | 0.316787i | 0.0300191 | − | 0.0242253i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.40033 | − | 12.8177i | −0.562637 | − | 0.974515i | −0.997265 | − | 0.0739055i | \(-0.976454\pi\) |
0.434629 | − | 0.900610i | \(-0.356880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.43181 | + | 4.41248i | −0.483444 | + | 0.331662i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 0.684450i | − | 0.0511582i | −0.999673 | − | 0.0255791i | \(-0.991857\pi\) | ||
0.999673 | − | 0.0255791i | \(-0.00814297\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.84745i | − | 0.583297i | −0.956526 | − | 0.291648i | \(-0.905796\pi\) | ||
0.956526 | − | 0.291648i | \(-0.0942037\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.84678 | − | 0.688752i | 0.653973 | − | 0.0509140i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.28070 | + | 9.14644i | −0.388245 | + | 0.672459i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.36128 | − | 0.785934i | 0.0995464 | − | 0.0574732i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9694 | − | 9.79729i | 1.22786 | − | 0.708907i | 0.261281 | − | 0.965263i | \(-0.415855\pi\) |
0.966582 | + | 0.256356i | \(0.0825219\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.18116 | + | 15.9022i | −0.660875 | + | 1.14467i | 0.319512 | + | 0.947582i | \(0.396481\pi\) |
−0.980386 | + | 0.197086i | \(0.936852\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −17.6264 | + | 1.37227i | −1.26225 | + | 0.0982705i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.92313i | 0.422006i | 0.977485 | + | 0.211003i | \(0.0676730\pi\) | ||||
−0.977485 | + | 0.211003i | \(0.932327\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.7348i | 1.11541i | 0.830039 | + | 0.557706i | \(0.188318\pi\) | ||||
−0.830039 | + | 0.557706i | \(0.811682\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.44157 | + | 5.79126i | −0.595423 | + | 0.408484i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.77653 | + | 4.80909i | 0.193921 | + | 0.335881i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.12487 | − | 26.3307i | −0.286699 | − | 1.83011i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.328332 | + | 0.568688i | 0.0227112 | + | 0.0393370i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.06619 | − | 8.77489i | 0.348771 | − | 0.604088i | −0.637261 | − | 0.770648i | \(-0.719933\pi\) |
0.986031 | + | 0.166560i | \(0.0532659\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.53862 | − | 17.8628i | 0.585057 | − | 1.22394i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.08462 | 0.414968 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.22321 | − | 10.9270i | 0.352952 | − | 0.738376i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.11061 | − | 1.21856i | −0.141975 | − | 0.0819693i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.3944 | + | 7.73325i | −0.896955 | + | 0.517857i | −0.876211 | − | 0.481928i | \(-0.839937\pi\) |
−0.0207437 | + | 0.999785i | \(0.506603\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.33058 | + | 6.04089i | −0.155372 | + | 0.402726i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.0360 | − | 24.3110i | −0.931600 | − | 1.61358i | −0.780588 | − | 0.625046i | \(-0.785080\pi\) |
−0.151011 | − | 0.988532i | \(-0.548253\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.7453 | − | 8.51319i | −0.974396 | − | 0.562568i | −0.0738222 | − | 0.997271i | \(-0.523520\pi\) |
−0.900573 | + | 0.434704i | \(0.856853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.4769i | − | 1.21047i | −0.796049 | − | 0.605233i | \(-0.793080\pi\) | ||
0.796049 | − | 0.605233i | \(-0.206920\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.7833 | 0.964358 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.162394 | + | 2.08590i | 0.0105486 | + | 0.135493i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.06656 | − | 3.50253i | −0.392413 | − | 0.226560i | 0.290792 | − | 0.956786i | \(-0.406081\pi\) |
−0.683205 | + | 0.730226i | \(0.739415\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.38459 | − | 3.10879i | 0.346852 | − | 0.200255i | −0.316446 | − | 0.948611i | \(-0.602490\pi\) |
0.663298 | + | 0.748355i | \(0.269156\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.54170 | − | 12.3270i | 0.612101 | − | 0.790780i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.509067 | − | 0.881730i | 0.0323912 | − | 0.0561031i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.0487612 | + | 0.626321i | 0.00309012 | + | 0.0396915i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.81844 | −0.619734 | −0.309867 | − | 0.950780i | \(-0.600285\pi\) | ||||
−0.309867 | + | 0.950780i | \(0.600285\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.6952 | 2.18127 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.969055 | − | 0.664810i | 0.0606846 | − | 0.0416320i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.667904 | − | 1.15684i | 0.0416627 | − | 0.0721619i | −0.844442 | − | 0.535647i | \(-0.820068\pi\) |
0.886105 | + | 0.463485i | \(0.153401\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.8886 | − | 7.67302i | −1.23107 | − | 0.474948i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.6238 | + | 10.1751i | −1.08673 | + | 0.627424i | −0.932704 | − | 0.360643i | \(-0.882557\pi\) |
−0.154026 | + | 0.988067i | \(0.549224\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.33814 | + | 4.81402i | 0.512208 | + | 0.295723i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.32947 | + | 2.06954i | 0.264959 | + | 0.126654i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.7228 | 1.62932 | 0.814659 | − | 0.579940i | \(-0.196924\pi\) | ||||
0.814659 | + | 0.579940i | \(0.196924\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.34764i | 0.264100i | 0.991243 | + | 0.132050i | \(0.0421560\pi\) | ||||
−0.991243 | + | 0.132050i | \(0.957844\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.29968 | − | 4.21447i | −0.440187 | − | 0.254142i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.19901 | + | 3.80880i | 0.132126 | + | 0.228849i | 0.924496 | − | 0.381192i | \(-0.124486\pi\) |
−0.792370 | + | 0.610041i | \(0.791153\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.91940 | − | 18.6357i | −0.174780 | − | 1.11569i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.62273 | − | 2.66893i | 0.275769 | − | 0.159215i | −0.355738 | − | 0.934586i | \(-0.615770\pi\) |
0.631506 | + | 0.775371i | \(0.282437\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5431 | + | 8.97381i | 0.923941 | + | 0.533437i | 0.884890 | − | 0.465800i | \(-0.154233\pi\) |
0.0390505 | + | 0.999237i | \(0.487567\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.277732 | + | 0.404833i | 0.0164514 | + | 0.0239802i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8380 | −0.990471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.01476 | + | 0.0790022i | −0.0594861 | + | 0.00463119i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.1126 | − | 22.7117i | 0.766048 | − | 1.32683i | −0.173642 | − | 0.984809i | \(-0.555554\pi\) |
0.939691 | − | 0.342026i | \(-0.111113\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.79566 | − | 6.57428i | −0.220992 | − | 0.382769i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.9315 | + | 14.7553i | 0.808386 | + | 0.856188i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −26.8968 | − | 46.5867i | −1.55548 | − | 2.69418i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.86152 | + | 23.9106i | 0.106942 | + | 1.37363i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.63628i | 0.494512i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.19520i | − | 0.410652i | −0.978694 | − | 0.205326i | \(-0.934175\pi\) | ||
0.978694 | − | 0.205326i | \(-0.0658254\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.8358 | − | 17.2524i | −0.673317 | − | 0.981454i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.08721 | − | 1.88311i | 0.0616503 | − | 0.106781i | −0.833553 | − | 0.552440i | \(-0.813697\pi\) |
0.895203 | + | 0.445658i | \(0.147030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.2870 | − | 5.93922i | 0.581457 | − | 0.335704i | −0.180255 | − | 0.983620i | \(-0.557692\pi\) |
0.761712 | + | 0.647916i | \(0.224359\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.09969 | + | 4.09901i | −0.398758 | + | 0.230223i | −0.685948 | − | 0.727651i | \(-0.740612\pi\) |
0.287190 | + | 0.957874i | \(0.407279\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.8754 | − | 24.0329i | 0.776875 | − | 1.34559i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.7402 | − | 28.7445i | 0.766903 | − | 1.60436i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0676757i | 0.00376558i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.0688i | 0.724924i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.2220 | − | 8.23231i | −0.952379 | − | 0.455248i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.58540 | − | 14.8704i | −0.471897 | − | 0.817349i | 0.527586 | − | 0.849501i | \(-0.323097\pi\) |
−0.999483 | + | 0.0321526i | \(0.989764\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.8037 | − | 14.6267i | −0.646839 | − | 0.801540i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.98170 | − | 8.62856i | −0.272179 | − | 0.471428i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.95399 | − | 6.84850i | 0.215387 | − | 0.373062i | −0.738005 | − | 0.674795i | \(-0.764232\pi\) |
0.953392 | + | 0.301733i | \(0.0975653\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.33644 | + | 12.1515i | 0.452773 | + | 0.659981i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.5557 | 1.32977 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 25.8610 | − | 2.01336i | 1.39231 | − | 0.108396i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.443850 | + | 0.256257i | 0.0238271 | + | 0.0137566i | 0.511866 | − | 0.859065i | \(-0.328954\pi\) |
−0.488039 | + | 0.872822i | \(0.662288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.74612 | + | 3.31752i | −0.307583 | + | 0.177583i | −0.645844 | − | 0.763469i | \(-0.723494\pi\) |
0.338262 | + | 0.941052i | \(0.390161\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.01239 | − | 30.1451i | 0.481046 | − | 1.60903i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.03437 | − | 15.6480i | −0.480851 | − | 0.832858i | 0.518908 | − | 0.854830i | \(-0.326339\pi\) |
−0.999759 | + | 0.0219721i | \(0.993006\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.6877 | + | 9.63465i | 0.885691 | + | 0.511354i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 1.76296i | − | 0.0930453i | −0.998917 | − | 0.0465227i | \(-0.985186\pi\) | ||
0.998917 | − | 0.0465227i | \(-0.0148140\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9717 | 0.998512 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.07294 | + | 4.16628i | −0.318747 | + | 0.218673i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.2081 | + | 5.89367i | 0.534318 | + | 0.308489i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.9614 | + | 16.7209i | −1.51177 | + | 0.872822i | −0.511867 | + | 0.859065i | \(0.671046\pi\) |
−0.999905 | + | 0.0137576i | \(0.995621\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.76335 | + | 1.52949i | −0.508260 | + | 0.0796221i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.7844 | + | 22.1433i | −0.661952 | + | 1.14653i | 0.318150 | + | 0.948040i | \(0.396938\pi\) |
−0.980102 | + | 0.198494i | \(0.936395\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.8570 | − | 9.01386i | −0.973773 | − | 0.465474i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −43.0267 | −2.21599 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.7920 | 1.32485 | 0.662423 | − | 0.749130i | \(-0.269528\pi\) | ||||
0.662423 | + | 0.749130i | \(0.269528\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.6133 | + | 7.94133i | 0.851124 | + | 0.406847i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.4158 | + | 28.4330i | −0.838808 | + | 1.45286i | 0.0520838 | + | 0.998643i | \(0.483414\pi\) |
−0.890892 | + | 0.454215i | \(0.849920\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.89760 | + | 10.1026i | −0.198126 | + | 0.513546i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.4542 | − | 10.0772i | 0.884965 | − | 0.510935i | 0.0126730 | − | 0.999920i | \(-0.495966\pi\) |
0.872292 | + | 0.488985i | \(0.162633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.09663 | + | 1.78784i | 0.156603 | + | 0.0904150i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.04771 | − | 6.20709i | 0.456396 | − | 0.313106i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.03626 | −0.102456 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 34.8864i | − | 1.75090i | −0.483311 | − | 0.875449i | \(-0.660566\pi\) | ||
0.483311 | − | 0.875449i | \(-0.339434\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.36793 | − | 4.83122i | −0.417874 | − | 0.241260i | 0.276293 | − | 0.961073i | \(-0.410894\pi\) |
−0.694167 | + | 0.719814i | \(0.744227\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.0364 | − | 32.9719i | −0.948268 | − | 1.64245i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.2404 | + | 10.1898i | 0.558541 | + | 0.506334i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.1897 | − | 12.2339i | 1.05034 | − | 0.606412i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.1202 | − | 18.5446i | −1.58824 | − | 0.916973i | −0.993597 | − | 0.112986i | \(-0.963958\pi\) |
−0.594647 | − | 0.803987i | \(-0.702708\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.7446 | − | 2.23786i | 1.41787 | − | 0.110386i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.611419 | −0.0300134 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.79731 | + | 6.99275i | 0.234925 | + | 0.342436i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.84193 | + | 3.19031i | −0.0899841 | + | 0.155857i | −0.907504 | − | 0.420043i | \(-0.862015\pi\) |
0.817520 | + | 0.575900i | \(0.195348\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.55139 | − | 14.8114i | −0.416769 | − | 0.721866i | 0.578843 | − | 0.815439i | \(-0.303504\pi\) |
−0.995612 | + | 0.0935732i | \(0.970171\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.46969 | + | 24.5456i | −0.460432 | + | 1.19345i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.434342 | − | 0.752303i | −0.0210687 | − | 0.0364921i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 36.9541 | + | 17.6644i | 1.78416 | + | 0.852847i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.5512i | 1.51977i | 0.650058 | + | 0.759885i | \(0.274745\pi\) | ||||
−0.650058 | + | 0.759885i | \(0.725255\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.0692i | − | 0.483893i | −0.970290 | − | 0.241947i | \(-0.922214\pi\) | ||
0.970290 | − | 0.241947i | \(-0.0777859\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.94777 | − | 18.7188i | 0.429013 | − | 0.897496i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.746890 | + | 1.29365i | −0.0357286 | + | 0.0618837i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.1966 | + | 13.9699i | −1.15484 | + | 0.666748i | −0.950062 | − | 0.312060i | \(-0.898981\pi\) |
−0.204779 | + | 0.978808i | \(0.565648\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.1930 | − | 17.4319i | 1.43451 | − | 0.828215i | 0.437050 | − | 0.899437i | \(-0.356023\pi\) |
0.997460 | + | 0.0712223i | \(0.0226900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.33518 | + | 4.04466i | −0.110698 | + | 0.191735i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.18038 | − | 7.55113i | −0.245023 | − | 0.357156i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.2411i | 1.09682i | 0.836211 | + | 0.548408i | \(0.184766\pi\) | ||||
−0.836211 | + | 0.548408i | \(0.815234\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 12.8649i | − | 0.605783i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.96056 | − | 25.1828i | −0.0921153 | − | 1.18319i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.10938 | + | 5.38560i | 0.145451 | + | 0.251928i | 0.929541 | − | 0.368719i | \(-0.120203\pi\) |
−0.784090 | + | 0.620647i | \(0.786870\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.483079 | + | 2.03483i | 0.0225482 | + | 0.0949777i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.17165 | + | 3.76140i | 0.101144 | + | 0.175186i | 0.912156 | − | 0.409843i | \(-0.134416\pi\) |
−0.811012 | + | 0.585029i | \(0.801083\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.57451 | − | 6.19124i | 0.166122 | − | 0.287731i | −0.770931 | − | 0.636918i | \(-0.780209\pi\) |
0.937053 | + | 0.349187i | \(0.113542\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.3032 | − | 1.42497i | 0.848791 | − | 0.0660813i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.88890 | 0.0874080 | 0.0437040 | − | 0.999045i | \(-0.486084\pi\) | ||||
0.0437040 | + | 0.999045i | \(0.486084\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.4420 | − | 25.4242i | −0.803686 | − | 1.17148i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.2078 | − | 7.04818i | −0.561316 | − | 0.324076i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.314283 | − | 0.181451i | 0.0144203 | − | 0.00832555i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.3341 | + | 10.7606i | −0.610527 | + | 0.492693i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.22491 | + | 9.04981i | 0.238732 | + | 0.413497i | 0.960351 | − | 0.278794i | \(-0.0899348\pi\) |
−0.721618 | + | 0.692291i | \(0.756601\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.8539 | − | 18.9682i | −1.49801 | − | 0.864875i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 0.990611i | − | 0.0449813i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.6596 | 1.07212 | 0.536060 | − | 0.844180i | \(-0.319912\pi\) | ||||
0.536060 | + | 0.844180i | \(0.319912\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.150715 | + | 0.0720434i | 0.00681557 | + | 0.00325792i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.6767 | − | 6.74152i | −0.526960 | − | 0.304241i | 0.212817 | − | 0.977092i | \(-0.431736\pi\) |
−0.739778 | + | 0.672851i | \(0.765069\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.47683 | − | 1.43000i | 0.111551 | − | 0.0644039i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.3698 | + | 12.4034i | −0.690823 | + | 0.557491i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.04035 | − | 10.4622i | 0.270403 | − | 0.468352i | −0.698562 | − | 0.715550i | \(-0.746176\pi\) |
0.968965 | + | 0.247197i | \(0.0795096\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.08050 | − | 4.85751i | 0.316333 | − | 0.217017i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.5283 | −0.915310 | −0.457655 | − | 0.889130i | \(-0.651310\pi\) | ||||
−0.457655 | + | 0.889130i | \(0.651310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.3417 | −1.03869 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.18148 | − | 40.8650i | −0.141294 | − | 1.81488i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.09043 | + | 7.08483i | −0.181305 | + | 0.314029i | −0.942325 | − | 0.334699i | \(-0.891365\pi\) |
0.761020 | + | 0.648728i | \(0.224699\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.850073 | + | 0.201812i | −0.0375316 | + | 0.00891020i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.6345 | − | 10.1813i | 0.777070 | − | 0.448642i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.6603 | − | 17.1244i | −1.30446 | − | 0.753131i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.98979 | + | 25.5582i | 0.0873421 | + | 1.12188i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.7491 | 1.21571 | 0.607856 | − | 0.794048i | \(-0.292030\pi\) | ||||
0.607856 | + | 0.794048i | \(0.292030\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.9604i | 1.00399i | 0.864872 | + | 0.501993i | \(0.167400\pi\) | ||||
−0.864872 | + | 0.501993i | \(0.832600\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.19166 | + | 1.26535i | 0.0954700 | + | 0.0551196i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.9623 | + | 48.4322i | 1.21575 | + | 2.10575i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.3470 | − | 2.09089i | 0.579211 | − | 0.0907370i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.2742 | + | 9.97325i | −0.748228 | + | 0.431990i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.8536 | + | 15.5039i | 1.16098 | + | 0.670292i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.511274 | + | 1.06959i | −0.0220631 | + | 0.0461561i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.20810 | 0.223914 | 0.111957 | − | 0.993713i | \(-0.464288\pi\) | ||||
0.111957 | + | 0.993713i | \(0.464288\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.86193 | + | 12.2632i | −0.251559 | + | 0.526263i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.28902 | − | 16.0890i | 0.397898 | − | 0.689179i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6224 | + | 18.3985i | 0.454181 | + | 0.786664i | 0.998641 | − | 0.0521229i | \(-0.0165988\pi\) |
−0.544460 | + | 0.838787i | \(0.683265\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.3393 | − | 5.53210i | −0.611987 | − | 0.236104i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.597397 | + | 1.03472i | 0.0254500 | + | 0.0440807i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.0844 | − | 10.3485i | 0.640296 | − | 0.439269i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.8109i | 0.542813i | 0.962465 | + | 0.271407i | \(0.0874888\pi\) | ||||
−0.962465 | + | 0.271407i | \(0.912511\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.8559i | 0.924406i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.71434 | + | 0.211321i | −0.114600 | + | 0.00892197i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.7396 | + | 32.4580i | −0.789781 | + | 1.36794i | 0.136319 | + | 0.990665i | \(0.456473\pi\) |
−0.926101 | + | 0.377277i | \(0.876861\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.4207 | + | 7.17109i | −0.522542 | + | 0.301690i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.94906 | + | 3.43469i | −0.249397 | + | 0.143990i | −0.619488 | − | 0.785006i | \(-0.712660\pi\) |
0.370091 | + | 0.928996i | \(0.379327\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.0847909 | + | 0.146862i | −0.00354839 | + | 0.00614599i | −0.867794 | − | 0.496924i | \(-0.834463\pi\) |
0.864246 | + | 0.503070i | \(0.167796\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −33.8364 | + | 2.63428i | −1.41354 | + | 0.110049i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 19.1741i | − | 0.799617i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.24916i | 0.260156i | 0.991504 | + | 0.130078i | \(0.0415228\pi\) | ||||
−0.991504 | + | 0.130078i | \(0.958477\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.2261 | − | 17.9921i | 1.08992 | − | 0.747728i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.1527 | − | 19.3171i | −0.461900 | − | 0.800033i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 28.5697 | + | 11.0222i | 1.18121 | + | 0.455712i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.7881 | + | 18.6855i | 0.445273 | + | 0.771235i | 0.998071 | − | 0.0620801i | \(-0.0197734\pi\) |
−0.552799 | + | 0.833315i | \(0.686440\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.528615 | + | 0.915588i | −0.0217812 | + | 0.0377261i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.42449 | − | 9.25605i | 0.181999 | − | 0.380743i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.26071 | −0.339227 | −0.169613 | − | 0.985511i | \(-0.554252\pi\) | ||||
−0.169613 | + | 0.985511i | \(0.554252\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.7537 | − | 24.5887i | 0.481046 | − | 1.00635i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.7618 | − | 17.7603i | −1.25689 | − | 0.725667i | −0.284422 | − | 0.958699i | \(-0.591802\pi\) |
−0.972469 | + | 0.233033i | \(0.925135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.8981 | − | 20.7258i | 1.46432 | − | 0.845423i | 0.465109 | − | 0.885254i | \(-0.346015\pi\) |
0.999206 | + | 0.0398308i | \(0.0126819\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.5176 | − | 2.74424i | 0.713371 | − | 0.111754i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.58388 | − | 6.20746i | −0.145705 | − | 0.252369i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.09569 | − | 1.20995i | −0.0850616 | − | 0.0491103i | 0.456866 | − | 0.889536i | \(-0.348972\pi\) |
−0.541927 | + | 0.840425i | \(0.682305\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 53.1015i | 2.14826i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.6456 | −1.72244 | −0.861219 | − | 0.508234i | \(-0.830298\pi\) | ||||
−0.861219 | + | 0.508234i | \(0.830298\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.746549 | − | 9.58916i | −0.0301038 | − | 0.386672i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.2535 | + | 7.65193i | 0.533567 | + | 0.308055i | 0.742468 | − | 0.669882i | \(-0.233655\pi\) |
−0.208901 | + | 0.977937i | \(0.566989\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.9177 | − | 13.8089i | 0.961334 | − | 0.555026i | 0.0647505 | − | 0.997901i | \(-0.479375\pi\) |
0.896583 | + | 0.442875i | \(0.146042\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.2227 | + | 44.2281i | −0.530610 | + | 1.77481i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.77517 | − | 8.27084i | 0.191007 | − | 0.330834i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0882815 | − | 1.13395i | −0.00352562 | − | 0.0452854i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.52164 | 0.100545 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.28775 | 0.329930 | 0.164965 | − | 0.986299i | \(-0.447249\pi\) | ||||
0.164965 | + | 0.986299i | \(0.447249\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.4716 | + | 9.92811i | −0.575195 | + | 0.394607i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.96069 | + | 15.5204i | −0.355594 | + | 0.615907i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −26.6865 | + | 21.5359i | −1.05570 | + | 0.851947i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.58307 | − | 4.95544i | 0.339011 | − | 0.195728i | −0.320824 | − | 0.947139i | \(-0.603960\pi\) |
0.659835 | + | 0.751411i | \(0.270626\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.83668 | + | 3.94716i | 0.269612 | + | 0.155661i | 0.628711 | − | 0.777639i | \(-0.283583\pi\) |
−0.359099 | + | 0.933299i | \(0.616916\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.50841 | − | 4.54512i | −0.374393 | − | 0.178964i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.31931 | −0.169810 | −0.0849049 | − | 0.996389i | \(-0.527059\pi\) | ||||
−0.0849049 | + | 0.996389i | \(0.527059\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.5870i | 0.690349i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.5853 | − | 21.6999i | −1.47082 | − | 0.849181i | −0.471361 | − | 0.881940i | \(-0.656237\pi\) |
−0.999463 | + | 0.0327591i | \(0.989571\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.33940 | + | 9.24812i | 0.208628 | + | 0.361354i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.3246 | + | 13.1739i | −0.636882 | + | 0.513961i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.34894 | + | 5.39761i | −0.364183 | + | 0.210261i | −0.670914 | − | 0.741535i | \(-0.734098\pi\) |
0.306731 | + | 0.951796i | \(0.400765\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.39495 | − | 1.96008i | −0.132048 | − | 0.0762381i | 0.432521 | − | 0.901624i | \(-0.357624\pi\) |
−0.564569 | + | 0.825386i | \(0.690958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.38799 | + | 3.48083i | 0.0927419 | + | 0.135184i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 63.1276 | 2.44431 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.7080 | − | 2.07931i | 1.03259 | − | 0.0803906i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.0039 | − | 17.3273i | 0.386197 | − | 0.668913i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.3404 | − | 21.3742i | −0.475687 | − | 0.823915i | 0.523925 | − | 0.851765i | \(-0.324467\pi\) |
−0.999612 | + | 0.0278497i | \(0.991134\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.15443 | − | 7.69916i | 0.313864 | − | 0.296341i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.36327 | + | 12.7536i | 0.282994 | + | 0.490159i | 0.972121 | − | 0.234481i | \(-0.0753392\pi\) |
−0.689127 | + | 0.724641i | \(0.742006\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.77397 | + | 48.4753i | 0.144619 | + | 1.85758i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.84900i | 0.0707499i | 0.999374 | + | 0.0353750i | \(0.0112625\pi\) | ||||
−0.999374 | + | 0.0353750i | \(0.988737\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.0606i | 1.07214i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.6831 | + | 24.3180i | 0.636502 | + | 0.927790i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.2919 | + | 29.9505i | −0.658769 | + | 1.14102i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.7613 | − | 19.4921i | 1.28434 | − | 0.741514i | 0.306701 | − | 0.951806i | \(-0.400775\pi\) |
0.977639 | + | 0.210292i | \(0.0674415\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.14764 | + | 4.12669i | −0.271126 | + | 0.156534i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.662926 | − | 1.14822i | 0.0251101 | − | 0.0434920i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.8020 | + | 28.8738i | −0.522040 | + | 1.09211i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 25.4389i | − | 0.960813i | −0.877046 | − | 0.480406i | \(-0.840489\pi\) | ||
0.877046 | − | 0.480406i | \(-0.159511\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.05344i | 0.0397314i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23.1018 | − | 11.0429i | −0.870065 | − | 0.415900i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.14517 | + | 12.3758i | 0.268342 | + | 0.464783i | 0.968434 | − | 0.249270i | \(-0.0801908\pi\) |
−0.700092 | + | 0.714053i | \(0.746857\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.30436 | − | 3.38092i | 0.0489173 | − | 0.126794i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.9296 | + | 48.3756i | 1.04597 | + | 1.81168i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.9319 | + | 34.5230i | −0.745410 | + | 1.29109i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.86384 | + | 10.0050i | 0.256335 | + | 0.373644i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.4688 | 1.24818 | 0.624088 | − | 0.781354i | \(-0.285471\pi\) | ||||
0.624088 | + | 0.781354i | \(0.285471\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.7367 | + | 0.835888i | −0.399302 | + | 0.0310870i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.2817 | − | 7.66819i | −0.493269 | − | 0.284789i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.1354 | − | 7.00636i | 0.450076 | − | 0.259851i | −0.257786 | − | 0.966202i | \(-0.582993\pi\) |
0.707862 | + | 0.706350i | \(0.249660\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.1189 | + | 12.1359i | −0.893292 | + | 0.449477i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.726384 | − | 1.25813i | −0.0268663 | − | 0.0465338i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.6491 | + | 13.6538i | 0.873501 | + | 0.504316i | 0.868510 | − | 0.495672i | \(-0.165078\pi\) |
0.00499085 | + | 0.999988i | \(0.498411\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.0824i | 0.850251i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −52.6314 | −1.93608 | −0.968039 | − | 0.250801i | \(-0.919306\pi\) | ||||
−0.968039 | + | 0.250801i | \(0.919306\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.45416 | + | 0.997609i | −0.0534197 | + | 0.0366481i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.9523 | − | 17.8703i | −1.13553 | − | 0.655599i | −0.190211 | − | 0.981743i | \(-0.560917\pi\) |
−0.945320 | + | 0.326144i | \(0.894250\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.71839 | − | 4.45621i | 0.282780 | − | 0.163263i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.391654 | − | 1.01517i | 0.0143299 | − | 0.0371432i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.5641 | − | 28.6899i | 0.604433 | − | 1.04691i | −0.387708 | − | 0.921782i | \(-0.626733\pi\) |
0.992141 | − | 0.125126i | \(-0.0399336\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.3432 | + | 7.33423i | 0.559138 | + | 0.267274i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.5836 | 0.894687 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.6903 | −0.497584 | −0.248792 | − | 0.968557i | \(-0.580034\pi\) | ||||
−0.248792 | + | 0.968557i | \(0.580034\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −54.2180 | − | 25.9168i | −1.96799 | − | 0.940721i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.51737 | − | 11.2884i | 0.236255 | − | 0.409205i | −0.723382 | − | 0.690448i | \(-0.757413\pi\) |
0.959637 | + | 0.281243i | \(0.0907467\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.01094 | + | 0.315026i | −0.0727057 | + | 0.0113898i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.6147 | − | 13.6340i | 0.852678 | − | 0.492294i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.4866 | − | 10.6732i | −0.666642 | − | 0.384886i | 0.128161 | − | 0.991753i | \(-0.459093\pi\) |
−0.794803 | + | 0.606867i | \(0.792426\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.90788 | + | 1.30888i | −0.0687104 | + | 0.0471381i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.4788 | 0.412864 | 0.206432 | − | 0.978461i | \(-0.433815\pi\) | ||||
0.206432 | + | 0.978461i | \(0.433815\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 13.5706i | − | 0.487470i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.479682 | + | 0.276944i | 0.0171864 | + | 0.00992256i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.3208 | − | 38.6607i | −0.798701 | − | 1.38339i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 25.3482 | + | 26.8471i | 0.905870 | + | 0.959436i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.9873 | − | 15.0038i | 0.927528 | − | 0.535509i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.6808 | − | 20.6003i | −1.27188 | − | 0.734322i | −0.296541 | − | 0.955020i | \(-0.595833\pi\) |
−0.975342 | + | 0.220698i | \(0.929166\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 35.1413 | − | 2.73587i | 1.25106 | − | 0.0973994i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.0214 | −1.10160 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.43395 | − | 13.7513i | −0.334588 | − | 0.487709i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.0066 | − | 43.3127i | 0.885779 | − | 1.53421i | 0.0409600 | − | 0.999161i | \(-0.486958\pi\) |
0.844819 | − | 0.535053i | \(-0.179708\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.76484 | − | 3.05679i | −0.0624355 | − | 0.108141i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.21973 | − | 6.46810i | −0.184430 | − | 0.228539i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.6540 | − | 23.6494i | −0.481838 | − | 0.834568i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −41.7596 | − | 19.9615i | −1.47001 | − | 0.702679i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 50.6908i | − | 1.78219i | −0.453812 | − | 0.891097i | \(-0.649936\pi\) | ||
0.453812 | − | 0.891097i | \(-0.350064\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.96566i | − | 0.314827i | −0.987533 | − | 0.157413i | \(-0.949684\pi\) | ||
0.987533 | − | 0.157413i | \(-0.0503155\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.24762 | − | 6.79403i | 0.113899 | − | 0.238277i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.0812910 | + | 0.140800i | −0.00284750 | + | 0.00493201i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.525599 | − | 0.303455i | 0.0183884 | − | 0.0106165i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.2190 | − | 16.2922i | 0.984849 | − | 0.568603i | 0.0811184 | − | 0.996704i | \(-0.474151\pi\) |
0.903731 | + | 0.428102i | \(0.140817\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0877 | − | 17.4724i | 0.351636 | − | 0.609051i | −0.634901 | − | 0.772594i | \(-0.718959\pi\) |
0.986536 | + | 0.163543i | \(0.0522923\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.25902 | + | 12.0387i | 0.287542 | + | 0.419133i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 0.253288i | − | 0.00880770i | −0.999990 | − | 0.00440385i | \(-0.998598\pi\) | ||
0.999990 | − | 0.00440385i | \(-0.00140179\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.05416i | 0.245001i | 0.992468 | + | 0.122501i | \(0.0390913\pi\) | ||||
−0.992468 | + | 0.122501i | \(0.960909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.591268 | − | 7.59463i | −0.0205108 | − | 0.263455i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.17848 | + | 7.23733i | 0.144602 | + | 0.250458i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.35845 | + | 31.3026i | −0.323475 | + | 1.08198i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.0936 | − | 29.6069i | −0.590136 | − | 1.02215i | −0.994214 | − | 0.107420i | \(-0.965741\pi\) |
0.404078 | − | 0.914725i | \(-0.367592\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7462 | − | 18.6130i | 0.370558 | − | 0.641826i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.21756 | + | 0.717619i | −0.317470 | + | 0.0247161i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 39.8926 | 1.37235 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.5858 | − | 25.6338i | −0.603543 | − | 0.879749i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48.2024 | + | 27.8296i | 1.65236 | + | 0.953988i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.7586 | + | 12.5623i | −0.745000 | + | 0.430126i | −0.823884 | − | 0.566758i | \(-0.808198\pi\) |
0.0788844 | + | 0.996884i | \(0.474864\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.131606 | − | 0.840092i | −0.00450082 | − | 0.0287305i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.0954 | − | 36.5383i | −0.720604 | − | 1.24812i | −0.960758 | − | 0.277388i | \(-0.910531\pi\) |
0.240154 | − | 0.970735i | \(-0.422802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.08139 | + | 2.35639i | 0.139255 | + | 0.0803990i | 0.568009 | − | 0.823022i | \(-0.307714\pi\) |
−0.428754 | + | 0.903421i | \(0.641047\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.6120i | 1.21225i | 0.795371 | + | 0.606123i | \(0.207276\pi\) | ||||
−0.795371 | + | 0.606123i | \(0.792724\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.9500 | −0.848326 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.3127 | + | 12.5777i | 0.893625 | + | 0.427162i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.08543 | + | 2.35873i | 0.138589 | + | 0.0800143i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.9937 | − | 17.8942i | 1.05018 | − | 0.606322i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.64477 | + | 0.634551i | 0.0556669 | + | 0.0214763i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.4532 | + | 35.4260i | −0.690655 | + | 1.19625i | 0.280969 | + | 0.959717i | \(0.409344\pi\) |
−0.971624 | + | 0.236532i | \(0.923989\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −37.4564 | + | 25.6966i | −1.26337 | + | 0.866724i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.4443 | 1.26153 | 0.630765 | − | 0.775974i | \(-0.282741\pi\) | ||||
0.630765 | + | 0.775974i | \(0.282741\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.8357 | −1.67711 | −0.838553 | − | 0.544821i | \(-0.816598\pi\) | ||||
−0.838553 | + | 0.544821i | \(0.816598\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.02057 | + | 13.1089i | 0.0343061 | + | 0.440650i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.4482 | + | 25.0251i | −0.485124 | + | 0.840260i | −0.999854 | − | 0.0170929i | \(-0.994559\pi\) |
0.514730 | + | 0.857352i | \(0.327892\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.7487 | − | 33.4646i | −0.360094 | − | 1.12111i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.27701 | − | 0.737280i | 0.0427334 | − | 0.0246721i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.999223 | − | 0.576902i | −0.0334003 | − | 0.0192837i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.23198 | + | 92.8922i | 0.241469 | + | 3.10158i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 44.6789 | 1.49012 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.29880i | − | 0.0765841i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.4564 | − | 6.61437i | −0.380825 | − | 0.219869i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.43498 | + | 12.8778i | 0.246874 | + | 0.427599i | 0.962657 | − | 0.270724i | \(-0.0872632\pi\) |
−0.715783 | + | 0.698323i | \(0.753930\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.9519 | − | 38.7555i | 0.495923 | − | 1.28544i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.81616 | − | 4.51266i | 0.258961 | − | 0.149511i | −0.364899 | − | 0.931047i | \(-0.618897\pi\) |
0.623861 | + | 0.781536i | \(0.285563\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.22671 | + | 0.708243i | 0.0405982 | + | 0.0234394i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.45117 | − | 13.4959i | 0.213269 | − | 0.446160i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.4166 | −0.871403 | −0.435702 | − | 0.900091i | \(-0.643500\pi\) | ||||
−0.435702 | + | 0.900091i | \(0.643500\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.37471 | + | 11.2439i | −0.177103 | + | 0.370499i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.6075 | + | 59.9420i | −1.13912 | + | 1.97302i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.76100 | − | 11.7104i | −0.222300 | − | 0.385036i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.60851 | + | 35.8014i | 0.184208 | + | 1.17587i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.1259 | + | 19.2706i | 0.365029 | + | 0.632249i | 0.988781 | − | 0.149373i | \(-0.0477257\pi\) |
−0.623752 | + | 0.781623i | \(0.714392\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.10564 | + | 2.13059i | −0.101674 | + | 0.0697525i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2.64976i | − | 0.0866563i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.6822i | 0.479647i | 0.970817 | + | 0.239823i | \(0.0770896\pi\) | ||||
−0.970817 | + | 0.239823i | \(0.922910\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.5120 | + | 1.59693i | −0.669383 | + | 0.0521137i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.0396 | − | 39.9058i | 0.751070 | − | 1.30089i | −0.196235 | − | 0.980557i | \(-0.562871\pi\) |
0.947305 | − | 0.320334i | \(-0.103795\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.3442 | − | 14.6325i | 0.825322 | − | 0.476500i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.96116 | + | 4.01903i | −0.226207 | + | 0.130601i | −0.608821 | − | 0.793308i | \(-0.708357\pi\) |
0.382614 | + | 0.923908i | \(0.375024\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.1700 | + | 36.6675i | −0.687206 | + | 1.19028i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.1565 | − | 1.10213i | 0.459057 | − | 0.0357392i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.9348i | 1.77951i | 0.456437 | + | 0.889756i | \(0.349125\pi\) | ||||
−0.456437 | + | 0.889756i | \(0.650875\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 33.0313i | − | 1.06887i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −39.6353 | + | 27.1914i | −1.28123 | + | 0.878974i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.26733 | + | 7.39124i | 0.137656 | + | 0.238427i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42.9435 | + | 34.6552i | −1.38383 | + | 1.11675i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.4770 | + | 26.8070i | 0.498223 | + | 0.862948i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.5917 | + | 46.0582i | −0.855132 | + | 1.48113i | 0.0213900 | + | 0.999771i | \(0.493191\pi\) |
−0.876522 | + | 0.481361i | \(0.840143\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0505527 | − | 0.105756i | 0.00162399 | − | 0.00339739i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.2281 | −0.488692 | −0.244346 | − | 0.969688i | \(-0.578573\pi\) | ||||
−0.244346 | + | 0.969688i | \(0.578573\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.76217 | − | 20.4225i | 0.312640 | − | 0.654043i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.49418 | − | 0.862667i | −0.0478031 | − | 0.0275992i | 0.475908 | − | 0.879495i | \(-0.342120\pi\) |
−0.523711 | + | 0.851896i | \(0.675453\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.37033 | − | 5.40997i | 0.299477 | − | 0.172903i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.7633 | + | 25.7292i | 0.662922 | + | 0.821469i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.1191 | + | 52.1679i | 0.960651 | + | 1.66390i | 0.720871 | + | 0.693070i | \(0.243742\pi\) |
0.239780 | + | 0.970827i | \(0.422925\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.64713 | + | 4.99242i | 0.275521 | + | 0.159072i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 32.0664i | − | 1.01965i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.74624 | 0.182535 | 0.0912676 | − | 0.995826i | \(-0.470908\pi\) | ||||
0.0912676 | + | 0.995826i | \(0.470908\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.30843 | + | 29.6510i | 0.0732558 | + | 0.940946i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.9711 | + | 13.2624i | 0.728234 | + | 0.420446i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.0224508 | − | 0.0129620i | 0.000711024 | − | 0.000410510i | −0.499644 | − | 0.866231i | \(-0.666536\pi\) |
0.500355 | + | 0.865820i | \(0.333203\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.51964 | + | 31.6743i | 0.237911 | + | 1.00213i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))