Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,2,Mod(177,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.t (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.5205430369\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.432972864.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{6} + 4x^{5} - 6x^{4} + 8x^{3} + 4x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 177.4 | ||
Root | \(-1.41156 + 0.0865986i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.177 |
Dual form | 1568.2.t.d.753.4 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.61578 | − | 1.51022i | 1.51022 | − | 0.871928i | 0.510295 | − | 0.859999i | \(-0.329536\pi\) |
0.999929 | − | 0.0119288i | \(-0.00379716\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.46890 | − | 0.848071i | −0.656913 | − | 0.379269i | 0.134187 | − | 0.990956i | \(-0.457158\pi\) |
−0.791100 | + | 0.611687i | \(0.790491\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.06155 | − | 5.30277i | 1.02052 | − | 1.76759i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.14688 | + | 0.662153i | −0.345798 | + | 0.199647i | −0.662833 | − | 0.748767i | \(-0.730646\pi\) |
0.317035 | + | 0.948414i | \(0.397313\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.69614i | − | 0.470425i | −0.971944 | − | 0.235212i | \(-0.924421\pi\) | ||
0.971944 | − | 0.235212i | \(-0.0755786\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.12311 | −1.32278 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | − | 1.73205i | −0.242536 | − | 0.420084i | 0.718900 | − | 0.695113i | \(-0.244646\pi\) |
−0.961436 | + | 0.275029i | \(0.911312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.61578 | − | 1.51022i | −0.600102 | − | 0.346469i | 0.168980 | − | 0.985620i | \(-0.445953\pi\) |
−0.769082 | + | 0.639150i | \(0.779286\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.56155 | − | 4.43674i | 0.534121 | − | 0.925124i | −0.465085 | − | 0.885266i | \(-0.653976\pi\) |
0.999205 | − | 0.0398580i | \(-0.0126905\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.06155 | − | 1.83866i | −0.212311 | − | 0.367733i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 9.43318i | − | 1.81542i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.04090i | 1.12177i | 0.827895 | + | 0.560883i | \(0.189538\pi\) | ||||
−0.827895 | + | 0.560883i | \(0.810462\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.12311 | − | 8.87348i | −0.920137 | − | 1.59372i | −0.799201 | − | 0.601064i | \(-0.794744\pi\) |
−0.120936 | − | 0.992660i | \(-0.538589\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00000 | + | 3.46410i | −0.348155 | + | 0.603023i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.23157 | + | 3.02045i | 0.860065 | + | 0.496559i | 0.864034 | − | 0.503434i | \(-0.167930\pi\) |
−0.00396926 | + | 0.999992i | \(0.501263\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.56155 | − | 4.43674i | −0.410177 | − | 0.710447i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24621 | 0.663147 | 0.331573 | − | 0.943429i | \(-0.392421\pi\) | ||||
0.331573 | + | 0.943429i | \(0.392421\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.32431i | − | 0.201955i | −0.994889 | − | 0.100977i | \(-0.967803\pi\) | ||
0.994889 | − | 0.100977i | \(-0.0321970\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.99424 | + | 5.19283i | −1.34078 | + | 0.774101i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.23157 | − | 3.02045i | −0.732566 | − | 0.422947i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.29377 | − | 1.32431i | 0.315073 | − | 0.181908i | −0.334121 | − | 0.942530i | \(-0.608440\pi\) |
0.649194 | + | 0.760623i | \(0.275106\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.24621 | 0.302879 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.12311 | −1.20838 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.322018 | + | 0.185917i | −0.0419231 | + | 0.0242043i | −0.520815 | − | 0.853670i | \(-0.674372\pi\) |
0.478892 | + | 0.877874i | \(0.341039\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.46890 | + | 0.848071i | 0.188074 | + | 0.108584i | 0.591080 | − | 0.806613i | \(-0.298702\pi\) |
−0.403007 | + | 0.915197i | \(0.632035\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.43845 | + | 2.49146i | −0.178417 | + | 0.309028i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.96029 | + | 5.75058i | −1.21684 | + | 0.702545i | −0.964241 | − | 0.265026i | \(-0.914620\pi\) |
−0.252602 | + | 0.967570i | \(0.581286\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 15.4741i | − | 1.86286i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00000 | + | 5.19615i | 0.351123 | + | 0.608164i | 0.986447 | − | 0.164083i | \(-0.0524664\pi\) |
−0.635323 | + | 0.772246i | \(0.719133\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.55359 | − | 3.20636i | −0.641273 | − | 0.370239i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.06155 | − | 8.76687i | −0.562395 | − | 0.974096i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.66906i | − | 0.622260i | −0.950367 | − | 0.311130i | \(-0.899292\pi\) | ||
0.950367 | − | 0.311130i | \(-0.100708\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.39228i | 0.367945i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.12311 | + | 15.8017i | 0.978100 | + | 1.69412i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.12311 | − | 14.0696i | 0.861047 | − | 1.49138i | −0.00987147 | − | 0.999951i | \(-0.503142\pi\) |
0.870919 | − | 0.491427i | \(-0.163524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −26.8019 | − | 15.4741i | −2.77923 | − | 1.60459i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.56155 | + | 4.43674i | 0.262810 | + | 0.455200i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2462 | 1.24341 | 0.621707 | − | 0.783250i | \(-0.286439\pi\) | ||||
0.621707 | + | 0.783250i | \(0.286439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.10887i | 0.814972i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.99424 | − | 5.19283i | 0.894960 | − | 0.516705i | 0.0193984 | − | 0.999812i | \(-0.493825\pi\) |
0.875562 | + | 0.483106i | \(0.160492\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.12311 | − | 1.94528i | 0.110663 | − | 0.191674i | −0.805375 | − | 0.592766i | \(-0.798036\pi\) |
0.916038 | + | 0.401092i | \(0.131369\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.2541 | − | 7.07488i | −1.18464 | − | 0.683955i | −0.227560 | − | 0.973764i | \(-0.573075\pi\) |
−0.957084 | + | 0.289809i | \(0.906408\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.6947 | + | 9.06134i | −1.50328 | + | 0.867919i | −0.503288 | + | 0.864119i | \(0.667876\pi\) |
−0.999993 | + | 0.00380035i | \(0.998790\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.2462 | 1.73185 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.87689 | 0.458780 | 0.229390 | − | 0.973335i | \(-0.426327\pi\) | ||||
0.229390 | + | 0.973335i | \(0.426327\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.52534 | + | 4.34475i | −0.701741 | + | 0.405150i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.99424 | − | 5.19283i | −0.831518 | − | 0.480077i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.62311 | + | 8.00745i | −0.420282 | + | 0.727950i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.1072 | − | 6.41273i | 1.00150 | − | 0.578216i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0818i | 1.08063i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.1231 | −1.16449 | −0.582244 | − | 0.813014i | \(-0.697825\pi\) | ||||
−0.582244 | + | 0.813014i | \(0.697825\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.00000 | − | 3.46410i | −0.176090 | − | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7852 | + | 6.22681i | 0.942303 | + | 0.544039i | 0.890682 | − | 0.454628i | \(-0.150228\pi\) |
0.0516218 | + | 0.998667i | \(0.483561\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.00000 | + | 13.8564i | −0.688530 | + | 1.19257i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.12311 | + | 14.0696i | 0.694004 | + | 1.20205i | 0.970515 | + | 0.241039i | \(0.0774882\pi\) |
−0.276512 | + | 0.961011i | \(0.589178\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.31768i | 0.705496i | 0.935718 | + | 0.352748i | \(0.114753\pi\) | ||||
−0.935718 | + | 0.352748i | \(0.885247\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.12311 | + | 1.94528i | 0.0939188 | + | 0.162672i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.12311 | − | 8.87348i | 0.425451 | − | 0.736902i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.7569 | + | 7.36520i | 1.04509 | + | 0.603381i | 0.921270 | − | 0.388924i | \(-0.127153\pi\) |
0.123817 | + | 0.992305i | \(0.460487\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.43845 | + | 9.41967i | 0.442575 | + | 0.766562i | 0.997880 | − | 0.0650850i | \(-0.0207319\pi\) |
−0.555305 | + | 0.831647i | \(0.687399\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.2462 | −0.990048 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.3790i | 1.39592i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.34451 | + | 4.24035i | −0.586155 | + | 0.338417i | −0.763576 | − | 0.645718i | \(-0.776558\pi\) |
0.177420 | + | 0.984135i | \(0.443225\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.00000 | − | 6.92820i | 0.317221 | − | 0.549442i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.6100 | + | 6.70305i | 0.909367 | + | 0.525023i | 0.880227 | − | 0.474552i | \(-0.157390\pi\) |
0.0291396 | + | 0.999575i | \(0.490723\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.87560 | − | 3.39228i | 0.457415 | − | 0.264089i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.1231 | 0.778700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.0167 | + | 9.24726i | −1.22483 | + | 0.707156i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.5196 | + | 9.53758i | 1.25596 | + | 0.725129i | 0.972287 | − | 0.233792i | \(-0.0751135\pi\) |
0.283673 | + | 0.958921i | \(0.408447\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.561553 | + | 0.972638i | −0.0422089 | + | 0.0731079i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.08469 | + | 2.35829i | −0.305304 | + | 0.176267i | −0.644823 | − | 0.764332i | \(-0.723069\pi\) |
0.339519 | + | 0.940599i | \(0.389736\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.99337i | − | 0.519813i | −0.965634 | − | 0.259906i | \(-0.916308\pi\) | ||
0.965634 | − | 0.259906i | \(-0.0836917\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.12311 | 0.378711 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.12311 | − | 8.87348i | −0.376658 | − | 0.652391i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.29377 | + | 1.32431i | 0.167737 | + | 0.0968429i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | − | 13.8564i | 0.578860 | − | 1.00261i | −0.416751 | − | 0.909021i | \(-0.636831\pi\) |
0.995610 | − | 0.0935936i | \(-0.0298354\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.56155 | + | 9.63289i | 0.400329 | + | 0.693391i | 0.993766 | − | 0.111490i | \(-0.0355624\pi\) |
−0.593436 | + | 0.804881i | \(0.702229\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.68951i | 0.622269i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 21.5150i | − | 1.53288i | −0.642317 | − | 0.766439i | \(-0.722027\pi\) | ||
0.642317 | − | 0.766439i | \(-0.277973\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.12311 | − | 15.8017i | −0.646720 | − | 1.12015i | −0.983901 | − | 0.178712i | \(-0.942807\pi\) |
0.337182 | − | 0.941440i | \(-0.390526\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.3693 | + | 30.0845i | −1.22514 | + | 2.12200i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.23726 | − | 3.60109i | −0.435629 | − | 0.251511i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.6847 | − | 27.1666i | −1.09016 | − | 1.88821i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.71659i | − | 0.324703i | −0.986733 | − | 0.162352i | \(-0.948092\pi\) | ||
0.986733 | − | 0.162352i | \(-0.0519079\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.9263 | − | 12.0818i | 1.43384 | − | 0.827831i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.12311 | + | 1.94528i | −0.0765952 | + | 0.132667i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.6947 | + | 9.06134i | 1.06055 | + | 0.612309i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.93780 | + | 1.69614i | −0.197618 | + | 0.114095i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.75379 | 0.385302 | 0.192651 | − | 0.981267i | \(-0.438291\pi\) | ||||
0.192651 | + | 0.981267i | \(0.438291\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0000 | −0.866667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.49139 | − | 4.90251i | 0.563593 | − | 0.325391i | −0.190993 | − | 0.981591i | \(-0.561171\pi\) |
0.754586 | + | 0.656201i | \(0.227837\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.3952 | − | 12.9299i | −1.47992 | − | 0.854429i | −0.480174 | − | 0.877173i | \(-0.659426\pi\) |
−0.999741 | + | 0.0227441i | \(0.992760\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.12311 | − | 14.0696i | 0.532162 | − | 0.921732i | −0.467133 | − | 0.884187i | \(-0.654713\pi\) |
0.999295 | − | 0.0375449i | \(-0.0119537\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.6155 | 1.13945 | 0.569727 | − | 0.821834i | \(-0.307049\pi\) | ||||
0.569727 | + | 0.821834i | \(0.307049\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.87689 | + | 3.25088i | 0.120901 | + | 0.209407i | 0.920123 | − | 0.391629i | \(-0.128088\pi\) |
−0.799222 | + | 0.601036i | \(0.794755\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.97175 | − | 1.13839i | −0.126488 | − | 0.0730277i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.56155 | + | 4.43674i | −0.162988 | + | 0.282303i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.56155 | − | 14.8290i | −0.542566 | − | 0.939753i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 10.9663i | − | 0.692186i | −0.938200 | − | 0.346093i | \(-0.887508\pi\) | ||
0.938200 | − | 0.346093i | \(-0.112492\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.78456i | 0.426542i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.12311 | + | 8.87348i | 0.320821 | + | 0.555679i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.2462 | + | 19.4790i | −0.701519 | + | 1.21507i | 0.266414 | + | 0.963859i | \(0.414161\pi\) |
−0.967933 | + | 0.251208i | \(0.919172\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 32.0335 | + | 18.4945i | 1.98282 | + | 1.14478i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.24621 | + | 10.8188i | 0.385158 | + | 0.667113i | 0.991791 | − | 0.127869i | \(-0.0408137\pi\) |
−0.606633 | + | 0.794982i | \(0.707480\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.49242 | −0.275967 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 49.0708i | − | 3.00309i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.2823 | − | 5.93649i | 0.626923 | − | 0.361954i | −0.152636 | − | 0.988282i | \(-0.548776\pi\) |
0.779560 | + | 0.626328i | \(0.215443\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.12311 | − | 8.87348i | 0.311207 | − | 0.539025i | −0.667417 | − | 0.744684i | \(-0.732600\pi\) |
0.978624 | + | 0.205658i | \(0.0659336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.43495 | + | 1.40582i | 0.146833 | + | 0.0847742i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.29377 | − | 1.32431i | 0.137819 | − | 0.0795699i | −0.429505 | − | 0.903064i | \(-0.641312\pi\) |
0.567324 | + | 0.823495i | \(0.307979\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −62.7386 | −3.75606 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.9545 | − | 10.9434i | 1.12673 | − | 0.650518i | 0.183619 | − | 0.982997i | \(-0.441219\pi\) |
0.943110 | + | 0.332480i | \(0.107885\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.4009 | + | 7.73704i | 0.793803 | + | 0.458303i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 32.0335 | − | 18.4945i | 1.87783 | − | 1.08417i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.3857i | 0.606736i | 0.952873 | + | 0.303368i | \(0.0981112\pi\) | ||||
−0.952873 | + | 0.303368i | \(0.901889\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.630683 | 0.0367198 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.24621 | + | 10.8188i | 0.362442 | + | 0.627768i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.52534 | − | 4.34475i | −0.435201 | − | 0.251264i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.6847 | − | 27.1666i | 0.901060 | − | 1.56068i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.43845 | − | 2.49146i | −0.0823652 | − | 0.142661i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.2791i | 1.44275i | 0.692543 | + | 0.721377i | \(0.256490\pi\) | ||||
−0.692543 | + | 0.721377i | \(0.743510\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 6.78456i | − | 0.385960i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.24621 | − | 10.8188i | −0.354190 | − | 0.613475i | 0.632789 | − | 0.774324i | \(-0.281910\pi\) |
−0.986979 | + | 0.160849i | \(0.948577\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.3693 | − | 17.9602i | 0.586108 | − | 1.01517i | −0.408628 | − | 0.912701i | \(-0.633993\pi\) |
0.994736 | − | 0.102468i | \(-0.0326741\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.58184 | − | 2.06798i | −0.201176 | − | 0.116149i | 0.396028 | − | 0.918238i | \(-0.370388\pi\) |
−0.597204 | + | 0.802089i | \(0.703722\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | − | 6.92820i | −0.223957 | − | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −42.7386 | −2.38544 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.04090i | 0.336124i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.11863 | + | 1.80054i | −0.172991 | + | 0.0998762i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.3693 | + | 47.4050i | −1.51353 | + | 2.62151i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.8981 | + | 7.44672i | 0.708943 | + | 0.409309i | 0.810670 | − | 0.585504i | \(-0.199103\pi\) |
−0.101726 | + | 0.994812i | \(0.532437\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 32.0335 | − | 18.4945i | 1.75542 | − | 1.01349i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.5076 | 1.06581 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.876894 | −0.0477675 | −0.0238837 | − | 0.999715i | \(-0.507603\pi\) | ||||
−0.0238837 | + | 0.999715i | \(0.507603\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.7569 | − | 7.36520i | 0.692860 | − | 0.400023i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.7512 | + | 6.78456i | 0.636364 | + | 0.367405i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.1231 | + | 22.7299i | −0.706524 | + | 1.22374i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.02249 | + | 4.05444i | −0.376987 | + | 0.217654i | −0.676507 | − | 0.736437i | \(-0.736507\pi\) |
0.299520 | + | 0.954090i | \(0.403174\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.3471i | 1.46385i | 0.681383 | + | 0.731927i | \(0.261379\pi\) | ||||
−0.681383 | + | 0.731927i | \(0.738621\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.0000 | −0.854017 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.87689 | − | 6.71498i | −0.206346 | − | 0.357402i | 0.744215 | − | 0.667941i | \(-0.232824\pi\) |
−0.950561 | + | 0.310538i | \(0.899491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.7512 | − | 6.78456i | −0.623689 | − | 0.360087i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.6847 | + | 27.1666i | −0.827805 | + | 1.43380i | 0.0719522 | + | 0.997408i | \(0.477077\pi\) |
−0.899757 | + | 0.436392i | \(0.856256\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.93845 | − | 8.55364i | −0.259918 | − | 0.450192i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 27.9277i | 1.46582i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 10.1768i | − | 0.532680i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.12311 | + | 8.87348i | 0.267424 | + | 0.463192i | 0.968196 | − | 0.250194i | \(-0.0804943\pi\) |
−0.700772 | + | 0.713385i | \(0.747161\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.0000 | − | 22.5167i | 0.676753 | − | 1.17217i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.7569 | + | 7.36520i | 0.660528 | + | 0.381356i | 0.792478 | − | 0.609901i | \(-0.208791\pi\) |
−0.131950 | + | 0.991256i | \(0.542124\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.2462 | + | 31.6034i | 0.942230 | + | 1.63199i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.2462 | 0.527707 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.4084i | 1.87017i | 0.354418 | + | 0.935087i | \(0.384679\pi\) | ||||
−0.354418 | + | 0.935087i | \(0.615321\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −34.3272 | + | 19.8188i | −1.75864 | + | 1.01535i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.24621 | + | 3.89055i | −0.114776 | + | 0.198798i | −0.917690 | − | 0.397297i | \(-0.869948\pi\) |
0.802914 | + | 0.596095i | \(0.203282\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.02249 | − | 4.05444i | −0.356973 | − | 0.206099i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.5703 | − | 12.4536i | 1.09366 | − | 0.631424i | 0.159110 | − | 0.987261i | \(-0.449137\pi\) |
0.934548 | + | 0.355837i | \(0.115804\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.2462 | −0.518173 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 37.6155 | 1.89745 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.8076 | − | 10.2812i | −0.893740 | − | 0.516001i | −0.0185761 | − | 0.999827i | \(-0.505913\pi\) |
−0.875164 | + | 0.483826i | \(0.839247\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.438447 | − | 0.759413i | 0.0218950 | − | 0.0379233i | −0.854870 | − | 0.518842i | \(-0.826363\pi\) |
0.876765 | + | 0.480919i | \(0.159697\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.0507 | + | 8.68951i | −0.749727 | + | 0.432855i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.1702i | 0.853195i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.0000 | − | 22.5167i | −0.642809 | − | 1.11338i | −0.984803 | − | 0.173675i | \(-0.944436\pi\) |
0.341994 | − | 0.939702i | \(-0.388898\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 42.4966 | + | 24.5354i | 2.09620 | + | 1.21024i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.80776 | + | 8.32729i | −0.236004 | + | 0.408771i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.5616 | + | 21.7572i | 0.615142 | + | 1.06546i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 27.9277i | − | 1.36436i | −0.731185 | − | 0.682179i | \(-0.761033\pi\) | ||
0.731185 | − | 0.682179i | \(-0.238967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.8122i | 1.30675i | 0.757036 | + | 0.653373i | \(0.226647\pi\) | ||||
−0.757036 | + | 0.653373i | \(0.773353\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.12311 | + | 3.67733i | −0.102986 | + | 0.178377i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.87560 | + | 3.39228i | 0.283677 | + | 0.163781i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.80776 | + | 15.2555i | 0.424255 | + | 0.734831i | 0.996351 | − | 0.0853557i | \(-0.0272027\pi\) |
−0.572095 | + | 0.820187i | \(0.693869\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.4924 | −0.888689 | −0.444345 | − | 0.895856i | \(-0.646563\pi\) | ||||
−0.444345 | + | 0.895856i | \(0.646563\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 30.9481i | − | 1.48385i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.4009 | + | 7.73704i | −0.641054 | + | 0.370113i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.3693 | − | 19.6922i | 0.542628 | − | 0.939859i | −0.456124 | − | 0.889916i | \(-0.650763\pi\) |
0.998752 | − | 0.0499429i | \(-0.0159039\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.37845 | − | 3.68260i | −0.303049 | − | 0.174966i | 0.340763 | − | 0.940149i | \(-0.389315\pi\) |
−0.643812 | + | 0.765184i | \(0.722648\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.8641 | + | 13.7779i | −1.13127 | + | 0.653137i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 44.4924 | 2.10442 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.7386 | 0.789945 | 0.394972 | − | 0.918693i | \(-0.370754\pi\) | ||||
0.394972 | + | 0.918693i | \(0.370754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.86991 | + | 2.81164i | −0.229315 | + | 0.132395i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.4516 | + | 16.4265i | 1.33677 | + | 0.771786i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.68466 | + | 15.0423i | −0.406251 | + | 0.703648i | −0.994466 | − | 0.105057i | \(-0.966498\pi\) |
0.588215 | + | 0.808705i | \(0.299831\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.3387 | + | 9.43318i | −0.762627 | + | 0.440303i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.3724i | 1.13514i | 0.823327 | + | 0.567568i | \(0.192115\pi\) | ||||
−0.823327 | + | 0.567568i | \(0.807885\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 26.2462 | + | 45.4598i | 1.21714 | + | 2.10815i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.61578 | − | 1.51022i | −0.121044 | − | 0.0698848i | 0.438255 | − | 0.898850i | \(-0.355597\pi\) |
−0.559300 | + | 0.828966i | \(0.688930\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.8078 | + | 22.1837i | −0.590151 | + | 1.02217i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.876894 | + | 1.51883i | 0.0403196 | + | 0.0698357i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.41273i | 0.294236i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 16.2177i | − | 0.742559i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.12311 | + | 8.87348i | 0.234081 | + | 0.405440i | 0.959005 | − | 0.283389i | \(-0.0914587\pi\) |
−0.724924 | + | 0.688828i | \(0.758125\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.12311 | − | 8.87348i | 0.233594 | − | 0.404596i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.9885 | − | 10.3857i | −0.816815 | − | 0.471588i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.315342 | + | 0.546188i | 0.0142895 | + | 0.0247501i | 0.873082 | − | 0.487574i | \(-0.162118\pi\) |
−0.858792 | + | 0.512324i | \(0.828785\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.4924 | 1.83113 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 34.1774i | − | 1.54240i | −0.636590 | − | 0.771202i | \(-0.719656\pi\) | ||
0.636590 | − | 0.771202i | \(-0.280344\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.4631 | − | 6.04090i | 0.471236 | − | 0.272068i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.87689 | − | 11.9111i | 0.309093 | − | 0.535366i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.66652 | − | 4.42627i | −0.343201 | − | 0.198147i | 0.318486 | − | 0.947928i | \(-0.396826\pi\) |
−0.661687 | + | 0.749781i | \(0.730159\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.9263 | + | 12.0818i | −0.934917 | + | 0.539775i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.7538 | −0.613251 | −0.306626 | − | 0.951830i | \(-0.599200\pi\) | ||||
−0.306626 | + | 0.951830i | \(0.599200\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.6155 | −0.783881 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 26.4799 | − | 15.2882i | 1.17601 | − | 0.678971i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.6211 | + | 15.3697i | 1.17996 | + | 0.681249i | 0.956005 | − | 0.293351i | \(-0.0947706\pi\) |
0.223953 | + | 0.974600i | \(0.428104\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.2462 | + | 24.6752i | −0.628986 | + | 1.08944i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.29946 | + | 1.90495i | −0.145392 | + | 0.0839419i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 57.6155 | 2.52904 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.0000 | + | 19.0526i | 0.481919 | + | 0.834708i | 0.999785 | − | 0.0207541i | \(-0.00660670\pi\) |
−0.517866 | + | 0.855462i | \(0.673273\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.6549 | − | 20.5854i | −1.55908 | − | 0.900136i | −0.997345 | − | 0.0728196i | \(-0.976800\pi\) |
−0.561736 | − | 0.827316i | \(-0.689866\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.2462 | + | 17.7470i | −0.446332 | + | 0.773070i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.62311 | − | 2.81130i | −0.0705698 | − | 0.122230i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.27678i | 0.0988038i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 7.20217i | − | 0.311961i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0000 | + | 20.7846i | 0.518805 | + | 0.898597i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.12311 | + | 12.3376i | −0.307385 | + | 0.532406i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.4688 | + | 6.62153i | 0.493084 | + | 0.284682i | 0.725853 | − | 0.687850i | \(-0.241445\pi\) |
−0.232769 | + | 0.972532i | \(0.574779\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.5616 | − | 18.2931i | −0.453240 | − | 0.785034i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.7386 | 1.31670 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 9.59621i | − | 0.410304i | −0.978730 | − | 0.205152i | \(-0.934231\pi\) | ||
0.978730 | − | 0.205152i | \(-0.0657689\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.99424 | − | 5.19283i | 0.383865 | − | 0.221624i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.12311 | − | 15.8017i | 0.388657 | − | 0.673174i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −26.8019 | − | 15.4741i | −1.13768 | − | 0.656838i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.29377 | + | 1.32431i | −0.0971900 | + | 0.0561127i | −0.547807 | − | 0.836605i | \(-0.684537\pi\) |
0.450617 | + | 0.892717i | \(0.351204\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.24621 | −0.0950046 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.8358 | + | 14.9163i | −1.08885 | + | 0.628648i | −0.933270 | − | 0.359175i | \(-0.883058\pi\) |
−0.155580 | + | 0.987823i | \(0.549725\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.16368 | − | 4.13595i | −0.301378 | − | 0.174001i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.68466 | − | 11.5782i | 0.280235 | − | 0.485382i | −0.691207 | − | 0.722657i | \(-0.742921\pi\) |
0.971443 | + | 0.237275i | \(0.0762541\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.02818 | − | 4.63507i | 0.335969 | − | 0.193972i | −0.322519 | − | 0.946563i | \(-0.604530\pi\) |
0.658488 | + | 0.752591i | \(0.271196\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 48.3272i | − | 2.01890i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.8769 | −0.453598 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.87689 | − | 6.71498i | −0.161397 | − | 0.279548i | 0.773973 | − | 0.633219i | \(-0.218267\pi\) |
−0.935370 | + | 0.353671i | \(0.884933\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.0956 | + | 16.7984i | 1.20917 | + | 0.698117i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.75379 | + | 3.03765i | −0.0726345 | + | 0.125807i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.80776 | + | 15.2555i | 0.364156 | + | 0.630737i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.8868i | 0.903365i | 0.892179 | + | 0.451683i | \(0.149176\pi\) | ||||
−0.892179 | + | 0.451683i | \(0.850824\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.9481i | 1.27520i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32.4924 | − | 56.2785i | −1.33656 | − | 2.31499i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.00000 | + | 15.5885i | −0.369586 | + | 0.640141i | −0.989501 | − | 0.144528i | \(-0.953834\pi\) |
0.619915 | + | 0.784669i | \(0.287167\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −47.7282 | − | 27.5559i | −1.95338 | − | 1.12779i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.24621 | − | 10.8188i | −0.255213 | − | 0.442042i | 0.709740 | − | 0.704464i | \(-0.248812\pi\) |
−0.964953 | + | 0.262421i | \(0.915479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.2462 | −0.662697 | −0.331348 | − | 0.943508i | \(-0.607504\pi\) | ||||
−0.331348 | + | 0.943508i | \(0.607504\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 70.4228i | 2.86784i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.5818 | − | 7.84144i | 0.552178 | − | 0.318800i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.4924 | − | 35.4939i | 0.831762 | − | 1.44065i | −0.0648782 | − | 0.997893i | \(-0.520666\pi\) |
0.896640 | − | 0.442760i | \(-0.146001\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.93211 | + | 1.11550i | −0.0780371 | + | 0.0450547i | −0.538511 | − | 0.842619i | \(-0.681013\pi\) |
0.460474 | + | 0.887673i | \(0.347680\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.7538 | −0.877197 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.3693 | −1.18236 | −0.591182 | − | 0.806538i | \(-0.701339\pi\) | ||||
−0.591182 | + | 0.806538i | \(0.701339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.0224 | + | 9.82790i | −0.684189 | + | 0.395017i | −0.801431 | − | 0.598087i | \(-0.795928\pi\) |
0.117243 | + | 0.993103i | \(0.462595\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −41.8526 | − | 24.1636i | −1.67949 | − | 0.969651i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.93845 | − | 8.55364i | 0.197538 | − | 0.342146i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.4631 | − | 6.04090i | 0.417858 | − | 0.241250i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 12.0818i | − | 0.481733i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.50758 | 0.139634 | 0.0698172 | − | 0.997560i | \(-0.477758\pi\) | ||||
0.0698172 | + | 0.997560i | \(0.477758\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.12311 | − | 12.3376i | −0.283118 | − | 0.490375i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.2765 | + | 11.1293i | 0.764966 | + | 0.441654i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.4924 | − | 42.4221i | 0.968905 | − | 1.67819i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.68466 | + | 4.64996i | 0.106038 | + | 0.183663i | 0.914162 | − | 0.405350i | \(-0.132850\pi\) |
−0.808124 | + | 0.589012i | \(0.799517\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5.66906i | − | 0.223566i | −0.993733 | − | 0.111783i | \(-0.964344\pi\) | ||
0.993733 | − | 0.111783i | \(-0.0356562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.78456i | 0.267142i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.6155 | + | 37.4392i | 0.849794 | + | 1.47189i | 0.881392 | + | 0.472386i | \(0.156607\pi\) |
−0.0315977 | + | 0.999501i | \(0.510060\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.246211 | − | 0.426450i | 0.00966464 | − | 0.0167396i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.4459 | + | 15.8459i | 1.07404 | + | 0.620098i | 0.929283 | − | 0.369369i | \(-0.120426\pi\) |
0.144759 | + | 0.989467i | \(0.453759\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.5616 | − | 18.2931i | −0.412674 | − | 0.714772i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.7386 | 1.43331 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 6.62153i | − | 0.257938i | −0.991649 | − | 0.128969i | \(-0.958833\pi\) | ||
0.991649 | − | 0.128969i | \(-0.0411668\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.7339 | + | 22.3630i | −1.50657 | + | 0.869821i | −0.506604 | + | 0.862179i | \(0.669099\pi\) |
−0.999971 | + | 0.00764267i | \(0.997567\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.12311 | + | 8.87348i | −0.198965 | + | 0.344617i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.8019 | + | 15.4741i | 1.03777 | + | 0.599159i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.0507 | − | 8.68951i | 0.581893 | − | 0.335956i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.24621 | −0.0867140 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.9848 | −1.50276 | −0.751378 | − | 0.659872i | \(-0.770610\pi\) | ||||
−0.751378 | + | 0.659872i | \(0.770610\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.3444 | + | 10.0138i | −0.667588 | + | 0.385432i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.8698 | − | 8.58511i | −0.571494 | − | 0.329952i | 0.186252 | − | 0.982502i | \(-0.440366\pi\) |
−0.757746 | + | 0.652550i | \(0.773699\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.8078 | − | 25.6478i | 0.567435 | − | 0.982826i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.502848 | − | 0.290319i | 0.0192409 | − | 0.0111088i | −0.490349 | − | 0.871526i | \(-0.663131\pi\) |
0.509590 | + | 0.860418i | \(0.329797\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 27.5559i | − | 1.05286i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −78.1080 | −2.98000 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.24621 | − | 3.89055i | −0.0855738 | − | 0.148218i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.6435 | − | 19.4241i | −1.27986 | − | 0.738928i | −0.303038 | − | 0.952978i | \(-0.598001\pi\) |
−0.976823 | + | 0.214051i | \(0.931334\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.05398 | − | 12.2178i | 0.267573 | − | 0.463449i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.24621 | − | 7.35465i | −0.160837 | − | 0.278577i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 49.0708i | − | 1.85603i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.23100i | 0.0842639i | 0.999112 | + | 0.0421319i | \(0.0134150\pi\) | ||||
−0.999112 | + | 0.0421319i | \(0.986585\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.12311 | − | 15.8017i | −0.344084 | − | 0.595972i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.8698 | − | 14.3586i | −0.934004 | − | 0.539247i | −0.0459283 | − | 0.998945i | \(-0.514625\pi\) |
−0.888076 | + | 0.459697i | \(0.847958\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −52.4924 | −1.96586 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 3.80989i | − | 0.142482i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 46.0784 | − | 26.6034i | 1.72083 | − | 0.993522i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.2462 | + | 45.4598i | −0.978819 | + | 1.69536i | −0.312108 | + | 0.950047i | \(0.601035\pi\) |
−0.666711 | + | 0.745317i | \(0.732298\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.81910 | + | 5.66906i | 0.365176 | + | 0.210835i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.1072 | − | 6.41273i | 0.412510 | − | 0.238163i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9848 | 0.629933 | 0.314967 | − | 0.949103i | \(-0.398007\pi\) | ||||
0.314967 | + | 0.949103i | \(0.398007\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.4924 | 0.870090 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.29377 | + | 1.32431i | −0.0848380 | + | 0.0489813i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.3330 | − | 14.6260i | −0.935695 | − | 0.540224i | −0.0470868 | − | 0.998891i | \(-0.514994\pi\) |
−0.888608 | + | 0.458667i | \(0.848327\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.61553 | − | 13.1905i | 0.280522 | − | 0.485878i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.4913 | − | 10.6760i | 0.680214 | − | 0.392722i | −0.119721 | − | 0.992808i | \(-0.538200\pi\) |
0.799936 | + | 0.600086i | \(0.204867\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.4741i | 0.568454i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.630683 | −0.0231375 | −0.0115688 | − | 0.999933i | \(-0.503683\pi\) | ||||
−0.0115688 | + | 0.999933i | \(0.503683\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.4924 | − | 21.6375i | −0.457687 | − | 0.792737i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −30.0617 | − | 17.3561i | −1.09990 | − | 0.635028i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.31534 | − | 7.47439i | 0.157469 | − | 0.272744i | −0.776486 | − | 0.630134i | \(-0.783000\pi\) |
0.933955 | + | 0.357390i | \(0.116333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.5616 | − | 28.6855i | −0.603537 | − | 1.04536i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 18.4487i | − | 0.671419i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 26.3946i | − | 0.959328i | −0.877452 | − | 0.479664i | \(-0.840759\pi\) | ||
0.877452 | − | 0.479664i | \(-0.159241\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.2462 | + | 17.7470i | 0.371914 | + | 0.644174i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.36932 | + | 7.56788i | −0.158388 | + | 0.274335i | −0.934287 | − | 0.356521i | \(-0.883963\pi\) |
0.775900 | + | 0.630856i | \(0.217296\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.9885 | + | 10.3857i | 0.650375 | + | 0.375494i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.315342 | + | 0.546188i | 0.0113863 | + | 0.0197217i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.2462 | −1.45132 | −0.725658 | − | 0.688056i | \(-0.758464\pi\) | ||||
−0.725658 | + | 0.688056i | \(0.758464\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 67.9372i | 2.44670i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.46890 | − | 0.848071i | 0.0528327 | − | 0.0305030i | −0.473351 | − | 0.880874i | \(-0.656956\pi\) |
0.526184 | + | 0.850371i | \(0.323622\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.8769 | + | 18.8393i | −0.390710 | + | 0.676729i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.1072 | − | 6.41273i | −0.397956 | − | 0.229760i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.17507 | + | 5.29723i | −0.328310 | + | 0.189550i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 56.9848 | 2.03647 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.3845 | 0.513404 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.13543 | + | 5.27434i | −0.325643 | + | 0.188010i | −0.653905 | − | 0.756577i | \(-0.726870\pi\) |
0.328262 | + | 0.944587i | \(0.393537\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 32.6775 | + | 18.8664i | 1.16335 | + | 0.671660i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.43845 | − | 2.49146i | 0.0510808 | − | 0.0884745i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.7512 | + | 6.78456i | −0.416772 | + | 0.240624i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 25.8597i | − | 0.915998i | −0.888953 | − | 0.457999i | \(-0.848566\pi\) | ||
0.888953 | − | 0.457999i | \(-0.151434\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −49.7386 | − | 86.1498i | −1.75743 | − | 3.04395i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.88130 | − | 3.97292i | −0.242836 | − | 0.140201i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.9309 | − | 31.0572i | 0.631197 | − | 1.09326i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.9309 | − | 32.7892i | −0.665574 | − | 1.15281i | −0.979129 | − | 0.203238i | \(-0.934853\pi\) |
0.313555 | − | 0.949570i | \(-0.398480\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 15.8459i | − | 0.556425i | −0.960520 | − | 0.278213i | \(-0.910258\pi\) | ||
0.960520 | − | 0.278213i | \(-0.0897420\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 30.9481i | − | 1.08540i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.3693 | − | 19.6922i | −0.398250 | − | 0.689789i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.00000 | + | 3.46410i | −0.0699711 | + | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.0956 | − | 16.7984i | −1.01545 | − | 0.586268i | −0.102664 | − | 0.994716i | \(-0.532737\pi\) |
−0.912781 | + | 0.408449i | \(0.866070\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.4924 | − | 28.5657i | −0.574890 | − | 0.995738i | −0.996054 | − | 0.0887536i | \(-0.971712\pi\) |
0.421164 | − | 0.906985i | \(-0.361622\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.49242 | 0.295668 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 6.20393i | − | 0.215732i | −0.994165 | − | 0.107866i | \(-0.965598\pi\) | ||
0.994165 | − | 0.107866i | \(-0.0344017\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.3837 | − | 23.3155i | 1.40258 | − | 0.809781i | 0.407925 | − | 0.913015i | \(-0.366252\pi\) |
0.994657 | + | 0.103234i | \(0.0329191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.00000 | − | 6.92820i | 0.138758 | − | 0.240337i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.7512 | + | 6.78456i | 0.406667 | + | 0.234790i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −83.7051 | + | 48.3272i | −2.89327 | + | 1.67043i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.73863 | 0.232643 | 0.116322 | − | 0.993212i | \(-0.462890\pi\) | ||||
0.116322 | + | 0.993212i | \(0.462890\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.49242 | −0.258359 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.6947 | + | 9.06134i | −0.540554 | + | 0.312089i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.8698 | − | 8.58511i | −0.511538 | − | 0.295337i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 33.0540 | − | 57.2512i | 1.13441 | − | 1.96485i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.8019 | − | 15.4741i | 0.918757 | − | 0.530444i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 25.4421i | − | 0.871121i | −0.900159 | − | 0.435561i | \(-0.856550\pi\) | ||
0.900159 | − | 0.435561i | \(-0.143450\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31.3693 | 1.07281 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.4924 | + | 40.6901i | 0.802486 | + | 1.38995i | 0.917975 | + | 0.396638i | \(0.129823\pi\) |
−0.115489 | + | 0.993309i | \(0.536844\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.5478 | + | 14.1727i | 0.837559 | + | 0.483565i | 0.856434 | − | 0.516257i | \(-0.172675\pi\) |
−0.0188750 | + | 0.999822i | \(0.506008\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.2462 | − | 31.6034i | 0.621108 | − | 1.07579i | −0.368171 | − | 0.929758i | \(-0.620016\pi\) |
0.989280 | − | 0.146033i | \(-0.0466506\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.1771 | − | 28.0195i | −0.550037 | − | 0.952692i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 39.2658i | − | 1.33354i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.75379 | + | 16.8941i | 0.330495 | + | 0.572433i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 37.4924 | − | 64.9388i | 1.26893 | − | 2.19784i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.7454 | + | 17.7509i | 1.03820 | + | 0.599404i | 0.919322 | − | 0.393505i | \(-0.128738\pi\) |
0.118875 | + | 0.992909i | \(0.462071\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.6847 | + | 27.1666i | 0.529030 | + | 0.916308i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.2462 | 1.49069 | 0.745346 | − | 0.666677i | \(-0.232284\pi\) | ||||
0.745346 | + | 0.666677i | \(0.232284\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4.71659i | − | 0.158726i | −0.996846 | − | 0.0793629i | \(-0.974711\pi\) | ||
0.996846 | − | 0.0793629i | \(-0.0252886\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.64973 | − | 0.952473i | 0.0554551 | − | 0.0320170i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.2462 | + | 24.6752i | −0.478341 | + | 0.828511i | −0.999692 | − | 0.0248317i | \(-0.992095\pi\) |
0.521351 | + | 0.853343i | \(0.325428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.6100 | + | 6.70305i | 0.388950 | + | 0.224561i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | 0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −26.2462 | −0.876335 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 53.6038 | − | 30.9481i | 1.78779 | − | 1.03218i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.58753 | − | 2.64861i | −0.152833 | − | 0.0882381i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.93087 | + | 10.2726i | −0.197149 | + | 0.341472i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.6492 | + | 25.7782i | −1.48255 | + | 0.855951i | −0.999804 | − | 0.0198082i | \(-0.993694\pi\) |
−0.482748 | + | 0.875760i | \(0.660361\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 63.5924i | − | 2.10923i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.8617 | −0.392997 | −0.196498 | − | 0.980504i | \(-0.562957\pi\) | ||||
−0.196498 | + | 0.980504i | \(0.562957\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.75379 | + | 6.50175i | 0.124232 | + | 0.215177i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.52534 | − | 4.34475i | −0.248780 | − | 0.143633i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00000 | − | 6.92820i | 0.131948 | − | 0.228540i | −0.792480 | − | 0.609898i | \(-0.791210\pi\) |
0.924427 | + | 0.381358i | \(0.124544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 38.1771 | + | 66.1246i | 1.25798 | + | 2.17888i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 13.5691i | − | 0.446633i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 12.8255i | − | 0.421699i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.87689 | − | 11.9111i | −0.225867 | − | 0.391213i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.24621 | − | 2.15850i | 0.0408869 | − | 0.0708181i | −0.844858 | − | 0.534991i | \(-0.820315\pi\) |
0.885745 | + | 0.464173i | \(0.153648\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −32.6775 | − | 18.8664i | −1.06981 | − | 0.617657i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.24621 | − | 3.89055i | −0.0734590 | − | 0.127235i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.9848 | 1.14291 | 0.571453 | − | 0.820635i | \(-0.306380\pi\) | ||||
0.571453 | + | 0.820635i | \(0.306380\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 62.6400i | − | 2.04418i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.6211 | + | 15.3697i | −0.867821 | + | 0.501037i | −0.866624 | − | 0.498962i | \(-0.833715\pi\) |
−0.00119780 | + | 0.999999i | \(0.500381\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.8769 | − | 18.8393i | 0.354200 | − | 0.613493i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.1181 | − | 20.8528i | −1.17368 | − | 0.677625i | −0.219137 | − | 0.975694i | \(-0.570324\pi\) |
−0.954544 | + | 0.298069i | \(0.903658\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.81341 | − | 5.08842i | 0.286095 | − | 0.165177i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.4924 | −0.405095 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.5076 | −0.567126 | −0.283563 | − | 0.958954i | \(-0.591517\pi\) | ||||
−0.283563 | + | 0.958954i | \(0.591517\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.5024 | + | 13.5691i | −0.760520 | + | 0.439087i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.9263 | − | 12.0818i | −0.676450 | − | 0.390549i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −36.9924 | + | 64.0728i | −1.19330 | + | 2.06686i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −75.0329 | + | 43.3203i | −2.41790 | + | 1.39598i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 18.8664i | − | 0.607329i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.8769 | 0.349777 | 0.174889 | − | 0.984588i | \(-0.444043\pi\) | ||||
0.174889 | + | 0.984588i | \(0.444043\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.12311 | + | 15.8017i | 0.293076 | + | 0.507623i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.49709 | + | 5.48314i | 0.304776 | + | 0.175962i | 0.644586 | − | 0.764531i | \(-0.277030\pi\) |
−0.339810 | + | 0.940494i | \(0.610363\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.43845 | + | 9.41967i | −0.174170 | + | 0.301671i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.8769 | − | 20.5714i | −0.379976 | − | 0.658137i | 0.611083 | − | 0.791567i | \(-0.290734\pi\) |
−0.991058 | + | 0.133430i | \(0.957401\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.5150i | 0.687621i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 110.967i | 3.54291i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.1231 | − | 29.6581i | −0.546142 | − | 0.945946i | −0.998534 | − | 0.0541268i | \(-0.982762\pi\) |
0.452392 | − | 0.891819i | \(-0.350571\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.2462 | + | 31.6034i | −0.581373 | + | 1.00697i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.87560 | − | 3.39228i | −0.186833 | − | 0.107868i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.2462 | − | 31.6034i | −0.579610 | − | 1.00391i | −0.995524 | − | 0.0945100i | \(-0.969872\pi\) |
0.415914 | − | 0.909404i | \(-0.363462\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 44.9848 | 1.42755 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.9481i | 0.981122i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.6324 | + | 16.5309i | −0.906799 | + | 0.523540i | −0.879400 | − | 0.476084i | \(-0.842056\pi\) |
−0.0273989 | + | 0.999625i | \(0.508722\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 28.4924 | − | 49.3503i | 0.901460 | − | 1.56138i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))