Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(68,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.68");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.i (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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 68.10 | ||
Character | \(\chi\) | \(=\) | 441.68 |
Dual form | 441.2.i.d.227.16 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.981621i | − | 0.694111i | −0.937845 | − | 0.347056i | \(-0.887182\pi\) | ||
0.937845 | − | 0.347056i | \(-0.112818\pi\) | |||||||
\(3\) | 1.73160 | + | 0.0395255i | 0.999740 | + | 0.0228200i | ||||
\(4\) | 1.03642 | 0.518210 | ||||||||
\(5\) | 0.940599 | + | 1.62916i | 0.420648 | + | 0.728585i | 0.996003 | − | 0.0893196i | \(-0.0284692\pi\) |
−0.575355 | + | 0.817904i | \(0.695136\pi\) | |||||||
\(6\) | 0.0387990 | − | 1.69978i | 0.0158396 | − | 0.693930i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.98061i | − | 1.05381i | ||||||
\(9\) | 2.99688 | + | 0.136885i | 0.998958 | + | 0.0456282i | ||||
\(10\) | 1.59922 | − | 0.923312i | 0.505719 | − | 0.291977i | ||||
\(11\) | −3.54040 | − | 2.04405i | −1.06747 | − | 0.616304i | −0.139980 | − | 0.990154i | \(-0.544704\pi\) |
−0.927489 | + | 0.373850i | \(0.878037\pi\) | |||||||
\(12\) | 1.79466 | + | 0.0409650i | 0.518075 | + | 0.0118256i | ||||
\(13\) | −3.51415 | − | 2.02890i | −0.974651 | − | 0.562715i | −0.0739997 | − | 0.997258i | \(-0.523576\pi\) |
−0.900651 | + | 0.434544i | \(0.856910\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.56435 | + | 2.85824i | 0.403913 | + | 0.737994i | ||||
\(16\) | −0.852996 | −0.213249 | ||||||||
\(17\) | 0.810727 | + | 1.40422i | 0.196630 | + | 0.340574i | 0.947434 | − | 0.319952i | \(-0.103667\pi\) |
−0.750803 | + | 0.660526i | \(0.770333\pi\) | |||||||
\(18\) | 0.134369 | − | 2.94180i | 0.0316710 | − | 0.693388i | ||||
\(19\) | 7.03722 | + | 4.06294i | 1.61445 | + | 0.932103i | 0.988322 | + | 0.152382i | \(0.0486945\pi\) |
0.626128 | + | 0.779720i | \(0.284639\pi\) | |||||||
\(20\) | 0.974855 | + | 1.68850i | 0.217984 | + | 0.377560i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00648 | + | 3.47533i | −0.427783 | + | 0.740943i | ||||
\(23\) | −3.73318 | + | 2.15535i | −0.778423 | + | 0.449423i | −0.835871 | − | 0.548926i | \(-0.815037\pi\) |
0.0574484 | + | 0.998348i | \(0.481704\pi\) | |||||||
\(24\) | 0.117810 | − | 5.16123i | 0.0240479 | − | 1.05353i | ||||
\(25\) | 0.730548 | − | 1.26535i | 0.146110 | − | 0.253069i | ||||
\(26\) | −1.99161 | + | 3.44957i | −0.390587 | + | 0.676516i | ||||
\(27\) | 5.18398 | + | 0.355482i | 0.997657 | + | 0.0684126i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.542317 | + | 0.313107i | −0.100706 | + | 0.0581425i | −0.549507 | − | 0.835489i | \(-0.685184\pi\) |
0.448801 | + | 0.893632i | \(0.351851\pi\) | |||||||
\(30\) | 2.80571 | − | 1.53560i | 0.512250 | − | 0.280360i | ||||
\(31\) | 4.27047i | 0.766999i | 0.923541 | + | 0.383499i | \(0.125281\pi\) | ||||
−0.923541 | + | 0.383499i | \(0.874719\pi\) | |||||||
\(32\) | − | 5.12391i | − | 0.905788i | ||||||
\(33\) | −6.04976 | − | 3.67941i | −1.05313 | − | 0.640503i | ||||
\(34\) | 1.37841 | − | 0.795827i | 0.236396 | − | 0.136483i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.10602 | + | 0.141870i | 0.517670 | + | 0.0236450i | ||||
\(37\) | −3.97076 | + | 6.87757i | −0.652790 | + | 1.13066i | 0.329653 | + | 0.944102i | \(0.393068\pi\) |
−0.982443 | + | 0.186563i | \(0.940265\pi\) | |||||||
\(38\) | 3.98827 | − | 6.90789i | 0.646983 | − | 1.12061i | ||||
\(39\) | −6.00491 | − | 3.65214i | −0.961556 | − | 0.584810i | ||||
\(40\) | 4.85591 | − | 2.80356i | 0.767787 | − | 0.443282i | ||||
\(41\) | −0.912023 | + | 1.57967i | −0.142434 | + | 0.246703i | −0.928413 | − | 0.371551i | \(-0.878826\pi\) |
0.785979 | + | 0.618254i | \(0.212160\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.53614 | − | 6.12477i | −0.539256 | − | 0.934019i | −0.998944 | − | 0.0459387i | \(-0.985372\pi\) |
0.459688 | − | 0.888080i | \(-0.347961\pi\) | |||||||
\(44\) | −3.66933 | − | 2.11849i | −0.553173 | − | 0.319375i | ||||
\(45\) | 2.59585 | + | 5.01116i | 0.386966 | + | 0.747019i | ||||
\(46\) | 2.11574 | + | 3.66457i | 0.311949 | + | 0.540312i | ||||
\(47\) | −7.93736 | −1.15778 | −0.578891 | − | 0.815405i | \(-0.696515\pi\) | ||||
−0.578891 | + | 0.815405i | \(0.696515\pi\) | |||||||
\(48\) | −1.47705 | − | 0.0337151i | −0.213194 | − | 0.00486635i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.24209 | − | 0.717122i | −0.175658 | − | 0.101416i | ||||
\(51\) | 1.34835 | + | 2.46359i | 0.188807 | + | 0.344972i | ||||
\(52\) | −3.64214 | − | 2.10279i | −0.505073 | − | 0.291604i | ||||
\(53\) | −7.24978 | + | 4.18567i | −0.995835 | + | 0.574945i | −0.907013 | − | 0.421102i | \(-0.861643\pi\) |
−0.0888214 | + | 0.996048i | \(0.528310\pi\) | |||||||
\(54\) | 0.348949 | − | 5.08870i | 0.0474859 | − | 0.692485i | ||||
\(55\) | − | 7.69052i | − | 1.03699i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.0251 | + | 7.31354i | 1.59276 | + | 0.968702i | ||||
\(58\) | 0.307352 | + | 0.532350i | 0.0403573 | + | 0.0699009i | ||||
\(59\) | −8.17430 | −1.06420 | −0.532101 | − | 0.846681i | \(-0.678598\pi\) | ||||
−0.532101 | + | 0.846681i | \(0.678598\pi\) | |||||||
\(60\) | 1.62132 | + | 2.96233i | 0.209311 | + | 0.382436i | ||||
\(61\) | − | 3.74415i | − | 0.479390i | −0.970848 | − | 0.239695i | \(-0.922953\pi\) | ||
0.970848 | − | 0.239695i | \(-0.0770474\pi\) | |||||||
\(62\) | 4.19198 | 0.532382 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.73573 | −0.841966 | ||||||||
\(65\) | − | 7.63351i | − | 0.946820i | ||||||
\(66\) | −3.61179 | + | 5.93857i | −0.444580 | + | 0.730988i | ||||
\(67\) | 12.5312 | 1.53093 | 0.765464 | − | 0.643479i | \(-0.222510\pi\) | ||||
0.765464 | + | 0.643479i | \(0.222510\pi\) | |||||||
\(68\) | 0.840253 | + | 1.45536i | 0.101896 | + | 0.176489i | ||||
\(69\) | −6.54957 | + | 3.58466i | −0.788476 | + | 0.431542i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.4969i | − | 1.72047i | −0.509898 | − | 0.860235i | \(-0.670317\pi\) | ||
0.509898 | − | 0.860235i | \(-0.329683\pi\) | |||||||
\(72\) | 0.408000 | − | 8.93253i | 0.0480833 | − | 1.05271i | ||||
\(73\) | −3.28167 | + | 1.89468i | −0.384091 | + | 0.221755i | −0.679597 | − | 0.733586i | \(-0.737845\pi\) |
0.295506 | + | 0.955341i | \(0.404512\pi\) | |||||||
\(74\) | 6.75117 | + | 3.89779i | 0.784807 | + | 0.453109i | ||||
\(75\) | 1.31503 | − | 2.16220i | 0.151847 | − | 0.249669i | ||||
\(76\) | 7.29351 | + | 4.21091i | 0.836623 | + | 0.483025i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.58501 | + | 5.89455i | −0.405923 | + | 0.667426i | ||||
\(79\) | 8.36133 | 0.940723 | 0.470361 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470361 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(80\) | −0.802327 | − | 1.38967i | −0.0897029 | − | 0.155370i | ||||
\(81\) | 8.96253 | + | 0.820452i | 0.995836 | + | 0.0911613i | ||||
\(82\) | 1.55064 | + | 0.895261i | 0.171239 | + | 0.0988651i | ||||
\(83\) | −4.38300 | − | 7.59159i | −0.481097 | − | 0.833285i | 0.518668 | − | 0.854976i | \(-0.326428\pi\) |
−0.999765 | + | 0.0216912i | \(0.993095\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.52514 | + | 2.64162i | −0.165424 | + | 0.286524i | ||||
\(86\) | −6.01221 | + | 3.47115i | −0.648313 | + | 0.374304i | ||||
\(87\) | −0.951451 | + | 0.520740i | −0.102006 | + | 0.0558292i | ||||
\(88\) | −6.09252 | + | 10.5526i | −0.649465 | + | 1.12491i | ||||
\(89\) | −4.90379 | + | 8.49362i | −0.519801 | + | 0.900322i | 0.479934 | + | 0.877305i | \(0.340661\pi\) |
−0.999735 | + | 0.0230174i | \(0.992673\pi\) | |||||||
\(90\) | 4.91906 | − | 2.54814i | 0.518514 | − | 0.268598i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.86914 | + | 2.23385i | −0.403386 | + | 0.232895i | ||||
\(93\) | −0.168792 | + | 7.39474i | −0.0175029 | + | 0.766799i | ||||
\(94\) | 7.79148i | 0.803630i | ||||||||
\(95\) | 15.2864i | 1.56835i | ||||||||
\(96\) | 0.202525 | − | 8.87256i | 0.0206701 | − | 0.905552i | ||||
\(97\) | −11.4579 | + | 6.61525i | −1.16338 | + | 0.671677i | −0.952111 | − | 0.305752i | \(-0.901092\pi\) |
−0.211267 | + | 0.977428i | \(0.567759\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.3303 | − | 6.61038i | −1.03824 | − | 0.664369i | ||||
\(100\) | 0.757155 | − | 1.31143i | 0.0757155 | − | 0.131143i | ||||
\(101\) | 0.524900 | − | 0.909154i | 0.0522295 | − | 0.0904642i | −0.838729 | − | 0.544550i | \(-0.816701\pi\) |
0.890958 | + | 0.454085i | \(0.150034\pi\) | |||||||
\(102\) | 2.41832 | − | 1.32357i | 0.239449 | − | 0.131053i | ||||
\(103\) | −1.41937 | + | 0.819472i | −0.139854 | + | 0.0807449i | −0.568295 | − | 0.822825i | \(-0.692397\pi\) |
0.428440 | + | 0.903570i | \(0.359063\pi\) | |||||||
\(104\) | −6.04736 | + | 10.4743i | −0.592992 | + | 1.02709i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.10874 | + | 7.11654i | 0.399076 | + | 0.691220i | ||||
\(107\) | 2.97522 | + | 1.71775i | 0.287626 | + | 0.166061i | 0.636871 | − | 0.770971i | \(-0.280229\pi\) |
−0.349245 | + | 0.937031i | \(0.613562\pi\) | |||||||
\(108\) | 5.37278 | + | 0.368429i | 0.516996 | + | 0.0354521i | ||||
\(109\) | −1.84529 | − | 3.19614i | −0.176747 | − | 0.306134i | 0.764018 | − | 0.645195i | \(-0.223224\pi\) |
−0.940764 | + | 0.339061i | \(0.889891\pi\) | |||||||
\(110\) | −7.54918 | −0.719786 | ||||||||
\(111\) | −7.14761 | + | 11.7522i | −0.678421 | + | 1.11547i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.0858 | + | 8.70977i | 1.41915 | + | 0.819346i | 0.996224 | − | 0.0868183i | \(-0.0276699\pi\) |
0.422925 | + | 0.906165i | \(0.361003\pi\) | |||||||
\(114\) | 7.17913 | − | 11.8041i | 0.672387 | − | 1.10555i | ||||
\(115\) | −7.02285 | − | 4.05465i | −0.654885 | − | 0.378098i | ||||
\(116\) | −0.562068 | + | 0.324510i | −0.0521867 | + | 0.0301300i | ||||
\(117\) | −10.2538 | − | 6.56138i | −0.947960 | − | 0.606600i | ||||
\(118\) | 8.02407i | 0.738675i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.51931 | − | 4.66271i | 0.777703 | − | 0.425646i | ||||
\(121\) | 2.85627 | + | 4.94720i | 0.259661 | + | 0.449746i | ||||
\(122\) | −3.67534 | −0.332750 | ||||||||
\(123\) | −1.64170 | + | 2.69931i | −0.148027 | + | 0.243388i | ||||
\(124\) | 4.42600i | 0.397466i | ||||||||
\(125\) | 12.1546 | 1.08714 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.1288 | −0.898783 | −0.449391 | − | 0.893335i | \(-0.648359\pi\) | ||||
−0.449391 | + | 0.893335i | \(0.648359\pi\) | |||||||
\(128\) | − | 3.63588i | − | 0.321369i | ||||||
\(129\) | −5.88109 | − | 10.7454i | −0.517801 | − | 0.946082i | ||||
\(130\) | −7.49322 | −0.657199 | ||||||||
\(131\) | 2.48851 | + | 4.31022i | 0.217422 | + | 0.376586i | 0.954019 | − | 0.299746i | \(-0.0969019\pi\) |
−0.736597 | + | 0.676332i | \(0.763569\pi\) | |||||||
\(132\) | −6.27008 | − | 3.81341i | −0.545741 | − | 0.331915i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 12.3009i | − | 1.06263i | ||||||
\(135\) | 4.29690 | + | 8.77992i | 0.369819 | + | 0.755655i | ||||
\(136\) | 4.18544 | − | 2.41647i | 0.358899 | − | 0.207210i | ||||
\(137\) | −0.728035 | − | 0.420331i | −0.0622003 | − | 0.0359113i | 0.468577 | − | 0.883422i | \(-0.344767\pi\) |
−0.530778 | + | 0.847511i | \(0.678100\pi\) | |||||||
\(138\) | 3.51877 | + | 6.42920i | 0.299538 | + | 0.547290i | ||||
\(139\) | 5.74392 | + | 3.31626i | 0.487193 | + | 0.281281i | 0.723409 | − | 0.690419i | \(-0.242574\pi\) |
−0.236216 | + | 0.971701i | \(0.575907\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.7443 | − | 0.313728i | −1.15748 | − | 0.0264206i | ||||
\(142\) | −14.2305 | −1.19420 | ||||||||
\(143\) | 8.29433 | + | 14.3662i | 0.693606 | + | 1.20136i | ||||
\(144\) | −2.55632 | − | 0.116762i | −0.213027 | − | 0.00973017i | ||||
\(145\) | −1.02020 | − | 0.589015i | −0.0847234 | − | 0.0489151i | ||||
\(146\) | 1.85985 | + | 3.22136i | 0.153923 | + | 0.266602i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.11538 | + | 7.12804i | −0.338282 | + | 0.585921i | ||||
\(149\) | 14.7023 | − | 8.48838i | 1.20446 | − | 0.695395i | 0.242916 | − | 0.970047i | \(-0.421896\pi\) |
0.961544 | + | 0.274652i | \(0.0885627\pi\) | |||||||
\(150\) | −2.12246 | − | 1.29086i | −0.173298 | − | 0.105398i | ||||
\(151\) | −0.975709 | + | 1.68998i | −0.0794021 | + | 0.137528i | −0.902992 | − | 0.429657i | \(-0.858634\pi\) |
0.823590 | + | 0.567186i | \(0.191968\pi\) | |||||||
\(152\) | 12.1101 | − | 20.9752i | 0.982256 | − | 1.70132i | ||||
\(153\) | 2.23743 | + | 4.31925i | 0.180886 | + | 0.349191i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.95730 | + | 4.01680i | −0.558823 | + | 0.322637i | ||||
\(156\) | −6.22361 | − | 3.78514i | −0.498287 | − | 0.303054i | ||||
\(157\) | − | 9.52118i | − | 0.759873i | −0.925013 | − | 0.379936i | \(-0.875946\pi\) | ||
0.925013 | − | 0.379936i | \(-0.124054\pi\) | |||||||
\(158\) | − | 8.20766i | − | 0.652966i | ||||||
\(159\) | −12.7192 | + | 6.96135i | −1.00870 | + | 0.552071i | ||||
\(160\) | 8.34769 | − | 4.81954i | 0.659943 | − | 0.381018i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.805373 | − | 8.79781i | 0.0632761 | − | 0.691221i | ||||
\(163\) | −0.555106 | + | 0.961472i | −0.0434793 | + | 0.0753083i | −0.886946 | − | 0.461873i | \(-0.847178\pi\) |
0.843467 | + | 0.537181i | \(0.180511\pi\) | |||||||
\(164\) | −0.945238 | + | 1.63720i | −0.0738107 | + | 0.127844i | ||||
\(165\) | 0.303971 | − | 13.3169i | 0.0236641 | − | 1.03672i | ||||
\(166\) | −7.45206 | + | 4.30245i | −0.578392 | + | 0.333935i | ||||
\(167\) | 7.00830 | − | 12.1387i | 0.542319 | − | 0.939324i | −0.456452 | − | 0.889748i | \(-0.650880\pi\) |
0.998770 | − | 0.0495754i | \(-0.0157868\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.73285 | + | 3.00138i | 0.133296 | + | 0.230875i | ||||
\(170\) | 2.59307 | + | 1.49711i | 0.198879 | + | 0.114823i | ||||
\(171\) | 20.5335 | + | 13.1394i | 1.57024 | + | 1.00480i | ||||
\(172\) | −3.66492 | − | 6.34783i | −0.279448 | − | 0.484018i | ||||
\(173\) | 7.11768 | 0.541147 | 0.270574 | − | 0.962699i | \(-0.412787\pi\) | ||||
0.270574 | + | 0.962699i | \(0.412787\pi\) | |||||||
\(174\) | 0.511170 | + | 0.933965i | 0.0387517 | + | 0.0708037i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.01994 | + | 1.74357i | 0.227637 | + | 0.131426i | ||||
\(177\) | −14.1546 | − | 0.323093i | −1.06393 | − | 0.0242851i | ||||
\(178\) | 8.33752 | + | 4.81367i | 0.624924 | + | 0.360800i | ||||
\(179\) | 5.19845 | − | 3.00133i | 0.388550 | − | 0.224330i | −0.292981 | − | 0.956118i | \(-0.594647\pi\) |
0.681532 | + | 0.731788i | \(0.261314\pi\) | |||||||
\(180\) | 2.69039 | + | 5.19366i | 0.200530 | + | 0.387113i | ||||
\(181\) | − | 1.30283i | − | 0.0968385i | −0.998827 | − | 0.0484192i | \(-0.984582\pi\) | ||
0.998827 | − | 0.0484192i | \(-0.0154184\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.147989 | − | 6.48337i | 0.0109397 | − | 0.479265i | ||||
\(184\) | 6.42428 | + | 11.1272i | 0.473604 | + | 0.820307i | ||||
\(185\) | −14.9396 | −1.09838 | ||||||||
\(186\) | 7.25884 | + | 0.165690i | 0.532244 | + | 0.0121490i | ||||
\(187\) | − | 6.62866i | − | 0.484736i | ||||||
\(188\) | −8.22643 | −0.599974 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.0054 | 1.08861 | ||||||||
\(191\) | 5.73288i | 0.414817i | 0.978254 | + | 0.207408i | \(0.0665029\pi\) | ||||
−0.978254 | + | 0.207408i | \(0.933497\pi\) | |||||||
\(192\) | −11.6636 | − | 0.266233i | −0.841747 | − | 0.0192137i | ||||
\(193\) | 1.55904 | 0.112222 | 0.0561109 | − | 0.998425i | \(-0.482130\pi\) | ||||
0.0561109 | + | 0.998425i | \(0.482130\pi\) | |||||||
\(194\) | 6.49367 | + | 11.2474i | 0.466218 | + | 0.807514i | ||||
\(195\) | 0.301718 | − | 13.2182i | 0.0216065 | − | 0.946574i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.5504i | 1.39291i | 0.717602 | + | 0.696454i | \(0.245240\pi\) | ||||
−0.717602 | + | 0.696454i | \(0.754760\pi\) | |||||||
\(198\) | −6.48889 | + | 10.1405i | −0.461146 | + | 0.720652i | ||||
\(199\) | 0.845590 | − | 0.488202i | 0.0599423 | − | 0.0346077i | −0.469729 | − | 0.882810i | \(-0.655648\pi\) |
0.529672 | + | 0.848203i | \(0.322315\pi\) | |||||||
\(200\) | −3.77151 | − | 2.17748i | −0.266686 | − | 0.153971i | ||||
\(201\) | 21.6990 | + | 0.495301i | 1.53053 | + | 0.0349358i | ||||
\(202\) | −0.892445 | − | 0.515253i | −0.0627922 | − | 0.0362531i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.39746 | + | 2.55332i | 0.0978417 | + | 0.178768i | ||||
\(205\) | −3.43139 | −0.239659 | ||||||||
\(206\) | 0.804411 | + | 1.39328i | 0.0560460 | + | 0.0970745i | ||||
\(207\) | −11.4829 | + | 5.94831i | −0.798118 | + | 0.413436i | ||||
\(208\) | 2.99756 | + | 1.73064i | 0.207843 | + | 0.119998i | ||||
\(209\) | −16.6097 | − | 28.7688i | −1.14892 | − | 1.98998i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9752 | − | 20.7417i | 0.824408 | − | 1.42792i | −0.0779625 | − | 0.996956i | \(-0.524841\pi\) |
0.902371 | − | 0.430961i | \(-0.141825\pi\) | |||||||
\(212\) | −7.51382 | + | 4.33810i | −0.516051 | + | 0.297942i | ||||
\(213\) | 0.572998 | − | 25.1029i | 0.0392612 | − | 1.72002i | ||||
\(214\) | 1.68618 | − | 2.92054i | 0.115265 | − | 0.199644i | ||||
\(215\) | 6.65218 | − | 11.5219i | 0.453675 | − | 0.785787i | ||||
\(216\) | 1.05956 | − | 15.4514i | 0.0720936 | − | 1.05134i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.13740 | + | 1.81138i | −0.212491 | + | 0.122682i | ||||
\(219\) | −5.75744 | + | 3.15111i | −0.389051 | + | 0.212932i | ||||
\(220\) | − | 7.97060i | − | 0.537378i | ||||||
\(221\) | − | 6.57953i | − | 0.442587i | ||||||
\(222\) | 11.5363 | + | 7.01625i | 0.774263 | + | 0.470900i | ||||
\(223\) | 2.68394 | − | 1.54957i | 0.179730 | − | 0.103767i | −0.407436 | − | 0.913234i | \(-0.633577\pi\) |
0.587166 | + | 0.809467i | \(0.300244\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.36257 | − | 3.69209i | 0.157505 | − | 0.246139i | ||||
\(226\) | 8.54970 | − | 14.8085i | 0.568717 | − | 0.985047i | ||||
\(227\) | 10.8991 | − | 18.8779i | 0.723401 | − | 1.25297i | −0.236228 | − | 0.971698i | \(-0.575911\pi\) |
0.959629 | − | 0.281269i | \(-0.0907554\pi\) | |||||||
\(228\) | 12.4630 | + | 7.57989i | 0.825383 | + | 0.501991i | ||||
\(229\) | −11.1810 | + | 6.45536i | −0.738862 | + | 0.426582i | −0.821655 | − | 0.569985i | \(-0.806949\pi\) |
0.0827937 | + | 0.996567i | \(0.473616\pi\) | |||||||
\(230\) | −3.98013 | + | 6.89378i | −0.262442 | + | 0.454563i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.933250 | + | 1.61644i | 0.0612709 | + | 0.106124i | ||||
\(233\) | −0.699758 | − | 0.404005i | −0.0458427 | − | 0.0264673i | 0.476904 | − | 0.878956i | \(-0.341759\pi\) |
−0.522746 | + | 0.852488i | \(0.675092\pi\) | |||||||
\(234\) | −6.44080 | + | 10.0653i | −0.421048 | + | 0.657989i | ||||
\(235\) | −7.46587 | − | 12.9313i | −0.487020 | − | 0.843543i | ||||
\(236\) | −8.47200 | −0.551480 | ||||||||
\(237\) | 14.4785 | + | 0.330485i | 0.940478 | + | 0.0214673i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.2032 | + | 7.04552i | 0.789360 | + | 0.455737i | 0.839737 | − | 0.542993i | \(-0.182709\pi\) |
−0.0503775 | + | 0.998730i | \(0.516042\pi\) | |||||||
\(240\) | −1.33438 | − | 2.43807i | −0.0861340 | − | 0.157377i | ||||
\(241\) | 16.0205 | + | 9.24943i | 1.03197 | + | 0.595808i | 0.917549 | − | 0.397624i | \(-0.130165\pi\) |
0.114422 | + | 0.993432i | \(0.463498\pi\) | |||||||
\(242\) | 4.85628 | − | 2.80377i | 0.312173 | − | 0.180233i | ||||
\(243\) | 15.4871 | + | 1.77494i | 0.993497 | + | 0.113863i | ||||
\(244\) | − | 3.88051i | − | 0.248424i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.64970 | + | 1.61152i | 0.168939 | + | 0.102747i | ||||
\(247\) | −16.4866 | − | 28.5556i | −1.04902 | − | 1.81695i | ||||
\(248\) | 12.7286 | 0.808268 | ||||||||
\(249\) | −7.28955 | − | 13.3188i | −0.461956 | − | 0.844046i | ||||
\(250\) | − | 11.9312i | − | 0.754596i | ||||||
\(251\) | 22.1733 | 1.39957 | 0.699783 | − | 0.714355i | \(-0.253280\pi\) | ||||
0.699783 | + | 0.714355i | \(0.253280\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.6226 | 1.10792 | ||||||||
\(254\) | 9.94262i | 0.623855i | ||||||||
\(255\) | −2.74534 | + | 4.51394i | −0.171920 | + | 0.282674i | ||||
\(256\) | −17.0405 | −1.06503 | ||||||||
\(257\) | 2.02896 | + | 3.51427i | 0.126563 | + | 0.219214i | 0.922343 | − | 0.386372i | \(-0.126272\pi\) |
−0.795780 | + | 0.605586i | \(0.792939\pi\) | |||||||
\(258\) | −10.5479 | + | 5.77301i | −0.656686 | + | 0.359412i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 7.91152i | − | 0.490652i | ||||||
\(261\) | −1.66812 | + | 0.864107i | −0.103254 | + | 0.0534869i | ||||
\(262\) | 4.23100 | − | 2.44277i | 0.261392 | − | 0.150915i | ||||
\(263\) | 8.62617 | + | 4.98032i | 0.531913 | + | 0.307100i | 0.741795 | − | 0.670627i | \(-0.233975\pi\) |
−0.209882 | + | 0.977727i | \(0.567308\pi\) | |||||||
\(264\) | −10.9669 | + | 18.0320i | −0.674966 | + | 1.10979i | ||||
\(265\) | −13.6383 | − | 7.87406i | −0.837793 | − | 0.483700i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.82712 | + | 14.5137i | −0.540211 | + | 0.888226i | ||||
\(268\) | 12.9876 | 0.793341 | ||||||||
\(269\) | 4.98399 | + | 8.63253i | 0.303880 | + | 0.526335i | 0.977011 | − | 0.213188i | \(-0.0683846\pi\) |
−0.673132 | + | 0.739523i | \(0.735051\pi\) | |||||||
\(270\) | 8.61856 | − | 4.21793i | 0.524509 | − | 0.256695i | ||||
\(271\) | −16.4822 | − | 9.51601i | −1.00122 | − | 0.578057i | −0.0926133 | − | 0.995702i | \(-0.529522\pi\) |
−0.908610 | + | 0.417646i | \(0.862855\pi\) | |||||||
\(272\) | −0.691547 | − | 1.19780i | −0.0419312 | − | 0.0726270i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.412606 | + | 0.714655i | −0.0249265 | + | 0.0431739i | ||||
\(275\) | −5.17286 | + | 2.98655i | −0.311935 | + | 0.180096i | ||||
\(276\) | −6.78810 | + | 3.71521i | −0.408596 | + | 0.223629i | ||||
\(277\) | 7.81184 | − | 13.5305i | 0.469368 | − | 0.812969i | −0.530019 | − | 0.847986i | \(-0.677815\pi\) |
0.999387 | + | 0.0350166i | \(0.0111484\pi\) | |||||||
\(278\) | 3.25531 | − | 5.63836i | 0.195240 | − | 0.338166i | ||||
\(279\) | −0.584561 | + | 12.7981i | −0.0349968 | + | 0.766200i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.8780 | + | 12.0539i | −1.24547 | + | 0.719075i | −0.970203 | − | 0.242292i | \(-0.922101\pi\) |
−0.275271 | + | 0.961367i | \(0.588768\pi\) | |||||||
\(282\) | −0.307962 | + | 13.4917i | −0.0183389 | + | 0.803421i | ||||
\(283\) | − | 3.01779i | − | 0.179389i | −0.995969 | − | 0.0896946i | \(-0.971411\pi\) | ||
0.995969 | − | 0.0896946i | \(-0.0285891\pi\) | |||||||
\(284\) | − | 15.0249i | − | 0.891564i | ||||||
\(285\) | −0.604202 | + | 26.4699i | −0.0357898 | + | 1.56794i | ||||
\(286\) | 14.1022 | − | 8.14189i | 0.833879 | − | 0.481440i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.701384 | − | 15.3557i | 0.0413295 | − | 0.904844i | ||||
\(289\) | 7.18544 | − | 12.4456i | 0.422673 | − | 0.732091i | ||||
\(290\) | −0.578190 | + | 1.00145i | −0.0339525 | + | 0.0588074i | ||||
\(291\) | −20.1021 | + | 11.0021i | −1.17840 | + | 0.644954i | ||||
\(292\) | −3.40119 | + | 1.96368i | −0.199040 | + | 0.114916i | ||||
\(293\) | −14.9237 | + | 25.8485i | −0.871849 | + | 1.51009i | −0.0117671 | + | 0.999931i | \(0.503746\pi\) |
−0.860082 | + | 0.510156i | \(0.829588\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.68873 | − | 13.3173i | −0.447655 | − | 0.775362i | ||||
\(296\) | 20.4994 | + | 11.8353i | 1.19150 | + | 0.687914i | ||||
\(297\) | −17.6267 | − | 11.8549i | −1.02281 | − | 0.687888i | ||||
\(298\) | −8.33238 | − | 14.4321i | −0.482682 | − | 0.836029i | ||||
\(299\) | 17.4920 | 1.01159 | ||||||||
\(300\) | 1.36292 | − | 2.24095i | 0.0786884 | − | 0.129381i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.65892 | + | 0.957777i | 0.0954600 | + | 0.0551139i | ||||
\(303\) | 0.944852 | − | 1.55354i | 0.0542803 | − | 0.0892487i | ||||
\(304\) | −6.00272 | − | 3.46567i | −0.344280 | − | 0.198770i | ||||
\(305\) | 6.09984 | − | 3.52175i | 0.349276 | − | 0.201655i | ||||
\(306\) | 4.23987 | − | 2.19631i | 0.242377 | − | 0.125555i | ||||
\(307\) | 2.68853i | 0.153442i | 0.997053 | + | 0.0767212i | \(0.0244451\pi\) | ||||
−0.997053 | + | 0.0767212i | \(0.975555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.49016 | + | 1.36290i | −0.141661 | + | 0.0775324i | ||||
\(310\) | 3.94297 | + | 6.82943i | 0.223946 | + | 0.387886i | ||||
\(311\) | 11.0753 | 0.628020 | 0.314010 | − | 0.949420i | \(-0.398327\pi\) | ||||
0.314010 | + | 0.949420i | \(0.398327\pi\) | |||||||
\(312\) | −10.8856 | + | 17.8983i | −0.616276 | + | 1.01329i | ||||
\(313\) | 16.7397i | 0.946186i | 0.881013 | + | 0.473093i | \(0.156863\pi\) | ||||
−0.881013 | + | 0.473093i | \(0.843137\pi\) | |||||||
\(314\) | −9.34619 | −0.527436 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.66584 | 0.487492 | ||||||||
\(317\) | − | 2.94187i | − | 0.165232i | −0.996581 | − | 0.0826160i | \(-0.973672\pi\) | ||
0.996581 | − | 0.0826160i | \(-0.0263275\pi\) | |||||||
\(318\) | 6.83341 | + | 12.4854i | 0.383198 | + | 0.700147i | ||||
\(319\) | 2.56002 | 0.143334 | ||||||||
\(320\) | −6.33562 | − | 10.9736i | −0.354172 | − | 0.613444i | ||||
\(321\) | 5.08400 | + | 3.09205i | 0.283761 | + | 0.172581i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.1758i | 0.733118i | ||||||||
\(324\) | 9.28893 | + | 0.850332i | 0.516052 | + | 0.0472407i | ||||
\(325\) | −5.13452 | + | 2.96442i | −0.284812 | + | 0.164436i | ||||
\(326\) | 0.943801 | + | 0.544904i | 0.0522723 | + | 0.0301794i | ||||
\(327\) | −3.06898 | − | 5.60737i | −0.169715 | − | 0.310088i | ||||
\(328\) | 4.70839 | + | 2.71839i | 0.259977 | + | 0.150098i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −13.0722 | − | 0.298385i | −0.719598 | − | 0.0164255i | ||||
\(331\) | 4.88153 | 0.268313 | 0.134157 | − | 0.990960i | \(-0.457167\pi\) | ||||
0.134157 | + | 0.990960i | \(0.457167\pi\) | |||||||
\(332\) | −4.54263 | − | 7.86807i | −0.249309 | − | 0.431816i | ||||
\(333\) | −12.8413 | + | 20.0677i | −0.703700 | + | 1.09970i | ||||
\(334\) | −11.9156 | − | 6.87950i | −0.651995 | − | 0.376429i | ||||
\(335\) | 11.7868 | + | 20.4154i | 0.643982 | + | 1.11541i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.51421 | − | 11.2830i | 0.354852 | − | 0.614621i | −0.632241 | − | 0.774772i | \(-0.717865\pi\) |
0.987093 | + | 0.160151i | \(0.0511980\pi\) | |||||||
\(338\) | 2.94622 | − | 1.70100i | 0.160253 | − | 0.0925221i | ||||
\(339\) | 25.7783 | + | 15.6781i | 1.40008 | + | 0.851518i | ||||
\(340\) | −1.58068 | + | 2.73782i | −0.0857245 | + | 0.148479i | ||||
\(341\) | 8.72904 | − | 15.1191i | 0.472704 | − | 0.818748i | ||||
\(342\) | 12.8979 | − | 20.1561i | 0.697440 | − | 1.08992i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −18.2556 | + | 10.5399i | −0.984275 | + | 0.568272i | ||||
\(345\) | −12.0005 | − | 7.29861i | −0.646086 | − | 0.392944i | ||||
\(346\) | − | 6.98687i | − | 0.375617i | ||||||
\(347\) | 2.15180i | 0.115515i | 0.998331 | + | 0.0577573i | \(0.0183949\pi\) | ||||
−0.998331 | + | 0.0577573i | \(0.981605\pi\) | |||||||
\(348\) | −0.986102 | + | 0.539705i | −0.0528606 | + | 0.0289312i | ||||
\(349\) | −25.2919 | + | 14.6023i | −1.35384 | + | 0.781642i | −0.988785 | − | 0.149343i | \(-0.952284\pi\) |
−0.365058 | + | 0.930985i | \(0.618951\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.4961 | − | 11.7670i | −0.933870 | − | 0.628075i | ||||
\(352\) | −10.4735 | + | 18.1407i | −0.558240 | + | 0.966901i | ||||
\(353\) | −5.41764 | + | 9.38362i | −0.288352 | + | 0.499440i | −0.973416 | − | 0.229042i | \(-0.926441\pi\) |
0.685065 | + | 0.728482i | \(0.259774\pi\) | |||||||
\(354\) | −0.317155 | + | 13.8945i | −0.0168566 | + | 0.738483i | ||||
\(355\) | 23.6179 | − | 13.6358i | 1.25351 | − | 0.723713i | ||||
\(356\) | −5.08239 | + | 8.80295i | −0.269366 | + | 0.466556i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.94617 | − | 5.10291i | −0.155710 | − | 0.269697i | ||||
\(359\) | 18.1425 | + | 10.4746i | 0.957527 | + | 0.552829i | 0.895411 | − | 0.445240i | \(-0.146882\pi\) |
0.0621161 | + | 0.998069i | \(0.480215\pi\) | |||||||
\(360\) | 14.9363 | − | 7.73723i | 0.787213 | − | 0.407788i | ||||
\(361\) | 23.5150 | + | 40.7292i | 1.23763 | + | 2.14364i | ||||
\(362\) | −1.27888 | −0.0672167 | ||||||||
\(363\) | 4.75037 | + | 8.67947i | 0.249330 | + | 0.455554i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.17348 | − | 3.56426i | −0.323135 | − | 0.186562i | ||||
\(366\) | −6.36422 | − | 0.145270i | −0.332663 | − | 0.00759336i | ||||
\(367\) | −4.97835 | − | 2.87425i | −0.259868 | − | 0.150035i | 0.364407 | − | 0.931240i | \(-0.381272\pi\) |
−0.624274 | + | 0.781205i | \(0.714605\pi\) | |||||||
\(368\) | 3.18439 | − | 1.83851i | 0.165998 | − | 0.0958389i | ||||
\(369\) | −2.94945 | + | 4.60923i | −0.153542 | + | 0.239947i | ||||
\(370\) | 14.6650i | 0.762398i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.174940 | + | 7.66405i | −0.00907019 | + | 0.397363i | ||||
\(373\) | −14.4467 | − | 25.0224i | −0.748023 | − | 1.29561i | −0.948769 | − | 0.315970i | \(-0.897670\pi\) |
0.200747 | − | 0.979643i | \(-0.435663\pi\) | |||||||
\(374\) | −6.50684 | −0.336461 | ||||||||
\(375\) | 21.0469 | + | 0.480416i | 1.08686 | + | 0.0248086i | ||||
\(376\) | 23.6582i | 1.22008i | ||||||||
\(377\) | 2.54104 | 0.130870 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.411434 | −0.0211339 | −0.0105670 | − | 0.999944i | \(-0.503364\pi\) | ||||
−0.0105670 | + | 0.999944i | \(0.503364\pi\) | |||||||
\(380\) | 15.8431i | 0.812734i | ||||||||
\(381\) | −17.5390 | − | 0.400344i | −0.898549 | − | 0.0205103i | ||||
\(382\) | 5.62752 | 0.287929 | ||||||||
\(383\) | −12.4007 | − | 21.4787i | −0.633648 | − | 1.09751i | −0.986800 | − | 0.161944i | \(-0.948223\pi\) |
0.353152 | − | 0.935566i | \(-0.385110\pi\) | |||||||
\(384\) | 0.143710 | − | 6.29589i | 0.00733366 | − | 0.321286i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1.53038i | − | 0.0778944i | ||||||
\(387\) | −9.75898 | − | 18.8392i | −0.496077 | − | 0.957652i | ||||
\(388\) | −11.8752 | + | 6.85617i | −0.602874 | + | 0.348069i | ||||
\(389\) | −3.82694 | − | 2.20948i | −0.194033 | − | 0.112025i | 0.399836 | − | 0.916587i | \(-0.369067\pi\) |
−0.593869 | + | 0.804561i | \(0.702400\pi\) | |||||||
\(390\) | −12.9753 | − | 0.296173i | −0.657028 | − | 0.0149973i | ||||
\(391\) | −6.05319 | − | 3.49481i | −0.306123 | − | 0.176740i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.13873 | + | 7.56193i | 0.208772 | + | 0.381449i | ||||
\(394\) | 19.1911 | 0.966833 | ||||||||
\(395\) | 7.86465 | + | 13.6220i | 0.395714 | + | 0.685396i | ||||
\(396\) | −10.7066 | − | 6.85113i | −0.538024 | − | 0.344282i | ||||
\(397\) | −19.2780 | − | 11.1301i | −0.967533 | − | 0.558605i | −0.0690495 | − | 0.997613i | \(-0.521997\pi\) |
−0.898483 | + | 0.439008i | \(0.855330\pi\) | |||||||
\(398\) | −0.479229 | − | 0.830049i | −0.0240216 | − | 0.0416066i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.623155 | + | 1.07934i | −0.0311578 | + | 0.0539668i | ||||
\(401\) | 5.31899 | − | 3.07092i | 0.265617 | − | 0.153354i | −0.361277 | − | 0.932459i | \(-0.617659\pi\) |
0.626894 | + | 0.779104i | \(0.284326\pi\) | |||||||
\(402\) | 0.486198 | − | 21.3002i | 0.0242493 | − | 1.06236i | ||||
\(403\) | 8.66434 | − | 15.0071i | 0.431602 | − | 0.747556i | ||||
\(404\) | 0.544017 | − | 0.942265i | 0.0270658 | − | 0.0468794i | ||||
\(405\) | 7.09349 | + | 15.3731i | 0.352478 | + | 0.763898i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.1162 | − | 16.2329i | 1.39367 | − | 0.804633i | ||||
\(408\) | 7.34302 | − | 4.01892i | 0.363534 | − | 0.198966i | ||||
\(409\) | 0.884369i | 0.0437293i | 0.999761 | + | 0.0218646i | \(0.00696028\pi\) | ||||
−0.999761 | + | 0.0218646i | \(0.993040\pi\) | |||||||
\(410\) | 3.36833i | 0.166350i | ||||||||
\(411\) | −1.24405 | − | 0.756622i | −0.0613646 | − | 0.0373214i | ||||
\(412\) | −1.47106 | + | 0.849316i | −0.0724739 | + | 0.0418428i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.83899 | + | 11.2719i | 0.286971 | + | 0.553983i | ||||
\(415\) | 8.24530 | − | 14.2813i | 0.404746 | − | 0.701040i | ||||
\(416\) | −10.3959 | + | 18.0062i | −0.509700 | + | 0.882827i | ||||
\(417\) | 9.81510 | + | 5.96946i | 0.480648 | + | 0.292326i | ||||
\(418\) | −28.2401 | + | 16.3044i | −1.38127 | + | 0.797476i | ||||
\(419\) | 7.59365 | − | 13.1526i | 0.370974 | − | 0.642546i | −0.618742 | − | 0.785595i | \(-0.712357\pi\) |
0.989716 | + | 0.143049i | \(0.0456905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.3318 | + | 23.0914i | 0.649753 | + | 1.12541i | 0.983182 | + | 0.182630i | \(0.0584611\pi\) |
−0.333428 | + | 0.942775i | \(0.608206\pi\) | |||||||
\(422\) | −20.3605 | − | 11.7551i | −0.991133 | − | 0.572231i | ||||
\(423\) | −23.7873 | − | 1.08650i | −1.15658 | − | 0.0528275i | ||||
\(424\) | 12.4759 | + | 21.6088i | 0.605881 | + | 1.04942i | ||||
\(425\) | 2.36910 | 0.114918 | ||||||||
\(426\) | −24.6415 | − | 0.562467i | −1.19389 | − | 0.0272516i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.08358 | + | 1.78031i | 0.149050 | + | 0.0860543i | ||||
\(429\) | 13.7946 | + | 25.2043i | 0.666011 | + | 1.21688i | ||||
\(430\) | −11.3102 | − | 6.52992i | −0.545424 | − | 0.314901i | ||||
\(431\) | 4.06785 | − | 2.34857i | 0.195941 | − | 0.113127i | −0.398820 | − | 0.917029i | \(-0.630580\pi\) |
0.594761 | + | 0.803903i | \(0.297247\pi\) | |||||||
\(432\) | −4.42191 | − | 0.303225i | −0.212749 | − | 0.0145889i | ||||
\(433\) | − | 8.97714i | − | 0.431414i | −0.976458 | − | 0.215707i | \(-0.930794\pi\) | ||
0.976458 | − | 0.215707i | \(-0.0692056\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.74331 | − | 1.06026i | −0.0835851 | − | 0.0508357i | ||||
\(436\) | −1.91250 | − | 3.31254i | −0.0915919 | − | 0.158642i | ||||
\(437\) | −35.0283 | −1.67563 | ||||||||
\(438\) | 3.09320 | + | 5.65162i | 0.147799 | + | 0.270045i | ||||
\(439\) | − | 16.5136i | − | 0.788151i | −0.919078 | − | 0.394075i | \(-0.871065\pi\) | ||
0.919078 | − | 0.394075i | \(-0.128935\pi\) | |||||||
\(440\) | −22.9225 | −1.09279 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.45861 | −0.307205 | ||||||||
\(443\) | 1.06368i | 0.0505368i | 0.999681 | + | 0.0252684i | \(0.00804404\pi\) | ||||
−0.999681 | + | 0.0252684i | \(0.991956\pi\) | |||||||
\(444\) | −7.40792 | + | 12.1803i | −0.351565 | + | 0.578049i | ||||
\(445\) | −18.4500 | −0.874614 | ||||||||
\(446\) | −1.52110 | − | 2.63461i | −0.0720260 | − | 0.124753i | ||||
\(447\) | 25.7940 | − | 14.1174i | 1.22002 | − | 0.667728i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 15.9081i | − | 0.750749i | −0.926873 | − | 0.375374i | \(-0.877514\pi\) | ||
0.926873 | − | 0.375374i | \(-0.122486\pi\) | |||||||
\(450\) | −3.62423 | − | 2.31915i | −0.170848 | − | 0.109326i | ||||
\(451\) | 6.45785 | − | 3.72844i | 0.304088 | − | 0.175565i | ||||
\(452\) | 15.6352 | + | 9.02697i | 0.735417 | + | 0.424593i | ||||
\(453\) | −1.75634 | + | 2.88780i | −0.0825198 | + | 0.135681i | ||||
\(454\) | −18.5309 | − | 10.6988i | −0.869698 | − | 0.502121i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 21.7988 | − | 35.8421i | 1.02082 | − | 1.67846i | ||||
\(457\) | −32.7925 | −1.53397 | −0.766985 | − | 0.641666i | \(-0.778244\pi\) | ||||
−0.766985 | + | 0.641666i | \(0.778244\pi\) | |||||||
\(458\) | 6.33672 | + | 10.9755i | 0.296095 | + | 0.512852i | ||||
\(459\) | 3.70362 | + | 7.56765i | 0.172870 | + | 0.353228i | ||||
\(460\) | −7.27862 | − | 4.20231i | −0.339368 | − | 0.195934i | ||||
\(461\) | 9.23690 | + | 15.9988i | 0.430205 | + | 0.745138i | 0.996891 | − | 0.0787967i | \(-0.0251078\pi\) |
−0.566685 | + | 0.823934i | \(0.691774\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.201921 | + | 0.349738i | −0.00938408 | + | 0.0162537i | −0.870679 | − | 0.491851i | \(-0.836320\pi\) |
0.861295 | + | 0.508105i | \(0.169654\pi\) | |||||||
\(464\) | 0.462594 | − | 0.267079i | 0.0214754 | − | 0.0123988i | ||||
\(465\) | −12.2060 | + | 6.68049i | −0.566041 | + | 0.309801i | ||||
\(466\) | −0.396580 | + | 0.686897i | −0.0183712 | + | 0.0318199i | ||||
\(467\) | −7.51283 | + | 13.0126i | −0.347652 | + | 0.602151i | −0.985832 | − | 0.167736i | \(-0.946354\pi\) |
0.638180 | + | 0.769887i | \(0.279688\pi\) | |||||||
\(468\) | −10.6272 | − | 6.80035i | −0.491242 | − | 0.314346i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −12.6936 | + | 7.32866i | −0.585512 | + | 0.338046i | ||||
\(471\) | 0.376329 | − | 16.4869i | 0.0173403 | − | 0.759675i | ||||
\(472\) | 24.3644i | 1.12146i | ||||||||
\(473\) | 28.9122i | 1.32938i | ||||||||
\(474\) | 0.324412 | − | 14.2124i | 0.0149007 | − | 0.652796i | ||||
\(475\) | 10.2821 | − | 5.93635i | 0.471773 | − | 0.272379i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.2997 | + | 11.5515i | −1.02103 | + | 0.528908i | ||||
\(478\) | 6.91604 | − | 11.9789i | 0.316332 | − | 0.547903i | ||||
\(479\) | 15.5400 | − | 26.9161i | 0.710041 | − | 1.22983i | −0.254800 | − | 0.966994i | \(-0.582010\pi\) |
0.964841 | − | 0.262833i | \(-0.0846569\pi\) | |||||||
\(480\) | 14.6454 | − | 8.01557i | 0.668466 | − | 0.365859i | ||||
\(481\) | 27.9077 | − | 16.1125i | 1.27248 | − | 0.734669i | ||||
\(482\) | 9.07944 | − | 15.7261i | 0.413557 | − | 0.716302i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.96029 | + | 5.12738i | 0.134559 | + | 0.233063i | ||||
\(485\) | −21.5547 | − | 12.4446i | −0.978747 | − | 0.565080i | ||||
\(486\) | 1.74232 | − | 15.2024i | 0.0790333 | − | 0.689597i | ||||
\(487\) | −6.74782 | − | 11.6876i | −0.305773 | − | 0.529614i | 0.671660 | − | 0.740859i | \(-0.265582\pi\) |
−0.977433 | + | 0.211245i | \(0.932248\pi\) | |||||||
\(488\) | −11.1599 | −0.505184 | ||||||||
\(489\) | −0.999224 | + | 1.64294i | −0.0451865 | + | 0.0742965i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.07098 | − | 4.08243i | −0.319109 | − | 0.184238i | 0.331886 | − | 0.943319i | \(-0.392315\pi\) |
−0.650995 | + | 0.759082i | \(0.725648\pi\) | |||||||
\(492\) | −1.70149 | + | 2.79762i | −0.0767089 | + | 0.126126i | ||||
\(493\) | −0.879342 | − | 0.507688i | −0.0396036 | − | 0.0228651i | ||||
\(494\) | −28.0308 | + | 16.1836i | −1.26116 | + | 0.728134i | ||||
\(495\) | 1.05271 | − | 23.0475i | 0.0473159 | − | 1.03591i | ||||
\(496\) | − | 3.64269i | − | 0.163562i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −13.0740 | + | 7.15558i | −0.585862 | + | 0.320649i | ||||
\(499\) | 14.0097 | + | 24.2655i | 0.627159 | + | 1.08627i | 0.988119 | + | 0.153690i | \(0.0491158\pi\) |
−0.360960 | + | 0.932581i | \(0.617551\pi\) | |||||||
\(500\) | 12.5973 | 0.563367 | ||||||||
\(501\) | 12.6154 | − | 20.7424i | 0.563613 | − | 0.926703i | ||||
\(502\) | − | 21.7658i | − | 0.971455i | ||||||
\(503\) | 5.89656 | 0.262915 | 0.131457 | − | 0.991322i | \(-0.458034\pi\) | ||||
0.131457 | + | 0.991322i | \(0.458034\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.97488 | 0.0878811 | ||||||||
\(506\) | − | 17.2987i | − | 0.769022i | ||||||
\(507\) | 2.88196 | + | 5.26567i | 0.127993 | + | 0.233857i | ||||
\(508\) | −10.4977 | −0.465758 | ||||||||
\(509\) | 7.01957 | + | 12.1582i | 0.311137 | + | 0.538905i | 0.978609 | − | 0.205730i | \(-0.0659569\pi\) |
−0.667472 | + | 0.744635i | \(0.732624\pi\) | |||||||
\(510\) | 4.43098 | + | 2.69488i | 0.196207 | + | 0.119331i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 9.45558i | 0.417882i | ||||||||
\(513\) | 35.0365 | + | 23.5638i | 1.54690 | + | 1.04037i | ||||
\(514\) | 3.44968 | − | 1.99168i | 0.152159 | − | 0.0878490i | ||||
\(515\) | −2.67011 | − | 1.54159i | −0.117659 | − | 0.0679305i | ||||
\(516\) | −6.09528 | − | 11.1368i | −0.268330 | − | 0.490269i | ||||
\(517\) | 28.1014 | + | 16.2243i | 1.23590 | + | 0.713546i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.3250 | + | 0.281330i | 0.541007 | + | 0.0123490i | ||||
\(520\) | −22.7526 | −0.997765 | ||||||||
\(521\) | −19.2229 | − | 33.2950i | −0.842170 | − | 1.45868i | −0.888057 | − | 0.459734i | \(-0.847945\pi\) |
0.0458870 | − | 0.998947i | \(-0.485389\pi\) | |||||||
\(522\) | 0.848226 | + | 1.63746i | 0.0371258 | + | 0.0716696i | ||||
\(523\) | 9.08734 | + | 5.24658i | 0.397362 | + | 0.229417i | 0.685345 | − | 0.728219i | \(-0.259651\pi\) |
−0.287983 | + | 0.957635i | \(0.592985\pi\) | |||||||
\(524\) | 2.57914 | + | 4.46720i | 0.112670 | + | 0.195150i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.88879 | − | 8.46764i | 0.213161 | − | 0.369207i | ||||
\(527\) | −5.99668 | + | 3.46219i | −0.261220 | + | 0.150815i | ||||
\(528\) | 5.16042 | + | 3.13852i | 0.224578 | + | 0.136587i | ||||
\(529\) | −2.20889 | + | 3.82591i | −0.0960388 | + | 0.166344i | ||||
\(530\) | −7.72935 | + | 13.3876i | −0.335741 | + | 0.581521i | ||||
\(531\) | −24.4974 | − | 1.11894i | −1.06309 | − | 0.0485576i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.40998 | − | 3.70080i | 0.277647 | − | 0.160300i | ||||
\(534\) | 14.2470 | + | 8.66489i | 0.616527 | + | 0.374967i | ||||
\(535\) | 6.46284i | 0.279413i | ||||||||
\(536\) | − | 37.3506i | − | 1.61330i | ||||||
\(537\) | 9.12026 | − | 4.99163i | 0.393568 | − | 0.215405i | ||||
\(538\) | 8.47388 | − | 4.89240i | 0.365335 | − | 0.210926i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.45339 | + | 9.09968i | 0.191644 | + | 0.391588i | ||||
\(541\) | −22.5783 | + | 39.1067i | −0.970715 | + | 1.68133i | −0.277311 | + | 0.960780i | \(0.589443\pi\) |
−0.693405 | + | 0.720548i | \(0.743890\pi\) | |||||||
\(542\) | −9.34112 | + | 16.1793i | −0.401236 | + | 0.694960i | ||||
\(543\) | 0.0514949 | − | 2.25598i | 0.00220986 | − | 0.0968133i | ||||
\(544\) | 7.19510 | − | 4.15409i | 0.308487 | − | 0.178105i | ||||
\(545\) | 3.47136 | − | 6.01257i | 0.148697 | − | 0.257550i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.05733 | − | 7.02751i | −0.173479 | − | 0.300475i | 0.766155 | − | 0.642656i | \(-0.222168\pi\) |
−0.939634 | + | 0.342181i | \(0.888834\pi\) | |||||||
\(548\) | −0.754550 | − | 0.435640i | −0.0322328 | − | 0.0186096i | ||||
\(549\) | 0.512517 | − | 11.2208i | 0.0218737 | − | 0.478890i | ||||
\(550\) | 2.93166 | + | 5.07779i | 0.125007 | + | 0.216518i | ||||
\(551\) | −5.08854 | −0.216779 | ||||||||
\(552\) | 10.6845 | + | 19.5217i | 0.454762 | + | 0.830901i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −13.2818 | − | 7.66827i | −0.564291 | − | 0.325794i | ||||
\(555\) | −25.8694 | − | 0.590494i | −1.09809 | − | 0.0250651i | ||||
\(556\) | 5.95311 | + | 3.43703i | 0.252468 | + | 0.145763i | ||||
\(557\) | 14.0925 | − | 8.13633i | 0.597120 | − | 0.344747i | −0.170788 | − | 0.985308i | \(-0.554631\pi\) |
0.767908 | + | 0.640561i | \(0.221298\pi\) | |||||||
\(558\) | 12.5629 | + | 0.573818i | 0.531828 | + | 0.0242916i | ||||
\(559\) | 28.6978i | 1.21379i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.262001 | − | 11.4782i | 0.0110617 | − | 0.484610i | ||||
\(562\) | 11.8324 | + | 20.4942i | 0.499118 | + | 0.864498i | ||||
\(563\) | 10.2719 | 0.432908 | 0.216454 | − | 0.976293i | \(-0.430551\pi\) | ||||
0.216454 | + | 0.976293i | \(0.430551\pi\) | |||||||
\(564\) | −14.2449 | − | 0.325154i | −0.599818 | − | 0.0136914i | ||||
\(565\) | 32.7696i | 1.37863i | ||||||||
\(566\) | −2.96233 | −0.124516 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −43.2098 | −1.81304 | ||||||||
\(569\) | − | 20.6157i | − | 0.864256i | −0.901812 | − | 0.432128i | \(-0.857763\pi\) | ||
0.901812 | − | 0.432128i | \(-0.142237\pi\) | |||||||
\(570\) | 25.9834 | + | 0.593097i | 1.08833 | + | 0.0248421i | ||||
\(571\) | 4.25655 | 0.178131 | 0.0890656 | − | 0.996026i | \(-0.471612\pi\) | ||||
0.0890656 | + | 0.996026i | \(0.471612\pi\) | |||||||
\(572\) | 8.59640 | + | 14.8894i | 0.359434 | + | 0.622557i | ||||
\(573\) | −0.226595 | + | 9.92706i | −0.00946614 | + | 0.414709i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.29836i | 0.262660i | ||||||||
\(576\) | −20.1861 | − | 0.922018i | −0.841090 | − | 0.0384174i | ||||
\(577\) | 14.6609 | − | 8.46446i | 0.610340 | − | 0.352380i | −0.162758 | − | 0.986666i | \(-0.552039\pi\) |
0.773099 | + | 0.634286i | \(0.218706\pi\) | |||||||
\(578\) | −12.2168 | − | 7.05338i | −0.508153 | − | 0.293382i | ||||
\(579\) | 2.69963 | + | 0.0616216i | 0.112193 | + | 0.00256091i | ||||
\(580\) | −1.05736 | − | 0.610467i | −0.0439045 | − | 0.0253483i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.7999 | + | 19.7326i | 0.447669 | + | 0.817943i | ||||
\(583\) | 34.2228 | 1.41736 | ||||||||
\(584\) | 5.64730 | + | 9.78141i | 0.233687 | + | 0.404758i | ||||
\(585\) | 1.04491 | − | 22.8767i | 0.0432017 | − | 0.945834i | ||||
\(586\) | 25.3735 | + | 14.6494i | 1.04817 | + | 0.605160i | ||||
\(587\) | −12.0558 | − | 20.8812i | −0.497594 | − | 0.861858i | 0.502402 | − | 0.864634i | \(-0.332450\pi\) |
−0.999996 | + | 0.00277589i | \(0.999116\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.3507 | + | 30.0522i | −0.714922 | + | 1.23828i | ||||
\(590\) | −13.0725 | + | 7.54743i | −0.538187 | + | 0.310723i | ||||
\(591\) | −0.772738 | + | 33.8534i | −0.0317862 | + | 1.39254i | ||||
\(592\) | 3.38705 | − | 5.86654i | 0.139207 | − | 0.241113i | ||||
\(593\) | −19.2908 | + | 33.4126i | −0.792178 | + | 1.37209i | 0.132437 | + | 0.991191i | \(0.457720\pi\) |
−0.924616 | + | 0.380902i | \(0.875614\pi\) | |||||||
\(594\) | −11.6370 | + | 17.3028i | −0.477471 | + | 0.709941i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.2378 | − | 8.79752i | 0.624163 | − | 0.360360i | ||||
\(597\) | 1.48352 | − | 0.811947i | 0.0607164 | − | 0.0332308i | ||||
\(598\) | − | 17.1705i | − | 0.702154i | ||||||
\(599\) | 33.8236i | 1.38199i | 0.722857 | + | 0.690997i | \(0.242828\pi\) | ||||
−0.722857 | + | 0.690997i | \(0.757172\pi\) | |||||||
\(600\) | −6.44468 | − | 3.91960i | −0.263103 | − | 0.160017i | ||||
\(601\) | 27.4855 | − | 15.8688i | 1.12116 | − | 0.647300i | 0.179461 | − | 0.983765i | \(-0.442565\pi\) |
0.941696 | + | 0.336465i | \(0.109231\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 37.5544 | + | 1.71533i | 1.52933 | + | 0.0698534i | ||||
\(604\) | −1.01124 | + | 1.75153i | −0.0411469 | + | 0.0712686i | ||||
\(605\) | −5.37320 | + | 9.30666i | −0.218452 | + | 0.378370i | ||||
\(606\) | −1.52499 | − | 0.927487i | −0.0619486 | − | 0.0376766i | ||||
\(607\) | −0.169355 | + | 0.0977772i | −0.00687391 | + | 0.00396865i | −0.503433 | − | 0.864034i | \(-0.667930\pi\) |
0.496559 | + | 0.868003i | \(0.334597\pi\) | |||||||
\(608\) | 20.8181 | − | 36.0581i | 0.844287 | − | 1.46235i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.45702 | − | 5.98774i | −0.139971 | − | 0.242436i | ||||
\(611\) | 27.8931 | + | 16.1041i | 1.12843 | + | 0.651502i | ||||
\(612\) | 2.31892 | + | 4.47656i | 0.0937367 | + | 0.180954i | ||||
\(613\) | −1.46664 | − | 2.54029i | −0.0592370 | − | 0.102602i | 0.834886 | − | 0.550423i | \(-0.185533\pi\) |
−0.894123 | + | 0.447821i | \(0.852200\pi\) | |||||||
\(614\) | 2.63912 | 0.106506 | ||||||||
\(615\) | −5.94180 | − | 0.135627i | −0.239596 | − | 0.00546902i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.86982 | − | 4.54365i | −0.316827 | − | 0.182920i | 0.333150 | − | 0.942874i | \(-0.391888\pi\) |
−0.649977 | + | 0.759953i | \(0.725222\pi\) | |||||||
\(618\) | 1.33785 | + | 2.44440i | 0.0538161 | + | 0.0983282i | ||||
\(619\) | 24.8586 | + | 14.3521i | 0.999152 | + | 0.576861i | 0.907997 | − | 0.418976i | \(-0.137611\pi\) |
0.0911550 | + | 0.995837i | \(0.470944\pi\) | |||||||
\(620\) | −7.21068 | + | 4.16309i | −0.289588 | + | 0.167194i | ||||
\(621\) | −20.1189 | + | 9.84623i | −0.807345 | + | 0.395116i | ||||
\(622\) | − | 10.8717i | − | 0.435916i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.12217 | + | 3.11526i | 0.205051 | + | 0.124710i | ||||
\(625\) | 7.77986 | + | 13.4751i | 0.311194 | + | 0.539004i | ||||
\(626\) | 16.4321 | 0.656758 | ||||||||
\(627\) | −27.6243 | − | 50.4726i | −1.10321 | − | 2.01568i | ||||
\(628\) | − | 9.86793i | − | 0.393773i | ||||||
\(629\) | −12.8768 | −0.513433 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.7691 | −0.826805 | −0.413403 | − | 0.910548i | \(-0.635660\pi\) | ||||
−0.413403 | + | 0.910548i | \(0.635660\pi\) | |||||||
\(632\) | − | 24.9219i | − | 0.991340i | ||||||
\(633\) | 21.5561 | − | 35.4430i | 0.856779 | − | 1.40873i | ||||
\(634\) | −2.88781 | −0.114689 | ||||||||
\(635\) | −9.52711 | − | 16.5014i | −0.378072 | − | 0.654839i | ||||
\(636\) | −13.1824 | + | 7.21487i | −0.522716 | + | 0.286088i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 2.51297i | − | 0.0994895i | ||||||
\(639\) | 1.98441 | − | 43.4455i | 0.0785019 | − | 1.71868i | ||||
\(640\) | 5.92345 | − | 3.41990i | 0.234145 | − | 0.135184i | ||||
\(641\) | −39.7733 | − | 22.9632i | −1.57095 | − | 0.906990i | −0.996052 | − | 0.0887664i | \(-0.971708\pi\) |
−0.574900 | − | 0.818224i | \(-0.694959\pi\) | |||||||
\(642\) | 3.03522 | − | 4.99057i | 0.119791 | − | 0.196962i | ||||
\(643\) | −9.15428 | − | 5.28523i | −0.361010 | − | 0.208429i | 0.308514 | − | 0.951220i | \(-0.400168\pi\) |
−0.669524 | + | 0.742791i | \(0.733502\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.9743 | − | 19.6884i | 0.471488 | − | 0.775230i | ||||
\(646\) | 12.9336 | 0.508866 | ||||||||
\(647\) | −19.2562 | − | 33.3526i | −0.757038 | − | 1.31123i | −0.944355 | − | 0.328928i | \(-0.893313\pi\) |
0.187317 | − | 0.982299i | \(-0.440021\pi\) | |||||||
\(648\) | 2.44545 | − | 26.7138i | 0.0960664 | − | 1.04942i | ||||
\(649\) | 28.9402 | + | 16.7087i | 1.13600 | + | 0.655872i | ||||
\(650\) | 2.90993 | + | 5.04015i | 0.114137 | + | 0.197691i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.575323 | + | 0.996488i | −0.0225314 | + | 0.0390255i | ||||
\(653\) | 11.0867 | − | 6.40089i | 0.433855 | − | 0.250486i | −0.267133 | − | 0.963660i | \(-0.586076\pi\) |
0.700988 | + | 0.713173i | \(0.252743\pi\) | |||||||
\(654\) | −5.50431 | + | 3.01257i | −0.215236 | + | 0.117801i | ||||
\(655\) | −4.68137 | + | 8.10837i | −0.182916 | + | 0.316820i | ||||
\(656\) | 0.777952 | − | 1.34745i | 0.0303739 | − | 0.0526092i | ||||
\(657\) | −10.0941 | + | 5.22890i | −0.393809 | + | 0.203999i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.5777 | − | 24.0049i | 1.61964 | − | 0.935097i | 0.632622 | − | 0.774461i | \(-0.281979\pi\) |
0.987014 | − | 0.160636i | \(-0.0513546\pi\) | |||||||
\(660\) | 0.315042 | − | 13.8019i | 0.0122630 | − | 0.537238i | ||||
\(661\) | − | 10.8312i | − | 0.421285i | −0.977563 | − | 0.210643i | \(-0.932444\pi\) | ||
0.977563 | − | 0.210643i | \(-0.0675557\pi\) | |||||||
\(662\) | − | 4.79182i | − | 0.186239i | ||||||
\(663\) | 0.260059 | − | 11.3931i | 0.0100998 | − | 0.442472i | ||||
\(664\) | −22.6276 | + | 13.0640i | −0.878121 | + | 0.506983i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 19.6989 | + | 12.6053i | 0.763315 | + | 0.488446i | ||||
\(667\) | 1.34971 | − | 2.33777i | 0.0522611 | − | 0.0905188i | ||||
\(668\) | 7.26354 | − | 12.5808i | 0.281035 | − | 0.486767i | ||||
\(669\) | 4.70876 | − | 2.57716i | 0.182051 | − | 0.0996387i | ||||
\(670\) | 20.0402 | − | 11.5702i | 0.774219 | − | 0.446995i | ||||
\(671\) | −7.65323 | + | 13.2558i | −0.295450 | + | 0.511734i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.19553 | − | 10.7310i | −0.238820 | − | 0.413649i | 0.721556 | − | 0.692356i | \(-0.243427\pi\) |
−0.960376 | + | 0.278707i | \(0.910094\pi\) | |||||||
\(674\) | −11.0756 | − | 6.39449i | −0.426616 | − | 0.246307i | ||||
\(675\) | 4.23696 | − | 6.29983i | 0.163081 | − | 0.242481i | ||||
\(676\) | 1.79595 | + | 3.11068i | 0.0690752 | + | 0.119642i | ||||
\(677\) | 28.9895 | 1.11416 | 0.557078 | − | 0.830460i | \(-0.311922\pi\) | ||||
0.557078 | + | 0.830460i | \(0.311922\pi\) | |||||||
\(678\) | 15.3900 | − | 25.3045i | 0.591048 | − | 0.971813i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.87364 | + | 4.54585i | 0.301940 | + | 0.174325i | ||||
\(681\) | 19.6191 | − | 32.2581i | 0.751805 | − | 1.23613i | ||||
\(682\) | −14.8413 | − | 8.56862i | −0.568302 | − | 0.328109i | ||||
\(683\) | −0.132048 | + | 0.0762380i | −0.00505268 | + | 0.00291717i | −0.502524 | − | 0.864563i | \(-0.667595\pi\) |
0.497472 | + | 0.867480i | \(0.334262\pi\) | |||||||
\(684\) | 21.2813 | + | 13.6179i | 0.813712 | + | 0.520695i | ||||
\(685\) | − | 1.58145i | − | 0.0604242i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.6162 | + | 10.7362i | −0.748404 | + | 0.409610i | ||||
\(688\) | 3.01631 | + | 5.22441i | 0.114996 | + | 0.199179i | ||||
\(689\) | 33.9691 | 1.29412 | ||||||||
\(690\) | −7.16447 | + | 11.7800i | −0.272747 | + | 0.448455i | ||||
\(691\) | 43.2353i | 1.64475i | 0.568948 | + | 0.822373i | \(0.307350\pi\) | ||||
−0.568948 | + | 0.822373i | \(0.692650\pi\) | |||||||
\(692\) | 7.37691 | 0.280428 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.11225 | 0.0801799 | ||||||||
\(695\) | 12.4771i | 0.473282i | ||||||||
\(696\) | 1.55213 | + | 2.83591i | 0.0588332 | + | 0.107495i | ||||
\(697\) | −2.95761 | −0.112027 | ||||||||
\(698\) | 14.3339 | + | 24.8271i | 0.542546 | + | 0.939718i | ||||
\(699\) | −1.19573 | − | 0.727234i | −0.0452267 | − | 0.0275065i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.5821i | 0.437451i | 0.975786 | + | 0.218726i | \(0.0701900\pi\) | ||||
−0.975786 | + | 0.218726i | \(0.929810\pi\) | |||||||
\(702\) | −11.5507 | + | 17.1745i | −0.435954 | + | 0.648210i | ||||
\(703\) | −55.8863 | + | 32.2660i | −2.10779 | + | 1.21693i | ||||
\(704\) | 23.8472 | + | 13.7682i | 0.898774 | + | 0.518907i | ||||
\(705\) | −12.4168 | − | 22.6869i | −0.467643 | − | 0.854437i | ||||
\(706\) | 9.21116 | + | 5.31807i | 0.346667 | + | 0.200148i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −14.6701 | − | 0.334860i | −0.551337 | − | 0.0125848i | ||||
\(709\) | −37.8948 | −1.42317 | −0.711584 | − | 0.702601i | \(-0.752022\pi\) | ||||
−0.711584 | + | 0.702601i | \(0.752022\pi\) | |||||||
\(710\) | −13.3852 | − | 23.1838i | −0.502337 | − | 0.870073i | ||||
\(711\) | 25.0579 | + | 1.14454i | 0.939743 | + | 0.0429235i | ||||
\(712\) | 25.3162 | + | 14.6163i | 0.948765 | + | 0.547770i | ||||
\(713\) | −9.20437 | − | 15.9424i | −0.344707 | − | 0.597049i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.6033 | + | 27.0256i | −0.583529 | + | 1.01070i | ||||
\(716\) | 5.38777 | − | 3.11063i | 0.201351 | − | 0.116250i | ||||
\(717\) | 20.8526 | + | 12.6824i | 0.778754 | + | 0.473631i | ||||
\(718\) | 10.2821 | − | 17.8091i | 0.383724 | − | 0.664630i | ||||
\(719\) | −23.3158 | + | 40.3842i | −0.869534 | + | 1.50608i | −0.00706058 | + | 0.999975i | \(0.502247\pi\) |
−0.862474 | + | 0.506102i | \(0.831086\pi\) | |||||||
\(720\) | −2.21425 | − | 4.27450i | −0.0825202 | − | 0.159301i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 39.9806 | − | 23.0828i | 1.48792 | − | 0.859054i | ||||
\(723\) | 27.3755 | + | 16.6495i | 1.01811 | + | 0.619203i | ||||
\(724\) | − | 1.35028i | − | 0.0501826i | ||||||
\(725\) | 0.914958i | 0.0339807i | ||||||||
\(726\) | 8.51995 | − | 4.66307i | 0.316205 | − | 0.173063i | ||||
\(727\) | 3.72659 | − | 2.15155i | 0.138212 | − | 0.0797965i | −0.429300 | − | 0.903162i | \(-0.641240\pi\) |
0.567511 | + | 0.823366i | \(0.307906\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.7473 | + | 3.68562i | 0.990639 | + | 0.136505i | ||||
\(730\) | −3.49875 | + | 6.06002i | −0.129495 | + | 0.224291i | ||||
\(731\) | 5.73369 | − | 9.93104i | 0.212068 | − | 0.367313i | ||||
\(732\) | 0.153379 | − | 6.71949i | 0.00566905 | − | 0.248360i | ||||
\(733\) | 12.1337 | − | 7.00539i | 0.448168 | − | 0.258750i | −0.258888 | − | 0.965907i | \(-0.583356\pi\) |
0.707056 | + | 0.707157i | \(0.250023\pi\) | |||||||
\(734\) | −2.82143 | + | 4.88685i | −0.104141 | + | 0.180377i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.0438 | + | 19.1285i | 0.407081 | + | 0.705086i | ||||
\(737\) | −44.3653 | − | 25.6143i | −1.63422 | − | 0.943516i | ||||
\(738\) | 4.52452 | + | 2.89525i | 0.166550 | + | 0.106575i | ||||
\(739\) | −18.9313 | − | 32.7901i | −0.696401 | − | 1.20620i | −0.969706 | − | 0.244274i | \(-0.921450\pi\) |
0.273305 | − | 0.961927i | \(-0.411883\pi\) | |||||||
\(740\) | −15.4837 | −0.569191 | ||||||||
\(741\) | −27.4195 | − | 50.0985i | −1.00728 | − | 1.84041i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.0489 | − | 13.8847i | −0.882269 | − | 0.509378i | −0.0108634 | − | 0.999941i | \(-0.503458\pi\) |
−0.871406 | + | 0.490563i | \(0.836791\pi\) | |||||||
\(744\) | 22.0409 | + | 0.503105i | 0.808058 | + | 0.0184447i | ||||
\(745\) | 27.6579 | + | 15.9683i | 1.01331 | + | 0.585034i | ||||
\(746\) | −24.5626 | + | 14.1812i | −0.899300 | + | 0.519211i | ||||
\(747\) | −12.0961 | − | 23.3510i | −0.442575 | − | 0.854369i | ||||
\(748\) | − | 6.87007i | − | 0.251195i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.471587 | − | 20.6601i | 0.0172199 | − | 0.754400i | ||||
\(751\) | 8.67540 | + | 15.0262i | 0.316570 | + | 0.548315i | 0.979770 | − | 0.200127i | \(-0.0641355\pi\) |
−0.663200 | + | 0.748442i | \(0.730802\pi\) | |||||||
\(752\) | 6.77054 | 0.246896 | ||||||||
\(753\) | 38.3953 | + | 0.876410i | 1.39920 | + | 0.0319382i | ||||
\(754\) | − | 2.49434i | − | 0.0908387i | ||||||
\(755\) | −3.67100 | −0.133601 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.8111 | 0.683701 | 0.341850 | − | 0.939754i | \(-0.388946\pi\) | ||||
0.341850 | + | 0.939754i | \(0.388946\pi\) | |||||||
\(758\) | 0.403872i | 0.0146693i | ||||||||
\(759\) | 30.5153 | + | 0.696541i | 1.10763 | + | 0.0252828i | ||||
\(760\) | 45.5628 | 1.65274 | ||||||||
\(761\) | −4.22520 | − | 7.31825i | −0.153163 | − | 0.265286i | 0.779225 | − | 0.626744i | \(-0.215613\pi\) |
−0.932389 | + | 0.361457i | \(0.882279\pi\) | |||||||
\(762\) | −0.392986 | + | 17.2166i | −0.0142364 | + | 0.623693i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.94167i | 0.214962i | ||||||||
\(765\) | −4.93224 | + | 7.70783i | −0.178326 | + | 0.278677i | ||||
\(766\) | −21.0840 | + | 12.1728i | −0.761794 | + | 0.439822i | ||||
\(767\) | 28.7257 | + | 16.5848i | 1.03723 | + | 0.598843i | ||||
\(768\) | −29.5074 | − | 0.673534i | −1.06476 | − | 0.0243041i | ||||
\(769\) | −19.8100 | − | 11.4373i | −0.714366 | − | 0.412440i | 0.0983092 | − | 0.995156i | \(-0.468657\pi\) |
−0.812676 | + | 0.582716i | \(0.801990\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.37445 | + | 6.16550i | 0.121528 | + | 0.222045i | ||||
\(772\) | 1.61581 | 0.0581544 | ||||||||
\(773\) | 18.8374 | + | 32.6273i | 0.677533 | + | 1.17352i | 0.975722 | + | 0.219015i | \(0.0702843\pi\) |
−0.298189 | + | 0.954507i | \(0.596382\pi\) | |||||||
\(774\) | −18.4930 | + | 9.57963i | −0.664717 | + | 0.344333i | ||||
\(775\) | 5.40363 | + | 3.11978i | 0.194104 | + | 0.112066i | ||||
\(776\) | 19.7175 | + | 34.1517i | 0.707817 | + | 1.22598i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.16888 | + | 3.75660i | −0.0777579 | + | 0.134681i | ||||
\(779\) | −12.8362 | + | 7.41099i | −0.459905 | + | 0.265526i | ||||
\(780\) | 0.312706 | − | 13.6996i | 0.0111967 | − | 0.490524i | ||||
\(781\) | −29.6324 | + | 51.3249i | −1.06033 | + | 1.83655i | ||||
\(782\) | −3.43058 | + | 5.94194i | −0.122677 | + | 0.212483i | ||||
\(783\) | −2.92266 | + | 1.43035i | −0.104447 | + | 0.0511167i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.5116 | − | 8.95561i | 0.553632 | − | 0.319639i | ||||
\(786\) | 7.42296 | − | 4.06267i | 0.264768 | − | 0.144911i | ||||
\(787\) | − | 23.4661i | − | 0.836475i | −0.908338 | − | 0.418237i | \(-0.862648\pi\) | ||
0.908338 | − | 0.418237i | \(-0.137352\pi\) | |||||||
\(788\) | 20.2624i | 0.721818i | ||||||||
\(789\) | 14.7402 | + | 8.96488i | 0.524766 | + | 0.319158i | ||||
\(790\) | 13.3716 | − | 7.72011i | 0.475741 | − | 0.274669i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −19.7030 | + | 30.7907i | −0.700116 | + | 1.09410i | ||||
\(793\) | −7.59650 | + | 13.1575i | −0.269760 | + | 0.467237i | ||||
\(794\) | −10.9256 | + | 18.9237i | −0.387734 | + | 0.671575i | ||||
\(795\) | −23.3048 | − | 14.1738i | −0.826536 | − | 0.502692i | ||||
\(796\) | 0.876386 | − | 0.505981i | 0.0310627 | − | 0.0179340i | ||||
\(797\) | 22.8856 | − | 39.6390i | 0.810648 | − | 1.40408i | −0.101763 | − | 0.994809i | \(-0.532448\pi\) |
0.912411 | − | 0.409275i | \(-0.134218\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.43503 | − | 11.1458i | −0.227655 | − | 0.394310i | ||||
\(800\) | −6.48352 | − | 3.74326i | −0.229227 | − | 0.132344i | ||||
\(801\) | −15.8587 | + | 24.7831i | −0.560340 | + | 0.875667i | ||||
\(802\) | −3.01448 | − | 5.22123i | −0.106445 | − | 0.184368i | ||||
\(803\) | 15.4912 | 0.546674 | ||||||||
\(804\) | 22.4893 | + | 0.513339i | 0.793135 | + | 0.0181041i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.7313 | − | 8.50510i | −0.518887 | − | 0.299579i | ||||
\(807\) | 8.28908 | + | 15.1451i | 0.291789 | + | 0.533132i | ||||
\(808\) | −2.70984 | − | 1.56453i | −0.0953317 | − | 0.0550398i | ||||
\(809\) | 11.4669 | − | 6.62041i | 0.403154 | − | 0.232761i | −0.284690 | − | 0.958620i | \(-0.591891\pi\) |
0.687844 | + | 0.725858i | \(0.258557\pi\) | |||||||
\(810\) | 15.0906 | − | 6.96312i | 0.530230 | − | 0.244659i | ||||
\(811\) | − | 56.0437i | − | 1.96796i | −0.178275 | − | 0.983981i | \(-0.557052\pi\) | ||
0.178275 | − | 0.983981i | \(-0.442948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.1645 | − | 17.1294i | −0.987771 | − | 0.600754i | ||||
\(814\) | −15.9345 | − | 27.5994i | −0.558505 | − | 0.967359i | ||||
\(815\) | −2.08853 | −0.0731579 | ||||||||
\(816\) | −1.15014 | − | 2.10144i | −0.0402629 | − | 0.0735650i | ||||
\(817\) | − | 57.4685i | − | 2.01057i | ||||||
\(818\) | 0.868116 | 0.0303530 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.55636 | −0.124193 | ||||||||
\(821\) | 56.3224i | 1.96567i | 0.184499 | + | 0.982833i | \(0.440934\pi\) | ||||
−0.184499 | + | 0.982833i | \(0.559066\pi\) | |||||||
\(822\) | −0.742716 | + | 1.22119i | −0.0259052 | + | 0.0425938i | ||||
\(823\) | 17.0436 | 0.594103 | 0.297051 | − | 0.954862i | \(-0.403997\pi\) | ||||
0.297051 | + | 0.954862i | \(0.403997\pi\) | |||||||
\(824\) | 2.44253 | + | 4.23058i | 0.0850895 | + | 0.147379i | ||||
\(825\) | −9.07537 | + | 4.96705i | −0.315964 | + | 0.172931i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 45.7715i | − | 1.59163i | −0.605539 | − | 0.795816i | \(-0.707042\pi\) | ||
0.605539 | − | 0.795816i | \(-0.292958\pi\) | |||||||
\(828\) | −11.9011 | + | 6.16495i | −0.413593 | + | 0.214247i | ||||
\(829\) | 30.5567 | − | 17.6419i | 1.06128 | − | 0.612730i | 0.135493 | − | 0.990778i | \(-0.456738\pi\) |
0.925786 | + | 0.378049i | \(0.123405\pi\) | |||||||
\(830\) | −14.0188 | − | 8.09376i | −0.486600 | − | 0.280938i | ||||
\(831\) | 14.0618 | − | 23.1207i | 0.487798 | − | 0.802047i | ||||
\(832\) | 23.6704 | + | 13.6661i | 0.820623 | + | 0.473787i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5.85975 | − | 9.63472i | 0.202907 | − | 0.333623i | ||||
\(835\) | 26.3680 | 0.912502 | ||||||||
\(836\) | −17.2146 | − | 29.8166i | −0.595380 | − | 1.03123i | ||||
\(837\) | −1.51808 | + | 22.1380i | −0.0524724 | + | 0.765202i | ||||
\(838\) | −12.9109 | − | 7.45409i | −0.445998 | − | 0.257497i | ||||
\(839\) | 22.3195 | + | 38.6585i | 0.770555 | + | 1.33464i | 0.937259 | + | 0.348634i | \(0.113354\pi\) |
−0.166704 | + | 0.986007i | \(0.553312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.3039 | + | 24.7751i | −0.493239 | + | 0.854315i | ||||
\(842\) | 22.6670 | − | 13.0868i | 0.781157 | − | 0.451001i | ||||
\(843\) | −36.6287 | + | 20.0473i | −1.26156 | + | 0.690466i | ||||
\(844\) | 12.4114 | − | 21.4971i | 0.427216 | − | 0.739960i | ||||
\(845\) | −3.25982 | + | 5.64618i | −0.112141 | + | 0.194235i | ||||
\(846\) | −1.06653 | + | 23.3501i | −0.0366682 | + | 0.802793i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.18404 | − | 3.57036i | 0.212361 | − | 0.122607i | ||||
\(849\) | 0.119280 | − | 5.22561i | 0.00409367 | − | 0.179342i | ||||
\(850\) | − | 2.32556i | − | 0.0797661i | ||||||
\(851\) | − | 34.2336i | − | 1.17351i | ||||||
\(852\) | 0.593866 | − | 26.0171i | 0.0203455 | − | 0.891332i | ||||
\(853\) | −47.7652 | + | 27.5772i | −1.63545 | + | 0.944227i | −0.653077 | + | 0.757292i | \(0.726522\pi\) |
−0.982372 | + | 0.186935i | \(0.940145\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.09247 | + | 45.8114i | −0.0715610 | + | 1.56672i | ||||
\(856\) | 5.11994 | − | 8.86800i | 0.174996 | − | 0.303102i | ||||
\(857\) | −19.0771 | + | 33.0425i | −0.651660 | + | 1.12871i | 0.331059 | + | 0.943610i | \(0.392594\pi\) |
−0.982720 | + | 0.185099i | \(0.940739\pi\) | |||||||
\(858\) | 24.7411 | − | 13.5411i | 0.844648 | − | 0.462286i | ||||
\(859\) | −35.0465 | + | 20.2341i | −1.19577 | + | 0.690378i | −0.959609 | − | 0.281336i | \(-0.909222\pi\) |
−0.236160 | + | 0.971714i | \(0.575889\pi\) | |||||||
\(860\) | 6.89444 | − | 11.9415i | 0.235099 | − | 0.407203i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.30541 | − | 3.99309i | −0.0785226 | − | 0.136005i | ||||
\(863\) | −31.3519 | − | 18.1011i | −1.06723 | − | 0.616167i | −0.139808 | − | 0.990179i | \(-0.544649\pi\) |
−0.927424 | + | 0.374012i | \(0.877982\pi\) | |||||||
\(864\) | 1.82146 | − | 26.5622i | 0.0619673 | − | 0.903666i | ||||
\(865\) | 6.69488 | + | 11.5959i | 0.227633 | + | 0.394272i | ||||
\(866\) | −8.81216 | −0.299449 | ||||||||
\(867\) | 12.9342 | − | 21.2667i | 0.439269 | − | 0.722255i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.6024 | − | 17.0910i | −1.00419 | − | 0.579771i | ||||
\(870\) | −1.04078 | + | 1.71127i | −0.0352856 | + | 0.0580173i | ||||
\(871\) | −44.0365 | − | 25.4245i | −1.49212 | − | 0.861475i | ||||
\(872\) | −9.52645 | + | 5.50010i | −0.322606 | + | 0.186257i | ||||
\(873\) | −35.2436 | + | 18.2567i | −1.19281 | + | 0.617894i | ||||
\(874\) | 34.3846i | 1.16307i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.96712 | + | 3.26587i | −0.201610 | + | 0.110344i | ||||
\(877\) | 5.53439 | + | 9.58584i | 0.186883 | + | 0.323691i | 0.944209 | − | 0.329346i | \(-0.106828\pi\) |
−0.757326 | + | 0.653036i | \(0.773495\pi\) | |||||||
\(878\) | −16.2101 | −0.547064 | ||||||||
\(879\) | −26.8635 | + | 44.1694i | −0.906082 | + | 1.48980i | ||||
\(880\) | 6.55998i | 0.221137i | ||||||||
\(881\) | −8.87036 | −0.298850 | −0.149425 | − | 0.988773i | \(-0.547742\pi\) | ||||
−0.149425 | + | 0.988773i | \(0.547742\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.1903 | −0.477540 | −0.238770 | − | 0.971076i | \(-0.576744\pi\) | ||||
−0.238770 | + | 0.971076i | \(0.576744\pi\) | |||||||
\(884\) | − | 6.81915i | − | 0.229353i | ||||||
\(885\) | −12.7874 | − | 23.3641i | −0.429845 | − | 0.785375i | ||||
\(886\) | 1.04413 | 0.0350782 | ||||||||
\(887\) | −19.5180 | − | 33.8062i | −0.655350 | − | 1.13510i | −0.981806 | − | 0.189887i | \(-0.939188\pi\) |
0.326456 | − | 0.945213i | \(-0.394146\pi\) | |||||||
\(888\) | 35.0289 | + | 21.3043i | 1.17549 | + | 0.714925i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 18.1109i | 0.607080i | ||||||||
\(891\) | −30.0538 | − | 21.2246i | −1.00684 | − | 0.711050i | ||||
\(892\) | 2.78169 | − | 1.60601i | 0.0931378 | − | 0.0537732i | ||||
\(893\) | −55.8570 | − | 32.2490i | −1.86918 | − | 1.07917i | ||||
\(894\) | −13.8579 | − | 25.3200i | −0.463478 | − | 0.846826i | ||||
\(895\) | 9.77931 | + | 5.64609i | 0.326886 | + | 0.188728i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30.2891 | + | 0.691378i | 1.01132 | + | 0.0230844i | ||||
\(898\) | −15.6157 | −0.521103 | ||||||||
\(899\) | −1.33711 | − | 2.31595i | −0.0445952 | − | 0.0772411i | ||||
\(900\) | 2.44861 | − | 3.82655i | 0.0816204 | − | 0.127552i | ||||
\(901\) | −11.7552 | − | 6.78687i | −0.391622 | − | 0.226103i | ||||
\(902\) | −3.65992 | − | 6.33916i | −0.121862 | − | 0.211071i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 25.9605 | − | 44.9648i | 0.863432 | − | 1.49551i | ||||
\(905\) | 2.12252 | − | 1.22544i | 0.0705550 | − | 0.0407350i | ||||
\(906\) | 2.83473 | + | 1.72406i | 0.0941775 | + | 0.0572779i | ||||
\(907\) | −4.93487 | + | 8.54745i | −0.163860 | + | 0.283813i | −0.936250 | − | 0.351335i | \(-0.885728\pi\) |
0.772390 | + | 0.635148i | \(0.219061\pi\) | |||||||
\(908\) | 11.2961 | − | 19.5654i | 0.374873 | − | 0.649300i | ||||
\(909\) | 1.69751 | − | 2.65277i | 0.0563028 | − | 0.0879868i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.6335 | + | 26.9239i | −1.54504 | + | 0.892028i | −0.546529 | + | 0.837440i | \(0.684051\pi\) |
−0.998509 | + | 0.0545881i | \(0.982615\pi\) | |||||||
\(912\) | −10.2573 | − | 6.23842i | −0.339654 | − | 0.206575i | ||||
\(913\) | 35.8363i | 1.18601i | ||||||||
\(914\) | 32.1898i | 1.06475i | ||||||||
\(915\) | 10.7017 | − | 5.85715i | 0.353787 | − | 0.193632i | ||||
\(916\) | −11.5882 | + | 6.69046i | −0.382885 | + | 0.221059i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 7.42857 | − | 3.63555i | 0.245179 | − | 0.119991i | ||||
\(919\) | −11.0899 | + | 19.2084i | −0.365824 | + | 0.633625i | −0.988908 | − | 0.148530i | \(-0.952546\pi\) |
0.623084 | + | 0.782155i | \(0.285879\pi\) | |||||||
\(920\) | −12.0853 | + | 20.9324i | −0.398442 | + | 0.690122i | ||||
\(921\) | −0.106265 | + | 4.65545i | −0.00350156 | + | 0.153402i | ||||
\(922\) | 15.7047 | − | 9.06714i | 0.517208 | − | 0.298610i | ||||
\(923\) | −29.4128 | + | 50.9444i | −0.968133 | + | 1.67686i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.80167 | + | 10.0488i | 0.190758 | + | 0.330402i | ||||
\(926\) | 0.343310 | + | 0.198210i | 0.0112819 | + | 0.00651359i | ||||
\(927\) | −4.36584 | + | 2.26157i | −0.143393 | + | 0.0742796i | ||||
\(928\) | 1.60433 | + | 2.77878i | 0.0526647 | + | 0.0912180i | ||||
\(929\) | −54.9907 | −1.80419 | −0.902093 | − | 0.431541i | \(-0.857970\pi\) | ||||
−0.902093 | + | 0.431541i | \(0.857970\pi\) | |||||||
\(930\) | 6.55772 | + | 11.9817i | 0.215036 | + | 0.392895i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.725243 | − | 0.418719i | −0.0237561 | − | 0.0137156i | ||||
\(933\) | 19.1779 | + | 0.437754i | 0.627856 | + | 0.0143314i | ||||
\(934\) | 12.7734 | + | 7.37475i | 0.417960 | + | 0.241309i | ||||
\(935\) | 10.7992 | − | 6.23491i | 0.353171 | − | 0.203903i | ||||
\(936\) | −19.5570 | + | 30.5625i | −0.639239 | + | 0.998966i | ||||
\(937\) | 29.3132i | 0.957622i | 0.877918 | + | 0.478811i | \(0.158932\pi\) | ||||
−0.877918 | + | 0.478811i | \(0.841068\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.661646 | + | 28.9865i | −0.0215920 | + | 0.945940i | ||||
\(940\) | −7.73777 | − | 13.4022i | −0.252378 | − | 0.437132i | ||||
\(941\) | −15.1752 | −0.494696 | −0.247348 | − | 0.968927i | \(-0.579559\pi\) | ||||
−0.247348 | + | 0.968927i | \(0.579559\pi\) | |||||||
\(942\) | −16.1839 | − | 0.369413i | −0.527299 | − | 0.0120361i | ||||
\(943\) | − | 7.86293i | − | 0.256052i | ||||||
\(944\) | 6.97265 | 0.226940 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28.3808 | 0.922739 | ||||||||
\(947\) | 2.62670i | 0.0853561i | 0.999089 | + | 0.0426781i | \(0.0135890\pi\) | ||||
−0.999089 | + | 0.0426781i | \(0.986411\pi\) | |||||||
\(948\) | 15.0058 | + | 0.342521i | 0.487365 | + | 0.0111246i | ||||
\(949\) | 15.3764 | 0.499139 | ||||||||
\(950\) | −5.82725 | − | 10.0931i | −0.189061 | − | 0.327463i | ||||
\(951\) | 0.116279 | − | 5.09415i | 0.00377060 | − | 0.165189i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.5520i | 1.31361i | 0.754061 | + | 0.656805i | \(0.228092\pi\) | ||||
−0.754061 | + | 0.656805i | \(0.771908\pi\) | |||||||
\(954\) | 11.3392 | + | 21.8898i | 0.367121 | + | 0.708709i | ||||
\(955\) | −9.33981 | + | 5.39234i | −0.302229 | + | 0.174492i | ||||
\(956\) | 12.6476 | + | 7.30212i | 0.409054 | + | 0.236167i | ||||
\(957\) | 4.43293 | + | 0.101186i | 0.143296 | + | 0.00327088i | ||||
\(958\) | −26.4214 | − | 15.2544i | −0.853637 | − | 0.492847i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −10.5370 | − | 19.2523i | −0.340081 | − | 0.621366i | ||||
\(961\) | 12.7631 | 0.411713 | ||||||||
\(962\) | −15.8164 | − | 27.3948i | −0.509942 | − | 0.883245i | ||||
\(963\) | 8.68124 | + | 5.55513i | 0.279749 | + | 0.179012i | ||||
\(964\) | 16.6039 | + | 9.58629i | 0.534777 | + | 0.308754i | ||||
\(965\) | 1.46643 | + | 2.53993i | 0.0472059 | + | 0.0817631i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.47468 | − | 11.2145i | 0.208212 | − | 0.360633i | −0.742939 | − | 0.669359i | \(-0.766569\pi\) |
0.951151 | + | 0.308725i | \(0.0999023\pi\) | |||||||
\(968\) | 14.7457 | − | 8.51343i | 0.473945 | − | 0.273632i | ||||
\(969\) | −0.520778 | + | 22.8151i | −0.0167298 | + | 0.732927i | ||||
\(970\) | −12.2159 | + | 21.1585i | −0.392228 | + | 0.679359i | ||||
\(971\) | −8.26077 | + | 14.3081i | −0.265101 | + | 0.459168i | −0.967590 | − | 0.252526i | \(-0.918739\pi\) |
0.702489 | + | 0.711694i | \(0.252072\pi\) | |||||||
\(972\) | 16.0511 | + | 1.83958i | 0.514839 | + | 0.0590047i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −11.4728 | + | 6.62381i | −0.367611 | + | 0.212240i | ||||
\(975\) | −9.00810 | + | 4.93024i | −0.288490 | + | 0.157894i | ||||
\(976\) | 3.19375i | 0.102229i | ||||||||
\(977\) | − | 6.35928i | − | 0.203451i | −0.994812 | − | 0.101726i | \(-0.967564\pi\) | ||
0.994812 | − | 0.101726i | \(-0.0324364\pi\) | |||||||
\(978\) | 1.61275 | + | 0.980860i | 0.0515700 | + | 0.0313644i | ||||
\(979\) | 34.7227 | − | 20.0472i | 1.10974 | − | 0.640711i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.09261 | − | 9.83102i | −0.162594 | − | 0.313880i | ||||
\(982\) | −4.00740 | + | 6.94103i | −0.127881 | + | 0.221497i | ||||
\(983\) | 1.11487 | − | 1.93102i | 0.0355590 | − | 0.0615899i | −0.847698 | − | 0.530479i | \(-0.822012\pi\) |
0.883257 | + | 0.468889i | \(0.155346\pi\) | |||||||
\(984\) | 8.04560 | + | 4.89326i | 0.256484 | + | 0.155992i | ||||
\(985\) | −31.8508 | + | 18.3891i | −1.01485 | + | 0.585924i | ||||
\(986\) | −0.498358 | + | 0.863181i | −0.0158709 | + | 0.0274893i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.0870 | − | 29.5956i | −0.543610 | − | 0.941561i | ||||
\(989\) | 26.4021 | + | 15.2433i | 0.839538 | + | 0.484708i | ||||
\(990\) | −22.6239 | − | 1.03337i | −0.719036 | − | 0.0328425i | ||||
\(991\) | 24.7285 | + | 42.8310i | 0.785527 | + | 1.36057i | 0.928684 | + | 0.370872i | \(0.120941\pi\) |
−0.143157 | + | 0.989700i | \(0.545726\pi\) | |||||||
\(992\) | 21.8815 | 0.694738 | ||||||||
\(993\) | 8.45286 | + | 0.192945i | 0.268243 | + | 0.00612292i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.59072 | + | 0.918403i | 0.0504293 | + | 0.0291153i | ||||
\(996\) | −7.55503 | − | 13.8039i | −0.239390 | − | 0.437393i | ||||
\(997\) | 7.28219 | + | 4.20437i | 0.230629 | + | 0.133154i | 0.610862 | − | 0.791737i | \(-0.290823\pi\) |
−0.380233 | + | 0.924891i | \(0.624156\pi\) | |||||||
\(998\) | 23.8195 | − | 13.7522i | 0.753993 | − | 0.435318i | ||||
\(999\) | −23.0292 | + | 34.2416i | −0.728612 | + | 1.08336i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.2.i.d.68.10 | 48 | ||
3.2 | odd | 2 | 1323.2.i.d.1097.8 | 48 | |||
7.2 | even | 3 | 441.2.o.e.293.9 | yes | 48 | ||
7.3 | odd | 6 | 441.2.s.d.374.16 | 48 | |||
7.4 | even | 3 | 441.2.s.d.374.15 | 48 | |||
7.5 | odd | 6 | 441.2.o.e.293.10 | yes | 48 | ||
7.6 | odd | 2 | inner | 441.2.i.d.68.9 | 48 | ||
9.2 | odd | 6 | 441.2.s.d.362.16 | 48 | |||
9.7 | even | 3 | 1323.2.s.d.656.9 | 48 | |||
21.2 | odd | 6 | 1323.2.o.e.881.16 | 48 | |||
21.5 | even | 6 | 1323.2.o.e.881.15 | 48 | |||
21.11 | odd | 6 | 1323.2.s.d.962.10 | 48 | |||
21.17 | even | 6 | 1323.2.s.d.962.9 | 48 | |||
21.20 | even | 2 | 1323.2.i.d.1097.18 | 48 | |||
63.2 | odd | 6 | 441.2.o.e.146.10 | yes | 48 | ||
63.11 | odd | 6 | inner | 441.2.i.d.227.15 | 48 | ||
63.16 | even | 3 | 1323.2.o.e.440.15 | 48 | |||
63.20 | even | 6 | 441.2.s.d.362.15 | 48 | |||
63.25 | even | 3 | 1323.2.i.d.521.18 | 48 | |||
63.34 | odd | 6 | 1323.2.s.d.656.10 | 48 | |||
63.38 | even | 6 | inner | 441.2.i.d.227.16 | 48 | ||
63.47 | even | 6 | 441.2.o.e.146.9 | ✓ | 48 | ||
63.52 | odd | 6 | 1323.2.i.d.521.8 | 48 | |||
63.61 | odd | 6 | 1323.2.o.e.440.16 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.9 | 48 | 7.6 | odd | 2 | inner | ||
441.2.i.d.68.10 | 48 | 1.1 | even | 1 | trivial | ||
441.2.i.d.227.15 | 48 | 63.11 | odd | 6 | inner | ||
441.2.i.d.227.16 | 48 | 63.38 | even | 6 | inner | ||
441.2.o.e.146.9 | ✓ | 48 | 63.47 | even | 6 | ||
441.2.o.e.146.10 | yes | 48 | 63.2 | odd | 6 | ||
441.2.o.e.293.9 | yes | 48 | 7.2 | even | 3 | ||
441.2.o.e.293.10 | yes | 48 | 7.5 | odd | 6 | ||
441.2.s.d.362.15 | 48 | 63.20 | even | 6 | |||
441.2.s.d.362.16 | 48 | 9.2 | odd | 6 | |||
441.2.s.d.374.15 | 48 | 7.4 | even | 3 | |||
441.2.s.d.374.16 | 48 | 7.3 | odd | 6 | |||
1323.2.i.d.521.8 | 48 | 63.52 | odd | 6 | |||
1323.2.i.d.521.18 | 48 | 63.25 | even | 3 | |||
1323.2.i.d.1097.8 | 48 | 3.2 | odd | 2 | |||
1323.2.i.d.1097.18 | 48 | 21.20 | even | 2 | |||
1323.2.o.e.440.15 | 48 | 63.16 | even | 3 | |||
1323.2.o.e.440.16 | 48 | 63.61 | odd | 6 | |||
1323.2.o.e.881.15 | 48 | 21.5 | even | 6 | |||
1323.2.o.e.881.16 | 48 | 21.2 | odd | 6 | |||
1323.2.s.d.656.9 | 48 | 9.7 | even | 3 | |||
1323.2.s.d.656.10 | 48 | 63.34 | odd | 6 | |||
1323.2.s.d.962.9 | 48 | 21.17 | even | 6 | |||
1323.2.s.d.962.10 | 48 | 21.11 | odd | 6 |