Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (of order \(3\), 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 673.2 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.673 |
Dual form | 1008.2.r.e.337.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −1.00000 | + | 1.41421i | −0.577350 | + | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.72474 | − | 2.98735i | −0.771329 | − | 1.33598i | −0.936835 | − | 0.349773i | \(-0.886259\pi\) |
0.165505 | − | 0.986209i | \(-0.447075\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | − | 2.82843i | −0.333333 | − | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44949 | + | 4.24264i | 0.679366 | + | 1.17670i | 0.975172 | + | 0.221449i | \(0.0710785\pi\) |
−0.295806 | + | 0.955248i | \(0.595588\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.94949 | + | 0.548188i | 1.53615 | + | 0.141542i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.44949 | −1.70903 | −0.854515 | − | 0.519427i | \(-0.826146\pi\) | ||||
−0.854515 | + | 0.519427i | \(0.826146\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.724745 | − | 1.57313i | −0.158152 | − | 0.343286i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | 0.809177 | − | 0.587565i | \(-0.199913\pi\) |
−0.913434 | + | 0.406986i | \(0.866580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.44949 | + | 5.97469i | −0.689898 | + | 1.19494i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | + | 1.41421i | 0.962250 | + | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.44949 | + | 2.51059i | −0.269163 | + | 0.466205i | −0.968646 | − | 0.248445i | \(-0.920081\pi\) |
0.699483 | + | 0.714650i | \(0.253414\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | + | 5.19615i | 0.538816 | + | 0.933257i | 0.998968 | + | 0.0454165i | \(0.0144615\pi\) |
−0.460152 | + | 0.887840i | \(0.652205\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.44949 | + | 3.14626i | 0.252324 | + | 0.547694i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.44949 | 0.583070 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.79796 | −1.28198 | −0.640988 | − | 0.767551i | \(-0.721475\pi\) | ||||
−0.640988 | + | 0.767551i | \(0.721475\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.44949 | − | 0.778539i | −1.35300 | − | 0.124666i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.89898 | + | 8.48528i | 0.765092 | + | 1.32518i | 0.940198 | + | 0.340629i | \(0.110640\pi\) |
−0.175106 | + | 0.984550i | \(0.556027\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.44949 | + | 2.51059i | −0.221045 | + | 0.382861i | −0.955126 | − | 0.296201i | \(-0.904280\pi\) |
0.734080 | + | 0.679062i | \(0.237613\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.72474 | + | 7.86566i | −1.00247 | + | 1.17254i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.89898 | + | 8.48528i | −0.714590 | + | 1.23771i | 0.248528 | + | 0.968625i | \(0.420053\pi\) |
−0.963118 | + | 0.269081i | \(0.913280\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | + | 2.82843i | −0.280056 | + | 0.396059i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.10102 | −0.151237 | −0.0756184 | − | 0.997137i | \(-0.524093\pi\) | ||||
−0.0756184 | + | 0.997137i | \(0.524093\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.89898 | −0.930258 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.44949 | − | 10.5352i | 0.986709 | − | 1.39542i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | − | 1.73205i | −0.130189 | − | 0.225494i | 0.793560 | − | 0.608492i | \(-0.208225\pi\) |
−0.923749 | + | 0.382998i | \(0.874892\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.72474 | + | 9.91555i | −0.732978 | + | 1.26956i | 0.222626 | + | 0.974904i | \(0.428537\pi\) |
−0.955605 | + | 0.294652i | \(0.904796\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.94949 | + | 0.548188i | 0.371601 | + | 0.0690652i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.44949 | − | 14.6349i | 1.04803 | − | 1.81524i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.55051 | − | 2.68556i | −0.189425 | − | 0.328094i | 0.755634 | − | 0.654994i | \(-0.227329\pi\) |
−0.945059 | + | 0.326901i | \(0.893996\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.72474 | + | 0.158919i | 0.207635 | + | 0.0191316i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.89898 | −1.17479 | −0.587396 | − | 0.809299i | \(-0.699847\pi\) | ||||
−0.587396 | + | 0.809299i | \(0.699847\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.89898 | 0.339300 | 0.169650 | − | 0.985504i | \(-0.445736\pi\) | ||||
0.169650 | + | 0.985504i | \(0.445736\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.00000 | − | 10.8530i | −0.577350 | − | 1.25320i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | + | 1.73205i | 0.113961 | + | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.94949 | − | 6.84072i | 0.444352 | − | 0.769641i | −0.553655 | − | 0.832746i | \(-0.686767\pi\) |
0.998007 | + | 0.0631057i | \(0.0201005\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.00000 | − | 1.73205i | 0.109764 | − | 0.190117i | −0.805910 | − | 0.592037i | \(-0.798324\pi\) |
0.915675 | + | 0.401920i | \(0.131657\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.44949 | − | 5.97469i | −0.374150 | − | 0.648046i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.10102 | − | 4.56048i | −0.225253 | − | 0.488935i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.10102 | −0.752707 | −0.376353 | − | 0.926476i | \(-0.622822\pi\) | ||||
−0.376353 | + | 0.926476i | \(0.622822\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.89898 | −0.513553 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.3485 | − | 0.953512i | −1.07309 | − | 0.0988746i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.8485 | + | 22.2542i | 1.31823 | + | 2.28323i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.44949 | − | 5.97469i | 0.350243 | − | 0.606638i | −0.636049 | − | 0.771649i | \(-0.719432\pi\) |
0.986292 | + | 0.165011i | \(0.0527658\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.89898 | − | 1.09638i | −0.592870 | − | 0.110190i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.62372 | + | 6.27647i | −0.360574 | + | 0.624533i | −0.988055 | − | 0.154099i | \(-0.950753\pi\) |
0.627481 | + | 0.778632i | \(0.284086\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.00000 | + | 12.1244i | 0.689730 | + | 1.19465i | 0.971925 | + | 0.235291i | \(0.0756043\pi\) |
−0.282194 | + | 0.959357i | \(0.591062\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.44949 | + | 4.87832i | −0.336636 | + | 0.476075i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.6969 | −1.59928 | −0.799638 | − | 0.600482i | \(-0.794975\pi\) | ||||
−0.799638 | + | 0.600482i | \(0.794975\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.79796 | − | 11.0280i | 0.740150 | − | 1.04673i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.94949 | + | 13.7689i | 0.747825 | + | 1.29527i | 0.948863 | + | 0.315688i | \(0.102235\pi\) |
−0.201038 | + | 0.979583i | \(0.564431\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.72474 | + | 2.98735i | −0.160833 | + | 0.278571i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.55051 | − | 11.1708i | 0.882945 | − | 1.03274i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.00000 | + | 1.73205i | −0.0916698 | + | 0.158777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.8990 | − | 1.55708i | −1.52373 | − | 0.140397i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.55051 | 0.585895 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.00000 | 0.266207 | 0.133103 | − | 0.991102i | \(-0.457506\pi\) | ||||
0.133103 | + | 0.991102i | \(0.457506\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.10102 | − | 4.56048i | −0.184985 | − | 0.401528i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.72474 | − | 11.6476i | −0.587544 | − | 1.01766i | −0.994553 | − | 0.104232i | \(-0.966762\pi\) |
0.407009 | − | 0.913424i | \(-0.366572\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.72474 | − | 6.45145i | 0.322976 | − | 0.559411i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.39898 | − | 17.3759i | −0.378604 | − | 1.49548i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.89898 | − | 10.2173i | 0.503984 | − | 0.872926i | −0.496006 | − | 0.868319i | \(-0.665200\pi\) |
0.999989 | − | 0.00460626i | \(-0.00146622\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.72474 | + | 8.18350i | 0.400748 | + | 0.694115i | 0.993816 | − | 0.111037i | \(-0.0354171\pi\) |
−0.593069 | + | 0.805152i | \(0.702084\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.10102 | − | 15.4135i | −0.598014 | − | 1.29805i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.79796 | 0.819346 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0000 | 0.830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.72474 | + | 0.158919i | 0.142255 | + | 0.0131074i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50000 | + | 4.33013i | −0.203447 | + | 0.352381i | −0.949637 | − | 0.313353i | \(-0.898548\pi\) |
0.746190 | + | 0.665733i | \(0.231881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | − | 5.65685i | −0.161690 | − | 0.457330i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.3485 | − | 17.9241i | 0.831209 | − | 1.43970i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.17423 | − | 5.49794i | −0.253332 | − | 0.438783i | 0.711109 | − | 0.703081i | \(-0.248193\pi\) |
−0.964441 | + | 0.264298i | \(0.914860\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.10102 | − | 1.55708i | 0.0873166 | − | 0.123484i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.202041 | 0.0158251 | 0.00791254 | − | 0.999969i | \(-0.497481\pi\) | ||||
0.00791254 | + | 0.999969i | \(0.497481\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.89898 | − | 9.75663i | 0.537085 | − | 0.759553i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.34847 | + | 16.1920i | 0.723406 | + | 1.25298i | 0.959627 | + | 0.281277i | \(0.0907579\pi\) |
−0.236220 | + | 0.971700i | \(0.575909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.50000 | + | 9.52628i | −0.423077 | + | 0.732791i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.44949 | + | 21.0703i | 0.569677 | + | 1.61129i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.44949 | − | 11.1708i | 0.490346 | − | 0.849304i | −0.509593 | − | 0.860416i | \(-0.670204\pi\) |
0.999938 | + | 0.0111123i | \(0.00353722\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.44949 | − | 5.97469i | −0.260757 | − | 0.451644i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.44949 | + | 0.317837i | 0.259280 | + | 0.0238901i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.69694 | 0.650040 | 0.325020 | − | 0.945707i | \(-0.394629\pi\) | ||||
0.325020 | + | 0.945707i | \(0.394629\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.34847 | 0.323219 | 0.161610 | − | 0.986855i | \(-0.448331\pi\) | ||||
0.161610 | + | 0.986855i | \(0.448331\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.29796 | − | 18.0116i | −0.613403 | − | 1.33145i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.4495 | + | 23.2952i | 0.988826 | + | 1.71270i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | − | 3.46410i | 0.146254 | − | 0.253320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.72474 | + | 3.62302i | −0.270935 | + | 0.263536i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.94949 | − | 12.0369i | 0.502847 | − | 0.870957i | −0.497147 | − | 0.867666i | \(-0.665619\pi\) |
0.999995 | − | 0.00329106i | \(-0.00104758\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.05051 | + | 7.01569i | 0.291562 | + | 0.505000i | 0.974179 | − | 0.225776i | \(-0.0724917\pi\) |
−0.682617 | + | 0.730776i | \(0.739158\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.2474 | + | 26.5843i | 0.877058 | + | 1.90374i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.6969 | −0.904619 | −0.452310 | − | 0.891861i | \(-0.649400\pi\) | ||||
−0.452310 | + | 0.891861i | \(0.649400\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.89898 | −0.489056 | −0.244528 | − | 0.969642i | \(-0.578633\pi\) | ||||
−0.244528 | + | 0.969642i | \(0.578633\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.34847 | + | 0.492810i | 0.377252 | + | 0.0347601i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.44949 | − | 2.51059i | −0.101734 | − | 0.176209i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.8990 | − | 29.2699i | 1.18028 | − | 2.04430i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.94949 | + | 2.28024i | −0.135499 | + | 0.158488i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.44949 | + | 12.9029i | −0.515292 | + | 0.892512i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.55051 | + | 2.68556i | 0.106742 | + | 0.184882i | 0.914448 | − | 0.404703i | \(-0.132625\pi\) |
−0.807707 | + | 0.589584i | \(0.799292\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.89898 | − | 13.9993i | 0.678267 | − | 0.959214i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.0000 | 0.681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | −0.407307 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.89898 | + | 4.09978i | −0.195895 | + | 0.277037i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.89898 | + | 8.48528i | 0.329541 | + | 0.570782i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.4495 | + | 18.0990i | −0.699750 | + | 1.21200i | 0.268804 | + | 0.963195i | \(0.413372\pi\) |
−0.968553 | + | 0.248807i | \(0.919962\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20.3485 | + | 3.78194i | 1.35656 | + | 0.252129i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.275255 | + | 0.476756i | −0.0182693 | + | 0.0316434i | −0.875016 | − | 0.484095i | \(-0.839149\pi\) |
0.856746 | + | 0.515738i | \(0.172482\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.6237 | + | 20.1329i | 0.768117 | + | 1.33042i | 0.938583 | + | 0.345055i | \(0.112140\pi\) |
−0.170465 | + | 0.985364i | \(0.554527\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.44949 | − | 0.317837i | −0.226960 | − | 0.0209122i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.00000 | −0.458585 | −0.229293 | − | 0.973358i | \(-0.573641\pi\) | ||||
−0.229293 | + | 0.973358i | \(0.573641\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.7980 | 2.20474 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.72474 | + | 12.4261i | 0.371862 | + | 0.807164i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.39898 | − | 11.0834i | −0.413916 | − | 0.716923i | 0.581398 | − | 0.813619i | \(-0.302506\pi\) |
−0.995314 | + | 0.0966962i | \(0.969172\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.44949 | − | 7.70674i | 0.286617 | − | 0.496435i | −0.686383 | − | 0.727240i | \(-0.740803\pi\) |
0.973000 | + | 0.230805i | \(0.0741360\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | − | 15.5563i | −0.0641500 | − | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.72474 | + | 2.98735i | −0.110190 | + | 0.190855i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.2474 | − | 31.6055i | −1.16106 | − | 2.01101i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.44949 | + | 3.14626i | 0.0918577 | + | 0.199386i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.5505 | −0.792181 | −0.396091 | − | 0.918211i | \(-0.629633\pi\) | ||||
−0.396091 | + | 0.918211i | \(0.629633\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.8990 | + | 1.09638i | 0.745143 | + | 0.0686577i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.8990 | − | 24.0737i | −0.866995 | − | 1.50168i | −0.865053 | − | 0.501680i | \(-0.832715\pi\) |
−0.00194150 | − | 0.999998i | \(-0.500618\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.89898 | − | 6.75323i | 0.242271 | − | 0.419625i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.55051 | + | 1.58919i | 0.529263 | + | 0.0983682i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.05051 | − | 13.9439i | 0.496416 | − | 0.859817i | −0.503576 | − | 0.863951i | \(-0.667983\pi\) |
0.999991 | + | 0.00413383i | \(0.00131584\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.89898 | + | 3.28913i | 0.116653 | + | 0.202050i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.10102 | − | 10.0424i | 0.434575 | − | 0.614582i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.65153 | −0.222638 | −0.111319 | − | 0.993785i | \(-0.535507\pi\) | ||||
−0.111319 | + | 0.993785i | \(0.535507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.8990 | −1.02654 | −0.513270 | − | 0.858227i | \(-0.671566\pi\) | ||||
−0.513270 | + | 0.858227i | \(0.671566\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.89898 | − | 6.92820i | 0.296500 | − | 0.419314i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.89898 | + | 11.9494i | 0.416024 | + | 0.720575i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.34847 | + | 9.26382i | −0.321358 | + | 0.556609i | −0.980769 | − | 0.195174i | \(-0.937473\pi\) |
0.659410 | + | 0.751783i | \(0.270806\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.6969 | − | 13.6814i | 0.700277 | − | 0.819086i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.50000 | − | 16.4545i | 0.566722 | − | 0.981592i | −0.430165 | − | 0.902750i | \(-0.641545\pi\) |
0.996887 | − | 0.0788417i | \(-0.0251222\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.2753 | − | 17.7973i | −0.610801 | − | 1.05794i | −0.991106 | − | 0.133077i | \(-0.957514\pi\) |
0.380305 | − | 0.924861i | \(-0.375819\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −44.3207 | − | 4.08372i | −2.62533 | − | 0.241899i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.79796 | −0.578355 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.00000 | + | 10.8530i | 0.293105 | + | 0.636215i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.6237 | − | 23.5970i | −0.795906 | − | 1.37855i | −0.922262 | − | 0.386565i | \(-0.873661\pi\) |
0.126356 | − | 0.991985i | \(-0.459672\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.44949 | + | 5.97469i | −0.200837 | + | 0.347860i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.44949 | − | 7.24604i | 0.432263 | − | 0.420458i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.44949 | − | 4.24264i | 0.141658 | − | 0.245358i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.44949 | − | 2.51059i | −0.0835472 | − | 0.144708i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.25255 | − | 11.4012i | −0.301751 | − | 0.654982i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 39.4949 | 2.26147 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.752551 | −0.0429504 | −0.0214752 | − | 0.999769i | \(-0.506836\pi\) | ||||
−0.0214752 | + | 0.999769i | \(0.506836\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.1464 | − | 2.22486i | −1.37364 | − | 0.126568i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.651531 | + | 1.12848i | 0.0369449 | + | 0.0639905i | 0.883907 | − | 0.467663i | \(-0.154904\pi\) |
−0.846962 | + | 0.531654i | \(0.821571\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.3485 | + | 21.3882i | −0.697977 | + | 1.20893i | 0.271190 | + | 0.962526i | \(0.412583\pi\) |
−0.969167 | + | 0.246405i | \(0.920751\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.44949 | − | 9.75663i | −0.194357 | − | 0.549724i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.34847 | − | 7.53177i | 0.244234 | − | 0.423026i | −0.717682 | − | 0.696371i | \(-0.754797\pi\) |
0.961916 | + | 0.273345i | \(0.0881300\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.89898 | + | 5.02118i | 0.162312 | + | 0.281132i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.0000 | + | 16.9706i | −0.669775 | + | 0.947204i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.8990 | −0.829001 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −33.7980 | −1.87477 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.6969 | − | 23.6130i | 0.923343 | − | 1.30580i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.89898 | − | 8.48528i | −0.270089 | − | 0.467809i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.3485 | + | 21.3882i | −0.678733 | + | 1.17560i | 0.296629 | + | 0.954993i | \(0.404137\pi\) |
−0.975363 | + | 0.220608i | \(0.929196\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.79796 | + | 22.0560i | 0.427326 | + | 1.20866i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.34847 | + | 9.26382i | −0.292218 | + | 0.506137i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.6969 | − | 30.6520i | −0.964014 | − | 1.66972i | −0.712242 | − | 0.701934i | \(-0.752320\pi\) |
−0.251772 | − | 0.967787i | \(-0.581013\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.4217 | − | 2.52664i | −1.48934 | − | 0.137228i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.50000 | − | 5.42650i | −0.134595 | − | 0.292153i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.79796 | − | 16.9706i | −0.525982 | − | 0.911028i | −0.999542 | − | 0.0302659i | \(-0.990365\pi\) |
0.473560 | − | 0.880762i | \(-0.342969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.4495 | + | 18.0990i | −0.559348 | + | 0.968820i | 0.438203 | + | 0.898876i | \(0.355615\pi\) |
−0.997551 | + | 0.0699435i | \(0.977718\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.24745 | + | 24.6773i | 0.333464 | + | 1.31718i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.00000 | − | 5.19615i | 0.159674 | − | 0.276563i | −0.775077 | − | 0.631867i | \(-0.782289\pi\) |
0.934751 | + | 0.355303i | \(0.115622\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.0732 | + | 29.5717i | 0.906152 | + | 1.56950i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.44949 | − | 3.14626i | −0.0767151 | − | 0.166518i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.7980 | −0.569894 | −0.284947 | − | 0.958543i | \(-0.591976\pi\) | ||||
−0.284947 | + | 0.958543i | \(0.591976\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.4949 | 1.92078 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.0732 | − | 1.11243i | −0.633679 | − | 0.0583875i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.00000 | − | 8.66025i | −0.261712 | − | 0.453298i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.89898 | − | 5.02118i | 0.151325 | − | 0.262103i | −0.780389 | − | 0.625294i | \(-0.784979\pi\) |
0.931715 | + | 0.363190i | \(0.118313\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.1010 | − | 22.3417i | 0.994359 | − | 1.16306i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.550510 | − | 0.953512i | 0.0285811 | − | 0.0495039i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.44949 | − | 2.51059i | −0.0750517 | − | 0.129993i | 0.826057 | − | 0.563587i | \(-0.190579\pi\) |
−0.901109 | + | 0.433593i | \(0.857246\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.55051 | + | 9.26382i | −0.338267 | + | 0.478382i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.2020 | −0.731442 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.4949 | 1.36095 | 0.680476 | − | 0.732771i | \(-0.261773\pi\) | ||||
0.680476 | + | 0.732771i | \(0.261773\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.00000 | + | 4.24264i | −0.153695 | + | 0.217357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.44949 | + | 5.97469i | 0.176261 | + | 0.305292i | 0.940597 | − | 0.339526i | \(-0.110266\pi\) |
−0.764336 | + | 0.644818i | \(0.776933\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.44949 | − | 5.97469i | 0.175802 | − | 0.304498i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.55051 | + | 1.58919i | 0.434647 | + | 0.0807829i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.55051 | − | 13.0779i | 0.382826 | − | 0.663074i | −0.608639 | − | 0.793447i | \(-0.708284\pi\) |
0.991465 | + | 0.130373i | \(0.0416175\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00000 | − | 1.73205i | −0.0505722 | − | 0.0875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.1969 | + | 2.13737i | 1.17013 | + | 0.107816i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.2474 | −1.37097 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.30306 | 0.466907 | 0.233454 | − | 0.972368i | \(-0.424997\pi\) | ||||
0.233454 | + | 0.972368i | \(0.424997\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.39898 | + | 11.7190i | 0.270287 | + | 0.586685i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.05051 | + | 8.74774i | 0.252210 | + | 0.436841i | 0.964134 | − | 0.265416i | \(-0.0855091\pi\) |
−0.711924 | + | 0.702257i | \(0.752176\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.6969 | + | 25.4558i | −0.732107 | + | 1.26805i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 28.9722 | + | 11.1548i | 1.43964 | + | 0.554286i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.79796 | + | 13.5065i | −0.386530 | + | 0.669490i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.89898 | − | 5.02118i | −0.143345 | − | 0.248281i | 0.785409 | − | 0.618977i | \(-0.212453\pi\) |
−0.928754 | + | 0.370696i | \(0.879119\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.55051 | + | 18.5597i | 0.421766 | + | 0.915485i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.00000 | 0.0984136 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.89898 | −0.338658 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.2980 | − | 1.50170i | −0.798114 | − | 0.0735386i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.2753 | + | 21.2614i | 0.599685 | + | 1.03869i | 0.992867 | + | 0.119225i | \(0.0380410\pi\) |
−0.393182 | + | 0.919461i | \(0.628626\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.55051 | + | 11.3458i | −0.319252 | + | 0.552961i | −0.980332 | − | 0.197354i | \(-0.936765\pi\) |
0.661080 | + | 0.750316i | \(0.270098\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 28.8990 | + | 5.37113i | 1.40512 | + | 0.261153i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.89898 | + | 11.9494i | −0.334650 | + | 0.579630i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.72474 | − | 9.91555i | −0.277040 | − | 0.479847i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.79796 | + | 13.8564i | −0.473050 | + | 0.668994i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.59592 | 0.365882 | 0.182941 | − | 0.983124i | \(-0.441438\pi\) | ||||
0.182941 | + | 0.983124i | \(0.441438\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.7980 | 0.566974 | 0.283487 | − | 0.958976i | \(-0.408509\pi\) | ||||
0.283487 | + | 0.958976i | \(0.408509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.0000 | + | 14.1421i | −0.479463 | + | 0.678064i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.72474 | + | 6.45145i | 0.178179 | + | 0.308615i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.8990 | − | 18.8776i | 0.520180 | − | 0.900978i | −0.479545 | − | 0.877517i | \(-0.659198\pi\) |
0.999725 | − | 0.0234607i | \(-0.00746845\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.94949 | + | 2.28024i | −0.0928328 | + | 0.108583i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.55051 | + | 4.41761i | −0.121178 | + | 0.209887i | −0.920233 | − | 0.391372i | \(-0.872001\pi\) |
0.799054 | + | 0.601259i | \(0.205334\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.2474 | + | 21.2132i | 0.580585 | + | 1.00560i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.3485 | − | 0.953512i | −0.489466 | − | 0.0450996i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.5959 | −0.877596 | −0.438798 | − | 0.898586i | \(-0.644596\pi\) | ||||
−0.438798 | + | 0.898586i | \(0.644596\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.5959 | 0.922736 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.62372 | − | 7.86566i | −0.170257 | − | 0.369561i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.44949 | + | 14.6349i | 0.396118 | + | 0.686097i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.7474 | + | 27.2754i | −0.736635 | + | 1.27589i | 0.217368 | + | 0.976090i | \(0.430253\pi\) |
−0.954002 | + | 0.299799i | \(0.903080\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.0000 | + | 2.82843i | 0.466760 | + | 0.132020i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.1742 | + | 17.6223i | −0.473861 | + | 0.820752i | −0.999552 | − | 0.0299238i | \(-0.990474\pi\) |
0.525691 | + | 0.850676i | \(0.323807\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.8485 | − | 22.2542i | −0.597119 | − | 1.03424i | −0.993244 | − | 0.116044i | \(-0.962979\pi\) |
0.396125 | − | 0.918197i | \(-0.370355\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.0000 | + | 32.5590i | 0.695608 | + | 1.50989i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.0000 | −0.462745 | −0.231372 | − | 0.972865i | \(-0.574322\pi\) | ||||
−0.231372 | + | 0.972865i | \(0.574322\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.10102 | 0.143192 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.9495 | + | 1.00889i | 0.504526 | + | 0.0464872i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.89898 | + | 5.02118i | 0.133295 | + | 0.230874i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.6969 | − | 44.5084i | 1.17906 | − | 2.04219i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.10102 | + | 3.11416i | 0.0504123 | + | 0.142587i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.7980 | + | 25.6308i | −0.676136 | + | 1.17110i | 0.299999 | + | 0.953939i | \(0.403013\pi\) |
−0.976135 | + | 0.217163i | \(0.930320\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.1010 | − | 33.0839i | −0.870932 | − | 1.50850i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | + | 1.41421i | −0.0455016 | + | 0.0643489i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.7980 | −1.08061 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.3939 | −1.01476 | −0.507382 | − | 0.861721i | \(-0.669387\pi\) | ||||
−0.507382 | + | 0.861721i | \(0.669387\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.202041 | + | 0.285729i | −0.00913661 | + | 0.0129211i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.89898 | − | 3.28913i | −0.0856997 | − | 0.148436i | 0.819989 | − | 0.572379i | \(-0.193979\pi\) |
−0.905689 | + | 0.423942i | \(0.860646\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.89898 | + | 5.02118i | −0.130563 | + | 0.226143i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.89898 | + | 19.5133i | 0.310086 | + | 0.877056i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.94949 | − | 8.57277i | 0.222015 | − | 0.384541i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.6969 | + | 28.9199i | 0.747458 | + | 1.29463i | 0.949038 | + | 0.315163i | \(0.102059\pi\) |
−0.201580 | + | 0.979472i | \(0.564608\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.2474 | − | 2.97129i | −1.44071 | − | 0.132748i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.4949 | −1.09217 | −0.546087 | − | 0.837729i | \(-0.683883\pi\) | ||||
−0.546087 | + | 0.837729i | \(0.683883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.0000 | 1.11249 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.97219 | − | 17.3045i | −0.354058 | − | 0.768518i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.44949 | + | 14.6349i | 0.374517 | + | 0.648683i | 0.990255 | − | 0.139269i | \(-0.0444752\pi\) |
−0.615738 | + | 0.787951i | \(0.711142\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.44949 | + | 2.51059i | −0.0641217 | + | 0.111062i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −37.2474 | − | 10.5352i | −1.64452 | − | 0.465139i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.1464 | − | 41.8228i | 1.06402 | − | 1.84293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.79796 | + | 16.9706i | 0.430914 | + | 0.746364i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.34847 | + | 20.2918i | 0.410352 | + | 0.890711i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.6969 | −1.69534 | −0.847672 | − | 0.530521i | \(-0.821996\pi\) | ||||
−0.847672 | + | 0.530521i | \(0.821996\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.348469 | −0.0152375 | −0.00761875 | − | 0.999971i | \(-0.502425\pi\) | ||||
−0.00761875 | + | 0.999971i | \(0.502425\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.8990 | + | 1.09638i | 0.519314 | + | 0.0478498i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000 | + | 10.3923i | 0.261364 | + | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.89898 | + | 4.56048i | −0.169201 | + | 0.197908i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.0000 | + | 41.5692i | −1.03956 | + | 1.80056i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.6969 | − | 35.8481i | −0.894807 | − | 1.54985i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.69694 | + | 12.2993i | −0.375301 | + | 0.530755i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.00000 | −0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.4949 | 1.31108 | 0.655539 | − | 0.755161i | \(-0.272441\pi\) | ||||
0.655539 | + | 0.755161i | \(0.272441\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.34847 | + | 6.14966i | −0.186611 | + | 0.263907i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.7980 | + | 49.8795i | 1.23357 | + | 2.13660i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7980 | − | 27.3629i | 0.675472 | − | 1.16995i | −0.300859 | − | 0.953669i | \(-0.597273\pi\) |
0.976331 | − | 0.216283i | \(-0.0693934\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 33.7702 | + | 6.27647i | 1.44127 | + | 0.267873i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.7980 | − | 18.7026i | 0.460009 | − | 0.796758i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.94949 | + | 6.84072i | 0.167949 | + | 0.290897i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −46.3939 | − | 4.27475i | −1.96931 | − | 0.181453i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.10102 | −0.131394 | −0.0656972 | − | 0.997840i | \(-0.520927\pi\) | ||||
−0.0656972 | + | 0.997840i | \(0.520927\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.2020 | −0.600682 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.89898 | + | 6.29253i | 0.122395 | + | 0.265671i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.97219 | + | 12.0762i | 0.293843 | + | 0.508951i | 0.974715 | − | 0.223451i | \(-0.0717324\pi\) |
−0.680872 | + | 0.732402i | \(0.738399\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.4217 | − | 47.4957i | 1.15364 | − | 1.99816i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.39898 | − | 8.89060i | −0.0587516 | − | 0.373370i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.0000 | − | 25.9808i | 0.628833 | − | 1.08917i | −0.358954 | − | 0.933355i | \(-0.616866\pi\) |
0.987786 | − | 0.155815i | \(-0.0498003\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.10102 | + | 12.2993i | 0.297168 | + | 0.514711i | 0.975487 | − | 0.220057i | \(-0.0706244\pi\) |
−0.678319 | + | 0.734768i | \(0.737291\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.0732 | + | 21.8649i | 0.420815 | + | 0.913421i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.89898 | 0.287707 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.5959 | 0.982311 | 0.491155 | − | 0.871072i | \(-0.336575\pi\) | ||||
0.491155 | + | 0.871072i | \(0.336575\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.9722 | − | 1.28740i | −0.580665 | − | 0.0535026i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.00000 | + | 1.73205i | 0.0414870 | + | 0.0718576i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.10102 | + | 1.90702i | −0.0455996 | + | 0.0789808i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −49.8434 | − | 9.26382i | −2.06077 | − | 0.383012i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.07321 | + | 15.7153i | −0.374492 | + | 0.648639i | −0.990251 | − | 0.139296i | \(-0.955516\pi\) |
0.615759 | + | 0.787934i | \(0.288849\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.3485 | − | 38.7087i | −0.920853 | − | 1.59496i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.6969 | − | 17.9562i | 0.522282 | − | 0.738619i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.6969 | −0.603531 | −0.301765 | − | 0.953382i | \(-0.597576\pi\) | ||||
−0.301765 | + | 0.953382i | \(0.597576\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.89898 | 0.282831 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.89898 | − | 9.75663i | 0.282356 | − | 0.399312i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.10102 | − | 12.2993i | −0.290140 | − | 0.502537i | 0.683703 | − | 0.729761i | \(-0.260368\pi\) |
−0.973843 | + | 0.227224i | \(0.927035\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.34847 | − | 10.9959i | 0.258959 | − | 0.448531i | −0.707004 | − | 0.707210i | \(-0.749954\pi\) |
0.965963 | + | 0.258679i | \(0.0832871\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.04541 | + | 7.07107i | −0.246188 | + | 0.287956i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.0732 | − | 20.9114i | 0.490846 | − | 0.850170i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.34847 | − | 7.53177i | −0.176499 | − | 0.305705i | 0.764180 | − | 0.645003i | \(-0.223144\pi\) |
−0.940679 | + | 0.339298i | \(0.889811\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.00000 | + | 0.460702i | 0.202610 | + | 0.0186686i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −48.0000 | −1.94187 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.6969 | 0.593604 | 0.296802 | − | 0.954939i | \(-0.404080\pi\) | ||||
0.296802 | + | 0.954939i | \(0.404080\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.4949 | + | 53.1687i | 0.987730 | + | 2.14397i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.6969 | − | 37.5802i | −0.873486 | − | 1.51292i | −0.858367 | − | 0.513036i | \(-0.828521\pi\) |
−0.0151189 | − | 0.999886i | \(-0.504813\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.07321 | + | 3.59091i | −0.0833295 | + | 0.144331i | −0.904678 | − | 0.426096i | \(-0.859889\pi\) |
0.821349 | + | 0.570426i | \(0.193222\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.27526 | − | 5.03723i | −0.0511742 | − | 0.202137i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.55051 | − | 6.14966i | 0.142248 | − | 0.246381i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.94949 | + | 10.3048i | 0.237980 | + | 0.412193i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.7980 | − | 23.4381i | −0.431229 | − | 0.936026i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.5959 | −0.621850 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.1010 | −0.720590 | −0.360295 | − | 0.932838i | \(-0.617324\pi\) | ||||
−0.360295 | + | 0.932838i | \(0.617324\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.34847 | − | 0.492810i | −0.212583 | − | 0.0195874i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.17423 | − | 8.96204i | −0.205333 | − | 0.355648i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.44949 | − | 4.24264i | 0.0970523 | − | 0.168100i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.89898 | + | 27.9985i | 0.391598 | + | 1.10761i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.7474 | + | 35.9356i | −0.819475 | + | 1.41937i | 0.0865947 | + | 0.996244i | \(0.472401\pi\) |
−0.906070 | + | 0.423129i | \(0.860932\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.69694 | + | 16.7956i | 0.382410 | + | 0.662353i | 0.991406 | − | 0.130820i | \(-0.0417609\pi\) |
−0.608996 | + | 0.793173i | \(0.708428\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.0000 | + | 14.1421i | −0.393750 | + | 0.556846i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.3031 | 0.837510 | 0.418755 | − | 0.908099i | \(-0.362467\pi\) | ||||
0.418755 | + | 0.908099i | \(0.362467\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.00000 | −0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.00000 | − | 8.48528i | 0.235159 | − | 0.332564i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.89898 | + | 8.48528i | 0.191712 | + | 0.332055i | 0.945818 | − | 0.324698i | \(-0.105263\pi\) |
−0.754106 | + | 0.656753i | \(0.771929\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.1969 | + | 40.1783i | −0.906379 | + | 1.56990i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.89898 | − | 8.19955i | −0.113100 | − | 0.319895i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.34847 | − | 4.06767i | 0.0914834 | − | 0.158454i | −0.816652 | − | 0.577130i | \(-0.804172\pi\) |
0.908136 | + | 0.418676i | \(0.137506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.72474 | − | 8.18350i | −0.183771 | − | 0.318301i | 0.759391 | − | 0.650635i | \(-0.225497\pi\) |
−0.943162 | + | 0.332334i | \(0.892164\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.8990 | − | 1.55708i | −0.656302 | − | 0.0604719i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −25.6969 | −0.996485 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.89898 | 0.112249 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.1464 | − | 32.8769i | −0.585595 | − | 1.27109i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.4495 | + | 19.8311i | 0.442003 | + | 0.765571i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.2980 | + | 26.4968i | −0.589693 | + | 1.02138i | 0.404579 | + | 0.914503i | \(0.367418\pi\) |
−0.994272 | + | 0.106875i | \(0.965915\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.6969 | + | 24.9951i | −0.989076 | + | 0.962063i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.34847 | − | 12.7279i | 0.282425 | − | 0.489174i | −0.689557 | − | 0.724232i | \(-0.742195\pi\) |
0.971981 | + | 0.235058i | \(0.0755280\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.44949 | + | 5.97469i | 0.132379 | + | 0.229288i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.398979 | − | 0.866025i | −0.0152889 | − | 0.0331862i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.2020 | −1.23218 | −0.616088 | − | 0.787677i | \(-0.711284\pi\) | ||||
−0.616088 | + | 0.787677i | \(0.711284\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −40.6969 | −1.55495 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −40.0959 | − | 3.69445i | −1.52975 | − | 0.140952i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.69694 | − | 4.67123i | −0.102745 | − | 0.177960i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.47730 | − | 6.02285i | 0.132283 | − | 0.229120i | −0.792274 | − | 0.610166i | \(-0.791103\pi\) |
0.924556 | + | 0.381046i | \(0.124436\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.89898 | − | 4.56048i | 0.148110 | − | 0.173238i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.2980 | − | 28.2289i | 0.618217 | − | 1.07078i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.79796 | + | 16.9706i | 0.371124 | + | 0.642806i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.00000 | − | 9.89949i | 0.264764 | − | 0.374433i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 51.3939 | 1.94112 | 0.970560 | − | 0.240860i | \(-0.0774293\pi\) | ||||
0.970560 | + | 0.240860i | \(0.0774293\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 58.0908 | 2.19094 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −33.7980 | + | 47.7975i | −1.27290 | + | 1.80016i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.62372 | − | 6.27647i | −0.136284 | − | 0.236051i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.79796 | − | 10.0424i | 0.217747 | − | 0.377149i | −0.736372 | − | 0.676577i | \(-0.763463\pi\) |
0.954119 | + | 0.299428i | \(0.0967959\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.2980 | − | 4.33013i | −0.873742 | − | 0.162392i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.00000 | − | 5.19615i | 0.112351 | − | 0.194597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.8990 | − | 29.2699i | −0.631986 | − | 1.09463i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.0732 | + | 2.03383i | 0.824339 | + | 0.0759549i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.79796 | 0.365402 | 0.182701 | − | 0.983169i | \(-0.441516\pi\) | ||||
0.182701 | + | 0.983169i | \(0.441516\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0000 | −0.521387 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.44949 | + | 13.9993i | 0.239859 | + | 0.520638i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.0000 | − | 17.3205i | −0.371391 | − | 0.643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.2474 | − | 35.0696i | 0.750936 | − | 1.30066i | −0.196433 | − | 0.980517i | \(-0.562936\pi\) |
0.947369 | − | 0.320143i | \(-0.103731\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.89898 | + | 5.02118i | −0.107223 | + | 0.185715i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.27526 | + | 10.8691i | 0.231782 | + | 0.401458i | 0.958333 | − | 0.285655i | \(-0.0922111\pi\) |
−0.726551 | + | 0.687113i | \(0.758878\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.50000 | − | 5.42650i | −0.0922139 | − | 0.200160i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.20204 | −0.228455 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.5959 | 0.941561 | 0.470781 | − | 0.882250i | \(-0.343972\pi\) | ||||
0.470781 | + | 0.882250i | \(0.343972\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 62.9444 | + | 5.79972i | 2.31232 | + | 0.213058i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.0000 | + | 31.1769i | 0.660356 | + | 1.14377i | 0.980522 | + | 0.196409i | \(0.0629279\pi\) |
−0.320166 | + | 0.947361i | \(0.603739\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.3485 | − | 17.9241i | 0.379139 | − | 0.656687i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.89898 | − | 1.09638i | −0.215832 | − | 0.0401143i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | + | 10.3923i | −0.219235 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.2980 | + | 35.1571i | 0.740683 | + | 1.28290i | 0.952185 | + | 0.305523i | \(0.0988313\pi\) |
−0.211502 | + | 0.977378i | \(0.567835\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.5505 | − | 17.7491i | 0.457366 | − | 0.646813i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.2474 | 0.627699 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.3939 | 0.850265 | 0.425132 | − | 0.905131i | \(-0.360228\pi\) | ||||
0.425132 | + | 0.905131i | \(0.360228\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.00000 | − | 2.82843i | 0.0725954 | − | 0.102665i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.00000 | − | 1.73205i | −0.0362500 | − | 0.0627868i | 0.847331 | − | 0.531065i | \(-0.178208\pi\) |
−0.883581 | + | 0.468278i | \(0.844875\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.34847 | − | 14.4600i | 0.302235 | − | 0.523486i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.4495 | + | 15.7313i | −0.486267 | + | 0.568767i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.89898 | − | 8.48528i | 0.176892 | − | 0.306386i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.0454 | − | 46.8440i | −0.975282 | − | 1.68924i | −0.679000 | − | 0.734138i | \(-0.737586\pi\) |
−0.296282 | − | 0.955100i | \(-0.595747\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 47.9444 | + | 4.41761i | 1.72667 | + | 0.159096i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.9444 | −0.717350 | −0.358675 | − | 0.933463i | \(-0.616771\pi\) | ||||
−0.358675 | + | 0.933463i | \(0.616771\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −41.3939 | −1.48691 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.65153 | + | 12.2672i | 0.202748 | + | 0.440084i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36.4949 | − | 63.2110i | −1.30757 | − | 2.26477i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.89898 | + | 17.1455i | −0.354213 | + | 0.613515i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.7980 | + | 10.5031i | −0.385888 | + | 0.375349i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.9495 | + | 18.9651i | −0.390804 | + | 0.676892i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.6969 | + | 41.0443i | 0.844705 | + | 1.46307i | 0.885877 | + | 0.463919i | \(0.153557\pi\) |
−0.0411728 | + | 0.999152i | \(0.513109\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.6691 | + | 25.3290i | 0.415432 | + | 0.901737i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.8990 | −0.565303 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −56.0908 | −1.99184 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.55051 | − | 0.603566i | −0.232323 | − | 0.0214063i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.9722 | − | 31.1288i | −0.636608 | − | 1.10264i | −0.986172 | − | 0.165725i | \(-0.947004\pi\) |
0.349564 | − | 0.936912i | \(-0.386330\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.79796 | + | 16.9706i | −0.346627 | + | 0.600375i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.10102 | + | 20.0847i | 0.250902 | + | 0.709659i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.89898 | − | 5.02118i | 0.102303 | − | 0.177194i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.72474 | − | 2.98735i | −0.0607893 | − | 0.105290i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.65153 | − | 5.16404i | 0.128540 | − | 0.181783i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.7980 | −1.25859 | −0.629295 | − | 0.777167i | \(-0.716656\pi\) | ||||
−0.629295 | + | 0.777167i | \(0.716656\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.8990 | − | 23.8988i | 0.592673 | − | 0.838166i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.348469 | − | 0.603566i | −0.0122063 | − | 0.0211420i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.7980 | − | 18.7026i | 0.377773 | − | 0.654322i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.89898 | + | 13.8564i | 0.171184 | + | 0.484182i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.7980 | + | 34.2911i | −0.690954 | + | 1.19677i | 0.280572 | + | 0.959833i | \(0.409476\pi\) |
−0.971526 | + | 0.236934i | \(0.923858\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.6969 | + | 39.3123i | 0.791166 | + | 1.37034i | 0.925246 | + | 0.379368i | \(0.123859\pi\) |
−0.134080 | + | 0.990970i | \(0.542808\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −23.7980 | − | 2.19275i | −0.828539 | − | 0.0763418i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.4949 | −0.434490 | −0.217245 | − | 0.976117i | \(-0.569707\pi\) | ||||
−0.217245 | + | 0.976117i | \(0.569707\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.6969 | 1.06615 | 0.533074 | − | 0.846068i | \(-0.321037\pi\) | ||||
0.533074 | + | 0.846068i | \(0.321037\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.75255 | − | 16.8277i | −0.268933 | − | 0.583746i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.00000 | − | 1.73205i | −0.0346479 | − | 0.0600120i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.2474 | − | 55.8542i | 1.11597 | − | 1.93291i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.65153 | + | 30.2234i | 0.264476 | + | 1.04467i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.4495 | + | 38.8837i | −0.775042 | + | 1.34241i | 0.159728 | + | 0.987161i | \(0.448938\pi\) |
−0.934771 | + | 0.355252i | \(0.884395\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.2980 | + | 17.8366i | 0.355102 | + | 0.615055i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.7702 | + | 29.8895i | 0.474269 | + | 1.02945i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.9444 | 1.30533 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.00000 | −0.240523 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 35.4444 | + | 3.26586i | 1.21645 | + | 0.112084i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.89898 | + | 6.75323i | 0.133655 | + | 0.231498i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.4217 | − | 33.6393i | 0.664986 | − | 1.15179i | −0.314303 | − | 0.949323i | \(-0.601771\pi\) |
0.979289 | − | 0.202467i | \(-0.0648957\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 50.0959 | − | 58.5952i | 1.71324 | − | 2.00391i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.5505 | − | 21.7381i | 0.428717 | − | 0.742560i | −0.568042 | − | 0.822999i | \(-0.692299\pi\) |
0.996760 | + | 0.0804393i | \(0.0256323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.00000 | − | 8.66025i | −0.170598 | − | 0.295484i | 0.768031 | − | 0.640412i | \(-0.221237\pi\) |
−0.938629 | + | 0.344928i | \(0.887903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.79796 | − | 13.8564i | 0.333914 | − | 0.472225i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.10102 | −0.0715196 | −0.0357598 | − | 0.999360i | \(-0.511385\pi\) | ||||
−0.0357598 | + | 0.999360i | \(0.511385\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.4949 | −1.51287 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | − | 18.3848i | 0.441503 | − | 0.624380i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.89898 | − | 13.6814i | −0.267955 | − | 0.464111i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.59592 | − | 13.1565i | 0.257378 | − | 0.445792i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.3485 | − | 3.78194i | −0.688691 | − | 0.127999i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.27526 | + | 5.67291i | −0.110724 | + | 0.191779i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.2474 | + | 22.9453i | 0.447335 | + | 0.774806i | 0.998212 | − | 0.0597803i | \(-0.0190400\pi\) |
−0.550877 | + | 0.834586i | \(0.685707\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 46.9949 | + | 4.33013i | 1.58510 | + | 0.146052i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.5959 | −0.660203 | −0.330102 | − | 0.943945i | \(-0.607083\pi\) | ||||
−0.330102 | + | 0.943945i | \(0.607083\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.202041 | 0.00679922 | 0.00339961 | − | 0.999994i | \(-0.498918\pi\) | ||||
0.00339961 | + | 0.999994i | \(0.498918\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.00000 | − | 10.8530i | −0.168073 | − | 0.364820i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.8990 | − | 29.2699i | −0.567412 | − | 0.982787i | −0.996821 | − | 0.0796764i | \(-0.974611\pi\) |
0.429409 | − | 0.903110i | \(-0.358722\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.50000 | + | 2.59808i | −0.0503084 | + | 0.0871367i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.79796 | + | 17.7812i | 0.0937352 | + | 0.595693i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.4949 | − | 63.2110i | 1.22126 | − | 2.11528i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.0000 | − | 25.9808i | −0.501395 | − | 0.868441i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.55051 | + | 7.70674i | 0.118548 | + | 0.257321i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.3939 | −0.580118 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.20204 | −0.0733606 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.00000 | + | 0.460702i | 0.166390 | + | 0.0153312i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.50000 | − | 12.9904i | −0.249308 | − | 0.431815i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.3485 | + | 23.1202i | −0.443229 | + | 0.767695i | −0.997927 | − | 0.0643570i | \(-0.979500\pi\) |
0.554698 | + | 0.832052i | \(0.312834\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.3763 | + | 3.97297i | 0.709006 | + | 0.131775i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.9949 | + | 39.8283i | −0.761855 | + | 1.31957i | 0.180038 | + | 0.983660i | \(0.442378\pi\) |
−0.941893 | + | 0.335912i | \(0.890956\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.00000 | − | 3.46410i | −0.0661903 | − | 0.114645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −39.4949 | + | 55.8542i | −1.30566 | + | 1.84648i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.4495 | 0.444141 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.69694 | −0.121951 | −0.0609754 | − | 0.998139i | \(-0.519421\pi\) | ||||
−0.0609754 | + | 0.998139i | \(0.519421\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.752551 | − | 1.06427i | 0.0247974 | − | 0.0350688i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.2474 | − | 41.9978i | −0.798114 | − | 1.38237i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.8990 | − | 46.5904i | 0.884433 | − | 1.53188i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 27.2929 | − | 31.9233i | 0.896415 | − | 1.04850i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.1464 | − | 29.6985i | 0.562556 | − | 0.974376i | −0.434716 | − | 0.900567i | \(-0.643151\pi\) |
0.997272 | − | 0.0738083i | \(-0.0235153\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.72474 | + | 6.45145i | 0.122074 | + | 0.211438i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.24745 | − | 0.207081i | −0.0735782 | − | 0.00677952i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.7980 | −0.451242 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.40408 | 0.209212 | 0.104606 | − | 0.994514i | \(-0.466642\pi\) | ||||
0.104606 | + | 0.994514i | \(0.466642\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.8990 | − | 38.8515i | −0.584111 | − | 1.26787i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.72474 | − | 2.98735i | −0.0562251 | − | 0.0973847i | 0.836543 | − | 0.547901i | \(-0.184573\pi\) |
−0.892768 | + | 0.450517i | \(0.851240\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.89898 | − | 8.48528i | 0.159533 | − | 0.276319i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.2474 | + | 4.87832i | 0.561060 | + | 0.158692i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.75255 | − | 3.03551i | 0.0569503 | − | 0.0986408i | −0.836145 | − | 0.548509i | \(-0.815196\pi\) |
0.893095 | + | 0.449868i | \(0.148529\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.10102 | + | 12.2993i | 0.230509 | + | 0.399253i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.30306 | + | 13.6814i | 0.204391 | + | 0.443651i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.3939 | 1.79438 | 0.897192 | − | 0.441641i | \(-0.145604\pi\) | ||||
0.897192 | + | 0.441641i | \(0.145604\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −47.9444 | −1.55144 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.0000 | − | 0.921404i | −0.323254 | − | 0.0297848i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.89898 | + | 10.2173i | 0.190488 | + | 0.329935i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | + | 4.33013i | −0.0806452 | + | 0.139682i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.0000 | − | 33.9411i | −0.386695 | − | 1.09374i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.9722 | − | 24.2005i | 0.449781 | − | 0.779043i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.29796 | − | 12.6404i | −0.234687 | − | 0.406489i | 0.724495 | − | 0.689280i | \(-0.242073\pi\) |
−0.959182 | + | 0.282791i | \(0.908740\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.8990 | − | 21.0703i | 0.478624 | − | 0.676877i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.9444 | 1.73116 | 0.865579 | − | 0.500773i | \(-0.166951\pi\) | ||||
0.865579 | + | 0.500773i | \(0.166951\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.44949 | −0.302937 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 33.7980 | − | 47.7975i | 1.08240 | − | 1.53075i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.797959 | − | 1.38211i | −0.0255290 | − | 0.0442175i | 0.852979 | − | 0.521946i | \(-0.174794\pi\) |
−0.878508 | + | 0.477728i | \(0.841460\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.10102 | + | 12.2993i | −0.226950 | + | 0.393088i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.6969 | + | 47.2261i | 0.533092 | + | 1.50781i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.5959 | − | 39.1373i | 0.720698 | − | 1.24829i | −0.240023 | − | 0.970767i | \(-0.577155\pi\) |
0.960720 | − | 0.277518i | \(-0.0895118\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.8990 | + | 37.9301i | 0.697760 | + | 1.20855i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.8990 | + | 1.55708i | 0.537900 | + | 0.0495623i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.89898 | 0.0921822 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.7980 | −0.565371 | −0.282685 | − | 0.959213i | \(-0.591225\pi\) | ||||
−0.282685 | + | 0.959213i | \(0.591225\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.8990 | − | 38.8515i | −0.568007 | − | 1.23292i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.8990 | + | 20.6096i | 0.377223 | + | 0.653369i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.92679 | + | 15.4616i | −0.282714 | + | 0.489675i | −0.972052 | − | 0.234764i | \(-0.924568\pi\) |
0.689338 | + | 0.724440i | \(0.257901\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −38.9898 | − | 11.0280i | −1.23358 | − | 0.348910i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))