Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [396,2,Mod(307,396)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(396, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("396.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 396 = 2^{2} \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 396.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.16207592004\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 44) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 307.3 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 396.307 |
Dual form | 396.2.h.b.307.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/396\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(199\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 1.22474i | 0.500000 | − | 0.866025i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843 | 1.06904 | 0.534522 | − | 0.845154i | \(-0.320491\pi\) | ||||
0.534522 | + | 0.845154i | \(0.320491\pi\) | |||||||
\(8\) | −2.82843 | −1.00000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.707107 | − | 1.22474i | 0.223607 | − | 0.387298i | ||||
\(11\) | 2.82843 | + | 1.73205i | 0.852803 | + | 0.522233i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.89898i | − | 1.35873i | −0.733799 | − | 0.679366i | \(-0.762255\pi\) | ||
0.733799 | − | 0.679366i | \(-0.237745\pi\) | |||||||
\(14\) | 2.00000 | − | 3.46410i | 0.534522 | − | 0.925820i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | − | 4.89898i | − | 1.18818i | −0.804400 | − | 0.594089i | \(-0.797513\pi\) | ||
0.804400 | − | 0.594089i | \(-0.202487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | −1.00000 | − | 1.73205i | −0.223607 | − | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.12132 | − | 2.23936i | 0.878668 | − | 0.477432i | ||||
\(23\) | 5.19615i | 1.08347i | 0.840548 | + | 0.541736i | \(0.182233\pi\) | ||||
−0.840548 | + | 0.541736i | \(0.817767\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | −6.00000 | − | 3.46410i | −1.17670 | − | 0.679366i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.82843 | − | 4.89898i | −0.534522 | − | 0.925820i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.73205i | 0.311086i | 0.987829 | + | 0.155543i | \(0.0497126\pi\) | ||||
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 2.82843 | + | 4.89898i | 0.500000 | + | 0.866025i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.00000 | − | 3.46410i | −1.02899 | − | 0.594089i | ||||
\(35\) | 2.82843 | 0.478091 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | −2.00000 | + | 3.46410i | −0.324443 | + | 0.561951i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.82843 | −0.447214 | ||||||||
\(41\) | 4.89898i | 0.765092i | 0.923936 | + | 0.382546i | \(0.124953\pi\) | ||||
−0.923936 | + | 0.382546i | \(0.875047\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.65685 | 0.862662 | 0.431331 | − | 0.902194i | \(-0.358044\pi\) | ||||
0.431331 | + | 0.902194i | \(0.358044\pi\) | |||||||
\(44\) | 0.171573 | − | 6.63103i | 0.0258656 | − | 0.999665i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.36396 | + | 3.67423i | 0.938315 | + | 0.541736i | ||||
\(47\) | − | 3.46410i | − | 0.505291i | −0.967559 | − | 0.252646i | \(-0.918699\pi\) | ||
0.967559 | − | 0.252646i | \(-0.0813007\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.82843 | + | 4.89898i | −0.400000 | + | 0.692820i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.48528 | + | 4.89898i | −1.17670 | + | 0.679366i | ||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.82843 | + | 1.73205i | 0.381385 | + | 0.233550i | ||||
\(56\) | −8.00000 | −1.06904 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.73205i | − | 0.225494i | −0.993624 | − | 0.112747i | \(-0.964035\pi\) | ||
0.993624 | − | 0.112747i | \(-0.0359649\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.79796i | 1.25450i | 0.778818 | + | 0.627250i | \(0.215820\pi\) | ||||
−0.778818 | + | 0.627250i | \(0.784180\pi\) | |||||||
\(62\) | 2.12132 | + | 1.22474i | 0.269408 | + | 0.155543i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | − | 4.89898i | − | 0.607644i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.66025i | 1.05802i | 0.848616 | + | 0.529009i | \(0.177436\pi\) | ||||
−0.848616 | + | 0.529009i | \(0.822564\pi\) | |||||||
\(68\) | −8.48528 | + | 4.89898i | −1.02899 | + | 0.594089i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.00000 | − | 3.46410i | 0.239046 | − | 0.414039i | ||||
\(71\) | 12.1244i | 1.43890i | 0.694546 | + | 0.719448i | \(0.255605\pi\) | ||||
−0.694546 | + | 0.719448i | \(0.744395\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.89898i | 0.573382i | 0.958023 | + | 0.286691i | \(0.0925553\pi\) | ||||
−0.958023 | + | 0.286691i | \(0.907445\pi\) | |||||||
\(74\) | 2.12132 | − | 3.67423i | 0.246598 | − | 0.427121i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.82843 | + | 4.89898i | 0.324443 | + | 0.561951i | ||||
\(77\) | 8.00000 | + | 4.89898i | 0.911685 | + | 0.558291i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3137 | −1.27289 | −0.636446 | − | 0.771321i | \(-0.719596\pi\) | ||||
−0.636446 | + | 0.771321i | \(0.719596\pi\) | |||||||
\(80\) | −2.00000 | + | 3.46410i | −0.223607 | + | 0.387298i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.00000 | + | 3.46410i | 0.662589 | + | 0.382546i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 4.89898i | − | 0.531369i | ||||||
\(86\) | 4.00000 | − | 6.92820i | 0.431331 | − | 0.747087i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.00000 | − | 4.89898i | −0.852803 | − | 0.522233i | ||||
\(89\) | 1.00000 | 0.106000 | 0.0529999 | − | 0.998595i | \(-0.483122\pi\) | ||||
0.0529999 | + | 0.998595i | \(0.483122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 13.8564i | − | 1.45255i | ||||||
\(92\) | 9.00000 | − | 5.19615i | 0.938315 | − | 0.541736i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.24264 | − | 2.44949i | −0.437595 | − | 0.252646i | ||||
\(95\) | −2.82843 | −0.290191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(98\) | 0.707107 | − | 1.22474i | 0.0714286 | − | 0.123718i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | + | 6.92820i | 0.400000 | + | 0.692820i | ||||
\(101\) | − | 4.89898i | − | 0.487467i | −0.969842 | − | 0.243733i | \(-0.921628\pi\) | ||
0.969842 | − | 0.243733i | \(-0.0783722\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.46410i | 0.341328i | 0.985329 | + | 0.170664i | \(0.0545913\pi\) | ||||
−0.985329 | + | 0.170664i | \(0.945409\pi\) | |||||||
\(104\) | 13.8564i | 1.35873i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.41421 | − | 2.44949i | 0.137361 | − | 0.237915i | ||||
\(107\) | −8.48528 | −0.820303 | −0.410152 | − | 0.912017i | \(-0.634524\pi\) | ||||
−0.410152 | + | 0.912017i | \(0.634524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.79796i | − | 0.938474i | −0.883072 | − | 0.469237i | \(-0.844529\pi\) | ||
0.883072 | − | 0.469237i | \(-0.155471\pi\) | |||||||
\(110\) | 4.12132 | − | 2.23936i | 0.392952 | − | 0.213514i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.65685 | + | 9.79796i | −0.534522 | + | 0.925820i | ||||
\(113\) | 5.00000 | 0.470360 | 0.235180 | − | 0.971952i | \(-0.424432\pi\) | ||||
0.235180 | + | 0.971952i | \(0.424432\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.19615i | 0.484544i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.12132 | − | 1.22474i | −0.195283 | − | 0.112747i | ||||
\(119\) | − | 13.8564i | − | 1.27021i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 9.79796i | 0.454545 | + | 0.890724i | ||||
\(122\) | 12.0000 | + | 6.92820i | 1.08643 | + | 0.627250i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.00000 | − | 1.73205i | 0.269408 | − | 0.155543i | ||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1421 | −1.25491 | −0.627456 | − | 0.778652i | \(-0.715904\pi\) | ||||
−0.627456 | + | 0.778652i | \(0.715904\pi\) | |||||||
\(128\) | 5.65685 | − | 9.79796i | 0.500000 | − | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.00000 | − | 3.46410i | −0.526235 | − | 0.303822i | ||||
\(131\) | 2.82843 | 0.247121 | 0.123560 | − | 0.992337i | \(-0.460569\pi\) | ||||
0.123560 | + | 0.992337i | \(0.460569\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | 10.6066 | + | 6.12372i | 0.916271 | + | 0.529009i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.8564i | 1.18818i | ||||||||
\(137\) | −19.0000 | −1.62328 | −0.811640 | − | 0.584158i | \(-0.801425\pi\) | ||||
−0.811640 | + | 0.584158i | \(0.801425\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.7990 | 1.67933 | 0.839664 | − | 0.543106i | \(-0.182752\pi\) | ||||
0.839664 | + | 0.543106i | \(0.182752\pi\) | |||||||
\(140\) | −2.82843 | − | 4.89898i | −0.239046 | − | 0.414039i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.8492 | + | 8.57321i | 1.24612 | + | 0.719448i | ||||
\(143\) | 8.48528 | − | 13.8564i | 0.709575 | − | 1.15873i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.00000 | + | 3.46410i | 0.496564 | + | 0.286691i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.00000 | − | 5.19615i | −0.246598 | − | 0.427121i | ||||
\(149\) | 14.6969i | 1.20402i | 0.798489 | + | 0.602010i | \(0.205633\pi\) | ||||
−0.798489 | + | 0.602010i | \(0.794367\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.65685 | −0.460348 | −0.230174 | − | 0.973149i | \(-0.573930\pi\) | ||||
−0.230174 | + | 0.973149i | \(0.573930\pi\) | |||||||
\(152\) | 8.00000 | 0.648886 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.6569 | − | 6.33386i | 0.939336 | − | 0.510397i | ||||
\(155\) | 1.73205i | 0.139122i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0000 | 0.877896 | 0.438948 | − | 0.898513i | \(-0.355351\pi\) | ||||
0.438948 | + | 0.898513i | \(0.355351\pi\) | |||||||
\(158\) | −8.00000 | + | 13.8564i | −0.636446 | + | 1.10236i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.82843 | + | 4.89898i | 0.223607 | + | 0.387298i | ||||
\(161\) | 14.6969i | 1.15828i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 17.3205i | − | 1.35665i | −0.734763 | − | 0.678323i | \(-0.762707\pi\) | ||
0.734763 | − | 0.678323i | \(-0.237293\pi\) | |||||||
\(164\) | 8.48528 | − | 4.89898i | 0.662589 | − | 0.382546i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.7990 | −1.53209 | −0.766046 | − | 0.642786i | \(-0.777779\pi\) | ||||
−0.766046 | + | 0.642786i | \(0.777779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | −6.00000 | − | 3.46410i | −0.460179 | − | 0.265684i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.65685 | − | 9.79796i | −0.431331 | − | 0.747087i | ||||
\(173\) | − | 9.79796i | − | 0.744925i | −0.928047 | − | 0.372463i | \(-0.878514\pi\) | ||
0.928047 | − | 0.372463i | \(-0.121486\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.3137 | −0.855236 | ||||||||
\(176\) | −11.6569 | + | 6.33386i | −0.878668 | + | 0.477432i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.707107 | − | 1.22474i | 0.0529999 | − | 0.0917985i | ||||
\(179\) | − | 8.66025i | − | 0.647298i | −0.946177 | − | 0.323649i | \(-0.895090\pi\) | ||
0.946177 | − | 0.323649i | \(-0.104910\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.0000 | −1.56092 | −0.780459 | − | 0.625207i | \(-0.785014\pi\) | ||||
−0.780459 | + | 0.625207i | \(0.785014\pi\) | |||||||
\(182\) | −16.9706 | − | 9.79796i | −1.25794 | − | 0.726273i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 14.6969i | − | 1.08347i | ||||||
\(185\) | 3.00000 | 0.220564 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.48528 | − | 13.8564i | 0.620505 | − | 1.01328i | ||||
\(188\) | −6.00000 | + | 3.46410i | −0.437595 | + | 0.252646i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.00000 | + | 3.46410i | −0.145095 | + | 0.251312i | ||||
\(191\) | 5.19615i | 0.375980i | 0.982171 | + | 0.187990i | \(0.0601973\pi\) | ||||
−0.982171 | + | 0.187990i | \(0.939803\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 9.79796i | − | 0.705273i | −0.935760 | − | 0.352636i | \(-0.885285\pi\) | ||
0.935760 | − | 0.352636i | \(-0.114715\pi\) | |||||||
\(194\) | 4.94975 | − | 8.57321i | 0.355371 | − | 0.615521i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | − | 1.73205i | −0.0714286 | − | 0.123718i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.3923i | − | 0.736691i | −0.929689 | − | 0.368345i | \(-0.879924\pi\) | ||
0.929689 | − | 0.368345i | \(-0.120076\pi\) | |||||||
\(200\) | 11.3137 | 0.800000 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.00000 | − | 3.46410i | −0.422159 | − | 0.243733i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.89898i | 0.342160i | ||||||||
\(206\) | 4.24264 | + | 2.44949i | 0.295599 | + | 0.170664i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 16.9706 | + | 9.79796i | 1.17670 | + | 0.679366i | ||||
\(209\) | −8.00000 | − | 4.89898i | −0.553372 | − | 0.338869i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.65685 | 0.389434 | 0.194717 | − | 0.980859i | \(-0.437621\pi\) | ||||
0.194717 | + | 0.980859i | \(0.437621\pi\) | |||||||
\(212\) | −2.00000 | − | 3.46410i | −0.137361 | − | 0.237915i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | + | 10.3923i | −0.410152 | + | 0.710403i | ||||
\(215\) | 5.65685 | 0.385794 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.89898i | 0.332564i | ||||||||
\(218\) | −12.0000 | − | 6.92820i | −0.812743 | − | 0.469237i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.171573 | − | 6.63103i | 0.0115674 | − | 0.447064i | ||||
\(221\) | −24.0000 | −1.61441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.5167i | 1.50783i | 0.656974 | + | 0.753914i | \(0.271836\pi\) | ||||
−0.656974 | + | 0.753914i | \(0.728164\pi\) | |||||||
\(224\) | 8.00000 | + | 13.8564i | 0.534522 | + | 0.925820i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.53553 | − | 6.12372i | 0.235180 | − | 0.407344i | ||||
\(227\) | 8.48528 | 0.563188 | 0.281594 | − | 0.959534i | \(-0.409137\pi\) | ||||
0.281594 | + | 0.959534i | \(0.409137\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | −0.0660819 | −0.0330409 | − | 0.999454i | \(-0.510519\pi\) | ||||
−0.0330409 | + | 0.999454i | \(0.510519\pi\) | |||||||
\(230\) | 6.36396 | + | 3.67423i | 0.419627 | + | 0.242272i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 19.5959i | − | 1.28377i | −0.766800 | − | 0.641886i | \(-0.778152\pi\) | ||
0.766800 | − | 0.641886i | \(-0.221848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3.46410i | − | 0.225973i | ||||||
\(236\) | −3.00000 | + | 1.73205i | −0.195283 | + | 0.112747i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −16.9706 | − | 9.79796i | −1.10004 | − | 0.635107i | ||||
\(239\) | −5.65685 | −0.365911 | −0.182956 | − | 0.983121i | \(-0.558567\pi\) | ||||
−0.182956 | + | 0.983121i | \(0.558567\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 29.3939i | − | 1.89343i | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||
0.322078 | − | 0.946713i | \(-0.395619\pi\) | |||||||
\(242\) | 15.5355 | + | 0.804479i | 0.998662 | + | 0.0517139i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 16.9706 | − | 9.79796i | 1.08643 | − | 0.627250i | ||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.8564i | 0.881662i | ||||||||
\(248\) | − | 4.89898i | − | 0.311086i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.36396 | + | 11.0227i | −0.402492 | + | 0.697137i | ||||
\(251\) | − | 22.5167i | − | 1.42124i | −0.703577 | − | 0.710620i | \(-0.748415\pi\) | ||
0.703577 | − | 0.710620i | \(-0.251585\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.00000 | + | 14.6969i | −0.565825 | + | 0.923989i | ||||
\(254\) | −10.0000 | + | 17.3205i | −0.627456 | + | 1.08679i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 22.0000 | 1.37232 | 0.686161 | − | 0.727450i | \(-0.259294\pi\) | ||||
0.686161 | + | 0.727450i | \(0.259294\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.48528 | 0.527250 | ||||||||
\(260\) | −8.48528 | + | 4.89898i | −0.526235 | + | 0.303822i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.00000 | − | 3.46410i | 0.123560 | − | 0.214013i | ||||
\(263\) | −14.1421 | −0.872041 | −0.436021 | − | 0.899937i | \(-0.643613\pi\) | ||||
−0.436021 | + | 0.899937i | \(0.643613\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.00000 | 0.122859 | ||||||||
\(266\) | −5.65685 | + | 9.79796i | −0.346844 | + | 0.600751i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.0000 | − | 8.66025i | 0.916271 | − | 0.529009i | ||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.82843 | −0.171815 | −0.0859074 | − | 0.996303i | \(-0.527379\pi\) | ||||
−0.0859074 | + | 0.996303i | \(0.527379\pi\) | |||||||
\(272\) | 16.9706 | + | 9.79796i | 1.02899 | + | 0.594089i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.4350 | + | 23.2702i | −0.811640 | + | 1.40580i | ||||
\(275\) | −11.3137 | − | 6.92820i | −0.682242 | − | 0.417786i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 9.79796i | − | 0.588702i | −0.955697 | − | 0.294351i | \(-0.904896\pi\) | ||
0.955697 | − | 0.294351i | \(-0.0951035\pi\) | |||||||
\(278\) | 14.0000 | − | 24.2487i | 0.839664 | − | 1.45434i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.00000 | −0.478091 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3137 | 0.672530 | 0.336265 | − | 0.941767i | \(-0.390836\pi\) | ||||
0.336265 | + | 0.941767i | \(0.390836\pi\) | |||||||
\(284\) | 21.0000 | − | 12.1244i | 1.24612 | − | 0.719448i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.9706 | − | 20.1903i | −0.648703 | − | 1.19388i | ||||
\(287\) | 13.8564i | 0.817918i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.48528 | − | 4.89898i | 0.496564 | − | 0.286691i | ||||
\(293\) | 4.89898i | 0.286201i | 0.989708 | + | 0.143101i | \(0.0457073\pi\) | ||||
−0.989708 | + | 0.143101i | \(0.954293\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.73205i | − | 0.100844i | ||||||
\(296\) | −8.48528 | −0.493197 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.0000 | + | 10.3923i | 1.04271 | + | 0.602010i | ||||
\(299\) | 25.4558 | 1.47215 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.0000 | 0.922225 | ||||||||
\(302\) | −4.00000 | + | 6.92820i | −0.230174 | + | 0.398673i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.65685 | − | 9.79796i | 0.324443 | − | 0.561951i | ||||
\(305\) | 9.79796i | 0.561029i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.7990 | −1.12999 | −0.564994 | − | 0.825095i | \(-0.691122\pi\) | ||||
−0.564994 | + | 0.825095i | \(0.691122\pi\) | |||||||
\(308\) | 0.485281 | − | 18.7554i | 0.0276515 | − | 1.06869i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.12132 | + | 1.22474i | 0.120483 | + | 0.0695608i | ||||
\(311\) | 10.3923i | 0.589294i | 0.955606 | + | 0.294647i | \(0.0952020\pi\) | ||||
−0.955606 | + | 0.294647i | \(0.904798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.0000 | 1.52613 | 0.763065 | − | 0.646322i | \(-0.223694\pi\) | ||||
0.763065 | + | 0.646322i | \(0.223694\pi\) | |||||||
\(314\) | 7.77817 | − | 13.4722i | 0.438948 | − | 0.760280i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.3137 | + | 19.5959i | 0.636446 | + | 1.10236i | ||||
\(317\) | 25.0000 | 1.40414 | 0.702070 | − | 0.712108i | \(-0.252259\pi\) | ||||
0.702070 | + | 0.712108i | \(0.252259\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 8.00000 | 0.447214 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.0000 | + | 10.3923i | 1.00310 | + | 0.579141i | ||||
\(323\) | 13.8564i | 0.770991i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.5959i | 1.08699i | ||||||||
\(326\) | −21.2132 | − | 12.2474i | −1.17489 | − | 0.678323i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 13.8564i | − | 0.765092i | ||||||
\(329\) | − | 9.79796i | − | 0.540179i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 5.19615i | − | 0.285606i | −0.989751 | − | 0.142803i | \(-0.954388\pi\) | ||
0.989751 | − | 0.142803i | \(-0.0456116\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.0000 | + | 24.2487i | −0.766046 | + | 1.32683i | ||||
\(335\) | 8.66025i | 0.473160i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.2929i | 1.86805i | 0.357206 | + | 0.934025i | \(0.383729\pi\) | ||||
−0.357206 | + | 0.934025i | \(0.616271\pi\) | |||||||
\(338\) | −7.77817 | + | 13.4722i | −0.423077 | + | 0.732791i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.48528 | + | 4.89898i | −0.460179 | + | 0.265684i | ||||
\(341\) | −3.00000 | + | 4.89898i | −0.162459 | + | 0.265295i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | −16.0000 | −0.862662 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0000 | − | 6.92820i | −0.645124 | − | 0.372463i | ||||
\(347\) | 25.4558 | 1.36654 | 0.683271 | − | 0.730165i | \(-0.260557\pi\) | ||||
0.683271 | + | 0.730165i | \(0.260557\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.89898i | − | 0.262236i | −0.991367 | − | 0.131118i | \(-0.958143\pi\) | ||
0.991367 | − | 0.131118i | \(-0.0418567\pi\) | |||||||
\(350\) | −8.00000 | + | 13.8564i | −0.427618 | + | 0.740656i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.485281 | + | 18.7554i | −0.0258656 | + | 0.999665i | ||||
\(353\) | 17.0000 | 0.904819 | 0.452409 | − | 0.891810i | \(-0.350565\pi\) | ||||
0.452409 | + | 0.891810i | \(0.350565\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.1244i | 0.643494i | ||||||||
\(356\) | −1.00000 | − | 1.73205i | −0.0529999 | − | 0.0917985i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.6066 | − | 6.12372i | −0.560576 | − | 0.323649i | ||||
\(359\) | −8.48528 | −0.447836 | −0.223918 | − | 0.974608i | \(-0.571885\pi\) | ||||
−0.223918 | + | 0.974608i | \(0.571885\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | −14.8492 | + | 25.7196i | −0.780459 | + | 1.35179i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.0000 | + | 13.8564i | −1.25794 | + | 0.726273i | ||||
\(365\) | 4.89898i | 0.256424i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.73205i | 0.0904123i | 0.998978 | + | 0.0452062i | \(0.0143945\pi\) | ||||
−0.998978 | + | 0.0452062i | \(0.985606\pi\) | |||||||
\(368\) | −18.0000 | − | 10.3923i | −0.938315 | − | 0.541736i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.12132 | − | 3.67423i | 0.110282 | − | 0.191014i | ||||
\(371\) | 5.65685 | 0.293689 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 14.6969i | − | 0.760979i | −0.924785 | − | 0.380489i | \(-0.875756\pi\) | ||
0.924785 | − | 0.380489i | \(-0.124244\pi\) | |||||||
\(374\) | −10.9706 | − | 20.1903i | −0.567274 | − | 1.04401i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.79796i | 0.505291i | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 12.1244i | − | 0.622786i | −0.950281 | − | 0.311393i | \(-0.899204\pi\) | ||
0.950281 | − | 0.311393i | \(-0.100796\pi\) | |||||||
\(380\) | 2.82843 | + | 4.89898i | 0.145095 | + | 0.251312i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.36396 | + | 3.67423i | 0.325609 | + | 0.187990i | ||||
\(383\) | 32.9090i | 1.68157i | 0.541370 | + | 0.840785i | \(0.317906\pi\) | ||||
−0.541370 | + | 0.840785i | \(0.682094\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.00000 | + | 4.89898i | 0.407718 | + | 0.249675i | ||||
\(386\) | −12.0000 | − | 6.92820i | −0.610784 | − | 0.352636i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.00000 | − | 12.1244i | −0.355371 | − | 0.615521i | ||||
\(389\) | −19.0000 | −0.963338 | −0.481669 | − | 0.876353i | \(-0.659969\pi\) | ||||
−0.481669 | + | 0.876353i | \(0.659969\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.4558 | 1.28736 | ||||||||
\(392\) | −2.82843 | −0.142857 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.3137 | −0.569254 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.00000 | 0.301131 | 0.150566 | − | 0.988600i | \(-0.451890\pi\) | ||||
0.150566 | + | 0.988600i | \(0.451890\pi\) | |||||||
\(398\) | −12.7279 | − | 7.34847i | −0.637993 | − | 0.368345i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.00000 | − | 13.8564i | 0.400000 | − | 0.692820i | ||||
\(401\) | −10.0000 | −0.499376 | −0.249688 | − | 0.968326i | \(-0.580328\pi\) | ||||
−0.249688 | + | 0.968326i | \(0.580328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.48528 | 0.422682 | ||||||||
\(404\) | −8.48528 | + | 4.89898i | −0.422159 | + | 0.243733i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.48528 | + | 5.19615i | 0.420600 | + | 0.257564i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 29.3939i | − | 1.45343i | −0.686937 | − | 0.726717i | \(-0.741045\pi\) | ||
0.686937 | − | 0.726717i | \(-0.258955\pi\) | |||||||
\(410\) | 6.00000 | + | 3.46410i | 0.296319 | + | 0.171080i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.00000 | − | 3.46410i | 0.295599 | − | 0.170664i | ||||
\(413\) | − | 4.89898i | − | 0.241063i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 24.0000 | − | 13.8564i | 1.17670 | − | 0.679366i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.6569 | + | 6.33386i | −0.570155 | + | 0.309799i | ||||
\(419\) | − | 10.3923i | − | 0.507697i | −0.967244 | − | 0.253849i | \(-0.918303\pi\) | ||
0.967244 | − | 0.253849i | \(-0.0816965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.0000 | 1.46211 | 0.731055 | − | 0.682318i | \(-0.239028\pi\) | ||||
0.731055 | + | 0.682318i | \(0.239028\pi\) | |||||||
\(422\) | 4.00000 | − | 6.92820i | 0.194717 | − | 0.337260i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.65685 | −0.274721 | ||||||||
\(425\) | 19.5959i | 0.950542i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.7128i | 1.34112i | ||||||||
\(428\) | 8.48528 | + | 14.6969i | 0.410152 | + | 0.710403i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.00000 | − | 6.92820i | 0.192897 | − | 0.334108i | ||||
\(431\) | −14.1421 | −0.681203 | −0.340601 | − | 0.940208i | \(-0.610631\pi\) | ||||
−0.340601 | + | 0.940208i | \(0.610631\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.0000 | −1.00920 | −0.504598 | − | 0.863355i | \(-0.668359\pi\) | ||||
−0.504598 | + | 0.863355i | \(0.668359\pi\) | |||||||
\(434\) | 6.00000 | + | 3.46410i | 0.288009 | + | 0.166282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.9706 | + | 9.79796i | −0.812743 | + | 0.469237i | ||||
\(437\) | − | 14.6969i | − | 0.703050i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.6274 | −1.07995 | −0.539974 | − | 0.841682i | \(-0.681566\pi\) | ||||
−0.539974 | + | 0.841682i | \(0.681566\pi\) | |||||||
\(440\) | −8.00000 | − | 4.89898i | −0.381385 | − | 0.233550i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.9706 | + | 29.3939i | −0.807207 | + | 1.39812i | ||||
\(443\) | 5.19615i | 0.246877i | 0.992352 | + | 0.123438i | \(0.0393921\pi\) | ||||
−0.992352 | + | 0.123438i | \(0.960608\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00000 | 0.0474045 | ||||||||
\(446\) | 27.5772 | + | 15.9217i | 1.30582 | + | 0.753914i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 22.6274 | 1.06904 | ||||||||
\(449\) | −23.0000 | −1.08544 | −0.542719 | − | 0.839915i | \(-0.682605\pi\) | ||||
−0.542719 | + | 0.839915i | \(0.682605\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.48528 | + | 13.8564i | −0.399556 | + | 0.652473i | ||||
\(452\) | −5.00000 | − | 8.66025i | −0.235180 | − | 0.407344i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.00000 | − | 10.3923i | 0.281594 | − | 0.487735i | ||||
\(455\) | − | 13.8564i | − | 0.649598i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.5959i | 0.916658i | 0.888783 | + | 0.458329i | \(0.151552\pi\) | ||||
−0.888783 | + | 0.458329i | \(0.848448\pi\) | |||||||
\(458\) | −0.707107 | + | 1.22474i | −0.0330409 | + | 0.0572286i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.00000 | − | 5.19615i | 0.419627 | − | 0.242272i | ||||
\(461\) | − | 29.3939i | − | 1.36901i | −0.729008 | − | 0.684505i | \(-0.760019\pi\) | ||
0.729008 | − | 0.684505i | \(-0.239981\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.3731i | 1.69040i | 0.534450 | + | 0.845200i | \(0.320519\pi\) | ||||
−0.534450 | + | 0.845200i | \(0.679481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.0000 | − | 13.8564i | −1.11178 | − | 0.641886i | ||||
\(467\) | 32.9090i | 1.52285i | 0.648256 | + | 0.761423i | \(0.275499\pi\) | ||||
−0.648256 | + | 0.761423i | \(0.724501\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.4949i | 1.13107i | ||||||||
\(470\) | −4.24264 | − | 2.44949i | −0.195698 | − | 0.112987i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.89898i | 0.225494i | ||||||||
\(473\) | 16.0000 | + | 9.79796i | 0.735681 | + | 0.450511i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.3137 | 0.519109 | ||||||||
\(476\) | −24.0000 | + | 13.8564i | −1.10004 | + | 0.635107i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.00000 | + | 6.92820i | −0.182956 | + | 0.316889i | ||||
\(479\) | −31.1127 | −1.42158 | −0.710788 | − | 0.703407i | \(-0.751661\pi\) | ||||
−0.710788 | + | 0.703407i | \(0.751661\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 14.6969i | − | 0.670123i | ||||||
\(482\) | −36.0000 | − | 20.7846i | −1.63976 | − | 0.946713i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.9706 | − | 18.4582i | 0.544116 | − | 0.839010i | ||||
\(485\) | 7.00000 | 0.317854 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 39.8372i | − | 1.80519i | −0.430486 | − | 0.902597i | \(-0.641658\pi\) | ||
0.430486 | − | 0.902597i | \(-0.358342\pi\) | |||||||
\(488\) | − | 27.7128i | − | 1.25450i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.707107 | − | 1.22474i | 0.0319438 | − | 0.0553283i | ||||
\(491\) | 33.9411 | 1.53174 | 0.765871 | − | 0.642995i | \(-0.222308\pi\) | ||||
0.765871 | + | 0.642995i | \(0.222308\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 16.9706 | + | 9.79796i | 0.763542 | + | 0.440831i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | − | 3.46410i | −0.269408 | − | 0.155543i | ||||
\(497\) | 34.2929i | 1.53824i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17.3205i | − | 0.775372i | −0.921791 | − | 0.387686i | \(-0.873274\pi\) | ||
0.921791 | − | 0.387686i | \(-0.126726\pi\) | |||||||
\(500\) | 9.00000 | + | 15.5885i | 0.402492 | + | 0.697137i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −27.5772 | − | 15.9217i | −1.23083 | − | 0.710620i | ||||
\(503\) | 39.5980 | 1.76559 | 0.882793 | − | 0.469762i | \(-0.155660\pi\) | ||||
0.882793 | + | 0.469762i | \(0.155660\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 4.89898i | − | 0.218002i | ||||||
\(506\) | 11.6360 | + | 21.4150i | 0.517285 | + | 0.952013i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.1421 | + | 24.4949i | 0.627456 | + | 1.08679i | ||||
\(509\) | 1.00000 | 0.0443242 | 0.0221621 | − | 0.999754i | \(-0.492945\pi\) | ||||
0.0221621 | + | 0.999754i | \(0.492945\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.8564i | 0.612971i | ||||||||
\(512\) | −22.6274 | −1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.5563 | − | 26.9444i | 0.686161 | − | 1.18847i | ||||
\(515\) | 3.46410i | 0.152647i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | − | 9.79796i | 0.263880 | − | 0.430914i | ||||
\(518\) | 6.00000 | − | 10.3923i | 0.263625 | − | 0.456612i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 13.8564i | 0.607644i | ||||||||
\(521\) | 17.0000 | 0.744784 | 0.372392 | − | 0.928076i | \(-0.378538\pi\) | ||||
0.372392 | + | 0.928076i | \(0.378538\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.7696 | 1.60782 | 0.803910 | − | 0.594751i | \(-0.202749\pi\) | ||||
0.803910 | + | 0.594751i | \(0.202749\pi\) | |||||||
\(524\) | −2.82843 | − | 4.89898i | −0.123560 | − | 0.214013i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.0000 | + | 17.3205i | −0.436021 | + | 0.755210i | ||||
\(527\) | 8.48528 | 0.369625 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.00000 | −0.173913 | ||||||||
\(530\) | 1.41421 | − | 2.44949i | 0.0614295 | − | 0.106399i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.00000 | + | 13.8564i | 0.346844 | + | 0.600751i | ||||
\(533\) | 24.0000 | 1.03956 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.48528 | −0.366851 | ||||||||
\(536\) | − | 24.4949i | − | 1.05802i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.07107 | − | 12.2474i | 0.304855 | − | 0.528025i | ||||
\(539\) | 2.82843 | + | 1.73205i | 0.121829 | + | 0.0746047i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 14.6969i | − | 0.631871i | −0.948781 | − | 0.315935i | \(-0.897682\pi\) | ||
0.948781 | − | 0.315935i | \(-0.102318\pi\) | |||||||
\(542\) | −2.00000 | + | 3.46410i | −0.0859074 | + | 0.148796i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 24.0000 | − | 13.8564i | 1.02899 | − | 0.594089i | ||||
\(545\) | − | 9.79796i | − | 0.419698i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.65685 | 0.241870 | 0.120935 | − | 0.992660i | \(-0.461411\pi\) | ||||
0.120935 | + | 0.992660i | \(0.461411\pi\) | |||||||
\(548\) | 19.0000 | + | 32.9090i | 0.811640 | + | 1.40580i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.4853 | + | 8.95743i | −0.702935 | + | 0.381946i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.0000 | −1.36078 | ||||||||
\(554\) | −12.0000 | − | 6.92820i | −0.509831 | − | 0.294351i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.7990 | − | 34.2929i | −0.839664 | − | 1.45434i | ||||
\(557\) | − | 24.4949i | − | 1.03788i | −0.854810 | − | 0.518941i | \(-0.826326\pi\) | ||
0.854810 | − | 0.518941i | \(-0.173674\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 27.7128i | − | 1.17213i | ||||||
\(560\) | −5.65685 | + | 9.79796i | −0.239046 | + | 0.414039i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.3137 | −0.476816 | −0.238408 | − | 0.971165i | \(-0.576626\pi\) | ||||
−0.238408 | + | 0.971165i | \(0.576626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.00000 | 0.210352 | ||||||||
\(566\) | 8.00000 | − | 13.8564i | 0.336265 | − | 0.582428i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 34.2929i | − | 1.43890i | ||||||
\(569\) | − | 19.5959i | − | 0.821504i | −0.911747 | − | 0.410752i | \(-0.865266\pi\) | ||
0.911747 | − | 0.410752i | \(-0.134734\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.65685 | −0.236732 | −0.118366 | − | 0.992970i | \(-0.537766\pi\) | ||||
−0.118366 | + | 0.992970i | \(0.537766\pi\) | |||||||
\(572\) | −32.4853 | − | 0.840532i | −1.35828 | − | 0.0351444i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 16.9706 | + | 9.79796i | 0.708338 | + | 0.408959i | ||||
\(575\) | − | 20.7846i | − | 0.866778i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.0000 | −0.707719 | −0.353860 | − | 0.935299i | \(-0.615131\pi\) | ||||
−0.353860 | + | 0.935299i | \(0.615131\pi\) | |||||||
\(578\) | −4.94975 | + | 8.57321i | −0.205882 | + | 0.356599i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.65685 | + | 3.46410i | 0.234283 | + | 0.143468i | ||||
\(584\) | − | 13.8564i | − | 0.573382i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | + | 3.46410i | 0.247858 | + | 0.143101i | ||||
\(587\) | − | 10.3923i | − | 0.428936i | −0.976731 | − | 0.214468i | \(-0.931198\pi\) | ||
0.976731 | − | 0.214468i | \(-0.0688018\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.89898i | − | 0.201859i | ||||||
\(590\) | −2.12132 | − | 1.22474i | −0.0873334 | − | 0.0504219i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.00000 | + | 10.3923i | −0.246598 | + | 0.427121i | ||||
\(593\) | − | 9.79796i | − | 0.402354i | −0.979555 | − | 0.201177i | \(-0.935523\pi\) | ||
0.979555 | − | 0.201177i | \(-0.0644766\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 13.8564i | − | 0.568057i | ||||||
\(596\) | 25.4558 | − | 14.6969i | 1.04271 | − | 0.602010i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 18.0000 | − | 31.1769i | 0.736075 | − | 1.27492i | ||||
\(599\) | − | 45.0333i | − | 1.84001i | −0.391905 | − | 0.920006i | \(-0.628184\pi\) | ||
0.391905 | − | 0.920006i | \(-0.371816\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 4.89898i | − | 0.199834i | −0.994996 | − | 0.0999168i | \(-0.968142\pi\) | ||
0.994996 | − | 0.0999168i | \(-0.0318577\pi\) | |||||||
\(602\) | 11.3137 | − | 19.5959i | 0.461112 | − | 0.798670i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.65685 | + | 9.79796i | 0.230174 | + | 0.398673i | ||||
\(605\) | 5.00000 | + | 9.79796i | 0.203279 | + | 0.398344i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.6274 | −0.918419 | −0.459209 | − | 0.888328i | \(-0.651867\pi\) | ||||
−0.459209 | + | 0.888328i | \(0.651867\pi\) | |||||||
\(608\) | −8.00000 | − | 13.8564i | −0.324443 | − | 0.561951i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.0000 | + | 6.92820i | 0.485866 | + | 0.280515i | ||||
\(611\) | −16.9706 | −0.686555 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 9.79796i | − | 0.395736i | −0.980229 | − | 0.197868i | \(-0.936598\pi\) | ||
0.980229 | − | 0.197868i | \(-0.0634017\pi\) | |||||||
\(614\) | −14.0000 | + | 24.2487i | −0.564994 | + | 0.978598i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.6274 | − | 13.8564i | −0.911685 | − | 0.558291i | ||||
\(617\) | −2.00000 | −0.0805170 | −0.0402585 | − | 0.999189i | \(-0.512818\pi\) | ||||
−0.0402585 | + | 0.999189i | \(0.512818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.73205i | 0.0696170i | 0.999394 | + | 0.0348085i | \(0.0110821\pi\) | ||||
−0.999394 | + | 0.0348085i | \(0.988918\pi\) | |||||||
\(620\) | 3.00000 | − | 1.73205i | 0.120483 | − | 0.0695608i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.7279 | + | 7.34847i | 0.510343 | + | 0.294647i | ||||
\(623\) | 2.82843 | 0.113319 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 19.0919 | − | 33.0681i | 0.763065 | − | 1.32167i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.0000 | − | 19.0526i | −0.438948 | − | 0.760280i | ||||
\(629\) | − | 14.6969i | − | 0.586005i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.3731i | 1.44799i | 0.689806 | + | 0.723994i | \(0.257696\pi\) | ||||
−0.689806 | + | 0.723994i | \(0.742304\pi\) | |||||||
\(632\) | 32.0000 | 1.27289 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.6777 | − | 30.6186i | 0.702070 | − | 1.21602i | ||||
\(635\) | −14.1421 | −0.561214 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.89898i | − | 0.194105i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.65685 | − | 9.79796i | 0.223607 | − | 0.387298i | ||||
\(641\) | −19.0000 | −0.750455 | −0.375227 | − | 0.926933i | \(-0.622435\pi\) | ||||
−0.375227 | + | 0.926933i | \(0.622435\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 25.9808i | − | 1.02458i | −0.858812 | − | 0.512291i | \(-0.828797\pi\) | ||
0.858812 | − | 0.512291i | \(-0.171203\pi\) | |||||||
\(644\) | 25.4558 | − | 14.6969i | 1.00310 | − | 0.579141i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.9706 | + | 9.79796i | 0.667698 | + | 0.385496i | ||||
\(647\) | − | 1.73205i | − | 0.0680939i | −0.999420 | − | 0.0340470i | \(-0.989160\pi\) | ||
0.999420 | − | 0.0340470i | \(-0.0108396\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.00000 | − | 4.89898i | 0.117760 | − | 0.192302i | ||||
\(650\) | 24.0000 | + | 13.8564i | 0.941357 | + | 0.543493i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −30.0000 | + | 17.3205i | −1.17489 | + | 0.678323i | ||||
\(653\) | −31.0000 | −1.21312 | −0.606562 | − | 0.795036i | \(-0.707452\pi\) | ||||
−0.606562 | + | 0.795036i | \(0.707452\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.82843 | 0.110516 | ||||||||
\(656\) | −16.9706 | − | 9.79796i | −0.662589 | − | 0.382546i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.0000 | − | 6.92820i | −0.467809 | − | 0.270089i | ||||
\(659\) | −45.2548 | −1.76288 | −0.881439 | − | 0.472298i | \(-0.843425\pi\) | ||||
−0.881439 | + | 0.472298i | \(0.843425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0000 | −0.661223 | −0.330612 | − | 0.943767i | \(-0.607255\pi\) | ||||
−0.330612 | + | 0.943767i | \(0.607255\pi\) | |||||||
\(662\) | −6.36396 | − | 3.67423i | −0.247342 | − | 0.142803i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.00000 | −0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 19.7990 | + | 34.2929i | 0.766046 | + | 1.32683i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.6066 | + | 6.12372i | 0.409769 | + | 0.236580i | ||||
\(671\) | −16.9706 | + | 27.7128i | −0.655141 | + | 1.06984i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 42.0000 | + | 24.2487i | 1.61778 | + | 0.934025i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.0000 | + | 19.0526i | 0.423077 | + | 0.732791i | ||||
\(677\) | 24.4949i | 0.941415i | 0.882289 | + | 0.470708i | \(0.156001\pi\) | ||||
−0.882289 | + | 0.470708i | \(0.843999\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.7990 | 0.759815 | ||||||||
\(680\) | 13.8564i | 0.531369i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.87868 | + | 7.13834i | 0.148522 | + | 0.273341i | ||||
\(683\) | 3.46410i | 0.132550i | 0.997801 | + | 0.0662751i | \(0.0211115\pi\) | ||||
−0.997801 | + | 0.0662751i | \(0.978889\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.0000 | −0.725953 | ||||||||
\(686\) | −12.0000 | + | 20.7846i | −0.458162 | + | 0.793560i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11.3137 | + | 19.5959i | −0.431331 | + | 0.747087i | ||||
\(689\) | − | 9.79796i | − | 0.373273i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.5885i | 0.593013i | 0.955031 | + | 0.296506i | \(0.0958216\pi\) | ||||
−0.955031 | + | 0.296506i | \(0.904178\pi\) | |||||||
\(692\) | −16.9706 | + | 9.79796i | −0.645124 | + | 0.372463i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.0000 | − | 31.1769i | 0.683271 | − | 1.18346i | ||||
\(695\) | 19.7990 | 0.751018 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000 | 0.909065 | ||||||||
\(698\) | −6.00000 | − | 3.46410i | −0.227103 | − | 0.131118i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 11.3137 | + | 19.5959i | 0.427618 | + | 0.740656i | ||||
\(701\) | 34.2929i | 1.29522i | 0.761971 | + | 0.647612i | \(0.224232\pi\) | ||||
−0.761971 | + | 0.647612i | \(0.775768\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.48528 | −0.320028 | ||||||||
\(704\) | 22.6274 | + | 13.8564i | 0.852803 | + | 0.522233i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.0208 | − | 20.8207i | 0.452409 | − | 0.783596i | ||||
\(707\) | − | 13.8564i | − | 0.521124i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.0000 | −0.938895 | −0.469447 | − | 0.882960i | \(-0.655547\pi\) | ||||
−0.469447 | + | 0.882960i | \(0.655547\pi\) | |||||||
\(710\) | 14.8492 | + | 8.57321i | 0.557282 | + | 0.321747i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.82843 | −0.106000 | ||||||||
\(713\) | −9.00000 | −0.337053 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.48528 | − | 13.8564i | 0.317332 | − | 0.518200i | ||||
\(716\) | −15.0000 | + | 8.66025i | −0.560576 | + | 0.323649i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.00000 | + | 10.3923i | −0.223918 | + | 0.387837i | ||||
\(719\) | − | 15.5885i | − | 0.581351i | −0.956822 | − | 0.290676i | \(-0.906120\pi\) | ||
0.956822 | − | 0.290676i | \(-0.0938801\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.79796i | 0.364895i | ||||||||
\(722\) | −7.77817 | + | 13.4722i | −0.289474 | + | 0.501383i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.0000 | + | 36.3731i | 0.780459 | + | 1.35179i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 25.9808i | − | 0.963573i | −0.876289 | − | 0.481787i | \(-0.839988\pi\) | ||
0.876289 | − | 0.481787i | \(-0.160012\pi\) | |||||||
\(728\) | 39.1918i | 1.45255i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.00000 | + | 3.46410i | 0.222070 | + | 0.128212i | ||||
\(731\) | − | 27.7128i | − | 1.02500i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.79796i | 0.361896i | 0.983493 | + | 0.180948i | \(0.0579166\pi\) | ||||
−0.983493 | + | 0.180948i | \(0.942083\pi\) | |||||||
\(734\) | 2.12132 | + | 1.22474i | 0.0782994 | + | 0.0452062i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −25.4558 | + | 14.6969i | −0.938315 | + | 0.541736i | ||||
\(737\) | −15.0000 | + | 24.4949i | −0.552532 | + | 0.902281i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.65685 | −0.208091 | −0.104045 | − | 0.994573i | \(-0.533179\pi\) | ||||
−0.104045 | + | 0.994573i | \(0.533179\pi\) | |||||||
\(740\) | −3.00000 | − | 5.19615i | −0.110282 | − | 0.191014i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.00000 | − | 6.92820i | 0.146845 | − | 0.254342i | ||||
\(743\) | 33.9411 | 1.24518 | 0.622590 | − | 0.782549i | \(-0.286081\pi\) | ||||
0.622590 | + | 0.782549i | \(0.286081\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.6969i | 0.538454i | ||||||||
\(746\) | −18.0000 | − | 10.3923i | −0.659027 | − | 0.380489i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −32.4853 | − | 0.840532i | −1.18778 | − | 0.0307329i | ||||
\(749\) | −24.0000 | −0.876941 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 5.19615i | − | 0.189610i | −0.995496 | − | 0.0948051i | \(-0.969777\pi\) | ||
0.995496 | − | 0.0948051i | \(-0.0302228\pi\) | |||||||
\(752\) | 12.0000 | + | 6.92820i | 0.437595 | + | 0.252646i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.65685 | −0.205874 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.0000 | 1.09037 | 0.545184 | − | 0.838316i | \(-0.316460\pi\) | ||||
0.545184 | + | 0.838316i | \(0.316460\pi\) | |||||||
\(758\) | −14.8492 | − | 8.57321i | −0.539349 | − | 0.311393i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.00000 | 0.290191 | ||||||||
\(761\) | − | 44.0908i | − | 1.59829i | −0.601138 | − | 0.799145i | \(-0.705286\pi\) | ||
0.601138 | − | 0.799145i | \(-0.294714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 27.7128i | − | 1.00327i | ||||||
\(764\) | 9.00000 | − | 5.19615i | 0.325609 | − | 0.187990i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 40.3051 | + | 23.2702i | 1.45628 | + | 0.840785i | ||||
\(767\) | −8.48528 | −0.306386 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 4.89898i | − | 0.176662i | −0.996091 | − | 0.0883309i | \(-0.971847\pi\) | ||
0.996091 | − | 0.0883309i | \(-0.0281533\pi\) | |||||||
\(770\) | 11.6569 | − | 6.33386i | 0.420084 | − | 0.228256i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.9706 | + | 9.79796i | −0.610784 | + | 0.352636i | ||||
\(773\) | 10.0000 | 0.359675 | 0.179838 | − | 0.983696i | \(-0.442443\pi\) | ||||
0.179838 | + | 0.983696i | \(0.442443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 6.92820i | − | 0.248868i | ||||||
\(776\) | −19.7990 | −0.710742 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13.4350 | + | 23.2702i | −0.481669 | + | 0.834275i | ||||
\(779\) | − | 13.8564i | − | 0.496457i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.0000 | + | 34.2929i | −0.751439 | + | 1.22709i | ||||
\(782\) | 18.0000 | − | 31.1769i | 0.643679 | − | 1.11488i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.00000 | + | 3.46410i | −0.0714286 | + | 0.123718i | ||||
\(785\) | 11.0000 | 0.392607 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.2843 | −1.00823 | −0.504113 | − | 0.863638i | \(-0.668180\pi\) | ||||
−0.504113 | + | 0.863638i | \(0.668180\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.00000 | + | 13.8564i | −0.284627 | + | 0.492989i | ||||
\(791\) | 14.1421 | 0.502836 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.0000 | 1.70453 | ||||||||
\(794\) | 4.24264 | − | 7.34847i | 0.150566 | − | 0.260787i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.0000 | + | 10.3923i | −0.637993 | + | 0.368345i | ||||
\(797\) | −7.00000 | −0.247953 | −0.123976 | − | 0.992285i | \(-0.539565\pi\) | ||||
−0.123976 | + | 0.992285i | \(0.539565\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.9706 | −0.600375 | ||||||||
\(800\) | −11.3137 | − | 19.5959i | −0.400000 | − | 0.692820i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.07107 | + | 12.2474i | −0.249688 | + | 0.432472i | ||||
\(803\) | −8.48528 | + | 13.8564i | −0.299439 | + | 0.488982i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.6969i | 0.517999i | ||||||||
\(806\) | 6.00000 | − | 10.3923i | 0.211341 | − | 0.366053i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.8564i | 0.487467i | ||||||||
\(809\) | 44.0908i | 1.55015i | 0.631869 | + | 0.775075i | \(0.282288\pi\) | ||||
−0.631869 | + | 0.775075i | \(0.717712\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.5980 | −1.39047 | −0.695237 | − | 0.718781i | \(-0.744700\pi\) | ||||
−0.695237 | + | 0.718781i | \(0.744700\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.3640 | − | 6.71807i | 0.433357 | − | 0.235468i | ||||
\(815\) | − | 17.3205i | − | 0.606711i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0000 | −0.559769 | ||||||||
\(818\) | −36.0000 | − | 20.7846i | −1.25871 | − | 0.726717i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.48528 | − | 4.89898i | 0.296319 | − | 0.171080i | ||||
\(821\) | 48.9898i | 1.70976i | 0.518829 | + | 0.854878i | \(0.326368\pi\) | ||||
−0.518829 | + | 0.854878i | \(0.673632\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.66025i | 0.301877i | 0.988543 | + | 0.150939i | \(0.0482296\pi\) | ||||
−0.988543 | + | 0.150939i | \(0.951770\pi\) | |||||||
\(824\) | − | 9.79796i | − | 0.341328i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | − | 3.46410i | −0.208767 | − | 0.120532i | ||||
\(827\) | −25.4558 | −0.885186 | −0.442593 | − | 0.896723i | \(-0.645941\pi\) | ||||
−0.442593 | + | 0.896723i | \(0.645941\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.0000 | −0.590434 | −0.295217 | − | 0.955430i | \(-0.595392\pi\) | ||||
−0.295217 | + | 0.955430i | \(0.595392\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 39.1918i | − | 1.35873i | ||||||
\(833\) | − | 4.89898i | − | 0.169740i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.7990 | −0.685172 | ||||||||
\(836\) | −0.485281 | + | 18.7554i | −0.0167838 | + | 0.648669i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.7279 | − | 7.34847i | −0.439679 | − | 0.253849i | ||||
\(839\) | 25.9808i | 0.896956i | 0.893794 | + | 0.448478i | \(0.148034\pi\) | ||||
−0.893794 | + | 0.448478i | \(0.851966\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 21.2132 | − | 36.7423i | 0.731055 | − | 1.26622i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.65685 | − | 9.79796i | −0.194717 | − | 0.337260i | ||||
\(845\) | −11.0000 | −0.378412 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.1421 | + | 27.7128i | 0.485930 | + | 0.952224i | ||||
\(848\) | −4.00000 | + | 6.92820i | −0.137361 | + | 0.237915i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.0000 | + | 13.8564i | 0.823193 | + | 0.475271i | ||||
\(851\) | 15.5885i | 0.534365i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 39.1918i | − | 1.34190i | −0.741501 | − | 0.670951i | \(-0.765886\pi\) | ||
0.741501 | − | 0.670951i | \(-0.234114\pi\) | |||||||
\(854\) | 33.9411 | + | 19.5959i | 1.16144 | + | 0.670559i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24.0000 | 0.820303 | ||||||||
\(857\) | 29.3939i | 1.00408i | 0.864846 | + | 0.502038i | \(0.167416\pi\) | ||||
−0.864846 | + | 0.502038i | \(0.832584\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.5885i | 0.531871i | 0.963991 | + | 0.265936i | \(0.0856809\pi\) | ||||
−0.963991 | + | 0.265936i | \(0.914319\pi\) | |||||||
\(860\) | −5.65685 | − | 9.79796i | −0.192897 | − | 0.334108i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.0000 | + | 17.3205i | −0.340601 | + | 0.589939i | ||||
\(863\) | − | 31.1769i | − | 1.06127i | −0.847599 | − | 0.530637i | \(-0.821953\pi\) | ||
0.847599 | − | 0.530637i | \(-0.178047\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 9.79796i | − | 0.333141i | ||||||
\(866\) | −14.8492 | + | 25.7196i | −0.504598 | + | 0.873989i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.48528 | − | 4.89898i | 0.288009 | − | 0.166282i | ||||
\(869\) | −32.0000 | − | 19.5959i | −1.08553 | − | 0.664746i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.4264 | 1.43756 | ||||||||
\(872\) | 27.7128i | 0.938474i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −18.0000 | − | 10.3923i | −0.608859 | − | 0.351525i | ||||
\(875\) | −25.4558 | −0.860565 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.8888i | 1.81969i | 0.414943 | + | 0.909847i | \(0.363801\pi\) | ||||
−0.414943 | + | 0.909847i | \(0.636199\pi\) | |||||||
\(878\) | −16.0000 | + | 27.7128i | −0.539974 | + | 0.935262i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −11.6569 | + | 6.33386i | −0.392952 | + | 0.213514i | ||||
\(881\) | 49.0000 | 1.65085 | 0.825426 | − | 0.564510i | \(-0.190935\pi\) | ||||
0.825426 | + | 0.564510i | \(0.190935\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.2487i | 0.816034i | 0.912974 | + | 0.408017i | \(0.133780\pi\) | ||||
−0.912974 | + | 0.408017i | \(0.866220\pi\) | |||||||
\(884\) | 24.0000 | + | 41.5692i | 0.807207 | + | 1.39812i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.36396 | + | 3.67423i | 0.213801 | + | 0.123438i | ||||
\(887\) | −16.9706 | −0.569816 | −0.284908 | − | 0.958555i | \(-0.591963\pi\) | ||||
−0.284908 | + | 0.958555i | \(0.591963\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.0000 | −1.34156 | ||||||||
\(890\) | 0.707107 | − | 1.22474i | 0.0237023 | − | 0.0410535i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 39.0000 | − | 22.5167i | 1.30582 | − | 0.753914i | ||||
\(893\) | 9.79796i | 0.327876i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 8.66025i | − | 0.289480i | ||||||
\(896\) | 16.0000 | − | 27.7128i | 0.534522 | − | 0.925820i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.2635 | + | 28.1691i | −0.542719 | + | 0.940016i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 9.79796i | − | 0.326417i | ||||||
\(902\) | 10.9706 | + | 20.1903i | 0.365280 | + | 0.672262i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.1421 | −0.470360 | ||||||||
\(905\) | −21.0000 | −0.698064 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 3.46410i | − | 0.115024i | −0.998345 | − | 0.0575118i | \(-0.981683\pi\) | ||
0.998345 | − | 0.0575118i | \(-0.0183167\pi\) | |||||||
\(908\) | −8.48528 | − | 14.6969i | −0.281594 | − | 0.487735i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −16.9706 | − | 9.79796i | −0.562569 | − | 0.324799i | ||||
\(911\) | 24.2487i | 0.803396i | 0.915772 | + | 0.401698i | \(0.131580\pi\) | ||||
−0.915772 | + | 0.401698i | \(0.868420\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 24.0000 | + | 13.8564i | 0.793849 | + | 0.458329i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.00000 | + | 1.73205i | 0.0330409 | + | 0.0572286i | ||||
\(917\) | 8.00000 | 0.264183 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.3137 | −0.373205 | −0.186602 | − | 0.982436i | \(-0.559748\pi\) | ||||
−0.186602 | + | 0.982436i | \(0.559748\pi\) | |||||||
\(920\) | − | 14.6969i | − | 0.484544i | ||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −36.0000 | − | 20.7846i | −1.18560 | − | 0.684505i | ||||
\(923\) | 59.3970 | 1.95508 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0000 | −0.394558 | ||||||||
\(926\) | 44.5477 | + | 25.7196i | 1.46393 | + | 0.845200i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.0000 | 0.721797 | 0.360898 | − | 0.932605i | \(-0.382470\pi\) | ||||
0.360898 | + | 0.932605i | \(0.382470\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.82843 | −0.0926980 | ||||||||
\(932\) | −33.9411 | + | 19.5959i | −1.11178 | + | 0.641886i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 40.3051 | + | 23.2702i | 1.31882 | + | 0.761423i | ||||
\(935\) | 8.48528 | − | 13.8564i | 0.277498 | − | 0.453153i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4.89898i | − | 0.160043i | −0.996793 | − | 0.0800213i | \(-0.974501\pi\) | ||
0.996793 | − | 0.0800213i | \(-0.0254988\pi\) | |||||||
\(938\) | 30.0000 | + | 17.3205i | 0.979535 | + | 0.565535i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.00000 | + | 3.46410i | −0.195698 | + | 0.112987i | ||||
\(941\) | − | 39.1918i | − | 1.27762i | −0.769366 | − | 0.638809i | \(-0.779428\pi\) | ||
0.769366 | − | 0.638809i | \(-0.220572\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.4558 | −0.828956 | ||||||||
\(944\) | 6.00000 | + | 3.46410i | 0.195283 | + | 0.112747i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.3137 | − | 12.6677i | 0.757994 | − | 0.411863i | ||||
\(947\) | − | 43.3013i | − | 1.40710i | −0.710645 | − | 0.703551i | \(-0.751597\pi\) | ||
0.710645 | − | 0.703551i | \(-0.248403\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | 8.00000 | − | 13.8564i | 0.259554 | − | 0.449561i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 39.1918i | 1.27021i | ||||||||
\(953\) | − | 34.2929i | − | 1.11085i | −0.831565 | − | 0.555427i | \(-0.812555\pi\) | ||
0.831565 | − | 0.555427i | \(-0.187445\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.19615i | 0.168144i | ||||||||
\(956\) | 5.65685 | + | 9.79796i | 0.182956 | + | 0.316889i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.0000 | + | 38.1051i | −0.710788 | + | 1.23112i | ||||
\(959\) | −53.7401 | −1.73536 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | −18.0000 | − | 10.3923i | −0.580343 | − | 0.335061i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −50.9117 | + | 29.3939i | −1.63976 | + | 0.946713i | ||||
\(965\) | − | 9.79796i | − | 0.315407i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.2548 | 1.45530 | 0.727649 | − | 0.685950i | \(-0.240613\pi\) | ||||
0.727649 | + | 0.685950i | \(0.240613\pi\) | |||||||
\(968\) | −14.1421 | − | 27.7128i | −0.454545 | − | 0.890724i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.94975 | − | 8.57321i | 0.158927 | − | 0.275269i | ||||
\(971\) | 32.9090i | 1.05610i | 0.849214 | + | 0.528049i | \(0.177076\pi\) | ||||
−0.849214 | + | 0.528049i | \(0.822924\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 56.0000 | 1.79528 | ||||||||
\(974\) | −48.7904 | − | 28.1691i | −1.56334 | − | 0.902597i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −33.9411 | − | 19.5959i | −1.08643 | − | 0.627250i | ||||
\(977\) | −19.0000 | −0.607864 | −0.303932 | − | 0.952694i | \(-0.598300\pi\) | ||||
−0.303932 | + | 0.952694i | \(0.598300\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.82843 | + | 1.73205i | 0.0903969 | + | 0.0553566i | ||||
\(980\) | −1.00000 | − | 1.73205i | −0.0319438 | − | 0.0553283i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 24.0000 | − | 41.5692i | 0.765871 | − | 1.32653i | ||||
\(983\) | − | 1.73205i | − | 0.0552438i | −0.999618 | − | 0.0276219i | \(-0.991207\pi\) | ||
0.999618 | − | 0.0276219i | \(-0.00879345\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 24.0000 | − | 13.8564i | 0.763542 | − | 0.440831i | ||||
\(989\) | 29.3939i | 0.934671i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 51.9615i | − | 1.65061i | −0.564686 | − | 0.825306i | \(-0.691003\pi\) | ||
0.564686 | − | 0.825306i | \(-0.308997\pi\) | |||||||
\(992\) | −8.48528 | + | 4.89898i | −0.269408 | + | 0.155543i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 42.0000 | + | 24.2487i | 1.33216 | + | 0.769122i | ||||
\(995\) | − | 10.3923i | − | 0.329458i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.89898i | 0.155152i | 0.996986 | + | 0.0775761i | \(0.0247181\pi\) | ||||
−0.996986 | + | 0.0775761i | \(0.975282\pi\) | |||||||
\(998\) | −21.2132 | − | 12.2474i | −0.671492 | − | 0.387686i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))