Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3630,2,Mod(1,3630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3630, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3630.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3630.a (trivial) |
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: | yes |
Analytic conductor: | \(28.9856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.52625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 24x^{2} + 19x + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 330) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.77556\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3630.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 5.10899 | 1.93102 | 0.965509 | − | 0.260370i | \(-0.0838447\pi\) | ||||
0.965509 | + | 0.260370i | \(0.0838447\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.33343 | 0.369826 | 0.184913 | − | 0.982755i | \(-0.440800\pi\) | ||||
0.184913 | + | 0.982755i | \(0.440800\pi\) | |||||||
\(14\) | −5.10899 | −1.36544 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.775565 | 0.188102 | 0.0940511 | − | 0.995567i | \(-0.470018\pi\) | ||||
0.0940511 | + | 0.995567i | \(0.470018\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −0.0785371 | −0.0180176 | −0.00900882 | − | 0.999959i | \(-0.502868\pi\) | ||||
−0.00900882 | + | 0.999959i | \(0.502868\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 5.10899 | 1.11487 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.64849 | 1.38631 | 0.693153 | − | 0.720791i | \(-0.256221\pi\) | ||||
0.693153 | + | 0.720791i | \(0.256221\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.33343 | −0.261507 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 5.10899 | 0.965509 | ||||||||
\(29\) | −2.01882 | −0.374886 | −0.187443 | − | 0.982275i | \(-0.560020\pi\) | ||||
−0.187443 | + | 0.982275i | \(0.560020\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 8.49096 | 1.52502 | 0.762511 | − | 0.646976i | \(-0.223967\pi\) | ||||
0.762511 | + | 0.646976i | \(0.223967\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.775565 | −0.133008 | ||||||||
\(35\) | −5.10899 | −0.863577 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.93310 | −0.646597 | −0.323298 | − | 0.946297i | \(-0.604792\pi\) | ||||
−0.323298 | + | 0.946297i | \(0.604792\pi\) | |||||||
\(38\) | 0.0785371 | 0.0127404 | ||||||||
\(39\) | 1.33343 | 0.213519 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −11.8962 | −1.85787 | −0.928936 | − | 0.370239i | \(-0.879276\pi\) | ||||
−0.928936 | + | 0.370239i | \(0.879276\pi\) | |||||||
\(42\) | −5.10899 | −0.788335 | ||||||||
\(43\) | −6.01163 | −0.916765 | −0.458383 | − | 0.888755i | \(-0.651571\pi\) | ||||
−0.458383 | + | 0.888755i | \(0.651571\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −6.64849 | −0.980266 | ||||||||
\(47\) | 6.56950 | 0.958259 | 0.479130 | − | 0.877744i | \(-0.340952\pi\) | ||||
0.479130 | + | 0.877744i | \(0.340952\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 19.1018 | 2.72883 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0.775565 | 0.108601 | ||||||||
\(52\) | 1.33343 | 0.184913 | ||||||||
\(53\) | 10.3451 | 1.42100 | 0.710502 | − | 0.703696i | \(-0.248468\pi\) | ||||
0.710502 | + | 0.703696i | \(0.248468\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.10899 | −0.682718 | ||||||||
\(57\) | −0.0785371 | −0.0104025 | ||||||||
\(58\) | 2.01882 | 0.265084 | ||||||||
\(59\) | −5.32624 | −0.693417 | −0.346709 | − | 0.937973i | \(-0.612701\pi\) | ||||
−0.346709 | + | 0.937973i | \(0.612701\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −3.74585 | −0.479607 | −0.239803 | − | 0.970821i | \(-0.577083\pi\) | ||||
−0.239803 | + | 0.970821i | \(0.577083\pi\) | |||||||
\(62\) | −8.49096 | −1.07835 | ||||||||
\(63\) | 5.10899 | 0.643673 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.33343 | −0.165391 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.588036 | 0.0718400 | 0.0359200 | − | 0.999355i | \(-0.488564\pi\) | ||||
0.0359200 | + | 0.999355i | \(0.488564\pi\) | |||||||
\(68\) | 0.775565 | 0.0940511 | ||||||||
\(69\) | 6.64849 | 0.800384 | ||||||||
\(70\) | 5.10899 | 0.610641 | ||||||||
\(71\) | −2.31506 | −0.274747 | −0.137374 | − | 0.990519i | \(-0.543866\pi\) | ||||
−0.137374 | + | 0.990519i | \(0.543866\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 10.9443 | 1.28093 | 0.640465 | − | 0.767987i | \(-0.278742\pi\) | ||||
0.640465 | + | 0.767987i | \(0.278742\pi\) | |||||||
\(74\) | 3.93310 | 0.457213 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −0.0785371 | −0.00900882 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.33343 | −0.150981 | ||||||||
\(79\) | 12.3267 | 1.38686 | 0.693431 | − | 0.720523i | \(-0.256098\pi\) | ||||
0.693431 | + | 0.720523i | \(0.256098\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.8962 | 1.31371 | ||||||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | 5.10899 | 0.557437 | ||||||||
\(85\) | −0.775565 | −0.0841218 | ||||||||
\(86\) | 6.01163 | 0.648251 | ||||||||
\(87\) | −2.01882 | −0.216440 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.67821 | −1.02589 | −0.512944 | − | 0.858422i | \(-0.671445\pi\) | ||||
−0.512944 | + | 0.858422i | \(0.671445\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 6.81247 | 0.714141 | ||||||||
\(92\) | 6.64849 | 0.693153 | ||||||||
\(93\) | 8.49096 | 0.880471 | ||||||||
\(94\) | −6.56950 | −0.677592 | ||||||||
\(95\) | 0.0785371 | 0.00805773 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −13.4541 | −1.36605 | −0.683026 | − | 0.730394i | \(-0.739336\pi\) | ||||
−0.683026 | + | 0.730394i | \(0.739336\pi\) | |||||||
\(98\) | −19.1018 | −1.92957 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −10.6408 | −1.05880 | −0.529402 | − | 0.848371i | \(-0.677584\pi\) | ||||
−0.529402 | + | 0.848371i | \(0.677584\pi\) | |||||||
\(102\) | −0.775565 | −0.0767924 | ||||||||
\(103\) | 16.7087 | 1.64635 | 0.823177 | − | 0.567785i | \(-0.192200\pi\) | ||||
0.823177 | + | 0.567785i | \(0.192200\pi\) | |||||||
\(104\) | −1.33343 | −0.130753 | ||||||||
\(105\) | −5.10899 | −0.498587 | ||||||||
\(106\) | −10.3451 | −1.00480 | ||||||||
\(107\) | 17.5511 | 1.69673 | 0.848366 | − | 0.529410i | \(-0.177587\pi\) | ||||
0.848366 | + | 0.529410i | \(0.177587\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −8.94427 | −0.856706 | −0.428353 | − | 0.903612i | \(-0.640906\pi\) | ||||
−0.428353 | + | 0.903612i | \(0.640906\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.93310 | −0.373313 | ||||||||
\(112\) | 5.10899 | 0.482754 | ||||||||
\(113\) | −5.72703 | −0.538753 | −0.269377 | − | 0.963035i | \(-0.586818\pi\) | ||||
−0.269377 | + | 0.963035i | \(0.586818\pi\) | |||||||
\(114\) | 0.0785371 | 0.00735567 | ||||||||
\(115\) | −6.64849 | −0.619975 | ||||||||
\(116\) | −2.01882 | −0.187443 | ||||||||
\(117\) | 1.33343 | 0.123275 | ||||||||
\(118\) | 5.32624 | 0.490320 | ||||||||
\(119\) | 3.96236 | 0.363229 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 3.74585 | 0.339133 | ||||||||
\(123\) | −11.8962 | −1.07264 | ||||||||
\(124\) | 8.49096 | 0.762511 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −5.10899 | −0.455145 | ||||||||
\(127\) | −6.96281 | −0.617850 | −0.308925 | − | 0.951086i | \(-0.599969\pi\) | ||||
−0.308925 | + | 0.951086i | \(0.599969\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −6.01163 | −0.529295 | ||||||||
\(130\) | 1.33343 | 0.116949 | ||||||||
\(131\) | −2.19916 | −0.192142 | −0.0960709 | − | 0.995374i | \(-0.530628\pi\) | ||||
−0.0960709 | + | 0.995374i | \(0.530628\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.401245 | −0.0347924 | ||||||||
\(134\) | −0.588036 | −0.0507985 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −0.775565 | −0.0665041 | ||||||||
\(137\) | −2.17590 | −0.185899 | −0.0929497 | − | 0.995671i | \(-0.529630\pi\) | ||||
−0.0929497 | + | 0.995671i | \(0.529630\pi\) | |||||||
\(138\) | −6.64849 | −0.565957 | ||||||||
\(139\) | 10.3074 | 0.874264 | 0.437132 | − | 0.899397i | \(-0.355994\pi\) | ||||
0.437132 | + | 0.899397i | \(0.355994\pi\) | |||||||
\(140\) | −5.10899 | −0.431789 | ||||||||
\(141\) | 6.56950 | 0.553251 | ||||||||
\(142\) | 2.31506 | 0.194276 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.01882 | 0.167654 | ||||||||
\(146\) | −10.9443 | −0.905754 | ||||||||
\(147\) | 19.1018 | 1.57549 | ||||||||
\(148\) | −3.93310 | −0.323298 | ||||||||
\(149\) | −15.2477 | −1.24914 | −0.624570 | − | 0.780969i | \(-0.714726\pi\) | ||||
−0.624570 | + | 0.780969i | \(0.714726\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 6.56921 | 0.534595 | 0.267297 | − | 0.963614i | \(-0.413869\pi\) | ||||
0.267297 | + | 0.963614i | \(0.413869\pi\) | |||||||
\(152\) | 0.0785371 | 0.00637020 | ||||||||
\(153\) | 0.775565 | 0.0627007 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.49096 | −0.682010 | ||||||||
\(156\) | 1.33343 | 0.106760 | ||||||||
\(157\) | −9.30815 | −0.742872 | −0.371436 | − | 0.928459i | \(-0.621134\pi\) | ||||
−0.371436 | + | 0.928459i | \(0.621134\pi\) | |||||||
\(158\) | −12.3267 | −0.980659 | ||||||||
\(159\) | 10.3451 | 0.820417 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 33.9671 | 2.67698 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −18.7018 | −1.46483 | −0.732417 | − | 0.680856i | \(-0.761608\pi\) | ||||
−0.732417 | + | 0.680856i | \(0.761608\pi\) | |||||||
\(164\) | −11.8962 | −0.928936 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.00000 | 0.620920 | ||||||||
\(167\) | −2.37478 | −0.183766 | −0.0918829 | − | 0.995770i | \(-0.529289\pi\) | ||||
−0.0918829 | + | 0.995770i | \(0.529289\pi\) | |||||||
\(168\) | −5.10899 | −0.394167 | ||||||||
\(169\) | −11.2220 | −0.863229 | ||||||||
\(170\) | 0.775565 | 0.0594831 | ||||||||
\(171\) | −0.0785371 | −0.00600588 | ||||||||
\(172\) | −6.01163 | −0.458383 | ||||||||
\(173\) | 2.91427 | 0.221568 | 0.110784 | − | 0.993845i | \(-0.464664\pi\) | ||||
0.110784 | + | 0.993845i | \(0.464664\pi\) | |||||||
\(174\) | 2.01882 | 0.153047 | ||||||||
\(175\) | 5.10899 | 0.386204 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.32624 | −0.400345 | ||||||||
\(178\) | 9.67821 | 0.725412 | ||||||||
\(179\) | 1.56231 | 0.116772 | 0.0583861 | − | 0.998294i | \(-0.481405\pi\) | ||||
0.0583861 | + | 0.998294i | \(0.481405\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 18.4721 | 1.37302 | 0.686512 | − | 0.727119i | \(-0.259141\pi\) | ||||
0.686512 | + | 0.727119i | \(0.259141\pi\) | |||||||
\(182\) | −6.81247 | −0.504974 | ||||||||
\(183\) | −3.74585 | −0.276901 | ||||||||
\(184\) | −6.64849 | −0.490133 | ||||||||
\(185\) | 3.93310 | 0.289167 | ||||||||
\(186\) | −8.49096 | −0.622587 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.56950 | 0.479130 | ||||||||
\(189\) | 5.10899 | 0.371625 | ||||||||
\(190\) | −0.0785371 | −0.00569768 | ||||||||
\(191\) | 20.7278 | 1.49981 | 0.749904 | − | 0.661546i | \(-0.230100\pi\) | ||||
0.749904 | + | 0.661546i | \(0.230100\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 1.37079 | 0.0986716 | 0.0493358 | − | 0.998782i | \(-0.484290\pi\) | ||||
0.0493358 | + | 0.998782i | \(0.484290\pi\) | |||||||
\(194\) | 13.4541 | 0.965945 | ||||||||
\(195\) | −1.33343 | −0.0954887 | ||||||||
\(196\) | 19.1018 | 1.36441 | ||||||||
\(197\) | −5.01135 | −0.357044 | −0.178522 | − | 0.983936i | \(-0.557132\pi\) | ||||
−0.178522 | + | 0.983936i | \(0.557132\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.3086 | 1.65230 | 0.826152 | − | 0.563448i | \(-0.190525\pi\) | ||||
0.826152 | + | 0.563448i | \(0.190525\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0.588036 | 0.0414768 | ||||||||
\(202\) | 10.6408 | 0.748687 | ||||||||
\(203\) | −10.3141 | −0.723911 | ||||||||
\(204\) | 0.775565 | 0.0543004 | ||||||||
\(205\) | 11.8962 | 0.830866 | ||||||||
\(206\) | −16.7087 | −1.16415 | ||||||||
\(207\) | 6.64849 | 0.462102 | ||||||||
\(208\) | 1.33343 | 0.0924566 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 5.10899 | 0.352554 | ||||||||
\(211\) | −20.0842 | −1.38265 | −0.691326 | − | 0.722543i | \(-0.742973\pi\) | ||||
−0.691326 | + | 0.722543i | \(0.742973\pi\) | |||||||
\(212\) | 10.3451 | 0.710502 | ||||||||
\(213\) | −2.31506 | −0.158625 | ||||||||
\(214\) | −17.5511 | −1.19977 | ||||||||
\(215\) | 6.01163 | 0.409990 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 43.3802 | 2.94484 | ||||||||
\(218\) | 8.94427 | 0.605783 | ||||||||
\(219\) | 10.9443 | 0.739545 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.03416 | 0.0695651 | ||||||||
\(222\) | 3.93310 | 0.263972 | ||||||||
\(223\) | 9.10899 | 0.609983 | 0.304992 | − | 0.952355i | \(-0.401346\pi\) | ||||
0.304992 | + | 0.952355i | \(0.401346\pi\) | |||||||
\(224\) | −5.10899 | −0.341359 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 5.72703 | 0.380956 | ||||||||
\(227\) | 20.6901 | 1.37325 | 0.686626 | − | 0.727011i | \(-0.259091\pi\) | ||||
0.686626 | + | 0.727011i | \(0.259091\pi\) | |||||||
\(228\) | −0.0785371 | −0.00520124 | ||||||||
\(229\) | 10.9819 | 0.725705 | 0.362853 | − | 0.931846i | \(-0.381803\pi\) | ||||
0.362853 | + | 0.931846i | \(0.381803\pi\) | |||||||
\(230\) | 6.64849 | 0.438388 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.01882 | 0.132542 | ||||||||
\(233\) | −2.96309 | −0.194119 | −0.0970594 | − | 0.995279i | \(-0.530944\pi\) | ||||
−0.0970594 | + | 0.995279i | \(0.530944\pi\) | |||||||
\(234\) | −1.33343 | −0.0871689 | ||||||||
\(235\) | −6.56950 | −0.428547 | ||||||||
\(236\) | −5.32624 | −0.346709 | ||||||||
\(237\) | 12.3267 | 0.800705 | ||||||||
\(238\) | −3.96236 | −0.256841 | ||||||||
\(239\) | 8.56978 | 0.554333 | 0.277166 | − | 0.960822i | \(-0.410605\pi\) | ||||
0.277166 | + | 0.960822i | \(0.410605\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 7.97000 | 0.513393 | 0.256696 | − | 0.966492i | \(-0.417366\pi\) | ||||
0.256696 | + | 0.966492i | \(0.417366\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −3.74585 | −0.239803 | ||||||||
\(245\) | −19.1018 | −1.22037 | ||||||||
\(246\) | 11.8962 | 0.758473 | ||||||||
\(247\) | −0.104723 | −0.00666339 | ||||||||
\(248\) | −8.49096 | −0.539176 | ||||||||
\(249\) | −8.00000 | −0.506979 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 20.2596 | 1.27878 | 0.639388 | − | 0.768884i | \(-0.279188\pi\) | ||||
0.639388 | + | 0.768884i | \(0.279188\pi\) | |||||||
\(252\) | 5.10899 | 0.321836 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 6.96281 | 0.436886 | ||||||||
\(255\) | −0.775565 | −0.0485678 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.9638 | −1.24531 | −0.622655 | − | 0.782497i | \(-0.713946\pi\) | ||||
−0.622655 | + | 0.782497i | \(0.713946\pi\) | |||||||
\(258\) | 6.01163 | 0.374268 | ||||||||
\(259\) | −20.0942 | −1.24859 | ||||||||
\(260\) | −1.33343 | −0.0826957 | ||||||||
\(261\) | −2.01882 | −0.124962 | ||||||||
\(262\) | 2.19916 | 0.135865 | ||||||||
\(263\) | −0.696114 | −0.0429242 | −0.0214621 | − | 0.999770i | \(-0.506832\pi\) | ||||
−0.0214621 | + | 0.999770i | \(0.506832\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.3451 | −0.635492 | ||||||||
\(266\) | 0.401245 | 0.0246019 | ||||||||
\(267\) | −9.67821 | −0.592297 | ||||||||
\(268\) | 0.588036 | 0.0359200 | ||||||||
\(269\) | 5.92175 | 0.361055 | 0.180528 | − | 0.983570i | \(-0.442219\pi\) | ||||
0.180528 | + | 0.983570i | \(0.442219\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −13.9146 | −0.845249 | −0.422625 | − | 0.906305i | \(-0.638891\pi\) | ||||
−0.422625 | + | 0.906305i | \(0.638891\pi\) | |||||||
\(272\) | 0.775565 | 0.0470255 | ||||||||
\(273\) | 6.81247 | 0.412309 | ||||||||
\(274\) | 2.17590 | 0.131451 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.64849 | 0.400192 | ||||||||
\(277\) | −10.1025 | −0.607003 | −0.303501 | − | 0.952831i | \(-0.598156\pi\) | ||||
−0.303501 | + | 0.952831i | \(0.598156\pi\) | |||||||
\(278\) | −10.3074 | −0.618198 | ||||||||
\(279\) | 8.49096 | 0.508340 | ||||||||
\(280\) | 5.10899 | 0.305321 | ||||||||
\(281\) | 28.9081 | 1.72451 | 0.862256 | − | 0.506472i | \(-0.169051\pi\) | ||||
0.862256 | + | 0.506472i | \(0.169051\pi\) | |||||||
\(282\) | −6.56950 | −0.391208 | ||||||||
\(283\) | −13.1211 | −0.779967 | −0.389984 | − | 0.920822i | \(-0.627519\pi\) | ||||
−0.389984 | + | 0.920822i | \(0.627519\pi\) | |||||||
\(284\) | −2.31506 | −0.137374 | ||||||||
\(285\) | 0.0785371 | 0.00465213 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −60.7775 | −3.58759 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.3985 | −0.964618 | ||||||||
\(290\) | −2.01882 | −0.118549 | ||||||||
\(291\) | −13.4541 | −0.788691 | ||||||||
\(292\) | 10.9443 | 0.640465 | ||||||||
\(293\) | 22.6601 | 1.32382 | 0.661909 | − | 0.749584i | \(-0.269746\pi\) | ||||
0.661909 | + | 0.749584i | \(0.269746\pi\) | |||||||
\(294\) | −19.1018 | −1.11404 | ||||||||
\(295\) | 5.32624 | 0.310106 | ||||||||
\(296\) | 3.93310 | 0.228607 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.2477 | 0.883276 | ||||||||
\(299\) | 8.86528 | 0.512692 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −30.7134 | −1.77029 | ||||||||
\(302\) | −6.56921 | −0.378016 | ||||||||
\(303\) | −10.6408 | −0.611300 | ||||||||
\(304\) | −0.0785371 | −0.00450441 | ||||||||
\(305\) | 3.74585 | 0.214487 | ||||||||
\(306\) | −0.775565 | −0.0443361 | ||||||||
\(307\) | −29.3158 | −1.67314 | −0.836571 | − | 0.547859i | \(-0.815443\pi\) | ||||
−0.836571 | + | 0.547859i | \(0.815443\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.7087 | 0.950522 | ||||||||
\(310\) | 8.49096 | 0.482254 | ||||||||
\(311\) | 11.3570 | 0.643995 | 0.321998 | − | 0.946741i | \(-0.395646\pi\) | ||||
0.321998 | + | 0.946741i | \(0.395646\pi\) | |||||||
\(312\) | −1.33343 | −0.0754905 | ||||||||
\(313\) | −3.17664 | −0.179554 | −0.0897770 | − | 0.995962i | \(-0.528615\pi\) | ||||
−0.0897770 | + | 0.995962i | \(0.528615\pi\) | |||||||
\(314\) | 9.30815 | 0.525290 | ||||||||
\(315\) | −5.10899 | −0.287859 | ||||||||
\(316\) | 12.3267 | 0.693431 | ||||||||
\(317\) | 4.73101 | 0.265720 | 0.132860 | − | 0.991135i | \(-0.457584\pi\) | ||||
0.132860 | + | 0.991135i | \(0.457584\pi\) | |||||||
\(318\) | −10.3451 | −0.580122 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 17.5511 | 0.979609 | ||||||||
\(322\) | −33.9671 | −1.89291 | ||||||||
\(323\) | −0.0609106 | −0.00338916 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.33343 | 0.0739652 | ||||||||
\(326\) | 18.7018 | 1.03579 | ||||||||
\(327\) | −8.94427 | −0.494619 | ||||||||
\(328\) | 11.8962 | 0.656857 | ||||||||
\(329\) | 33.5635 | 1.85042 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.0424 | 1.65128 | 0.825639 | − | 0.564199i | \(-0.190815\pi\) | ||||
0.825639 | + | 0.564199i | \(0.190815\pi\) | |||||||
\(332\) | −8.00000 | −0.439057 | ||||||||
\(333\) | −3.93310 | −0.215532 | ||||||||
\(334\) | 2.37478 | 0.129942 | ||||||||
\(335\) | −0.588036 | −0.0321278 | ||||||||
\(336\) | 5.10899 | 0.278718 | ||||||||
\(337\) | −25.3570 | −1.38128 | −0.690641 | − | 0.723198i | \(-0.742672\pi\) | ||||
−0.690641 | + | 0.723198i | \(0.742672\pi\) | |||||||
\(338\) | 11.2220 | 0.610395 | ||||||||
\(339\) | −5.72703 | −0.311049 | ||||||||
\(340\) | −0.775565 | −0.0420609 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.0785371 | 0.00424680 | ||||||||
\(343\) | 61.8280 | 3.33840 | ||||||||
\(344\) | 6.01163 | 0.324126 | ||||||||
\(345\) | −6.64849 | −0.357943 | ||||||||
\(346\) | −2.91427 | −0.156672 | ||||||||
\(347\) | −3.17664 | −0.170531 | −0.0852654 | − | 0.996358i | \(-0.527174\pi\) | ||||
−0.0852654 | + | 0.996358i | \(0.527174\pi\) | |||||||
\(348\) | −2.01882 | −0.108220 | ||||||||
\(349\) | −6.95865 | −0.372488 | −0.186244 | − | 0.982504i | \(-0.559632\pi\) | ||||
−0.186244 | + | 0.982504i | \(0.559632\pi\) | |||||||
\(350\) | −5.10899 | −0.273087 | ||||||||
\(351\) | 1.33343 | 0.0711731 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.01163 | 0.426416 | 0.213208 | − | 0.977007i | \(-0.431609\pi\) | ||||
0.213208 | + | 0.977007i | \(0.431609\pi\) | |||||||
\(354\) | 5.32624 | 0.283086 | ||||||||
\(355\) | 2.31506 | 0.122871 | ||||||||
\(356\) | −9.67821 | −0.512944 | ||||||||
\(357\) | 3.96236 | 0.209710 | ||||||||
\(358\) | −1.56231 | −0.0825704 | ||||||||
\(359\) | −0.180340 | −0.00951798 | −0.00475899 | − | 0.999989i | \(-0.501515\pi\) | ||||
−0.00475899 | + | 0.999989i | \(0.501515\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −18.9938 | −0.999675 | ||||||||
\(362\) | −18.4721 | −0.970874 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.81247 | 0.357070 | ||||||||
\(365\) | −10.9443 | −0.572849 | ||||||||
\(366\) | 3.74585 | 0.195799 | ||||||||
\(367\) | 30.8705 | 1.61142 | 0.805712 | − | 0.592307i | \(-0.201783\pi\) | ||||
0.805712 | + | 0.592307i | \(0.201783\pi\) | |||||||
\(368\) | 6.64849 | 0.346576 | ||||||||
\(369\) | −11.8962 | −0.619291 | ||||||||
\(370\) | −3.93310 | −0.204472 | ||||||||
\(371\) | 52.8528 | 2.74398 | ||||||||
\(372\) | 8.49096 | 0.440236 | ||||||||
\(373\) | 16.1018 | 0.833720 | 0.416860 | − | 0.908971i | \(-0.363131\pi\) | ||||
0.416860 | + | 0.908971i | \(0.363131\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −6.56950 | −0.338796 | ||||||||
\(377\) | −2.69195 | −0.138643 | ||||||||
\(378\) | −5.10899 | −0.262778 | ||||||||
\(379\) | 32.5487 | 1.67191 | 0.835956 | − | 0.548796i | \(-0.184914\pi\) | ||||
0.835956 | + | 0.548796i | \(0.184914\pi\) | |||||||
\(380\) | 0.0785371 | 0.00402887 | ||||||||
\(381\) | −6.96281 | −0.356716 | ||||||||
\(382\) | −20.7278 | −1.06052 | ||||||||
\(383\) | 2.10825 | 0.107727 | 0.0538634 | − | 0.998548i | \(-0.482846\pi\) | ||||
0.0538634 | + | 0.998548i | \(0.482846\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.37079 | −0.0697714 | ||||||||
\(387\) | −6.01163 | −0.305588 | ||||||||
\(388\) | −13.4541 | −0.683026 | ||||||||
\(389\) | −12.6032 | −0.639008 | −0.319504 | − | 0.947585i | \(-0.603516\pi\) | ||||
−0.319504 | + | 0.947585i | \(0.603516\pi\) | |||||||
\(390\) | 1.33343 | 0.0675207 | ||||||||
\(391\) | 5.15633 | 0.260767 | ||||||||
\(392\) | −19.1018 | −0.964787 | ||||||||
\(393\) | −2.19916 | −0.110933 | ||||||||
\(394\) | 5.01135 | 0.252468 | ||||||||
\(395\) | −12.3267 | −0.620223 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.6341 | −1.53748 | −0.768741 | − | 0.639560i | \(-0.779116\pi\) | ||||
−0.768741 | + | 0.639560i | \(0.779116\pi\) | |||||||
\(398\) | −23.3086 | −1.16836 | ||||||||
\(399\) | −0.401245 | −0.0200874 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −19.9671 | −0.997108 | −0.498554 | − | 0.866859i | \(-0.666136\pi\) | ||||
−0.498554 | + | 0.866859i | \(0.666136\pi\) | |||||||
\(402\) | −0.588036 | −0.0293285 | ||||||||
\(403\) | 11.3221 | 0.563993 | ||||||||
\(404\) | −10.6408 | −0.529402 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 10.3141 | 0.511883 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.775565 | −0.0383962 | ||||||||
\(409\) | −7.13962 | −0.353032 | −0.176516 | − | 0.984298i | \(-0.556483\pi\) | ||||
−0.176516 | + | 0.984298i | \(0.556483\pi\) | |||||||
\(410\) | −11.8962 | −0.587511 | ||||||||
\(411\) | −2.17590 | −0.107329 | ||||||||
\(412\) | 16.7087 | 0.823177 | ||||||||
\(413\) | −27.2117 | −1.33900 | ||||||||
\(414\) | −6.64849 | −0.326755 | ||||||||
\(415\) | 8.00000 | 0.392705 | ||||||||
\(416\) | −1.33343 | −0.0653767 | ||||||||
\(417\) | 10.3074 | 0.504756 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.3691 | −1.09280 | −0.546400 | − | 0.837524i | \(-0.684002\pi\) | ||||
−0.546400 | + | 0.837524i | \(0.684002\pi\) | |||||||
\(420\) | −5.10899 | −0.249293 | ||||||||
\(421\) | −6.06091 | −0.295391 | −0.147695 | − | 0.989033i | \(-0.547186\pi\) | ||||
−0.147695 | + | 0.989033i | \(0.547186\pi\) | |||||||
\(422\) | 20.0842 | 0.977682 | ||||||||
\(423\) | 6.56950 | 0.319420 | ||||||||
\(424\) | −10.3451 | −0.502401 | ||||||||
\(425\) | 0.775565 | 0.0376204 | ||||||||
\(426\) | 2.31506 | 0.112165 | ||||||||
\(427\) | −19.1375 | −0.926129 | ||||||||
\(428\) | 17.5511 | 0.848366 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.01163 | −0.289907 | ||||||||
\(431\) | 37.1623 | 1.79004 | 0.895021 | − | 0.446023i | \(-0.147160\pi\) | ||||
0.895021 | + | 0.446023i | \(0.147160\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 30.6540 | 1.47314 | 0.736568 | − | 0.676364i | \(-0.236445\pi\) | ||||
0.736568 | + | 0.676364i | \(0.236445\pi\) | |||||||
\(434\) | −43.3802 | −2.08232 | ||||||||
\(435\) | 2.01882 | 0.0967951 | ||||||||
\(436\) | −8.94427 | −0.428353 | ||||||||
\(437\) | −0.522153 | −0.0249780 | ||||||||
\(438\) | −10.9443 | −0.522938 | ||||||||
\(439\) | 7.06017 | 0.336964 | 0.168482 | − | 0.985705i | \(-0.446114\pi\) | ||||
0.168482 | + | 0.985705i | \(0.446114\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.1018 | 0.909610 | ||||||||
\(442\) | −1.03416 | −0.0491900 | ||||||||
\(443\) | 14.5925 | 0.693310 | 0.346655 | − | 0.937993i | \(-0.387318\pi\) | ||||
0.346655 | + | 0.937993i | \(0.387318\pi\) | |||||||
\(444\) | −3.93310 | −0.186656 | ||||||||
\(445\) | 9.67821 | 0.458791 | ||||||||
\(446\) | −9.10899 | −0.431323 | ||||||||
\(447\) | −15.2477 | −0.721192 | ||||||||
\(448\) | 5.10899 | 0.241377 | ||||||||
\(449\) | 12.7687 | 0.602590 | 0.301295 | − | 0.953531i | \(-0.402581\pi\) | ||||
0.301295 | + | 0.953531i | \(0.402581\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5.72703 | −0.269377 | ||||||||
\(453\) | 6.56921 | 0.308649 | ||||||||
\(454\) | −20.6901 | −0.971035 | ||||||||
\(455\) | −6.81247 | −0.319374 | ||||||||
\(456\) | 0.0785371 | 0.00367783 | ||||||||
\(457\) | −17.3426 | −0.811252 | −0.405626 | − | 0.914039i | \(-0.632947\pi\) | ||||
−0.405626 | + | 0.914039i | \(0.632947\pi\) | |||||||
\(458\) | −10.9819 | −0.513151 | ||||||||
\(459\) | 0.775565 | 0.0362003 | ||||||||
\(460\) | −6.64849 | −0.309987 | ||||||||
\(461\) | −2.99355 | −0.139424 | −0.0697118 | − | 0.997567i | \(-0.522208\pi\) | ||||
−0.0697118 | + | 0.997567i | \(0.522208\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.2589 | −0.755614 | −0.377807 | − | 0.925884i | \(-0.623322\pi\) | ||||
−0.377807 | + | 0.925884i | \(0.623322\pi\) | |||||||
\(464\) | −2.01882 | −0.0937215 | ||||||||
\(465\) | −8.49096 | −0.393759 | ||||||||
\(466\) | 2.96309 | 0.137263 | ||||||||
\(467\) | −18.5707 | −0.859349 | −0.429675 | − | 0.902984i | \(-0.641372\pi\) | ||||
−0.429675 | + | 0.902984i | \(0.641372\pi\) | |||||||
\(468\) | 1.33343 | 0.0616377 | ||||||||
\(469\) | 3.00427 | 0.138724 | ||||||||
\(470\) | 6.56950 | 0.303028 | ||||||||
\(471\) | −9.30815 | −0.428897 | ||||||||
\(472\) | 5.32624 | 0.245160 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −12.3267 | −0.566184 | ||||||||
\(475\) | −0.0785371 | −0.00360353 | ||||||||
\(476\) | 3.96236 | 0.181614 | ||||||||
\(477\) | 10.3451 | 0.473668 | ||||||||
\(478\) | −8.56978 | −0.391973 | ||||||||
\(479\) | −30.5554 | −1.39611 | −0.698056 | − | 0.716043i | \(-0.745951\pi\) | ||||
−0.698056 | + | 0.716043i | \(0.745951\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −5.24450 | −0.239129 | ||||||||
\(482\) | −7.97000 | −0.363024 | ||||||||
\(483\) | 33.9671 | 1.54556 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.4541 | 0.610917 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −0.508303 | −0.0230334 | −0.0115167 | − | 0.999934i | \(-0.503666\pi\) | ||||
−0.0115167 | + | 0.999934i | \(0.503666\pi\) | |||||||
\(488\) | 3.74585 | 0.169567 | ||||||||
\(489\) | −18.7018 | −0.845723 | ||||||||
\(490\) | 19.1018 | 0.862931 | ||||||||
\(491\) | 39.3943 | 1.77784 | 0.888921 | − | 0.458061i | \(-0.151456\pi\) | ||||
0.888921 | + | 0.458061i | \(0.151456\pi\) | |||||||
\(492\) | −11.8962 | −0.536322 | ||||||||
\(493\) | −1.56573 | −0.0705168 | ||||||||
\(494\) | 0.104723 | 0.00471173 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.49096 | 0.381255 | ||||||||
\(497\) | −11.8276 | −0.530542 | ||||||||
\(498\) | 8.00000 | 0.358489 | ||||||||
\(499\) | 21.4608 | 0.960717 | 0.480358 | − | 0.877072i | \(-0.340507\pi\) | ||||
0.480358 | + | 0.877072i | \(0.340507\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −2.37478 | −0.106097 | ||||||||
\(502\) | −20.2596 | −0.904231 | ||||||||
\(503\) | −23.5514 | −1.05011 | −0.525053 | − | 0.851070i | \(-0.675954\pi\) | ||||
−0.525053 | + | 0.851070i | \(0.675954\pi\) | |||||||
\(504\) | −5.10899 | −0.227573 | ||||||||
\(505\) | 10.6408 | 0.473511 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.2220 | −0.498385 | ||||||||
\(508\) | −6.96281 | −0.308925 | ||||||||
\(509\) | 38.7178 | 1.71614 | 0.858069 | − | 0.513535i | \(-0.171664\pi\) | ||||
0.858069 | + | 0.513535i | \(0.171664\pi\) | |||||||
\(510\) | 0.775565 | 0.0343426 | ||||||||
\(511\) | 55.9142 | 2.47350 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.0785371 | −0.00346750 | ||||||||
\(514\) | 19.9638 | 0.880567 | ||||||||
\(515\) | −16.7087 | −0.736272 | ||||||||
\(516\) | −6.01163 | −0.264647 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 20.0942 | 0.882887 | ||||||||
\(519\) | 2.91427 | 0.127922 | ||||||||
\(520\) | 1.33343 | 0.0584747 | ||||||||
\(521\) | 2.53921 | 0.111245 | 0.0556225 | − | 0.998452i | \(-0.482286\pi\) | ||||
0.0556225 | + | 0.998452i | \(0.482286\pi\) | |||||||
\(522\) | 2.01882 | 0.0883615 | ||||||||
\(523\) | 37.3202 | 1.63190 | 0.815950 | − | 0.578122i | \(-0.196214\pi\) | ||||
0.815950 | + | 0.578122i | \(0.196214\pi\) | |||||||
\(524\) | −2.19916 | −0.0960709 | ||||||||
\(525\) | 5.10899 | 0.222975 | ||||||||
\(526\) | 0.696114 | 0.0303520 | ||||||||
\(527\) | 6.58529 | 0.286860 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.2024 | 0.921844 | ||||||||
\(530\) | 10.3451 | 0.449361 | ||||||||
\(531\) | −5.32624 | −0.231139 | ||||||||
\(532\) | −0.401245 | −0.0173962 | ||||||||
\(533\) | −15.8627 | −0.687090 | ||||||||
\(534\) | 9.67821 | 0.418817 | ||||||||
\(535\) | −17.5511 | −0.758802 | ||||||||
\(536\) | −0.588036 | −0.0253993 | ||||||||
\(537\) | 1.56231 | 0.0674185 | ||||||||
\(538\) | −5.92175 | −0.255305 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −9.23515 | −0.397050 | −0.198525 | − | 0.980096i | \(-0.563615\pi\) | ||||
−0.198525 | + | 0.980096i | \(0.563615\pi\) | |||||||
\(542\) | 13.9146 | 0.597681 | ||||||||
\(543\) | 18.4721 | 0.792715 | ||||||||
\(544\) | −0.775565 | −0.0332521 | ||||||||
\(545\) | 8.94427 | 0.383131 | ||||||||
\(546\) | −6.81247 | −0.291547 | ||||||||
\(547\) | −25.3758 | −1.08499 | −0.542495 | − | 0.840059i | \(-0.682520\pi\) | ||||
−0.542495 | + | 0.840059i | \(0.682520\pi\) | |||||||
\(548\) | −2.17590 | −0.0929497 | ||||||||
\(549\) | −3.74585 | −0.159869 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.158552 | 0.00675456 | ||||||||
\(552\) | −6.64849 | −0.282978 | ||||||||
\(553\) | 62.9770 | 2.67805 | ||||||||
\(554\) | 10.1025 | 0.429216 | ||||||||
\(555\) | 3.93310 | 0.166951 | ||||||||
\(556\) | 10.3074 | 0.437132 | ||||||||
\(557\) | −10.6107 | −0.449589 | −0.224794 | − | 0.974406i | \(-0.572171\pi\) | ||||
−0.224794 | + | 0.974406i | \(0.572171\pi\) | |||||||
\(558\) | −8.49096 | −0.359451 | ||||||||
\(559\) | −8.01608 | −0.339044 | ||||||||
\(560\) | −5.10899 | −0.215894 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.9081 | −1.21941 | ||||||||
\(563\) | −4.64450 | −0.195742 | −0.0978712 | − | 0.995199i | \(-0.531203\pi\) | ||||
−0.0978712 | + | 0.995199i | \(0.531203\pi\) | |||||||
\(564\) | 6.56950 | 0.276626 | ||||||||
\(565\) | 5.72703 | 0.240938 | ||||||||
\(566\) | 13.1211 | 0.551520 | ||||||||
\(567\) | 5.10899 | 0.214558 | ||||||||
\(568\) | 2.31506 | 0.0971378 | ||||||||
\(569\) | −35.1105 | −1.47191 | −0.735954 | − | 0.677032i | \(-0.763266\pi\) | ||||
−0.735954 | + | 0.677032i | \(0.763266\pi\) | |||||||
\(570\) | −0.0785371 | −0.00328956 | ||||||||
\(571\) | 17.7758 | 0.743896 | 0.371948 | − | 0.928254i | \(-0.378690\pi\) | ||||
0.371948 | + | 0.928254i | \(0.378690\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.7278 | 0.865915 | ||||||||
\(574\) | 60.7775 | 2.53681 | ||||||||
\(575\) | 6.64849 | 0.277261 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 3.63439 | 0.151302 | 0.0756509 | − | 0.997134i | \(-0.475897\pi\) | ||||
0.0756509 | + | 0.997134i | \(0.475897\pi\) | |||||||
\(578\) | 16.3985 | 0.682088 | ||||||||
\(579\) | 1.37079 | 0.0569681 | ||||||||
\(580\) | 2.01882 | 0.0838270 | ||||||||
\(581\) | −40.8719 | −1.69565 | ||||||||
\(582\) | 13.4541 | 0.557688 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.9443 | −0.452877 | ||||||||
\(585\) | −1.33343 | −0.0551304 | ||||||||
\(586\) | −22.6601 | −0.936081 | ||||||||
\(587\) | 7.39314 | 0.305148 | 0.152574 | − | 0.988292i | \(-0.451244\pi\) | ||||
0.152574 | + | 0.988292i | \(0.451244\pi\) | |||||||
\(588\) | 19.1018 | 0.787745 | ||||||||
\(589\) | −0.666855 | −0.0274773 | ||||||||
\(590\) | −5.32624 | −0.219278 | ||||||||
\(591\) | −5.01135 | −0.206139 | ||||||||
\(592\) | −3.93310 | −0.161649 | ||||||||
\(593\) | −35.9315 | −1.47553 | −0.737766 | − | 0.675057i | \(-0.764119\pi\) | ||||
−0.737766 | + | 0.675057i | \(0.764119\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.96236 | −0.162441 | ||||||||
\(596\) | −15.2477 | −0.624570 | ||||||||
\(597\) | 23.3086 | 0.953958 | ||||||||
\(598\) | −8.86528 | −0.362528 | ||||||||
\(599\) | −20.5554 | −0.839871 | −0.419935 | − | 0.907554i | \(-0.637947\pi\) | ||||
−0.419935 | + | 0.907554i | \(0.637947\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −5.12136 | −0.208905 | −0.104452 | − | 0.994530i | \(-0.533309\pi\) | ||||
−0.104452 | + | 0.994530i | \(0.533309\pi\) | |||||||
\(602\) | 30.7134 | 1.25178 | ||||||||
\(603\) | 0.588036 | 0.0239467 | ||||||||
\(604\) | 6.56921 | 0.267297 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.6408 | 0.432255 | ||||||||
\(607\) | −37.3946 | −1.51780 | −0.758900 | − | 0.651207i | \(-0.774263\pi\) | ||||
−0.758900 | + | 0.651207i | \(0.774263\pi\) | |||||||
\(608\) | 0.0785371 | 0.00318510 | ||||||||
\(609\) | −10.3141 | −0.417950 | ||||||||
\(610\) | −3.74585 | −0.151665 | ||||||||
\(611\) | 8.75995 | 0.354389 | ||||||||
\(612\) | 0.775565 | 0.0313504 | ||||||||
\(613\) | −8.39685 | −0.339145 | −0.169573 | − | 0.985518i | \(-0.554239\pi\) | ||||
−0.169573 | + | 0.985518i | \(0.554239\pi\) | |||||||
\(614\) | 29.3158 | 1.18309 | ||||||||
\(615\) | 11.8962 | 0.479701 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.9029 | −1.04281 | −0.521406 | − | 0.853309i | \(-0.674592\pi\) | ||||
−0.521406 | + | 0.853309i | \(0.674592\pi\) | |||||||
\(618\) | −16.7087 | −0.672121 | ||||||||
\(619\) | 25.1441 | 1.01063 | 0.505313 | − | 0.862936i | \(-0.331377\pi\) | ||||
0.505313 | + | 0.862936i | \(0.331377\pi\) | |||||||
\(620\) | −8.49096 | −0.341005 | ||||||||
\(621\) | 6.64849 | 0.266795 | ||||||||
\(622\) | −11.3570 | −0.455373 | ||||||||
\(623\) | −49.4459 | −1.98101 | ||||||||
\(624\) | 1.33343 | 0.0533798 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.17664 | 0.126964 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.30815 | −0.371436 | ||||||||
\(629\) | −3.05037 | −0.121626 | ||||||||
\(630\) | 5.10899 | 0.203547 | ||||||||
\(631\) | −42.0436 | −1.67373 | −0.836864 | − | 0.547411i | \(-0.815613\pi\) | ||||
−0.836864 | + | 0.547411i | \(0.815613\pi\) | |||||||
\(632\) | −12.3267 | −0.490330 | ||||||||
\(633\) | −20.0842 | −0.798274 | ||||||||
\(634\) | −4.73101 | −0.187893 | ||||||||
\(635\) | 6.96281 | 0.276311 | ||||||||
\(636\) | 10.3451 | 0.410208 | ||||||||
\(637\) | 25.4709 | 1.00919 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.31506 | −0.0915824 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −2.11562 | −0.0835619 | −0.0417809 | − | 0.999127i | \(-0.513303\pi\) | ||||
−0.0417809 | + | 0.999127i | \(0.513303\pi\) | |||||||
\(642\) | −17.5511 | −0.692688 | ||||||||
\(643\) | −39.4827 | −1.55704 | −0.778522 | − | 0.627617i | \(-0.784030\pi\) | ||||
−0.778522 | + | 0.627617i | \(0.784030\pi\) | |||||||
\(644\) | 33.9671 | 1.33849 | ||||||||
\(645\) | 6.01163 | 0.236708 | ||||||||
\(646\) | 0.0609106 | 0.00239649 | ||||||||
\(647\) | −16.1454 | −0.634743 | −0.317371 | − | 0.948301i | \(-0.602800\pi\) | ||||
−0.317371 | + | 0.948301i | \(0.602800\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.33343 | −0.0523013 | ||||||||
\(651\) | 43.3802 | 1.70021 | ||||||||
\(652\) | −18.7018 | −0.732417 | ||||||||
\(653\) | −1.29134 | −0.0505340 | −0.0252670 | − | 0.999681i | \(-0.508044\pi\) | ||||
−0.0252670 | + | 0.999681i | \(0.508044\pi\) | |||||||
\(654\) | 8.94427 | 0.349749 | ||||||||
\(655\) | 2.19916 | 0.0859284 | ||||||||
\(656\) | −11.8962 | −0.464468 | ||||||||
\(657\) | 10.9443 | 0.426977 | ||||||||
\(658\) | −33.5635 | −1.30844 | ||||||||
\(659\) | −23.7015 | −0.923278 | −0.461639 | − | 0.887068i | \(-0.652738\pi\) | ||||
−0.461639 | + | 0.887068i | \(0.652738\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0796 | −0.664318 | −0.332159 | − | 0.943223i | \(-0.607777\pi\) | ||||
−0.332159 | + | 0.943223i | \(0.607777\pi\) | |||||||
\(662\) | −30.0424 | −1.16763 | ||||||||
\(663\) | 1.03416 | 0.0401634 | ||||||||
\(664\) | 8.00000 | 0.310460 | ||||||||
\(665\) | 0.401245 | 0.0155596 | ||||||||
\(666\) | 3.93310 | 0.152404 | ||||||||
\(667\) | −13.4221 | −0.519707 | ||||||||
\(668\) | −2.37478 | −0.0918829 | ||||||||
\(669\) | 9.10899 | 0.352174 | ||||||||
\(670\) | 0.588036 | 0.0227178 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −5.10899 | −0.197084 | ||||||||
\(673\) | −8.51069 | −0.328063 | −0.164032 | − | 0.986455i | \(-0.552450\pi\) | ||||
−0.164032 | + | 0.986455i | \(0.552450\pi\) | |||||||
\(674\) | 25.3570 | 0.976714 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −11.2220 | −0.431614 | ||||||||
\(677\) | 22.7125 | 0.872911 | 0.436456 | − | 0.899726i | \(-0.356234\pi\) | ||||
0.436456 | + | 0.899726i | \(0.356234\pi\) | |||||||
\(678\) | 5.72703 | 0.219945 | ||||||||
\(679\) | −68.7367 | −2.63787 | ||||||||
\(680\) | 0.775565 | 0.0297416 | ||||||||
\(681\) | 20.6901 | 0.792847 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.0419 | −0.422507 | −0.211254 | − | 0.977431i | \(-0.567755\pi\) | ||||
−0.211254 | + | 0.977431i | \(0.567755\pi\) | |||||||
\(684\) | −0.0785371 | −0.00300294 | ||||||||
\(685\) | 2.17590 | 0.0831367 | ||||||||
\(686\) | −61.8280 | −2.36060 | ||||||||
\(687\) | 10.9819 | 0.418986 | ||||||||
\(688\) | −6.01163 | −0.229191 | ||||||||
\(689\) | 13.7944 | 0.525524 | ||||||||
\(690\) | 6.64849 | 0.253104 | ||||||||
\(691\) | 9.49934 | 0.361372 | 0.180686 | − | 0.983541i | \(-0.442168\pi\) | ||||
0.180686 | + | 0.983541i | \(0.442168\pi\) | |||||||
\(692\) | 2.91427 | 0.110784 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.17664 | 0.120583 | ||||||||
\(695\) | −10.3074 | −0.390983 | ||||||||
\(696\) | 2.01882 | 0.0765233 | ||||||||
\(697\) | −9.22627 | −0.349470 | ||||||||
\(698\) | 6.95865 | 0.263389 | ||||||||
\(699\) | −2.96309 | −0.112075 | ||||||||
\(700\) | 5.10899 | 0.193102 | ||||||||
\(701\) | 25.7924 | 0.974165 | 0.487082 | − | 0.873356i | \(-0.338061\pi\) | ||||
0.487082 | + | 0.873356i | \(0.338061\pi\) | |||||||
\(702\) | −1.33343 | −0.0503270 | ||||||||
\(703\) | 0.308894 | 0.0116501 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.56950 | −0.247422 | ||||||||
\(706\) | −8.01163 | −0.301522 | ||||||||
\(707\) | −54.3640 | −2.04457 | ||||||||
\(708\) | −5.32624 | −0.200172 | ||||||||
\(709\) | −13.7924 | −0.517984 | −0.258992 | − | 0.965880i | \(-0.583390\pi\) | ||||
−0.258992 | + | 0.965880i | \(0.583390\pi\) | |||||||
\(710\) | −2.31506 | −0.0868827 | ||||||||
\(711\) | 12.3267 | 0.462287 | ||||||||
\(712\) | 9.67821 | 0.362706 | ||||||||
\(713\) | 56.4520 | 2.11415 | ||||||||
\(714\) | −3.96236 | −0.148287 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.56231 | 0.0583861 | ||||||||
\(717\) | 8.56978 | 0.320044 | ||||||||
\(718\) | 0.180340 | 0.00673022 | ||||||||
\(719\) | −19.4035 | −0.723629 | −0.361814 | − | 0.932250i | \(-0.617843\pi\) | ||||
−0.361814 | + | 0.932250i | \(0.617843\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 85.3644 | 3.17914 | ||||||||
\(722\) | 18.9938 | 0.706877 | ||||||||
\(723\) | 7.97000 | 0.296408 | ||||||||
\(724\) | 18.4721 | 0.686512 | ||||||||
\(725\) | −2.01882 | −0.0749772 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.37752 | −0.0510895 | −0.0255447 | − | 0.999674i | \(-0.508132\pi\) | ||||
−0.0255447 | + | 0.999674i | \(0.508132\pi\) | |||||||
\(728\) | −6.81247 | −0.252487 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 10.9443 | 0.405066 | ||||||||
\(731\) | −4.66241 | −0.172446 | ||||||||
\(732\) | −3.74585 | −0.138451 | ||||||||
\(733\) | 21.8778 | 0.808076 | 0.404038 | − | 0.914742i | \(-0.367606\pi\) | ||||
0.404038 | + | 0.914742i | \(0.367606\pi\) | |||||||
\(734\) | −30.8705 | −1.13945 | ||||||||
\(735\) | −19.1018 | −0.704581 | ||||||||
\(736\) | −6.64849 | −0.245067 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 11.8962 | 0.437905 | ||||||||
\(739\) | 0.525400 | 0.0193272 | 0.00966358 | − | 0.999953i | \(-0.496924\pi\) | ||||
0.00966358 | + | 0.999953i | \(0.496924\pi\) | |||||||
\(740\) | 3.93310 | 0.144583 | ||||||||
\(741\) | −0.104723 | −0.00384711 | ||||||||
\(742\) | −52.8528 | −1.94029 | ||||||||
\(743\) | 47.8868 | 1.75680 | 0.878399 | − | 0.477929i | \(-0.158612\pi\) | ||||
0.878399 | + | 0.477929i | \(0.158612\pi\) | |||||||
\(744\) | −8.49096 | −0.311294 | ||||||||
\(745\) | 15.2477 | 0.558633 | ||||||||
\(746\) | −16.1018 | −0.589529 | ||||||||
\(747\) | −8.00000 | −0.292705 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 89.6686 | 3.27642 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 36.1543 | 1.31929 | 0.659645 | − | 0.751577i | \(-0.270707\pi\) | ||||
0.659645 | + | 0.751577i | \(0.270707\pi\) | |||||||
\(752\) | 6.56950 | 0.239565 | ||||||||
\(753\) | 20.2596 | 0.738301 | ||||||||
\(754\) | 2.69195 | 0.0980352 | ||||||||
\(755\) | −6.56921 | −0.239078 | ||||||||
\(756\) | 5.10899 | 0.185812 | ||||||||
\(757\) | −43.6114 | −1.58508 | −0.792542 | − | 0.609818i | \(-0.791243\pi\) | ||||
−0.792542 | + | 0.609818i | \(0.791243\pi\) | |||||||
\(758\) | −32.5487 | −1.18222 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.0785371 | −0.00284884 | ||||||||
\(761\) | −1.10226 | −0.0399569 | −0.0199784 | − | 0.999800i | \(-0.506360\pi\) | ||||
−0.0199784 | + | 0.999800i | \(0.506360\pi\) | |||||||
\(762\) | 6.96281 | 0.252236 | ||||||||
\(763\) | −45.6962 | −1.65431 | ||||||||
\(764\) | 20.7278 | 0.749904 | ||||||||
\(765\) | −0.775565 | −0.0280406 | ||||||||
\(766\) | −2.10825 | −0.0761743 | ||||||||
\(767\) | −7.10215 | −0.256444 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −26.9983 | −0.973583 | −0.486791 | − | 0.873518i | \(-0.661833\pi\) | ||||
−0.486791 | + | 0.873518i | \(0.661833\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.9638 | −0.718980 | ||||||||
\(772\) | 1.37079 | 0.0493358 | ||||||||
\(773\) | −23.5077 | −0.845512 | −0.422756 | − | 0.906244i | \(-0.638937\pi\) | ||||
−0.422756 | + | 0.906244i | \(0.638937\pi\) | |||||||
\(774\) | 6.01163 | 0.216084 | ||||||||
\(775\) | 8.49096 | 0.305004 | ||||||||
\(776\) | 13.4541 | 0.482972 | ||||||||
\(777\) | −20.0942 | −0.720874 | ||||||||
\(778\) | 12.6032 | 0.451847 | ||||||||
\(779\) | 0.934292 | 0.0334745 | ||||||||
\(780\) | −1.33343 | −0.0477444 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.15633 | −0.184390 | ||||||||
\(783\) | −2.01882 | −0.0721468 | ||||||||
\(784\) | 19.1018 | 0.682207 | ||||||||
\(785\) | 9.30815 | 0.332222 | ||||||||
\(786\) | 2.19916 | 0.0784415 | ||||||||
\(787\) | −32.3634 | −1.15363 | −0.576816 | − | 0.816874i | \(-0.695705\pi\) | ||||
−0.576816 | + | 0.816874i | \(0.695705\pi\) | |||||||
\(788\) | −5.01135 | −0.178522 | ||||||||
\(789\) | −0.696114 | −0.0247823 | ||||||||
\(790\) | 12.3267 | 0.438564 | ||||||||
\(791\) | −29.2593 | −1.04034 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.99482 | −0.177371 | ||||||||
\(794\) | 30.6341 | 1.08716 | ||||||||
\(795\) | −10.3451 | −0.366901 | ||||||||
\(796\) | 23.3086 | 0.826152 | ||||||||
\(797\) | −40.4031 | −1.43115 | −0.715575 | − | 0.698536i | \(-0.753835\pi\) | ||||
−0.715575 | + | 0.698536i | \(0.753835\pi\) | |||||||
\(798\) | 0.401245 | 0.0142039 | ||||||||
\(799\) | 5.09507 | 0.180251 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −9.67821 | −0.341963 | ||||||||
\(802\) | 19.9671 | 0.705062 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.588036 | 0.0207384 | ||||||||
\(805\) | −33.9671 | −1.19718 | ||||||||
\(806\) | −11.3221 | −0.398803 | ||||||||
\(807\) | 5.92175 | 0.208455 | ||||||||
\(808\) | 10.6408 | 0.374344 | ||||||||
\(809\) | 12.2365 | 0.430213 | 0.215107 | − | 0.976591i | \(-0.430990\pi\) | ||||
0.215107 | + | 0.976591i | \(0.430990\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −15.1684 | −0.532635 | −0.266318 | − | 0.963885i | \(-0.585807\pi\) | ||||
−0.266318 | + | 0.963885i | \(0.585807\pi\) | |||||||
\(812\) | −10.3141 | −0.361956 | ||||||||
\(813\) | −13.9146 | −0.488005 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.7018 | 0.655094 | ||||||||
\(816\) | 0.775565 | 0.0271502 | ||||||||
\(817\) | 0.472136 | 0.0165179 | ||||||||
\(818\) | 7.13962 | 0.249631 | ||||||||
\(819\) | 6.81247 | 0.238047 | ||||||||
\(820\) | 11.8962 | 0.415433 | ||||||||
\(821\) | −14.4730 | −0.505113 | −0.252556 | − | 0.967582i | \(-0.581271\pi\) | ||||
−0.252556 | + | 0.967582i | \(0.581271\pi\) | |||||||
\(822\) | 2.17590 | 0.0758931 | ||||||||
\(823\) | 3.54640 | 0.123620 | 0.0618099 | − | 0.998088i | \(-0.480313\pi\) | ||||
0.0618099 | + | 0.998088i | \(0.480313\pi\) | |||||||
\(824\) | −16.7087 | −0.582074 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 27.2117 | 0.946816 | ||||||||
\(827\) | −37.2217 | −1.29432 | −0.647162 | − | 0.762352i | \(-0.724044\pi\) | ||||
−0.647162 | + | 0.762352i | \(0.724044\pi\) | |||||||
\(828\) | 6.64849 | 0.231051 | ||||||||
\(829\) | −40.8705 | −1.41949 | −0.709745 | − | 0.704459i | \(-0.751190\pi\) | ||||
−0.709745 | + | 0.704459i | \(0.751190\pi\) | |||||||
\(830\) | −8.00000 | −0.277684 | ||||||||
\(831\) | −10.1025 | −0.350453 | ||||||||
\(832\) | 1.33343 | 0.0462283 | ||||||||
\(833\) | 14.8147 | 0.513299 | ||||||||
\(834\) | −10.3074 | −0.356917 | ||||||||
\(835\) | 2.37478 | 0.0821825 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.49096 | 0.293490 | ||||||||
\(838\) | 22.3691 | 0.772727 | ||||||||
\(839\) | −16.4136 | −0.566661 | −0.283330 | − | 0.959022i | \(-0.591439\pi\) | ||||
−0.283330 | + | 0.959022i | \(0.591439\pi\) | |||||||
\(840\) | 5.10899 | 0.176277 | ||||||||
\(841\) | −24.9244 | −0.859461 | ||||||||
\(842\) | 6.06091 | 0.208873 | ||||||||
\(843\) | 28.9081 | 0.995648 | ||||||||
\(844\) | −20.0842 | −0.691326 | ||||||||
\(845\) | 11.2220 | 0.386048 | ||||||||
\(846\) | −6.56950 | −0.225864 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.3451 | 0.355251 | ||||||||
\(849\) | −13.1211 | −0.450314 | ||||||||
\(850\) | −0.775565 | −0.0266017 | ||||||||
\(851\) | −26.1491 | −0.896381 | ||||||||
\(852\) | −2.31506 | −0.0793127 | ||||||||
\(853\) | 18.1880 | 0.622745 | 0.311372 | − | 0.950288i | \(-0.399211\pi\) | ||||
0.311372 | + | 0.950288i | \(0.399211\pi\) | |||||||
\(854\) | 19.1375 | 0.654872 | ||||||||
\(855\) | 0.0785371 | 0.00268591 | ||||||||
\(856\) | −17.5511 | −0.599885 | ||||||||
\(857\) | 48.5679 | 1.65905 | 0.829525 | − | 0.558470i | \(-0.188611\pi\) | ||||
0.829525 | + | 0.558470i | \(0.188611\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.1564 | −0.994805 | −0.497402 | − | 0.867520i | \(-0.665713\pi\) | ||||
−0.497402 | + | 0.867520i | \(0.665713\pi\) | |||||||
\(860\) | 6.01163 | 0.204995 | ||||||||
\(861\) | −60.7775 | −2.07129 | ||||||||
\(862\) | −37.1623 | −1.26575 | ||||||||
\(863\) | −29.7157 | −1.01153 | −0.505767 | − | 0.862670i | \(-0.668790\pi\) | ||||
−0.505767 | + | 0.862670i | \(0.668790\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −2.91427 | −0.0990883 | ||||||||
\(866\) | −30.6540 | −1.04166 | ||||||||
\(867\) | −16.3985 | −0.556922 | ||||||||
\(868\) | 43.3802 | 1.47242 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.01882 | −0.0684445 | ||||||||
\(871\) | 0.784103 | 0.0265683 | ||||||||
\(872\) | 8.94427 | 0.302891 | ||||||||
\(873\) | −13.4541 | −0.455351 | ||||||||
\(874\) | 0.522153 | 0.0176621 | ||||||||
\(875\) | −5.10899 | −0.172715 | ||||||||
\(876\) | 10.9443 | 0.369773 | ||||||||
\(877\) | 26.7194 | 0.902249 | 0.451125 | − | 0.892461i | \(-0.351023\pi\) | ||||
0.451125 | + | 0.892461i | \(0.351023\pi\) | |||||||
\(878\) | −7.06017 | −0.238269 | ||||||||
\(879\) | 22.6601 | 0.764307 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.72012 | 0.0916431 | 0.0458216 | − | 0.998950i | \(-0.485409\pi\) | ||||
0.0458216 | + | 0.998950i | \(0.485409\pi\) | |||||||
\(882\) | −19.1018 | −0.643191 | ||||||||
\(883\) | 34.7250 | 1.16859 | 0.584295 | − | 0.811541i | \(-0.301371\pi\) | ||||
0.584295 | + | 0.811541i | \(0.301371\pi\) | |||||||
\(884\) | 1.03416 | 0.0347825 | ||||||||
\(885\) | 5.32624 | 0.179040 | ||||||||
\(886\) | −14.5925 | −0.490244 | ||||||||
\(887\) | −37.2657 | −1.25126 | −0.625630 | − | 0.780120i | \(-0.715158\pi\) | ||||
−0.625630 | + | 0.780120i | \(0.715158\pi\) | |||||||
\(888\) | 3.93310 | 0.131986 | ||||||||
\(889\) | −35.5730 | −1.19308 | ||||||||
\(890\) | −9.67821 | −0.324414 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.10899 | 0.304992 | ||||||||
\(893\) | −0.515949 | −0.0172656 | ||||||||
\(894\) | 15.2477 | 0.509959 | ||||||||
\(895\) | −1.56231 | −0.0522221 | ||||||||
\(896\) | −5.10899 | −0.170679 | ||||||||
\(897\) | 8.86528 | 0.296003 | ||||||||
\(898\) | −12.7687 | −0.426096 | ||||||||
\(899\) | −17.1417 | −0.571709 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 8.02327 | 0.267294 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.7134 | −1.02208 | ||||||||
\(904\) | 5.72703 | 0.190478 | ||||||||
\(905\) | −18.4721 | −0.614035 | ||||||||
\(906\) | −6.56921 | −0.218247 | ||||||||
\(907\) | −39.7936 | −1.32133 | −0.660663 | − | 0.750682i | \(-0.729725\pi\) | ||||
−0.660663 | + | 0.750682i | \(0.729725\pi\) | |||||||
\(908\) | 20.6901 | 0.686626 | ||||||||
\(909\) | −10.6408 | −0.352934 | ||||||||
\(910\) | 6.81247 | 0.225831 | ||||||||
\(911\) | −12.8234 | −0.424857 | −0.212429 | − | 0.977177i | \(-0.568137\pi\) | ||||
−0.212429 | + | 0.977177i | \(0.568137\pi\) | |||||||
\(912\) | −0.0785371 | −0.00260062 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 17.3426 | 0.573642 | ||||||||
\(915\) | 3.74585 | 0.123834 | ||||||||
\(916\) | 10.9819 | 0.362853 | ||||||||
\(917\) | −11.2355 | −0.371029 | ||||||||
\(918\) | −0.775565 | −0.0255975 | ||||||||
\(919\) | −37.1139 | −1.22427 | −0.612137 | − | 0.790752i | \(-0.709690\pi\) | ||||
−0.612137 | + | 0.790752i | \(0.709690\pi\) | |||||||
\(920\) | 6.64849 | 0.219194 | ||||||||
\(921\) | −29.3158 | −0.965988 | ||||||||
\(922\) | 2.99355 | 0.0985873 | ||||||||
\(923\) | −3.08697 | −0.101609 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.93310 | −0.129319 | ||||||||
\(926\) | 16.2589 | 0.534300 | ||||||||
\(927\) | 16.7087 | 0.548784 | ||||||||
\(928\) | 2.01882 | 0.0662711 | ||||||||
\(929\) | 9.97000 | 0.327105 | 0.163553 | − | 0.986535i | \(-0.447705\pi\) | ||||
0.163553 | + | 0.986535i | \(0.447705\pi\) | |||||||
\(930\) | 8.49096 | 0.278429 | ||||||||
\(931\) | −1.50020 | −0.0491670 | ||||||||
\(932\) | −2.96309 | −0.0970594 | ||||||||
\(933\) | 11.3570 | 0.371811 | ||||||||
\(934\) | 18.5707 | 0.607652 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.33343 | −0.0435844 | ||||||||
\(937\) | 11.9767 | 0.391263 | 0.195631 | − | 0.980677i | \(-0.437324\pi\) | ||||
0.195631 | + | 0.980677i | \(0.437324\pi\) | |||||||
\(938\) | −3.00427 | −0.0980929 | ||||||||
\(939\) | −3.17664 | −0.103666 | ||||||||
\(940\) | −6.56950 | −0.214273 | ||||||||
\(941\) | 5.50996 | 0.179619 | 0.0898097 | − | 0.995959i | \(-0.471374\pi\) | ||||
0.0898097 | + | 0.995959i | \(0.471374\pi\) | |||||||
\(942\) | 9.30815 | 0.303276 | ||||||||
\(943\) | −79.0917 | −2.57558 | ||||||||
\(944\) | −5.32624 | −0.173354 | ||||||||
\(945\) | −5.10899 | −0.166196 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.3946 | −0.890206 | −0.445103 | − | 0.895479i | \(-0.646833\pi\) | ||||
−0.445103 | + | 0.895479i | \(0.646833\pi\) | |||||||
\(948\) | 12.3267 | 0.400352 | ||||||||
\(949\) | 14.5934 | 0.473722 | ||||||||
\(950\) | 0.0785371 | 0.00254808 | ||||||||
\(951\) | 4.73101 | 0.153414 | ||||||||
\(952\) | −3.96236 | −0.128421 | ||||||||
\(953\) | 7.98985 | 0.258816 | 0.129408 | − | 0.991591i | \(-0.458692\pi\) | ||||
0.129408 | + | 0.991591i | \(0.458692\pi\) | |||||||
\(954\) | −10.3451 | −0.334934 | ||||||||
\(955\) | −20.7278 | −0.670735 | ||||||||
\(956\) | 8.56978 | 0.277166 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.5554 | 0.987200 | ||||||||
\(959\) | −11.1166 | −0.358975 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 41.0964 | 1.32569 | ||||||||
\(962\) | 5.24450 | 0.169089 | ||||||||
\(963\) | 17.5511 | 0.565577 | ||||||||
\(964\) | 7.97000 | 0.256696 | ||||||||
\(965\) | −1.37079 | −0.0441273 | ||||||||
\(966\) | −33.9671 | −1.09287 | ||||||||
\(967\) | −19.0966 | −0.614106 | −0.307053 | − | 0.951692i | \(-0.599343\pi\) | ||||
−0.307053 | + | 0.951692i | \(0.599343\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.0609106 | −0.00195673 | ||||||||
\(970\) | −13.4541 | −0.431984 | ||||||||
\(971\) | 0.149777 | 0.00480656 | 0.00240328 | − | 0.999997i | \(-0.499235\pi\) | ||||
0.00240328 | + | 0.999997i | \(0.499235\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 52.6605 | 1.68822 | ||||||||
\(974\) | 0.508303 | 0.0162871 | ||||||||
\(975\) | 1.33343 | 0.0427039 | ||||||||
\(976\) | −3.74585 | −0.119902 | ||||||||
\(977\) | −19.1384 | −0.612292 | −0.306146 | − | 0.951984i | \(-0.599040\pi\) | ||||
−0.306146 | + | 0.951984i | \(0.599040\pi\) | |||||||
\(978\) | 18.7018 | 0.598016 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −19.1018 | −0.610185 | ||||||||
\(981\) | −8.94427 | −0.285569 | ||||||||
\(982\) | −39.3943 | −1.25712 | ||||||||
\(983\) | 8.58575 | 0.273843 | 0.136921 | − | 0.990582i | \(-0.456279\pi\) | ||||
0.136921 | + | 0.990582i | \(0.456279\pi\) | |||||||
\(984\) | 11.8962 | 0.379237 | ||||||||
\(985\) | 5.01135 | 0.159675 | ||||||||
\(986\) | 1.56573 | 0.0498629 | ||||||||
\(987\) | 33.5635 | 1.06834 | ||||||||
\(988\) | −0.104723 | −0.00333170 | ||||||||
\(989\) | −39.9683 | −1.27092 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.3086 | −0.359230 | −0.179615 | − | 0.983737i | \(-0.557485\pi\) | ||||
−0.179615 | + | 0.983737i | \(0.557485\pi\) | |||||||
\(992\) | −8.49096 | −0.269588 | ||||||||
\(993\) | 30.0424 | 0.953366 | ||||||||
\(994\) | 11.8276 | 0.375150 | ||||||||
\(995\) | −23.3086 | −0.738933 | ||||||||
\(996\) | −8.00000 | −0.253490 | ||||||||
\(997\) | −37.0321 | −1.17282 | −0.586409 | − | 0.810015i | \(-0.699459\pi\) | ||||
−0.586409 | + | 0.810015i | \(0.699459\pi\) | |||||||
\(998\) | −21.4608 | −0.679329 | ||||||||
\(999\) | −3.93310 | −0.124438 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3630.2.a.bq.1.4 | 4 | ||
11.5 | even | 5 | 330.2.m.f.91.2 | ✓ | 8 | ||
11.9 | even | 5 | 330.2.m.f.301.2 | yes | 8 | ||
11.10 | odd | 2 | 3630.2.a.bs.1.1 | 4 | |||
33.5 | odd | 10 | 990.2.n.i.91.2 | 8 | |||
33.20 | odd | 10 | 990.2.n.i.631.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
330.2.m.f.91.2 | ✓ | 8 | 11.5 | even | 5 | ||
330.2.m.f.301.2 | yes | 8 | 11.9 | even | 5 | ||
990.2.n.i.91.2 | 8 | 33.5 | odd | 10 | |||
990.2.n.i.631.2 | 8 | 33.20 | odd | 10 | |||
3630.2.a.bq.1.4 | 4 | 1.1 | even | 1 | trivial | ||
3630.2.a.bs.1.1 | 4 | 11.10 | odd | 2 |