Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(165.876448532\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + \cdots - 23\!\cdots\!32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(16.2952\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.2952 | 1.44031 | 0.720154 | − | 0.693814i | \(-0.244071\pi\) | ||||
0.720154 | + | 0.693814i | \(0.244071\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 137.534 | 1.07449 | ||||||||
\(5\) | −495.569 | −1.77300 | −0.886502 | − | 0.462726i | \(-0.846872\pi\) | ||||
−0.886502 | + | 0.462726i | \(0.846872\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 565.301 | 0.622927 | 0.311463 | − | 0.950258i | \(-0.399181\pi\) | ||||
0.311463 | + | 0.950258i | \(0.399181\pi\) | |||||||
\(8\) | 155.363 | 0.107284 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8075.41 | −2.55367 | ||||||||
\(11\) | 826.834 | 0.187303 | 0.0936513 | − | 0.995605i | \(-0.470146\pi\) | ||||
0.0936513 | + | 0.995605i | \(0.470146\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11479.1 | 1.44913 | 0.724564 | − | 0.689207i | \(-0.242041\pi\) | ||||
0.724564 | + | 0.689207i | \(0.242041\pi\) | |||||||
\(14\) | 9211.71 | 0.897206 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −15072.7 | −0.919965 | ||||||||
\(17\) | 23564.6 | 1.16329 | 0.581646 | − | 0.813442i | \(-0.302409\pi\) | ||||
0.581646 | + | 0.813442i | \(0.302409\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −53546.6 | −1.79099 | −0.895497 | − | 0.445067i | \(-0.853180\pi\) | ||||
−0.895497 | + | 0.445067i | \(0.853180\pi\) | |||||||
\(20\) | −68157.8 | −1.90507 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 13473.4 | 0.269773 | ||||||||
\(23\) | 87155.1 | 1.49364 | 0.746819 | − | 0.665028i | \(-0.231580\pi\) | ||||
0.746819 | + | 0.665028i | \(0.231580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 167464. | 2.14354 | ||||||||
\(26\) | 187055. | 2.08719 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 77748.3 | 0.669326 | ||||||||
\(29\) | −26745.6 | −0.203638 | −0.101819 | − | 0.994803i | \(-0.532466\pi\) | ||||
−0.101819 | + | 0.994803i | \(0.532466\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −231681. | −1.39677 | −0.698384 | − | 0.715723i | \(-0.746097\pi\) | ||||
−0.698384 | + | 0.715723i | \(0.746097\pi\) | |||||||
\(32\) | −265500. | −1.43232 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 383990. | 1.67550 | ||||||||
\(35\) | −280146. | −1.10445 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 409893. | 1.33035 | 0.665173 | − | 0.746689i | \(-0.268358\pi\) | ||||
0.665173 | + | 0.746689i | \(0.268358\pi\) | |||||||
\(38\) | −872554. | −2.57958 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −76993.4 | −0.190214 | ||||||||
\(41\) | −189635. | −0.429710 | −0.214855 | − | 0.976646i | \(-0.568928\pi\) | ||||
−0.214855 | + | 0.976646i | \(0.568928\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −849460. | −1.62931 | −0.814654 | − | 0.579947i | \(-0.803073\pi\) | ||||
−0.814654 | + | 0.579947i | \(0.803073\pi\) | |||||||
\(44\) | 113718. | 0.201254 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.42021e6 | 2.15130 | ||||||||
\(47\) | 902990. | 1.26865 | 0.634323 | − | 0.773068i | \(-0.281279\pi\) | ||||
0.634323 | + | 0.773068i | \(0.281279\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −503977. | −0.611963 | ||||||||
\(50\) | 2.72886e6 | 3.08736 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.57877e6 | 1.55707 | ||||||||
\(53\) | 324949. | 0.299812 | 0.149906 | − | 0.988700i | \(-0.452103\pi\) | ||||
0.149906 | + | 0.988700i | \(0.452103\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −409753. | −0.332088 | ||||||||
\(56\) | 87827.2 | 0.0668299 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −435826. | −0.293302 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.58592e6 | −0.894598 | −0.447299 | − | 0.894384i | \(-0.647614\pi\) | ||||
−0.447299 | + | 0.894384i | \(0.647614\pi\) | |||||||
\(62\) | −3.77529e6 | −2.01178 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.39707e6 | −1.14301 | ||||||||
\(65\) | −5.68870e6 | −2.56931 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.57819e6 | −1.04726 | −0.523629 | − | 0.851947i | \(-0.675422\pi\) | ||||
−0.523629 | + | 0.851947i | \(0.675422\pi\) | |||||||
\(68\) | 3.24094e6 | 1.24994 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.56504e6 | −1.59075 | ||||||||
\(71\) | 678037. | 0.224827 | 0.112414 | − | 0.993661i | \(-0.464142\pi\) | ||||
0.112414 | + | 0.993661i | \(0.464142\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.50036e6 | 0.752269 | 0.376135 | − | 0.926565i | \(-0.377253\pi\) | ||||
0.376135 | + | 0.926565i | \(0.377253\pi\) | |||||||
\(74\) | 6.67930e6 | 1.91611 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.36449e6 | −1.92440 | ||||||||
\(77\) | 467410. | 0.116676 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.33035e6 | −1.67275 | −0.836373 | − | 0.548161i | \(-0.815328\pi\) | ||||
−0.836373 | + | 0.548161i | \(0.815328\pi\) | |||||||
\(80\) | 7.46957e6 | 1.63110 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.09015e6 | −0.618914 | ||||||||
\(83\) | −3.91602e6 | −0.751747 | −0.375874 | − | 0.926671i | \(-0.622657\pi\) | ||||
−0.375874 | + | 0.926671i | \(0.622657\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.16779e7 | −2.06252 | ||||||||
\(86\) | −1.38421e7 | −2.34670 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 128460. | 0.0200945 | ||||||||
\(89\) | −3.80382e6 | −0.571946 | −0.285973 | − | 0.958238i | \(-0.592317\pi\) | ||||
−0.285973 | + | 0.958238i | \(0.592317\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.48916e6 | 0.902700 | ||||||||
\(92\) | 1.19868e7 | 1.60489 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.47144e7 | 1.82724 | ||||||||
\(95\) | 2.65361e7 | 3.17544 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.68854e6 | −0.855348 | −0.427674 | − | 0.903933i | \(-0.640667\pi\) | ||||
−0.427674 | + | 0.903933i | \(0.640667\pi\) | |||||||
\(98\) | −8.21243e6 | −0.881414 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.30321e7 | 2.30321 | ||||||||
\(101\) | 1.11320e7 | 1.07510 | 0.537551 | − | 0.843231i | \(-0.319350\pi\) | ||||
0.537551 | + | 0.843231i | \(0.319350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.10836e6 | 0.821315 | 0.410658 | − | 0.911790i | \(-0.365299\pi\) | ||||
0.410658 | + | 0.911790i | \(0.365299\pi\) | |||||||
\(104\) | 1.78344e6 | 0.155468 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.29511e6 | 0.431822 | ||||||||
\(107\) | −2.43881e7 | −1.92458 | −0.962289 | − | 0.272029i | \(-0.912305\pi\) | ||||
−0.962289 | + | 0.272029i | \(0.912305\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.92554e7 | −1.42416 | −0.712080 | − | 0.702098i | \(-0.752247\pi\) | ||||
−0.712080 | + | 0.702098i | \(0.752247\pi\) | |||||||
\(110\) | −6.67702e6 | −0.478309 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.52062e6 | −0.573071 | ||||||||
\(113\) | −9.40627e6 | −0.613258 | −0.306629 | − | 0.951829i | \(-0.599201\pi\) | ||||
−0.306629 | + | 0.951829i | \(0.599201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.31914e7 | −2.64822 | ||||||||
\(116\) | −3.67844e6 | −0.218807 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.34670e6 | −0.187512 | ||||||||
\(119\) | 1.33211e7 | 0.724645 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.88035e7 | −0.964918 | ||||||||
\(122\) | −2.58430e7 | −1.28850 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.18641e7 | −1.50081 | ||||||||
\(125\) | −4.42737e7 | −2.02750 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.55998e7 | 1.10898 | 0.554490 | − | 0.832190i | \(-0.312913\pi\) | ||||
0.554490 | + | 0.832190i | \(0.312913\pi\) | |||||||
\(128\) | −5.07683e6 | −0.213972 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.26986e7 | −3.70060 | ||||||||
\(131\) | −2.04746e7 | −0.795729 | −0.397865 | − | 0.917444i | \(-0.630249\pi\) | ||||
−0.397865 | + | 0.917444i | \(0.630249\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.02700e7 | −1.11566 | ||||||||
\(134\) | −4.20122e7 | −1.50837 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.66108e6 | 0.124802 | ||||||||
\(137\) | −1.13505e6 | −0.0377132 | −0.0188566 | − | 0.999822i | \(-0.506003\pi\) | ||||
−0.0188566 | + | 0.999822i | \(0.506003\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.44843e7 | −0.457453 | −0.228726 | − | 0.973491i | \(-0.573456\pi\) | ||||
−0.228726 | + | 0.973491i | \(0.573456\pi\) | |||||||
\(140\) | −3.85297e7 | −1.18672 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.10488e7 | 0.323821 | ||||||||
\(143\) | 9.49132e6 | 0.271425 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.32543e7 | 0.361051 | ||||||||
\(146\) | 4.07440e7 | 1.08350 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.63744e7 | 1.42944 | ||||||||
\(149\) | −6.91223e7 | −1.71185 | −0.855926 | − | 0.517098i | \(-0.827012\pi\) | ||||
−0.855926 | + | 0.517098i | \(0.827012\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.36019e7 | 1.26695 | 0.633477 | − | 0.773762i | \(-0.281627\pi\) | ||||
0.633477 | + | 0.773762i | \(0.281627\pi\) | |||||||
\(152\) | −8.31919e6 | −0.192145 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.61655e6 | 0.168049 | ||||||||
\(155\) | 1.14814e8 | 2.47648 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.33413e7 | −1.71874 | −0.859372 | − | 0.511350i | \(-0.829145\pi\) | ||||
−0.859372 | + | 0.511350i | \(0.829145\pi\) | |||||||
\(158\) | −1.19450e8 | −2.40927 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.31574e8 | 2.53950 | ||||||||
\(161\) | 4.92689e7 | 0.930426 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.74632e6 | −0.103928 | −0.0519641 | − | 0.998649i | \(-0.516548\pi\) | ||||
−0.0519641 | + | 0.998649i | \(0.516548\pi\) | |||||||
\(164\) | −2.60813e7 | −0.461717 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.38125e7 | −1.08275 | ||||||||
\(167\) | 5.42463e7 | 0.901286 | 0.450643 | − | 0.892704i | \(-0.351195\pi\) | ||||
0.450643 | + | 0.892704i | \(0.351195\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.90217e7 | 1.09997 | ||||||||
\(170\) | −1.90294e8 | −2.97066 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.16830e8 | −1.75067 | ||||||||
\(173\) | 1.02709e8 | 1.50816 | 0.754081 | − | 0.656781i | \(-0.228082\pi\) | ||||
0.754081 | + | 0.656781i | \(0.228082\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.46676e7 | 1.33527 | ||||||||
\(176\) | −1.24626e7 | −0.172312 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.19841e7 | −0.823779 | ||||||||
\(179\) | −1.18297e8 | −1.54166 | −0.770828 | − | 0.637043i | \(-0.780157\pi\) | ||||
−0.770828 | + | 0.637043i | \(0.780157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.54155e7 | −0.945334 | −0.472667 | − | 0.881241i | \(-0.656709\pi\) | ||||
−0.472667 | + | 0.881241i | \(0.656709\pi\) | |||||||
\(182\) | 1.05742e8 | 1.30017 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.35407e7 | 0.160243 | ||||||||
\(185\) | −2.03131e8 | −2.35871 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.94840e7 | 0.217888 | ||||||||
\(188\) | 1.24192e8 | 1.36314 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.32411e8 | 4.57361 | ||||||||
\(191\) | −5.67288e7 | −0.589097 | −0.294548 | − | 0.955637i | \(-0.595169\pi\) | ||||
−0.294548 | + | 0.955637i | \(0.595169\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.56586e7 | 0.156784 | 0.0783920 | − | 0.996923i | \(-0.475021\pi\) | ||||
0.0783920 | + | 0.996923i | \(0.475021\pi\) | |||||||
\(194\) | −1.25286e8 | −1.23196 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.93142e7 | −0.657546 | ||||||||
\(197\) | −1.95180e6 | −0.0181888 | −0.00909440 | − | 0.999959i | \(-0.502895\pi\) | ||||
−0.00909440 | + | 0.999959i | \(0.502895\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.03128e7 | 0.362624 | 0.181312 | − | 0.983426i | \(-0.441966\pi\) | ||||
0.181312 | + | 0.983426i | \(0.441966\pi\) | |||||||
\(200\) | 2.60178e7 | 0.229967 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.81399e8 | 1.54848 | ||||||||
\(203\) | −1.51193e7 | −0.126852 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.39774e7 | 0.761877 | ||||||||
\(206\) | 1.48423e8 | 1.18295 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.73021e8 | −1.33315 | ||||||||
\(209\) | −4.42741e7 | −0.335458 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.16617e8 | 0.854620 | 0.427310 | − | 0.904105i | \(-0.359461\pi\) | ||||
0.427310 | + | 0.904105i | \(0.359461\pi\) | |||||||
\(212\) | 4.46916e7 | 0.322144 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.97410e8 | −2.77199 | ||||||||
\(215\) | 4.20966e8 | 2.88877 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.30970e8 | −0.870084 | ||||||||
\(218\) | −3.13770e8 | −2.05123 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.63552e7 | −0.356824 | ||||||||
\(221\) | 2.70501e8 | 1.68576 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.52043e8 | 0.918121 | 0.459060 | − | 0.888405i | \(-0.348186\pi\) | ||||
0.459060 | + | 0.888405i | \(0.348186\pi\) | |||||||
\(224\) | −1.50087e8 | −0.892228 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.53277e8 | −0.883280 | ||||||||
\(227\) | 2.19156e8 | 1.24355 | 0.621774 | − | 0.783197i | \(-0.286412\pi\) | ||||
0.621774 | + | 0.783197i | \(0.286412\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.50483e8 | −0.828061 | −0.414030 | − | 0.910263i | \(-0.635879\pi\) | ||||
−0.414030 | + | 0.910263i | \(0.635879\pi\) | |||||||
\(230\) | −7.03813e8 | −3.81426 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.15529e6 | −0.0218471 | ||||||||
\(233\) | −1.05923e8 | −0.548586 | −0.274293 | − | 0.961646i | \(-0.588444\pi\) | ||||
−0.274293 | + | 0.961646i | \(0.588444\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.47494e8 | −2.24931 | ||||||||
\(236\) | −2.82467e7 | −0.139886 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.17070e8 | 1.04371 | ||||||||
\(239\) | 2.39069e8 | 1.13274 | 0.566370 | − | 0.824151i | \(-0.308347\pi\) | ||||
0.566370 | + | 0.824151i | \(0.308347\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.39780e7 | −0.294422 | −0.147211 | − | 0.989105i | \(-0.547030\pi\) | ||||
−0.147211 | + | 0.989105i | \(0.547030\pi\) | |||||||
\(242\) | −3.06408e8 | −1.38978 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.18119e8 | −0.961234 | ||||||||
\(245\) | 2.49756e8 | 1.08501 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.14668e8 | −2.59538 | ||||||||
\(248\) | −3.59948e7 | −0.149851 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.21450e8 | −2.92022 | ||||||||
\(251\) | −1.43897e8 | −0.574373 | −0.287186 | − | 0.957875i | \(-0.592720\pi\) | ||||
−0.287186 | + | 0.957875i | \(0.592720\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.20627e7 | 0.279762 | ||||||||
\(254\) | 4.17155e8 | 1.59727 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.24097e8 | 0.834826 | ||||||||
\(257\) | 1.50715e8 | 0.553849 | 0.276925 | − | 0.960892i | \(-0.410685\pi\) | ||||
0.276925 | + | 0.960892i | \(0.410685\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.31713e8 | 0.828708 | ||||||||
\(260\) | −7.82391e8 | −2.76069 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.33638e8 | −1.14609 | ||||||||
\(263\) | 5.02309e8 | 1.70265 | 0.851325 | − | 0.524638i | \(-0.175799\pi\) | ||||
0.851325 | + | 0.524638i | \(0.175799\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.61035e8 | −0.531568 | ||||||||
\(266\) | −4.93256e8 | −1.60689 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.54590e8 | −1.12526 | ||||||||
\(269\) | 2.76426e8 | 0.865858 | 0.432929 | − | 0.901428i | \(-0.357480\pi\) | ||||
0.432929 | + | 0.901428i | \(0.357480\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.17995e8 | 0.360139 | 0.180069 | − | 0.983654i | \(-0.442368\pi\) | ||||
0.180069 | + | 0.983654i | \(0.442368\pi\) | |||||||
\(272\) | −3.55182e8 | −1.07019 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.84959e7 | −0.0543186 | ||||||||
\(275\) | 1.38465e8 | 0.401491 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.34905e7 | −0.179485 | −0.0897427 | − | 0.995965i | \(-0.528604\pi\) | ||||
−0.0897427 | + | 0.995965i | \(0.528604\pi\) | |||||||
\(278\) | −2.36025e8 | −0.658872 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.35245e7 | −0.118490 | ||||||||
\(281\) | −3.92031e8 | −1.05402 | −0.527009 | − | 0.849860i | \(-0.676687\pi\) | ||||
−0.527009 | + | 0.849860i | \(0.676687\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.91102e8 | 1.02574 | 0.512871 | − | 0.858466i | \(-0.328582\pi\) | ||||
0.512871 | + | 0.858466i | \(0.328582\pi\) | |||||||
\(284\) | 9.32533e7 | 0.241574 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.54663e8 | 0.390936 | ||||||||
\(287\) | −1.07201e8 | −0.267678 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.44951e8 | 0.353248 | ||||||||
\(290\) | 2.15982e8 | 0.520025 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.43886e8 | 0.808303 | ||||||||
\(293\) | 3.95594e8 | 0.918783 | 0.459392 | − | 0.888234i | \(-0.348067\pi\) | ||||
0.459392 | + | 0.888234i | \(0.348067\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.01780e8 | 0.230825 | ||||||||
\(296\) | 6.36824e7 | 0.142725 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.12636e9 | −2.46559 | ||||||||
\(299\) | 1.00046e9 | 2.16447 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.80201e8 | −1.01494 | ||||||||
\(302\) | 8.73455e8 | 1.82480 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.07092e8 | 1.64765 | ||||||||
\(305\) | 7.85935e8 | 1.58612 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.74974e8 | −0.739634 | −0.369817 | − | 0.929105i | \(-0.620580\pi\) | ||||
−0.369817 | + | 0.929105i | \(0.620580\pi\) | |||||||
\(308\) | 6.42849e7 | 0.125367 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.87092e9 | 3.56689 | ||||||||
\(311\) | −5.67572e8 | −1.06994 | −0.534970 | − | 0.844871i | \(-0.679677\pi\) | ||||
−0.534970 | + | 0.844871i | \(0.679677\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.61191e8 | −1.77176 | −0.885879 | − | 0.463916i | \(-0.846444\pi\) | ||||
−0.885879 | + | 0.463916i | \(0.846444\pi\) | |||||||
\(314\) | −1.35806e9 | −2.47552 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.00817e9 | −1.79734 | ||||||||
\(317\) | −1.03762e8 | −0.182950 | −0.0914748 | − | 0.995807i | \(-0.529158\pi\) | ||||
−0.0914748 | + | 0.995807i | \(0.529158\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.21142e7 | −0.0381420 | ||||||||
\(320\) | 1.18791e9 | 2.02656 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.02847e8 | 1.34010 | ||||||||
\(323\) | −1.26180e9 | −2.08345 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.92234e9 | 3.10626 | ||||||||
\(326\) | −9.36376e7 | −0.149689 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.94624e7 | −0.0461009 | ||||||||
\(329\) | 5.10462e8 | 0.790273 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.86499e8 | −0.737367 | −0.368684 | − | 0.929555i | \(-0.620191\pi\) | ||||
−0.368684 | + | 0.929555i | \(0.620191\pi\) | |||||||
\(332\) | −5.38587e8 | −0.807743 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.83956e8 | 1.29813 | ||||||||
\(335\) | 1.27767e9 | 1.85679 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.32747e8 | −0.331269 | −0.165634 | − | 0.986187i | \(-0.552967\pi\) | ||||
−0.165634 | + | 0.986187i | \(0.552967\pi\) | |||||||
\(338\) | 1.12472e9 | 1.58430 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.60611e9 | −2.21615 | ||||||||
\(341\) | −1.91562e8 | −0.261618 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.50449e8 | −1.00413 | ||||||||
\(344\) | −1.31975e8 | −0.174798 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.67367e9 | 2.17222 | ||||||||
\(347\) | 1.12320e8 | 0.144312 | 0.0721560 | − | 0.997393i | \(-0.477012\pi\) | ||||
0.0721560 | + | 0.997393i | \(0.477012\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.23358e9 | 1.55338 | 0.776688 | − | 0.629885i | \(-0.216898\pi\) | ||||
0.776688 | + | 0.629885i | \(0.216898\pi\) | |||||||
\(350\) | 1.54263e9 | 1.92320 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.19524e8 | −0.268277 | ||||||||
\(353\) | −1.25683e9 | −1.52078 | −0.760390 | − | 0.649466i | \(-0.774992\pi\) | ||||
−0.760390 | + | 0.649466i | \(0.774992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.36014e8 | −0.398619 | ||||||||
\(356\) | −5.23156e8 | −0.614549 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.92767e9 | −2.22046 | ||||||||
\(359\) | −1.53369e8 | −0.174947 | −0.0874735 | − | 0.996167i | \(-0.527879\pi\) | ||||
−0.0874735 | + | 0.996167i | \(0.527879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.97337e9 | 2.20766 | ||||||||
\(362\) | −1.22891e9 | −1.36157 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.92482e8 | 0.969940 | ||||||||
\(365\) | −1.23910e9 | −1.33378 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.10830e8 | −0.961847 | −0.480924 | − | 0.876762i | \(-0.659699\pi\) | ||||
−0.480924 | + | 0.876762i | \(0.659699\pi\) | |||||||
\(368\) | −1.31366e9 | −1.37409 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.31006e9 | −3.39727 | ||||||||
\(371\) | 1.83694e8 | 0.186761 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.48680e8 | −0.846766 | −0.423383 | − | 0.905951i | \(-0.639157\pi\) | ||||
−0.423383 | + | 0.905951i | \(0.639157\pi\) | |||||||
\(374\) | 3.17496e8 | 0.313825 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.40292e8 | 0.136105 | ||||||||
\(377\) | −3.07016e8 | −0.295098 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.11369e9 | 1.05082 | 0.525410 | − | 0.850849i | \(-0.323912\pi\) | ||||
0.525410 | + | 0.850849i | \(0.323912\pi\) | |||||||
\(380\) | 3.64962e9 | 3.41197 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.24408e8 | −0.848481 | ||||||||
\(383\) | 1.24305e9 | 1.13056 | 0.565279 | − | 0.824900i | \(-0.308768\pi\) | ||||
0.565279 | + | 0.824900i | \(0.308768\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.31634e8 | −0.206866 | ||||||||
\(386\) | 2.55160e8 | 0.225817 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.05744e9 | −0.919060 | ||||||||
\(389\) | −3.31934e8 | −0.285909 | −0.142955 | − | 0.989729i | \(-0.545660\pi\) | ||||
−0.142955 | + | 0.989729i | \(0.545660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.05377e9 | 1.73754 | ||||||||
\(392\) | −7.82997e7 | −0.0656536 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.18051e7 | −0.0261975 | ||||||||
\(395\) | 3.63270e9 | 2.96578 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.50412e8 | −0.200858 | −0.100429 | − | 0.994944i | \(-0.532021\pi\) | ||||
−0.100429 | + | 0.994944i | \(0.532021\pi\) | |||||||
\(398\) | 6.56906e8 | 0.522291 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.52414e9 | −1.97198 | ||||||||
\(401\) | −1.57100e9 | −1.21666 | −0.608332 | − | 0.793683i | \(-0.708161\pi\) | ||||
−0.608332 | + | 0.793683i | \(0.708161\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.65949e9 | −2.02410 | ||||||||
\(404\) | 1.53104e9 | 1.15518 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.46373e8 | −0.182705 | ||||||||
\(407\) | 3.38914e8 | 0.249177 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.37344e8 | −0.171532 | −0.0857661 | − | 0.996315i | \(-0.527334\pi\) | ||||
−0.0857661 | + | 0.996315i | \(0.527334\pi\) | |||||||
\(410\) | 1.53138e9 | 1.09734 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.25271e9 | 0.882492 | ||||||||
\(413\) | −1.16101e8 | −0.0810981 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.94066e9 | 1.33285 | ||||||||
\(416\) | −3.04770e9 | −2.07561 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.21457e8 | −0.483163 | ||||||||
\(419\) | 1.61768e9 | 1.07435 | 0.537173 | − | 0.843472i | \(-0.319492\pi\) | ||||
0.537173 | + | 0.843472i | \(0.319492\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.17270e9 | −0.765946 | −0.382973 | − | 0.923759i | \(-0.625100\pi\) | ||||
−0.382973 | + | 0.923759i | \(0.625100\pi\) | |||||||
\(422\) | 1.90030e9 | 1.23092 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.04852e7 | 0.0321650 | ||||||||
\(425\) | 3.94622e9 | 2.49356 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.96525e8 | −0.557269 | ||||||||
\(428\) | −3.35421e9 | −2.06793 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.85974e9 | 4.16071 | ||||||||
\(431\) | −2.74618e9 | −1.65219 | −0.826094 | − | 0.563533i | \(-0.809442\pi\) | ||||
−0.826094 | + | 0.563533i | \(0.809442\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.44724e8 | 0.0856709 | 0.0428355 | − | 0.999082i | \(-0.486361\pi\) | ||||
0.0428355 | + | 0.999082i | \(0.486361\pi\) | |||||||
\(434\) | −2.13418e9 | −1.25319 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.64827e9 | −1.53024 | ||||||||
\(437\) | −4.66686e9 | −2.67510 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.83060e8 | −0.159681 | −0.0798403 | − | 0.996808i | \(-0.525441\pi\) | ||||
−0.0798403 | + | 0.996808i | \(0.525441\pi\) | |||||||
\(440\) | −6.36607e7 | −0.0356276 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.40787e9 | 2.42801 | ||||||||
\(443\) | 6.58269e8 | 0.359741 | 0.179871 | − | 0.983690i | \(-0.442432\pi\) | ||||
0.179871 | + | 0.983690i | \(0.442432\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.88506e9 | 1.01406 | ||||||||
\(446\) | 2.47758e9 | 1.32238 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.35507e9 | −0.712012 | ||||||||
\(449\) | −2.96392e9 | −1.54527 | −0.772636 | − | 0.634850i | \(-0.781062\pi\) | ||||
−0.772636 | + | 0.634850i | \(0.781062\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.56797e8 | −0.0804857 | ||||||||
\(452\) | −1.29368e9 | −0.658937 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.57119e9 | 1.79109 | ||||||||
\(455\) | −3.21583e9 | −1.60049 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.62985e8 | −0.128891 | −0.0644456 | − | 0.997921i | \(-0.520528\pi\) | ||||
−0.0644456 | + | 0.997921i | \(0.520528\pi\) | |||||||
\(458\) | −2.45215e9 | −1.19266 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.94030e9 | −2.84548 | ||||||||
\(461\) | −7.39703e8 | −0.351645 | −0.175822 | − | 0.984422i | \(-0.556258\pi\) | ||||
−0.175822 | + | 0.984422i | \(0.556258\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00108e8 | −0.374641 | −0.187320 | − | 0.982299i | \(-0.559980\pi\) | ||||
−0.187320 | + | 0.982299i | \(0.559980\pi\) | |||||||
\(464\) | 4.03129e8 | 0.187340 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.72604e9 | −0.790132 | ||||||||
\(467\) | −3.44400e9 | −1.56478 | −0.782392 | − | 0.622786i | \(-0.786001\pi\) | ||||
−0.782392 | + | 0.622786i | \(0.786001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.45745e9 | −0.652364 | ||||||||
\(470\) | −7.29202e9 | −3.23970 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.19084e7 | −0.0139672 | ||||||||
\(473\) | −7.02362e8 | −0.305174 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.96713e9 | −3.83907 | ||||||||
\(476\) | 1.83211e9 | 0.778622 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.89568e9 | 1.63149 | ||||||||
\(479\) | 2.17648e9 | 0.904857 | 0.452429 | − | 0.891801i | \(-0.350558\pi\) | ||||
0.452429 | + | 0.891801i | \(0.350558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.70521e9 | 1.92784 | ||||||||
\(482\) | −1.04254e9 | −0.424059 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.58613e9 | −1.03679 | ||||||||
\(485\) | 3.81020e9 | 1.51653 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.73782e9 | 0.681796 | 0.340898 | − | 0.940100i | \(-0.389269\pi\) | ||||
0.340898 | + | 0.940100i | \(0.389269\pi\) | |||||||
\(488\) | −2.46395e8 | −0.0959758 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.06983e9 | 1.56275 | ||||||||
\(491\) | 7.21828e8 | 0.275200 | 0.137600 | − | 0.990488i | \(-0.456061\pi\) | ||||
0.137600 | + | 0.990488i | \(0.456061\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.30249e8 | −0.236891 | ||||||||
\(494\) | −1.00161e10 | −3.73815 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.49206e9 | 1.28498 | ||||||||
\(497\) | 3.83295e8 | 0.140051 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.78127e9 | −0.641769 | −0.320885 | − | 0.947118i | \(-0.603980\pi\) | ||||
−0.320885 | + | 0.947118i | \(0.603980\pi\) | |||||||
\(500\) | −6.08915e9 | −2.17852 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.34483e9 | −0.827273 | ||||||||
\(503\) | −1.72676e9 | −0.604986 | −0.302493 | − | 0.953152i | \(-0.597819\pi\) | ||||
−0.302493 | + | 0.953152i | \(0.597819\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.51669e9 | −1.90616 | ||||||||
\(506\) | 1.17428e9 | 0.402944 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.52085e9 | 1.19158 | ||||||||
\(509\) | −1.96038e8 | −0.0658912 | −0.0329456 | − | 0.999457i | \(-0.510489\pi\) | ||||
−0.0329456 | + | 0.999457i | \(0.510489\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.41346e9 | 0.468608 | ||||||||
\(512\) | 4.30154e9 | 1.41638 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.45594e9 | 0.797713 | ||||||||
\(515\) | −4.51383e9 | −1.45619 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.46623e8 | 0.237621 | ||||||||
\(518\) | 3.77582e9 | 1.19359 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.83816e8 | −0.275645 | ||||||||
\(521\) | 2.84883e9 | 0.882540 | 0.441270 | − | 0.897374i | \(-0.354528\pi\) | ||||
0.441270 | + | 0.897374i | \(0.354528\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.08000e9 | −0.941445 | −0.470722 | − | 0.882281i | \(-0.656007\pi\) | ||||
−0.470722 | + | 0.882281i | \(0.656007\pi\) | |||||||
\(524\) | −2.81596e9 | −0.855000 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.18523e9 | 2.45234 | ||||||||
\(527\) | −5.45947e9 | −1.62485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.19118e9 | 1.23095 | ||||||||
\(530\) | −2.62410e9 | −0.765621 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.16316e9 | −1.19876 | ||||||||
\(533\) | −2.17684e9 | −0.622705 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.20860e10 | 3.41228 | ||||||||
\(536\) | −4.00557e8 | −0.112354 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.50443e9 | 1.24710 | ||||||||
\(539\) | −4.16706e8 | −0.114622 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.69807e9 | 1.00412 | 0.502060 | − | 0.864833i | \(-0.332576\pi\) | ||||
0.502060 | + | 0.864833i | \(0.332576\pi\) | |||||||
\(542\) | 1.92275e9 | 0.518711 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.25639e9 | −1.66620 | ||||||||
\(545\) | 9.54237e9 | 2.52504 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.21521e9 | −0.317464 | −0.158732 | − | 0.987322i | \(-0.550741\pi\) | ||||
−0.158732 | + | 0.987322i | \(0.550741\pi\) | |||||||
\(548\) | −1.56108e8 | −0.0405223 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.25632e9 | 0.578270 | ||||||||
\(551\) | 1.43214e9 | 0.364715 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.14386e9 | −1.04200 | ||||||||
\(554\) | −1.03459e9 | −0.258514 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.99209e9 | −0.491527 | ||||||||
\(557\) | 6.35497e9 | 1.55819 | 0.779095 | − | 0.626906i | \(-0.215679\pi\) | ||||
0.779095 | + | 0.626906i | \(0.215679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.75105e9 | −2.36108 | ||||||||
\(560\) | 4.22256e9 | 1.01606 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.38823e9 | −1.51811 | ||||||||
\(563\) | −2.41689e9 | −0.570791 | −0.285395 | − | 0.958410i | \(-0.592125\pi\) | ||||
−0.285395 | + | 0.958410i | \(0.592125\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.66146e9 | 1.08731 | ||||||||
\(566\) | 6.37310e9 | 1.47738 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.05342e8 | 0.0241203 | ||||||||
\(569\) | −2.02038e9 | −0.459769 | −0.229884 | − | 0.973218i | \(-0.573835\pi\) | ||||
−0.229884 | + | 0.973218i | \(0.573835\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.09913e9 | −1.14622 | −0.573112 | − | 0.819477i | \(-0.694264\pi\) | ||||
−0.573112 | + | 0.819477i | \(0.694264\pi\) | |||||||
\(572\) | 1.30538e9 | 0.291643 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.74686e9 | −0.385538 | ||||||||
\(575\) | 1.45953e10 | 3.20167 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.65588e9 | −1.22570 | −0.612851 | − | 0.790199i | \(-0.709977\pi\) | ||||
−0.612851 | + | 0.790199i | \(0.709977\pi\) | |||||||
\(578\) | 2.36201e9 | 0.508785 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.82292e9 | 0.387945 | ||||||||
\(581\) | −2.21373e9 | −0.468283 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.68678e8 | 0.0561556 | ||||||||
\(584\) | 3.88465e8 | 0.0807063 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.44629e9 | 1.32333 | ||||||||
\(587\) | −8.74088e9 | −1.78370 | −0.891850 | − | 0.452331i | \(-0.850593\pi\) | ||||
−0.891850 | + | 0.452331i | \(0.850593\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.24057e10 | 2.50161 | ||||||||
\(590\) | 1.65852e9 | 0.332460 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.17820e9 | −1.22387 | ||||||||
\(593\) | 7.16535e9 | 1.41106 | 0.705531 | − | 0.708679i | \(-0.250709\pi\) | ||||
0.705531 | + | 0.708679i | \(0.250709\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.60153e9 | −1.28480 | ||||||||
\(596\) | −9.50669e9 | −1.83936 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.63028e10 | 3.11751 | ||||||||
\(599\) | 1.12486e8 | 0.0213847 | 0.0106923 | − | 0.999943i | \(-0.496596\pi\) | ||||
0.0106923 | + | 0.999943i | \(0.496596\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.43804e9 | 0.458121 | 0.229061 | − | 0.973412i | \(-0.426435\pi\) | ||||
0.229061 | + | 0.973412i | \(0.426435\pi\) | |||||||
\(602\) | −7.82498e9 | −1.46182 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.37210e9 | 1.36132 | ||||||||
\(605\) | 9.31845e9 | 1.71080 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.37659e9 | 0.612800 | 0.306400 | − | 0.951903i | \(-0.400876\pi\) | ||||
0.306400 | + | 0.951903i | \(0.400876\pi\) | |||||||
\(608\) | 1.42166e10 | 2.56527 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.28070e10 | 2.28451 | ||||||||
\(611\) | 1.03655e10 | 1.83843 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.64627e9 | −0.639348 | −0.319674 | − | 0.947528i | \(-0.603573\pi\) | ||||
−0.319674 | + | 0.947528i | \(0.603573\pi\) | |||||||
\(614\) | −6.11029e9 | −1.06530 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.26184e7 | 0.0125174 | ||||||||
\(617\) | 2.27884e8 | 0.0390585 | 0.0195293 | − | 0.999809i | \(-0.493783\pi\) | ||||
0.0195293 | + | 0.999809i | \(0.493783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.30512e9 | 0.390640 | 0.195320 | − | 0.980740i | \(-0.437426\pi\) | ||||
0.195320 | + | 0.980740i | \(0.437426\pi\) | |||||||
\(620\) | 1.57909e10 | 2.66094 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.24870e9 | −1.54104 | ||||||||
\(623\) | −2.15031e9 | −0.356280 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.85757e9 | 1.45122 | ||||||||
\(626\) | −1.56628e10 | −2.55188 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.14623e10 | −1.84677 | ||||||||
\(629\) | 9.65897e9 | 1.54758 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.67126e9 | 0.898622 | 0.449311 | − | 0.893375i | \(-0.351670\pi\) | ||||
0.449311 | + | 0.893375i | \(0.351670\pi\) | |||||||
\(632\) | −1.13887e9 | −0.179458 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.69083e9 | −0.263504 | ||||||||
\(635\) | −1.26865e10 | −1.96623 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.78522e9 | −0.886812 | ||||||||
\(638\) | −3.60355e8 | −0.0549362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.51592e9 | 0.379373 | ||||||||
\(641\) | 8.04557e9 | 1.20657 | 0.603287 | − | 0.797524i | \(-0.293858\pi\) | ||||
0.603287 | + | 0.797524i | \(0.293858\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.95787e9 | 1.03214 | 0.516069 | − | 0.856547i | \(-0.327395\pi\) | ||||
0.516069 | + | 0.856547i | \(0.327395\pi\) | |||||||
\(644\) | 6.77616e9 | 0.999731 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.05614e10 | −3.00081 | ||||||||
\(647\) | 1.50113e9 | 0.217898 | 0.108949 | − | 0.994047i | \(-0.465252\pi\) | ||||
0.108949 | + | 0.994047i | \(0.465252\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.69814e8 | −0.0243847 | ||||||||
\(650\) | 3.13250e10 | 4.47398 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.90316e8 | −0.111669 | ||||||||
\(653\) | 1.05745e9 | 0.148616 | 0.0743078 | − | 0.997235i | \(-0.476325\pi\) | ||||
0.0743078 | + | 0.997235i | \(0.476325\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.01466e10 | 1.41083 | ||||||||
\(656\) | 2.85831e9 | 0.395318 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.31808e9 | 1.13824 | ||||||||
\(659\) | 1.27158e10 | 1.73079 | 0.865396 | − | 0.501088i | \(-0.167067\pi\) | ||||
0.865396 | + | 0.501088i | \(0.167067\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.38832e10 | −1.86976 | −0.934878 | − | 0.354968i | \(-0.884492\pi\) | ||||
−0.934878 | + | 0.354968i | \(0.884492\pi\) | |||||||
\(662\) | −7.92761e9 | −1.06204 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.08407e8 | −0.0806503 | ||||||||
\(665\) | 1.50009e10 | 1.97807 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.33101e9 | −0.304162 | ||||||||
\(668\) | 7.46073e9 | 0.968420 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.08200e10 | 2.67435 | ||||||||
\(671\) | −1.31130e9 | −0.167560 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.66625e9 | 1.09592 | 0.547960 | − | 0.836505i | \(-0.315405\pi\) | ||||
0.547960 | + | 0.836505i | \(0.315405\pi\) | |||||||
\(674\) | −3.79267e9 | −0.477129 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.49284e9 | 1.18191 | ||||||||
\(677\) | 1.30940e10 | 1.62186 | 0.810929 | − | 0.585144i | \(-0.198962\pi\) | ||||
0.810929 | + | 0.585144i | \(0.198962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.34634e9 | −0.532819 | ||||||||
\(680\) | −1.81432e9 | −0.221275 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.12154e9 | −0.376811 | ||||||||
\(683\) | −5.07430e9 | −0.609402 | −0.304701 | − | 0.952448i | \(-0.598557\pi\) | ||||
−0.304701 | + | 0.952448i | \(0.598557\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.62496e8 | 0.0668656 | ||||||||
\(686\) | −1.22287e10 | −1.44626 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.28037e10 | 1.49891 | ||||||||
\(689\) | 3.73012e9 | 0.434466 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.09480e9 | 0.818026 | 0.409013 | − | 0.912529i | \(-0.365873\pi\) | ||||
0.409013 | + | 0.912529i | \(0.365873\pi\) | |||||||
\(692\) | 1.41260e10 | 1.62050 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.83027e9 | 0.207854 | ||||||||
\(695\) | 7.17798e9 | 0.811065 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.46867e9 | −0.499878 | ||||||||
\(698\) | 2.01014e10 | 2.23734 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.30200e10 | 1.43473 | ||||||||
\(701\) | −5.74769e9 | −0.630203 | −0.315101 | − | 0.949058i | \(-0.602039\pi\) | ||||
−0.315101 | + | 0.949058i | \(0.602039\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.19484e10 | −2.38264 | ||||||||
\(704\) | −1.98198e9 | −0.214089 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.04804e10 | −2.19039 | ||||||||
\(707\) | 6.29295e9 | 0.669709 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.47895e9 | −0.577345 | −0.288672 | − | 0.957428i | \(-0.593214\pi\) | ||||
−0.288672 | + | 0.957428i | \(0.593214\pi\) | |||||||
\(710\) | −5.47543e9 | −0.574135 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.90975e8 | −0.0613605 | ||||||||
\(713\) | −2.01922e10 | −2.08627 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.70361e9 | −0.481238 | ||||||||
\(716\) | −1.62699e10 | −1.65649 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.49918e9 | −0.251978 | ||||||||
\(719\) | −1.62636e10 | −1.63179 | −0.815895 | − | 0.578200i | \(-0.803755\pi\) | ||||
−0.815895 | + | 0.578200i | \(0.803755\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.14897e9 | 0.511619 | ||||||||
\(722\) | 3.21565e10 | 3.17971 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.03722e10 | −1.01575 | ||||||||
\(725\) | −4.47893e9 | −0.436507 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.55116e9 | −0.246245 | −0.123122 | − | 0.992391i | \(-0.539291\pi\) | ||||
−0.123122 | + | 0.992391i | \(0.539291\pi\) | |||||||
\(728\) | 1.00818e9 | 0.0968451 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.01915e10 | −1.92105 | ||||||||
\(731\) | −2.00172e10 | −1.89536 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.41305e10 | 1.32524 | 0.662619 | − | 0.748957i | \(-0.269445\pi\) | ||||
0.662619 | + | 0.748957i | \(0.269445\pi\) | |||||||
\(734\) | −1.48422e10 | −1.38536 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.31396e10 | −2.13936 | ||||||||
\(737\) | −2.13174e9 | −0.196154 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.92246e10 | 1.75227 | 0.876136 | − | 0.482064i | \(-0.160113\pi\) | ||||
0.876136 | + | 0.482064i | \(0.160113\pi\) | |||||||
\(740\) | −2.79374e10 | −2.53440 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.99333e9 | 0.268993 | ||||||||
\(743\) | −5.89705e9 | −0.527441 | −0.263721 | − | 0.964599i | \(-0.584950\pi\) | ||||
−0.263721 | + | 0.964599i | \(0.584950\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.42549e10 | 3.03512 | ||||||||
\(746\) | −1.38294e10 | −1.21960 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.67972e9 | 0.234117 | ||||||||
\(749\) | −1.37867e10 | −1.19887 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.11911e9 | −0.268715 | −0.134357 | − | 0.990933i | \(-0.542897\pi\) | ||||
−0.134357 | + | 0.990933i | \(0.542897\pi\) | |||||||
\(752\) | −1.36105e10 | −1.16711 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.00289e9 | −0.425032 | ||||||||
\(755\) | −2.65635e10 | −2.24631 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.03709e10 | −0.868921 | −0.434461 | − | 0.900691i | \(-0.643061\pi\) | ||||
−0.434461 | + | 0.900691i | \(0.643061\pi\) | |||||||
\(758\) | 1.81479e10 | 1.51350 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.12273e9 | 0.340673 | ||||||||
\(761\) | −1.48892e9 | −0.122468 | −0.0612342 | − | 0.998123i | \(-0.519504\pi\) | ||||
−0.0612342 | + | 0.998123i | \(0.519504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.08851e10 | −0.887147 | ||||||||
\(764\) | −7.80215e9 | −0.632977 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.02558e10 | 1.62835 | ||||||||
\(767\) | −2.35757e9 | −0.188660 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.76503e10 | 1.39962 | 0.699809 | − | 0.714330i | \(-0.253268\pi\) | ||||
0.699809 | + | 0.714330i | \(0.253268\pi\) | |||||||
\(770\) | −3.77453e9 | −0.297951 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.15359e9 | 0.168462 | ||||||||
\(773\) | 6.95196e8 | 0.0541351 | 0.0270676 | − | 0.999634i | \(-0.491383\pi\) | ||||
0.0270676 | + | 0.999634i | \(0.491383\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.87982e10 | −2.99403 | ||||||||
\(776\) | −1.19452e9 | −0.0917649 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.40894e9 | −0.411798 | ||||||||
\(779\) | 1.01543e10 | 0.769608 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.60624e8 | 0.0421107 | ||||||||
\(782\) | 3.34667e10 | 2.50259 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.59631e9 | 0.562984 | ||||||||
\(785\) | 4.13014e10 | 3.04734 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.19358e8 | −0.0526058 | −0.0263029 | − | 0.999654i | \(-0.508373\pi\) | ||||
−0.0263029 | + | 0.999654i | \(0.508373\pi\) | |||||||
\(788\) | −2.68440e8 | −0.0195436 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.91956e10 | 4.27164 | ||||||||
\(791\) | −5.31738e9 | −0.382014 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.82050e10 | −1.29639 | ||||||||
\(794\) | −4.08052e9 | −0.289297 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.54439e9 | 0.389635 | ||||||||
\(797\) | −4.07407e9 | −0.285052 | −0.142526 | − | 0.989791i | \(-0.545523\pi\) | ||||
−0.142526 | + | 0.989791i | \(0.545523\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.12786e10 | 1.47581 | ||||||||
\(800\) | −4.44616e10 | −3.07023 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.55998e10 | −1.75237 | ||||||||
\(803\) | 2.06739e9 | 0.140902 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.44161e10 | −1.64965 | ||||||||
\(806\) | −4.33371e10 | −2.91532 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.72951e9 | 0.115341 | ||||||||
\(809\) | 1.12391e10 | 0.746296 | 0.373148 | − | 0.927772i | \(-0.378278\pi\) | ||||
0.373148 | + | 0.927772i | \(0.378278\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.57592e10 | 1.03744 | 0.518719 | − | 0.854945i | \(-0.326409\pi\) | ||||
0.518719 | + | 0.854945i | \(0.326409\pi\) | |||||||
\(812\) | −2.07943e9 | −0.136300 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.52267e9 | 0.358892 | ||||||||
\(815\) | 2.84770e9 | 0.184265 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.54857e10 | 2.91808 | ||||||||
\(818\) | −3.86757e9 | −0.247059 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.29251e10 | 0.818627 | ||||||||
\(821\) | 1.83331e10 | 1.15621 | 0.578103 | − | 0.815964i | \(-0.303793\pi\) | ||||
0.578103 | + | 0.815964i | \(0.303793\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.71121e9 | 0.232069 | 0.116034 | − | 0.993245i | \(-0.462982\pi\) | ||||
0.116034 | + | 0.993245i | \(0.462982\pi\) | |||||||
\(824\) | 1.41511e9 | 0.0881138 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.89189e9 | −0.116806 | ||||||||
\(827\) | −3.00461e9 | −0.184722 | −0.0923610 | − | 0.995726i | \(-0.529441\pi\) | ||||
−0.0923610 | + | 0.995726i | \(0.529441\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.97799e10 | 1.20582 | 0.602912 | − | 0.797808i | \(-0.294007\pi\) | ||||
0.602912 | + | 0.797808i | \(0.294007\pi\) | |||||||
\(830\) | 3.16235e10 | 1.91971 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.75162e10 | −1.65637 | ||||||||
\(833\) | −1.18760e10 | −0.711891 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.68828e10 | −1.59798 | ||||||||
\(836\) | −6.08921e9 | −0.360445 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.63605e10 | 1.54739 | ||||||||
\(839\) | 7.17247e9 | 0.419278 | 0.209639 | − | 0.977779i | \(-0.432771\pi\) | ||||
0.209639 | + | 0.977779i | \(0.432771\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.65345e10 | −0.958531 | ||||||||
\(842\) | −1.91094e10 | −1.10320 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.60388e10 | 0.918278 | ||||||||
\(845\) | −3.42050e10 | −1.95025 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.06297e10 | −0.601073 | ||||||||
\(848\) | −4.89786e9 | −0.275817 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.43046e10 | 3.59150 | ||||||||
\(851\) | 3.57243e10 | 1.98706 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.70770e9 | −0.149375 | −0.0746877 | − | 0.997207i | \(-0.523796\pi\) | ||||
−0.0746877 | + | 0.997207i | \(0.523796\pi\) | |||||||
\(854\) | −1.46091e10 | −0.802639 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.78903e9 | −0.206476 | ||||||||
\(857\) | 1.93553e10 | 1.05043 | 0.525215 | − | 0.850969i | \(-0.323985\pi\) | ||||
0.525215 | + | 0.850969i | \(0.323985\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.02146e10 | −1.62645 | −0.813224 | − | 0.581951i | \(-0.802290\pi\) | ||||
−0.813224 | + | 0.581951i | \(0.802290\pi\) | |||||||
\(860\) | 5.78973e10 | 3.10394 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.47497e10 | −2.37966 | ||||||||
\(863\) | −4.20793e9 | −0.222859 | −0.111430 | − | 0.993772i | \(-0.535543\pi\) | ||||
−0.111430 | + | 0.993772i | \(0.535543\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.08996e10 | −2.67398 | ||||||||
\(866\) | 2.35831e9 | 0.123393 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.80128e10 | −0.934894 | ||||||||
\(869\) | −6.06098e9 | −0.313310 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.95954e10 | −1.51761 | ||||||||
\(872\) | −2.99158e9 | −0.152789 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.60475e10 | −3.85296 | ||||||||
\(875\) | −2.50280e10 | −1.26298 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.97999e10 | −0.991206 | −0.495603 | − | 0.868549i | \(-0.665053\pi\) | ||||
−0.495603 | + | 0.868549i | \(0.665053\pi\) | |||||||
\(878\) | −4.61252e9 | −0.229989 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.17609e9 | 0.305509 | ||||||||
\(881\) | −5.47108e9 | −0.269561 | −0.134781 | − | 0.990875i | \(-0.543033\pi\) | ||||
−0.134781 | + | 0.990875i | \(0.543033\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.99701e10 | 0.976153 | 0.488076 | − | 0.872801i | \(-0.337699\pi\) | ||||
0.488076 | + | 0.872801i | \(0.337699\pi\) | |||||||
\(884\) | 3.72031e10 | 1.81133 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.07266e10 | 0.518138 | ||||||||
\(887\) | 6.76780e9 | 0.325623 | 0.162811 | − | 0.986657i | \(-0.447944\pi\) | ||||
0.162811 | + | 0.986657i | \(0.447944\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.44716e10 | 0.690813 | ||||||||
\(890\) | 3.07174e10 | 1.46056 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.09111e10 | 0.986508 | ||||||||
\(893\) | −4.83521e10 | −2.27214 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.86243e10 | 2.73336 | ||||||||
\(896\) | −2.86994e9 | −0.133289 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.82978e10 | −2.22567 | ||||||||
\(899\) | 6.19645e9 | 0.284436 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.65728e9 | 0.348769 | ||||||||
\(902\) | −2.55504e9 | −0.115924 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.46139e9 | −0.0657926 | ||||||||
\(905\) | 3.73736e10 | 1.67608 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.47127e10 | −1.09975 | −0.549877 | − | 0.835246i | \(-0.685325\pi\) | ||||
−0.549877 | + | 0.835246i | \(0.685325\pi\) | |||||||
\(908\) | 3.01414e10 | 1.33618 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.24027e10 | −2.30520 | ||||||||
\(911\) | 3.74402e9 | 0.164068 | 0.0820340 | − | 0.996630i | \(-0.473858\pi\) | ||||
0.0820340 | + | 0.996630i | \(0.473858\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.23790e9 | −0.140804 | ||||||||
\(914\) | −4.28539e9 | −0.185643 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.06965e10 | −0.889740 | ||||||||
\(917\) | −1.15743e10 | −0.495681 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.76618e9 | −0.160065 | −0.0800326 | − | 0.996792i | \(-0.525502\pi\) | ||||
−0.0800326 | + | 0.996792i | \(0.525502\pi\) | |||||||
\(920\) | −6.71036e9 | −0.284111 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.20536e10 | −0.506477 | ||||||||
\(923\) | 7.78326e9 | 0.325804 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.86424e10 | 2.85165 | ||||||||
\(926\) | −1.30379e10 | −0.539598 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.10095e9 | 0.291675 | ||||||||
\(929\) | −3.28415e10 | −1.34390 | −0.671952 | − | 0.740595i | \(-0.734544\pi\) | ||||
−0.671952 | + | 0.740595i | \(0.734544\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.69863e10 | 1.09602 | ||||||||
\(932\) | −1.45680e10 | −0.589448 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.61208e10 | −2.25377 | ||||||||
\(935\) | −9.65567e9 | −0.386315 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.67023e10 | −1.45749 | −0.728744 | − | 0.684787i | \(-0.759895\pi\) | ||||
−0.728744 | + | 0.684787i | \(0.759895\pi\) | |||||||
\(938\) | −2.37496e10 | −0.939605 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.15458e10 | −2.41686 | ||||||||
\(941\) | −2.52107e10 | −0.986329 | −0.493165 | − | 0.869936i | \(-0.664160\pi\) | ||||
−0.493165 | + | 0.869936i | \(0.664160\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.65277e10 | −0.641831 | ||||||||
\(944\) | 3.09562e9 | 0.119769 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.14451e10 | −0.439544 | ||||||||
\(947\) | −8.87956e9 | −0.339755 | −0.169878 | − | 0.985465i | \(-0.554337\pi\) | ||||
−0.169878 | + | 0.985465i | \(0.554337\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.87020e10 | 1.09013 | ||||||||
\(950\) | −1.46121e11 | −5.52944 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.06961e9 | 0.0777427 | ||||||||
\(953\) | −1.58158e10 | −0.591925 | −0.295962 | − | 0.955200i | \(-0.595640\pi\) | ||||
−0.295962 | + | 0.955200i | \(0.595640\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.81131e10 | 1.04447 | ||||||||
\(956\) | 3.28802e10 | 1.21711 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.54662e10 | 1.30327 | ||||||||
\(959\) | −6.41645e8 | −0.0234925 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.61635e10 | 0.950963 | ||||||||
\(962\) | 7.66725e10 | 2.77669 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.79917e9 | −0.316353 | ||||||||
\(965\) | −7.75992e9 | −0.277979 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.18915e10 | 1.84546 | 0.922728 | − | 0.385451i | \(-0.125954\pi\) | ||||
0.922728 | + | 0.385451i | \(0.125954\pi\) | |||||||
\(968\) | −2.92138e9 | −0.103520 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.20881e10 | 2.18428 | ||||||||
\(971\) | 1.69159e10 | 0.592963 | 0.296481 | − | 0.955039i | \(-0.404187\pi\) | ||||
0.296481 | + | 0.955039i | \(0.404187\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.18800e9 | −0.284959 | ||||||||
\(974\) | 2.83182e10 | 0.981996 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.39042e10 | 0.822999 | ||||||||
\(977\) | −8.24427e9 | −0.282827 | −0.141414 | − | 0.989951i | \(-0.545165\pi\) | ||||
−0.141414 | + | 0.989951i | \(0.545165\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.14513e9 | −0.107127 | ||||||||
\(980\) | 3.43500e10 | 1.16583 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.17623e10 | 0.396373 | ||||||||
\(983\) | 4.10669e9 | 0.137897 | 0.0689484 | − | 0.997620i | \(-0.478036\pi\) | ||||
0.0689484 | + | 0.997620i | \(0.478036\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.67254e8 | 0.0322488 | ||||||||
\(986\) | −1.02701e10 | −0.341196 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.45379e10 | −2.78870 | ||||||||
\(989\) | −7.40347e10 | −2.43359 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.53943e9 | −0.0502460 | −0.0251230 | − | 0.999684i | \(-0.507998\pi\) | ||||
−0.0251230 | + | 0.999684i | \(0.507998\pi\) | |||||||
\(992\) | 6.15112e10 | 2.00062 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.24588e9 | 0.201716 | ||||||||
\(995\) | −1.99778e10 | −0.642934 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.17704e10 | −0.695717 | −0.347858 | − | 0.937547i | \(-0.613091\pi\) | ||||
−0.347858 | + | 0.937547i | \(0.613091\pi\) | |||||||
\(998\) | −2.90263e10 | −0.924345 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 531.8.a.b.1.14 | 16 | ||
3.2 | odd | 2 | 177.8.a.a.1.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.a.1.3 | ✓ | 16 | 3.2 | odd | 2 | ||
531.8.a.b.1.14 | 16 | 1.1 | even | 1 | trivial |