Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
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: | \( x^{16} - 4 x^{15} - 14 x^{14} + 68 x^{13} + 64 x^{12} - 456 x^{11} - 54 x^{10} + 1532 x^{9} - 400 x^{8} - 2708 x^{7} + 1218 x^{6} + 2424 x^{5} - 1276 x^{4} - 960 x^{3} + 500 x^{2} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-1.49558\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.49558 | 1.05753 | 0.528767 | − | 0.848767i | \(-0.322655\pi\) | ||||
0.528767 | + | 0.848767i | \(0.322655\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.236756 | 0.118378 | ||||||||
\(5\) | 1.30108 | 0.581859 | 0.290929 | − | 0.956745i | \(-0.406036\pi\) | ||||
0.290929 | + | 0.956745i | \(0.406036\pi\) | |||||||
\(6\) | 1.49558 | 0.610567 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.63707 | −0.932345 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.94586 | 0.615335 | ||||||||
\(11\) | −0.750331 | −0.226233 | −0.113117 | − | 0.993582i | \(-0.536083\pi\) | ||||
−0.113117 | + | 0.993582i | \(0.536083\pi\) | |||||||
\(12\) | 0.236756 | 0.0683456 | ||||||||
\(13\) | −4.40274 | −1.22110 | −0.610551 | − | 0.791977i | \(-0.709052\pi\) | ||||
−0.610551 | + | 0.791977i | \(0.709052\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.30108 | 0.335936 | ||||||||
\(16\) | −4.41746 | −1.10436 | ||||||||
\(17\) | −4.00199 | −0.970626 | −0.485313 | − | 0.874341i | \(-0.661294\pi\) | ||||
−0.485313 | + | 0.874341i | \(0.661294\pi\) | |||||||
\(18\) | 1.49558 | 0.352511 | ||||||||
\(19\) | 5.38274 | 1.23489 | 0.617443 | − | 0.786616i | \(-0.288169\pi\) | ||||
0.617443 | + | 0.786616i | \(0.288169\pi\) | |||||||
\(20\) | 0.308037 | 0.0688792 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.12218 | −0.239249 | ||||||||
\(23\) | 3.23452 | 0.674443 | 0.337222 | − | 0.941425i | \(-0.390513\pi\) | ||||
0.337222 | + | 0.941425i | \(0.390513\pi\) | |||||||
\(24\) | −2.63707 | −0.538290 | ||||||||
\(25\) | −3.30720 | −0.661441 | ||||||||
\(26\) | −6.58465 | −1.29136 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.07532 | −0.571073 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(30\) | 1.94586 | 0.355264 | ||||||||
\(31\) | −9.02077 | −1.62018 | −0.810089 | − | 0.586307i | \(-0.800581\pi\) | ||||
−0.810089 | + | 0.586307i | \(0.800581\pi\) | |||||||
\(32\) | −1.33252 | −0.235558 | ||||||||
\(33\) | −0.750331 | −0.130616 | ||||||||
\(34\) | −5.98530 | −1.02647 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.236756 | 0.0394593 | ||||||||
\(37\) | 0.222437 | 0.0365685 | 0.0182842 | − | 0.999833i | \(-0.494180\pi\) | ||||
0.0182842 | + | 0.999833i | \(0.494180\pi\) | |||||||
\(38\) | 8.05032 | 1.30593 | ||||||||
\(39\) | −4.40274 | −0.705003 | ||||||||
\(40\) | −3.43103 | −0.542493 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.320612 | 0.0488929 | 0.0244465 | − | 0.999701i | \(-0.492218\pi\) | ||||
0.0244465 | + | 0.999701i | \(0.492218\pi\) | |||||||
\(44\) | −0.177645 | −0.0267810 | ||||||||
\(45\) | 1.30108 | 0.193953 | ||||||||
\(46\) | 4.83747 | 0.713247 | ||||||||
\(47\) | −3.80784 | −0.555430 | −0.277715 | − | 0.960663i | \(-0.589577\pi\) | ||||
−0.277715 | + | 0.960663i | \(0.589577\pi\) | |||||||
\(48\) | −4.41746 | −0.637605 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.94618 | −0.699496 | ||||||||
\(51\) | −4.00199 | −0.560391 | ||||||||
\(52\) | −1.04238 | −0.144552 | ||||||||
\(53\) | −5.43224 | −0.746175 | −0.373088 | − | 0.927796i | \(-0.621701\pi\) | ||||
−0.373088 | + | 0.927796i | \(0.621701\pi\) | |||||||
\(54\) | 1.49558 | 0.203522 | ||||||||
\(55\) | −0.976237 | −0.131636 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.38274 | 0.712962 | ||||||||
\(58\) | −4.59939 | −0.603929 | ||||||||
\(59\) | −1.91525 | −0.249344 | −0.124672 | − | 0.992198i | \(-0.539788\pi\) | ||||
−0.124672 | + | 0.992198i | \(0.539788\pi\) | |||||||
\(60\) | 0.308037 | 0.0397674 | ||||||||
\(61\) | 10.2528 | 1.31274 | 0.656371 | − | 0.754439i | \(-0.272091\pi\) | ||||
0.656371 | + | 0.754439i | \(0.272091\pi\) | |||||||
\(62\) | −13.4913 | −1.71339 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.84203 | 0.855254 | ||||||||
\(65\) | −5.72830 | −0.710508 | ||||||||
\(66\) | −1.12218 | −0.138131 | ||||||||
\(67\) | −10.1905 | −1.24497 | −0.622485 | − | 0.782632i | \(-0.713877\pi\) | ||||
−0.622485 | + | 0.782632i | \(0.713877\pi\) | |||||||
\(68\) | −0.947496 | −0.114901 | ||||||||
\(69\) | 3.23452 | 0.389390 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.199216 | 0.0236426 | 0.0118213 | − | 0.999930i | \(-0.496237\pi\) | ||||
0.0118213 | + | 0.999930i | \(0.496237\pi\) | |||||||
\(72\) | −2.63707 | −0.310782 | ||||||||
\(73\) | −14.2100 | −1.66315 | −0.831574 | − | 0.555413i | \(-0.812560\pi\) | ||||
−0.831574 | + | 0.555413i | \(0.812560\pi\) | |||||||
\(74\) | 0.332673 | 0.0386724 | ||||||||
\(75\) | −3.30720 | −0.381883 | ||||||||
\(76\) | 1.27440 | 0.146183 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.58465 | −0.745565 | ||||||||
\(79\) | −12.7948 | −1.43953 | −0.719766 | − | 0.694216i | \(-0.755751\pi\) | ||||
−0.719766 | + | 0.694216i | \(0.755751\pi\) | |||||||
\(80\) | −5.74745 | −0.642584 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.49558 | 0.165159 | ||||||||
\(83\) | −9.59023 | −1.05266 | −0.526332 | − | 0.850279i | \(-0.676433\pi\) | ||||
−0.526332 | + | 0.850279i | \(0.676433\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.20689 | −0.564767 | ||||||||
\(86\) | 0.479501 | 0.0517060 | ||||||||
\(87\) | −3.07532 | −0.329709 | ||||||||
\(88\) | 1.97868 | 0.210928 | ||||||||
\(89\) | 4.12065 | 0.436788 | 0.218394 | − | 0.975861i | \(-0.429918\pi\) | ||||
0.218394 | + | 0.975861i | \(0.429918\pi\) | |||||||
\(90\) | 1.94586 | 0.205112 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.765791 | 0.0798392 | ||||||||
\(93\) | −9.02077 | −0.935410 | ||||||||
\(94\) | −5.69492 | −0.587386 | ||||||||
\(95\) | 7.00336 | 0.718529 | ||||||||
\(96\) | −1.33252 | −0.135999 | ||||||||
\(97\) | −6.19741 | −0.629252 | −0.314626 | − | 0.949216i | \(-0.601879\pi\) | ||||
−0.314626 | + | 0.949216i | \(0.601879\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.750331 | −0.0754111 | ||||||||
\(100\) | −0.783000 | −0.0783000 | ||||||||
\(101\) | 17.1028 | 1.70179 | 0.850897 | − | 0.525332i | \(-0.176059\pi\) | ||||
0.850897 | + | 0.525332i | \(0.176059\pi\) | |||||||
\(102\) | −5.98530 | −0.592633 | ||||||||
\(103\) | 8.58842 | 0.846242 | 0.423121 | − | 0.906073i | \(-0.360934\pi\) | ||||
0.423121 | + | 0.906073i | \(0.360934\pi\) | |||||||
\(104\) | 11.6103 | 1.13849 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.12434 | −0.789106 | ||||||||
\(107\) | −16.8587 | −1.62979 | −0.814894 | − | 0.579610i | \(-0.803205\pi\) | ||||
−0.814894 | + | 0.579610i | \(0.803205\pi\) | |||||||
\(108\) | 0.236756 | 0.0227819 | ||||||||
\(109\) | 9.66152 | 0.925406 | 0.462703 | − | 0.886513i | \(-0.346880\pi\) | ||||
0.462703 | + | 0.886513i | \(0.346880\pi\) | |||||||
\(110\) | −1.46004 | −0.139209 | ||||||||
\(111\) | 0.222437 | 0.0211128 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.5574 | −0.993155 | −0.496578 | − | 0.867992i | \(-0.665410\pi\) | ||||
−0.496578 | + | 0.867992i | \(0.665410\pi\) | |||||||
\(114\) | 8.05032 | 0.753981 | ||||||||
\(115\) | 4.20835 | 0.392431 | ||||||||
\(116\) | −0.728101 | −0.0676025 | ||||||||
\(117\) | −4.40274 | −0.407034 | ||||||||
\(118\) | −2.86441 | −0.263690 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.43103 | −0.313208 | ||||||||
\(121\) | −10.4370 | −0.948818 | ||||||||
\(122\) | 15.3339 | 1.38827 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | −2.13572 | −0.191793 | ||||||||
\(125\) | −10.8083 | −0.966723 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.01008 | 0.267101 | 0.133551 | − | 0.991042i | \(-0.457362\pi\) | ||||
0.133551 | + | 0.991042i | \(0.457362\pi\) | |||||||
\(128\) | 12.8978 | 1.14002 | ||||||||
\(129\) | 0.320612 | 0.0282284 | ||||||||
\(130\) | −8.56713 | −0.751387 | ||||||||
\(131\) | 12.9015 | 1.12721 | 0.563603 | − | 0.826046i | \(-0.309415\pi\) | ||||
0.563603 | + | 0.826046i | \(0.309415\pi\) | |||||||
\(132\) | −0.177645 | −0.0154620 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −15.2407 | −1.31660 | ||||||||
\(135\) | 1.30108 | 0.111979 | ||||||||
\(136\) | 10.5535 | 0.904958 | ||||||||
\(137\) | 4.96393 | 0.424097 | 0.212049 | − | 0.977259i | \(-0.431986\pi\) | ||||
0.212049 | + | 0.977259i | \(0.431986\pi\) | |||||||
\(138\) | 4.83747 | 0.411793 | ||||||||
\(139\) | 12.1564 | 1.03109 | 0.515546 | − | 0.856862i | \(-0.327589\pi\) | ||||
0.515546 | + | 0.856862i | \(0.327589\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.80784 | −0.320678 | ||||||||
\(142\) | 0.297944 | 0.0250029 | ||||||||
\(143\) | 3.30352 | 0.276254 | ||||||||
\(144\) | −4.41746 | −0.368122 | ||||||||
\(145\) | −4.00123 | −0.332284 | ||||||||
\(146\) | −21.2521 | −1.75884 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.0526634 | 0.00432890 | ||||||||
\(149\) | −14.8763 | −1.21872 | −0.609359 | − | 0.792894i | \(-0.708573\pi\) | ||||
−0.609359 | + | 0.792894i | \(0.708573\pi\) | |||||||
\(150\) | −4.94618 | −0.403854 | ||||||||
\(151\) | −0.301545 | −0.0245394 | −0.0122697 | − | 0.999925i | \(-0.503906\pi\) | ||||
−0.0122697 | + | 0.999925i | \(0.503906\pi\) | |||||||
\(152\) | −14.1947 | −1.15134 | ||||||||
\(153\) | −4.00199 | −0.323542 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.7367 | −0.942714 | ||||||||
\(156\) | −1.04238 | −0.0834569 | ||||||||
\(157\) | 4.70368 | 0.375395 | 0.187697 | − | 0.982227i | \(-0.439898\pi\) | ||||
0.187697 | + | 0.982227i | \(0.439898\pi\) | |||||||
\(158\) | −19.1357 | −1.52235 | ||||||||
\(159\) | −5.43224 | −0.430804 | ||||||||
\(160\) | −1.73370 | −0.137061 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.49558 | 0.117504 | ||||||||
\(163\) | −5.64405 | −0.442076 | −0.221038 | − | 0.975265i | \(-0.570944\pi\) | ||||
−0.221038 | + | 0.975265i | \(0.570944\pi\) | |||||||
\(164\) | 0.236756 | 0.0184875 | ||||||||
\(165\) | −0.976237 | −0.0760000 | ||||||||
\(166\) | −14.3429 | −1.11323 | ||||||||
\(167\) | −14.1707 | −1.09656 | −0.548282 | − | 0.836293i | \(-0.684718\pi\) | ||||
−0.548282 | + | 0.836293i | \(0.684718\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.38416 | 0.491089 | ||||||||
\(170\) | −7.78732 | −0.597260 | ||||||||
\(171\) | 5.38274 | 0.411629 | ||||||||
\(172\) | 0.0759069 | 0.00578785 | ||||||||
\(173\) | 4.35168 | 0.330852 | 0.165426 | − | 0.986222i | \(-0.447100\pi\) | ||||
0.165426 | + | 0.986222i | \(0.447100\pi\) | |||||||
\(174\) | −4.59939 | −0.348679 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.31456 | 0.249844 | ||||||||
\(177\) | −1.91525 | −0.143959 | ||||||||
\(178\) | 6.16276 | 0.461918 | ||||||||
\(179\) | −3.44395 | −0.257413 | −0.128706 | − | 0.991683i | \(-0.541082\pi\) | ||||
−0.128706 | + | 0.991683i | \(0.541082\pi\) | |||||||
\(180\) | 0.308037 | 0.0229597 | ||||||||
\(181\) | 21.0180 | 1.56226 | 0.781129 | − | 0.624370i | \(-0.214644\pi\) | ||||
0.781129 | + | 0.624370i | \(0.214644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.2528 | 0.757911 | ||||||||
\(184\) | −8.52965 | −0.628814 | ||||||||
\(185\) | 0.289408 | 0.0212777 | ||||||||
\(186\) | −13.4913 | −0.989228 | ||||||||
\(187\) | 3.00282 | 0.219588 | ||||||||
\(188\) | −0.901529 | −0.0657507 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.4741 | 0.759869 | ||||||||
\(191\) | 17.6175 | 1.27476 | 0.637379 | − | 0.770551i | \(-0.280019\pi\) | ||||
0.637379 | + | 0.770551i | \(0.280019\pi\) | |||||||
\(192\) | 6.84203 | 0.493781 | ||||||||
\(193\) | −24.4497 | −1.75993 | −0.879964 | − | 0.475040i | \(-0.842434\pi\) | ||||
−0.879964 | + | 0.475040i | \(0.842434\pi\) | |||||||
\(194\) | −9.26872 | −0.665455 | ||||||||
\(195\) | −5.72830 | −0.410212 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.8760 | −0.774880 | −0.387440 | − | 0.921895i | \(-0.626641\pi\) | ||||
−0.387440 | + | 0.921895i | \(0.626641\pi\) | |||||||
\(198\) | −1.12218 | −0.0797498 | ||||||||
\(199\) | 9.38454 | 0.665252 | 0.332626 | − | 0.943059i | \(-0.392065\pi\) | ||||
0.332626 | + | 0.943059i | \(0.392065\pi\) | |||||||
\(200\) | 8.72133 | 0.616691 | ||||||||
\(201\) | −10.1905 | −0.718783 | ||||||||
\(202\) | 25.5786 | 1.79971 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.947496 | −0.0663380 | ||||||||
\(205\) | 1.30108 | 0.0908710 | ||||||||
\(206\) | 12.8447 | 0.894930 | ||||||||
\(207\) | 3.23452 | 0.224814 | ||||||||
\(208\) | 19.4489 | 1.34854 | ||||||||
\(209\) | −4.03884 | −0.279372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.1085 | −1.24664 | −0.623319 | − | 0.781968i | \(-0.714216\pi\) | ||||
−0.623319 | + | 0.781968i | \(0.714216\pi\) | |||||||
\(212\) | −1.28611 | −0.0883307 | ||||||||
\(213\) | 0.199216 | 0.0136501 | ||||||||
\(214\) | −25.2135 | −1.72356 | ||||||||
\(215\) | 0.417141 | 0.0284488 | ||||||||
\(216\) | −2.63707 | −0.179430 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.4496 | 0.978648 | ||||||||
\(219\) | −14.2100 | −0.960219 | ||||||||
\(220\) | −0.231130 | −0.0155828 | ||||||||
\(221\) | 17.6198 | 1.18523 | ||||||||
\(222\) | 0.332673 | 0.0223275 | ||||||||
\(223\) | −20.6736 | −1.38441 | −0.692203 | − | 0.721703i | \(-0.743360\pi\) | ||||
−0.692203 | + | 0.721703i | \(0.743360\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.30720 | −0.220480 | ||||||||
\(226\) | −15.7894 | −1.05030 | ||||||||
\(227\) | −17.2707 | −1.14629 | −0.573147 | − | 0.819452i | \(-0.694278\pi\) | ||||
−0.573147 | + | 0.819452i | \(0.694278\pi\) | |||||||
\(228\) | 1.27440 | 0.0843990 | ||||||||
\(229\) | 8.57141 | 0.566415 | 0.283207 | − | 0.959059i | \(-0.408602\pi\) | ||||
0.283207 | + | 0.959059i | \(0.408602\pi\) | |||||||
\(230\) | 6.29392 | 0.415009 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.10984 | 0.532437 | ||||||||
\(233\) | 16.0030 | 1.04839 | 0.524196 | − | 0.851598i | \(-0.324366\pi\) | ||||
0.524196 | + | 0.851598i | \(0.324366\pi\) | |||||||
\(234\) | −6.58465 | −0.430452 | ||||||||
\(235\) | −4.95428 | −0.323182 | ||||||||
\(236\) | −0.453447 | −0.0295169 | ||||||||
\(237\) | −12.7948 | −0.831115 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.31197 | 0.602341 | 0.301171 | − | 0.953570i | \(-0.402623\pi\) | ||||
0.301171 | + | 0.953570i | \(0.402623\pi\) | |||||||
\(240\) | −5.74745 | −0.370996 | ||||||||
\(241\) | 13.4089 | 0.863742 | 0.431871 | − | 0.901935i | \(-0.357854\pi\) | ||||
0.431871 | + | 0.901935i | \(0.357854\pi\) | |||||||
\(242\) | −15.6094 | −1.00341 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.42742 | 0.155400 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.49558 | 0.0953546 | ||||||||
\(247\) | −23.6988 | −1.50792 | ||||||||
\(248\) | 23.7884 | 1.51056 | ||||||||
\(249\) | −9.59023 | −0.607756 | ||||||||
\(250\) | −16.1647 | −1.02234 | ||||||||
\(251\) | 0.0581644 | 0.00367130 | 0.00183565 | − | 0.999998i | \(-0.499416\pi\) | ||||
0.00183565 | + | 0.999998i | \(0.499416\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.42696 | −0.152582 | ||||||||
\(254\) | 4.50181 | 0.282468 | ||||||||
\(255\) | −5.20689 | −0.326068 | ||||||||
\(256\) | 5.60566 | 0.350354 | ||||||||
\(257\) | 19.6323 | 1.22463 | 0.612314 | − | 0.790615i | \(-0.290239\pi\) | ||||
0.612314 | + | 0.790615i | \(0.290239\pi\) | |||||||
\(258\) | 0.479501 | 0.0298524 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.35621 | −0.0841085 | ||||||||
\(261\) | −3.07532 | −0.190358 | ||||||||
\(262\) | 19.2951 | 1.19206 | ||||||||
\(263\) | −1.71718 | −0.105886 | −0.0529431 | − | 0.998598i | \(-0.516860\pi\) | ||||
−0.0529431 | + | 0.998598i | \(0.516860\pi\) | |||||||
\(264\) | 1.97868 | 0.121779 | ||||||||
\(265\) | −7.06775 | −0.434168 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.12065 | 0.252180 | ||||||||
\(268\) | −2.41266 | −0.147377 | ||||||||
\(269\) | 13.1932 | 0.804404 | 0.402202 | − | 0.915551i | \(-0.368245\pi\) | ||||
0.402202 | + | 0.915551i | \(0.368245\pi\) | |||||||
\(270\) | 1.94586 | 0.118421 | ||||||||
\(271\) | −0.787682 | −0.0478483 | −0.0239241 | − | 0.999714i | \(-0.507616\pi\) | ||||
−0.0239241 | + | 0.999714i | \(0.507616\pi\) | |||||||
\(272\) | 17.6786 | 1.07192 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.42395 | 0.448497 | ||||||||
\(275\) | 2.48150 | 0.149640 | ||||||||
\(276\) | 0.765791 | 0.0460952 | ||||||||
\(277\) | 9.56370 | 0.574627 | 0.287314 | − | 0.957837i | \(-0.407238\pi\) | ||||
0.287314 | + | 0.957837i | \(0.407238\pi\) | |||||||
\(278\) | 18.1808 | 1.09041 | ||||||||
\(279\) | −9.02077 | −0.540059 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.48602 | 0.446579 | 0.223289 | − | 0.974752i | \(-0.428321\pi\) | ||||
0.223289 | + | 0.974752i | \(0.428321\pi\) | |||||||
\(282\) | −5.69492 | −0.339128 | ||||||||
\(283\) | 30.8025 | 1.83102 | 0.915509 | − | 0.402298i | \(-0.131789\pi\) | ||||
0.915509 | + | 0.402298i | \(0.131789\pi\) | |||||||
\(284\) | 0.0471656 | 0.00279876 | ||||||||
\(285\) | 7.00336 | 0.414843 | ||||||||
\(286\) | 4.94067 | 0.292148 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.33252 | −0.0785193 | ||||||||
\(289\) | −0.984056 | −0.0578856 | ||||||||
\(290\) | −5.98415 | −0.351401 | ||||||||
\(291\) | −6.19741 | −0.363299 | ||||||||
\(292\) | −3.36429 | −0.196880 | ||||||||
\(293\) | 1.19896 | 0.0700440 | 0.0350220 | − | 0.999387i | \(-0.488850\pi\) | ||||
0.0350220 | + | 0.999387i | \(0.488850\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.49188 | −0.145083 | ||||||||
\(296\) | −0.586583 | −0.0340944 | ||||||||
\(297\) | −0.750331 | −0.0435386 | ||||||||
\(298\) | −22.2488 | −1.28884 | ||||||||
\(299\) | −14.2407 | −0.823564 | ||||||||
\(300\) | −0.783000 | −0.0452065 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.450984 | −0.0259512 | ||||||||
\(303\) | 17.1028 | 0.982532 | ||||||||
\(304\) | −23.7780 | −1.36376 | ||||||||
\(305\) | 13.3397 | 0.763830 | ||||||||
\(306\) | −5.98530 | −0.342157 | ||||||||
\(307\) | −14.2847 | −0.815268 | −0.407634 | − | 0.913145i | \(-0.633646\pi\) | ||||
−0.407634 | + | 0.913145i | \(0.633646\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.58842 | 0.488578 | ||||||||
\(310\) | −17.5532 | −0.996952 | ||||||||
\(311\) | 0.370661 | 0.0210183 | 0.0105091 | − | 0.999945i | \(-0.496655\pi\) | ||||
0.0105091 | + | 0.999945i | \(0.496655\pi\) | |||||||
\(312\) | 11.6103 | 0.657306 | ||||||||
\(313\) | 23.9391 | 1.35312 | 0.676559 | − | 0.736388i | \(-0.263470\pi\) | ||||
0.676559 | + | 0.736388i | \(0.263470\pi\) | |||||||
\(314\) | 7.03473 | 0.396993 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.02926 | −0.170409 | ||||||||
\(317\) | −6.14198 | −0.344968 | −0.172484 | − | 0.985012i | \(-0.555179\pi\) | ||||
−0.172484 | + | 0.985012i | \(0.555179\pi\) | |||||||
\(318\) | −8.12434 | −0.455590 | ||||||||
\(319\) | 2.30751 | 0.129196 | ||||||||
\(320\) | 8.90200 | 0.497637 | ||||||||
\(321\) | −16.8587 | −0.940959 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.5417 | −1.19861 | ||||||||
\(324\) | 0.236756 | 0.0131531 | ||||||||
\(325\) | 14.5608 | 0.807686 | ||||||||
\(326\) | −8.44112 | −0.467510 | ||||||||
\(327\) | 9.66152 | 0.534283 | ||||||||
\(328\) | −2.63707 | −0.145608 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.46004 | −0.0803725 | ||||||||
\(331\) | −19.8031 | −1.08848 | −0.544239 | − | 0.838930i | \(-0.683182\pi\) | ||||
−0.544239 | + | 0.838930i | \(0.683182\pi\) | |||||||
\(332\) | −2.27054 | −0.124612 | ||||||||
\(333\) | 0.222437 | 0.0121895 | ||||||||
\(334\) | −21.1935 | −1.15965 | ||||||||
\(335\) | −13.2586 | −0.724396 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.16733 | 0.390429 | 0.195215 | − | 0.980761i | \(-0.437460\pi\) | ||||
0.195215 | + | 0.980761i | \(0.437460\pi\) | |||||||
\(338\) | 9.54801 | 0.519343 | ||||||||
\(339\) | −10.5574 | −0.573399 | ||||||||
\(340\) | −1.23276 | −0.0668560 | ||||||||
\(341\) | 6.76856 | 0.366538 | ||||||||
\(342\) | 8.05032 | 0.435311 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.845478 | −0.0455851 | ||||||||
\(345\) | 4.20835 | 0.226570 | ||||||||
\(346\) | 6.50828 | 0.349887 | ||||||||
\(347\) | 31.6998 | 1.70173 | 0.850867 | − | 0.525381i | \(-0.176077\pi\) | ||||
0.850867 | + | 0.525381i | \(0.176077\pi\) | |||||||
\(348\) | −0.728101 | −0.0390303 | ||||||||
\(349\) | 34.3013 | 1.83611 | 0.918054 | − | 0.396456i | \(-0.129760\pi\) | ||||
0.918054 | + | 0.396456i | \(0.129760\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.40274 | −0.235001 | ||||||||
\(352\) | 0.999829 | 0.0532910 | ||||||||
\(353\) | 15.5061 | 0.825304 | 0.412652 | − | 0.910889i | \(-0.364603\pi\) | ||||
0.412652 | + | 0.910889i | \(0.364603\pi\) | |||||||
\(354\) | −2.86441 | −0.152242 | ||||||||
\(355\) | 0.259195 | 0.0137567 | ||||||||
\(356\) | 0.975589 | 0.0517061 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.15069 | −0.272223 | ||||||||
\(359\) | −27.0959 | −1.43007 | −0.715033 | − | 0.699091i | \(-0.753588\pi\) | ||||
−0.715033 | + | 0.699091i | \(0.753588\pi\) | |||||||
\(360\) | −3.43103 | −0.180831 | ||||||||
\(361\) | 9.97394 | 0.524944 | ||||||||
\(362\) | 31.4341 | 1.65214 | ||||||||
\(363\) | −10.4370 | −0.547801 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.4882 | −0.967717 | ||||||||
\(366\) | 15.3339 | 0.801517 | ||||||||
\(367\) | −15.2872 | −0.797987 | −0.398994 | − | 0.916954i | \(-0.630640\pi\) | ||||
−0.398994 | + | 0.916954i | \(0.630640\pi\) | |||||||
\(368\) | −14.2883 | −0.744831 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 0.432832 | 0.0225019 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.13572 | −0.110732 | ||||||||
\(373\) | −5.41590 | −0.280424 | −0.140212 | − | 0.990121i | \(-0.544778\pi\) | ||||
−0.140212 | + | 0.990121i | \(0.544778\pi\) | |||||||
\(374\) | 4.49095 | 0.232222 | ||||||||
\(375\) | −10.8083 | −0.558138 | ||||||||
\(376\) | 10.0415 | 0.517853 | ||||||||
\(377\) | 13.5399 | 0.697338 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.5728 | 1.62179 | 0.810893 | − | 0.585195i | \(-0.198982\pi\) | ||||
0.810893 | + | 0.585195i | \(0.198982\pi\) | |||||||
\(380\) | 1.65809 | 0.0850580 | ||||||||
\(381\) | 3.01008 | 0.154211 | ||||||||
\(382\) | 26.3484 | 1.34810 | ||||||||
\(383\) | −18.4875 | −0.944666 | −0.472333 | − | 0.881420i | \(-0.656588\pi\) | ||||
−0.472333 | + | 0.881420i | \(0.656588\pi\) | |||||||
\(384\) | 12.8978 | 0.658190 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −36.5665 | −1.86118 | ||||||||
\(387\) | 0.320612 | 0.0162976 | ||||||||
\(388\) | −1.46727 | −0.0744896 | ||||||||
\(389\) | 0.290515 | 0.0147297 | 0.00736485 | − | 0.999973i | \(-0.497656\pi\) | ||||
0.00736485 | + | 0.999973i | \(0.497656\pi\) | |||||||
\(390\) | −8.56713 | −0.433813 | ||||||||
\(391\) | −12.9445 | −0.654632 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.9015 | 0.650792 | ||||||||
\(394\) | −16.2658 | −0.819462 | ||||||||
\(395\) | −16.6471 | −0.837604 | ||||||||
\(396\) | −0.177645 | −0.00892701 | ||||||||
\(397\) | −33.5002 | −1.68133 | −0.840663 | − | 0.541559i | \(-0.817834\pi\) | ||||
−0.840663 | + | 0.541559i | \(0.817834\pi\) | |||||||
\(398\) | 14.0353 | 0.703527 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.6094 | 0.730472 | ||||||||
\(401\) | 9.39811 | 0.469319 | 0.234660 | − | 0.972078i | \(-0.424602\pi\) | ||||
0.234660 | + | 0.972078i | \(0.424602\pi\) | |||||||
\(402\) | −15.2407 | −0.760138 | ||||||||
\(403\) | 39.7161 | 1.97840 | ||||||||
\(404\) | 4.04920 | 0.201455 | ||||||||
\(405\) | 1.30108 | 0.0646509 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.166902 | −0.00827301 | ||||||||
\(408\) | 10.5535 | 0.522478 | ||||||||
\(409\) | −21.9938 | −1.08752 | −0.543761 | − | 0.839240i | \(-0.683000\pi\) | ||||
−0.543761 | + | 0.839240i | \(0.683000\pi\) | |||||||
\(410\) | 1.94586 | 0.0960992 | ||||||||
\(411\) | 4.96393 | 0.244853 | ||||||||
\(412\) | 2.03336 | 0.100176 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.83747 | 0.237749 | ||||||||
\(415\) | −12.4776 | −0.612502 | ||||||||
\(416\) | 5.86673 | 0.287640 | ||||||||
\(417\) | 12.1564 | 0.595301 | ||||||||
\(418\) | −6.04040 | −0.295446 | ||||||||
\(419\) | 12.5798 | 0.614564 | 0.307282 | − | 0.951619i | \(-0.400581\pi\) | ||||
0.307282 | + | 0.951619i | \(0.400581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.04947 | −0.246096 | −0.123048 | − | 0.992401i | \(-0.539267\pi\) | ||||
−0.123048 | + | 0.992401i | \(0.539267\pi\) | |||||||
\(422\) | −27.0826 | −1.31836 | ||||||||
\(423\) | −3.80784 | −0.185143 | ||||||||
\(424\) | 14.3252 | 0.695693 | ||||||||
\(425\) | 13.2354 | 0.642011 | ||||||||
\(426\) | 0.297944 | 0.0144354 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.99139 | −0.192931 | ||||||||
\(429\) | 3.30352 | 0.159495 | ||||||||
\(430\) | 0.623867 | 0.0300855 | ||||||||
\(431\) | −12.1483 | −0.585161 | −0.292580 | − | 0.956241i | \(-0.594514\pi\) | ||||
−0.292580 | + | 0.956241i | \(0.594514\pi\) | |||||||
\(432\) | −4.41746 | −0.212535 | ||||||||
\(433\) | −19.0236 | −0.914217 | −0.457108 | − | 0.889411i | \(-0.651115\pi\) | ||||
−0.457108 | + | 0.889411i | \(0.651115\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.00123 | −0.191844 | ||||||||
\(436\) | 2.28742 | 0.109548 | ||||||||
\(437\) | 17.4106 | 0.832861 | ||||||||
\(438\) | −21.2521 | −1.01546 | ||||||||
\(439\) | −23.3222 | −1.11311 | −0.556553 | − | 0.830812i | \(-0.687876\pi\) | ||||
−0.556553 | + | 0.830812i | \(0.687876\pi\) | |||||||
\(440\) | 2.57441 | 0.122730 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 26.3517 | 1.25342 | ||||||||
\(443\) | 24.9061 | 1.18332 | 0.591662 | − | 0.806186i | \(-0.298472\pi\) | ||||
0.591662 | + | 0.806186i | \(0.298472\pi\) | |||||||
\(444\) | 0.0526634 | 0.00249929 | ||||||||
\(445\) | 5.36128 | 0.254149 | ||||||||
\(446\) | −30.9190 | −1.46406 | ||||||||
\(447\) | −14.8763 | −0.703627 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.2477 | −1.19151 | −0.595756 | − | 0.803165i | \(-0.703147\pi\) | ||||
−0.595756 | + | 0.803165i | \(0.703147\pi\) | |||||||
\(450\) | −4.94618 | −0.233165 | ||||||||
\(451\) | −0.750331 | −0.0353317 | ||||||||
\(452\) | −2.49952 | −0.117568 | ||||||||
\(453\) | −0.301545 | −0.0141678 | ||||||||
\(454\) | −25.8296 | −1.21225 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.1947 | −0.664727 | ||||||||
\(457\) | −13.0645 | −0.611130 | −0.305565 | − | 0.952171i | \(-0.598845\pi\) | ||||
−0.305565 | + | 0.952171i | \(0.598845\pi\) | |||||||
\(458\) | 12.8192 | 0.599003 | ||||||||
\(459\) | −4.00199 | −0.186797 | ||||||||
\(460\) | 0.996352 | 0.0464551 | ||||||||
\(461\) | −31.7275 | −1.47769 | −0.738847 | − | 0.673873i | \(-0.764630\pi\) | ||||
−0.738847 | + | 0.673873i | \(0.764630\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.68283 | −0.171156 | −0.0855779 | − | 0.996331i | \(-0.527274\pi\) | ||||
−0.0855779 | + | 0.996331i | \(0.527274\pi\) | |||||||
\(464\) | 13.5851 | 0.630673 | ||||||||
\(465\) | −11.7367 | −0.544276 | ||||||||
\(466\) | 23.9338 | 1.10871 | ||||||||
\(467\) | −29.4057 | −1.36074 | −0.680368 | − | 0.732871i | \(-0.738180\pi\) | ||||
−0.680368 | + | 0.732871i | \(0.738180\pi\) | |||||||
\(468\) | −1.04238 | −0.0481838 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7.40952 | −0.341776 | ||||||||
\(471\) | 4.70368 | 0.216734 | ||||||||
\(472\) | 5.05065 | 0.232475 | ||||||||
\(473\) | −0.240566 | −0.0110612 | ||||||||
\(474\) | −19.1357 | −0.878932 | ||||||||
\(475\) | −17.8018 | −0.816804 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.43224 | −0.248725 | ||||||||
\(478\) | 13.9268 | 0.636996 | ||||||||
\(479\) | 17.2828 | 0.789670 | 0.394835 | − | 0.918752i | \(-0.370802\pi\) | ||||
0.394835 | + | 0.918752i | \(0.370802\pi\) | |||||||
\(480\) | −1.73370 | −0.0791324 | ||||||||
\(481\) | −0.979335 | −0.0446538 | ||||||||
\(482\) | 20.0540 | 0.913436 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.47102 | −0.112319 | ||||||||
\(485\) | −8.06330 | −0.366136 | ||||||||
\(486\) | 1.49558 | 0.0678408 | ||||||||
\(487\) | −40.0005 | −1.81260 | −0.906298 | − | 0.422640i | \(-0.861104\pi\) | ||||
−0.906298 | + | 0.422640i | \(0.861104\pi\) | |||||||
\(488\) | −27.0374 | −1.22393 | ||||||||
\(489\) | −5.64405 | −0.255233 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.17562 | 0.414090 | 0.207045 | − | 0.978331i | \(-0.433615\pi\) | ||||
0.207045 | + | 0.978331i | \(0.433615\pi\) | |||||||
\(492\) | 0.236756 | 0.0106738 | ||||||||
\(493\) | 12.3074 | 0.554298 | ||||||||
\(494\) | −35.4435 | −1.59468 | ||||||||
\(495\) | −0.976237 | −0.0438786 | ||||||||
\(496\) | 39.8489 | 1.78927 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −14.3429 | −0.642723 | ||||||||
\(499\) | 33.3392 | 1.49247 | 0.746233 | − | 0.665685i | \(-0.231861\pi\) | ||||
0.746233 | + | 0.665685i | \(0.231861\pi\) | |||||||
\(500\) | −2.55893 | −0.114439 | ||||||||
\(501\) | −14.1707 | −0.633102 | ||||||||
\(502\) | 0.0869894 | 0.00388253 | ||||||||
\(503\) | −8.10607 | −0.361432 | −0.180716 | − | 0.983535i | \(-0.557841\pi\) | ||||
−0.180716 | + | 0.983535i | \(0.557841\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.2521 | 0.990204 | ||||||||
\(506\) | −3.62971 | −0.161360 | ||||||||
\(507\) | 6.38416 | 0.283530 | ||||||||
\(508\) | 0.712654 | 0.0316189 | ||||||||
\(509\) | −20.6817 | −0.916698 | −0.458349 | − | 0.888772i | \(-0.651559\pi\) | ||||
−0.458349 | + | 0.888772i | \(0.651559\pi\) | |||||||
\(510\) | −7.78732 | −0.344828 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −17.4120 | −0.769507 | ||||||||
\(513\) | 5.38274 | 0.237654 | ||||||||
\(514\) | 29.3616 | 1.29508 | ||||||||
\(515\) | 11.1742 | 0.492393 | ||||||||
\(516\) | 0.0759069 | 0.00334162 | ||||||||
\(517\) | 2.85714 | 0.125657 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.35168 | 0.191018 | ||||||||
\(520\) | 15.1059 | 0.662439 | ||||||||
\(521\) | 12.6259 | 0.553152 | 0.276576 | − | 0.960992i | \(-0.410800\pi\) | ||||
0.276576 | + | 0.960992i | \(0.410800\pi\) | |||||||
\(522\) | −4.59939 | −0.201310 | ||||||||
\(523\) | 29.9917 | 1.31145 | 0.655724 | − | 0.755001i | \(-0.272364\pi\) | ||||
0.655724 | + | 0.755001i | \(0.272364\pi\) | |||||||
\(524\) | 3.05450 | 0.133436 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.56818 | −0.111978 | ||||||||
\(527\) | 36.1010 | 1.57259 | ||||||||
\(528\) | 3.31456 | 0.144248 | ||||||||
\(529\) | −12.5379 | −0.545126 | ||||||||
\(530\) | −10.5704 | −0.459148 | ||||||||
\(531\) | −1.91525 | −0.0831148 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.40274 | −0.190704 | ||||||||
\(534\) | 6.16276 | 0.266689 | ||||||||
\(535\) | −21.9344 | −0.948306 | ||||||||
\(536\) | 26.8731 | 1.16074 | ||||||||
\(537\) | −3.44395 | −0.148617 | ||||||||
\(538\) | 19.7315 | 0.850685 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.308037 | 0.0132558 | ||||||||
\(541\) | 5.29585 | 0.227687 | 0.113843 | − | 0.993499i | \(-0.463684\pi\) | ||||
0.113843 | + | 0.993499i | \(0.463684\pi\) | |||||||
\(542\) | −1.17804 | −0.0506012 | ||||||||
\(543\) | 21.0180 | 0.901970 | ||||||||
\(544\) | 5.33272 | 0.228639 | ||||||||
\(545\) | 12.5704 | 0.538455 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.0194 | 0.770452 | 0.385226 | − | 0.922822i | \(-0.374123\pi\) | ||||
0.385226 | + | 0.922822i | \(0.374123\pi\) | |||||||
\(548\) | 1.17524 | 0.0502038 | ||||||||
\(549\) | 10.2528 | 0.437580 | ||||||||
\(550\) | 3.71128 | 0.158249 | ||||||||
\(551\) | −16.5537 | −0.705210 | ||||||||
\(552\) | −8.52965 | −0.363046 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14.3033 | 0.607688 | ||||||||
\(555\) | 0.289408 | 0.0122847 | ||||||||
\(556\) | 2.87810 | 0.122059 | ||||||||
\(557\) | 34.1481 | 1.44690 | 0.723451 | − | 0.690375i | \(-0.242555\pi\) | ||||
0.723451 | + | 0.690375i | \(0.242555\pi\) | |||||||
\(558\) | −13.4913 | −0.571131 | ||||||||
\(559\) | −1.41157 | −0.0597033 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.00282 | 0.126779 | ||||||||
\(562\) | 11.1959 | 0.472272 | ||||||||
\(563\) | 24.4327 | 1.02972 | 0.514859 | − | 0.857275i | \(-0.327844\pi\) | ||||
0.514859 | + | 0.857275i | \(0.327844\pi\) | |||||||
\(564\) | −0.901529 | −0.0379612 | ||||||||
\(565\) | −13.7360 | −0.577876 | ||||||||
\(566\) | 46.0675 | 1.93636 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.525347 | −0.0220431 | ||||||||
\(569\) | −12.6126 | −0.528746 | −0.264373 | − | 0.964420i | \(-0.585165\pi\) | ||||
−0.264373 | + | 0.964420i | \(0.585165\pi\) | |||||||
\(570\) | 10.4741 | 0.438710 | ||||||||
\(571\) | −1.85956 | −0.0778203 | −0.0389101 | − | 0.999243i | \(-0.512389\pi\) | ||||
−0.0389101 | + | 0.999243i | \(0.512389\pi\) | |||||||
\(572\) | 0.782127 | 0.0327024 | ||||||||
\(573\) | 17.6175 | 0.735981 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.6972 | −0.446104 | ||||||||
\(576\) | 6.84203 | 0.285085 | ||||||||
\(577\) | 16.1880 | 0.673915 | 0.336958 | − | 0.941520i | \(-0.390602\pi\) | ||||
0.336958 | + | 0.941520i | \(0.390602\pi\) | |||||||
\(578\) | −1.47173 | −0.0612160 | ||||||||
\(579\) | −24.4497 | −1.01610 | ||||||||
\(580\) | −0.947314 | −0.0393351 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −9.26872 | −0.384201 | ||||||||
\(583\) | 4.07598 | 0.168810 | ||||||||
\(584\) | 37.4726 | 1.55063 | ||||||||
\(585\) | −5.72830 | −0.236836 | ||||||||
\(586\) | 1.79314 | 0.0740739 | ||||||||
\(587\) | 16.1967 | 0.668511 | 0.334256 | − | 0.942482i | \(-0.391515\pi\) | ||||
0.334256 | + | 0.942482i | \(0.391515\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.5565 | −2.00073 | ||||||||
\(590\) | −3.72681 | −0.153430 | ||||||||
\(591\) | −10.8760 | −0.447377 | ||||||||
\(592\) | −0.982608 | −0.0403849 | ||||||||
\(593\) | −21.0639 | −0.864990 | −0.432495 | − | 0.901636i | \(-0.642367\pi\) | ||||
−0.432495 | + | 0.901636i | \(0.642367\pi\) | |||||||
\(594\) | −1.12218 | −0.0460436 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.52206 | −0.144269 | ||||||||
\(597\) | 9.38454 | 0.384084 | ||||||||
\(598\) | −21.2982 | −0.870947 | ||||||||
\(599\) | −14.7515 | −0.602731 | −0.301365 | − | 0.953509i | \(-0.597442\pi\) | ||||
−0.301365 | + | 0.953509i | \(0.597442\pi\) | |||||||
\(600\) | 8.72133 | 0.356047 | ||||||||
\(601\) | 29.3384 | 1.19674 | 0.598370 | − | 0.801220i | \(-0.295815\pi\) | ||||
0.598370 | + | 0.801220i | \(0.295815\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.1905 | −0.414990 | ||||||||
\(604\) | −0.0713926 | −0.00290492 | ||||||||
\(605\) | −13.5793 | −0.552078 | ||||||||
\(606\) | 25.5786 | 1.03906 | ||||||||
\(607\) | −2.93492 | −0.119125 | −0.0595624 | − | 0.998225i | \(-0.518971\pi\) | ||||
−0.0595624 | + | 0.998225i | \(0.518971\pi\) | |||||||
\(608\) | −7.17260 | −0.290887 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 19.9506 | 0.807776 | ||||||||
\(611\) | 16.7649 | 0.678237 | ||||||||
\(612\) | −0.947496 | −0.0383002 | ||||||||
\(613\) | 19.1580 | 0.773785 | 0.386892 | − | 0.922125i | \(-0.373548\pi\) | ||||
0.386892 | + | 0.922125i | \(0.373548\pi\) | |||||||
\(614\) | −21.3638 | −0.862174 | ||||||||
\(615\) | 1.30108 | 0.0524644 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.15081 | 0.287881 | 0.143940 | − | 0.989586i | \(-0.454023\pi\) | ||||
0.143940 | + | 0.989586i | \(0.454023\pi\) | |||||||
\(618\) | 12.8447 | 0.516688 | ||||||||
\(619\) | 3.52506 | 0.141684 | 0.0708421 | − | 0.997488i | \(-0.477431\pi\) | ||||
0.0708421 | + | 0.997488i | \(0.477431\pi\) | |||||||
\(620\) | −2.77873 | −0.111597 | ||||||||
\(621\) | 3.23452 | 0.129797 | ||||||||
\(622\) | 0.554353 | 0.0222275 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 19.4489 | 0.778581 | ||||||||
\(625\) | 2.47361 | 0.0989444 | ||||||||
\(626\) | 35.8028 | 1.43097 | ||||||||
\(627\) | −4.03884 | −0.161296 | ||||||||
\(628\) | 1.11363 | 0.0444385 | ||||||||
\(629\) | −0.890193 | −0.0354943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.3841 | 1.32900 | 0.664499 | − | 0.747289i | \(-0.268645\pi\) | ||||
0.664499 | + | 0.747289i | \(0.268645\pi\) | |||||||
\(632\) | 33.7409 | 1.34214 | ||||||||
\(633\) | −18.1085 | −0.719747 | ||||||||
\(634\) | −9.18581 | −0.364815 | ||||||||
\(635\) | 3.91634 | 0.155415 | ||||||||
\(636\) | −1.28611 | −0.0509978 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.45106 | 0.136629 | ||||||||
\(639\) | 0.199216 | 0.00788087 | ||||||||
\(640\) | 16.7811 | 0.663329 | ||||||||
\(641\) | 22.5473 | 0.890565 | 0.445282 | − | 0.895390i | \(-0.353103\pi\) | ||||
0.445282 | + | 0.895390i | \(0.353103\pi\) | |||||||
\(642\) | −25.2135 | −0.995096 | ||||||||
\(643\) | −15.8629 | −0.625572 | −0.312786 | − | 0.949824i | \(-0.601262\pi\) | ||||
−0.312786 | + | 0.949824i | \(0.601262\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.417141 | 0.0164249 | ||||||||
\(646\) | −32.2173 | −1.26757 | ||||||||
\(647\) | 6.50471 | 0.255727 | 0.127863 | − | 0.991792i | \(-0.459188\pi\) | ||||
0.127863 | + | 0.991792i | \(0.459188\pi\) | |||||||
\(648\) | −2.63707 | −0.103594 | ||||||||
\(649\) | 1.43707 | 0.0564100 | ||||||||
\(650\) | 21.7768 | 0.854156 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.33626 | −0.0523321 | ||||||||
\(653\) | −49.5602 | −1.93944 | −0.969721 | − | 0.244216i | \(-0.921470\pi\) | ||||
−0.969721 | + | 0.244216i | \(0.921470\pi\) | |||||||
\(654\) | 14.4496 | 0.565023 | ||||||||
\(655\) | 16.7858 | 0.655874 | ||||||||
\(656\) | −4.41746 | −0.172473 | ||||||||
\(657\) | −14.2100 | −0.554383 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.3186 | −1.06418 | −0.532091 | − | 0.846687i | \(-0.678593\pi\) | ||||
−0.532091 | + | 0.846687i | \(0.678593\pi\) | |||||||
\(660\) | −0.231130 | −0.00899672 | ||||||||
\(661\) | −25.6016 | −0.995786 | −0.497893 | − | 0.867239i | \(-0.665893\pi\) | ||||
−0.497893 | + | 0.867239i | \(0.665893\pi\) | |||||||
\(662\) | −29.6172 | −1.15110 | ||||||||
\(663\) | 17.6198 | 0.684294 | ||||||||
\(664\) | 25.2901 | 0.981447 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.332673 | 0.0128908 | ||||||||
\(667\) | −9.94718 | −0.385156 | ||||||||
\(668\) | −3.35501 | −0.129809 | ||||||||
\(669\) | −20.6736 | −0.799287 | ||||||||
\(670\) | −19.8293 | −0.766073 | ||||||||
\(671\) | −7.69302 | −0.296986 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.96774 | −0.230039 | −0.115020 | − | 0.993363i | \(-0.536693\pi\) | ||||
−0.115020 | + | 0.993363i | \(0.536693\pi\) | |||||||
\(674\) | 10.7193 | 0.412892 | ||||||||
\(675\) | −3.30720 | −0.127294 | ||||||||
\(676\) | 1.51149 | 0.0581341 | ||||||||
\(677\) | 19.9773 | 0.767789 | 0.383894 | − | 0.923377i | \(-0.374583\pi\) | ||||
0.383894 | + | 0.923377i | \(0.374583\pi\) | |||||||
\(678\) | −15.7894 | −0.606388 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 13.7309 | 0.526558 | ||||||||
\(681\) | −17.2707 | −0.661813 | ||||||||
\(682\) | 10.1229 | 0.387627 | ||||||||
\(683\) | 23.9569 | 0.916686 | 0.458343 | − | 0.888775i | \(-0.348443\pi\) | ||||
0.458343 | + | 0.888775i | \(0.348443\pi\) | |||||||
\(684\) | 1.27440 | 0.0487278 | ||||||||
\(685\) | 6.45845 | 0.246765 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.57141 | 0.327020 | ||||||||
\(688\) | −1.41629 | −0.0539956 | ||||||||
\(689\) | 23.9168 | 0.911156 | ||||||||
\(690\) | 6.29392 | 0.239605 | ||||||||
\(691\) | 40.9688 | 1.55853 | 0.779264 | − | 0.626696i | \(-0.215593\pi\) | ||||
0.779264 | + | 0.626696i | \(0.215593\pi\) | |||||||
\(692\) | 1.03029 | 0.0391656 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 47.4095 | 1.79964 | ||||||||
\(695\) | 15.8164 | 0.599949 | ||||||||
\(696\) | 8.10984 | 0.307403 | ||||||||
\(697\) | −4.00199 | −0.151586 | ||||||||
\(698\) | 51.3003 | 1.94175 | ||||||||
\(699\) | 16.0030 | 0.605290 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.7542 | 1.69034 | 0.845171 | − | 0.534495i | \(-0.179498\pi\) | ||||
0.845171 | + | 0.534495i | \(0.179498\pi\) | |||||||
\(702\) | −6.58465 | −0.248522 | ||||||||
\(703\) | 1.19732 | 0.0451579 | ||||||||
\(704\) | −5.13379 | −0.193487 | ||||||||
\(705\) | −4.95428 | −0.186589 | ||||||||
\(706\) | 23.1905 | 0.872787 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.453447 | −0.0170416 | ||||||||
\(709\) | −41.9685 | −1.57616 | −0.788081 | − | 0.615572i | \(-0.788925\pi\) | ||||
−0.788081 | + | 0.615572i | \(0.788925\pi\) | |||||||
\(710\) | 0.387647 | 0.0145481 | ||||||||
\(711\) | −12.7948 | −0.479844 | ||||||||
\(712\) | −10.8664 | −0.407237 | ||||||||
\(713\) | −29.1778 | −1.09272 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.29812 | 0.160741 | ||||||||
\(716\) | −0.815375 | −0.0304720 | ||||||||
\(717\) | 9.31197 | 0.347762 | ||||||||
\(718\) | −40.5240 | −1.51234 | ||||||||
\(719\) | −13.0723 | −0.487516 | −0.243758 | − | 0.969836i | \(-0.578380\pi\) | ||||
−0.243758 | + | 0.969836i | \(0.578380\pi\) | |||||||
\(720\) | −5.74745 | −0.214195 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 14.9168 | 0.555146 | ||||||||
\(723\) | 13.4089 | 0.498682 | ||||||||
\(724\) | 4.97614 | 0.184937 | ||||||||
\(725\) | 10.1707 | 0.377731 | ||||||||
\(726\) | −15.6094 | −0.579318 | ||||||||
\(727\) | −12.7634 | −0.473367 | −0.236683 | − | 0.971587i | \(-0.576060\pi\) | ||||
−0.236683 | + | 0.971587i | \(0.576060\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −27.6506 | −1.02339 | ||||||||
\(731\) | −1.28309 | −0.0474568 | ||||||||
\(732\) | 2.42742 | 0.0897200 | ||||||||
\(733\) | −28.9108 | −1.06785 | −0.533923 | − | 0.845533i | \(-0.679283\pi\) | ||||
−0.533923 | + | 0.845533i | \(0.679283\pi\) | |||||||
\(734\) | −22.8633 | −0.843899 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.31005 | −0.158870 | ||||||||
\(737\) | 7.64626 | 0.281653 | ||||||||
\(738\) | 1.49558 | 0.0550530 | ||||||||
\(739\) | −23.0344 | −0.847336 | −0.423668 | − | 0.905818i | \(-0.639258\pi\) | ||||
−0.423668 | + | 0.905818i | \(0.639258\pi\) | |||||||
\(740\) | 0.0685190 | 0.00251881 | ||||||||
\(741\) | −23.6988 | −0.870599 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.6971 | −0.759304 | −0.379652 | − | 0.925129i | \(-0.623956\pi\) | ||||
−0.379652 | + | 0.925129i | \(0.623956\pi\) | |||||||
\(744\) | 23.7884 | 0.872125 | ||||||||
\(745\) | −19.3552 | −0.709121 | ||||||||
\(746\) | −8.09990 | −0.296558 | ||||||||
\(747\) | −9.59023 | −0.350888 | ||||||||
\(748\) | 0.710935 | 0.0259944 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −16.1647 | −0.590250 | ||||||||
\(751\) | 12.8521 | 0.468980 | 0.234490 | − | 0.972118i | \(-0.424658\pi\) | ||||
0.234490 | + | 0.972118i | \(0.424658\pi\) | |||||||
\(752\) | 16.8210 | 0.613398 | ||||||||
\(753\) | 0.0581644 | 0.00211963 | ||||||||
\(754\) | 20.2499 | 0.737459 | ||||||||
\(755\) | −0.392333 | −0.0142784 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.1896 | 0.733805 | 0.366902 | − | 0.930259i | \(-0.380418\pi\) | ||||
0.366902 | + | 0.930259i | \(0.380418\pi\) | |||||||
\(758\) | 47.2196 | 1.71509 | ||||||||
\(759\) | −2.42696 | −0.0880930 | ||||||||
\(760\) | −18.4683 | −0.669917 | ||||||||
\(761\) | −29.9222 | −1.08468 | −0.542339 | − | 0.840160i | \(-0.682461\pi\) | ||||
−0.542339 | + | 0.840160i | \(0.682461\pi\) | |||||||
\(762\) | 4.50181 | 0.163083 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.17105 | 0.150903 | ||||||||
\(765\) | −5.20689 | −0.188256 | ||||||||
\(766\) | −27.6495 | −0.999016 | ||||||||
\(767\) | 8.43235 | 0.304475 | ||||||||
\(768\) | 5.60566 | 0.202277 | ||||||||
\(769\) | 38.0982 | 1.37386 | 0.686929 | − | 0.726725i | \(-0.258959\pi\) | ||||
0.686929 | + | 0.726725i | \(0.258959\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.6323 | 0.707039 | ||||||||
\(772\) | −5.78861 | −0.208337 | ||||||||
\(773\) | −42.3581 | −1.52352 | −0.761758 | − | 0.647861i | \(-0.775664\pi\) | ||||
−0.761758 | + | 0.647861i | \(0.775664\pi\) | |||||||
\(774\) | 0.479501 | 0.0172353 | ||||||||
\(775\) | 29.8335 | 1.07165 | ||||||||
\(776\) | 16.3430 | 0.586680 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.434489 | 0.0155772 | ||||||||
\(779\) | 5.38274 | 0.192857 | ||||||||
\(780\) | −1.35621 | −0.0485601 | ||||||||
\(781\) | −0.149478 | −0.00534875 | ||||||||
\(782\) | −19.3595 | −0.692296 | ||||||||
\(783\) | −3.07532 | −0.109903 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.11985 | 0.218427 | ||||||||
\(786\) | 19.2951 | 0.688235 | ||||||||
\(787\) | 28.1447 | 1.00325 | 0.501625 | − | 0.865085i | \(-0.332736\pi\) | ||||
0.501625 | + | 0.865085i | \(0.332736\pi\) | |||||||
\(788\) | −2.57495 | −0.0917287 | ||||||||
\(789\) | −1.71718 | −0.0611334 | ||||||||
\(790\) | −24.8970 | −0.885795 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.97868 | 0.0703092 | ||||||||
\(793\) | −45.1406 | −1.60299 | ||||||||
\(794\) | −50.1022 | −1.77806 | ||||||||
\(795\) | −7.06775 | −0.250667 | ||||||||
\(796\) | 2.22185 | 0.0787512 | ||||||||
\(797\) | −6.52825 | −0.231242 | −0.115621 | − | 0.993293i | \(-0.536886\pi\) | ||||
−0.115621 | + | 0.993293i | \(0.536886\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.2389 | 0.539115 | ||||||||
\(800\) | 4.40690 | 0.155808 | ||||||||
\(801\) | 4.12065 | 0.145596 | ||||||||
\(802\) | 14.0556 | 0.496321 | ||||||||
\(803\) | 10.6622 | 0.376260 | ||||||||
\(804\) | −2.41266 | −0.0850881 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 59.3986 | 2.09223 | ||||||||
\(807\) | 13.1932 | 0.464423 | ||||||||
\(808\) | −45.1014 | −1.58666 | ||||||||
\(809\) | −10.0066 | −0.351813 | −0.175906 | − | 0.984407i | \(-0.556286\pi\) | ||||
−0.175906 | + | 0.984407i | \(0.556286\pi\) | |||||||
\(810\) | 1.94586 | 0.0683706 | ||||||||
\(811\) | −40.0564 | −1.40657 | −0.703286 | − | 0.710907i | \(-0.748284\pi\) | ||||
−0.703286 | + | 0.710907i | \(0.748284\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.787682 | −0.0276252 | ||||||||
\(814\) | −0.249615 | −0.00874899 | ||||||||
\(815\) | −7.34333 | −0.257226 | ||||||||
\(816\) | 17.6786 | 0.618876 | ||||||||
\(817\) | 1.72578 | 0.0603772 | ||||||||
\(818\) | −32.8934 | −1.15009 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.308037 | 0.0107571 | ||||||||
\(821\) | −33.9009 | −1.18315 | −0.591574 | − | 0.806250i | \(-0.701493\pi\) | ||||
−0.591574 | + | 0.806250i | \(0.701493\pi\) | |||||||
\(822\) | 7.42395 | 0.258940 | ||||||||
\(823\) | 24.9240 | 0.868797 | 0.434399 | − | 0.900721i | \(-0.356961\pi\) | ||||
0.434399 | + | 0.900721i | \(0.356961\pi\) | |||||||
\(824\) | −22.6483 | −0.788990 | ||||||||
\(825\) | 2.48150 | 0.0863947 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.7154 | −0.963759 | −0.481880 | − | 0.876237i | \(-0.660046\pi\) | ||||
−0.481880 | + | 0.876237i | \(0.660046\pi\) | |||||||
\(828\) | 0.765791 | 0.0266131 | ||||||||
\(829\) | 6.18951 | 0.214971 | 0.107485 | − | 0.994207i | \(-0.465720\pi\) | ||||
0.107485 | + | 0.994207i | \(0.465720\pi\) | |||||||
\(830\) | −18.6612 | −0.647741 | ||||||||
\(831\) | 9.56370 | 0.331761 | ||||||||
\(832\) | −30.1237 | −1.04435 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 18.1808 | 0.629551 | ||||||||
\(835\) | −18.4372 | −0.638045 | ||||||||
\(836\) | −0.956220 | −0.0330715 | ||||||||
\(837\) | −9.02077 | −0.311803 | ||||||||
\(838\) | 18.8141 | 0.649922 | ||||||||
\(839\) | 5.58456 | 0.192801 | 0.0964003 | − | 0.995343i | \(-0.469267\pi\) | ||||
0.0964003 | + | 0.995343i | \(0.469267\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.5424 | −0.673876 | ||||||||
\(842\) | −7.55188 | −0.260255 | ||||||||
\(843\) | 7.48602 | 0.257832 | ||||||||
\(844\) | −4.28729 | −0.147574 | ||||||||
\(845\) | 8.30627 | 0.285744 | ||||||||
\(846\) | −5.69492 | −0.195795 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 23.9967 | 0.824049 | ||||||||
\(849\) | 30.8025 | 1.05714 | ||||||||
\(850\) | 19.7946 | 0.678949 | ||||||||
\(851\) | 0.719477 | 0.0246634 | ||||||||
\(852\) | 0.0471656 | 0.00161587 | ||||||||
\(853\) | 16.2181 | 0.555299 | 0.277649 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277649 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.00336 | 0.239510 | ||||||||
\(856\) | 44.4575 | 1.51953 | ||||||||
\(857\) | −54.1267 | −1.84893 | −0.924466 | − | 0.381265i | \(-0.875489\pi\) | ||||
−0.924466 | + | 0.381265i | \(0.875489\pi\) | |||||||
\(858\) | 4.94067 | 0.168672 | ||||||||
\(859\) | 47.8992 | 1.63430 | 0.817149 | − | 0.576426i | \(-0.195553\pi\) | ||||
0.817149 | + | 0.576426i | \(0.195553\pi\) | |||||||
\(860\) | 0.0987606 | 0.00336771 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.1687 | −0.618827 | ||||||||
\(863\) | 54.5776 | 1.85784 | 0.928922 | − | 0.370275i | \(-0.120737\pi\) | ||||
0.928922 | + | 0.370275i | \(0.120737\pi\) | |||||||
\(864\) | −1.33252 | −0.0453331 | ||||||||
\(865\) | 5.66186 | 0.192509 | ||||||||
\(866\) | −28.4513 | −0.966815 | ||||||||
\(867\) | −0.984056 | −0.0334203 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.60037 | 0.325670 | ||||||||
\(870\) | −5.98415 | −0.202882 | ||||||||
\(871\) | 44.8662 | 1.52023 | ||||||||
\(872\) | −25.4781 | −0.862798 | ||||||||
\(873\) | −6.19741 | −0.209751 | ||||||||
\(874\) | 26.0389 | 0.880778 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.36429 | −0.113669 | ||||||||
\(877\) | −8.01308 | −0.270582 | −0.135291 | − | 0.990806i | \(-0.543197\pi\) | ||||
−0.135291 | + | 0.990806i | \(0.543197\pi\) | |||||||
\(878\) | −34.8801 | −1.17715 | ||||||||
\(879\) | 1.19896 | 0.0404399 | ||||||||
\(880\) | 4.31249 | 0.145374 | ||||||||
\(881\) | 16.7655 | 0.564842 | 0.282421 | − | 0.959291i | \(-0.408862\pi\) | ||||
0.282421 | + | 0.959291i | \(0.408862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.5687 | −1.49986 | −0.749928 | − | 0.661520i | \(-0.769912\pi\) | ||||
−0.749928 | + | 0.661520i | \(0.769912\pi\) | |||||||
\(884\) | 4.17158 | 0.140305 | ||||||||
\(885\) | −2.49188 | −0.0837638 | ||||||||
\(886\) | 37.2490 | 1.25141 | ||||||||
\(887\) | 16.0532 | 0.539015 | 0.269508 | − | 0.962998i | \(-0.413139\pi\) | ||||
0.269508 | + | 0.962998i | \(0.413139\pi\) | |||||||
\(888\) | −0.586583 | −0.0196844 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.01821 | 0.268771 | ||||||||
\(891\) | −0.750331 | −0.0251370 | ||||||||
\(892\) | −4.89460 | −0.163883 | ||||||||
\(893\) | −20.4966 | −0.685893 | ||||||||
\(894\) | −22.2488 | −0.744110 | ||||||||
\(895\) | −4.48083 | −0.149778 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.2407 | −0.475485 | ||||||||
\(898\) | −37.7599 | −1.26006 | ||||||||
\(899\) | 27.7418 | 0.925240 | ||||||||
\(900\) | −0.783000 | −0.0261000 | ||||||||
\(901\) | 21.7398 | 0.724257 | ||||||||
\(902\) | −1.12218 | −0.0373645 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.8406 | 0.925964 | ||||||||
\(905\) | 27.3460 | 0.909013 | ||||||||
\(906\) | −0.450984 | −0.0149829 | ||||||||
\(907\) | 0.619038 | 0.0205548 | 0.0102774 | − | 0.999947i | \(-0.496729\pi\) | ||||
0.0102774 | + | 0.999947i | \(0.496729\pi\) | |||||||
\(908\) | −4.08893 | −0.135696 | ||||||||
\(909\) | 17.1028 | 0.567265 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.0071 | −0.430944 | −0.215472 | − | 0.976510i | \(-0.569129\pi\) | ||||
−0.215472 | + | 0.976510i | \(0.569129\pi\) | |||||||
\(912\) | −23.7780 | −0.787370 | ||||||||
\(913\) | 7.19585 | 0.238148 | ||||||||
\(914\) | −19.5389 | −0.646290 | ||||||||
\(915\) | 13.3397 | 0.440997 | ||||||||
\(916\) | 2.02933 | 0.0670510 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.98530 | −0.197544 | ||||||||
\(919\) | 25.0989 | 0.827936 | 0.413968 | − | 0.910291i | \(-0.364142\pi\) | ||||
0.413968 | + | 0.910291i | \(0.364142\pi\) | |||||||
\(920\) | −11.0977 | −0.365881 | ||||||||
\(921\) | −14.2847 | −0.470695 | ||||||||
\(922\) | −47.4509 | −1.56271 | ||||||||
\(923\) | −0.877098 | −0.0288700 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.735646 | −0.0241879 | ||||||||
\(926\) | −5.50797 | −0.181003 | ||||||||
\(927\) | 8.58842 | 0.282081 | ||||||||
\(928\) | 4.09792 | 0.134521 | ||||||||
\(929\) | 57.5537 | 1.88828 | 0.944138 | − | 0.329551i | \(-0.106897\pi\) | ||||
0.944138 | + | 0.329551i | \(0.106897\pi\) | |||||||
\(930\) | −17.5532 | −0.575591 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.78881 | 0.124107 | ||||||||
\(933\) | 0.370661 | 0.0121349 | ||||||||
\(934\) | −43.9786 | −1.43902 | ||||||||
\(935\) | 3.90689 | 0.127769 | ||||||||
\(936\) | 11.6103 | 0.379496 | ||||||||
\(937\) | 55.4319 | 1.81088 | 0.905440 | − | 0.424474i | \(-0.139541\pi\) | ||||
0.905440 | + | 0.424474i | \(0.139541\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.9391 | 0.781223 | ||||||||
\(940\) | −1.17296 | −0.0382576 | ||||||||
\(941\) | −28.9348 | −0.943247 | −0.471623 | − | 0.881800i | \(-0.656332\pi\) | ||||
−0.471623 | + | 0.881800i | \(0.656332\pi\) | |||||||
\(942\) | 7.03473 | 0.229204 | ||||||||
\(943\) | 3.23452 | 0.105330 | ||||||||
\(944\) | 8.46054 | 0.275367 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.359785 | −0.0116976 | ||||||||
\(947\) | 19.5413 | 0.635006 | 0.317503 | − | 0.948257i | \(-0.397156\pi\) | ||||
0.317503 | + | 0.948257i | \(0.397156\pi\) | |||||||
\(948\) | −3.02926 | −0.0983857 | ||||||||
\(949\) | 62.5628 | 2.03087 | ||||||||
\(950\) | −26.6240 | −0.863798 | ||||||||
\(951\) | −6.14198 | −0.199167 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.2403 | −0.979580 | −0.489790 | − | 0.871840i | \(-0.662927\pi\) | ||||
−0.489790 | + | 0.871840i | \(0.662927\pi\) | |||||||
\(954\) | −8.12434 | −0.263035 | ||||||||
\(955\) | 22.9217 | 0.741728 | ||||||||
\(956\) | 2.20466 | 0.0713040 | ||||||||
\(957\) | 2.30751 | 0.0745912 | ||||||||
\(958\) | 25.8478 | 0.835103 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.90200 | 0.287311 | ||||||||
\(961\) | 50.3742 | 1.62498 | ||||||||
\(962\) | −1.46467 | −0.0472229 | ||||||||
\(963\) | −16.8587 | −0.543263 | ||||||||
\(964\) | 3.17463 | 0.102248 | ||||||||
\(965\) | −31.8109 | −1.02403 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.3054 | 1.19966 | 0.599831 | − | 0.800127i | \(-0.295234\pi\) | ||||
0.599831 | + | 0.800127i | \(0.295234\pi\) | |||||||
\(968\) | 27.5231 | 0.884626 | ||||||||
\(969\) | −21.5417 | −0.692019 | ||||||||
\(970\) | −12.0593 | −0.387201 | ||||||||
\(971\) | −14.7476 | −0.473274 | −0.236637 | − | 0.971598i | \(-0.576045\pi\) | ||||
−0.236637 | + | 0.971598i | \(0.576045\pi\) | |||||||
\(972\) | 0.236756 | 0.00759395 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −59.8239 | −1.91688 | ||||||||
\(975\) | 14.5608 | 0.466318 | ||||||||
\(976\) | −45.2915 | −1.44974 | ||||||||
\(977\) | −29.6133 | −0.947413 | −0.473706 | − | 0.880683i | \(-0.657084\pi\) | ||||
−0.473706 | + | 0.880683i | \(0.657084\pi\) | |||||||
\(978\) | −8.44112 | −0.269917 | ||||||||
\(979\) | −3.09185 | −0.0988160 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.66152 | 0.308469 | ||||||||
\(982\) | 13.7229 | 0.437914 | ||||||||
\(983\) | −43.6571 | −1.39245 | −0.696223 | − | 0.717826i | \(-0.745137\pi\) | ||||
−0.696223 | + | 0.717826i | \(0.745137\pi\) | |||||||
\(984\) | −2.63707 | −0.0840667 | ||||||||
\(985\) | −14.1504 | −0.450870 | ||||||||
\(986\) | 18.4067 | 0.586189 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.61084 | −0.178505 | ||||||||
\(989\) | 1.03703 | 0.0329755 | ||||||||
\(990\) | −1.46004 | −0.0464031 | ||||||||
\(991\) | −34.3757 | −1.09198 | −0.545990 | − | 0.837792i | \(-0.683846\pi\) | ||||
−0.545990 | + | 0.837792i | \(0.683846\pi\) | |||||||
\(992\) | 12.0203 | 0.381646 | ||||||||
\(993\) | −19.8031 | −0.628434 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.2100 | 0.387083 | ||||||||
\(996\) | −2.27054 | −0.0719449 | ||||||||
\(997\) | −8.09059 | −0.256232 | −0.128116 | − | 0.991759i | \(-0.540893\pi\) | ||||
−0.128116 | + | 0.991759i | \(0.540893\pi\) | |||||||
\(998\) | 49.8613 | 1.57833 | ||||||||
\(999\) | 0.222437 | 0.00703761 |
(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 | 6027.2.a.bm.1.13 | yes | 16 | |
7.6 | odd | 2 | 6027.2.a.bl.1.13 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bl.1.13 | ✓ | 16 | 7.6 | odd | 2 | ||
6027.2.a.bm.1.13 | yes | 16 | 1.1 | even | 1 | trivial |