Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,4,Mod(1,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.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: | \(38.2332376837\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 19x^{3} + 4x^{2} + 81x + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 72) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.80998\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 12.3969 | 1.10881 | 0.554405 | − | 0.832247i | \(-0.312946\pi\) | ||||
0.554405 | + | 0.832247i | \(0.312946\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 30.6325 | 1.65400 | 0.827001 | − | 0.562200i | \(-0.190045\pi\) | ||||
0.827001 | + | 0.562200i | \(0.190045\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.944238 | 0.0258817 | 0.0129408 | − | 0.999916i | \(-0.495881\pi\) | ||||
0.0129408 | + | 0.999916i | \(0.495881\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 90.8738 | 1.93876 | 0.969379 | − | 0.245568i | \(-0.0789745\pi\) | ||||
0.969379 | + | 0.245568i | \(0.0789745\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 53.4025 | 0.761882 | 0.380941 | − | 0.924599i | \(-0.375600\pi\) | ||||
0.380941 | + | 0.924599i | \(0.375600\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −70.4876 | −0.851104 | −0.425552 | − | 0.904934i | \(-0.639920\pi\) | ||||
−0.425552 | + | 0.904934i | \(0.639920\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 97.1887 | 0.881098 | 0.440549 | − | 0.897729i | \(-0.354784\pi\) | ||||
0.440549 | + | 0.897729i | \(0.354784\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 28.6823 | 0.229459 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −156.610 | −1.00282 | −0.501410 | − | 0.865210i | \(-0.667185\pi\) | ||||
−0.501410 | + | 0.865210i | \(0.667185\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −43.0772 | −0.249577 | −0.124789 | − | 0.992183i | \(-0.539825\pi\) | ||||
−0.124789 | + | 0.992183i | \(0.539825\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 379.748 | 1.83397 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −64.1933 | −0.285225 | −0.142612 | − | 0.989779i | \(-0.545550\pi\) | ||||
−0.142612 | + | 0.989779i | \(0.545550\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −85.0644 | −0.324020 | −0.162010 | − | 0.986789i | \(-0.551798\pi\) | ||||
−0.162010 | + | 0.986789i | \(0.551798\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 167.284 | 0.593271 | 0.296635 | − | 0.954991i | \(-0.404135\pi\) | ||||
0.296635 | + | 0.954991i | \(0.404135\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −558.822 | −1.73431 | −0.867156 | − | 0.498037i | \(-0.834054\pi\) | ||||
−0.867156 | + | 0.498037i | \(0.834054\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 595.353 | 1.73572 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −503.158 | −1.30404 | −0.652020 | − | 0.758202i | \(-0.726078\pi\) | ||||
−0.652020 | + | 0.758202i | \(0.726078\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.7056 | 0.0286979 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −61.7789 | −0.136321 | −0.0681604 | − | 0.997674i | \(-0.521713\pi\) | ||||
−0.0681604 | + | 0.997674i | \(0.521713\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 269.008 | 0.564638 | 0.282319 | − | 0.959321i | \(-0.408896\pi\) | ||||
0.282319 | + | 0.959321i | \(0.408896\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1126.55 | 2.14971 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −126.506 | −0.230673 | −0.115337 | − | 0.993326i | \(-0.536795\pi\) | ||||
−0.115337 | + | 0.993326i | \(0.536795\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −854.343 | −1.42805 | −0.714027 | − | 0.700118i | \(-0.753131\pi\) | ||||
−0.714027 | + | 0.700118i | \(0.753131\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 404.568 | 0.648645 | 0.324323 | − | 0.945947i | \(-0.394864\pi\) | ||||
0.324323 | + | 0.945947i | \(0.394864\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 28.9244 | 0.0428084 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 646.318 | 0.920462 | 0.460231 | − | 0.887799i | \(-0.347767\pi\) | ||||
0.460231 | + | 0.887799i | \(0.347767\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −822.859 | −1.08820 | −0.544099 | − | 0.839021i | \(-0.683128\pi\) | ||||
−0.544099 | + | 0.839021i | \(0.683128\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 662.023 | 0.844782 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1185.67 | 1.41214 | 0.706070 | − | 0.708142i | \(-0.250467\pi\) | ||||
0.706070 | + | 0.708142i | \(0.250467\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2783.70 | 3.20671 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −873.826 | −0.943712 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 130.566 | 0.136670 | 0.0683350 | − | 0.997662i | \(-0.478231\pi\) | ||||
0.0683350 | + | 0.997662i | \(0.478231\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1553.31 | 1.53030 | 0.765148 | − | 0.643855i | \(-0.222666\pi\) | ||||
0.765148 | + | 0.643855i | \(0.222666\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 189.382 | 0.181168 | 0.0905842 | − | 0.995889i | \(-0.471127\pi\) | ||||
0.0905842 | + | 0.995889i | \(0.471127\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −179.800 | −0.162448 | −0.0812239 | − | 0.996696i | \(-0.525883\pi\) | ||||
−0.0812239 | + | 0.996696i | \(0.525883\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1720.46 | 1.51184 | 0.755918 | − | 0.654666i | \(-0.227191\pi\) | ||||
0.755918 | + | 0.654666i | \(0.227191\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1279.48 | 1.06517 | 0.532583 | − | 0.846378i | \(-0.321221\pi\) | ||||
0.532583 | + | 0.846378i | \(0.321221\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1204.84 | 0.976969 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1635.85 | 1.26015 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.11 | −0.999330 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1194.04 | −0.854384 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1583.06 | −1.10609 | −0.553047 | − | 0.833150i | \(-0.686535\pi\) | ||||
−0.553047 | + | 0.833150i | \(0.686535\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −763.730 | −0.509370 | −0.254685 | − | 0.967024i | \(-0.581972\pi\) | ||||
−0.254685 | + | 0.967024i | \(0.581972\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2159.22 | −1.40773 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −965.233 | −0.601937 | −0.300969 | − | 0.953634i | \(-0.597310\pi\) | ||||
−0.300969 | + | 0.953634i | \(0.597310\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1405.25 | 0.857496 | 0.428748 | − | 0.903424i | \(-0.358955\pi\) | ||||
0.428748 | + | 0.903424i | \(0.358955\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 85.8066 | 0.0501784 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1941.48 | −1.11194 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 358.567 | 0.197148 | 0.0985738 | − | 0.995130i | \(-0.468572\pi\) | ||||
0.0985738 | + | 0.995130i | \(0.468572\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −762.546 | −0.410961 | −0.205481 | − | 0.978661i | \(-0.565876\pi\) | ||||
−0.205481 | + | 0.978661i | \(0.565876\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −534.022 | −0.276733 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 939.097 | 0.477376 | 0.238688 | − | 0.971096i | \(-0.423283\pi\) | ||||
0.238688 | + | 0.971096i | \(0.423283\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2977.14 | 1.45734 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −988.378 | −0.474943 | −0.237472 | − | 0.971394i | \(-0.576319\pi\) | ||||
−0.237472 | + | 0.971394i | \(0.576319\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1729.58 | 0.801432 | 0.400716 | − | 0.916202i | \(-0.368761\pi\) | ||||
0.400716 | + | 0.916202i | \(0.368761\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6061.05 | 2.75879 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3557.68 | −1.56350 | −0.781750 | − | 0.623593i | \(-0.785672\pi\) | ||||
−0.781750 | + | 0.623593i | \(0.785672\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 878.613 | 0.379525 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3718.32 | −1.55263 | −0.776313 | − | 0.630348i | \(-0.782912\pi\) | ||||
−0.776313 | + | 0.630348i | \(0.782912\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 849.530 | 0.348868 | 0.174434 | − | 0.984669i | \(-0.444190\pi\) | ||||
0.174434 | + | 0.984669i | \(0.444190\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −795.796 | −0.316260 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 50.4247 | 0.0197188 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2344.71 | −0.888259 | −0.444130 | − | 0.895963i | \(-0.646487\pi\) | ||||
−0.444130 | + | 0.895963i | \(0.646487\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 644.601 | 0.240411 | 0.120206 | − | 0.992749i | \(-0.461645\pi\) | ||||
0.120206 | + | 0.992749i | \(0.461645\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1697.78 | 0.614018 | 0.307009 | − | 0.951707i | \(-0.400672\pi\) | ||||
0.307009 | + | 0.951707i | \(0.400672\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1085.70 | 0.386748 | 0.193374 | − | 0.981125i | \(-0.438057\pi\) | ||||
0.193374 | + | 0.981125i | \(0.438057\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4797.37 | −1.65867 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1054.53 | −0.359277 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −66.5571 | −0.0220280 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4665.49 | 1.52221 | 0.761104 | − | 0.648630i | \(-0.224658\pi\) | ||||
0.761104 | + | 0.648630i | \(0.224658\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2073.80 | 0.657824 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1319.56 | −0.412801 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4852.89 | 1.47711 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5353.59 | −1.60764 | −0.803818 | − | 0.594876i | \(-0.797201\pi\) | ||||
−0.803818 | + | 0.594876i | \(0.797201\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3710.51 | −1.08491 | −0.542456 | − | 0.840084i | \(-0.682506\pi\) | ||||
−0.542456 | + | 0.840084i | \(0.682506\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3587.12 | −1.03512 | −0.517562 | − | 0.855646i | \(-0.673160\pi\) | ||||
−0.517562 | + | 0.855646i | \(0.673160\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5513.12 | 1.55011 | 0.775057 | − | 0.631892i | \(-0.217721\pi\) | ||||
0.775057 | + | 0.631892i | \(0.217721\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6927.65 | −1.92302 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1160.40 | −0.314058 | −0.157029 | − | 0.987594i | \(-0.550192\pi\) | ||||
−0.157029 | + | 0.987594i | \(0.550192\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 108.331 | 0.0289552 | 0.0144776 | − | 0.999895i | \(-0.495391\pi\) | ||||
0.0144776 | + | 0.999895i | \(0.495391\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7380.51 | 1.92459 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6405.48 | −1.65009 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3819.74 | −0.960558 | −0.480279 | − | 0.877116i | \(-0.659465\pi\) | ||||
−0.480279 | + | 0.877116i | \(0.659465\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 91.7693 | 0.0228043 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1840.57 | 0.446737 | 0.223368 | − | 0.974734i | \(-0.428295\pi\) | ||||
0.223368 | + | 0.974734i | \(0.428295\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1966.40 | −0.471762 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1840.16 | 0.431442 | 0.215721 | − | 0.976455i | \(-0.430790\pi\) | ||||
0.215721 | + | 0.976455i | \(0.430790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6237.59 | −1.44593 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5336.35 | −1.20953 | −0.604764 | − | 0.796405i | \(-0.706732\pi\) | ||||
−0.604764 | + | 0.796405i | \(0.706732\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1649.56 | −0.369755 | −0.184878 | − | 0.982762i | \(-0.559189\pi\) | ||||
−0.184878 | + | 0.982762i | \(0.559189\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 27.0830 | 0.00593878 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3627.20 | −0.786778 | −0.393389 | − | 0.919372i | \(-0.628697\pi\) | ||||
−0.393389 | + | 0.919372i | \(0.628697\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1905.22 | −0.404468 | −0.202234 | − | 0.979337i | \(-0.564820\pi\) | ||||
−0.202234 | + | 0.979337i | \(0.564820\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6015.01 | −1.26345 | −0.631723 | − | 0.775194i | \(-0.717652\pi\) | ||||
−0.631723 | + | 0.775194i | \(0.717652\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2605.74 | −0.535930 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2061.18 | −0.419535 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6129.45 | 1.22214 | 0.611068 | − | 0.791578i | \(-0.290740\pi\) | ||||
0.611068 | + | 0.791578i | \(0.290740\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −765.865 | −0.151154 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8831.91 | 1.70824 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5124.35 | 0.981271 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3334.85 | 0.626076 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3453.04 | 0.641939 | 0.320970 | − | 0.947090i | \(-0.395991\pi\) | ||||
0.320970 | + | 0.947090i | \(0.395991\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3391.61 | −0.618395 | −0.309197 | − | 0.950998i | \(-0.600060\pi\) | ||||
−0.309197 | + | 0.950998i | \(0.600060\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6189.64 | −1.11776 | −0.558880 | − | 0.829248i | \(-0.688769\pi\) | ||||
−0.558880 | + | 0.829248i | \(0.688769\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6057.64 | 1.07328 | 0.536642 | − | 0.843810i | \(-0.319693\pi\) | ||||
0.536642 | + | 0.843810i | \(0.319693\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −147.877 | −0.0259547 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3764.21 | −0.648441 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2606.47 | 0.444865 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17118.2 | −2.86855 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1080.21 | 0.179376 | 0.0896881 | − | 0.995970i | \(-0.471413\pi\) | ||||
0.0896881 | + | 0.995970i | \(0.471413\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1568.27 | −0.255773 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 304.332 | 0.0491929 | 0.0245965 | − | 0.999697i | \(-0.492170\pi\) | ||||
0.0245965 | + | 0.999697i | \(0.492170\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −40.6751 | −0.00645948 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7730.22 | 1.21689 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7765.41 | 1.20135 | 0.600676 | − | 0.799493i | \(-0.294898\pi\) | ||||
0.600676 | + | 0.799493i | \(0.294898\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8139.66 | −1.24844 | −0.624221 | − | 0.781248i | \(-0.714583\pi\) | ||||
−0.624221 | + | 0.781248i | \(0.714583\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1467.59 | 0.221280 | 0.110640 | − | 0.993861i | \(-0.464710\pi\) | ||||
0.110640 | + | 0.993861i | \(0.464710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10591.2 | −1.58344 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7409.40 | 1.08928 | 0.544642 | − | 0.838669i | \(-0.316665\pi\) | ||||
0.544642 | + | 0.838669i | \(0.316665\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1890.49 | −0.275622 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5015.38 | 0.719224 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10865.4 | 1.54543 | 0.772713 | − | 0.634756i | \(-0.218899\pi\) | ||||
0.772713 | + | 0.634756i | \(0.218899\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15413.0 | −2.15688 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7075.08 | −0.982128 | −0.491064 | − | 0.871124i | \(-0.663392\pi\) | ||||
−0.491064 | + | 0.871124i | \(0.663392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14231.8 | −1.94423 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1585.21 | 0.214847 | 0.107423 | − | 0.994213i | \(-0.465740\pi\) | ||||
0.107423 | + | 0.994213i | \(0.465740\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4616.39 | −0.615891 | −0.307946 | − | 0.951404i | \(-0.599641\pi\) | ||||
−0.307946 | + | 0.951404i | \(0.599641\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 358.572 | 0.0474663 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3829.85 | −0.499180 | −0.249590 | − | 0.968352i | \(-0.580296\pi\) | ||||
−0.249590 | + | 0.968352i | \(0.580296\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5190.12 | 0.671293 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8012.32 | 1.02062 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3476.78 | −0.439532 | −0.219766 | − | 0.975553i | \(-0.570529\pi\) | ||||
−0.219766 | + | 0.975553i | \(0.570529\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 231.262 | 0.0287996 | 0.0143998 | − | 0.999896i | \(-0.495416\pi\) | ||||
0.0143998 | + | 0.999896i | \(0.495416\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3914.59 | −0.483870 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −60.6138 | −0.00738209 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6459.67 | 0.780954 | 0.390477 | − | 0.920613i | \(-0.372310\pi\) | ||||
0.390477 | + | 0.920613i | \(0.372310\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1892.45 | −0.225475 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10200.9 | −1.20660 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5235.99 | −0.610489 | −0.305244 | − | 0.952274i | \(-0.598738\pi\) | ||||
−0.305244 | + | 0.952274i | \(0.598738\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1934.90 | 0.223994 | 0.111997 | − | 0.993709i | \(-0.464275\pi\) | ||||
0.111997 | + | 0.993709i | \(0.464275\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1531.71 | 0.174820 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8240.39 | 0.933912 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4607.87 | 0.514973 | 0.257487 | − | 0.966282i | \(-0.417106\pi\) | ||||
0.257487 | + | 0.966282i | \(0.417106\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15913.6 | −1.76619 | −0.883094 | − | 0.469196i | \(-0.844544\pi\) | ||||
−0.883094 | + | 0.469196i | \(0.844544\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6850.60 | −0.749906 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3143.43 | −0.341749 | −0.170874 | − | 0.985293i | \(-0.554659\pi\) | ||||
−0.170874 | + | 0.985293i | \(0.554659\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5716.29 | −0.613068 | −0.306534 | − | 0.951860i | \(-0.599169\pi\) | ||||
−0.306534 | + | 0.951860i | \(0.599169\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14698.6 | 1.56579 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1282.73 | −0.134823 | −0.0674116 | − | 0.997725i | \(-0.521474\pi\) | ||||
−0.0674116 | + | 0.997725i | \(0.521474\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −80.3211 | −0.00838619 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 34509.1 | 3.55563 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18913.3 | 1.93595 | 0.967973 | − | 0.251053i | \(-0.0807769\pi\) | ||||
0.967973 | + | 0.251053i | \(0.0807769\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4721.62 | 0.477023 | 0.238512 | − | 0.971140i | \(-0.423340\pi\) | ||||
0.238512 | + | 0.971140i | \(0.423340\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4841.35 | 0.485954 | 0.242977 | − | 0.970032i | \(-0.421876\pi\) | ||||
0.242977 | + | 0.970032i | \(0.421876\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5794.52 | 0.574172 | 0.287086 | − | 0.957905i | \(-0.407313\pi\) | ||||
0.287086 | + | 0.957905i | \(0.407313\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3875.19 | −0.381534 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 157.956 | 0.0153548 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2021.75 | −0.195293 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11908.1 | 1.13590 | 0.567949 | − | 0.823064i | \(-0.307737\pi\) | ||||
0.567949 | + | 0.823064i | \(0.307737\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5833.49 | −0.552982 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1618.61 | 0.151541 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1937.87 | 0.180315 | 0.0901574 | − | 0.995928i | \(-0.471263\pi\) | ||||
0.0901574 | + | 0.995928i | \(0.471263\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6917.13 | −0.635776 | −0.317888 | − | 0.948128i | \(-0.602974\pi\) | ||||
−0.317888 | + | 0.948128i | \(0.602974\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8363.37 | −0.764031 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26170.7 | −2.36201 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6456.01 | −0.579179 | −0.289590 | − | 0.957151i | \(-0.593519\pi\) | ||||
−0.289590 | + | 0.957151i | \(0.593519\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3324.68 | 0.294712 | 0.147356 | − | 0.989084i | \(-0.452924\pi\) | ||||
0.147356 | + | 0.989084i | \(0.452924\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19256.1 | 1.69681 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5507.96 | −0.479638 | −0.239819 | − | 0.970818i | \(-0.577088\pi\) | ||||
−0.239819 | + | 0.970818i | \(0.577088\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12392.9 | 1.07286 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2347.74 | 0.200881 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −527.662 | −0.0448869 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18594.3 | 1.56359 | 0.781794 | − | 0.623536i | \(-0.214305\pi\) | ||||
0.781794 | + | 0.623536i | \(0.214305\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9587.79 | −0.801615 | −0.400807 | − | 0.916162i | \(-0.631270\pi\) | ||||
−0.400807 | + | 0.916162i | \(0.631270\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2300.43 | −0.190148 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2721.36 | −0.223667 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7730.13 | −0.628197 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2228.96 | −0.180124 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 562.155 | 0.0449235 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16195.6 | 1.28707 | 0.643535 | − | 0.765416i | \(-0.277467\pi\) | ||||
0.643535 | + | 0.765416i | \(0.277467\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21328.3 | 1.67634 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8954.74 | 0.699958 | 0.349979 | − | 0.936758i | \(-0.386189\pi\) | ||||
0.349979 | + | 0.936758i | \(0.386189\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11039.1 | 0.853505 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19798.4 | 1.52245 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2729.48 | −0.207633 | −0.103817 | − | 0.994596i | \(-0.533106\pi\) | ||||
−0.103817 | + | 0.994596i | \(0.533106\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15201.8 | 1.15021 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23175.6 | −1.73487 | −0.867437 | − | 0.497546i | \(-0.834234\pi\) | ||||
−0.867437 | + | 0.497546i | \(0.834234\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15861.6 | 1.18107 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15079.5 | 1.11101 | 0.555507 | − | 0.831512i | \(-0.312524\pi\) | ||||
0.555507 | + | 0.831512i | \(0.312524\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12295.4 | 0.901134 | 0.450567 | − | 0.892743i | \(-0.351222\pi\) | ||||
0.450567 | + | 0.892743i | \(0.351222\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2787.60 | 0.202175 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17778.8 | 1.28274 | 0.641370 | − | 0.767232i | \(-0.278366\pi\) | ||||
0.641370 | + | 0.767232i | \(0.278366\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25206.3 | −1.79988 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −475.102 | −0.0337508 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6848.86 | 0.481572 | 0.240786 | − | 0.970578i | \(-0.422595\pi\) | ||||
0.240786 | + | 0.970578i | \(0.422595\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3036.41 | 0.212416 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12568.2 | −0.870342 | −0.435171 | − | 0.900348i | \(-0.643312\pi\) | ||||
−0.435171 | + | 0.900348i | \(0.643312\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20279.5 | 1.39727 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20486.0 | 1.39739 | 0.698693 | − | 0.715422i | \(-0.253765\pi\) | ||||
0.698693 | + | 0.715422i | \(0.253765\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4563.59 | −0.309738 | −0.154869 | − | 0.987935i | \(-0.549496\pi\) | ||||
−0.154869 | + | 0.987935i | \(0.549496\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16489.2 | −1.10807 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24197.6 | 1.61804 | 0.809019 | − | 0.587782i | \(-0.199999\pi\) | ||||
0.809019 | + | 0.587782i | \(0.199999\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −50782.3 | −3.36241 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8861.98 | 0.583902 | 0.291951 | − | 0.956433i | \(-0.405696\pi\) | ||||
0.291951 | + | 0.956433i | \(0.405696\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16360.7 | 1.06752 | 0.533759 | − | 0.845637i | \(-0.320779\pi\) | ||||
0.533759 | + | 0.845637i | \(0.320779\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10312.4 | −0.669612 | −0.334806 | − | 0.942287i | \(-0.608671\pi\) | ||||
−0.334806 | + | 0.942287i | \(0.608671\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36320.0 | 2.33568 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18387.6 | −1.17681 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3428.08 | −0.217308 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4335.08 | −0.273497 | −0.136749 | − | 0.990606i | \(-0.543665\pi\) | ||||
−0.136749 | + | 0.990606i | \(0.543665\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19625.0 | −1.22645 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 54102.0 | 3.36515 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18368.9 | 1.13187 | 0.565935 | − | 0.824450i | \(-0.308515\pi\) | ||||
0.565935 | + | 0.824450i | \(0.308515\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8048.87 | −0.493649 | −0.246824 | − | 0.969060i | \(-0.579387\pi\) | ||||
−0.246824 | + | 0.969060i | \(0.579387\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4001.44 | 0.243142 | 0.121571 | − | 0.992583i | \(-0.461207\pi\) | ||||
0.121571 | + | 0.992583i | \(0.461207\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −58.3340 | −0.00352821 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3093.01 | −0.185358 | −0.0926792 | − | 0.995696i | \(-0.529543\pi\) | ||||
−0.0926792 | + | 0.995696i | \(0.529543\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9467.86 | −0.564794 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18334.9 | −1.08380 | −0.541902 | − | 0.840442i | \(-0.682296\pi\) | ||||
−0.541902 | + | 0.840442i | \(0.682296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32425.5 | −1.90803 | −0.954013 | − | 0.299764i | \(-0.903092\pi\) | ||||
−0.954013 | + | 0.299764i | \(0.903092\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −26767.5 | −1.56090 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15220.7 | −0.883583 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 254.007 | 0.0146138 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27780.7 | −1.59118 | −0.795591 | − | 0.605834i | \(-0.792840\pi\) | ||||
−0.795591 | + | 0.605834i | \(0.792840\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33485.5 | −1.90096 | −0.950482 | − | 0.310780i | \(-0.899410\pi\) | ||||
−0.950482 | + | 0.310780i | \(0.899410\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3999.58 | 0.226053 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32940.7 | 1.84545 | 0.922724 | − | 0.385461i | \(-0.125958\pi\) | ||||
0.922724 | + | 0.385461i | \(0.125958\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11965.9 | −0.667434 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −45723.9 | −2.52822 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33655.5 | −1.85285 | −0.926423 | − | 0.376484i | \(-0.877133\pi\) | ||||
−0.926423 | + | 0.376484i | \(0.877133\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17420.7 | 0.950800 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4542.65 | −0.246865 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4650.86 | 0.250585 | 0.125293 | − | 0.992120i | \(-0.460013\pi\) | ||||
0.125293 | + | 0.992120i | \(0.460013\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4524.83 | 0.242756 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 47581.8 | 2.53111 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25747.6 | −1.36385 | −0.681926 | − | 0.731421i | \(-0.738857\pi\) | ||||
−0.681926 | + | 0.731421i | \(0.738857\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4186.61 | −0.219902 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1063.73 | 0.0556382 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29032.1 | 1.50586 | 0.752931 | − | 0.658100i | \(-0.228639\pi\) | ||||
0.752931 | + | 0.658100i | \(0.228639\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5801.25 | 0.299653 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4491.95 | −0.230106 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20219.0 | 1.03147 | 0.515736 | − | 0.856748i | \(-0.327519\pi\) | ||||
0.515736 | + | 0.856748i | \(0.327519\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8933.40 | 0.452002 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4972.66 | −0.250572 | −0.125286 | − | 0.992121i | \(-0.539985\pi\) | ||||
−0.125286 | + | 0.992121i | \(0.539985\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −119.451 | −0.00597022 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29562.3 | 1.47154 | 0.735769 | − | 0.677233i | \(-0.236821\pi\) | ||||
0.735769 | + | 0.677233i | \(0.236821\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2935.04 | −0.144921 | −0.0724603 | − | 0.997371i | \(-0.523085\pi\) | ||||
−0.0724603 | + | 0.997371i | \(0.523085\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4445.11 | 0.218599 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5507.73 | −0.268689 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10344.6 | −0.502636 | −0.251318 | − | 0.967905i | \(-0.580864\pi\) | ||||
−0.251318 | + | 0.967905i | \(0.580864\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9453.18 | −0.455678 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39052.5 | −1.87502 | −0.937508 | − | 0.347962i | \(-0.886874\pi\) | ||||
−0.937508 | + | 0.347962i | \(0.886874\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21790.8 | 1.03800 | 0.518998 | − | 0.854776i | \(-0.326305\pi\) | ||||
0.518998 | + | 0.854776i | \(0.326305\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 52702.0 | 2.50058 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5614.09 | −0.264293 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24968.5 | 1.17085 | 0.585426 | − | 0.810726i | \(-0.300927\pi\) | ||||
0.585426 | + | 0.810726i | \(0.300927\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13776.8 | −0.641033 | −0.320516 | − | 0.947243i | \(-0.603856\pi\) | ||||
−0.320516 | + | 0.947243i | \(0.603856\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1235.55 | −0.0572676 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5995.99 | 0.275775 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −806.704 | −0.0369605 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11641.9 | 0.529320 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15211.2 | 0.688971 | 0.344485 | − | 0.938792i | \(-0.388053\pi\) | ||||
0.344485 | + | 0.938792i | \(0.388053\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39193.9 | 1.76179 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24445.7 | 1.09470 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6556.81 | −0.291410 | −0.145705 | − | 0.989328i | \(-0.546545\pi\) | ||||
−0.145705 | + | 0.989328i | \(0.546545\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29842.5 | −1.32134 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 382.009 | 0.0167880 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 36907.2 | 1.61591 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16020.5 | 0.696231 | 0.348115 | − | 0.937452i | \(-0.386822\pi\) | ||||
0.348115 | + | 0.937452i | \(0.386822\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18637.9 | −0.806984 | −0.403492 | − | 0.914983i | \(-0.632204\pi\) | ||||
−0.403492 | + | 0.914983i | \(0.632204\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12252.8 | −0.526622 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11791.5 | −0.504935 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4934.86 | 0.209778 | 0.104889 | − | 0.994484i | \(-0.466551\pi\) | ||||
0.104889 | + | 0.994484i | \(0.466551\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14397.3 | −0.609791 | −0.304895 | − | 0.952386i | \(-0.598621\pi\) | ||||
−0.304895 | + | 0.952386i | \(0.598621\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30026.5 | −1.26254 | −0.631271 | − | 0.775562i | \(-0.717466\pi\) | ||||
−0.631271 | + | 0.775562i | \(0.717466\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16117.7 | −0.675262 | −0.337631 | − | 0.941279i | \(-0.609626\pi\) | ||||
−0.337631 | + | 0.941279i | \(0.609626\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31793.3 | 1.32242 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21441.4 | 0.888636 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46793.8 | −1.92551 | −0.962753 | − | 0.270381i | \(-0.912850\pi\) | ||||
−0.962753 | + | 0.270381i | \(0.912850\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 137.780 | 0.00564927 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 75138.1 | 3.05897 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −40744.6 | −1.65289 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6238.86 | −0.251311 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20288.3 | 0.814371 | 0.407186 | − | 0.913345i | \(-0.366510\pi\) | ||||
0.407186 | + | 0.913345i | \(0.366510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22542.0 | −0.898507 | −0.449253 | − | 0.893404i | \(-0.648310\pi\) | ||||
−0.449253 | + | 0.893404i | \(0.648310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26490.5 | 1.05220 | 0.526102 | − | 0.850422i | \(-0.323653\pi\) | ||||
0.526102 | + | 0.850422i | \(0.323653\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24555.8 | −0.968585 | −0.484293 | − | 0.874906i | \(-0.660923\pi\) | ||||
−0.484293 | + | 0.874906i | \(0.660923\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44104.1 | −1.73362 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 610.279 | 0.0238231 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11496.1 | −0.447220 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −36576.4 | −1.41315 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42047.4 | −1.61897 | −0.809487 | − | 0.587138i | \(-0.800255\pi\) | ||||
−0.809487 | + | 0.587138i | \(0.800255\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35487.4 | −1.35709 | −0.678547 | − | 0.734557i | \(-0.737390\pi\) | ||||
−0.678547 | + | 0.734557i | \(0.737390\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32872.6 | −1.25283 | −0.626416 | − | 0.779489i | \(-0.715479\pi\) | ||||
−0.626416 | + | 0.779489i | \(0.715479\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41109.7 | 1.55618 | 0.778088 | − | 0.628156i | \(-0.216190\pi\) | ||||
0.778088 | + | 0.628156i | \(0.216190\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48493.2 | −1.82948 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39390.1 | 1.47608 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46095.5 | −1.72157 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6746.33 | 0.250281 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26869.9 | −0.993525 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10531.5 | 0.386828 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3948.63 | −0.144556 | −0.0722779 | − | 0.997385i | \(-0.523027\pi\) | ||||
−0.0722779 | + | 0.997385i | \(0.523027\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2354.34 | −0.0856232 | −0.0428116 | − | 0.999083i | \(-0.513632\pi\) | ||||
−0.0428116 | + | 0.999083i | \(0.513632\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −776.975 | −0.0281644 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23395.0 | −0.842499 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46120.8 | 1.65548 | 0.827739 | − | 0.561114i | \(-0.189627\pi\) | ||||
0.827739 | + | 0.561114i | \(0.189627\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −77637.4 | −2.76865 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1841.21 | −0.0654472 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31332.7 | 1.10656 | 0.553278 | − | 0.832996i | \(-0.313377\pi\) | ||||
0.553278 | + | 0.832996i | \(0.313377\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41965.0 | −1.47728 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 625.108 | 0.0218644 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1934.65 | −0.0674516 | −0.0337258 | − | 0.999431i | \(-0.510737\pi\) | ||||
−0.0337258 | + | 0.999431i | \(0.510737\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20684.1 | 0.716559 | 0.358280 | − | 0.933614i | \(-0.383363\pi\) | ||||
0.358280 | + | 0.933614i | \(0.383363\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8267.30 | −0.285493 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4841.49 | −0.166132 | −0.0830661 | − | 0.996544i | \(-0.526471\pi\) | ||||
−0.0830661 | + | 0.996544i | \(0.526471\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36764.6 | 1.25757 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24802.0 | −0.843038 | −0.421519 | − | 0.906820i | \(-0.638503\pi\) | ||||
−0.421519 | + | 0.906820i | \(0.638503\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29067.1 | −0.984910 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −29567.5 | −0.995606 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27935.4 | −0.937711 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7991.03 | 0.266570 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48565.1 | −1.61504 | −0.807522 | − | 0.589837i | \(-0.799192\pi\) | ||||
−0.807522 | + | 0.589837i | \(0.799192\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20272.7 | −0.670012 | −0.335006 | − | 0.942216i | \(-0.608738\pi\) | ||||
−0.335006 | + | 0.942216i | \(0.608738\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 43046.5 | 1.41830 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12109.5 | −0.396539 | −0.198270 | − | 0.980148i | \(-0.563532\pi\) | ||||
−0.198270 | + | 0.980148i | \(0.563532\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1119.55 | 0.0365486 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25330.4 | −0.821885 | −0.410942 | − | 0.911661i | \(-0.634800\pi\) | ||||
−0.410942 | + | 0.911661i | \(0.634800\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21047.1 | 0.680829 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16258.2 | 0.522729 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54229.7 | −1.73831 | −0.869154 | − | 0.494541i | \(-0.835336\pi\) | ||||
−0.869154 | + | 0.494541i | \(0.835336\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13459.2 | 0.428830 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33647.4 | −1.06883 | −0.534415 | − | 0.845222i | \(-0.679468\pi\) | ||||
−0.534415 | + | 0.845222i | \(0.679468\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 648.4.a.l.1.4 | 5 | ||
3.2 | odd | 2 | 648.4.a.k.1.2 | 5 | |||
4.3 | odd | 2 | 1296.4.a.bd.1.4 | 5 | |||
9.2 | odd | 6 | 216.4.i.b.145.4 | 10 | |||
9.4 | even | 3 | 72.4.i.b.25.2 | ✓ | 10 | ||
9.5 | odd | 6 | 216.4.i.b.73.4 | 10 | |||
9.7 | even | 3 | 72.4.i.b.49.2 | yes | 10 | ||
12.11 | even | 2 | 1296.4.a.bc.1.2 | 5 | |||
36.7 | odd | 6 | 144.4.i.f.49.4 | 10 | |||
36.11 | even | 6 | 432.4.i.f.145.4 | 10 | |||
36.23 | even | 6 | 432.4.i.f.289.4 | 10 | |||
36.31 | odd | 6 | 144.4.i.f.97.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.4.i.b.25.2 | ✓ | 10 | 9.4 | even | 3 | ||
72.4.i.b.49.2 | yes | 10 | 9.7 | even | 3 | ||
144.4.i.f.49.4 | 10 | 36.7 | odd | 6 | |||
144.4.i.f.97.4 | 10 | 36.31 | odd | 6 | |||
216.4.i.b.73.4 | 10 | 9.5 | odd | 6 | |||
216.4.i.b.145.4 | 10 | 9.2 | odd | 6 | |||
432.4.i.f.145.4 | 10 | 36.11 | even | 6 | |||
432.4.i.f.289.4 | 10 | 36.23 | even | 6 | |||
648.4.a.k.1.2 | 5 | 3.2 | odd | 2 | |||
648.4.a.l.1.4 | 5 | 1.1 | even | 1 | trivial | ||
1296.4.a.bc.1.2 | 5 | 12.11 | even | 2 | |||
1296.4.a.bd.1.4 | 5 | 4.3 | odd | 2 |