Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.24740 | 0.882044 | 0.441022 | − | 0.897496i | \(-0.354616\pi\) | ||||
0.441022 | + | 0.897496i | \(0.354616\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.443996 | −0.221998 | ||||||||
\(5\) | −1.34151 | −0.599940 | −0.299970 | − | 0.953949i | \(-0.596977\pi\) | ||||
−0.299970 | + | 0.953949i | \(0.596977\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −3.04864 | −1.07786 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.67339 | −0.529173 | ||||||||
\(11\) | 5.34830 | 1.61257 | 0.806287 | − | 0.591525i | \(-0.201474\pi\) | ||||
0.806287 | + | 0.591525i | \(0.201474\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.35012 | −1.20651 | −0.603253 | − | 0.797550i | \(-0.706129\pi\) | ||||
−0.603253 | + | 0.797550i | \(0.706129\pi\) | |||||||
\(14\) | −1.24740 | −0.333381 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.91487 | −0.728719 | ||||||||
\(17\) | 3.15816 | 0.765965 | 0.382983 | − | 0.923756i | \(-0.374897\pi\) | ||||
0.382983 | + | 0.923756i | \(0.374897\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.16622 | 0.496965 | 0.248483 | − | 0.968636i | \(-0.420068\pi\) | ||||
0.248483 | + | 0.968636i | \(0.420068\pi\) | |||||||
\(20\) | 0.595623 | 0.133185 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.67146 | 1.42236 | ||||||||
\(23\) | −6.10623 | −1.27324 | −0.636618 | − | 0.771179i | \(-0.719667\pi\) | ||||
−0.636618 | + | 0.771179i | \(0.719667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.20036 | −0.640073 | ||||||||
\(26\) | −5.42633 | −1.06419 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.443996 | 0.0839074 | ||||||||
\(29\) | 1.86915 | 0.347092 | 0.173546 | − | 0.984826i | \(-0.444477\pi\) | ||||
0.173546 | + | 0.984826i | \(0.444477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.389776 | 0.0700059 | 0.0350029 | − | 0.999387i | \(-0.488856\pi\) | ||||
0.0350029 | + | 0.999387i | \(0.488856\pi\) | |||||||
\(32\) | 2.46126 | 0.435094 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.93948 | 0.675615 | ||||||||
\(35\) | 1.34151 | 0.226756 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.82278 | 0.299664 | 0.149832 | − | 0.988711i | \(-0.452127\pi\) | ||||
0.149832 | + | 0.988711i | \(0.452127\pi\) | |||||||
\(38\) | 2.70214 | 0.438345 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.08977 | 0.646649 | ||||||||
\(41\) | −4.04302 | −0.631414 | −0.315707 | − | 0.948857i | \(-0.602242\pi\) | ||||
−0.315707 | + | 0.948857i | \(0.602242\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.1420 | −1.85164 | −0.925821 | − | 0.377962i | \(-0.876625\pi\) | ||||
−0.925821 | + | 0.377962i | \(0.876625\pi\) | |||||||
\(44\) | −2.37462 | −0.357988 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.61690 | −1.12305 | ||||||||
\(47\) | 2.55141 | 0.372162 | 0.186081 | − | 0.982534i | \(-0.440421\pi\) | ||||
0.186081 | + | 0.982534i | \(0.440421\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.99213 | −0.564572 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.93144 | 0.267842 | ||||||||
\(53\) | 0.687516 | 0.0944376 | 0.0472188 | − | 0.998885i | \(-0.484964\pi\) | ||||
0.0472188 | + | 0.998885i | \(0.484964\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.17477 | −0.967446 | ||||||||
\(56\) | 3.04864 | 0.407391 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.33157 | 0.306151 | ||||||||
\(59\) | 7.83644 | 1.02022 | 0.510109 | − | 0.860110i | \(-0.329605\pi\) | ||||
0.510109 | + | 0.860110i | \(0.329605\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.37683 | −1.07254 | −0.536272 | − | 0.844045i | \(-0.680168\pi\) | ||||
−0.536272 | + | 0.844045i | \(0.680168\pi\) | |||||||
\(62\) | 0.486206 | 0.0617483 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.89993 | 1.11249 | ||||||||
\(65\) | 5.83571 | 0.723831 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.01012 | 0.245576 | 0.122788 | − | 0.992433i | \(-0.460817\pi\) | ||||
0.122788 | + | 0.992433i | \(0.460817\pi\) | |||||||
\(68\) | −1.40221 | −0.170043 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.67339 | 0.200009 | ||||||||
\(71\) | 16.1489 | 1.91652 | 0.958258 | − | 0.285904i | \(-0.0922938\pi\) | ||||
0.958258 | + | 0.285904i | \(0.0922938\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.64873 | 0.427051 | 0.213526 | − | 0.976937i | \(-0.431505\pi\) | ||||
0.213526 | + | 0.976937i | \(0.431505\pi\) | |||||||
\(74\) | 2.27374 | 0.264317 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.961794 | −0.110325 | ||||||||
\(77\) | −5.34830 | −0.609495 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.25997 | 0.816810 | 0.408405 | − | 0.912801i | \(-0.366085\pi\) | ||||
0.408405 | + | 0.912801i | \(0.366085\pi\) | |||||||
\(80\) | 3.91032 | 0.437187 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.04326 | −0.556935 | ||||||||
\(83\) | −1.44730 | −0.158861 | −0.0794307 | − | 0.996840i | \(-0.525310\pi\) | ||||
−0.0794307 | + | 0.996840i | \(0.525310\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.23668 | −0.459533 | ||||||||
\(86\) | −15.1460 | −1.63323 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −16.3050 | −1.73812 | ||||||||
\(89\) | −5.15405 | −0.546328 | −0.273164 | − | 0.961967i | \(-0.588070\pi\) | ||||
−0.273164 | + | 0.961967i | \(0.588070\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.35012 | 0.456016 | ||||||||
\(92\) | 2.71114 | 0.282656 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.18263 | 0.328263 | ||||||||
\(95\) | −2.90600 | −0.298149 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.05155 | 0.106769 | 0.0533843 | − | 0.998574i | \(-0.482999\pi\) | ||||
0.0533843 | + | 0.998574i | \(0.482999\pi\) | |||||||
\(98\) | 1.24740 | 0.126006 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.42095 | 0.142095 | ||||||||
\(101\) | 11.1364 | 1.10811 | 0.554055 | − | 0.832480i | \(-0.313080\pi\) | ||||
0.554055 | + | 0.832480i | \(0.313080\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.94345 | 0.290027 | 0.145013 | − | 0.989430i | \(-0.453677\pi\) | ||||
0.145013 | + | 0.989430i | \(0.453677\pi\) | |||||||
\(104\) | 13.2619 | 1.30044 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.857607 | 0.0832981 | ||||||||
\(107\) | −17.8510 | −1.72572 | −0.862858 | − | 0.505446i | \(-0.831328\pi\) | ||||
−0.862858 | + | 0.505446i | \(0.831328\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.89841 | 0.660748 | 0.330374 | − | 0.943850i | \(-0.392825\pi\) | ||||
0.330374 | + | 0.943850i | \(0.392825\pi\) | |||||||
\(110\) | −8.94980 | −0.853330 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.91487 | 0.275430 | ||||||||
\(113\) | −7.27356 | −0.684239 | −0.342119 | − | 0.939656i | \(-0.611145\pi\) | ||||
−0.342119 | + | 0.939656i | \(0.611145\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.19154 | 0.763865 | ||||||||
\(116\) | −0.829895 | −0.0770538 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.77516 | 0.899877 | ||||||||
\(119\) | −3.15816 | −0.289508 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.6043 | 1.60039 | ||||||||
\(122\) | −10.4492 | −0.946030 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.173059 | −0.0155412 | ||||||||
\(125\) | 11.0008 | 0.983944 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 6.17923 | 0.546172 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.27946 | 0.638451 | ||||||||
\(131\) | −0.921159 | −0.0804820 | −0.0402410 | − | 0.999190i | \(-0.512813\pi\) | ||||
−0.0402410 | + | 0.999190i | \(0.512813\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.16622 | −0.187835 | ||||||||
\(134\) | 2.50743 | 0.216609 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.62807 | −0.825600 | ||||||||
\(137\) | 8.98921 | 0.768000 | 0.384000 | − | 0.923333i | \(-0.374546\pi\) | ||||
0.384000 | + | 0.923333i | \(0.374546\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.44202 | −0.291948 | −0.145974 | − | 0.989288i | \(-0.546632\pi\) | ||||
−0.145974 | + | 0.989288i | \(0.546632\pi\) | |||||||
\(140\) | −0.595623 | −0.0503394 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 20.1441 | 1.69045 | ||||||||
\(143\) | −23.2657 | −1.94558 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.50747 | −0.208234 | ||||||||
\(146\) | 4.55142 | 0.376678 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.809309 | −0.0665248 | ||||||||
\(149\) | 1.20512 | 0.0987276 | 0.0493638 | − | 0.998781i | \(-0.484281\pi\) | ||||
0.0493638 | + | 0.998781i | \(0.484281\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.6943 | 1.11443 | 0.557214 | − | 0.830369i | \(-0.311870\pi\) | ||||
0.557214 | + | 0.830369i | \(0.311870\pi\) | |||||||
\(152\) | −6.60403 | −0.535657 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.67146 | −0.537602 | ||||||||
\(155\) | −0.522887 | −0.0419993 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.2880 | 1.53935 | 0.769674 | − | 0.638437i | \(-0.220419\pi\) | ||||
0.769674 | + | 0.638437i | \(0.220419\pi\) | |||||||
\(158\) | 9.05607 | 0.720463 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.30180 | −0.261030 | ||||||||
\(161\) | 6.10623 | 0.481238 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.43179 | −0.425451 | −0.212725 | − | 0.977112i | \(-0.568234\pi\) | ||||
−0.212725 | + | 0.977112i | \(0.568234\pi\) | |||||||
\(164\) | 1.79509 | 0.140173 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.80536 | −0.140123 | ||||||||
\(167\) | 7.20217 | 0.557321 | 0.278660 | − | 0.960390i | \(-0.410110\pi\) | ||||
0.278660 | + | 0.960390i | \(0.410110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.92354 | 0.455657 | ||||||||
\(170\) | −5.28483 | −0.405328 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.39102 | 0.411061 | ||||||||
\(173\) | 19.7557 | 1.50200 | 0.751000 | − | 0.660302i | \(-0.229572\pi\) | ||||
0.751000 | + | 0.660302i | \(0.229572\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.20036 | 0.241925 | ||||||||
\(176\) | −15.5896 | −1.17511 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.42915 | −0.481885 | ||||||||
\(179\) | 17.8014 | 1.33054 | 0.665269 | − | 0.746604i | \(-0.268317\pi\) | ||||
0.665269 | + | 0.746604i | \(0.268317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.4288 | 1.74145 | 0.870723 | − | 0.491773i | \(-0.163651\pi\) | ||||
0.870723 | + | 0.491773i | \(0.163651\pi\) | |||||||
\(182\) | 5.42633 | 0.402227 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 18.6157 | 1.37237 | ||||||||
\(185\) | −2.44528 | −0.179780 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.8908 | 1.23517 | ||||||||
\(188\) | −1.13282 | −0.0826192 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.62494 | −0.262981 | ||||||||
\(191\) | −16.1706 | −1.17006 | −0.585030 | − | 0.811011i | \(-0.698917\pi\) | ||||
−0.585030 | + | 0.811011i | \(0.698917\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0893 | −0.726243 | −0.363121 | − | 0.931742i | \(-0.618289\pi\) | ||||
−0.363121 | + | 0.931742i | \(0.618289\pi\) | |||||||
\(194\) | 1.31170 | 0.0941745 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.443996 | −0.0317140 | ||||||||
\(197\) | 4.50647 | 0.321073 | 0.160536 | − | 0.987030i | \(-0.448678\pi\) | ||||
0.160536 | + | 0.987030i | \(0.448678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.4241 | 1.58960 | 0.794800 | − | 0.606871i | \(-0.207576\pi\) | ||||
0.794800 | + | 0.606871i | \(0.207576\pi\) | |||||||
\(200\) | 9.75675 | 0.689906 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.8915 | 0.977402 | ||||||||
\(203\) | −1.86915 | −0.131189 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.42374 | 0.378810 | ||||||||
\(206\) | 3.67166 | 0.255817 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.6801 | 0.879204 | ||||||||
\(209\) | 11.5856 | 0.801393 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.809347 | 0.0557178 | 0.0278589 | − | 0.999612i | \(-0.491131\pi\) | ||||
0.0278589 | + | 0.999612i | \(0.491131\pi\) | |||||||
\(212\) | −0.305255 | −0.0209650 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −22.2673 | −1.52216 | ||||||||
\(215\) | 16.2886 | 1.11087 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.389776 | −0.0264597 | ||||||||
\(218\) | 8.60506 | 0.582809 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.18557 | 0.214771 | ||||||||
\(221\) | −13.7384 | −0.924142 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.93385 | 0.464325 | 0.232162 | − | 0.972677i | \(-0.425420\pi\) | ||||
0.232162 | + | 0.972677i | \(0.425420\pi\) | |||||||
\(224\) | −2.46126 | −0.164450 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.07303 | −0.603529 | ||||||||
\(227\) | −10.5103 | −0.697590 | −0.348795 | − | 0.937199i | \(-0.613409\pi\) | ||||
−0.348795 | + | 0.937199i | \(0.613409\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.7823 | −1.04293 | −0.521463 | − | 0.853274i | \(-0.674614\pi\) | ||||
−0.521463 | + | 0.853274i | \(0.674614\pi\) | |||||||
\(230\) | 10.2181 | 0.673763 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.69836 | −0.374116 | ||||||||
\(233\) | −2.53665 | −0.166182 | −0.0830908 | − | 0.996542i | \(-0.526479\pi\) | ||||
−0.0830908 | + | 0.996542i | \(0.526479\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.42273 | −0.223274 | ||||||||
\(236\) | −3.47935 | −0.226486 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.93948 | −0.255359 | ||||||||
\(239\) | −11.0886 | −0.717263 | −0.358631 | − | 0.933479i | \(-0.616756\pi\) | ||||
−0.358631 | + | 0.933479i | \(0.616756\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.3087 | 1.69469 | 0.847345 | − | 0.531042i | \(-0.178200\pi\) | ||||
0.847345 | + | 0.531042i | \(0.178200\pi\) | |||||||
\(242\) | 21.9596 | 1.41162 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.71928 | 0.238103 | ||||||||
\(245\) | −1.34151 | −0.0857057 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.42333 | −0.599592 | ||||||||
\(248\) | −1.18829 | −0.0754563 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.7224 | 0.867882 | ||||||||
\(251\) | 12.5462 | 0.791911 | 0.395956 | − | 0.918270i | \(-0.370413\pi\) | ||||
0.395956 | + | 0.918270i | \(0.370413\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.6579 | −2.05319 | ||||||||
\(254\) | 1.24740 | 0.0782688 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.0919 | −0.630743 | ||||||||
\(257\) | 5.65644 | 0.352839 | 0.176420 | − | 0.984315i | \(-0.443548\pi\) | ||||
0.176420 | + | 0.984315i | \(0.443548\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.82278 | −0.113262 | ||||||||
\(260\) | −2.59103 | −0.160689 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.14905 | −0.0709887 | ||||||||
\(263\) | 17.2959 | 1.06651 | 0.533256 | − | 0.845954i | \(-0.320968\pi\) | ||||
0.533256 | + | 0.845954i | \(0.320968\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.922307 | −0.0566569 | ||||||||
\(266\) | −2.70214 | −0.165679 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.892487 | −0.0545173 | ||||||||
\(269\) | 27.3003 | 1.66453 | 0.832265 | − | 0.554378i | \(-0.187044\pi\) | ||||
0.832265 | + | 0.554378i | \(0.187044\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.959296 | −0.0582731 | −0.0291365 | − | 0.999575i | \(-0.509276\pi\) | ||||
−0.0291365 | + | 0.999575i | \(0.509276\pi\) | |||||||
\(272\) | −9.20563 | −0.558173 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.2131 | 0.677410 | ||||||||
\(275\) | −17.1165 | −1.03216 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.6931 | 0.702568 | 0.351284 | − | 0.936269i | \(-0.385745\pi\) | ||||
0.351284 | + | 0.936269i | \(0.385745\pi\) | |||||||
\(278\) | −4.29357 | −0.257511 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.08977 | −0.244410 | ||||||||
\(281\) | 5.71153 | 0.340721 | 0.170361 | − | 0.985382i | \(-0.445507\pi\) | ||||
0.170361 | + | 0.985382i | \(0.445507\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.87883 | −0.468348 | −0.234174 | − | 0.972195i | \(-0.575239\pi\) | ||||
−0.234174 | + | 0.972195i | \(0.575239\pi\) | |||||||
\(284\) | −7.17003 | −0.425463 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29.0217 | −1.71609 | ||||||||
\(287\) | 4.04302 | 0.238652 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.02605 | −0.413297 | ||||||||
\(290\) | −3.12782 | −0.183672 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.62002 | −0.0948046 | ||||||||
\(293\) | −22.9436 | −1.34038 | −0.670189 | − | 0.742190i | \(-0.733787\pi\) | ||||
−0.670189 | + | 0.742190i | \(0.733787\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.5126 | −0.612069 | ||||||||
\(296\) | −5.55701 | −0.322995 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.50327 | 0.0870821 | ||||||||
\(299\) | 26.5628 | 1.53617 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.1420 | 0.699855 | ||||||||
\(302\) | 17.0823 | 0.982975 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.31427 | −0.362148 | ||||||||
\(305\) | 11.2376 | 0.643461 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.06672 | 0.517465 | 0.258732 | − | 0.965949i | \(-0.416695\pi\) | ||||
0.258732 | + | 0.965949i | \(0.416695\pi\) | |||||||
\(308\) | 2.37462 | 0.135307 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.652249 | −0.0370452 | ||||||||
\(311\) | 12.3150 | 0.698319 | 0.349160 | − | 0.937063i | \(-0.386467\pi\) | ||||
0.349160 | + | 0.937063i | \(0.386467\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.643671 | 0.0363824 | 0.0181912 | − | 0.999835i | \(-0.494209\pi\) | ||||
0.0181912 | + | 0.999835i | \(0.494209\pi\) | |||||||
\(314\) | 24.0598 | 1.35777 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.22340 | −0.181330 | ||||||||
\(317\) | 21.7594 | 1.22213 | 0.611066 | − | 0.791580i | \(-0.290741\pi\) | ||||
0.611066 | + | 0.791580i | \(0.290741\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.99677 | 0.559712 | ||||||||
\(320\) | −11.9393 | −0.667427 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.61690 | 0.424473 | ||||||||
\(323\) | 6.84127 | 0.380658 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.9220 | 0.772251 | ||||||||
\(326\) | −6.77561 | −0.375267 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.3257 | 0.680573 | ||||||||
\(329\) | −2.55141 | −0.140664 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.5245 | 1.23806 | 0.619029 | − | 0.785368i | \(-0.287526\pi\) | ||||
0.619029 | + | 0.785368i | \(0.287526\pi\) | |||||||
\(332\) | 0.642594 | 0.0352669 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.98398 | 0.491582 | ||||||||
\(335\) | −2.69659 | −0.147331 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.9305 | 0.976735 | 0.488368 | − | 0.872638i | \(-0.337593\pi\) | ||||
0.488368 | + | 0.872638i | \(0.337593\pi\) | |||||||
\(338\) | 7.38902 | 0.401910 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.88107 | 0.102015 | ||||||||
\(341\) | 2.08464 | 0.112890 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 37.0167 | 1.99580 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.6433 | 1.32483 | ||||||||
\(347\) | 10.9499 | 0.587820 | 0.293910 | − | 0.955833i | \(-0.405043\pi\) | ||||
0.293910 | + | 0.955833i | \(0.405043\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0008 | 0.695917 | 0.347959 | − | 0.937510i | \(-0.386875\pi\) | ||||
0.347959 | + | 0.937510i | \(0.386875\pi\) | |||||||
\(350\) | 3.99213 | 0.213388 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.1636 | 0.701621 | ||||||||
\(353\) | −6.83064 | −0.363558 | −0.181779 | − | 0.983339i | \(-0.558186\pi\) | ||||
−0.181779 | + | 0.983339i | \(0.558186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.6638 | −1.14979 | ||||||||
\(356\) | 2.28838 | 0.121284 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.2054 | 1.17359 | ||||||||
\(359\) | −15.5017 | −0.818147 | −0.409074 | − | 0.912501i | \(-0.634148\pi\) | ||||
−0.409074 | + | 0.912501i | \(0.634148\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.3075 | −0.753025 | ||||||||
\(362\) | 29.2250 | 1.53603 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.93144 | −0.101235 | ||||||||
\(365\) | −4.89479 | −0.256205 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.57294 | −0.499704 | −0.249852 | − | 0.968284i | \(-0.580382\pi\) | ||||
−0.249852 | + | 0.968284i | \(0.580382\pi\) | |||||||
\(368\) | 17.7989 | 0.927831 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.05023 | −0.158574 | ||||||||
\(371\) | −0.687516 | −0.0356941 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.99725 | −0.414082 | −0.207041 | − | 0.978332i | \(-0.566383\pi\) | ||||
−0.207041 | + | 0.978332i | \(0.566383\pi\) | |||||||
\(374\) | 21.0695 | 1.08948 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.77833 | −0.401137 | ||||||||
\(377\) | −8.13102 | −0.418769 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.0692 | −0.876785 | −0.438393 | − | 0.898784i | \(-0.644452\pi\) | ||||
−0.438393 | + | 0.898784i | \(0.644452\pi\) | |||||||
\(380\) | 1.29025 | 0.0661886 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.1711 | −1.03205 | ||||||||
\(383\) | 6.50697 | 0.332491 | 0.166245 | − | 0.986084i | \(-0.446836\pi\) | ||||
0.166245 | + | 0.986084i | \(0.446836\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.17477 | 0.365660 | ||||||||
\(386\) | −12.5854 | −0.640578 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.466883 | −0.0237024 | ||||||||
\(389\) | −7.96414 | −0.403798 | −0.201899 | − | 0.979406i | \(-0.564711\pi\) | ||||
−0.201899 | + | 0.979406i | \(0.564711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.2844 | −0.975255 | ||||||||
\(392\) | −3.04864 | −0.153979 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.62137 | 0.283200 | ||||||||
\(395\) | −9.73929 | −0.490037 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.65801 | 0.283967 | 0.141984 | − | 0.989869i | \(-0.454652\pi\) | ||||
0.141984 | + | 0.989869i | \(0.454652\pi\) | |||||||
\(398\) | 27.9718 | 1.40210 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.32866 | 0.466433 | ||||||||
\(401\) | −8.34238 | −0.416598 | −0.208299 | − | 0.978065i | \(-0.566793\pi\) | ||||
−0.208299 | + | 0.978065i | \(0.566793\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.69557 | −0.0844625 | ||||||||
\(404\) | −4.94451 | −0.245998 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.33157 | −0.115714 | ||||||||
\(407\) | 9.74880 | 0.483230 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.1591 | 1.73850 | 0.869252 | − | 0.494370i | \(-0.164601\pi\) | ||||
0.869252 | + | 0.494370i | \(0.164601\pi\) | |||||||
\(410\) | 6.76556 | 0.334127 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.30688 | −0.0643854 | ||||||||
\(413\) | −7.83644 | −0.385606 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.94156 | 0.0953072 | ||||||||
\(416\) | −10.7068 | −0.524944 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.4519 | 0.706864 | ||||||||
\(419\) | −5.32538 | −0.260162 | −0.130081 | − | 0.991503i | \(-0.541524\pi\) | ||||
−0.130081 | + | 0.991503i | \(0.541524\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.82064 | 0.429892 | 0.214946 | − | 0.976626i | \(-0.431043\pi\) | ||||
0.214946 | + | 0.976626i | \(0.431043\pi\) | |||||||
\(422\) | 1.00958 | 0.0491455 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.09599 | −0.101790 | ||||||||
\(425\) | −10.1072 | −0.490273 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.37683 | 0.405383 | ||||||||
\(428\) | 7.92575 | 0.383106 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 20.3184 | 0.979839 | ||||||||
\(431\) | −19.9202 | −0.959524 | −0.479762 | − | 0.877399i | \(-0.659277\pi\) | ||||
−0.479762 | + | 0.877399i | \(0.659277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.1919 | −0.970360 | −0.485180 | − | 0.874414i | \(-0.661246\pi\) | ||||
−0.485180 | + | 0.874414i | \(0.661246\pi\) | |||||||
\(434\) | −0.486206 | −0.0233387 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.06287 | −0.146685 | ||||||||
\(437\) | −13.2274 | −0.632754 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.8589 | 1.28190 | 0.640952 | − | 0.767581i | \(-0.278540\pi\) | ||||
0.640952 | + | 0.767581i | \(0.278540\pi\) | |||||||
\(440\) | 21.8733 | 1.04277 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.1372 | −0.815134 | ||||||||
\(443\) | −8.75427 | −0.415928 | −0.207964 | − | 0.978137i | \(-0.566684\pi\) | ||||
−0.207964 | + | 0.978137i | \(0.566684\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.91419 | 0.327764 | ||||||||
\(446\) | 8.64927 | 0.409555 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.89993 | −0.420482 | ||||||||
\(449\) | 8.94965 | 0.422360 | 0.211180 | − | 0.977447i | \(-0.432269\pi\) | ||||
0.211180 | + | 0.977447i | \(0.432269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.6233 | −1.01820 | ||||||||
\(452\) | 3.22943 | 0.151900 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.1105 | −0.615305 | ||||||||
\(455\) | −5.83571 | −0.273582 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.94645 | −0.184607 | −0.0923035 | − | 0.995731i | \(-0.529423\pi\) | ||||
−0.0923035 | + | 0.995731i | \(0.529423\pi\) | |||||||
\(458\) | −19.6869 | −0.919907 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.63701 | −0.169577 | ||||||||
\(461\) | −17.6827 | −0.823566 | −0.411783 | − | 0.911282i | \(-0.635094\pi\) | ||||
−0.411783 | + | 0.911282i | \(0.635094\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.1389 | 0.889460 | 0.444730 | − | 0.895665i | \(-0.353300\pi\) | ||||
0.444730 | + | 0.895665i | \(0.353300\pi\) | |||||||
\(464\) | −5.44834 | −0.252933 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.16422 | −0.146580 | ||||||||
\(467\) | −21.0237 | −0.972861 | −0.486430 | − | 0.873719i | \(-0.661701\pi\) | ||||
−0.486430 | + | 0.873719i | \(0.661701\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.01012 | −0.0928189 | ||||||||
\(470\) | −4.26951 | −0.196938 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −23.8905 | −1.09965 | ||||||||
\(473\) | −64.9392 | −2.98591 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.93270 | −0.318094 | ||||||||
\(476\) | 1.40221 | 0.0642701 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.8319 | −0.632657 | ||||||||
\(479\) | −2.35198 | −0.107465 | −0.0537324 | − | 0.998555i | \(-0.517112\pi\) | ||||
−0.0537324 | + | 0.998555i | \(0.517112\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.92933 | −0.361546 | ||||||||
\(482\) | 32.8174 | 1.49479 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.81625 | −0.355284 | ||||||||
\(485\) | −1.41066 | −0.0640546 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.2298 | 1.23390 | 0.616949 | − | 0.787003i | \(-0.288368\pi\) | ||||
0.616949 | + | 0.787003i | \(0.288368\pi\) | |||||||
\(488\) | 25.5379 | 1.15605 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.67339 | −0.0755962 | ||||||||
\(491\) | −10.4846 | −0.473165 | −0.236583 | − | 0.971611i | \(-0.576027\pi\) | ||||
−0.236583 | + | 0.971611i | \(0.576027\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.90306 | 0.265861 | ||||||||
\(494\) | −11.7546 | −0.528867 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.13615 | −0.0510146 | ||||||||
\(497\) | −16.1489 | −0.724375 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.97856 | 0.446702 | 0.223351 | − | 0.974738i | \(-0.428300\pi\) | ||||
0.223351 | + | 0.974738i | \(0.428300\pi\) | |||||||
\(500\) | −4.88433 | −0.218434 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.6502 | 0.698501 | ||||||||
\(503\) | −11.4444 | −0.510283 | −0.255141 | − | 0.966904i | \(-0.582122\pi\) | ||||
−0.255141 | + | 0.966904i | \(0.582122\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.9395 | −0.664799 | ||||||||
\(506\) | −40.7375 | −1.81100 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.443996 | −0.0196991 | ||||||||
\(509\) | 2.37848 | 0.105424 | 0.0527121 | − | 0.998610i | \(-0.483213\pi\) | ||||
0.0527121 | + | 0.998610i | \(0.483213\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.64873 | −0.161410 | ||||||||
\(512\) | −24.9471 | −1.10252 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.05584 | 0.311220 | ||||||||
\(515\) | −3.94866 | −0.173999 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.6457 | 0.600138 | ||||||||
\(518\) | −2.27374 | −0.0999024 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −17.7910 | −0.780186 | ||||||||
\(521\) | −17.4353 | −0.763856 | −0.381928 | − | 0.924192i | \(-0.624740\pi\) | ||||
−0.381928 | + | 0.924192i | \(0.624740\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.1999 | 1.40800 | 0.704001 | − | 0.710199i | \(-0.251395\pi\) | ||||
0.704001 | + | 0.710199i | \(0.251395\pi\) | |||||||
\(524\) | 0.408991 | 0.0178669 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.5749 | 0.940711 | ||||||||
\(527\) | 1.23097 | 0.0536221 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.2860 | 0.621131 | ||||||||
\(530\) | −1.15048 | −0.0499739 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.961794 | 0.0416991 | ||||||||
\(533\) | 17.5876 | 0.761805 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.9472 | 1.03533 | ||||||||
\(536\) | −6.12814 | −0.264695 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 34.0544 | 1.46819 | ||||||||
\(539\) | 5.34830 | 0.230368 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6946 | −0.459795 | −0.229897 | − | 0.973215i | \(-0.573839\pi\) | ||||
−0.229897 | + | 0.973215i | \(0.573839\pi\) | |||||||
\(542\) | −1.19662 | −0.0513994 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.77306 | 0.333267 | ||||||||
\(545\) | −9.25425 | −0.396409 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.0976 | 0.944825 | 0.472413 | − | 0.881377i | \(-0.343383\pi\) | ||||
0.472413 | + | 0.881377i | \(0.343383\pi\) | |||||||
\(548\) | −3.99118 | −0.170495 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −21.3511 | −0.910414 | ||||||||
\(551\) | 4.04899 | 0.172493 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.25997 | −0.308725 | ||||||||
\(554\) | 14.5859 | 0.619696 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.52824 | 0.0648120 | ||||||||
\(557\) | −29.3270 | −1.24262 | −0.621312 | − | 0.783563i | \(-0.713400\pi\) | ||||
−0.621312 | + | 0.783563i | \(0.713400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52.8193 | 2.23402 | ||||||||
\(560\) | −3.91032 | −0.165241 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.12456 | 0.300531 | ||||||||
\(563\) | −34.8575 | −1.46907 | −0.734533 | − | 0.678572i | \(-0.762599\pi\) | ||||
−0.734533 | + | 0.678572i | \(0.762599\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.75752 | 0.410502 | ||||||||
\(566\) | −9.82805 | −0.413104 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −49.2320 | −2.06573 | ||||||||
\(569\) | −10.5395 | −0.441840 | −0.220920 | − | 0.975292i | \(-0.570906\pi\) | ||||
−0.220920 | + | 0.975292i | \(0.570906\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.46093 | −0.354079 | −0.177040 | − | 0.984204i | \(-0.556652\pi\) | ||||
−0.177040 | + | 0.984204i | \(0.556652\pi\) | |||||||
\(572\) | 10.3299 | 0.431915 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.04326 | 0.210502 | ||||||||
\(575\) | 19.5421 | 0.814964 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.0207 | 0.708579 | 0.354290 | − | 0.935136i | \(-0.384723\pi\) | ||||
0.354290 | + | 0.935136i | \(0.384723\pi\) | |||||||
\(578\) | −8.76429 | −0.364546 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.11331 | 0.0462276 | ||||||||
\(581\) | 1.44730 | 0.0600440 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.67704 | 0.152288 | ||||||||
\(584\) | −11.1236 | −0.460300 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.6198 | −1.18227 | ||||||||
\(587\) | 39.3515 | 1.62421 | 0.812104 | − | 0.583512i | \(-0.198322\pi\) | ||||
0.812104 | + | 0.583512i | \(0.198322\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.844342 | 0.0347905 | ||||||||
\(590\) | −13.1134 | −0.539872 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.31319 | −0.218371 | ||||||||
\(593\) | 36.0916 | 1.48211 | 0.741053 | − | 0.671447i | \(-0.234327\pi\) | ||||
0.741053 | + | 0.671447i | \(0.234327\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.23668 | 0.173687 | ||||||||
\(596\) | −0.535070 | −0.0219173 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 33.1344 | 1.35497 | ||||||||
\(599\) | −16.7381 | −0.683899 | −0.341950 | − | 0.939718i | \(-0.611087\pi\) | ||||
−0.341950 | + | 0.939718i | \(0.611087\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.8782 | 1.42271 | 0.711357 | − | 0.702831i | \(-0.248081\pi\) | ||||
0.711357 | + | 0.702831i | \(0.248081\pi\) | |||||||
\(602\) | 15.1460 | 0.617303 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.08023 | −0.247401 | ||||||||
\(605\) | −23.6163 | −0.960138 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.1367 | −0.695555 | −0.347778 | − | 0.937577i | \(-0.613064\pi\) | ||||
−0.347778 | + | 0.937577i | \(0.613064\pi\) | |||||||
\(608\) | 5.33165 | 0.216227 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.0177 | 0.567561 | ||||||||
\(611\) | −11.0989 | −0.449015 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.2408 | 0.777130 | 0.388565 | − | 0.921421i | \(-0.372971\pi\) | ||||
0.388565 | + | 0.921421i | \(0.372971\pi\) | |||||||
\(614\) | 11.3098 | 0.456427 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.3050 | 0.656948 | ||||||||
\(617\) | −30.2743 | −1.21880 | −0.609398 | − | 0.792864i | \(-0.708589\pi\) | ||||
−0.609398 | + | 0.792864i | \(0.708589\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.7250 | −1.39571 | −0.697857 | − | 0.716237i | \(-0.745863\pi\) | ||||
−0.697857 | + | 0.716237i | \(0.745863\pi\) | |||||||
\(620\) | 0.232160 | 0.00932376 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.3617 | 0.615948 | ||||||||
\(623\) | 5.15405 | 0.206493 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.24413 | 0.0497654 | ||||||||
\(626\) | 0.802914 | 0.0320909 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.56379 | −0.341732 | ||||||||
\(629\) | 5.75664 | 0.229532 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.79750 | −0.151176 | −0.0755881 | − | 0.997139i | \(-0.524083\pi\) | ||||
−0.0755881 | + | 0.997139i | \(0.524083\pi\) | |||||||
\(632\) | −22.1330 | −0.880404 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 27.1427 | 1.07797 | ||||||||
\(635\) | −1.34151 | −0.0532360 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.35012 | −0.172358 | ||||||||
\(638\) | 12.4700 | 0.493690 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.28947 | −0.327670 | ||||||||
\(641\) | −3.57080 | −0.141038 | −0.0705190 | − | 0.997510i | \(-0.522466\pi\) | ||||
−0.0705190 | + | 0.997510i | \(0.522466\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.5350 | −0.967565 | −0.483782 | − | 0.875188i | \(-0.660737\pi\) | ||||
−0.483782 | + | 0.875188i | \(0.660737\pi\) | |||||||
\(644\) | −2.71114 | −0.106834 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.53379 | 0.335757 | ||||||||
\(647\) | 3.17518 | 0.124829 | 0.0624147 | − | 0.998050i | \(-0.480120\pi\) | ||||
0.0624147 | + | 0.998050i | \(0.480120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41.9116 | 1.64517 | ||||||||
\(650\) | 17.3662 | 0.681160 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.41170 | 0.0944493 | ||||||||
\(653\) | −17.8809 | −0.699733 | −0.349866 | − | 0.936800i | \(-0.613773\pi\) | ||||
−0.349866 | + | 0.936800i | \(0.613773\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.23574 | 0.0482843 | ||||||||
\(656\) | 11.7849 | 0.460123 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.18263 | −0.124072 | ||||||||
\(659\) | −18.7474 | −0.730295 | −0.365148 | − | 0.930950i | \(-0.618982\pi\) | ||||
−0.365148 | + | 0.930950i | \(0.618982\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −47.9298 | −1.86425 | −0.932127 | − | 0.362131i | \(-0.882049\pi\) | ||||
−0.932127 | + | 0.362131i | \(0.882049\pi\) | |||||||
\(662\) | 28.0970 | 1.09202 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.41228 | 0.171230 | ||||||||
\(665\) | 2.90600 | 0.112690 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.4134 | −0.441930 | ||||||||
\(668\) | −3.19774 | −0.123724 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.36373 | −0.129952 | ||||||||
\(671\) | −44.8018 | −1.72955 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.8538 | 1.42061 | 0.710305 | − | 0.703894i | \(-0.248557\pi\) | ||||
0.710305 | + | 0.703894i | \(0.248557\pi\) | |||||||
\(674\) | 22.3665 | 0.861523 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.63003 | −0.101155 | ||||||||
\(677\) | 5.44042 | 0.209092 | 0.104546 | − | 0.994520i | \(-0.466661\pi\) | ||||
0.104546 | + | 0.994520i | \(0.466661\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.05155 | −0.0403547 | ||||||||
\(680\) | 12.9161 | 0.495310 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.60038 | 0.0995736 | ||||||||
\(683\) | −33.7346 | −1.29082 | −0.645408 | − | 0.763838i | \(-0.723313\pi\) | ||||
−0.645408 | + | 0.763838i | \(0.723313\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0591 | −0.460754 | ||||||||
\(686\) | −1.24740 | −0.0476259 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 35.3925 | 1.34933 | ||||||||
\(689\) | −2.99078 | −0.113940 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.00717620 | 0.000272995 0 | 0.000136498 | − | 1.00000i | \(-0.499957\pi\) | ||||
0.000136498 | 1.00000i | \(0.499957\pi\) | ||||||||
\(692\) | −8.77147 | −0.333441 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.6589 | 0.518484 | ||||||||
\(695\) | 4.61749 | 0.175151 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.7685 | −0.483641 | ||||||||
\(698\) | 16.2172 | 0.613830 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.42095 | −0.0537068 | ||||||||
\(701\) | 40.5873 | 1.53296 | 0.766480 | − | 0.642268i | \(-0.222006\pi\) | ||||
0.766480 | + | 0.642268i | \(0.222006\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.94856 | 0.148923 | ||||||||
\(704\) | 47.5995 | 1.79397 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.52053 | −0.320675 | ||||||||
\(707\) | −11.1364 | −0.418826 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.8397 | −0.970430 | −0.485215 | − | 0.874395i | \(-0.661259\pi\) | ||||
−0.485215 | + | 0.874395i | \(0.661259\pi\) | |||||||
\(710\) | −27.0234 | −1.01417 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.7128 | 0.588863 | ||||||||
\(713\) | −2.38006 | −0.0891340 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.2111 | 1.16723 | ||||||||
\(716\) | −7.90375 | −0.295377 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19.3368 | −0.721642 | ||||||||
\(719\) | −11.3043 | −0.421581 | −0.210791 | − | 0.977531i | \(-0.567604\pi\) | ||||
−0.210791 | + | 0.977531i | \(0.567604\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.94345 | −0.109620 | ||||||||
\(722\) | −17.8471 | −0.664202 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.4023 | −0.386598 | ||||||||
\(725\) | −5.98195 | −0.222164 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.2507 | −1.34446 | −0.672232 | − | 0.740340i | \(-0.734664\pi\) | ||||
−0.672232 | + | 0.740340i | \(0.734664\pi\) | |||||||
\(728\) | −13.2619 | −0.491520 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.10575 | −0.225984 | ||||||||
\(731\) | −38.3464 | −1.41829 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.7267 | 1.54121 | 0.770605 | − | 0.637313i | \(-0.219954\pi\) | ||||
0.770605 | + | 0.637313i | \(0.219954\pi\) | |||||||
\(734\) | −11.9413 | −0.440761 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.0290 | −0.553978 | ||||||||
\(737\) | 10.7507 | 0.396009 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.4262 | 1.30317 | 0.651587 | − | 0.758574i | \(-0.274104\pi\) | ||||
0.651587 | + | 0.758574i | \(0.274104\pi\) | |||||||
\(740\) | 1.08569 | 0.0399109 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.857607 | −0.0314837 | ||||||||
\(743\) | −33.0960 | −1.21417 | −0.607087 | − | 0.794635i | \(-0.707662\pi\) | ||||
−0.607087 | + | 0.794635i | \(0.707662\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.61668 | −0.0592306 | ||||||||
\(746\) | −9.97577 | −0.365239 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.49943 | −0.274206 | ||||||||
\(749\) | 17.8510 | 0.652260 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.221433 | −0.00808019 | −0.00404010 | − | 0.999992i | \(-0.501286\pi\) | ||||
−0.00404010 | + | 0.999992i | \(0.501286\pi\) | |||||||
\(752\) | −7.43704 | −0.271201 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.1426 | −0.369373 | ||||||||
\(755\) | −18.3710 | −0.668589 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.55021 | 0.347108 | 0.173554 | − | 0.984824i | \(-0.444475\pi\) | ||||
0.173554 | + | 0.984824i | \(0.444475\pi\) | |||||||
\(758\) | −21.2921 | −0.773363 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.85934 | 0.321362 | ||||||||
\(761\) | 29.0094 | 1.05159 | 0.525794 | − | 0.850612i | \(-0.323768\pi\) | ||||
0.525794 | + | 0.850612i | \(0.323768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.89841 | −0.249739 | ||||||||
\(764\) | 7.17967 | 0.259751 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.11679 | 0.293271 | ||||||||
\(767\) | −34.0894 | −1.23090 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.1448 | −1.66402 | −0.832012 | − | 0.554758i | \(-0.812811\pi\) | ||||
−0.832012 | + | 0.554758i | \(0.812811\pi\) | |||||||
\(770\) | 8.94980 | 0.322529 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.47961 | 0.161225 | ||||||||
\(773\) | 9.10578 | 0.327512 | 0.163756 | − | 0.986501i | \(-0.447639\pi\) | ||||
0.163756 | + | 0.986501i | \(0.447639\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.24743 | −0.0448088 | ||||||||
\(776\) | −3.20579 | −0.115081 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.93446 | −0.356168 | ||||||||
\(779\) | −8.75808 | −0.313791 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 86.3689 | 3.09052 | ||||||||
\(782\) | −24.0554 | −0.860218 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.91487 | −0.104103 | ||||||||
\(785\) | −25.8749 | −0.923516 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.1514 | −0.575734 | −0.287867 | − | 0.957670i | \(-0.592946\pi\) | ||||
−0.287867 | + | 0.957670i | \(0.592946\pi\) | |||||||
\(788\) | −2.00086 | −0.0712776 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.1488 | −0.432234 | ||||||||
\(791\) | 7.27356 | 0.258618 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.4402 | 1.29403 | ||||||||
\(794\) | 7.05780 | 0.250472 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.95620 | −0.352888 | ||||||||
\(797\) | −42.5067 | −1.50566 | −0.752832 | − | 0.658213i | \(-0.771313\pi\) | ||||
−0.752832 | + | 0.658213i | \(0.771313\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.05775 | 0.285063 | ||||||||
\(800\) | −7.87694 | −0.278492 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.4063 | −0.367458 | ||||||||
\(803\) | 19.5145 | 0.688651 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.19154 | −0.288714 | ||||||||
\(806\) | −2.11506 | −0.0744997 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −33.9508 | −1.19438 | ||||||||
\(809\) | 15.8564 | 0.557482 | 0.278741 | − | 0.960366i | \(-0.410083\pi\) | ||||
0.278741 | + | 0.960366i | \(0.410083\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.5190 | −1.21213 | −0.606063 | − | 0.795417i | \(-0.707252\pi\) | ||||
−0.606063 | + | 0.795417i | \(0.707252\pi\) | |||||||
\(812\) | 0.829895 | 0.0291236 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.1606 | 0.426230 | ||||||||
\(815\) | 7.28678 | 0.255245 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.3023 | −0.920202 | ||||||||
\(818\) | 43.8574 | 1.53344 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.40812 | −0.0840951 | ||||||||
\(821\) | 30.4097 | 1.06130 | 0.530652 | − | 0.847590i | \(-0.321947\pi\) | ||||
0.530652 | + | 0.847590i | \(0.321947\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −49.9569 | −1.74139 | −0.870694 | − | 0.491826i | \(-0.836330\pi\) | ||||
−0.870694 | + | 0.491826i | \(0.836330\pi\) | |||||||
\(824\) | −8.97352 | −0.312607 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.77516 | −0.340121 | ||||||||
\(827\) | 38.7472 | 1.34737 | 0.673685 | − | 0.739018i | \(-0.264710\pi\) | ||||
0.673685 | + | 0.739018i | \(0.264710\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.4751 | −0.468009 | −0.234004 | − | 0.972236i | \(-0.575183\pi\) | ||||
−0.234004 | + | 0.972236i | \(0.575183\pi\) | |||||||
\(830\) | 2.42189 | 0.0840652 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −38.7158 | −1.34223 | ||||||||
\(833\) | 3.15816 | 0.109424 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.66176 | −0.334359 | ||||||||
\(836\) | −5.14396 | −0.177908 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.64288 | −0.229474 | ||||||||
\(839\) | 12.9736 | 0.447899 | 0.223949 | − | 0.974601i | \(-0.428105\pi\) | ||||
0.223949 | + | 0.974601i | \(0.428105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.5063 | −0.879527 | ||||||||
\(842\) | 11.0029 | 0.379183 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.359347 | −0.0123692 | ||||||||
\(845\) | −7.94647 | −0.273367 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.6043 | −0.604891 | ||||||||
\(848\) | −2.00402 | −0.0688185 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.6078 | −0.432443 | ||||||||
\(851\) | −11.1303 | −0.381543 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.5643 | 0.875305 | 0.437653 | − | 0.899144i | \(-0.355810\pi\) | ||||
0.437653 | + | 0.899144i | \(0.355810\pi\) | |||||||
\(854\) | 10.4492 | 0.357566 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 54.4211 | 1.86007 | ||||||||
\(857\) | 33.0517 | 1.12903 | 0.564513 | − | 0.825424i | \(-0.309064\pi\) | ||||
0.564513 | + | 0.825424i | \(0.309064\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.4442 | 1.51641 | 0.758207 | − | 0.652013i | \(-0.226075\pi\) | ||||
0.758207 | + | 0.652013i | \(0.226075\pi\) | |||||||
\(860\) | −7.23208 | −0.246612 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.8485 | −0.846342 | ||||||||
\(863\) | 23.4382 | 0.797845 | 0.398923 | − | 0.916985i | \(-0.369384\pi\) | ||||
0.398923 | + | 0.916985i | \(0.369384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.5024 | −0.901109 | ||||||||
\(866\) | −25.1873 | −0.855901 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.173059 | 0.00587401 | ||||||||
\(869\) | 38.8285 | 1.31717 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.74428 | −0.296289 | ||||||||
\(872\) | −21.0307 | −0.712191 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16.4999 | −0.558117 | ||||||||
\(875\) | −11.0008 | −0.371896 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.3000 | −0.584178 | −0.292089 | − | 0.956391i | \(-0.594350\pi\) | ||||
−0.292089 | + | 0.956391i | \(0.594350\pi\) | |||||||
\(878\) | 33.5037 | 1.13070 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 20.9136 | 0.704996 | ||||||||
\(881\) | −39.8133 | −1.34135 | −0.670673 | − | 0.741753i | \(-0.733995\pi\) | ||||
−0.670673 | + | 0.741753i | \(0.733995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.6937 | −0.393525 | −0.196763 | − | 0.980451i | \(-0.563043\pi\) | ||||
−0.196763 | + | 0.980451i | \(0.563043\pi\) | |||||||
\(884\) | 6.09978 | 0.205158 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.9201 | −0.366867 | ||||||||
\(887\) | 15.0546 | 0.505484 | 0.252742 | − | 0.967534i | \(-0.418668\pi\) | ||||
0.252742 | + | 0.967534i | \(0.418668\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 8.62475 | 0.289102 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.07860 | −0.103079 | ||||||||
\(893\) | 5.52692 | 0.184951 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.8807 | −0.798242 | ||||||||
\(896\) | −6.17923 | −0.206434 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.1638 | 0.372540 | ||||||||
\(899\) | 0.728550 | 0.0242985 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.17128 | 0.0723359 | ||||||||
\(902\) | −26.9729 | −0.898098 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22.1744 | 0.737511 | ||||||||
\(905\) | −31.4298 | −1.04476 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.3901 | −0.544225 | −0.272112 | − | 0.962265i | \(-0.587722\pi\) | ||||
−0.272112 | + | 0.962265i | \(0.587722\pi\) | |||||||
\(908\) | 4.66651 | 0.154864 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.27946 | −0.241312 | ||||||||
\(911\) | −37.9073 | −1.25592 | −0.627962 | − | 0.778244i | \(-0.716111\pi\) | ||||
−0.627962 | + | 0.778244i | \(0.716111\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.74057 | −0.256176 | ||||||||
\(914\) | −4.92279 | −0.162832 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.00730 | 0.231528 | ||||||||
\(917\) | 0.921159 | 0.0304193 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.73720 | 0.222240 | 0.111120 | − | 0.993807i | \(-0.464556\pi\) | ||||
0.111120 | + | 0.993807i | \(0.464556\pi\) | |||||||
\(920\) | −24.9730 | −0.823337 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.0574 | −0.726422 | ||||||||
\(923\) | −70.2495 | −2.31229 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.83357 | −0.191807 | ||||||||
\(926\) | 23.8738 | 0.784543 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.60047 | 0.151018 | ||||||||
\(929\) | −1.91596 | −0.0628605 | −0.0314302 | − | 0.999506i | \(-0.510006\pi\) | ||||
−0.0314302 | + | 0.999506i | \(0.510006\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.16622 | 0.0709951 | ||||||||
\(932\) | 1.12626 | 0.0368920 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26.2249 | −0.858106 | ||||||||
\(935\) | −22.6591 | −0.741030 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.3384 | 0.762433 | 0.381216 | − | 0.924486i | \(-0.375505\pi\) | ||||
0.381216 | + | 0.924486i | \(0.375505\pi\) | |||||||
\(938\) | −2.50743 | −0.0818704 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.51968 | 0.0495665 | ||||||||
\(941\) | 38.3365 | 1.24973 | 0.624867 | − | 0.780731i | \(-0.285153\pi\) | ||||
0.624867 | + | 0.780731i | \(0.285153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.6876 | 0.803939 | ||||||||
\(944\) | −22.8422 | −0.743451 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −81.0051 | −2.63370 | ||||||||
\(947\) | −59.7658 | −1.94213 | −0.971064 | − | 0.238821i | \(-0.923239\pi\) | ||||
−0.971064 | + | 0.238821i | \(0.923239\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.8724 | −0.515240 | ||||||||
\(950\) | −8.64784 | −0.280573 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.62807 | 0.312048 | ||||||||
\(953\) | −52.0956 | −1.68754 | −0.843771 | − | 0.536703i | \(-0.819670\pi\) | ||||
−0.843771 | + | 0.536703i | \(0.819670\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.6929 | 0.701966 | ||||||||
\(956\) | 4.92330 | 0.159231 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.93386 | −0.0947886 | ||||||||
\(959\) | −8.98921 | −0.290277 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8481 | −0.995099 | ||||||||
\(962\) | −9.89104 | −0.318900 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.6809 | −0.376218 | ||||||||
\(965\) | 13.5348 | 0.435702 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.9971 | 0.578748 | 0.289374 | − | 0.957216i | \(-0.406553\pi\) | ||||
0.289374 | + | 0.957216i | \(0.406553\pi\) | |||||||
\(968\) | −53.6692 | −1.72499 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.75965 | −0.0564990 | ||||||||
\(971\) | −21.2618 | −0.682324 | −0.341162 | − | 0.940005i | \(-0.610820\pi\) | ||||
−0.341162 | + | 0.940005i | \(0.610820\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.44202 | 0.110346 | ||||||||
\(974\) | 33.9664 | 1.08835 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.4174 | 0.781582 | ||||||||
\(977\) | −41.7439 | −1.33551 | −0.667753 | − | 0.744383i | \(-0.732744\pi\) | ||||
−0.667753 | + | 0.744383i | \(0.732744\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.5654 | −0.880994 | ||||||||
\(980\) | 0.595623 | 0.0190265 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.0785 | −0.417353 | ||||||||
\(983\) | −24.8258 | −0.791821 | −0.395910 | − | 0.918289i | \(-0.629571\pi\) | ||||
−0.395910 | + | 0.918289i | \(0.629571\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.04546 | −0.192624 | ||||||||
\(986\) | 7.36347 | 0.234501 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.18392 | 0.133108 | ||||||||
\(989\) | 74.1420 | 2.35758 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.9314 | 1.17317 | 0.586583 | − | 0.809889i | \(-0.300473\pi\) | ||||
0.586583 | + | 0.809889i | \(0.300473\pi\) | |||||||
\(992\) | 0.959342 | 0.0304591 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20.1441 | −0.638931 | ||||||||
\(995\) | −30.0820 | −0.953664 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.3243 | 1.34042 | 0.670212 | − | 0.742169i | \(-0.266203\pi\) | ||||
0.670212 | + | 0.742169i | \(0.266203\pi\) | |||||||
\(998\) | 12.4472 | 0.394011 | ||||||||
\(999\) | 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 | 8001.2.a.y.1.19 | yes | 28 | |
3.2 | odd | 2 | inner | 8001.2.a.y.1.10 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.y.1.10 | ✓ | 28 | 3.2 | odd | 2 | inner | |
8001.2.a.y.1.19 | yes | 28 | 1.1 | even | 1 | trivial |