Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1328,2,Mod(1,1328)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1328, 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("1328.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1328 = 2^{4} \cdot 83 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1328.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: | \(10.6041333884\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 18x^{6} + 33x^{5} + 87x^{4} - 127x^{3} - 126x^{2} + 100x - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 664) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.297635\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1328.1 |
$q$-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 | ||||||||
\(3\) | −0.297635 | −0.171840 | −0.0859198 | − | 0.996302i | \(-0.527383\pi\) | ||||
−0.0859198 | + | 0.996302i | \(0.527383\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.84665 | 1.72027 | 0.860136 | − | 0.510064i | \(-0.170378\pi\) | ||||
0.860136 | + | 0.510064i | \(0.170378\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.95246 | −0.737961 | −0.368981 | − | 0.929437i | \(-0.620293\pi\) | ||||
−0.368981 | + | 0.929437i | \(0.620293\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.91141 | −0.970471 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.36179 | −1.01362 | −0.506808 | − | 0.862059i | \(-0.669175\pi\) | ||||
−0.506808 | + | 0.862059i | \(0.669175\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.30849 | 1.19496 | 0.597480 | − | 0.801884i | \(-0.296169\pi\) | ||||
0.597480 | + | 0.801884i | \(0.296169\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.14490 | −0.295611 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.55797 | −0.862934 | −0.431467 | − | 0.902129i | \(-0.642004\pi\) | ||||
−0.431467 | + | 0.902129i | \(0.642004\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.21341 | 1.42545 | 0.712727 | − | 0.701441i | \(-0.247460\pi\) | ||||
0.712727 | + | 0.701441i | \(0.247460\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.581121 | 0.126811 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.13909 | 1.28009 | 0.640044 | − | 0.768338i | \(-0.278916\pi\) | ||||
0.640044 | + | 0.768338i | \(0.278916\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.79670 | 1.95934 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.75944 | 0.338605 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.67464 | 1.79653 | 0.898267 | − | 0.439449i | \(-0.144826\pi\) | ||||
0.898267 | + | 0.439449i | \(0.144826\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.49202 | 0.806790 | 0.403395 | − | 0.915026i | \(-0.367830\pi\) | ||||
0.403395 | + | 0.915026i | \(0.367830\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00058 | 0.174179 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.51043 | −1.26949 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.91141 | 0.971830 | 0.485915 | − | 0.874006i | \(-0.338486\pi\) | ||||
0.485915 | + | 0.874006i | \(0.338486\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.28236 | −0.205341 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.02818 | −1.09762 | −0.548809 | − | 0.835948i | \(-0.684919\pi\) | ||||
−0.548809 | + | 0.835948i | \(0.684919\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.98694 | 1.21800 | 0.608998 | − | 0.793172i | \(-0.291572\pi\) | ||||
0.608998 | + | 0.793172i | \(0.291572\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.1992 | −1.66948 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.67793 | −0.974076 | −0.487038 | − | 0.873381i | \(-0.661923\pi\) | ||||
−0.487038 | + | 0.873381i | \(0.661923\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.18789 | −0.455413 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.05898 | 0.148286 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.940210 | 0.129148 | 0.0645739 | − | 0.997913i | \(-0.479431\pi\) | ||||
0.0645739 | + | 0.997913i | \(0.479431\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.9316 | −1.74370 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.84933 | −0.244949 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.84423 | 0.630666 | 0.315333 | − | 0.948981i | \(-0.397884\pi\) | ||||
0.315333 | + | 0.948981i | \(0.397884\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.67464 | 1.23871 | 0.619355 | − | 0.785111i | \(-0.287394\pi\) | ||||
0.619355 | + | 0.785111i | \(0.287394\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.68442 | 0.716170 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.5732 | 2.05566 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.8131 | −1.56537 | −0.782687 | − | 0.622415i | \(-0.786152\pi\) | ||||
−0.782687 | + | 0.622415i | \(0.786152\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.82721 | −0.219970 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.78876 | 1.04303 | 0.521517 | − | 0.853241i | \(-0.325366\pi\) | ||||
0.521517 | + | 0.853241i | \(0.325366\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.27320 | −0.617181 | −0.308591 | − | 0.951195i | \(-0.599857\pi\) | ||||
−0.308591 | + | 0.951195i | \(0.599857\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.91584 | −0.336692 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.56376 | 0.748010 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.0101 | −1.46375 | −0.731876 | − | 0.681438i | \(-0.761355\pi\) | ||||
−0.731876 | + | 0.681438i | \(0.761355\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.21057 | 0.912285 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.00000 | 0.109764 | ||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.6863 | −1.48448 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.87951 | −0.308716 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.89620 | 0.200997 | 0.100498 | − | 0.994937i | \(-0.467956\pi\) | ||||
0.100498 | + | 0.994937i | \(0.467956\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.41216 | −0.881834 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.33698 | −0.138638 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.9008 | 2.45217 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.58949 | 0.567527 | 0.283764 | − | 0.958894i | \(-0.408417\pi\) | ||||
0.283764 | + | 0.958894i | \(0.408417\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.78755 | 0.983686 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.92663 | −0.987736 | −0.493868 | − | 0.869537i | \(-0.664417\pi\) | ||||
−0.493868 | + | 0.869537i | \(0.664417\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.1172 | 1.68660 | 0.843302 | − | 0.537439i | \(-0.180608\pi\) | ||||
0.843302 | + | 0.537439i | \(0.180608\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.23537 | 0.218149 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.96471 | −0.479957 | −0.239978 | − | 0.970778i | \(-0.577140\pi\) | ||||
−0.239978 | + | 0.970778i | \(0.577140\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.2864 | −1.94309 | −0.971543 | − | 0.236862i | \(-0.923881\pi\) | ||||
−0.971543 | + | 0.236862i | \(0.923881\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.75944 | −0.166999 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.69082 | −0.441275 | −0.220637 | − | 0.975356i | \(-0.570814\pi\) | ||||
−0.220637 | + | 0.975356i | \(0.570814\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.6149 | 2.20210 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.5438 | −1.15967 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.94680 | 0.636812 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.301612 | 0.0274193 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.09183 | 0.188614 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 18.4512 | 1.65033 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.30316 | −0.470579 | −0.235290 | − | 0.971925i | \(-0.575604\pi\) | ||||
−0.235290 | + | 0.971925i | \(0.575604\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.37719 | −0.209300 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.57603 | −0.312439 | −0.156219 | − | 0.987722i | \(-0.549931\pi\) | ||||
−0.156219 | + | 0.987722i | \(0.549931\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.1314 | −1.05193 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.76795 | 0.582493 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.89497 | 0.332770 | 0.166385 | − | 0.986061i | \(-0.446791\pi\) | ||||
0.166385 | + | 0.986061i | \(0.446791\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.8799 | 1.00764 | 0.503819 | − | 0.863809i | \(-0.331928\pi\) | ||||
0.503819 | + | 0.863809i | \(0.331928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.98758 | 0.167385 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.4842 | −1.21123 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 37.2149 | 3.09053 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.948828 | 0.0782580 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.607903 | −0.0498013 | −0.0249007 | − | 0.999690i | \(-0.507927\pi\) | ||||
−0.0249007 | + | 0.999690i | \(0.507927\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.9340 | 1.54083 | 0.770415 | − | 0.637543i | \(-0.220049\pi\) | ||||
0.770415 | + | 0.637543i | \(0.220049\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.3587 | 0.837453 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.2792 | 1.38790 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.6682 | −1.41008 | −0.705040 | − | 0.709168i | \(-0.749071\pi\) | ||||
−0.705040 | + | 0.709168i | \(0.749071\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.279839 | −0.0221927 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.9863 | −0.944656 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.8366 | 1.39707 | 0.698534 | − | 0.715577i | \(-0.253836\pi\) | ||||
0.698534 | + | 0.715577i | \(0.253836\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.84890 | 0.299636 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.87561 | −0.145139 | −0.0725693 | − | 0.997363i | \(-0.523120\pi\) | ||||
−0.0725693 | + | 0.997363i | \(0.523120\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.56306 | 0.427928 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.0898 | −1.38336 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.83264 | 0.215361 | 0.107681 | − | 0.994186i | \(-0.465658\pi\) | ||||
0.107681 | + | 0.994186i | \(0.465658\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −19.1277 | −1.44592 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.44181 | −0.108373 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.63502 | −0.720155 | −0.360078 | − | 0.932922i | \(-0.617250\pi\) | ||||
−0.360078 | + | 0.932922i | \(0.617250\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0440 | −1.04388 | −0.521941 | − | 0.852982i | \(-0.674792\pi\) | ||||
−0.521941 | + | 0.852982i | \(0.674792\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.87951 | −0.212859 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.7391 | 1.67181 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.9611 | 0.874685 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.43524 | −0.249877 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.7727 | −0.851846 | −0.425923 | − | 0.904759i | \(-0.640050\pi\) | ||||
−0.425923 | + | 0.904759i | \(0.640050\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.4497 | −1.54399 | −0.771993 | − | 0.635631i | \(-0.780740\pi\) | ||||
−0.771993 | + | 0.635631i | \(0.780740\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.93277 | −0.353243 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.87874 | 0.703831 | 0.351916 | − | 0.936032i | \(-0.385530\pi\) | ||||
0.351916 | + | 0.936032i | \(0.385530\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.5924 | 1.10531 | 0.552656 | − | 0.833409i | \(-0.313614\pi\) | ||||
0.552656 | + | 0.833409i | \(0.313614\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.81364 | 0.268993 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.8894 | −1.32577 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −27.0349 | −1.88820 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −17.8734 | −1.24229 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.8882 | −1.44486 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.5994 | −0.729695 | −0.364848 | − | 0.931067i | \(-0.618879\pi\) | ||||
−0.364848 | + | 0.931067i | \(0.618879\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.61584 | −0.179234 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 30.7229 | 2.09529 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.77049 | −0.595380 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.56949 | 0.106056 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.3295 | −1.03117 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.2459 | −1.42273 | −0.711365 | − | 0.702822i | \(-0.751923\pi\) | ||||
−0.711365 | + | 0.702822i | \(0.751923\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −28.5222 | −1.90148 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.67282 | −0.111029 | −0.0555144 | − | 0.998458i | \(-0.517680\pi\) | ||||
−0.0555144 | + | 0.998458i | \(0.517680\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.6746 | 0.903641 | 0.451821 | − | 0.892109i | \(-0.350775\pi\) | ||||
0.451821 | + | 0.892109i | \(0.350775\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.95360 | −0.128538 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.0677 | 0.987120 | 0.493560 | − | 0.869712i | \(-0.335695\pi\) | ||||
0.493560 | + | 0.869712i | \(0.335695\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.6876 | −1.67568 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.87226 | 0.251530 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.13774 | −0.202963 | −0.101482 | − | 0.994837i | \(-0.532358\pi\) | ||||
−0.101482 | + | 0.994837i | \(0.532358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.0347 | 1.35497 | 0.677483 | − | 0.735538i | \(-0.263071\pi\) | ||||
0.677483 | + | 0.735538i | \(0.263071\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.72208 | −0.495372 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.2627 | −0.783435 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.7704 | 1.70336 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.297635 | −0.0188618 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.7003 | −1.49595 | −0.747976 | − | 0.663726i | \(-0.768974\pi\) | ||||
−0.747976 | + | 0.663726i | \(0.768974\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.6383 | −1.29752 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.07351 | 0.255093 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.78673 | −0.548101 | −0.274050 | − | 0.961715i | \(-0.588364\pi\) | ||||
−0.274050 | + | 0.961715i | \(0.588364\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.5418 | −0.717173 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28.1669 | −1.74349 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.33838 | −0.575829 | −0.287915 | − | 0.957656i | \(-0.592962\pi\) | ||||
−0.287915 | + | 0.957656i | \(0.592962\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.61666 | 0.222169 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.564375 | −0.0345392 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.1829 | 1.59640 | 0.798198 | − | 0.602395i | \(-0.205787\pi\) | ||||
0.798198 | + | 0.602395i | \(0.205787\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.8483 | −1.08421 | −0.542103 | − | 0.840312i | \(-0.682372\pi\) | ||||
−0.542103 | + | 0.840312i | \(0.682372\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.50375 | 0.151534 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −32.9344 | −1.98602 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.1906 | −0.852631 | −0.426315 | − | 0.904575i | \(-0.640189\pi\) | ||||
−0.426315 | + | 0.904575i | \(0.640189\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.0781 | −0.782967 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.1483 | 0.605397 | 0.302699 | − | 0.953086i | \(-0.402112\pi\) | ||||
0.302699 | + | 0.953086i | \(0.402112\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.5364 | 0.626327 | 0.313163 | − | 0.949699i | \(-0.398611\pi\) | ||||
0.313163 | + | 0.949699i | \(0.398611\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.11371 | −0.421380 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.7223 | 0.809999 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.34085 | −0.255344 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.66363 | −0.0975236 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.49114 | 0.203954 | 0.101977 | − | 0.994787i | \(-0.467483\pi\) | ||||
0.101977 | + | 0.994787i | \(0.467483\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.6341 | 1.08492 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.91487 | −0.343216 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 26.4502 | 1.52965 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.5942 | −0.898834 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.95451 | 0.169732 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 37.2149 | 2.13092 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.48031 | 0.255705 | 0.127852 | − | 0.991793i | \(-0.459192\pi\) | ||||
0.127852 | + | 0.991793i | \(0.459192\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.09466 | −0.289825 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.9209 | −1.52654 | −0.763271 | − | 0.646079i | \(-0.776408\pi\) | ||||
−0.763271 | + | 0.646079i | \(0.776408\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.7811 | 0.892000 | 0.446000 | − | 0.895033i | \(-0.352848\pi\) | ||||
0.446000 | + | 0.895033i | \(0.352848\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 21.8660 | 1.23201 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.6425 | −0.766242 | −0.383121 | − | 0.923698i | \(-0.625151\pi\) | ||||
−0.383121 | + | 0.923698i | \(0.625151\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.5241 | −1.82100 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.47767 | 0.0824756 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.1071 | −1.23007 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 42.2089 | 2.34133 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.03794 | 0.333899 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.0384 | 0.718831 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.95696 | 0.272459 | 0.136229 | − | 0.990677i | \(-0.456502\pi\) | ||||
0.136229 | + | 0.990677i | \(0.456502\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.2106 | −0.943133 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −49.2876 | −2.69287 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.29444 | −0.397354 | −0.198677 | − | 0.980065i | \(-0.563664\pi\) | ||||
−0.198677 | + | 0.980065i | \(0.563664\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.39615 | 0.0758285 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.1012 | −0.817776 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8915 | 1.07404 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.02862 | −0.378408 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.57397 | −0.0844949 | −0.0422474 | − | 0.999107i | \(-0.513452\pi\) | ||||
−0.0422474 | + | 0.999107i | \(0.513452\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.8257 | 1.43595 | 0.717973 | − | 0.696071i | \(-0.245070\pi\) | ||||
0.717973 | + | 0.696071i | \(0.245070\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.58054 | 0.404619 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.4802 | −0.717480 | −0.358740 | − | 0.933438i | \(-0.616794\pi\) | ||||
−0.358740 | + | 0.933438i | \(0.616794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.8072 | 1.79430 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.06761 | −0.109429 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.5146 | −0.924387 | −0.462194 | − | 0.886779i | \(-0.652938\pi\) | ||||
−0.462194 | + | 0.886779i | \(0.652938\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.6065 | 1.03192 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0897702 | −0.00471171 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.2841 | −1.06172 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.0719 | 1.83074 | 0.915368 | − | 0.402618i | \(-0.131900\pi\) | ||||
0.915368 | + | 0.402618i | \(0.131900\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.4619 | 1.06521 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.83572 | −0.0953061 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.1613 | −0.526134 | −0.263067 | − | 0.964778i | \(-0.584734\pi\) | ||||
−0.263067 | + | 0.964778i | \(0.584734\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.49172 | −0.283591 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 41.6831 | 2.14679 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.67281 | 0.188659 | 0.0943297 | − | 0.995541i | \(-0.469929\pi\) | ||||
0.0943297 | + | 0.995541i | \(0.469929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.57841 | 0.0808642 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.03677 | 0.104074 | 0.0520369 | − | 0.998645i | \(-0.483429\pi\) | ||||
0.0520369 | + | 0.998645i | \(0.483429\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.2485 | 1.28678 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −23.2533 | −1.18203 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36.2283 | −1.83685 | −0.918424 | − | 0.395598i | \(-0.870537\pi\) | ||||
−0.918424 | + | 0.395598i | \(0.870537\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.8427 | −1.10463 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.06435 | 0.0536894 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −50.0453 | −2.51805 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.63505 | 0.483569 | 0.241785 | − | 0.970330i | \(-0.422267\pi\) | ||||
0.241785 | + | 0.970330i | \(0.422267\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.61074 | 0.180763 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.2376 | −1.01062 | −0.505310 | − | 0.862938i | \(-0.668622\pi\) | ||||
−0.505310 | + | 0.862938i | \(0.668622\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.3538 | 0.964082 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 31.5832 | 1.56938 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.8729 | −0.985064 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.7170 | −0.876049 | −0.438025 | − | 0.898963i | \(-0.644322\pi\) | ||||
−0.438025 | + | 0.898963i | \(0.644322\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.15928 | −0.0571830 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.45818 | −0.465407 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.84665 | 0.188824 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.53586 | −0.173152 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.9831 | 1.26936 | 0.634679 | − | 0.772776i | \(-0.281132\pi\) | ||||
0.634679 | + | 0.772776i | \(0.281132\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.7959 | 1.59837 | 0.799186 | − | 0.601084i | \(-0.205264\pi\) | ||||
0.799186 | + | 0.601084i | \(0.205264\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.4422 | 0.945313 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.8563 | −1.69078 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.8894 | −0.914120 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.31101 | 0.208137 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.6017 | −1.08869 | −0.544343 | − | 0.838862i | \(-0.683221\pi\) | ||||
−0.544343 | + | 0.838862i | \(0.683221\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.9384 | −0.669837 | −0.334919 | − | 0.942247i | \(-0.608709\pi\) | ||||
−0.334919 | + | 0.942247i | \(0.608709\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.0765 | −0.531075 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 38.1447 | 1.82471 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.493599 | 0.0235582 | 0.0117791 | − | 0.999931i | \(-0.496251\pi\) | ||||
0.0117791 | + | 0.999931i | \(0.496251\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.28128 | 0.441966 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.85429 | 0.135611 | 0.0678056 | − | 0.997699i | \(-0.478400\pi\) | ||||
0.0678056 | + | 0.997699i | \(0.478400\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.29401 | 0.345769 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.180933 | 0.00855784 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.1490 | 0.762118 | 0.381059 | − | 0.924551i | \(-0.375560\pi\) | ||||
0.381059 | + | 0.924551i | \(0.375560\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.6273 | 1.11256 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.63543 | −0.264775 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −32.3586 | −1.51699 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.1732 | 0.756552 | 0.378276 | − | 0.925693i | \(-0.376517\pi\) | ||||
0.378276 | + | 0.925693i | \(0.376517\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.26004 | −0.292194 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.0789 | 0.748868 | 0.374434 | − | 0.927253i | \(-0.377837\pi\) | ||||
0.374434 | + | 0.927253i | \(0.377837\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.53936 | 0.303910 | 0.151955 | − | 0.988387i | \(-0.451443\pi\) | ||||
0.151955 | + | 0.988387i | \(0.451443\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.14289 | −0.238496 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 32.9651 | 1.52544 | 0.762720 | − | 0.646728i | \(-0.223863\pi\) | ||||
0.762720 | + | 0.646728i | \(0.223863\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.0172 | 1.15519 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.25869 | 0.242307 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.8504 | −1.23458 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 60.8709 | 2.79295 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.73734 | −0.125334 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.1201 | −1.19346 | −0.596729 | − | 0.802443i | \(-0.703533\pi\) | ||||
−0.596729 | + | 0.802443i | \(0.703533\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.4693 | 1.16130 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.56755 | 0.162329 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.5008 | 0.976301 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.4977 | 0.883524 | 0.441762 | − | 0.897132i | \(-0.354354\pi\) | ||||
0.441762 | + | 0.897132i | \(0.354354\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.30878 | −0.240071 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.3626 | −0.467658 | −0.233829 | − | 0.972278i | \(-0.575126\pi\) | ||||
−0.233829 | + | 0.972278i | \(0.575126\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.4221 | −1.55029 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 37.6493 | 1.69221 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.1597 | −0.769718 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.4833 | −1.27509 | −0.637543 | − | 0.770415i | \(-0.720049\pi\) | ||||
−0.637543 | + | 0.770415i | \(0.720049\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.558245 | 0.0249406 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.6186 | −1.23145 | −0.615726 | − | 0.787960i | \(-0.711137\pi\) | ||||
−0.615726 | + | 0.787960i | \(0.711137\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −38.1842 | −1.69918 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.65576 | −0.0735349 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.4135 | −0.638868 | −0.319434 | − | 0.947608i | \(-0.603493\pi\) | ||||
−0.319434 | + | 0.947608i | \(0.603493\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.2957 | 0.455456 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.9321 | 0.482666 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 65.8437 | 2.90142 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.4498 | 0.987340 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.843092 | −0.0370076 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.2567 | −1.50081 | −0.750407 | − | 0.660976i | \(-0.770142\pi\) | ||||
−0.750407 | + | 0.660976i | \(0.770142\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.1449 | 1.66796 | 0.833979 | − | 0.551796i | \(-0.186057\pi\) | ||||
0.833979 | + | 0.551796i | \(0.186057\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.69306 | 0.248466 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.9825 | −0.696207 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.6884 | 0.638627 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.1036 | −0.612043 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.2808 | −1.31161 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.0975 | −0.825657 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.86772 | 0.123751 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.7170 | 0.461615 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0253 | −0.431020 | −0.215510 | − | 0.976502i | \(-0.569141\pi\) | ||||
−0.215510 | + | 0.976502i | \(0.569141\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.17998 | 0.179380 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −78.0347 | −3.34264 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.9306 | −0.723902 | −0.361951 | − | 0.932197i | \(-0.617889\pi\) | ||||
−0.361951 | + | 0.932197i | \(0.617889\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −28.1669 | −1.20213 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 60.1125 | 2.56088 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.4017 | 1.08019 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.76795 | −0.287284 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.9200 | 1.26775 | 0.633875 | − | 0.773435i | \(-0.281463\pi\) | ||||
0.633875 | + | 0.773435i | \(0.281463\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.4116 | 1.45546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.56005 | −0.150305 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.9551 | −1.22031 | −0.610156 | − | 0.792281i | \(-0.708893\pi\) | ||||
−0.610156 | + | 0.792281i | \(0.708893\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0439 | −0.759113 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.0308 | −0.673231 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.68034 | 0.0704436 | 0.0352218 | − | 0.999380i | \(-0.488786\pi\) | ||||
0.0352218 | + | 0.999380i | \(0.488786\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.5579 | −1.44620 | −0.723101 | − | 0.690742i | \(-0.757284\pi\) | ||||
−0.723101 | + | 0.690742i | \(0.757284\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.50398 | 0.146381 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 60.1428 | 2.50813 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.8924 | 0.911391 | 0.455696 | − | 0.890136i | \(-0.349391\pi\) | ||||
0.455696 | + | 0.890136i | \(0.349391\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.38419 | 0.265318 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.95246 | −0.0810018 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.16079 | −0.130906 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −48.2515 | −1.99496 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.6431 | −0.852033 | −0.426017 | − | 0.904715i | \(-0.640083\pi\) | ||||
−0.426017 | + | 0.904715i | \(0.640083\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.9108 | 1.15004 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.94026 | −0.120946 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.3731 | −0.508101 | −0.254051 | − | 0.967191i | \(-0.581763\pi\) | ||||
−0.254051 | + | 0.967191i | \(0.581763\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.7219 | 1.09549 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.64083 | −0.189936 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.1498 | −0.945874 | −0.472937 | − | 0.881096i | \(-0.656806\pi\) | ||||
−0.472937 | + | 0.881096i | \(0.656806\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.86867 | 0.157806 | 0.0789031 | − | 0.996882i | \(-0.474858\pi\) | ||||
0.0789031 | + | 0.996882i | \(0.474858\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 37.3044 | 1.51915 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.16019 | 0.0471686 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.269972 | −0.0109578 | −0.00547892 | − | 0.999985i | \(-0.501744\pi\) | ||||
−0.00547892 | + | 0.999985i | \(0.501744\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.62213 | 0.227820 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.7718 | −1.16398 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.98773 | −0.241842 | −0.120921 | − | 0.992662i | \(-0.538585\pi\) | ||||
−0.120921 | + | 0.992662i | \(0.538585\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.04654 | 0.324468 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.35394 | 0.255800 | 0.127900 | − | 0.991787i | \(-0.459176\pi\) | ||||
0.127900 | + | 0.991787i | \(0.459176\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.5269 | −1.62891 | −0.814457 | − | 0.580224i | \(-0.802965\pi\) | ||||
−0.814457 | + | 0.580224i | \(0.802965\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.8014 | 0.433444 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.70225 | −0.148328 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.9918 | 0.879671 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.21704 | 0.248285 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.0326 | −0.838626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.95010 | −0.236870 | −0.118435 | − | 0.992962i | \(-0.537788\pi\) | ||||
−0.118435 | + | 0.992962i | \(0.537788\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.15476 | 0.125390 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.3994 | −0.809525 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.7350 | −0.544200 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.5877 | −1.01223 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.4627 | 0.808229 | 0.404114 | − | 0.914708i | \(-0.367580\pi\) | ||||
0.404114 | + | 0.914708i | \(0.367580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.7374 | −1.21217 | −0.606083 | − | 0.795401i | \(-0.707260\pi\) | ||||
−0.606083 | + | 0.795401i | \(0.707260\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.14421 | −0.360053 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.2440 | 0.835188 | 0.417594 | − | 0.908634i | \(-0.362873\pi\) | ||||
0.417594 | + | 0.908634i | \(0.362873\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.2853 | −0.639253 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.61040 | 0.102310 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.26029 | 0.244984 | 0.122492 | − | 0.992470i | \(-0.460911\pi\) | ||||
0.122492 | + | 0.992470i | \(0.460911\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.7557 | −0.537480 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.3525 | 0.598957 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.2457 | 0.438071 | 0.219035 | − | 0.975717i | \(-0.429709\pi\) | ||||
0.219035 | + | 0.975717i | \(0.429709\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.9620 | −1.47655 | −0.738276 | − | 0.674499i | \(-0.764360\pi\) | ||||
−0.738276 | + | 0.674499i | \(0.764360\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.56258 | 0.177196 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −46.6654 | −1.80961 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 59.3935 | 2.29972 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.32352 | 0.244481 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.5241 | −1.25558 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.4720 | 0.750590 | 0.375295 | − | 0.926905i | \(-0.377541\pi\) | ||||
0.375295 | + | 0.926905i | \(0.377541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.2367 | 0.663442 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.4654 | 1.74738 | 0.873689 | − | 0.486485i | \(-0.161721\pi\) | ||||
0.873689 | + | 0.486485i | \(0.161721\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.9133 | −0.418813 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.497889 | 0.0190791 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.8810 | 0.531143 | 0.265572 | − | 0.964091i | \(-0.414439\pi\) | ||||
0.265572 | + | 0.964091i | \(0.414439\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.9826 | 0.572455 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.07003 | −0.155281 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.05088 | 0.154326 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.3175 | −1.38158 | −0.690791 | − | 0.723055i | \(-0.742737\pi\) | ||||
−0.690791 | + | 0.723055i | \(0.742737\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −19.1098 | −0.725922 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 45.6977 | 1.73341 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.0061 | 0.947172 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.48468 | −0.169626 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.8289 | 0.522310 | 0.261155 | − | 0.965297i | \(-0.415897\pi\) | ||||
0.261155 | + | 0.965297i | \(0.415897\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.7300 | 1.38530 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.64554 | 0.287948 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.3814 | 0.728911 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.6187 | 1.78836 | 0.894179 | − | 0.447709i | \(-0.147760\pi\) | ||||
0.894179 | + | 0.447709i | \(0.147760\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37.8778 | 1.42053 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.5769 | 1.03276 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −55.7157 | −2.08365 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.933900 | 0.0348771 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.8666 | 0.442551 | 0.221276 | − | 0.975211i | \(-0.428978\pi\) | ||||
0.221276 | + | 0.975211i | \(0.428978\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.4206 | −1.24465 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.26067 | −0.232837 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 94.7795 | 3.52002 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.3613 | 1.49692 | 0.748459 | − | 0.663181i | \(-0.230794\pi\) | ||||
0.748459 | + | 0.663181i | \(0.230794\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.3333 | −0.827161 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.4173 | −1.05105 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.1559 | −0.744474 | −0.372237 | − | 0.928138i | \(-0.621409\pi\) | ||||
−0.372237 | + | 0.928138i | \(0.621409\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.64981 | 0.134625 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 43.0751 | 1.58669 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.2713 | 0.524979 | 0.262490 | − | 0.964935i | \(-0.415456\pi\) | ||||
0.262490 | + | 0.964935i | \(0.415456\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.96780 | −0.292705 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.60118 | 0.352233 | 0.176117 | − | 0.984369i | \(-0.443646\pi\) | ||||
0.176117 | + | 0.984369i | \(0.443646\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.33839 | −0.0856719 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.91141 | −0.106523 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.69341 | 0.354190 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.5839 | −0.860588 | −0.430294 | − | 0.902689i | \(-0.641590\pi\) | ||||
−0.430294 | + | 0.902689i | \(0.641590\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.05404 | 0.257064 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 72.8326 | 2.65065 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.7513 | 1.26306 | 0.631529 | − | 0.775352i | \(-0.282428\pi\) | ||||
0.631529 | + | 0.775352i | \(0.282428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.14268 | 0.222965 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.3425 | −1.06366 | −0.531832 | − | 0.846850i | \(-0.678496\pi\) | ||||
−0.531832 | + | 0.846850i | \(0.678496\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39.6085 | 1.43392 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 39.8463 | 1.44065 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.8713 | 0.753620 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.0896 | −0.832634 | −0.416317 | − | 0.909220i | \(-0.636679\pi\) | ||||
−0.416317 | + | 0.909220i | \(0.636679\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.61524 | 0.0941854 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.8924 | −0.535642 | −0.267821 | − | 0.963469i | \(-0.586304\pi\) | ||||
−0.267821 | + | 0.963469i | \(0.586304\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 44.0069 | 1.58078 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.43524 | 0.123239 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −43.6690 | −1.56460 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.5459 | −1.05724 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.0220 | 0.608315 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −67.9635 | −2.42572 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.6419 | 0.985329 | 0.492664 | − | 0.870219i | \(-0.336023\pi\) | ||||
0.492664 | + | 0.870219i | \(0.336023\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.77943 | 0.0989503 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.15864 | 0.325644 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.6831 | 1.48021 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.07644 | −0.0381775 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.0693 | −0.746313 | −0.373156 | − | 0.927768i | \(-0.621725\pi\) | ||||
−0.373156 | + | 0.927768i | \(0.621725\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.7599 | 0.840564 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.52062 | −0.195061 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.7274 | 0.625586 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −46.1072 | −1.62507 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.79293 | −0.274324 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.7319 | −0.728894 | −0.364447 | − | 0.931224i | \(-0.618742\pi\) | ||||
−0.364447 | + | 0.931224i | \(0.618742\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.37186 | −0.223746 | −0.111873 | − | 0.993723i | \(-0.535685\pi\) | ||||
−0.111873 | + | 0.993723i | \(0.535685\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.31227 | 0.186310 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 68.6110 | 2.40334 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 49.6261 | 1.73620 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24.4913 | 0.855794 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.34818 | −0.326254 | −0.163127 | − | 0.986605i | \(-0.552158\pi\) | ||||
−0.163127 | + | 0.986605i | \(0.552158\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.2177 | 1.43676 | 0.718380 | − | 0.695651i | \(-0.244884\pi\) | ||||
0.718380 | + | 0.695651i | \(0.244884\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.80242 | 0.341277 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −51.7970 | −1.80116 | −0.900579 | − | 0.434692i | \(-0.856857\pi\) | ||||
−0.900579 | + | 0.434692i | \(0.856857\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.3785 | −0.881432 | −0.440716 | − | 0.897647i | \(-0.645275\pi\) | ||||
−0.440716 | + | 0.897647i | \(0.645275\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.22362 | 0.146516 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.3424 | 0.392992 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.21479 | −0.249678 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.90345 | 0.273183 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.7612 | −0.958423 | −0.479211 | − | 0.877699i | \(-0.659077\pi\) | ||||
−0.479211 | + | 0.877699i | \(0.659077\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64.5986 | 2.22754 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.02049 | −0.104031 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.3991 | 0.736153 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.588886 | −0.0202343 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.13601 | −0.107628 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.2907 | 1.24403 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.2122 | 1.03445 | 0.517223 | − | 0.855851i | \(-0.326966\pi\) | ||||
0.517223 | + | 0.855851i | \(0.326966\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −69.5851 | −2.37976 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.9691 | −1.67275 | −0.836376 | − | 0.548156i | \(-0.815330\pi\) | ||||
−0.836376 | + | 0.548156i | \(0.815330\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.9356 | −0.748434 | −0.374217 | − | 0.927341i | \(-0.622089\pi\) | ||||
−0.374217 | + | 0.927341i | \(0.622089\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.08422 | −0.139190 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.2136 | −0.892322 | −0.446161 | − | 0.894953i | \(-0.647209\pi\) | ||||
−0.446161 | + | 0.894953i | \(0.647209\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.8962 | 0.370480 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.29199 | 0.0438782 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 43.7372 | 1.48368 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −55.2053 | −1.87056 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.2733 | −0.550769 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −36.0253 | −1.21788 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.1584 | −1.05214 | −0.526072 | − | 0.850440i | \(-0.676336\pi\) | ||||
−0.526072 | + | 0.850440i | \(0.676336\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.03908 | −0.0350474 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.0918 | 0.542148 | 0.271074 | − | 0.962559i | \(-0.412621\pi\) | ||||
0.271074 | + | 0.962559i | \(0.412621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.5401 | 0.926800 | 0.463400 | − | 0.886149i | \(-0.346629\pi\) | ||||
0.463400 | + | 0.886149i | \(0.346629\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.54614 | −0.186432 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.8811 | −0.801848 | −0.400924 | − | 0.916111i | \(-0.631311\pi\) | ||||
−0.400924 | + | 0.916111i | \(0.631311\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.3542 | 0.347269 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.6022 | −0.924708 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −41.4927 | −1.38850 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37.0625 | −1.23886 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.87250 | −0.262855 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 43.4586 | 1.44943 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.34524 | −0.111446 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.64137 | 0.154455 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −54.0223 | −1.79576 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.5303 | −0.615289 | −0.307645 | − | 0.951501i | \(-0.599541\pi\) | ||||
−0.307645 | + | 0.951501i | \(0.599541\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 28.9005 | 0.958570 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.0016 | −1.45784 | −0.728920 | − | 0.684599i | \(-0.759977\pi\) | ||||
−0.728920 | + | 0.684599i | \(0.759977\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.36179 | −0.111259 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.0765 | −0.366176 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.98206 | 0.230568 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.0668 | −0.694931 | −0.347465 | − | 0.937693i | \(-0.612958\pi\) | ||||
−0.347465 | + | 0.937693i | \(0.612958\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.33349 | −0.0439402 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.8662 | 1.24638 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 57.9123 | 1.90415 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −49.8352 | −1.63680 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.43686 | 0.112760 | 0.0563798 | − | 0.998409i | \(-0.482044\pi\) | ||||
0.0563798 | + | 0.998409i | \(0.482044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.8077 | −0.649171 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.01258 | 0.262320 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 46.0103 | 1.50470 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.9722 | 0.717800 | 0.358900 | − | 0.933376i | \(-0.383152\pi\) | ||||
0.358900 | + | 0.933376i | \(0.383152\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.69700 | −0.153281 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.3096 | 1.41185 | 0.705926 | − | 0.708286i | \(-0.250531\pi\) | ||||
0.705926 | + | 0.708286i | \(0.250531\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43.1466 | −1.40505 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.2142 | −0.429857 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.9590 | 1.26600 | 0.632999 | − | 0.774153i | \(-0.281824\pi\) | ||||
0.632999 | + | 0.774153i | \(0.281824\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.7195 | −0.737507 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.06050 | 0.131671 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.1725 | −0.523877 | −0.261939 | − | 0.965085i | \(-0.584362\pi\) | ||||
−0.261939 | + | 0.965085i | \(0.584362\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −45.2856 | −1.46541 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.68029 | 0.312919 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.60478 | −0.245571 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.8218 | −0.349089 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.4543 | 0.465784 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −82.5096 | −2.65608 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.34049 | 0.236054 | 0.118027 | − | 0.993010i | \(-0.462343\pi\) | ||||
0.118027 | + | 0.993010i | \(0.462343\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.57985 | 0.211375 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.6682 | 0.952097 | 0.476049 | − | 0.879419i | \(-0.342069\pi\) | ||||
0.476049 | + | 0.879419i | \(0.342069\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.1950 | −0.743598 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.5628 | −0.402333 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.1712 | −0.485369 | −0.242684 | − | 0.970105i | \(-0.578028\pi\) | ||||
−0.242684 | + | 0.970105i | \(0.578028\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.37462 | −0.203734 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 59.0622 | 1.88571 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.3016 | 0.743206 | 0.371603 | − | 0.928392i | \(-0.378808\pi\) | ||||
0.371603 | + | 0.928392i | \(0.378808\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.0000 | 1.21078 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.88068 | −0.123524 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 49.0325 | 1.55914 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.2039 | 0.546501 | 0.273251 | − | 0.961943i | \(-0.411901\pi\) | ||||
0.273251 | + | 0.961943i | \(0.411901\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.47536 | −0.0468192 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 59.9783 | 1.90144 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.5624 | 0.714559 | 0.357279 | − | 0.933998i | \(-0.383704\pi\) | ||||
0.357279 | + | 0.933998i | \(0.383704\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.4008 | 0.329066 |
(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 | 1328.2.a.n.1.5 | 8 | ||
4.3 | odd | 2 | 664.2.a.f.1.4 | ✓ | 8 | ||
8.3 | odd | 2 | 5312.2.a.br.1.5 | 8 | |||
8.5 | even | 2 | 5312.2.a.bs.1.4 | 8 | |||
12.11 | even | 2 | 5976.2.a.s.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
664.2.a.f.1.4 | ✓ | 8 | 4.3 | odd | 2 | ||
1328.2.a.n.1.5 | 8 | 1.1 | even | 1 | trivial | ||
5312.2.a.br.1.5 | 8 | 8.3 | odd | 2 | |||
5312.2.a.bs.1.4 | 8 | 8.5 | even | 2 | |||
5976.2.a.s.1.2 | 8 | 12.11 | even | 2 |