Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 15x^{7} + 45x^{6} + 64x^{5} - 201x^{4} - 63x^{3} + 282x^{2} + 3x - 116 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.10969\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | −1.10969 | −0.640680 | −0.320340 | − | 0.947303i | \(-0.603797\pi\) | ||||
−0.320340 | + | 0.947303i | \(0.603797\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.48203 | −1.11000 | −0.554998 | − | 0.831851i | \(-0.687281\pi\) | ||||
−0.554998 | + | 0.831851i | \(0.687281\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.76859 | −0.589530 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.75428 | 0.711152 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.03031 | −1.46257 | −0.731283 | − | 0.682075i | \(-0.761078\pi\) | ||||
−0.731283 | + | 0.682075i | \(0.761078\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.989367 | 0.226976 | 0.113488 | − | 0.993539i | \(-0.463798\pi\) | ||||
0.113488 | + | 0.993539i | \(0.463798\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.10969 | 0.242154 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.81617 | 1.83830 | 0.919149 | − | 0.393909i | \(-0.128878\pi\) | ||||
0.919149 | + | 0.393909i | \(0.128878\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.16047 | 0.232093 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.29165 | 1.01838 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.44880 | −0.826122 | −0.413061 | − | 0.910703i | \(-0.635540\pi\) | ||||
−0.413061 | + | 0.910703i | \(0.635540\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.66711 | 0.479027 | 0.239514 | − | 0.970893i | \(-0.423012\pi\) | ||||
0.239514 | + | 0.970893i | \(0.423012\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.10969 | −0.193172 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.48203 | 0.419539 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0381 | −1.65026 | −0.825129 | − | 0.564945i | \(-0.808897\pi\) | ||||
−0.825129 | + | 0.564945i | \(0.808897\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.10969 | 0.177693 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.71649 | −0.268070 | −0.134035 | − | 0.990977i | \(-0.542793\pi\) | ||||
−0.134035 | + | 0.990977i | \(0.542793\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.1359 | −1.85070 | −0.925350 | − | 0.379113i | \(-0.876229\pi\) | ||||
−0.925350 | + | 0.379113i | \(0.876229\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.38969 | 0.654376 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.96869 | −0.433028 | −0.216514 | − | 0.976279i | \(-0.569469\pi\) | ||||
−0.216514 | + | 0.976279i | \(0.569469\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.69178 | 0.937036 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.19148 | −0.987825 | −0.493913 | − | 0.869512i | \(-0.664434\pi\) | ||||
−0.493913 | + | 0.869512i | \(0.664434\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.48203 | −0.334677 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.09789 | −0.145419 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.72532 | −1.00575 | −0.502876 | − | 0.864359i | \(-0.667725\pi\) | ||||
−0.502876 | + | 0.864359i | \(0.667725\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.918973 | −0.117662 | −0.0588312 | − | 0.998268i | \(-0.518737\pi\) | ||||
−0.0588312 | + | 0.998268i | \(0.518737\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.76859 | 0.222821 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.48203 | 0.307858 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.50502 | 0.550376 | 0.275188 | − | 0.961390i | \(-0.411260\pi\) | ||||
0.275188 | + | 0.961390i | \(0.411260\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.78321 | −1.17776 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.7548 | −1.51371 | −0.756856 | − | 0.653582i | \(-0.773266\pi\) | ||||
−0.756856 | + | 0.653582i | \(0.773266\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.38509 | −0.630277 | −0.315139 | − | 0.949046i | \(-0.602051\pi\) | ||||
−0.315139 | + | 0.949046i | \(0.602051\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.28776 | −0.148697 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.36852 | −0.604005 | −0.302003 | − | 0.953307i | \(-0.597655\pi\) | ||||
−0.302003 | + | 0.953307i | \(0.597655\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.566329 | −0.0629255 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.96934 | −0.325928 | −0.162964 | − | 0.986632i | \(-0.552105\pi\) | ||||
−0.162964 | + | 0.986632i | \(0.552105\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.9674 | 1.62344 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.93679 | 0.529280 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.26674 | 0.346274 | 0.173137 | − | 0.984898i | \(-0.444610\pi\) | ||||
0.173137 | + | 0.984898i | \(0.444610\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.95966 | −0.306903 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.45564 | −0.251943 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.0794 | −1.53108 | −0.765542 | − | 0.643386i | \(-0.777529\pi\) | ||||
−0.765542 | + | 0.643386i | \(0.777529\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.76859 | −0.177750 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.98437 | −0.694971 | −0.347486 | − | 0.937685i | \(-0.612964\pi\) | ||||
−0.347486 | + | 0.937685i | \(0.612964\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.84018 | −0.871048 | −0.435524 | − | 0.900177i | \(-0.643437\pi\) | ||||
−0.435524 | + | 0.900177i | \(0.643437\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.75428 | −0.268790 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.6040 | 1.41182 | 0.705909 | − | 0.708303i | \(-0.250539\pi\) | ||||
0.705909 | + | 0.708303i | \(0.250539\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.61938 | 0.825587 | 0.412794 | − | 0.910825i | \(-0.364553\pi\) | ||||
0.412794 | + | 0.910825i | \(0.364553\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.1392 | 1.05729 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.38285 | 0.412304 | 0.206152 | − | 0.978520i | \(-0.433906\pi\) | ||||
0.206152 | + | 0.978520i | \(0.433906\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.8820 | −2.04051 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.76859 | 0.163506 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.03031 | 0.552798 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.90477 | 0.171747 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.52983 | 0.852374 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.11501 | 0.542619 | 0.271310 | − | 0.962492i | \(-0.412543\pi\) | ||||
0.271310 | + | 0.962492i | \(0.412543\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.4670 | 1.18571 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.9037 | −1.56425 | −0.782125 | − | 0.623121i | \(-0.785864\pi\) | ||||
−0.782125 | + | 0.623121i | \(0.785864\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.989367 | −0.0857890 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.1340 | −1.13040 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.1604 | 1.63698 | 0.818492 | − | 0.574517i | \(-0.194810\pi\) | ||||
0.818492 | + | 0.574517i | \(0.194810\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.32781 | 0.451899 | 0.225949 | − | 0.974139i | \(-0.427452\pi\) | ||||
0.225949 | + | 0.974139i | \(0.427452\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.29433 | 0.277432 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.0421 | 0.916993 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.10969 | −0.0915257 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.39378 | −0.769568 | −0.384784 | − | 0.923007i | \(-0.625724\pi\) | ||||
−0.384784 | + | 0.923007i | \(0.625724\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.99856 | −0.813671 | −0.406836 | − | 0.913501i | \(-0.633368\pi\) | ||||
−0.406836 | + | 0.913501i | \(0.633368\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.6651 | 0.862225 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.61984 | −0.531719 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.9963 | 1.27664 | 0.638320 | − | 0.769771i | \(-0.279630\pi\) | ||||
0.638320 | + | 0.769771i | \(0.279630\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.98031 | 0.632880 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.81617 | −0.694812 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.21793 | 0.408700 | 0.204350 | − | 0.978898i | \(-0.434492\pi\) | ||||
0.204350 | + | 0.978898i | \(0.434492\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.75428 | 0.214421 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.2181 | 1.48714 | 0.743571 | − | 0.668657i | \(-0.233130\pi\) | ||||
0.743571 | + | 0.668657i | \(0.233130\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.74978 | −0.133809 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.7424 | −0.892755 | −0.446378 | − | 0.894845i | \(-0.647286\pi\) | ||||
−0.446378 | + | 0.894845i | \(0.647286\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.16047 | −0.0877229 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.57271 | 0.644365 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.27123 | 0.169760 | 0.0848800 | − | 0.996391i | \(-0.472949\pi\) | ||||
0.0848800 | + | 0.996391i | \(0.472949\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.6236 | 0.789644 | 0.394822 | − | 0.918758i | \(-0.370806\pi\) | ||||
0.394822 | + | 0.918758i | \(0.370806\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.01978 | 0.0753839 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.9149 | 1.83178 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.03031 | −0.440980 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.29165 | −0.384911 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.9117 | −1.00662 | −0.503309 | − | 0.864106i | \(-0.667884\pi\) | ||||
−0.503309 | + | 0.864106i | \(0.667884\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.9918 | 1.58301 | 0.791504 | − | 0.611164i | \(-0.209299\pi\) | ||||
0.791504 | + | 0.611164i | \(0.209299\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.75428 | −0.197238 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.25748 | 0.659568 | 0.329784 | − | 0.944056i | \(-0.393024\pi\) | ||||
0.329784 | + | 0.944056i | \(0.393024\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.45245 | 0.102961 | 0.0514806 | − | 0.998674i | \(-0.483606\pi\) | ||||
0.0514806 | + | 0.998674i | \(0.483606\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.99917 | −0.352615 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.44880 | 0.312245 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.26037 | 0.297557 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.5922 | −1.08373 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.989367 | 0.0684359 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.9804 | 0.893609 | 0.446804 | − | 0.894632i | \(-0.352562\pi\) | ||||
0.446804 | + | 0.894632i | \(0.352562\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.1538 | 0.969804 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 30.1215 | 2.05427 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.66711 | −0.181055 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.97578 | 0.403806 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.03031 | 0.405643 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.2513 | −1.08827 | −0.544134 | − | 0.838998i | \(-0.683142\pi\) | ||||
−0.544134 | + | 0.838998i | \(0.683142\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.05239 | −0.136826 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.33488 | 0.287716 | 0.143858 | − | 0.989598i | \(-0.454049\pi\) | ||||
0.143858 | + | 0.989598i | \(0.454049\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.2810 | −1.14196 | −0.570981 | − | 0.820963i | \(-0.693437\pi\) | ||||
−0.570981 | + | 0.820963i | \(0.693437\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.10969 | 0.0730122 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.3970 | 0.877667 | 0.438834 | − | 0.898568i | \(-0.355392\pi\) | ||||
0.438834 | + | 0.898568i | \(0.355392\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.36838 | 0.480660 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.95739 | 0.386974 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.4300 | 1.58025 | 0.790124 | − | 0.612947i | \(-0.210016\pi\) | ||||
0.790124 | + | 0.612947i | \(0.210016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.44977 | −0.544298 | −0.272149 | − | 0.962255i | \(-0.587734\pi\) | ||||
−0.272149 | + | 0.962255i | \(0.587734\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.2465 | −0.978064 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.48203 | −0.158571 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.989367 | −0.0629519 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.29505 | 0.208815 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.4581 | −1.16507 | −0.582533 | − | 0.812807i | \(-0.697938\pi\) | ||||
−0.582533 | + | 0.812807i | \(0.697938\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.81617 | 0.554268 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.6092 | −1.04011 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.5410 | −1.71796 | −0.858979 | − | 0.512010i | \(-0.828901\pi\) | ||||
−0.858979 | + | 0.512010i | \(0.828901\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0381 | 0.623739 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.86810 | 0.487023 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.4646 | 1.69354 | 0.846770 | − | 0.531960i | \(-0.178544\pi\) | ||||
0.846770 | + | 0.531960i | \(0.178544\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.8494 | 1.09648 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.62507 | −0.221851 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.4947 | −0.761816 | −0.380908 | − | 0.924613i | \(-0.624389\pi\) | ||||
−0.380908 | + | 0.924613i | \(0.624389\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.4898 | −1.66989 | −0.834944 | − | 0.550334i | \(-0.814500\pi\) | ||||
−0.834944 | + | 0.550334i | \(0.814500\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.10969 | −0.0671615 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.16047 | 0.0699787 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.64683 | −0.219117 | −0.109558 | − | 0.993980i | \(-0.534944\pi\) | ||||
−0.109558 | + | 0.993980i | \(0.534944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.71702 | −0.282401 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.5085 | 0.686540 | 0.343270 | − | 0.939237i | \(-0.388465\pi\) | ||||
0.343270 | + | 0.939237i | \(0.388465\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.1367 | 1.43478 | 0.717389 | − | 0.696673i | \(-0.245337\pi\) | ||||
0.717389 | + | 0.696673i | \(0.245337\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.72500 | 0.161415 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.71649 | 0.101321 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.3647 | 1.13910 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.7335 | 0.980934 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.14442 | −0.125278 | −0.0626391 | − | 0.998036i | \(-0.519952\pi\) | ||||
−0.0626391 | + | 0.998036i | \(0.519952\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.1745 | 1.11638 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.29165 | 0.307053 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.81617 | −0.509852 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.1359 | 0.699499 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.75049 | 0.445254 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.28092 | 0.130605 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.54498 | −0.544761 | −0.272380 | − | 0.962190i | \(-0.587811\pi\) | ||||
−0.272380 | + | 0.962190i | \(0.587811\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.80985 | 0.558063 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.82475 | 0.160177 | 0.0800885 | − | 0.996788i | \(-0.474480\pi\) | ||||
0.0800885 | + | 0.996788i | \(0.474480\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −35.0812 | −1.98291 | −0.991454 | − | 0.130459i | \(-0.958355\pi\) | ||||
−0.991454 | + | 0.130459i | \(0.958355\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.38969 | −0.247331 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.0605 | −0.845880 | −0.422940 | − | 0.906158i | \(-0.639002\pi\) | ||||
−0.422940 | + | 0.906158i | \(0.639002\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.44880 | −0.249085 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.2059 | −0.904523 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.96619 | −0.331968 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.16047 | −0.0643710 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.56484 | −0.528937 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.96869 | 0.163669 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.9479 | −1.64609 | −0.823044 | − | 0.567978i | \(-0.807726\pi\) | ||||
−0.823044 | + | 0.567978i | \(0.807726\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.7533 | 0.972875 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.1816 | −0.610915 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.0878 | 1.85688 | 0.928440 | − | 0.371482i | \(-0.121150\pi\) | ||||
0.928440 | + | 0.371482i | \(0.121150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.86360 | −0.264155 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.66711 | 0.144432 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.2822 | 1.30731 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.4981 | 0.885665 | 0.442833 | − | 0.896604i | \(-0.353974\pi\) | ||||
0.442833 | + | 0.896604i | \(0.353974\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.40543 | −0.0752312 | −0.0376156 | − | 0.999292i | \(-0.511976\pi\) | ||||
−0.0376156 | + | 0.999292i | \(0.511976\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.29165 | −0.282448 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.42294 | −0.448308 | −0.224154 | − | 0.974554i | \(-0.571962\pi\) | ||||
−0.224154 | + | 0.974554i | \(0.571962\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.6577 | 1.68022 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.69178 | −0.354166 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.1778 | 1.01216 | 0.506082 | − | 0.862485i | \(-0.331093\pi\) | ||||
0.506082 | + | 0.862485i | \(0.331093\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0212 | −0.948482 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.10969 | −0.0582436 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.3660 | 0.699606 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.4832 | −0.547218 | −0.273609 | − | 0.961841i | \(-0.588217\pi\) | ||||
−0.273609 | + | 0.961841i | \(0.588217\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.03576 | 0.158035 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.19148 | 0.373363 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.6005 | −1.01488 | −0.507438 | − | 0.861688i | \(-0.669407\pi\) | ||||
−0.507438 | + | 0.861688i | \(0.669407\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.5752 | −0.546099 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.44880 | 0.229125 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.64649 | 0.341407 | 0.170704 | − | 0.985322i | \(-0.445396\pi\) | ||||
0.170704 | + | 0.985322i | \(0.445396\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.78577 | −0.347645 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.0950 | 1.02681 | 0.513403 | − | 0.858148i | \(-0.328385\pi\) | ||||
0.513403 | + | 0.858148i | \(0.328385\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.48203 | 0.126496 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.4633 | 1.09104 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.1801 | 1.32738 | 0.663692 | − | 0.748006i | \(-0.268989\pi\) | ||||
0.663692 | + | 0.748006i | \(0.268989\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −53.1643 | −2.68863 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.8675 | 1.00218 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.3248 | 0.670444 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.5177 | 0.527867 | 0.263934 | − | 0.964541i | \(-0.414980\pi\) | ||||
0.263934 | + | 0.964541i | \(0.414980\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.09789 | 0.0549633 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.09285 | 0.154449 | 0.0772247 | − | 0.997014i | \(-0.475394\pi\) | ||||
0.0772247 | + | 0.997014i | \(0.475394\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.66711 | −0.132858 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.40565 | 0.0698471 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.0381 | −0.497571 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.2833 | 1.89299 | 0.946493 | − | 0.322724i | \(-0.104599\pi\) | ||||
0.946493 | + | 0.322724i | \(0.104599\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.2621 | −1.04878 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.72532 | 0.380138 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.36999 | 0.361779 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.91221 | −0.289522 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.97905 | 0.340949 | 0.170474 | − | 0.985362i | \(-0.445470\pi\) | ||||
0.170474 | + | 0.985362i | \(0.445470\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.1636 | 1.61630 | 0.808148 | − | 0.588979i | \(-0.200470\pi\) | ||||
0.808148 | + | 0.588979i | \(0.200470\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.25040 | 0.255283 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.99797 | −0.339451 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.918973 | 0.0444722 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.10969 | 0.0535763 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.0412 | 0.531837 | 0.265918 | − | 0.963996i | \(-0.414325\pi\) | ||||
0.265918 | + | 0.963996i | \(0.414325\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.7428 | 0.948781 | 0.474390 | − | 0.880315i | \(-0.342669\pi\) | ||||
0.474390 | + | 0.880315i | \(0.342669\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.2533 | −0.587499 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.72243 | 0.417250 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.1100 | 0.673434 | 0.336717 | − | 0.941606i | \(-0.390684\pi\) | ||||
0.336717 | + | 0.941606i | \(0.390684\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.76859 | −0.0842185 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.5077 | 1.73453 | 0.867267 | − | 0.497843i | \(-0.165874\pi\) | ||||
0.867267 | + | 0.497843i | \(0.165874\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.10814 | −0.384363 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.4242 | 0.493047 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.4557 | −1.72045 | −0.860225 | − | 0.509915i | \(-0.829677\pi\) | ||||
−0.860225 | + | 0.509915i | \(0.829677\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.71649 | −0.0808262 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.0953 | 0.521303 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.48203 | −0.116359 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.5370 | −1.56880 | −0.784398 | − | 0.620258i | \(-0.787028\pi\) | ||||
−0.784398 | + | 0.620258i | \(0.787028\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −31.9103 | −1.48945 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.9111 | 1.11365 | 0.556827 | − | 0.830629i | \(-0.312019\pi\) | ||||
0.556827 | + | 0.830629i | \(0.312019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 41.4760 | 1.92755 | 0.963776 | − | 0.266713i | \(-0.0859375\pi\) | ||||
0.963776 | + | 0.266713i | \(0.0859375\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.34597 | 0.340661 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.4556 | 1.27049 | 0.635247 | − | 0.772309i | \(-0.280898\pi\) | ||||
0.635247 | + | 0.772309i | \(0.280898\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.50502 | −0.208022 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.7509 | −0.817918 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.1359 | −0.558007 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.14813 | 0.0526796 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.7188 | 0.582352 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.0378 | 0.641406 | 0.320703 | − | 0.947180i | \(-0.396081\pi\) | ||||
0.320703 | + | 0.947180i | \(0.396081\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.0381 | 0.457699 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.78321 | 0.445152 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 37.4275 | 1.69950 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.2433 | 1.55171 | 0.775855 | − | 0.630911i | \(-0.217319\pi\) | ||||
0.775855 | + | 0.630911i | \(0.217319\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.79028 | −0.261846 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.53084 | −0.384991 | −0.192496 | − | 0.981298i | \(-0.561658\pi\) | ||||
−0.192496 | + | 0.981298i | \(0.561658\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.8277 | 1.20826 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.38969 | 0.197302 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.7548 | 0.572129 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.0063 | −1.16420 | −0.582101 | − | 0.813116i | \(-0.697769\pi\) | ||||
−0.582101 | + | 0.813116i | \(0.697769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.3261 | −0.952782 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.7598 | 1.54986 | 0.774932 | − | 0.632044i | \(-0.217784\pi\) | ||||
0.774932 | + | 0.632044i | \(0.217784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.3354 | 0.771416 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.10969 | −0.0492831 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.0026 | 1.24119 | 0.620597 | − | 0.784130i | \(-0.286890\pi\) | ||||
0.620597 | + | 0.784130i | \(0.286890\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.38509 | 0.238222 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.23539 | 0.231148 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.9416 | 0.966861 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.96869 | −0.130563 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.0304 | 0.571970 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.2247 | −0.667005 | −0.333503 | − | 0.942749i | \(-0.608231\pi\) | ||||
−0.333503 | + | 0.942749i | \(0.608231\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −42.4646 | −1.85685 | −0.928425 | − | 0.371521i | \(-0.878836\pi\) | ||||
−0.928425 | + | 0.371521i | \(0.878836\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.28776 | 0.0562023 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.0835 | −0.700608 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.7249 | 2.37934 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.6629 | 0.592920 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.71649 | 0.0743493 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −36.2474 | −1.56711 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.52037 | −0.108762 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.92402 | −0.0827200 | −0.0413600 | − | 0.999144i | \(-0.513169\pi\) | ||||
−0.0413600 | + | 0.999144i | \(0.513169\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.7889 | −0.505909 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.3936 | −0.916399 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.7332 | −0.458917 | −0.229458 | − | 0.973318i | \(-0.573695\pi\) | ||||
−0.229458 | + | 0.973318i | \(0.573695\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.62529 | 0.0693655 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.40150 | −0.187510 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.36852 | 0.228293 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −27.6478 | −1.17358 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.5557 | −1.16757 | −0.583787 | − | 0.811907i | \(-0.698430\pi\) | ||||
−0.583787 | + | 0.811907i | \(0.698430\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.1359 | 0.513292 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.69178 | 0.282527 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.04575 | −0.296943 | −0.148471 | − | 0.988917i | \(-0.547435\pi\) | ||||
−0.148471 | + | 0.988917i | \(0.547435\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.8784 | −0.457656 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.566329 | 0.0237836 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.387835 | 0.0162589 | 0.00812945 | − | 0.999967i | \(-0.497412\pi\) | ||||
0.00812945 | + | 0.999967i | \(0.497412\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.7970 | −1.87469 | −0.937347 | − | 0.348397i | \(-0.886726\pi\) | ||||
−0.937347 | + | 0.348397i | \(0.886726\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.4377 | 0.644920 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.2309 | 0.426656 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.851144 | 0.0354336 | 0.0177168 | − | 0.999843i | \(-0.494360\pi\) | ||||
0.0177168 | + | 0.999843i | \(0.494360\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.4041 | −1.01420 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.96934 | 0.123189 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.19148 | −0.297841 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.38969 | −0.181491 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.49139 | 0.350477 | 0.175239 | − | 0.984526i | \(-0.443930\pi\) | ||||
0.175239 | + | 0.984526i | \(0.443930\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.63875 | 0.108728 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.2729 | −0.422572 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.03257 | 0.329858 | 0.164929 | − | 0.986305i | \(-0.447260\pi\) | ||||
0.164929 | + | 0.986305i | \(0.447260\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.9674 | −0.613604 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.61177 | −0.0659652 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.57221 | −0.391110 | −0.195555 | − | 0.980693i | \(-0.562651\pi\) | ||||
−0.195555 | + | 0.980693i | \(0.562651\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.4101 | 1.03650 | 0.518250 | − | 0.855229i | \(-0.326584\pi\) | ||||
0.518250 | + | 0.855229i | \(0.326584\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.96753 | −0.324463 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.48203 | −0.100909 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.9052 | −0.807928 | −0.403964 | − | 0.914775i | \(-0.632368\pi\) | ||||
−0.403964 | + | 0.914775i | \(0.632368\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.93679 | −0.200049 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.96869 | 0.120100 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.6275 | −0.833137 | −0.416569 | − | 0.909104i | \(-0.636767\pi\) | ||||
−0.416569 | + | 0.909104i | \(0.636767\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.72769 | −0.190639 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.60189 | −0.145006 | −0.0725032 | − | 0.997368i | \(-0.523099\pi\) | ||||
−0.0725032 | + | 0.997368i | \(0.523099\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.8811 | −0.598122 | −0.299061 | − | 0.954234i | \(-0.596673\pi\) | ||||
−0.299061 | + | 0.954234i | \(0.596673\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 46.6521 | 1.87209 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.26674 | −0.130879 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.4556 | −1.17823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.09789 | −0.0438455 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 60.5330 | 2.41361 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.2235 | 1.16337 | 0.581685 | − | 0.813414i | \(-0.302394\pi\) | ||||
0.581685 | + | 0.813414i | \(0.302394\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.4042 | −0.572517 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.1776 | −0.602306 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.5579 | 0.892378 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.4385 | 1.63672 | 0.818361 | − | 0.574705i | \(-0.194883\pi\) | ||||
0.818361 | + | 0.574705i | \(0.194883\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.05683 | −0.317730 | −0.158865 | − | 0.987300i | \(-0.550784\pi\) | ||||
−0.158865 | + | 0.987300i | \(0.550784\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33.4256 | −1.31613 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.54677 | −0.178752 | −0.0893760 | − | 0.995998i | \(-0.528487\pi\) | ||||
−0.0893760 | + | 0.995998i | \(0.528487\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.72532 | −0.303246 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.95966 | 0.115998 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.68144 | 0.261465 | 0.130732 | − | 0.991418i | \(-0.458267\pi\) | ||||
0.130732 | + | 0.991418i | \(0.458267\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 44.4374 | 1.73631 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.52401 | 0.371567 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.7669 | −0.770008 | −0.385004 | − | 0.922915i | \(-0.625800\pi\) | ||||
−0.385004 | + | 0.922915i | \(0.625800\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.8726 | −1.12301 | −0.561507 | − | 0.827472i | \(-0.689778\pi\) | ||||
−0.561507 | + | 0.827472i | \(0.689778\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.69178 | −0.259887 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.45564 | 0.0952255 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −39.2214 | −1.51866 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.0339 | 0.697231 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.918973 | −0.0354766 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.94704 | −0.383430 | −0.191715 | − | 0.981451i | \(-0.561405\pi\) | ||||
−0.191715 | + | 0.981451i | \(0.561405\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.14078 | 0.236359 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.6891 | 0.410814 | 0.205407 | − | 0.978677i | \(-0.434148\pi\) | ||||
0.205407 | + | 0.978677i | \(0.434148\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.0794 | 0.578695 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.81038 | −0.184334 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −46.4976 | −1.77918 | −0.889591 | − | 0.456759i | \(-0.849010\pi\) | ||||
−0.889591 | + | 0.456759i | \(0.849010\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −47.5567 | −1.81705 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.1766 | 0.731632 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.19148 | 0.273973 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.3058 | −0.848552 | −0.424276 | − | 0.905533i | \(-0.639471\pi\) | ||||
−0.424276 | + | 0.905533i | \(0.639471\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.76859 | 0.0671831 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.2238 | −0.501606 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.3510 | 0.392070 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.8665 | −0.562303 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.8494 | −0.938550 | −0.469275 | − | 0.883052i | \(-0.655485\pi\) | ||||
−0.469275 | + | 0.883052i | \(0.655485\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.93139 | −0.374569 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.17662 | −0.307949 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.98437 | 0.262674 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.07357 | −0.190542 | −0.0952710 | − | 0.995451i | \(-0.530372\pi\) | ||||
−0.0952710 | + | 0.995451i | \(0.530372\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.49470 | 0.356079 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.5137 | 0.880595 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.48203 | 0.0928226 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.1098 | −1.01243 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.5939 | 0.917198 | 0.458599 | − | 0.888643i | \(-0.348351\pi\) | ||||
0.458599 | + | 0.888643i | \(0.348351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.84018 | 0.329225 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.37663 | 0.348721 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.16268 | −0.191737 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.9708 | −1.33408 | −0.667041 | − | 0.745021i | \(-0.732439\pi\) | ||||
−0.667041 | + | 0.745021i | \(0.732439\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.6179 | 0.689551 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 73.1830 | 2.70677 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.0419 | −0.961881 | −0.480940 | − | 0.876753i | \(-0.659705\pi\) | ||||
−0.480940 | + | 0.876753i | \(0.659705\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.75428 | 0.101593 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.50502 | 0.165945 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.49861 | −0.0551273 | −0.0275637 | − | 0.999620i | \(-0.508775\pi\) | ||||
−0.0275637 | + | 0.999620i | \(0.508775\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.09789 | 0.0403320 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.7628 | 1.09189 | 0.545946 | − | 0.837821i | \(-0.316170\pi\) | ||||
0.545946 | + | 0.837821i | \(0.316170\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.3156 | 0.854218 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.25154 | 0.192144 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.6040 | −0.533617 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.7513 | 1.23160 | 0.615801 | − | 0.787902i | \(-0.288833\pi\) | ||||
0.615801 | + | 0.787902i | \(0.288833\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.4828 | 0.746434 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.8167 | 0.903173 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.04320 | 0.183298 | 0.0916492 | − | 0.995791i | \(-0.470786\pi\) | ||||
0.0916492 | + | 0.995791i | \(0.470786\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.78321 | −0.355108 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.4530 | −0.596419 | −0.298210 | − | 0.954500i | \(-0.596389\pi\) | ||||
−0.298210 | + | 0.954500i | \(0.596389\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.61938 | −0.312043 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −26.4712 | −0.957068 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.72532 | 0.278945 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.3313 | −1.27408 | −0.637040 | − | 0.770831i | \(-0.719841\pi\) | ||||
−0.637040 | + | 0.770831i | \(0.719841\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.5619 | 1.10066 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.95778 | −0.214286 | −0.107143 | − | 0.994244i | \(-0.534170\pi\) | ||||
−0.107143 | + | 0.994244i | \(0.534170\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.09509 | 0.111179 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.1392 | −0.399617 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.69824 | −0.0608456 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.7548 | −0.456401 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23.5415 | −0.841306 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −39.7032 | −1.41707 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.9245 | −1.85091 | −0.925455 | − | 0.378858i | \(-0.876317\pi\) | ||||
−0.925455 | + | 0.378858i | \(0.876317\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30.4772 | −1.08502 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.38285 | −0.155836 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.918973 | 0.0326337 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.8074 | −0.702494 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.30557 | 0.0462458 | 0.0231229 | − | 0.999733i | \(-0.492639\pi\) | ||||
0.0231229 | + | 0.999733i | \(0.492639\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.9021 | 0.633332 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.77752 | −0.204139 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.38509 | −0.190036 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.8820 | 0.771239 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.8653 | 0.488080 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.6414 | −0.374132 | −0.187066 | − | 0.982347i | \(-0.559898\pi\) | ||||
−0.187066 | + | 0.982347i | \(0.559898\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.5136 | 1.52797 | 0.763985 | − | 0.645234i | \(-0.223240\pi\) | ||||
0.763985 | + | 0.645234i | \(0.223240\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.5052 | 1.06986 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.9511 | −0.453656 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0068 | −0.420065 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.76859 | −0.0617995 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.9076 | −1.11358 | −0.556792 | − | 0.830652i | \(-0.687968\pi\) | ||||
−0.556792 | + | 0.830652i | \(0.687968\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.2277 | −0.461088 | −0.230544 | − | 0.973062i | \(-0.574051\pi\) | ||||
−0.230544 | + | 0.973062i | \(0.574051\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.28776 | −0.0448339 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.9894 | 0.868965 | 0.434483 | − | 0.900680i | \(-0.356931\pi\) | ||||
0.434483 | + | 0.900680i | \(0.356931\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.8946 | 1.21194 | 0.605970 | − | 0.795488i | \(-0.292785\pi\) | ||||
0.605970 | + | 0.795488i | \(0.292785\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.04685 | 0.140384 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.03031 | −0.208938 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −47.6999 | −1.65072 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.1134 | 0.487831 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −50.3788 | −1.73927 | −0.869635 | − | 0.493695i | \(-0.835646\pi\) | ||||
−0.869635 | + | 0.493695i | \(0.835646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.20814 | −0.317522 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.7709 | −0.439852 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.48203 | −0.0853844 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.7843 | −0.919233 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −88.4978 | −3.03367 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.0728 | 1.61174 | 0.805870 | − | 0.592092i | \(-0.201698\pi\) | ||||
0.805870 | + | 0.592092i | \(0.201698\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.34301 | 0.148528 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.9002 | 1.05553 | 0.527765 | − | 0.849390i | \(-0.323030\pi\) | ||||
0.527765 | + | 0.849390i | \(0.323030\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.0452 | −0.479218 | −0.239609 | − | 0.970870i | \(-0.577019\pi\) | ||||
−0.239609 | + | 0.970870i | \(0.577019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.90477 | −0.0649143 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 51.5784 | 1.75575 | 0.877874 | − | 0.478892i | \(-0.158961\pi\) | ||||
0.877874 | + | 0.478892i | \(0.158961\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.1449 | 0.990955 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.4888 | −0.729797 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.36852 | −0.182115 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.50502 | −0.152647 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 26.6693 | 0.902619 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.52983 | −0.322167 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.2824 | 1.39401 | 0.697004 | − | 0.717067i | \(-0.254516\pi\) | ||||
0.697004 | + | 0.717067i | \(0.254516\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.37964 | 0.0802632 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.8066 | 0.768374 | 0.384187 | − | 0.923255i | \(-0.374482\pi\) | ||||
0.384187 | + | 0.923255i | \(0.374482\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.7317 | −1.53899 | −0.769497 | − | 0.638650i | \(-0.779493\pi\) | ||||
−0.769497 | + | 0.638650i | \(0.779493\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.2777 | −0.715243 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.6335 | 1.33076 | 0.665382 | − | 0.746503i | \(-0.268269\pi\) | ||||
0.665382 | + | 0.746503i | \(0.268269\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.11501 | −0.205091 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.566329 | −0.0189727 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.93713 | −0.0982872 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.63727 | −0.188433 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.78321 | 0.326652 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.8655 | −0.395735 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.3668 | 1.44476 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.4670 | −0.448155 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.3680 | −0.876503 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.4277 | 0.445861 | 0.222930 | − | 0.974834i | \(-0.428438\pi\) | ||||
0.222930 | + | 0.974834i | \(0.428438\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.3525 | 0.409706 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.6266 | −1.41228 | −0.706142 | − | 0.708070i | \(-0.749566\pi\) | ||||
−0.706142 | + | 0.708070i | \(0.749566\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.96934 | −0.0982708 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.53111 | −0.0836759 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.9037 | 0.591231 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.1665 | 0.401335 | 0.200667 | − | 0.979659i | \(-0.435689\pi\) | ||||
0.200667 | + | 0.979659i | \(0.435689\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.5920 | 0.349017 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.7548 | 0.419828 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.6489 | −0.383013 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.6346 | 0.513509 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.25073 | 0.205080 | 0.102540 | − | 0.994729i | \(-0.467303\pi\) | ||||
0.102540 | + | 0.994729i | \(0.467303\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.989367 | 0.0324252 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.13460 | −0.102622 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.9674 | 0.489486 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.0576 | 0.557247 | 0.278623 | − | 0.960400i | \(-0.410122\pi\) | ||||
0.278623 | + | 0.960400i | \(0.410122\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.9293 | 1.27041 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.68141 | 0.152610 | 0.0763048 | − | 0.997085i | \(-0.475688\pi\) | ||||
0.0763048 | + | 0.997085i | \(0.475688\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.1328 | −0.492793 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.1340 | 0.427250 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.1306 | −0.881625 | −0.440813 | − | 0.897599i | \(-0.645310\pi\) | ||||
−0.440813 | + | 0.897599i | \(0.645310\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.38509 | 0.174808 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.7124 | 0.541938 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.4961 | 0.469576 | 0.234788 | − | 0.972047i | \(-0.424560\pi\) | ||||
0.234788 | + | 0.972047i | \(0.424560\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.5293 | 1.11734 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.93679 | 0.159584 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.1604 | −0.618722 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.8865 | −0.770533 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.8284 | −0.832308 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −54.5844 | −1.75713 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.2518 | 1.39088 | 0.695442 | − | 0.718582i | \(-0.255209\pi\) | ||||
0.695442 | + | 0.718582i | \(0.255209\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.62062 | 0.212685 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.64313 | 0.149005 | 0.0745026 | − | 0.997221i | \(-0.476263\pi\) | ||||
0.0745026 | + | 0.997221i | \(0.476263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.32781 | −0.170802 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.28776 | 0.0412412 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 59.7703 | 1.91222 | 0.956110 | − | 0.293008i | \(-0.0946562\pi\) | ||||
0.956110 | + | 0.293008i | \(0.0946562\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.26674 | 0.104405 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.2441 | −0.486708 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.0910 | 0.449435 | 0.224717 | − | 0.974424i | \(-0.427854\pi\) | ||||
0.224717 | + | 0.974424i | \(0.427854\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.9773 | −0.732119 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.29433 | −0.104860 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −106.992 | −3.40214 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.3445 | 1.53571 | 0.767857 | − | 0.640621i | \(-0.221323\pi\) | ||||
0.767857 | + | 0.640621i | \(0.221323\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.2329 | 1.05462 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.60501 | −0.114287 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.9703 | −1.20253 | −0.601266 | − | 0.799049i | \(-0.705337\pi\) | ||||
−0.601266 | + | 0.799049i | \(0.705337\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −53.1183 | −1.68059 |
(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 | 8008.2.a.n.1.5 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.n.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial |