Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.106392688.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 9x^{4} + 12x^{3} + 25x^{2} - 10x - 16 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.14822\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | ||||||||
\(3\) | 3.14822 | 1.81763 | 0.908814 | − | 0.417201i | \(-0.136989\pi\) | ||||
0.908814 | + | 0.417201i | \(0.136989\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.677107 | 0.302812 | 0.151406 | − | 0.988472i | \(-0.451620\pi\) | ||||
0.151406 | + | 0.988472i | \(0.451620\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.67711 | 0.633887 | 0.316943 | − | 0.948444i | \(-0.397343\pi\) | ||||
0.316943 | + | 0.948444i | \(0.397343\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.91132 | 2.30377 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.16289 | −1.15458 | −0.577288 | − | 0.816540i | \(-0.695889\pi\) | ||||
−0.577288 | + | 0.816540i | \(0.695889\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.13169 | 0.550399 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.86889 | 1.66595 | 0.832976 | − | 0.553310i | \(-0.186635\pi\) | ||||
0.832976 | + | 0.553310i | \(0.186635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.27991 | 1.15217 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.14077 | −0.446382 | −0.223191 | − | 0.974775i | \(-0.571647\pi\) | ||||
−0.223191 | + | 0.974775i | \(0.571647\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.54153 | −0.908305 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.3137 | 2.36977 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.01005 | 0.373257 | 0.186628 | − | 0.982431i | \(-0.440244\pi\) | ||||
0.186628 | + | 0.982431i | \(0.440244\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.13169 | 0.382862 | 0.191431 | − | 0.981506i | \(-0.438687\pi\) | ||||
0.191431 | + | 0.981506i | \(0.438687\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.14822 | 0.548036 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.13558 | 0.191948 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.81297 | 0.462450 | 0.231225 | − | 0.972900i | \(-0.425727\pi\) | ||||
0.231225 | + | 0.972900i | \(0.425727\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13.1057 | −2.09859 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.9829 | 1.71524 | 0.857622 | − | 0.514280i | \(-0.171941\pi\) | ||||
0.857622 | + | 0.514280i | \(0.171941\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.39032 | −0.517019 | −0.258510 | − | 0.966009i | \(-0.583231\pi\) | ||||
−0.258510 | + | 0.966009i | \(0.583231\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.67970 | 0.697609 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.22974 | −0.179376 | −0.0896878 | − | 0.995970i | \(-0.528587\pi\) | ||||
−0.0896878 | + | 0.995970i | \(0.528587\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.18731 | −0.598187 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21.6248 | 3.02808 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.7292 | −1.61113 | −0.805564 | − | 0.592508i | \(-0.798138\pi\) | ||||
−0.805564 | + | 0.592508i | \(0.798138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.677107 | 0.0913011 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.14822 | −0.416993 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.37650 | 1.09053 | 0.545264 | − | 0.838264i | \(-0.316429\pi\) | ||||
0.545264 | + | 0.838264i | \(0.316429\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.52619 | 1.21970 | 0.609852 | − | 0.792516i | \(-0.291229\pi\) | ||||
0.609852 | + | 0.792516i | \(0.291229\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.5910 | 1.46033 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.81872 | −0.349619 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.64636 | 1.17849 | 0.589245 | − | 0.807954i | \(-0.299425\pi\) | ||||
0.589245 | + | 0.807954i | \(0.299425\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.73963 | −0.811356 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.6011 | −1.49547 | −0.747736 | − | 0.663996i | \(-0.768859\pi\) | ||||
−0.747736 | + | 0.663996i | \(0.768859\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.1743 | −1.65897 | −0.829485 | − | 0.558528i | \(-0.811366\pi\) | ||||
−0.829485 | + | 0.558528i | \(0.811366\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.2977 | −1.65096 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.67711 | 0.191124 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.2387 | 1.26445 | 0.632225 | − | 0.774785i | \(-0.282142\pi\) | ||||
0.632225 | + | 0.774785i | \(0.282142\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 18.0324 | 2.00360 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.75976 | 0.851744 | 0.425872 | − | 0.904783i | \(-0.359967\pi\) | ||||
0.425872 | + | 0.904783i | \(0.359967\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.65098 | 0.504469 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.32808 | 0.678442 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.08041 | −0.432523 | −0.216261 | − | 0.976336i | \(-0.569386\pi\) | ||||
−0.216261 | + | 0.976336i | \(0.569386\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.98160 | −0.731871 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.71102 | 0.695901 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.677107 | −0.0694697 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.4487 | −1.26398 | −0.631988 | − | 0.774978i | \(-0.717761\pi\) | ||||
−0.631988 | + | 0.774978i | \(0.717761\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.91132 | 0.694614 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.5645 | 1.15071 | 0.575353 | − | 0.817905i | \(-0.304865\pi\) | ||||
0.575353 | + | 0.817905i | \(0.304865\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0938 | −0.994569 | −0.497284 | − | 0.867588i | \(-0.665669\pi\) | ||||
−0.497284 | + | 0.867588i | \(0.665669\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.57506 | 0.348891 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.3080 | 1.38320 | 0.691601 | − | 0.722280i | \(-0.256906\pi\) | ||||
0.691601 | + | 0.722280i | \(0.256906\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.0639 | −1.92177 | −0.960887 | − | 0.276940i | \(-0.910680\pi\) | ||||
−0.960887 | + | 0.276940i | \(0.910680\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.85586 | 0.840561 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.7940 | −1.39171 | −0.695853 | − | 0.718185i | \(-0.744973\pi\) | ||||
−0.695853 | + | 0.718185i | \(0.744973\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.44953 | −0.135170 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −28.7710 | −2.65988 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.5199 | 1.05602 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 34.5767 | 3.11768 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.46064 | −0.577857 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.5225 | −0.933718 | −0.466859 | − | 0.884332i | \(-0.654614\pi\) | ||||
−0.466859 | + | 0.884332i | \(0.654614\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.6735 | −0.939749 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.76083 | 0.852808 | 0.426404 | − | 0.904533i | \(-0.359780\pi\) | ||||
0.426404 | + | 0.904533i | \(0.359780\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.67711 | −0.145424 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.33770 | 0.717595 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.72444 | 0.147329 | 0.0736644 | − | 0.997283i | \(-0.476531\pi\) | ||||
0.0736644 | + | 0.997283i | \(0.476531\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.73416 | 0.231908 | 0.115954 | − | 0.993255i | \(-0.463007\pi\) | ||||
0.115954 | + | 0.993255i | \(0.463007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.87149 | −0.326038 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.16289 | −0.348118 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.36102 | 0.113026 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.1826 | −1.08728 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.6670 | −1.52926 | −0.764632 | − | 0.644468i | \(-0.777079\pi\) | ||||
−0.764632 | + | 0.644468i | \(0.777079\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.5284 | 0.856791 | 0.428395 | − | 0.903591i | \(-0.359079\pi\) | ||||
0.428395 | + | 0.903591i | \(0.359079\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 47.4731 | 3.83797 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.44338 | 0.115935 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.6625 | −0.930765 | −0.465383 | − | 0.885110i | \(-0.654083\pi\) | ||||
−0.465383 | + | 0.885110i | \(0.654083\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −36.9261 | −2.92843 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.59030 | −0.282956 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.9612 | −1.17185 | −0.585926 | − | 0.810364i | \(-0.699269\pi\) | ||||
−0.585926 | + | 0.810364i | \(0.699269\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.13169 | 0.165951 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.5989 | 0.820164 | 0.410082 | − | 0.912049i | \(-0.365500\pi\) | ||||
0.410082 | + | 0.912049i | \(0.365500\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.32961 | 0.333047 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.91132 | −0.528522 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.76338 | 0.286124 | 0.143062 | − | 0.989714i | \(-0.454305\pi\) | ||||
0.143062 | + | 0.989714i | \(0.454305\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.61663 | −0.575763 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 26.3711 | 1.98217 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.50407 | 0.261907 | 0.130953 | − | 0.991389i | \(-0.458196\pi\) | ||||
0.130953 | + | 0.991389i | \(0.458196\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.3354 | 1.88317 | 0.941584 | − | 0.336778i | \(-0.109337\pi\) | ||||
0.941584 | + | 0.336778i | \(0.109337\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29.9906 | 2.21697 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.90468 | 0.140035 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.86889 | 0.502303 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 20.6514 | 1.50217 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.57468 | −0.331012 | −0.165506 | − | 0.986209i | \(-0.552926\pi\) | ||||
−0.165506 | + | 0.986209i | \(0.552926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.55348 | 0.111822 | 0.0559111 | − | 0.998436i | \(-0.482194\pi\) | ||||
0.0559111 | + | 0.998436i | \(0.482194\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.87396 | −0.635478 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.8166 | −1.05564 | −0.527821 | − | 0.849356i | \(-0.676991\pi\) | ||||
−0.527821 | + | 0.849356i | \(0.676991\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.99201 | 0.637427 | 0.318713 | − | 0.947851i | \(-0.396749\pi\) | ||||
0.318713 | + | 0.947851i | \(0.396749\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 30.3689 | 2.14206 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.37107 | 0.236602 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.43662 | 0.519396 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.7955 | −1.02836 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.56841 | −0.176817 | −0.0884083 | − | 0.996084i | \(-0.528178\pi\) | ||||
−0.0884083 | + | 0.996084i | \(0.528178\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −39.6710 | −2.71821 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.29561 | −0.156559 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.57506 | 0.242691 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −44.6237 | −3.01539 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.5944 | −1.92347 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.2774 | 0.755188 | 0.377594 | − | 0.925971i | \(-0.376752\pi\) | ||||
0.377594 | + | 0.925971i | \(0.376752\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −31.3879 | −2.09253 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.50002 | −0.298677 | −0.149339 | − | 0.988786i | \(-0.547714\pi\) | ||||
−0.149339 | + | 0.988786i | \(0.547714\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.9898 | 1.18880 | 0.594401 | − | 0.804169i | \(-0.297389\pi\) | ||||
0.594401 | + | 0.804169i | \(0.297389\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.27991 | 0.347393 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.65321 | −0.632403 | −0.316201 | − | 0.948692i | \(-0.602408\pi\) | ||||
−0.316201 | + | 0.948692i | \(0.602408\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.832664 | −0.0543170 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 35.3819 | 2.29830 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.36583 | −0.347087 | −0.173543 | − | 0.984826i | \(-0.555522\pi\) | ||||
−0.173543 | + | 0.984826i | \(0.555522\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.30762 | 0.148647 | 0.0743236 | − | 0.997234i | \(-0.476320\pi\) | ||||
0.0743236 | + | 0.997234i | \(0.476320\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.8288 | 1.27202 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.83526 | −0.181138 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.16289 | 0.264878 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 24.4295 | 1.54815 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.1322 | −0.702659 | −0.351330 | − | 0.936252i | \(-0.614270\pi\) | ||||
−0.351330 | + | 0.936252i | \(0.614270\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.14077 | −0.134589 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.6423 | 0.916937 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.10554 | 0.505609 | 0.252805 | − | 0.967517i | \(-0.418647\pi\) | ||||
0.252805 | + | 0.967517i | \(0.418647\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.71765 | 0.293141 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.8921 | 0.859898 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.5787 | −1.63891 | −0.819455 | − | 0.573143i | \(-0.805724\pi\) | ||||
−0.819455 | + | 0.573143i | \(0.805724\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.94192 | −0.487868 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.8460 | −0.786165 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.21563 | −0.257032 | −0.128516 | − | 0.991707i | \(-0.541021\pi\) | ||||
−0.128516 | + | 0.991707i | \(0.541021\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.870973 | −0.0529079 | −0.0264539 | − | 0.999650i | \(-0.508422\pi\) | ||||
−0.0264539 | + | 0.999650i | \(0.508422\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −21.9797 | −1.33027 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.54153 | −0.273864 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.0705 | −1.02567 | −0.512835 | − | 0.858487i | \(-0.671405\pi\) | ||||
−0.512835 | + | 0.858487i | \(0.671405\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.7328 | 0.882027 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.82059 | −0.227917 | −0.113959 | − | 0.993486i | \(-0.536353\pi\) | ||||
−0.113959 | + | 0.993486i | \(0.536353\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.7958 | 1.05785 | 0.528926 | − | 0.848668i | \(-0.322595\pi\) | ||||
0.528926 | + | 0.848668i | \(0.322595\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.13169 | −0.126270 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.4195 | 1.08727 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.1817 | 1.77539 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −39.1914 | −2.29744 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.68332 | −0.0983403 | −0.0491702 | − | 0.998790i | \(-0.515658\pi\) | ||||
−0.0491702 | + | 0.998790i | \(0.515658\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.67179 | 0.330224 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.3137 | 0.714514 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.91179 | 0.515382 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.68593 | −0.327732 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 36.4075 | 2.09156 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.45025 | 0.369340 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.93624 | −0.452945 | −0.226473 | − | 0.974018i | \(-0.572719\pi\) | ||||
−0.226473 | + | 0.974018i | \(0.572719\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −31.7775 | −1.80776 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.8589 | −1.69314 | −0.846570 | − | 0.532277i | \(-0.821337\pi\) | ||||
−0.846570 | + | 0.532277i | \(0.821337\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.8447 | 1.06516 | 0.532582 | − | 0.846378i | \(-0.321222\pi\) | ||||
0.532582 | + | 0.846378i | \(0.321222\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.84836 | 0.442205 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.77789 | 0.324518 | 0.162259 | − | 0.986748i | \(-0.448122\pi\) | ||||
0.162259 | + | 0.986748i | \(0.448122\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.01005 | 0.112541 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 45.0447 | 2.51415 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.86889 | −0.382195 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.9059 | 1.04871 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −63.1657 | −3.49307 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.06240 | −0.113704 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.4610 | −0.574991 | −0.287496 | − | 0.957782i | \(-0.592823\pi\) | ||||
−0.287496 | + | 0.957782i | \(0.592823\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.4413 | 1.06538 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.53162 | 0.356861 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.5246 | −1.44489 | −0.722444 | − | 0.691430i | \(-0.756981\pi\) | ||||
−0.722444 | + | 0.691430i | \(0.756981\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −46.5749 | −2.52960 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.13169 | 0.115437 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.7623 | −1.01307 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.56345 | −0.245688 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.94655 | 0.533959 | 0.266979 | − | 0.963702i | \(-0.413974\pi\) | ||||
0.266979 | + | 0.963702i | \(0.413974\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.51832 | 0.0812738 | 0.0406369 | − | 0.999174i | \(-0.487061\pi\) | ||||
0.0406369 | + | 0.999174i | \(0.487061\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −51.2605 | −2.73609 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.4107 | −1.83150 | −0.915749 | − | 0.401750i | \(-0.868402\pi\) | ||||
−0.915749 | + | 0.401750i | \(0.868402\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.53227 | −0.452846 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 36.2671 | 1.91946 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.31071 | −0.0691769 | −0.0345884 | − | 0.999402i | \(-0.511012\pi\) | ||||
−0.0345884 | + | 0.999402i | \(0.511012\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.14822 | 0.165239 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.59749 | −0.502355 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.2993 | 0.746415 | 0.373207 | − | 0.927748i | \(-0.378258\pi\) | ||||
0.373207 | + | 0.927748i | \(0.378258\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 75.9065 | 3.95153 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.6711 | −1.02127 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.7508 | −1.07443 | −0.537217 | − | 0.843444i | \(-0.680525\pi\) | ||||
−0.537217 | + | 0.843444i | \(0.680525\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −20.3395 | −1.05033 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.36760 | −0.430953 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.68867 | 0.497673 | 0.248837 | − | 0.968545i | \(-0.419952\pi\) | ||||
0.248837 | + | 0.968545i | \(0.419952\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −33.1271 | −1.69715 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 36.1499 | 1.84717 | 0.923587 | − | 0.383390i | \(-0.125243\pi\) | ||||
0.923587 | + | 0.383390i | \(0.125243\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.13558 | 0.0578746 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −23.4316 | −1.19109 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.0423 | −1.42180 | −0.710900 | − | 0.703293i | \(-0.751712\pi\) | ||||
−0.710900 | + | 0.703293i | \(0.751712\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.7047 | −0.743650 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.7293 | 1.55009 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.60979 | 0.382890 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.80222 | 0.391582 | 0.195791 | − | 0.980646i | \(-0.437273\pi\) | ||||
0.195791 | + | 0.980646i | \(0.437273\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.27991 | −0.264326 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.9629 | −1.09677 | −0.548387 | − | 0.836225i | \(-0.684758\pi\) | ||||
−0.548387 | + | 0.836225i | \(0.684758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.87396 | −0.442043 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.2098 | 0.606712 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.81297 | 0.139434 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.85738 | 0.0918414 | 0.0459207 | − | 0.998945i | \(-0.485378\pi\) | ||||
0.0459207 | + | 0.998945i | \(0.485378\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.42892 | 0.267789 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.0483 | 0.691271 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.25419 | 0.257918 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.60774 | 0.421523 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.01873 | −0.147474 | −0.0737372 | − | 0.997278i | \(-0.523493\pi\) | ||||
−0.0737372 | + | 0.997278i | \(0.523493\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.54661 | 0.221588 | 0.110794 | − | 0.993843i | \(-0.464661\pi\) | ||||
0.110794 | + | 0.993843i | \(0.464661\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.49910 | −0.413240 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −31.1953 | −1.51319 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.9764 | 0.773154 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.1057 | −0.632749 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.1446 | 0.584984 | 0.292492 | − | 0.956268i | \(-0.405516\pi\) | ||||
0.292492 | + | 0.956268i | \(0.405516\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.70207 | −0.225967 | −0.112983 | − | 0.993597i | \(-0.536041\pi\) | ||||
−0.112983 | + | 0.993597i | \(0.536041\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.28479 | 0.205440 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.14077 | 0.102407 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.9200 | −1.28482 | −0.642411 | − | 0.766360i | \(-0.722066\pi\) | ||||
−0.642411 | + | 0.766360i | \(0.722066\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −28.9398 | −1.37809 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.33483 | −0.205954 | −0.102977 | − | 0.994684i | \(-0.532837\pi\) | ||||
−0.102977 | + | 0.994684i | \(0.532837\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.76288 | −0.130973 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −58.7680 | −2.77963 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.4154 | 0.491533 | 0.245767 | − | 0.969329i | \(-0.420960\pi\) | ||||
0.245767 | + | 0.969329i | \(0.420960\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.9829 | 0.517166 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.1458 | 1.55733 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.72729 | −0.221619 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.4225 | −0.487543 | −0.243771 | − | 0.969833i | \(-0.578385\pi\) | ||||
−0.243771 | + | 0.969833i | \(0.578385\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 84.5815 | 3.94793 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.1110 | 1.58871 | 0.794355 | − | 0.607454i | \(-0.207809\pi\) | ||||
0.794355 | + | 0.607454i | \(0.207809\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.7298 | −1.33519 | −0.667594 | − | 0.744525i | \(-0.732676\pi\) | ||||
−0.667594 | + | 0.744525i | \(0.732676\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.54408 | 0.210727 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.6777 | −1.18822 | −0.594111 | − | 0.804383i | \(-0.702496\pi\) | ||||
−0.594111 | + | 0.804383i | \(0.702496\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.1780 | 0.747030 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −36.7160 | −1.69178 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.39032 | −0.155887 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.54153 | 0.208380 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −81.0642 | −3.71167 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.4486 | 1.16278 | 0.581389 | − | 0.813626i | \(-0.302509\pi\) | ||||
0.581389 | + | 0.813626i | \(0.302509\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.7101 | −0.533934 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.3031 | −0.514308 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.42912 | −0.382747 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.53376 | −0.296073 | −0.148036 | − | 0.988982i | \(-0.547295\pi\) | ||||
−0.148036 | + | 0.988982i | \(0.547295\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −47.1013 | −2.12999 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.5368 | 1.91966 | 0.959831 | − | 0.280580i | \(-0.0905269\pi\) | ||||
0.959831 | + | 0.280580i | \(0.0905269\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.8068 | 0.621827 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.67970 | 0.210337 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.1333 | −0.947960 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.6620 | 1.95458 | 0.977289 | − | 0.211912i | \(-0.0679690\pi\) | ||||
0.977289 | + | 0.211912i | \(0.0679690\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.3676 | 1.49075 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.1374 | 0.630354 | 0.315177 | − | 0.949033i | \(-0.397936\pi\) | ||||
0.315177 | + | 0.949033i | \(0.397936\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.83037 | 0.348447 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.6306 | 0.605356 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.20694 | 0.275118 | 0.137559 | − | 0.990494i | \(-0.456074\pi\) | ||||
0.137559 | + | 0.990494i | \(0.456074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.7717 | −1.05160 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.3137 | −0.543663 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.83456 | −0.301167 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.22974 | −0.0540838 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.8480 | 0.520067 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.7876 | 1.26121 | 0.630605 | − | 0.776104i | \(-0.282807\pi\) | ||||
0.630605 | + | 0.776104i | \(0.282807\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.1445 | 1.27440 | 0.637199 | − | 0.770699i | \(-0.280093\pi\) | ||||
0.637199 | + | 0.770699i | \(0.280093\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −23.9788 | −1.04652 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.6423 | 0.637829 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.4171 | −0.800743 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 57.8927 | 2.51233 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −45.7207 | −1.98038 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.68802 | 0.418850 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.0316 | 0.476049 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.18731 | −0.180360 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.3632 | 1.00446 | 0.502230 | − | 0.864734i | \(-0.332513\pi\) | ||||
0.502230 | + | 0.864734i | \(0.332513\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 79.7616 | 3.42290 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.5854 | −0.581935 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.8726 | 1.70483 | 0.852416 | − | 0.522865i | \(-0.175137\pi\) | ||||
0.852416 | + | 0.522865i | \(0.175137\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 65.8385 | 2.80992 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.01005 | −0.0856309 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.8485 | 0.801519 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.99637 | 0.254532 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.8257 | −0.712929 | −0.356465 | − | 0.934309i | \(-0.616018\pi\) | ||||
−0.356465 | + | 0.934309i | \(0.616018\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.1135 | 0.596938 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.6248 | 0.913000 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.68841 | −0.366173 | −0.183086 | − | 0.983097i | \(-0.558609\pi\) | ||||
−0.183086 | + | 0.983097i | \(0.558609\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0171 | −0.421424 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 30.2422 | 1.27005 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.7590 | 0.870262 | 0.435131 | − | 0.900367i | \(-0.356702\pi\) | ||||
0.435131 | + | 0.900367i | \(0.356702\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.5889 | 1.19641 | 0.598203 | − | 0.801344i | \(-0.295881\pi\) | ||||
0.598203 | + | 0.801344i | \(0.295881\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.4021 | −0.601657 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.72237 | 0.405451 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.97270 | 0.373538 | 0.186769 | − | 0.982404i | \(-0.440198\pi\) | ||||
0.186769 | + | 0.982404i | \(0.440198\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.89071 | 0.203251 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.0139 | 0.539909 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.7292 | −0.485774 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −19.4811 | −0.805443 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.59725 | −0.0659254 | −0.0329627 | − | 0.999457i | \(-0.510494\pi\) | ||||
−0.0329627 | + | 0.999457i | \(0.510494\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.13169 | −0.0878346 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −46.6461 | −1.91876 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.933009 | −0.0383141 | −0.0191571 | − | 0.999816i | \(-0.506098\pi\) | ||||
−0.0191571 | + | 0.999816i | \(0.506098\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.80018 | 0.319776 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 28.3089 | 1.15860 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.280302 | 0.0114528 | 0.00572641 | − | 0.999984i | \(-0.498177\pi\) | ||||
0.00572641 | + | 0.999984i | \(0.498177\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.5729 | −0.635230 | −0.317615 | − | 0.948220i | \(-0.602882\pi\) | ||||
−0.317615 | + | 0.948220i | \(0.602882\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 66.6691 | 2.71497 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.677107 | 0.0275283 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.305109 | 0.0123840 | 0.00619199 | − | 0.999981i | \(-0.498029\pi\) | ||||
0.00619199 | + | 0.999981i | \(0.498029\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.6129 | 0.430055 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.11925 | 0.207103 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.6347 | 1.19693 | 0.598467 | − | 0.801148i | \(-0.295777\pi\) | ||||
0.598467 | + | 0.801148i | \(0.295777\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23.4121 | 0.944069 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.8931 | −0.478798 | −0.239399 | − | 0.970921i | \(-0.576950\pi\) | ||||
−0.239399 | + | 0.970921i | \(0.576950\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.11269 | 0.366270 | 0.183135 | − | 0.983088i | \(-0.441375\pi\) | ||||
0.183135 | + | 0.983088i | \(0.441375\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.3608 | −1.05782 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.84329 | −0.274170 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.3331 | 0.733324 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.14822 | −0.125728 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.3220 | 0.770418 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.0964 | −1.07869 | −0.539346 | − | 0.842084i | \(-0.681329\pi\) | ||||
−0.539346 | + | 0.842084i | \(0.681329\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.08593 | −0.321387 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.12483 | −0.282740 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.4313 | 0.690653 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −87.0900 | −3.44523 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.8022 | −1.25611 | −0.628056 | − | 0.778168i | \(-0.716149\pi\) | ||||
−0.628056 | + | 0.778168i | \(0.716149\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.3861 | 1.35606 | 0.678028 | − | 0.735036i | \(-0.262835\pi\) | ||||
0.678028 | + | 0.735036i | \(0.262835\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.22710 | −0.284567 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.0285 | −1.21986 | −0.609928 | − | 0.792457i | \(-0.708802\pi\) | ||||
−0.609928 | + | 0.792457i | \(0.708802\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.37650 | 0.328806 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.2551 | 0.441122 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.9348 | −1.24971 | −0.624853 | − | 0.780743i | \(-0.714841\pi\) | ||||
−0.624853 | + | 0.780743i | \(0.714841\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.60913 | 0.258240 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −97.9628 | −3.82189 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.5268 | −1.77347 | −0.886736 | − | 0.462277i | \(-0.847033\pi\) | ||||
−0.886736 | + | 0.462277i | \(0.847033\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.2167 | −1.13640 | −0.568200 | − | 0.822891i | \(-0.692360\pi\) | ||||
−0.568200 | + | 0.822891i | \(0.692360\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −90.0216 | −3.49615 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.13558 | −0.0440359 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.30305 | −0.166615 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 35.5036 | 1.37265 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.52619 | 0.367754 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.9862 | 1.77264 | 0.886319 | − | 0.463076i | \(-0.153254\pi\) | ||||
0.886319 | + | 0.463076i | \(0.153254\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −55.9230 | −2.15248 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.9360 | −0.650904 | −0.325452 | − | 0.945559i | \(-0.605516\pi\) | ||||
−0.325452 | + | 0.945559i | \(0.605516\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.8779 | −0.801218 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.1671 | −0.542884 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.67863 | −0.0642308 | −0.0321154 | − | 0.999484i | \(-0.510224\pi\) | ||||
−0.0321154 | + | 0.999484i | \(0.510224\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.16763 | 0.0446129 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 56.6361 | 2.16080 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 48.8273 | 1.86017 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.2185 | −1.56803 | −0.784013 | − | 0.620744i | \(-0.786830\pi\) | ||||
−0.784013 | + | 0.620744i | \(0.786830\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.5910 | 0.440306 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.85132 | 0.0702244 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 75.4405 | 2.85751 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −30.3905 | −1.14947 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.4831 | −1.00025 | −0.500126 | − | 0.865953i | \(-0.666713\pi\) | ||||
−0.500126 | + | 0.865953i | \(0.666713\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.81297 | −0.106093 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.62141 | −0.0987281 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.3948 | 0.729418 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.8689 | 1.38464 | 0.692319 | − | 0.721591i | \(-0.256589\pi\) | ||||
0.692319 | + | 0.721591i | \(0.256589\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 77.6741 | 2.91301 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.56345 | −0.170903 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.81872 | −0.105414 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.8928 | −0.630875 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.7419 | 0.736250 | 0.368125 | − | 0.929776i | \(-0.380000\pi\) | ||||
0.368125 | + | 0.929776i | \(0.380000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.9283 | −0.630444 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.26492 | 0.270185 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.12869 | −0.339031 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.7540 | −1.25187 | −0.625934 | − | 0.779876i | \(-0.715282\pi\) | ||||
−0.625934 | + | 0.779876i | \(0.715282\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.32841 | 0.308460 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.2878 | −0.861329 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.0242 | −1.29365 | −0.646825 | − | 0.762639i | \(-0.723904\pi\) | ||||
−0.646825 | + | 0.762639i | \(0.723904\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.92603 | −0.329242 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.64636 | 0.355328 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.99477 | 0.330878 | 0.165439 | − | 0.986220i | \(-0.447096\pi\) | ||||
0.165439 | + | 0.986220i | \(0.447096\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.1057 | 0.481450 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.8359 | −0.654337 | −0.327168 | − | 0.944966i | \(-0.606094\pi\) | ||||
−0.327168 | + | 0.944966i | \(0.606094\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.6396 | −0.463079 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 53.6301 | 1.96222 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.9960 | 0.876794 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.8155 | 0.394662 | 0.197331 | − | 0.980337i | \(-0.436773\pi\) | ||||
0.197331 | + | 0.980337i | \(0.436773\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −35.0467 | −1.27717 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.12887 | 0.259446 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.0949 | 1.05747 | 0.528737 | − | 0.848786i | \(-0.322666\pi\) | ||||
0.528737 | + | 0.848786i | \(0.322666\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.73963 | −0.244633 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.8989 | −0.902586 | −0.451293 | − | 0.892376i | \(-0.649037\pi\) | ||||
−0.451293 | + | 0.892376i | \(0.649037\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.6493 | −1.21819 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 32.1444 | 1.16218 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −34.8704 | −1.25910 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.4656 | −0.810129 | −0.405064 | − | 0.914288i | \(-0.632751\pi\) | ||||
−0.405064 | + | 0.914288i | \(0.632751\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.5180 | 0.919010 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.491907 | −0.0176927 | −0.00884633 | − | 0.999961i | \(-0.502816\pi\) | ||||
−0.00884633 | + | 0.999961i | \(0.502816\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.68110 | −0.347756 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.8522 | 0.532821 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.9829 | −0.393504 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.6011 | −0.450902 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.7511 | 0.884534 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.89673 | −0.281846 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.7601 | −1.09648 | −0.548239 | − | 0.836322i | \(-0.684702\pi\) | ||||
−0.548239 | + | 0.836322i | \(0.684702\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −83.6756 | −2.97893 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.8112 | −0.882184 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.6564 | −1.40824 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −25.0030 | −0.886763 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −46.8176 | −1.65836 | −0.829182 | − | 0.558978i | \(-0.811193\pi\) | ||||
−0.829182 | + | 0.558978i | \(0.811193\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.44693 | −0.298831 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −28.2010 | −0.996434 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.1743 | −0.500199 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.43102 | −0.0856822 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.2718 | −0.467188 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.3194 | −0.538601 | −0.269300 | − | 0.963056i | \(-0.586792\pi\) | ||||
−0.269300 | + | 0.963056i | \(0.586792\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.0369 | −0.738706 | −0.369353 | − | 0.929289i | \(-0.620421\pi\) | ||||
−0.369353 | + | 0.929289i | \(0.620421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.74202 | −0.0961668 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.1303 | −0.354851 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.39032 | 0.118612 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −48.2521 | −1.68606 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.3342 | −1.72178 | −0.860888 | − | 0.508794i | \(-0.830092\pi\) | ||||
−0.860888 | + | 0.508794i | \(0.830092\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.7400 | −1.55954 | −0.779769 | − | 0.626067i | \(-0.784664\pi\) | ||||
−0.779769 | + | 0.626067i | \(0.784664\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.2977 | −0.497784 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.7710 | 1.48729 | 0.743646 | − | 0.668573i | \(-0.233095\pi\) | ||||
0.743646 | + | 0.668573i | \(0.233095\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.6840 | 1.69086 | 0.845432 | − | 0.534083i | \(-0.179343\pi\) | ||||
0.845432 | + | 0.534083i | \(0.179343\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −53.7419 | −1.86429 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.7622 | −0.996551 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.17656 | 0.248355 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 26.2489 | 0.907296 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 50.1921 | 1.73282 | 0.866412 | − | 0.499330i | \(-0.166421\pi\) | ||||
0.866412 | + | 0.499330i | \(0.166421\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.9597 | −0.860680 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.0281 | −0.414268 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.93161 | 0.100851 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.67711 | 0.0576261 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 56.0253 | 1.92278 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.02193 | −0.206429 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.6101 | −0.876874 | −0.438437 | − | 0.898762i | \(-0.644468\pi\) | ||||
−0.438437 | + | 0.898762i | \(0.644468\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.67970 | −0.160042 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.780477 | −0.0266606 | −0.0133303 | − | 0.999911i | \(-0.504243\pi\) | ||||
−0.0133303 | + | 0.999911i | \(0.504243\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.5597 | −0.633247 | −0.316624 | − | 0.948551i | \(-0.602549\pi\) | ||||
−0.316624 | + | 0.948551i | \(0.602549\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 57.9889 | 1.97625 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.5115 | −0.698220 | −0.349110 | − | 0.937082i | \(-0.613516\pi\) | ||||
−0.349110 | + | 0.937082i | \(0.613516\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.54821 | 0.0866417 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 95.0187 | 3.22700 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.2387 | 0.381246 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40.1567 | −1.36066 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −86.0371 | −2.91191 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.8352 | −0.366296 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.4072 | 0.486497 | 0.243248 | − | 0.969964i | \(-0.421787\pi\) | ||||
0.243248 | + | 0.969964i | \(0.421787\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.29945 | −0.178746 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.3794 | 1.12458 | 0.562291 | − | 0.826940i | \(-0.309920\pi\) | ||||
0.562291 | + | 0.826940i | \(0.309920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.6404 | −1.19940 | −0.599698 | − | 0.800226i | \(-0.704713\pi\) | ||||
−0.599698 | + | 0.800226i | \(0.704713\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.8561 | 0.600225 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.6762 | 0.425626 | 0.212813 | − | 0.977093i | \(-0.431737\pi\) | ||||
0.212813 | + | 0.977093i | \(0.431737\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.6473 | −0.591871 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.0324 | 0.604107 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.22974 | 0.0411516 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.37263 | 0.0793083 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.0563 | 0.936773 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.28479 | 0.142906 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −80.5666 | −2.68406 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.9006 | −0.595694 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.1548 | 0.570245 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.6608 | −1.21730 | −0.608651 | − | 0.793438i | \(-0.708289\pi\) | ||||
−0.608651 | + | 0.793438i | \(0.708289\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 79.9256 | 2.65097 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.6952 | 1.58021 | 0.790106 | − | 0.612970i | \(-0.210026\pi\) | ||||
0.790106 | + | 0.612970i | \(0.210026\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.75976 | 0.256810 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.3068 | 0.671323 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.3700 | 0.540584 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.7694 | 0.982001 | 0.491001 | − | 0.871159i | \(-0.336631\pi\) | ||||
0.491001 | + | 0.871159i | \(0.336631\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.9851 | −0.823286 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 52.4568 | 1.72664 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.7752 | −0.420045 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −69.7613 | −2.29126 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.6180 | −1.66072 | −0.830362 | − | 0.557225i | \(-0.811866\pi\) | ||||
−0.830362 | + | 0.557225i | \(0.811866\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.18731 | 0.137234 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −94.0024 | −3.07750 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.65098 | 0.152103 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.1084 | 0.526238 | 0.263119 | − | 0.964763i | \(-0.415249\pi\) | ||||
0.263119 | + | 0.964763i | \(0.415249\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 59.3273 | 1.93607 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.8109 | 0.548018 | 0.274009 | − | 0.961727i | \(-0.411650\pi\) | ||||
0.274009 | + | 0.961727i | \(0.411650\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.5119 | −0.765654 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.9832 | 0.454874 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.1350 | −1.17423 | −0.587114 | − | 0.809504i | \(-0.699736\pi\) | ||||
−0.587114 | + | 0.809504i | \(0.699736\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 59.0058 | 1.91541 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.1901 | 0.589854 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.1171 | −0.943197 | −0.471598 | − | 0.881813i | \(-0.656323\pi\) | ||||
−0.471598 | + | 0.881813i | \(0.656323\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.09755 | −0.100234 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.32808 | 0.204558 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.89207 | 0.0933898 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4559 | −0.853417 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 98.8868 | 3.18658 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.05187 | 0.0338610 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.1650 | −0.326883 | −0.163442 | − | 0.986553i | \(-0.552260\pi\) | ||||
−0.163442 | + | 0.986553i | \(0.552260\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.6248 | −0.694689 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.9729 | −0.512594 | −0.256297 | − | 0.966598i | \(-0.582503\pi\) | ||||
−0.256297 | + | 0.966598i | \(0.582503\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.58547 | 0.147003 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 59.5199 | 1.90616 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.7941 | 1.36910 | 0.684552 | − | 0.728964i | \(-0.259998\pi\) | ||||
0.684552 | + | 0.728964i | \(0.259998\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.08041 | −0.130410 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −138.668 | −4.42733 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.8981 | −0.443280 | −0.221640 | − | 0.975129i | \(-0.571141\pi\) | ||||
−0.221640 | + | 0.975129i | \(0.571141\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0325 | −0.319661 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.49290 | −0.206671 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.25790 | 0.230788 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.5286 | 1.57333 | 0.786664 | − | 0.617381i | \(-0.211806\pi\) | ||||
0.786664 | + | 0.617381i | \(0.211806\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32.9337 | −1.04512 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.08855 | 0.193020 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.6810 | 1.63675 | 0.818377 | − | 0.574682i | \(-0.194874\pi\) | ||||
0.818377 | + | 0.574682i | \(0.194874\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 34.6381 | 1.09590 |
(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 | 3344.2.a.z.1.6 | 6 | ||
4.3 | odd | 2 | 1672.2.a.i.1.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.i.1.1 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.z.1.6 | 6 | 1.1 | even | 1 | trivial |