Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8092,2,Mod(1,8092)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8092, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8092.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8092 = 2^{2} \cdot 7 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8092.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: | \(64.6149453156\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{12} - 24 x^{10} - 2 x^{9} + 216 x^{8} + 15 x^{7} - 924 x^{6} + 15 x^{5} + 1947 x^{4} - 251 x^{3} + \cdots + 456 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-2.41089\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8092.1 |
$q$-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 | ||||||||
\(3\) | 2.41089 | 1.39193 | 0.695963 | − | 0.718077i | \(-0.254978\pi\) | ||||
0.695963 | + | 0.718077i | \(0.254978\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.568538 | 0.254258 | 0.127129 | − | 0.991886i | \(-0.459424\pi\) | ||||
0.127129 | + | 0.991886i | \(0.459424\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.81238 | 0.937461 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.65717 | −1.70570 | −0.852851 | − | 0.522154i | \(-0.825128\pi\) | ||||
−0.852851 | + | 0.522154i | \(0.825128\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.69720 | −0.748068 | −0.374034 | − | 0.927415i | \(-0.622026\pi\) | ||||
−0.374034 | + | 0.927415i | \(0.622026\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.37068 | 0.353908 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.35893 | 1.68825 | 0.844127 | − | 0.536144i | \(-0.180119\pi\) | ||||
0.844127 | + | 0.536144i | \(0.180119\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.41089 | −0.526099 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.33235 | −0.486329 | −0.243164 | − | 0.969985i | \(-0.578185\pi\) | ||||
−0.243164 | + | 0.969985i | \(0.578185\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.67677 | −0.935353 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.452327 | −0.0870503 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.38860 | 1.55772 | 0.778862 | − | 0.627195i | \(-0.215797\pi\) | ||||
0.778862 | + | 0.627195i | \(0.215797\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.89756 | 0.700023 | 0.350012 | − | 0.936745i | \(-0.386178\pi\) | ||||
0.350012 | + | 0.936745i | \(0.386178\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −13.6388 | −2.37421 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.568538 | −0.0961004 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.68633 | 1.26362 | 0.631812 | − | 0.775122i | \(-0.282311\pi\) | ||||
0.631812 | + | 0.775122i | \(0.282311\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.50264 | −1.04126 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.27530 | −1.13621 | −0.568105 | − | 0.822956i | \(-0.692323\pi\) | ||||
−0.568105 | + | 0.822956i | \(0.692323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.0872 | −1.84327 | −0.921637 | − | 0.388054i | \(-0.873148\pi\) | ||||
−0.921637 | + | 0.388054i | \(0.873148\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.59894 | 0.238357 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.00152 | −1.31301 | −0.656503 | − | 0.754323i | \(-0.727965\pi\) | ||||
−0.656503 | + | 0.754323i | \(0.727965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.10982 | −0.839248 | −0.419624 | − | 0.907698i | \(-0.637838\pi\) | ||||
−0.419624 | + | 0.907698i | \(0.637838\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.21632 | −0.433688 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.7415 | 2.34993 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.55671 | 0.202667 | 0.101333 | − | 0.994853i | \(-0.467689\pi\) | ||||
0.101333 | + | 0.994853i | \(0.467689\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.71488 | −0.219568 | −0.109784 | − | 0.993955i | \(-0.535016\pi\) | ||||
−0.109784 | + | 0.993955i | \(0.535016\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.81238 | −0.354327 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.53346 | −0.190202 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.3442 | 1.63026 | 0.815130 | − | 0.579279i | \(-0.196666\pi\) | ||||
0.815130 | + | 0.579279i | \(0.196666\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.62304 | −0.676934 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.99168 | −0.948438 | −0.474219 | − | 0.880407i | \(-0.657269\pi\) | ||||
−0.474219 | + | 0.880407i | \(0.657269\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0752 | −1.41329 | −0.706645 | − | 0.707568i | \(-0.749792\pi\) | ||||
−0.706645 | + | 0.707568i | \(0.749792\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.2752 | −1.30194 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.65717 | 0.644695 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.65340 | 0.186022 | 0.0930108 | − | 0.995665i | \(-0.470351\pi\) | ||||
0.0930108 | + | 0.995665i | \(0.470351\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.52765 | −1.05863 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.40791 | −0.813124 | −0.406562 | − | 0.913623i | \(-0.633272\pi\) | ||||
−0.406562 | + | 0.913623i | \(0.633272\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 20.2240 | 2.16824 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.97278 | −0.951112 | −0.475556 | − | 0.879685i | \(-0.657753\pi\) | ||||
−0.475556 | + | 0.879685i | \(0.657753\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.69720 | 0.282743 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.39659 | 0.974381 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.18383 | 0.429251 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.10846 | 0.112547 | 0.0562736 | − | 0.998415i | \(-0.482078\pi\) | ||||
0.0562736 | + | 0.998415i | \(0.482078\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −15.9101 | −1.59903 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.3238 | 1.22626 | 0.613130 | − | 0.789982i | \(-0.289910\pi\) | ||||
0.613130 | + | 0.789982i | \(0.289910\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.31926 | −0.129990 | −0.0649951 | − | 0.997886i | \(-0.520703\pi\) | ||||
−0.0649951 | + | 0.997886i | \(0.520703\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.37068 | −0.133765 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.94798 | −0.284992 | −0.142496 | − | 0.989795i | \(-0.545513\pi\) | ||||
−0.142496 | + | 0.989795i | \(0.545513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.18034 | 0.208838 | 0.104419 | − | 0.994533i | \(-0.466702\pi\) | ||||
0.104419 | + | 0.994533i | \(0.466702\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.5309 | 1.75887 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.1626 | −1.23823 | −0.619115 | − | 0.785300i | \(-0.712509\pi\) | ||||
−0.619115 | + | 0.785300i | \(0.712509\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.32603 | −0.123653 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.58555 | −0.701284 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.0036 | 1.90942 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.5399 | −1.58152 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.50160 | −0.492078 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.7029 | −1.57088 | −0.785439 | − | 0.618939i | \(-0.787563\pi\) | ||||
−0.785439 | + | 0.618939i | \(0.787563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −29.1408 | −2.56570 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.811228 | 0.0708773 | 0.0354386 | − | 0.999372i | \(-0.488717\pi\) | ||||
0.0354386 | + | 0.999372i | \(0.488717\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.35893 | −0.638100 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.257165 | −0.0221332 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.2387 | −1.30193 | −0.650967 | − | 0.759106i | \(-0.725636\pi\) | ||||
−0.650967 | + | 0.759106i | \(0.725636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.699928 | −0.0593671 | −0.0296836 | − | 0.999559i | \(-0.509450\pi\) | ||||
−0.0296836 | + | 0.999559i | \(0.509450\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −21.7016 | −1.82761 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.2585 | 1.27598 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.76923 | 0.396063 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.41089 | 0.198847 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.115394 | 0.00945346 | 0.00472673 | − | 0.999989i | \(-0.498495\pi\) | ||||
0.00472673 | + | 0.999989i | \(0.498495\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3722 | −1.41373 | −0.706866 | − | 0.707348i | \(-0.749891\pi\) | ||||
−0.706866 | + | 0.707348i | \(0.749891\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.21591 | 0.177986 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.96992 | −0.715877 | −0.357939 | − | 0.933745i | \(-0.616520\pi\) | ||||
−0.357939 | + | 0.933745i | \(0.616520\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.7301 | −1.16817 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.33235 | 0.183815 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.29783 | 0.649936 | 0.324968 | − | 0.945725i | \(-0.394646\pi\) | ||||
0.324968 | + | 0.945725i | \(0.394646\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.75418 | −0.603662 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.3437 | −1.18733 | −0.593664 | − | 0.804713i | \(-0.702319\pi\) | ||||
−0.593664 | + | 0.804713i | \(0.702319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.72513 | −0.440394 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.6961 | 1.58267 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.41676 | 0.183743 | 0.0918716 | − | 0.995771i | \(-0.470715\pi\) | ||||
0.0918716 | + | 0.995771i | \(0.470715\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.67677 | 0.353530 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.75306 | 0.282097 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.96414 | 0.371037 | 0.185519 | − | 0.982641i | \(-0.440603\pi\) | ||||
0.185519 | + | 0.982641i | \(0.440603\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5483 | 1.15569 | 0.577847 | − | 0.816145i | \(-0.303893\pi\) | ||||
0.577847 | + | 0.816145i | \(0.303893\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.13438 | −0.305623 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.36996 | 0.321286 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.452327 | 0.0329019 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.35478 | −0.676888 | −0.338444 | − | 0.940986i | \(-0.609901\pi\) | ||||
−0.338444 | + | 0.940986i | \(0.609901\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.41662 | −0.389897 | −0.194948 | − | 0.980813i | \(-0.562454\pi\) | ||||
−0.194948 | + | 0.980813i | \(0.562454\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.69700 | −0.264747 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.575238 | −0.0409840 | −0.0204920 | − | 0.999790i | \(-0.506523\pi\) | ||||
−0.0204920 | + | 0.999790i | \(0.506523\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.7235 | −1.61083 | −0.805415 | − | 0.592712i | \(-0.798057\pi\) | ||||
−0.805415 | + | 0.592712i | \(0.798057\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32.1715 | 2.26920 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.38860 | −0.588764 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.13628 | −0.288890 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.55946 | −0.455914 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −41.6307 | −2.87966 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.16118 | −0.424153 | −0.212077 | − | 0.977253i | \(-0.568023\pi\) | ||||
−0.212077 | + | 0.977253i | \(0.568023\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −19.2670 | −1.32016 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.87200 | −0.468667 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.89756 | −0.264584 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −29.1118 | −1.96720 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.21427 | −0.483103 | −0.241552 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241552 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.1528 | −0.876857 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.1440 | 1.00514 | 0.502571 | − | 0.864536i | \(-0.332387\pi\) | ||||
0.502571 | + | 0.864536i | \(0.332387\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.443837 | −0.0293296 | −0.0146648 | − | 0.999892i | \(-0.504668\pi\) | ||||
−0.0146648 | + | 0.999892i | \(0.504668\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.6388 | 0.897368 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.82426 | −0.119511 | −0.0597555 | − | 0.998213i | \(-0.519032\pi\) | ||||
−0.0597555 | + | 0.998213i | \(0.519032\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.11770 | −0.333842 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.98615 | 0.258928 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.2627 | −1.37537 | −0.687684 | − | 0.726010i | \(-0.741373\pi\) | ||||
−0.687684 | + | 0.726010i | \(0.741373\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.3876 | 0.862372 | 0.431186 | − | 0.902263i | \(-0.358095\pi\) | ||||
0.431186 | + | 0.902263i | \(0.358095\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6131 | −1.38648 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.568538 | 0.0363225 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.8485 | −1.26293 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.8596 | −1.13181 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.4979 | 1.48317 | 0.741587 | − | 0.670857i | \(-0.234074\pi\) | ||||
0.741587 | + | 0.670857i | \(0.234074\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.1945 | 0.829532 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.2174 | 0.699724 | 0.349862 | − | 0.936801i | \(-0.386228\pi\) | ||||
0.349862 | + | 0.936801i | \(0.386228\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.68633 | −0.477605 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 23.5919 | 1.46030 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −31.0027 | −1.91171 | −0.955856 | − | 0.293837i | \(-0.905068\pi\) | ||||
−0.955856 | + | 0.293837i | \(0.905068\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.47366 | −0.213385 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.6324 | −1.32388 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.614893 | −0.0374907 | −0.0187453 | − | 0.999824i | \(-0.505967\pi\) | ||||
−0.0187453 | + | 0.999824i | \(0.505967\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.3262 | 1.72070 | 0.860348 | − | 0.509708i | \(-0.170246\pi\) | ||||
0.860348 | + | 0.509708i | \(0.170246\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.50264 | 0.393558 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26.4573 | 1.59543 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.4763 | 0.809714 | 0.404857 | − | 0.914380i | \(-0.367321\pi\) | ||||
0.404857 | + | 0.914380i | \(0.367321\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.9614 | 0.656244 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.7130 | 1.89184 | 0.945920 | − | 0.324400i | \(-0.105163\pi\) | ||||
0.945920 | + | 0.324400i | \(0.105163\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.94253 | 0.412690 | 0.206345 | − | 0.978479i | \(-0.433843\pi\) | ||||
0.206345 | + | 0.978479i | \(0.433843\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.0867 | 0.597487 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.27530 | 0.429447 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.67238 | 0.156657 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −33.1190 | −1.93483 | −0.967417 | − | 0.253190i | \(-0.918520\pi\) | ||||
−0.967417 | + | 0.253190i | \(0.918520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.885050 | 0.0515296 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.55889 | 0.148482 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.29081 | 0.363807 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0872 | 0.696692 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 29.7112 | 1.70686 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.974974 | −0.0558268 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.4377 | 1.10937 | 0.554685 | − | 0.832061i | \(-0.312839\pi\) | ||||
0.554685 | + | 0.832061i | \(0.312839\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.18058 | −0.180937 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.6306 | 1.11315 | 0.556575 | − | 0.830798i | \(-0.312115\pi\) | ||||
0.556575 | + | 0.830798i | \(0.312115\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.289182 | −0.0163455 | −0.00817276 | − | 0.999967i | \(-0.502602\pi\) | ||||
−0.00817276 | + | 0.999967i | \(0.502602\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.59894 | −0.0900903 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.06811 | −0.509316 | −0.254658 | − | 0.967031i | \(-0.581963\pi\) | ||||
−0.254658 | + | 0.967031i | \(0.581963\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −47.4558 | −2.65701 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.10726 | −0.396689 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.6142 | 0.699708 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.25655 | 0.290688 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.00152 | 0.496270 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.9745 | −1.92237 | −0.961185 | − | 0.275904i | \(-0.911023\pi\) | ||||
−0.961185 | + | 0.275904i | \(0.911023\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.6169 | 1.18460 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.58670 | 0.414506 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.462674 | −0.0252034 | −0.0126017 | − | 0.999921i | \(-0.504011\pi\) | ||||
−0.0126017 | + | 0.999921i | \(0.504011\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −31.7335 | −1.72353 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.0492 | −1.19403 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.19691 | −0.172116 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.26754 | 0.336459 | 0.168230 | − | 0.985748i | \(-0.446195\pi\) | ||||
0.168230 | + | 0.985748i | \(0.446195\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.9591 | 1.28250 | 0.641250 | − | 0.767332i | \(-0.278416\pi\) | ||||
0.641250 | + | 0.767332i | \(0.278416\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.22001 | 0.0651196 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.6998 | 1.52753 | 0.763767 | − | 0.645492i | \(-0.223348\pi\) | ||||
0.763767 | + | 0.645492i | \(0.223348\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.54357 | −0.241148 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.2307 | 1.17329 | 0.586645 | − | 0.809845i | \(-0.300449\pi\) | ||||
0.586645 | + | 0.809845i | \(0.300449\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 35.1538 | 1.85020 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 50.6374 | 2.65777 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.86518 | −0.359340 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.8200 | −1.29559 | −0.647796 | − | 0.761814i | \(-0.724309\pi\) | ||||
−0.647796 | + | 0.761814i | \(0.724309\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.4609 | −1.06515 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.10982 | 0.317206 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.54940 | −0.494449 | −0.247225 | − | 0.968958i | \(-0.579519\pi\) | ||||
−0.247225 | + | 0.968958i | \(0.579519\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.2638 | −0.684937 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.6257 | −1.16528 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.9899 | 1.54048 | 0.770238 | − | 0.637756i | \(-0.220137\pi\) | ||||
0.770238 | + | 0.637756i | \(0.220137\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −42.6797 | −2.18655 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.6937 | −1.15959 | −0.579796 | − | 0.814761i | \(-0.696868\pi\) | ||||
−0.579796 | + | 0.814761i | \(0.696868\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.21632 | 0.163919 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −33.9937 | −1.72800 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.53996 | −0.128781 | −0.0643904 | − | 0.997925i | \(-0.520510\pi\) | ||||
−0.0643904 | + | 0.997925i | \(0.520510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.95578 | 0.0986560 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.940017 | 0.0472974 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.1188 | 1.11011 | 0.555056 | − | 0.831813i | \(-0.312697\pi\) | ||||
0.555056 | + | 0.831813i | \(0.312697\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.7415 | −0.888188 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5121 | 0.824576 | 0.412288 | − | 0.911054i | \(-0.364730\pi\) | ||||
0.412288 | + | 0.911054i | \(0.364730\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.5125 | −0.523665 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.41683 | −0.269164 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −43.4829 | −2.15537 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0076 | 0.494844 | 0.247422 | − | 0.968908i | \(-0.420417\pi\) | ||||
0.247422 | + | 0.968908i | \(0.420417\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −36.7389 | −1.81220 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.55671 | −0.0766009 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.21168 | −0.206743 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.68745 | −0.0826347 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.3557 | 1.58068 | 0.790341 | − | 0.612668i | \(-0.209904\pi\) | ||||
0.790341 | + | 0.612668i | \(0.209904\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.6663 | 1.25090 | 0.625450 | − | 0.780264i | \(-0.284915\pi\) | ||||
0.625450 | + | 0.780264i | \(0.284915\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −25.3157 | −1.23089 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.71488 | 0.0829889 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 36.7866 | 1.77607 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.6239 | −0.704407 | −0.352203 | − | 0.935923i | \(-0.614567\pi\) | ||||
−0.352203 | + | 0.935923i | \(0.614567\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.9350 | −0.525501 | −0.262751 | − | 0.964864i | \(-0.584630\pi\) | ||||
−0.262751 | + | 0.964864i | \(0.584630\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.4981 | 0.551291 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17.1636 | −0.821046 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.6890 | 0.844251 | 0.422126 | − | 0.906537i | \(-0.361284\pi\) | ||||
0.422126 | + | 0.906537i | \(0.361284\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.81238 | 0.133923 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.31621 | 0.442626 | 0.221313 | − | 0.975203i | \(-0.428966\pi\) | ||||
0.221313 | + | 0.975203i | \(0.428966\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.10136 | −0.241828 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.278203 | 0.0131585 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.16217 | 0.102039 | 0.0510196 | − | 0.998698i | \(-0.483753\pi\) | ||||
0.0510196 | + | 0.998698i | \(0.483753\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 41.1576 | 1.93804 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −41.8825 | −1.96781 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.53346 | 0.0718896 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.45984 | 0.115066 | 0.0575331 | − | 0.998344i | \(-0.481677\pi\) | ||||
0.0575331 | + | 0.998344i | \(0.481677\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.117028 | 0.00545054 | 0.00272527 | − | 0.999996i | \(-0.499133\pi\) | ||||
0.00272527 | + | 0.999996i | \(0.499133\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0103 | −0.465220 | −0.232610 | − | 0.972570i | \(-0.574727\pi\) | ||||
−0.232610 | + | 0.972570i | \(0.574727\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.34232 | 0.247744 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.8895 | 1.05920 | 0.529599 | − | 0.848248i | \(-0.322342\pi\) | ||||
0.529599 | + | 0.848248i | \(0.322342\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.3442 | −0.616180 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.6255 | −0.996449 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 68.3791 | 3.14408 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34.4160 | −1.57911 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.1831 | −0.786762 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.0599 | 1.28209 | 0.641046 | − | 0.767503i | \(-0.278501\pi\) | ||||
0.641046 | + | 0.767503i | \(0.278501\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.7315 | −0.945277 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.62304 | 0.255857 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.630202 | 0.0286160 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.6111 | 1.43244 | 0.716218 | − | 0.697877i | \(-0.245872\pi\) | ||||
0.716218 | + | 0.697877i | \(0.245872\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.0051 | 0.904664 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.98626 | −0.134768 | −0.0673841 | − | 0.997727i | \(-0.521465\pi\) | ||||
−0.0673841 | + | 0.997727i | \(0.521465\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.04551 | −0.406565 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.99168 | 0.358476 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.1244 | 1.03519 | 0.517596 | − | 0.855625i | \(-0.326827\pi\) | ||||
0.517596 | + | 0.855625i | \(0.326827\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −36.9918 | −1.65267 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.9544 | −1.24643 | −0.623213 | − | 0.782052i | \(-0.714173\pi\) | ||||
−0.623213 | + | 0.782052i | \(0.714173\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.00652 | 0.311786 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.8026 | −0.612997 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −43.3280 | −1.92048 | −0.960239 | − | 0.279178i | \(-0.909938\pi\) | ||||
−0.960239 | + | 0.279178i | \(0.909938\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0752 | 0.534173 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.32864 | −0.146963 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.750047 | −0.0330510 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 50.9231 | 2.23960 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.82655 | 0.255757 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.8491 | 1.52677 | 0.763384 | − | 0.645945i | \(-0.223537\pi\) | ||||
0.763384 | + | 0.645945i | \(0.223537\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.2675 | −0.580146 | −0.290073 | − | 0.957005i | \(-0.593680\pi\) | ||||
−0.290073 | + | 0.957005i | \(0.593680\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.2752 | 0.492088 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5601 | −0.763484 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.37807 | 0.189992 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.6229 | 0.849963 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.67604 | −0.0724615 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.9680 | 0.516457 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.65717 | −0.243672 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.2078 | 0.997782 | 0.498891 | − | 0.866665i | \(-0.333741\pi\) | ||||
0.498891 | + | 0.866665i | \(0.333741\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 37.4852 | 1.60864 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.23960 | 0.0530988 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.4698 | 0.618685 | 0.309343 | − | 0.950951i | \(-0.399891\pi\) | ||||
0.309343 | + | 0.950951i | \(0.399891\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.82290 | −0.205836 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 61.7311 | 2.62983 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.65340 | −0.0703095 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.5355 | 0.447207 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.6049 | −0.576458 | −0.288229 | − | 0.957562i | \(-0.593066\pi\) | ||||
−0.288229 | + | 0.957562i | \(0.593066\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.6014 | 1.37889 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.8321 | −0.877967 | −0.438984 | − | 0.898495i | \(-0.644661\pi\) | ||||
−0.438984 | + | 0.898495i | \(0.644661\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.48342 | −0.314830 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.52765 | 0.400124 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.1604 | −1.01285 | −0.506427 | − | 0.862283i | \(-0.669034\pi\) | ||||
−0.506427 | + | 0.862283i | \(0.669034\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.58514 | 0.150033 | 0.0750167 | − | 0.997182i | \(-0.476099\pi\) | ||||
0.0750167 | + | 0.997182i | \(0.476099\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.5533 | −0.942179 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.9079 | 0.454889 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.25905 | −0.218937 | −0.109469 | − | 0.993990i | \(-0.534915\pi\) | ||||
−0.109469 | + | 0.993990i | \(0.534915\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.0589 | −0.542708 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.40791 | 0.307332 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34.5643 | 1.43151 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.31267 | −0.178307 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −46.1592 | −1.90519 | −0.952596 | − | 0.304238i | \(-0.901598\pi\) | ||||
−0.952596 | + | 0.304238i | \(0.901598\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.6819 | 1.18182 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.38683 | −0.0570468 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.9389 | −0.531335 | −0.265668 | − | 0.964065i | \(-0.585592\pi\) | ||||
−0.265668 | + | 0.964065i | \(0.585592\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −54.7839 | −2.24216 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.1670 | −0.415414 | −0.207707 | − | 0.978191i | \(-0.566600\pi\) | ||||
−0.207707 | + | 0.978191i | \(0.566600\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.0848 | −0.615322 | −0.307661 | − | 0.951496i | \(-0.599546\pi\) | ||||
−0.307661 | + | 0.951496i | \(0.599546\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 37.5291 | 1.52830 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.9413 | 0.485485 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.73230 | 0.0703121 | 0.0351560 | − | 0.999382i | \(-0.488807\pi\) | ||||
0.0351560 | + | 0.999382i | \(0.488807\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.2240 | −0.819517 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.2789 | 0.982218 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.7087 | −1.28070 | −0.640351 | − | 0.768083i | \(-0.721211\pi\) | ||||
−0.640351 | + | 0.768083i | \(0.721211\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.97211 | −0.402114 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.9478 | −1.28617 | −0.643085 | − | 0.765795i | \(-0.722346\pi\) | ||||
−0.643085 | + | 0.765795i | \(0.722346\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.1301 | 1.61297 | 0.806483 | − | 0.591257i | \(-0.201368\pi\) | ||||
0.806483 | + | 0.591257i | \(0.201368\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.05498 | 0.0423351 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.97278 | 0.359487 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.2560 | 0.810238 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −100.367 | −4.00827 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.65656 | 0.225184 | 0.112592 | − | 0.993641i | \(-0.464085\pi\) | ||||
0.112592 | + | 0.993641i | \(0.464085\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.8539 | −0.590390 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.0648 | −0.399408 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.69720 | −0.106867 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.4757 | −0.889123 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.39021 | 0.252398 | 0.126199 | − | 0.992005i | \(-0.459722\pi\) | ||||
0.126199 | + | 0.992005i | \(0.459722\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.1196 | −0.754004 | −0.377002 | − | 0.926212i | \(-0.623045\pi\) | ||||
−0.377002 | + | 0.926212i | \(0.623045\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.5676 | −0.652350 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.3455 | 1.27163 | 0.635817 | − | 0.771840i | \(-0.280663\pi\) | ||||
0.635817 | + | 0.771840i | \(0.280663\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.80660 | −0.345689 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.39659 | −0.368281 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.03022 | 0.118582 | 0.0592909 | − | 0.998241i | \(-0.481116\pi\) | ||||
0.0592909 | + | 0.998241i | \(0.481116\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.461213 | 0.0180211 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −33.9599 | −1.32490 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.0093 | 1.51959 | 0.759793 | − | 0.650166i | \(-0.225300\pi\) | ||||
0.759793 | + | 0.650166i | \(0.225300\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.96595 | −0.270944 | −0.135472 | − | 0.990781i | \(-0.543255\pi\) | ||||
−0.135472 | + | 0.990781i | \(0.543255\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.18383 | −0.162242 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.5652 | −0.757566 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.3928 | −0.672445 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.70138 | 0.374517 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.7759 | −0.531020 | −0.265510 | − | 0.964108i | \(-0.585540\pi\) | ||||
−0.265510 | + | 0.964108i | \(0.585540\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.11543 | 0.0814228 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 47.6413 | 1.83100 | 0.915502 | − | 0.402313i | \(-0.131794\pi\) | ||||
0.915502 | + | 0.402313i | \(0.131794\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.10846 | −0.0425388 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.5105 | 1.39909 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.6741 | 0.944130 | 0.472065 | − | 0.881564i | \(-0.343509\pi\) | ||||
0.472065 | + | 0.881564i | \(0.343509\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.66380 | −0.331027 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.07004 | −0.0408246 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.4794 | 0.627814 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.0484 | −1.63764 | −0.818820 | − | 0.574051i | \(-0.805371\pi\) | ||||
−0.818820 | + | 0.574051i | \(0.805371\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.9101 | 0.604376 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.397935 | −0.0150946 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.39808 | −0.166351 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.7893 | −1.38951 | −0.694757 | − | 0.719244i | \(-0.744488\pi\) | ||||
−0.694757 | + | 0.719244i | \(0.744488\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 56.5631 | 2.13332 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.3382 | −0.464684 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.3238 | −0.463483 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.8175 | −0.894484 | −0.447242 | − | 0.894413i | \(-0.647594\pi\) | ||||
−0.447242 | + | 0.894413i | \(0.647594\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.64998 | 0.174388 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.09049 | −0.340441 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.67504 | 0.324428 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −51.2619 | −1.91441 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.9059 | 1.00342 | 0.501710 | − | 0.865036i | \(-0.332704\pi\) | ||||
0.501710 | + | 0.865036i | \(0.332704\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.31926 | 0.0491317 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.2760 | 1.20036 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −39.2315 | −1.45702 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.9924 | 0.444773 | 0.222387 | − | 0.974959i | \(-0.428615\pi\) | ||||
0.222387 | + | 0.974959i | \(0.428615\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.5239 | −0.871255 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.17406 | 0.0803009 | 0.0401505 | − | 0.999194i | \(-0.487216\pi\) | ||||
0.0401505 | + | 0.999194i | \(0.487216\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.37068 | 0.0505583 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −75.4907 | −2.78074 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.3808 | −0.639363 | −0.319682 | − | 0.947525i | \(-0.603576\pi\) | ||||
−0.319682 | + | 0.947525i | \(0.603576\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −47.8525 | −1.75790 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.0790 | 0.846686 | 0.423343 | − | 0.905970i | \(-0.360857\pi\) | ||||
0.423343 | + | 0.905970i | \(0.360857\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.0656059 | 0.00240362 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.8339 | −0.762271 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.94798 | 0.107717 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.9497 | −1.71322 | −0.856609 | − | 0.515966i | \(-0.827433\pi\) | ||||
−0.856609 | + | 0.515966i | \(0.827433\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 56.6508 | 2.06447 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.87676 | −0.359452 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.52126 | 0.0916366 | 0.0458183 | − | 0.998950i | \(-0.485410\pi\) | ||||
0.0458183 | + | 0.998950i | \(0.485410\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 31.8105 | 1.15465 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.47670 | 0.198530 | 0.0992650 | − | 0.995061i | \(-0.468351\pi\) | ||||
0.0992650 | + | 0.995061i | \(0.468351\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.18034 | −0.0789335 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.19876 | −0.151609 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 54.0302 | 1.94838 | 0.974189 | − | 0.225732i | \(-0.0724774\pi\) | ||||
0.974189 | + | 0.225732i | \(0.0724774\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.0440 | 0.973965 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.1384 | −1.08400 | −0.542002 | − | 0.840377i | \(-0.682333\pi\) | ||||
−0.542002 | + | 0.840377i | \(0.682333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.2280 | −0.654769 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.5309 | −0.664791 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −53.5384 | −1.91821 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.2103 | 1.61775 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.79439 | −0.135600 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.09973 | −0.182017 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.9551 | −1.24602 | −0.623008 | − | 0.782216i | \(-0.714090\pi\) | ||||
−0.623008 | + | 0.782216i | \(0.714090\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −74.7442 | −2.66096 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.1626 | 0.468007 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.62537 | 0.164252 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.37460 | −0.297017 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.2322 | 0.645819 | 0.322909 | − | 0.946430i | \(-0.395339\pi\) | ||||
0.322909 | + | 0.946430i | \(0.395339\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25.2349 | −0.891630 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 68.3112 | 2.41065 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.32603 | 0.0467364 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.48244 | −0.0521843 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.4383 | 0.999839 | 0.499919 | − | 0.866072i | \(-0.333363\pi\) | ||||
0.499919 | + | 0.866072i | \(0.333363\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.6351 | −0.759712 | −0.379856 | − | 0.925046i | \(-0.624026\pi\) | ||||
−0.379856 | + | 0.925046i | \(0.624026\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 68.2913 | 2.39508 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.71763 | 0.165251 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −88.9485 | −3.11191 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.58555 | 0.265060 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.6565 | −0.895419 | −0.447710 | − | 0.894179i | \(-0.647760\pi\) | ||||
−0.447710 | + | 0.894179i | \(0.647760\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.5612 | 1.27444 | 0.637222 | − | 0.770680i | \(-0.280083\pi\) | ||||
0.637222 | + | 0.770680i | \(0.280083\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 63.7855 | 2.22073 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.5146 | 1.06110 | 0.530548 | − | 0.847655i | \(-0.321986\pi\) | ||||
0.530548 | + | 0.847655i | \(0.321986\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.5316 | 0.886750 | 0.443375 | − | 0.896336i | \(-0.353781\pi\) | ||||
0.443375 | + | 0.896336i | \(0.353781\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32.4899 | 1.12706 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.72345 | −0.301887 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.76297 | −0.0609373 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.41584 | 0.0834041 | 0.0417020 | − | 0.999130i | \(-0.486722\pi\) | ||||
0.0417020 | + | 0.999130i | \(0.486722\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41.3686 | 1.42650 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 76.4565 | 2.63330 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.25495 | −0.111974 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.0036 | −0.721693 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.7377 | 0.574435 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.9272 | −0.614537 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.01848 | 0.103351 | 0.0516754 | − | 0.998664i | \(-0.483544\pi\) | ||||
0.0516754 | + | 0.998664i | \(0.483544\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.7665 | 0.402406 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.8230 | 0.916256 | 0.458128 | − | 0.888886i | \(-0.348520\pi\) | ||||
0.458128 | + | 0.888886i | \(0.348520\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.9316 | 0.509460 | 0.254730 | − | 0.967012i | \(-0.418013\pi\) | ||||
0.254730 | + | 0.967012i | \(0.418013\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.5399 | 0.597759 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.9280 | −0.644318 | −0.322159 | − | 0.946686i | \(-0.604408\pi\) | ||||
−0.322159 | + | 0.946686i | \(0.604408\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.37402 | 0.0467181 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.35354 | −0.317297 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.9921 | −1.21954 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.11741 | 0.105509 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.50160 | 0.185988 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.8803 | 0.975218 | 0.487609 | − | 0.873062i | \(-0.337869\pi\) | ||||
0.487609 | + | 0.873062i | \(0.337869\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −79.8462 | −2.69315 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.9080 | 0.738099 | 0.369050 | − | 0.929410i | \(-0.379683\pi\) | ||||
0.369050 | + | 0.929410i | \(0.379683\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.8295 | 0.801927 | 0.400963 | − | 0.916094i | \(-0.368675\pi\) | ||||
0.400963 | + | 0.916094i | \(0.368675\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.13376 | 0.0717254 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.84186 | 0.229727 | 0.114864 | − | 0.993381i | \(-0.463357\pi\) | ||||
0.114864 | + | 0.993381i | \(0.463357\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.7029 | 0.593736 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 53.8996 | 1.80570 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −66.2415 | −2.21669 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.82230 | 0.0943391 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.1664 | 0.506393 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.6951 | 1.09044 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 29.1408 | 0.969744 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.83978 | 0.293844 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.3689 | −1.83849 | −0.919246 | − | 0.393683i | \(-0.871201\pi\) | ||||
−0.919246 | + | 0.393683i | \(0.871201\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 34.6591 | 1.14957 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.9987 | −1.12643 | −0.563213 | − | 0.826312i | \(-0.690435\pi\) | ||||
−0.563213 | + | 0.826312i | \(0.690435\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41.9078 | 1.38695 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.35055 | −0.0777069 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.811228 | −0.0267891 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −54.2903 | −1.79087 | −0.895437 | − | 0.445189i | \(-0.853136\pi\) | ||||
−0.895437 | + | 0.445189i | \(0.853136\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 46.8622 | 1.54416 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.5551 | 0.709496 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.9471 | −1.18193 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.71026 | −0.121861 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.6824 | −0.973849 | −0.486925 | − | 0.873444i | \(-0.661881\pi\) | ||||
−0.486925 | + | 0.873444i | \(0.661881\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.35893 | 0.241179 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 47.3272 | 1.54942 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.1014 | 1.21205 | 0.606025 | − | 0.795446i | \(-0.292763\pi\) | ||||
0.606025 | + | 0.795446i | \(0.292763\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.697185 | −0.0227518 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.79710 | 0.221579 | 0.110790 | − | 0.993844i | \(-0.464662\pi\) | ||||
0.110790 | + | 0.993844i | \(0.464662\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.9686 | 0.552572 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.257165 | 0.00836557 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.95594 | −0.0960551 | −0.0480275 | − | 0.998846i | \(-0.515294\pi\) | ||||
−0.0480275 | + | 0.998846i | \(0.515294\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.5691 | 1.05724 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.8622 | −0.708930 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49.5333 | 1.60454 | 0.802270 | − | 0.596961i | \(-0.203625\pi\) | ||||
0.802270 | + | 0.596961i | \(0.203625\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.31854 | −0.172104 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −114.411 | −3.69837 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.2387 | 0.492085 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.8090 | −0.509967 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.29086 | −0.267169 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.07955 | −0.0991343 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51.3202 | 1.65035 | 0.825173 | − | 0.564880i | \(-0.191077\pi\) | ||||
0.825173 | + | 0.564880i | \(0.191077\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.6740 | −1.40157 | −0.700783 | − | 0.713374i | \(-0.747166\pi\) | ||||
−0.700783 | + | 0.713374i | \(0.747166\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.699928 | 0.0224387 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 30.4113 | 0.973942 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.5093 | 0.464193 | 0.232096 | − | 0.972693i | \(-0.425442\pi\) | ||||
0.232096 | + | 0.972693i | \(0.425442\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 50.7605 | 1.62231 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.13194 | 0.195778 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −55.2463 | −1.76208 | −0.881041 | − | 0.473039i | \(-0.843157\pi\) | ||||
−0.881041 | + | 0.473039i | \(0.843157\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.327044 | −0.0104205 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.7016 | 0.690771 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 28.1915 | 0.896437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.28047 | −0.0724415 | −0.0362207 | − | 0.999344i | \(-0.511532\pi\) | ||||
−0.0362207 | + | 0.999344i | \(0.511532\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −84.3195 | −2.67580 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.9192 | −0.409566 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.9944 | 0.538217 | 0.269109 | − | 0.963110i | \(-0.413271\pi\) | ||||
0.269109 | + | 0.963110i | \(0.413271\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.47673 | −0.109999 |
(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 | 8092.2.a.v.1.11 | ✓ | 12 | |
17.16 | even | 2 | 8092.2.a.w.1.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8092.2.a.v.1.11 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8092.2.a.w.1.2 | yes | 12 | 17.16 | even | 2 |