Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8550,2,Mod(1,8550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, 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("8550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8550.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: | \(68.2720937282\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.788.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.476452\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8550.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.47645 | 0.558046 | 0.279023 | − | 0.960284i | \(-0.409989\pi\) | ||||
0.279023 | + | 0.960284i | \(0.409989\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.29654 | 0.692433 | 0.346217 | − | 0.938155i | \(-0.387466\pi\) | ||||
0.346217 | + | 0.938155i | \(0.387466\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.29654 | 1.46900 | 0.734498 | − | 0.678611i | \(-0.237418\pi\) | ||||
0.734498 | + | 0.678611i | \(0.237418\pi\) | |||||||
\(14\) | −1.47645 | −0.394598 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.47645 | −0.358092 | −0.179046 | − | 0.983841i | \(-0.557301\pi\) | ||||
−0.179046 | + | 0.983841i | \(0.557301\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.29654 | −0.489624 | ||||||||
\(23\) | 1.86719 | 0.389335 | 0.194668 | − | 0.980869i | \(-0.437637\pi\) | ||||
0.194668 | + | 0.980869i | \(0.437637\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.29654 | −1.03874 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.47645 | 0.279023 | ||||||||
\(29\) | −7.16373 | −1.33027 | −0.665135 | − | 0.746723i | \(-0.731626\pi\) | ||||
−0.665135 | + | 0.746723i | \(0.731626\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0470959 | 0.00845868 | 0.00422934 | − | 0.999991i | \(-0.498654\pi\) | ||||
0.00422934 | + | 0.999991i | \(0.498654\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.47645 | 0.253209 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.59308 | −1.08390 | −0.541948 | − | 0.840412i | \(-0.682313\pi\) | ||||
−0.541948 | + | 0.840412i | \(0.682313\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.179911 | −0.0280973 | −0.0140487 | − | 0.999901i | \(-0.504472\pi\) | ||||
−0.0140487 | + | 0.999901i | \(0.504472\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.98382 | −1.21752 | −0.608760 | − | 0.793354i | \(-0.708333\pi\) | ||||
−0.608760 | + | 0.793354i | \(0.708333\pi\) | |||||||
\(44\) | 2.29654 | 0.346217 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.86719 | −0.275301 | ||||||||
\(47\) | −12.4132 | −1.81065 | −0.905324 | − | 0.424722i | \(-0.860372\pi\) | ||||
−0.905324 | + | 0.424722i | \(0.860372\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.82009 | −0.688584 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.29654 | 0.734498 | ||||||||
\(53\) | −11.9367 | −1.63963 | −0.819817 | − | 0.572625i | \(-0.805925\pi\) | ||||
−0.819817 | + | 0.572625i | \(0.805925\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.47645 | −0.197299 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.16373 | 0.940643 | ||||||||
\(59\) | −6.34364 | −0.825871 | −0.412936 | − | 0.910760i | \(-0.635497\pi\) | ||||
−0.412936 | + | 0.910760i | \(0.635497\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.93672 | −1.27227 | −0.636133 | − | 0.771579i | \(-0.719467\pi\) | ||||
−0.636133 | + | 0.771579i | \(0.719467\pi\) | |||||||
\(62\) | −0.0470959 | −0.00598119 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.8039 | 1.80858 | 0.904292 | − | 0.426914i | \(-0.140399\pi\) | ||||
0.904292 | + | 0.426914i | \(0.140399\pi\) | |||||||
\(68\) | −1.47645 | −0.179046 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0695 | −1.66975 | −0.834873 | − | 0.550442i | \(-0.814459\pi\) | ||||
−0.834873 | + | 0.550442i | \(0.814459\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.4603 | 1.69245 | 0.846223 | − | 0.532829i | \(-0.178871\pi\) | ||||
0.846223 | + | 0.532829i | \(0.178871\pi\) | |||||||
\(74\) | 6.59308 | 0.766430 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 3.39073 | 0.386410 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.5460 | −1.41153 | −0.705767 | − | 0.708444i | \(-0.749397\pi\) | ||||
−0.705767 | + | 0.708444i | \(0.749397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.179911 | 0.0198678 | ||||||||
\(83\) | −6.11663 | −0.671387 | −0.335694 | − | 0.941971i | \(-0.608971\pi\) | ||||
−0.335694 | + | 0.941971i | \(0.608971\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.98382 | 0.860917 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.29654 | −0.244812 | ||||||||
\(89\) | 6.46027 | 0.684787 | 0.342394 | − | 0.939557i | \(-0.388762\pi\) | ||||
0.342394 | + | 0.939557i | \(0.388762\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.82009 | 0.819768 | ||||||||
\(92\) | 1.86719 | 0.194668 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.4132 | 1.28032 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.42936 | −0.449733 | −0.224866 | − | 0.974390i | \(-0.572195\pi\) | ||||
−0.224866 | + | 0.974390i | \(0.572195\pi\) | |||||||
\(98\) | 4.82009 | 0.486903 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.2965 | −1.32306 | −0.661528 | − | 0.749921i | \(-0.730092\pi\) | ||||
−0.661528 | + | 0.749921i | \(0.730092\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.227007 | 0.0223676 | 0.0111838 | − | 0.999937i | \(-0.496440\pi\) | ||||
0.0111838 | + | 0.999937i | \(0.496440\pi\) | |||||||
\(104\) | −5.29654 | −0.519369 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.9367 | 1.15940 | ||||||||
\(107\) | 7.20235 | 0.696277 | 0.348139 | − | 0.937443i | \(-0.386814\pi\) | ||||
0.348139 | + | 0.937443i | \(0.386814\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.04710 | −0.674989 | −0.337495 | − | 0.941327i | \(-0.609580\pi\) | ||||
−0.337495 | + | 0.941327i | \(0.609580\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.47645 | 0.139512 | ||||||||
\(113\) | 20.1004 | 1.89089 | 0.945445 | − | 0.325780i | \(-0.105627\pi\) | ||||
0.945445 | + | 0.325780i | \(0.105627\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.16373 | −0.665135 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.34364 | 0.583979 | ||||||||
\(119\) | −2.17991 | −0.199832 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.72590 | −0.520536 | ||||||||
\(122\) | 9.93672 | 0.899628 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.0470959 | 0.00422934 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.68727 | −0.504664 | −0.252332 | − | 0.967641i | \(-0.581198\pi\) | ||||
−0.252332 | + | 0.967641i | \(0.581198\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.2108 | −1.06686 | −0.533432 | − | 0.845843i | \(-0.679098\pi\) | ||||
−0.533432 | + | 0.845843i | \(0.679098\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.47645 | −0.128025 | ||||||||
\(134\) | −14.8039 | −1.27886 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.47645 | 0.126605 | ||||||||
\(137\) | 8.23326 | 0.703415 | 0.351708 | − | 0.936110i | \(-0.385601\pi\) | ||||
0.351708 | + | 0.936110i | \(0.385601\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.2023 | −1.11981 | −0.559904 | − | 0.828557i | \(-0.689162\pi\) | ||||
−0.559904 | + | 0.828557i | \(0.689162\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.0695 | 1.18069 | ||||||||
\(143\) | 12.1637 | 1.01718 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.4603 | −1.19674 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.59308 | −0.541948 | ||||||||
\(149\) | −6.85871 | −0.561888 | −0.280944 | − | 0.959724i | \(-0.590647\pi\) | ||||
−0.280944 | + | 0.959724i | \(0.590647\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.6788 | 0.869029 | 0.434514 | − | 0.900665i | \(-0.356920\pi\) | ||||
0.434514 | + | 0.900665i | \(0.356920\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.39073 | −0.273233 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.22701 | −0.257543 | −0.128772 | − | 0.991674i | \(-0.541103\pi\) | ||||
−0.128772 | + | 0.991674i | \(0.541103\pi\) | |||||||
\(158\) | 12.5460 | 0.998105 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.75681 | 0.217267 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | 0.469956 | 0.234978 | − | 0.972001i | \(-0.424498\pi\) | ||||
0.234978 | + | 0.972001i | \(0.424498\pi\) | |||||||
\(164\) | −0.179911 | −0.0140487 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.11663 | 0.474743 | ||||||||
\(167\) | −20.9205 | −1.61888 | −0.809440 | − | 0.587203i | \(-0.800229\pi\) | ||||
−0.809440 | + | 0.587203i | \(0.800229\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.0534 | 1.15795 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.98382 | −0.608760 | ||||||||
\(173\) | −1.25792 | −0.0956378 | −0.0478189 | − | 0.998856i | \(-0.515227\pi\) | ||||
−0.0478189 | + | 0.998856i | \(0.515227\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.29654 | 0.173108 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.46027 | −0.484218 | ||||||||
\(179\) | 6.49889 | 0.485750 | 0.242875 | − | 0.970058i | \(-0.421910\pi\) | ||||
0.242875 | + | 0.970058i | \(0.421910\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.6240 | 1.45864 | 0.729320 | − | 0.684173i | \(-0.239837\pi\) | ||||
0.729320 | + | 0.684173i | \(0.239837\pi\) | |||||||
\(182\) | −7.82009 | −0.579664 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.86719 | −0.137651 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.39073 | −0.247955 | ||||||||
\(188\) | −12.4132 | −0.905324 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.406917 | −0.0294435 | −0.0147217 | − | 0.999892i | \(-0.504686\pi\) | ||||
−0.0147217 | + | 0.999892i | \(0.504686\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.3970 | −0.892355 | −0.446177 | − | 0.894945i | \(-0.647215\pi\) | ||||
−0.446177 | + | 0.894945i | \(0.647215\pi\) | |||||||
\(194\) | 4.42936 | 0.318009 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.82009 | −0.344292 | ||||||||
\(197\) | 2.24945 | 0.160266 | 0.0801332 | − | 0.996784i | \(-0.474465\pi\) | ||||
0.0801332 | + | 0.996784i | \(0.474465\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.4665 | 1.30906 | 0.654529 | − | 0.756037i | \(-0.272867\pi\) | ||||
0.654529 | + | 0.756037i | \(0.272867\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.2965 | 0.935541 | ||||||||
\(203\) | −10.5769 | −0.742353 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.227007 | −0.0158163 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.29654 | 0.367249 | ||||||||
\(209\) | −2.29654 | −0.158855 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.3584 | 1.67690 | 0.838450 | − | 0.544979i | \(-0.183462\pi\) | ||||
0.838450 | + | 0.544979i | \(0.183462\pi\) | |||||||
\(212\) | −11.9367 | −0.819817 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.20235 | −0.492342 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.0695349 | 0.00472033 | ||||||||
\(218\) | 7.04710 | 0.477290 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.82009 | −0.526036 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.1946 | 1.35233 | 0.676167 | − | 0.736749i | \(-0.263640\pi\) | ||||
0.676167 | + | 0.736749i | \(0.263640\pi\) | |||||||
\(224\) | −1.47645 | −0.0986496 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.1004 | −1.33706 | ||||||||
\(227\) | −6.35982 | −0.422116 | −0.211058 | − | 0.977474i | \(-0.567691\pi\) | ||||
−0.211058 | + | 0.977474i | \(0.567691\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.8510 | −0.783136 | −0.391568 | − | 0.920149i | \(-0.628067\pi\) | ||||
−0.391568 | + | 0.920149i | \(0.628067\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.16373 | 0.470322 | ||||||||
\(233\) | 27.6155 | 1.80915 | 0.904576 | − | 0.426311i | \(-0.140187\pi\) | ||||
0.904576 | + | 0.426311i | \(0.140187\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.34364 | −0.412936 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.17991 | 0.141303 | ||||||||
\(239\) | −28.2248 | −1.82571 | −0.912855 | − | 0.408284i | \(-0.866127\pi\) | ||||
−0.912855 | + | 0.408284i | \(0.866127\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.38226 | 0.475533 | 0.237767 | − | 0.971322i | \(-0.423585\pi\) | ||||
0.237767 | + | 0.971322i | \(0.423585\pi\) | |||||||
\(242\) | 5.72590 | 0.368075 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.93672 | −0.636133 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.29654 | −0.337011 | ||||||||
\(248\) | −0.0470959 | −0.00299059 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.6317 | −0.986665 | −0.493332 | − | 0.869841i | \(-0.664221\pi\) | ||||
−0.493332 | + | 0.869841i | \(0.664221\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.28807 | 0.269589 | ||||||||
\(254\) | 5.68727 | 0.356851 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.13281 | −0.507311 | −0.253656 | − | 0.967295i | \(-0.581633\pi\) | ||||
−0.253656 | + | 0.967295i | \(0.581633\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.73437 | −0.604864 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.2108 | 0.754387 | ||||||||
\(263\) | 10.2270 | 0.630624 | 0.315312 | − | 0.948988i | \(-0.397891\pi\) | ||||
0.315312 | + | 0.948988i | \(0.397891\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.47645 | 0.0905271 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.8039 | 0.904292 | ||||||||
\(269\) | 8.59308 | 0.523930 | 0.261965 | − | 0.965077i | \(-0.415630\pi\) | ||||
0.261965 | + | 0.965077i | \(0.415630\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.78918 | 0.533905 | 0.266952 | − | 0.963710i | \(-0.413983\pi\) | ||||
0.266952 | + | 0.963710i | \(0.413983\pi\) | |||||||
\(272\) | −1.47645 | −0.0895231 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.23326 | −0.497390 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.7954 | −1.48981 | −0.744907 | − | 0.667169i | \(-0.767506\pi\) | ||||
−0.744907 | + | 0.667169i | \(0.767506\pi\) | |||||||
\(278\) | 13.2023 | 0.791824 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.5931 | −1.40745 | −0.703723 | − | 0.710475i | \(-0.748480\pi\) | ||||
−0.703723 | + | 0.710475i | \(0.748480\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.5460 | 0.805225 | 0.402613 | − | 0.915370i | \(-0.368102\pi\) | ||||
0.402613 | + | 0.915370i | \(0.368102\pi\) | |||||||
\(284\) | −14.0695 | −0.834873 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.1637 | −0.719256 | ||||||||
\(287\) | −0.265629 | −0.0156796 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8201 | −0.871770 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.4603 | 0.846223 | ||||||||
\(293\) | 24.7954 | 1.44856 | 0.724282 | − | 0.689504i | \(-0.242171\pi\) | ||||
0.724282 | + | 0.689504i | \(0.242171\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.59308 | 0.383215 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.85871 | 0.397315 | ||||||||
\(299\) | 9.88962 | 0.571932 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.7877 | −0.679433 | ||||||||
\(302\) | −10.6788 | −0.614496 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.6626 | 0.665621 | 0.332810 | − | 0.942994i | \(-0.392003\pi\) | ||||
0.332810 | + | 0.942994i | \(0.392003\pi\) | |||||||
\(308\) | 3.39073 | 0.193205 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.72590 | 0.211276 | 0.105638 | − | 0.994405i | \(-0.466311\pi\) | ||||
0.105638 | + | 0.994405i | \(0.466311\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.00847 | −0.283096 | −0.141548 | − | 0.989931i | \(-0.545208\pi\) | ||||
−0.141548 | + | 0.989931i | \(0.545208\pi\) | |||||||
\(314\) | 3.22701 | 0.182111 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.5460 | −0.705767 | ||||||||
\(317\) | −27.1637 | −1.52567 | −0.762833 | − | 0.646595i | \(-0.776192\pi\) | ||||
−0.762833 | + | 0.646595i | \(0.776192\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.4518 | −0.921124 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.75681 | −0.153631 | ||||||||
\(323\) | 1.47645 | 0.0821520 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.00000 | −0.332309 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.179911 | 0.00993390 | ||||||||
\(329\) | −18.3275 | −1.01043 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.80391 | −0.154117 | −0.0770583 | − | 0.997027i | \(-0.524553\pi\) | ||||
−0.0770583 | + | 0.997027i | \(0.524553\pi\) | |||||||
\(332\) | −6.11663 | −0.335694 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.9205 | 1.14472 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.85871 | −0.373618 | −0.186809 | − | 0.982396i | \(-0.559815\pi\) | ||||
−0.186809 | + | 0.982396i | \(0.559815\pi\) | |||||||
\(338\) | −15.0534 | −0.818794 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.108158 | 0.00585707 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.4518 | −0.942308 | ||||||||
\(344\) | 7.98382 | 0.430459 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.25792 | 0.0676261 | ||||||||
\(347\) | 19.7792 | 1.06181 | 0.530903 | − | 0.847433i | \(-0.321853\pi\) | ||||
0.530903 | + | 0.847433i | \(0.321853\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.39699 | −0.395952 | −0.197976 | − | 0.980207i | \(-0.563437\pi\) | ||||
−0.197976 | + | 0.980207i | \(0.563437\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.29654 | −0.122406 | ||||||||
\(353\) | 36.0372 | 1.91806 | 0.959032 | − | 0.283296i | \(-0.0914280\pi\) | ||||
0.959032 | + | 0.283296i | \(0.0914280\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.46027 | 0.342394 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.49889 | −0.343477 | ||||||||
\(359\) | −24.4132 | −1.28848 | −0.644239 | − | 0.764824i | \(-0.722826\pi\) | ||||
−0.644239 | + | 0.764824i | \(0.722826\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −19.6240 | −1.03141 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.82009 | 0.409884 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0695 | −0.525625 | −0.262813 | − | 0.964847i | \(-0.584650\pi\) | ||||
−0.262813 | + | 0.964847i | \(0.584650\pi\) | |||||||
\(368\) | 1.86719 | 0.0973338 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.6240 | −0.914992 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.5769 | 1.27254 | 0.636272 | − | 0.771465i | \(-0.280476\pi\) | ||||
0.636272 | + | 0.771465i | \(0.280476\pi\) | |||||||
\(374\) | 3.39073 | 0.175331 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.4132 | 0.640160 | ||||||||
\(377\) | −37.9430 | −1.95416 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.50111 | −0.179840 | −0.0899199 | − | 0.995949i | \(-0.528661\pi\) | ||||
−0.0899199 | + | 0.995949i | \(0.528661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.406917 | 0.0208197 | ||||||||
\(383\) | −18.9901 | −0.970347 | −0.485174 | − | 0.874418i | \(-0.661244\pi\) | ||||
−0.485174 | + | 0.874418i | \(0.661244\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.3970 | 0.630990 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.42936 | −0.224866 | ||||||||
\(389\) | −14.2333 | −0.721655 | −0.360828 | − | 0.932633i | \(-0.617506\pi\) | ||||
−0.360828 | + | 0.932633i | \(0.617506\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.75681 | −0.139418 | ||||||||
\(392\) | 4.82009 | 0.243451 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.24945 | −0.113325 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.3885 | −1.47497 | −0.737484 | − | 0.675365i | \(-0.763986\pi\) | ||||
−0.737484 | + | 0.675365i | \(0.763986\pi\) | |||||||
\(398\) | −18.4665 | −0.925643 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.5460 | 0.726392 | 0.363196 | − | 0.931713i | \(-0.381686\pi\) | ||||
0.363196 | + | 0.931713i | \(0.381686\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.249445 | 0.0124258 | ||||||||
\(404\) | −13.2965 | −0.661528 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.5769 | 0.524923 | ||||||||
\(407\) | −15.1413 | −0.750526 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.5931 | 0.919369 | 0.459684 | − | 0.888082i | \(-0.347963\pi\) | ||||
0.459684 | + | 0.888082i | \(0.347963\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.227007 | 0.0111838 | ||||||||
\(413\) | −9.36608 | −0.460874 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.29654 | −0.259684 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.29654 | 0.112328 | ||||||||
\(419\) | 10.2333 | 0.499928 | 0.249964 | − | 0.968255i | \(-0.419581\pi\) | ||||
0.249964 | + | 0.968255i | \(0.419581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.82856 | 0.479015 | 0.239507 | − | 0.970895i | \(-0.423014\pi\) | ||||
0.239507 | + | 0.970895i | \(0.423014\pi\) | |||||||
\(422\) | −24.3584 | −1.18575 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.9367 | 0.579698 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.6711 | −0.709984 | ||||||||
\(428\) | 7.20235 | 0.348139 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.0449 | −1.73622 | −0.868110 | − | 0.496371i | \(-0.834665\pi\) | ||||
−0.868110 | + | 0.496371i | \(0.834665\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.2881 | −0.926925 | −0.463463 | − | 0.886116i | \(-0.653393\pi\) | ||||
−0.463463 | + | 0.886116i | \(0.653393\pi\) | |||||||
\(434\) | −0.0695349 | −0.00333778 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.04710 | −0.337495 | ||||||||
\(437\) | −1.86719 | −0.0893196 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.4194 | 1.16548 | 0.582738 | − | 0.812660i | \(-0.301981\pi\) | ||||
0.582738 | + | 0.812660i | \(0.301981\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.82009 | 0.371964 | ||||||||
\(443\) | 13.8834 | 0.659619 | 0.329809 | − | 0.944048i | \(-0.393016\pi\) | ||||
0.329809 | + | 0.944048i | \(0.393016\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −20.1946 | −0.956244 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.47645 | 0.0697558 | ||||||||
\(449\) | −13.6016 | −0.641897 | −0.320949 | − | 0.947097i | \(-0.604002\pi\) | ||||
−0.320949 | + | 0.947097i | \(0.604002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.413172 | −0.0194555 | ||||||||
\(452\) | 20.1004 | 0.945445 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.35982 | 0.298481 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.5051 | 1.19308 | 0.596540 | − | 0.802583i | \(-0.296542\pi\) | ||||
0.596540 | + | 0.802583i | \(0.296542\pi\) | |||||||
\(458\) | 11.8510 | 0.553761 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.3598 | −0.761953 | −0.380976 | − | 0.924585i | \(-0.624412\pi\) | ||||
−0.380976 | + | 0.924585i | \(0.624412\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.7815 | 0.686953 | 0.343477 | − | 0.939161i | \(-0.388395\pi\) | ||||
0.343477 | + | 0.939161i | \(0.388395\pi\) | |||||||
\(464\) | −7.16373 | −0.332568 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.6155 | −1.27926 | ||||||||
\(467\) | 13.4055 | 0.620331 | 0.310165 | − | 0.950683i | \(-0.399616\pi\) | ||||
0.310165 | + | 0.950683i | \(0.399616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.8573 | 1.00927 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.34364 | 0.291990 | ||||||||
\(473\) | −18.3352 | −0.843052 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.17991 | −0.0999160 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 28.2248 | 1.29097 | ||||||||
\(479\) | 37.0534 | 1.69301 | 0.846505 | − | 0.532380i | \(-0.178702\pi\) | ||||
0.846505 | + | 0.532380i | \(0.178702\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.9205 | −1.59224 | ||||||||
\(482\) | −7.38226 | −0.336253 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.72590 | −0.260268 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.0471 | 0.591220 | 0.295610 | − | 0.955309i | \(-0.404477\pi\) | ||||
0.295610 | + | 0.955309i | \(0.404477\pi\) | |||||||
\(488\) | 9.93672 | 0.449814 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.7322 | 1.38692 | 0.693461 | − | 0.720494i | \(-0.256085\pi\) | ||||
0.693461 | + | 0.720494i | \(0.256085\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.5769 | 0.476360 | ||||||||
\(494\) | 5.29654 | 0.238303 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.0470959 | 0.00211467 | ||||||||
\(497\) | −20.7730 | −0.931796 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.3414 | −0.776309 | −0.388154 | − | 0.921594i | \(-0.626887\pi\) | ||||
−0.388154 | + | 0.921594i | \(0.626887\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.6317 | 0.697677 | ||||||||
\(503\) | 16.0000 | 0.713405 | 0.356702 | − | 0.934218i | \(-0.383901\pi\) | ||||
0.356702 | + | 0.934218i | \(0.383901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.28807 | −0.190628 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.68727 | −0.252332 | ||||||||
\(509\) | 25.3885 | 1.12533 | 0.562663 | − | 0.826686i | \(-0.309777\pi\) | ||||
0.562663 | + | 0.826686i | \(0.309777\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.3499 | 0.944464 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.13281 | 0.358723 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.5074 | −1.25375 | ||||||||
\(518\) | 9.73437 | 0.427704 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.7645 | −0.603035 | −0.301517 | − | 0.953461i | \(-0.597493\pi\) | ||||
−0.301517 | + | 0.953461i | \(0.597493\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.5931 | −0.813019 | −0.406509 | − | 0.913647i | \(-0.633254\pi\) | ||||
−0.406509 | + | 0.913647i | \(0.633254\pi\) | |||||||
\(524\) | −12.2108 | −0.533432 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.2270 | −0.445919 | ||||||||
\(527\) | −0.0695349 | −0.00302899 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.5136 | −0.848418 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.47645 | −0.0640123 | ||||||||
\(533\) | −0.952904 | −0.0412749 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.8039 | −0.639431 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.59308 | −0.370474 | ||||||||
\(539\) | −11.0695 | −0.476799 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.2557 | 1.47277 | 0.736384 | − | 0.676564i | \(-0.236532\pi\) | ||||
0.736384 | + | 0.676564i | \(0.236532\pi\) | |||||||
\(542\) | −8.78918 | −0.377527 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.47645 | 0.0633024 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.93672 | 0.339350 | 0.169675 | − | 0.985500i | \(-0.445728\pi\) | ||||
0.169675 | + | 0.985500i | \(0.445728\pi\) | |||||||
\(548\) | 8.23326 | 0.351708 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.16373 | 0.305185 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.5235 | −0.787701 | ||||||||
\(554\) | 24.7954 | 1.05346 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.2023 | −0.559904 | ||||||||
\(557\) | 1.46798 | 0.0622003 | 0.0311001 | − | 0.999516i | \(-0.490099\pi\) | ||||
0.0311001 | + | 0.999516i | \(0.490099\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.2866 | −1.78853 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.5931 | 0.995214 | ||||||||
\(563\) | 32.7160 | 1.37881 | 0.689407 | − | 0.724374i | \(-0.257871\pi\) | ||||
0.689407 | + | 0.724374i | \(0.257871\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.5460 | −0.569380 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.0695 | 0.590345 | ||||||||
\(569\) | 22.6873 | 0.951100 | 0.475550 | − | 0.879689i | \(-0.342249\pi\) | ||||
0.475550 | + | 0.879689i | \(0.342249\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.34364 | 0.349170 | 0.174585 | − | 0.984642i | \(-0.444142\pi\) | ||||
0.174585 | + | 0.984642i | \(0.444142\pi\) | |||||||
\(572\) | 12.1637 | 0.508591 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.265629 | 0.0110872 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.451795 | 0.0188085 | 0.00940424 | − | 0.999956i | \(-0.497006\pi\) | ||||
0.00940424 | + | 0.999956i | \(0.497006\pi\) | |||||||
\(578\) | 14.8201 | 0.616434 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.03091 | −0.374665 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.4132 | −1.13534 | ||||||||
\(584\) | −14.4603 | −0.598370 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.7954 | −1.02429 | ||||||||
\(587\) | −32.8812 | −1.35715 | −0.678575 | − | 0.734531i | \(-0.737402\pi\) | ||||
−0.678575 | + | 0.734531i | \(0.737402\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0470959 | −0.00194055 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.59308 | −0.270974 | ||||||||
\(593\) | −36.8882 | −1.51482 | −0.757408 | − | 0.652942i | \(-0.773534\pi\) | ||||
−0.757408 | + | 0.652942i | \(0.773534\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.85871 | −0.280944 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.88962 | −0.404417 | ||||||||
\(599\) | 43.7715 | 1.78846 | 0.894228 | − | 0.447611i | \(-0.147725\pi\) | ||||
0.894228 | + | 0.447611i | \(0.147725\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.9430 | 0.650328 | 0.325164 | − | 0.945658i | \(-0.394581\pi\) | ||||
0.325164 | + | 0.945658i | \(0.394581\pi\) | |||||||
\(602\) | 11.7877 | 0.480432 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.6788 | 0.434514 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.9444 | 0.809519 | 0.404760 | − | 0.914423i | \(-0.367355\pi\) | ||||
0.404760 | + | 0.914423i | \(0.367355\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −65.7469 | −2.65983 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.9205 | −1.49121 | −0.745603 | − | 0.666390i | \(-0.767839\pi\) | ||||
−0.745603 | + | 0.666390i | \(0.767839\pi\) | |||||||
\(614\) | −11.6626 | −0.470665 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.39073 | −0.136617 | ||||||||
\(617\) | 23.1538 | 0.932137 | 0.466068 | − | 0.884749i | \(-0.345670\pi\) | ||||
0.466068 | + | 0.884749i | \(0.345670\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.84475 | −0.234920 | −0.117460 | − | 0.993078i | \(-0.537475\pi\) | ||||
−0.117460 | + | 0.993078i | \(0.537475\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.72590 | −0.149395 | ||||||||
\(623\) | 9.53828 | 0.382143 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.00847 | 0.200179 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.22701 | −0.128772 | ||||||||
\(629\) | 9.73437 | 0.388135 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.5607 | 1.77393 | 0.886967 | − | 0.461833i | \(-0.152808\pi\) | ||||
0.886967 | + | 0.461833i | \(0.152808\pi\) | |||||||
\(632\) | 12.5460 | 0.499053 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 27.1637 | 1.07881 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.5298 | −1.01153 | ||||||||
\(638\) | 16.4518 | 0.651333 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.50736 | 0.178030 | 0.0890151 | − | 0.996030i | \(-0.471628\pi\) | ||||
0.0890151 | + | 0.996030i | \(0.471628\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.0596 | −0.751637 | −0.375819 | − | 0.926693i | \(-0.622638\pi\) | ||||
−0.375819 | + | 0.926693i | \(0.622638\pi\) | |||||||
\(644\) | 2.75681 | 0.108634 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.47645 | −0.0580902 | ||||||||
\(647\) | 21.0857 | 0.828965 | 0.414483 | − | 0.910057i | \(-0.363963\pi\) | ||||
0.414483 | + | 0.910057i | \(0.363963\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.5684 | −0.571861 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.00000 | 0.234978 | ||||||||
\(653\) | 11.3745 | 0.445121 | 0.222560 | − | 0.974919i | \(-0.428559\pi\) | ||||
0.222560 | + | 0.974919i | \(0.428559\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.179911 | −0.00702433 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.3275 | 0.714479 | ||||||||
\(659\) | −1.48493 | −0.0578445 | −0.0289222 | − | 0.999582i | \(-0.509208\pi\) | ||||
−0.0289222 | + | 0.999582i | \(0.509208\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.4216 | −0.794310 | −0.397155 | − | 0.917752i | \(-0.630002\pi\) | ||||
−0.397155 | + | 0.917752i | \(0.630002\pi\) | |||||||
\(662\) | 2.80391 | 0.108977 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.11663 | 0.237371 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.3760 | −0.517921 | ||||||||
\(668\) | −20.9205 | −0.809440 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.8201 | −0.880960 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.0224 | −0.887450 | −0.443725 | − | 0.896163i | \(-0.646343\pi\) | ||||
−0.443725 | + | 0.896163i | \(0.646343\pi\) | |||||||
\(674\) | 6.85871 | 0.264188 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.0534 | 0.578975 | ||||||||
\(677\) | 25.9198 | 0.996178 | 0.498089 | − | 0.867126i | \(-0.334035\pi\) | ||||
0.498089 | + | 0.867126i | \(0.334035\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.53973 | −0.250972 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.108158 | −0.00414157 | ||||||||
\(683\) | 3.56217 | 0.136303 | 0.0681513 | − | 0.997675i | \(-0.478290\pi\) | ||||
0.0681513 | + | 0.997675i | \(0.478290\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.4518 | 0.666313 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.98382 | −0.304380 | ||||||||
\(689\) | −63.2233 | −2.40862 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −50.6218 | −1.92574 | −0.962872 | − | 0.269960i | \(-0.912990\pi\) | ||||
−0.962872 | + | 0.269960i | \(0.912990\pi\) | |||||||
\(692\) | −1.25792 | −0.0478189 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.7792 | −0.750810 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.265629 | 0.0100614 | ||||||||
\(698\) | 7.39699 | 0.279980 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.82634 | 0.257827 | 0.128914 | − | 0.991656i | \(-0.458851\pi\) | ||||
0.128914 | + | 0.991656i | \(0.458851\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.59308 | 0.248663 | ||||||||
\(704\) | 2.29654 | 0.0865542 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −36.0372 | −1.35628 | ||||||||
\(707\) | −19.6317 | −0.738326 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.3499 | 1.44026 | 0.720130 | − | 0.693839i | \(-0.244082\pi\) | ||||
0.720130 | + | 0.693839i | \(0.244082\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.46027 | −0.242109 | ||||||||
\(713\) | 0.0879368 | 0.00329326 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.49889 | 0.242875 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.4132 | 0.911091 | ||||||||
\(719\) | −28.7020 | −1.07040 | −0.535202 | − | 0.844724i | \(-0.679765\pi\) | ||||
−0.535202 | + | 0.844724i | \(0.679765\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.335164 | 0.0124822 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19.6240 | 0.729320 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.51362 | 0.0561370 | 0.0280685 | − | 0.999606i | \(-0.491064\pi\) | ||||
0.0280685 | + | 0.999606i | \(0.491064\pi\) | |||||||
\(728\) | −7.82009 | −0.289832 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.7877 | 0.435985 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.8488 | 0.696196 | 0.348098 | − | 0.937458i | \(-0.386828\pi\) | ||||
0.348098 | + | 0.937458i | \(0.386828\pi\) | |||||||
\(734\) | 10.0695 | 0.371673 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.86719 | −0.0688254 | ||||||||
\(737\) | 33.9978 | 1.25232 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.4989 | −1.04835 | −0.524174 | − | 0.851611i | \(-0.675626\pi\) | ||||
−0.524174 | + | 0.851611i | \(0.675626\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17.6240 | 0.646997 | ||||||||
\(743\) | 11.1089 | 0.407547 | 0.203773 | − | 0.979018i | \(-0.434679\pi\) | ||||
0.203773 | + | 0.979018i | \(0.434679\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −24.5769 | −0.899824 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.39073 | −0.123977 | ||||||||
\(749\) | 10.6339 | 0.388555 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.6487 | −0.789971 | −0.394985 | − | 0.918687i | \(-0.629250\pi\) | ||||
−0.394985 | + | 0.918687i | \(0.629250\pi\) | |||||||
\(752\) | −12.4132 | −0.452662 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 37.9430 | 1.38180 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.99007 | 0.217713 | 0.108856 | − | 0.994057i | \(-0.465281\pi\) | ||||
0.108856 | + | 0.994057i | \(0.465281\pi\) | |||||||
\(758\) | 3.50111 | 0.127166 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.1615 | −0.694604 | −0.347302 | − | 0.937753i | \(-0.612902\pi\) | ||||
−0.347302 | + | 0.937753i | \(0.612902\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.4047 | −0.376675 | ||||||||
\(764\) | −0.406917 | −0.0147217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.9901 | 0.686139 | ||||||||
\(767\) | −33.5993 | −1.21320 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.9761 | −0.684296 | −0.342148 | − | 0.939646i | \(-0.611154\pi\) | ||||
−0.342148 | + | 0.939646i | \(0.611154\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.3970 | −0.446177 | ||||||||
\(773\) | −36.5438 | −1.31439 | −0.657194 | − | 0.753721i | \(-0.728257\pi\) | ||||
−0.657194 | + | 0.753721i | \(0.728257\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.42936 | 0.159005 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.2333 | 0.510287 | ||||||||
\(779\) | 0.179911 | 0.00644597 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.3113 | −1.15619 | ||||||||
\(782\) | 2.75681 | 0.0985833 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.82009 | −0.172146 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.5213 | −1.15926 | −0.579630 | − | 0.814880i | \(-0.696803\pi\) | ||||
−0.579630 | + | 0.814880i | \(0.696803\pi\) | |||||||
\(788\) | 2.24945 | 0.0801332 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.6773 | 1.05520 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −52.6302 | −1.86895 | ||||||||
\(794\) | 29.3885 | 1.04296 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.4665 | 0.654529 | ||||||||
\(797\) | −41.4110 | −1.46685 | −0.733426 | − | 0.679770i | \(-0.762080\pi\) | ||||
−0.733426 | + | 0.679770i | \(0.762080\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.3275 | 0.648379 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.5460 | −0.513637 | ||||||||
\(803\) | 33.2086 | 1.17191 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.249445 | −0.00878634 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.2965 | 0.467771 | ||||||||
\(809\) | 8.72444 | 0.306735 | 0.153368 | − | 0.988169i | \(-0.450988\pi\) | ||||
0.153368 | + | 0.988169i | \(0.450988\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.8425 | −0.415847 | −0.207924 | − | 0.978145i | \(-0.566671\pi\) | ||||
−0.207924 | + | 0.978145i | \(0.566671\pi\) | |||||||
\(812\) | −10.5769 | −0.371176 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15.1413 | 0.530702 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.98382 | 0.279318 | ||||||||
\(818\) | −18.5931 | −0.650092 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.03091 | −0.175580 | −0.0877900 | − | 0.996139i | \(-0.527980\pi\) | ||||
−0.0877900 | + | 0.996139i | \(0.527980\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.81162 | 0.272296 | 0.136148 | − | 0.990689i | \(-0.456528\pi\) | ||||
0.136148 | + | 0.990689i | \(0.456528\pi\) | |||||||
\(824\) | −0.227007 | −0.00790815 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.36608 | 0.325887 | ||||||||
\(827\) | 2.78070 | 0.0966946 | 0.0483473 | − | 0.998831i | \(-0.484605\pi\) | ||||
0.0483473 | + | 0.998831i | \(0.484605\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.9963 | 1.66698 | 0.833491 | − | 0.552534i | \(-0.186339\pi\) | ||||
0.833491 | + | 0.552534i | \(0.186339\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.29654 | 0.183625 | ||||||||
\(833\) | 7.11663 | 0.246577 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.29654 | −0.0794275 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.2333 | −0.353502 | ||||||||
\(839\) | 0.290286 | 0.0100218 | 0.00501090 | − | 0.999987i | \(-0.498405\pi\) | ||||
0.00501090 | + | 0.999987i | \(0.498405\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.3190 | 0.769620 | ||||||||
\(842\) | −9.82856 | −0.338715 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24.3584 | 0.838450 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.45401 | −0.290483 | ||||||||
\(848\) | −11.9367 | −0.409909 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.3105 | −0.421999 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.6725 | −0.468139 | −0.234070 | − | 0.972220i | \(-0.575204\pi\) | ||||
−0.234070 | + | 0.972220i | \(0.575204\pi\) | |||||||
\(854\) | 14.6711 | 0.502034 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.20235 | −0.246171 | ||||||||
\(857\) | −48.9569 | −1.67234 | −0.836169 | − | 0.548472i | \(-0.815210\pi\) | ||||
−0.836169 | + | 0.548472i | \(0.815210\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.985272 | −0.0336170 | −0.0168085 | − | 0.999859i | \(-0.505351\pi\) | ||||
−0.0168085 | + | 0.999859i | \(0.505351\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 36.0449 | 1.22769 | ||||||||
\(863\) | 9.31273 | 0.317009 | 0.158504 | − | 0.987358i | \(-0.449333\pi\) | ||||
0.158504 | + | 0.987358i | \(0.449333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19.2881 | 0.655435 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.0695349 | 0.00236017 | ||||||||
\(869\) | −28.8124 | −0.977393 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 78.4095 | 2.65680 | ||||||||
\(872\) | 7.04710 | 0.238645 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.86719 | 0.0631585 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.7469 | 1.07202 | 0.536008 | − | 0.844213i | \(-0.319932\pi\) | ||||
0.536008 | + | 0.844213i | \(0.319932\pi\) | |||||||
\(878\) | −24.4194 | −0.824116 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.78147 | −0.295855 | −0.147928 | − | 0.988998i | \(-0.547260\pi\) | ||||
−0.147928 | + | 0.988998i | \(0.547260\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.9044 | 0.568877 | 0.284438 | − | 0.958694i | \(-0.408193\pi\) | ||||
0.284438 | + | 0.958694i | \(0.408193\pi\) | |||||||
\(884\) | −7.82009 | −0.263018 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.8834 | −0.466421 | ||||||||
\(887\) | −17.6851 | −0.593806 | −0.296903 | − | 0.954908i | \(-0.595954\pi\) | ||||
−0.296903 | + | 0.954908i | \(0.595954\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.39699 | −0.281626 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.1946 | 0.676167 | ||||||||
\(893\) | 12.4132 | 0.415391 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.47645 | −0.0493248 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.6016 | 0.453890 | ||||||||
\(899\) | −0.337382 | −0.0112523 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.6240 | 0.587140 | ||||||||
\(902\) | 0.413172 | 0.0137571 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.1004 | −0.668531 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.0210 | −1.52810 | −0.764051 | − | 0.645156i | \(-0.776792\pi\) | ||||
−0.764051 | + | 0.645156i | \(0.776792\pi\) | |||||||
\(908\) | −6.35982 | −0.211058 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.1560 | −0.336484 | −0.168242 | − | 0.985746i | \(-0.553809\pi\) | ||||
−0.168242 | + | 0.985746i | \(0.553809\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.0471 | −0.464891 | ||||||||
\(914\) | −25.5051 | −0.843635 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.8510 | −0.391568 | ||||||||
\(917\) | −18.0287 | −0.595360 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.0820 | −1.32218 | −0.661092 | − | 0.750305i | \(-0.729907\pi\) | ||||
−0.661092 | + | 0.750305i | \(0.729907\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16.3598 | 0.538782 | ||||||||
\(923\) | −74.5199 | −2.45285 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14.7815 | −0.485749 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.16373 | 0.235161 | ||||||||
\(929\) | −29.2634 | −0.960101 | −0.480051 | − | 0.877241i | \(-0.659382\pi\) | ||||
−0.480051 | + | 0.877241i | \(0.659382\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.82009 | 0.157972 | ||||||||
\(932\) | 27.6155 | 0.904576 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.4055 | −0.438640 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.4989 | −0.865681 | −0.432841 | − | 0.901471i | \(-0.642489\pi\) | ||||
−0.432841 | + | 0.901471i | \(0.642489\pi\) | |||||||
\(938\) | −21.8573 | −0.713665 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.8749 | 0.647903 | 0.323952 | − | 0.946074i | \(-0.394989\pi\) | ||||
0.323952 | + | 0.946074i | \(0.394989\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.335926 | −0.0109393 | ||||||||
\(944\) | −6.34364 | −0.206468 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.3352 | 0.596128 | ||||||||
\(947\) | 31.0766 | 1.00985 | 0.504926 | − | 0.863163i | \(-0.331520\pi\) | ||||
0.504926 | + | 0.863163i | \(0.331520\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 76.5894 | 2.48620 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.17991 | 0.0706513 | ||||||||
\(953\) | 17.3275 | 0.561291 | 0.280646 | − | 0.959811i | \(-0.409451\pi\) | ||||
0.280646 | + | 0.959811i | \(0.409451\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −28.2248 | −0.912855 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37.0534 | −1.19714 | ||||||||
\(959\) | 12.1560 | 0.392538 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9978 | −0.999928 | ||||||||
\(962\) | 34.9205 | 1.12588 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.38226 | 0.237767 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.4989 | 0.401937 | 0.200969 | − | 0.979598i | \(-0.435591\pi\) | ||||
0.200969 | + | 0.979598i | \(0.435591\pi\) | |||||||
\(968\) | 5.72590 | 0.184037 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.3113 | 1.61457 | 0.807283 | − | 0.590165i | \(-0.200937\pi\) | ||||
0.807283 | + | 0.590165i | \(0.200937\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.4926 | −0.624905 | ||||||||
\(974\) | −13.0471 | −0.418056 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.93672 | −0.318067 | ||||||||
\(977\) | 30.9121 | 0.988965 | 0.494482 | − | 0.869188i | \(-0.335358\pi\) | ||||
0.494482 | + | 0.869188i | \(0.335358\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.8363 | 0.474169 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30.7322 | −0.980702 | ||||||||
\(983\) | −40.9128 | −1.30492 | −0.652458 | − | 0.757825i | \(-0.726262\pi\) | ||||
−0.652458 | + | 0.757825i | \(0.726262\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.5769 | −0.336837 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.29654 | −0.168505 | ||||||||
\(989\) | −14.9073 | −0.474023 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.25937 | 0.135303 | 0.0676517 | − | 0.997709i | \(-0.478449\pi\) | ||||
0.0676517 | + | 0.997709i | \(0.478449\pi\) | |||||||
\(992\) | −0.0470959 | −0.00149530 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 20.7730 | 0.658879 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.6070 | −1.60274 | −0.801371 | − | 0.598168i | \(-0.795896\pi\) | ||||
−0.801371 | + | 0.598168i | \(0.795896\pi\) | |||||||
\(998\) | 17.3414 | 0.548933 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8550.2.a.ch.1.2 | yes | 3 | |
3.2 | odd | 2 | 8550.2.a.ct.1.2 | yes | 3 | ||
5.4 | even | 2 | 8550.2.a.cm.1.2 | yes | 3 | ||
15.14 | odd | 2 | 8550.2.a.cc.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8550.2.a.cc.1.2 | ✓ | 3 | 15.14 | odd | 2 | ||
8550.2.a.ch.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
8550.2.a.cm.1.2 | yes | 3 | 5.4 | even | 2 | ||
8550.2.a.ct.1.2 | yes | 3 | 3.2 | odd | 2 |