Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 16x^{8} + 26x^{7} + 93x^{6} - 113x^{5} - 230x^{4} + 197x^{3} + 201x^{2} - 115x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.54918\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.54918 | 0.894422 | 0.447211 | − | 0.894429i | \(-0.352417\pi\) | ||||
0.447211 | + | 0.894429i | \(0.352417\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.356949 | −0.159633 | −0.0798163 | − | 0.996810i | \(-0.525433\pi\) | ||||
−0.0798163 | + | 0.996810i | \(0.525433\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.600028 | −0.200009 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.552981 | −0.142779 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.04878 | −1.46704 | −0.733522 | − | 0.679665i | \(-0.762125\pi\) | ||||
−0.733522 | + | 0.679665i | \(0.762125\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.48928 | 1.94757 | 0.973787 | − | 0.227462i | \(-0.0730427\pi\) | ||||
0.973787 | + | 0.227462i | \(0.0730427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.54918 | −0.338060 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.98257 | 1.66448 | 0.832241 | − | 0.554414i | \(-0.187058\pi\) | ||||
0.832241 | + | 0.554414i | \(0.187058\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.87259 | −0.974517 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.57711 | −1.07331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.31591 | 0.987140 | 0.493570 | − | 0.869706i | \(-0.335692\pi\) | ||||
0.493570 | + | 0.869706i | \(0.335692\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.77065 | −1.75486 | −0.877430 | − | 0.479705i | \(-0.840744\pi\) | ||||
−0.877430 | + | 0.479705i | \(0.840744\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.54918 | −0.269678 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.356949 | 0.0603355 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5368 | 1.73225 | 0.866123 | − | 0.499832i | \(-0.166605\pi\) | ||||
0.866123 | + | 0.499832i | \(0.166605\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.54918 | −0.248068 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.72233 | 1.36220 | 0.681099 | − | 0.732191i | \(-0.261502\pi\) | ||||
0.681099 | + | 0.732191i | \(0.261502\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.46133 | −1.13784 | −0.568921 | − | 0.822392i | \(-0.692639\pi\) | ||||
−0.568921 | + | 0.822392i | \(0.692639\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.214180 | 0.0319280 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.45382 | 0.212062 | 0.106031 | − | 0.994363i | \(-0.466186\pi\) | ||||
0.106031 | + | 0.994363i | \(0.466186\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.37067 | −1.31216 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.71369 | −0.235393 | −0.117696 | − | 0.993050i | \(-0.537551\pi\) | ||||
−0.117696 | + | 0.993050i | \(0.537551\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.356949 | 0.0481311 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.1515 | 1.74195 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.781383 | −0.101727 | −0.0508637 | − | 0.998706i | \(-0.516197\pi\) | ||||
−0.0508637 | + | 0.998706i | \(0.516197\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.31139 | −0.680053 | −0.340027 | − | 0.940416i | \(-0.610436\pi\) | ||||
−0.340027 | + | 0.940416i | \(0.610436\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.600028 | 0.0755964 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.356949 | 0.0442741 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.19727 | −0.757117 | −0.378559 | − | 0.925577i | \(-0.623580\pi\) | ||||
−0.378559 | + | 0.925577i | \(0.623580\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.3665 | 1.48875 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.65289 | −0.908231 | −0.454115 | − | 0.890943i | \(-0.650045\pi\) | ||||
−0.454115 | + | 0.890943i | \(0.650045\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.44764 | −0.286475 | −0.143237 | − | 0.989688i | \(-0.545751\pi\) | ||||
−0.143237 | + | 0.989688i | \(0.545751\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.54854 | −0.871630 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.8586 | −1.33420 | −0.667100 | − | 0.744968i | \(-0.732465\pi\) | ||||
−0.667100 | + | 0.744968i | \(0.732465\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.83988 | −0.759987 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.43355 | −0.596409 | −0.298205 | − | 0.954502i | \(-0.596388\pi\) | ||||
−0.298205 | + | 0.954502i | \(0.596388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.15911 | 0.234188 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.23533 | 0.882920 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.25740 | 0.981282 | 0.490641 | − | 0.871362i | \(-0.336763\pi\) | ||||
0.490641 | + | 0.871362i | \(0.336763\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −15.1365 | −1.56958 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.03024 | −0.310896 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.82384 | 0.388252 | 0.194126 | − | 0.980977i | \(-0.437813\pi\) | ||||
0.194126 | + | 0.980977i | \(0.437813\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.600028 | 0.0603051 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.64381 | −0.661084 | −0.330542 | − | 0.943791i | \(-0.607232\pi\) | ||||
−0.330542 | + | 0.943791i | \(0.607232\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.22802 | −0.909263 | −0.454632 | − | 0.890680i | \(-0.650229\pi\) | ||||
−0.454632 | + | 0.890680i | \(0.650229\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.552981 | 0.0539654 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.0799 | −1.07114 | −0.535569 | − | 0.844492i | \(-0.679903\pi\) | ||||
−0.535569 | + | 0.844492i | \(0.679903\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.6595 | −1.69147 | −0.845736 | − | 0.533602i | \(-0.820838\pi\) | ||||
−0.845736 | + | 0.533602i | \(0.820838\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.3235 | 1.54936 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.20701 | −0.207618 | −0.103809 | − | 0.994597i | \(-0.533103\pi\) | ||||
−0.103809 | + | 0.994597i | \(0.533103\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.84938 | −0.265706 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.600028 | 0.0554726 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.04878 | 0.554491 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.5125 | 1.21838 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.52401 | 0.315197 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.04203 | 0.536144 | 0.268072 | − | 0.963399i | \(-0.413614\pi\) | ||||
0.268072 | + | 0.963399i | \(0.413614\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.5590 | −1.01771 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.7877 | −1.90360 | −0.951799 | − | 0.306724i | \(-0.900767\pi\) | ||||
−0.951799 | + | 0.306724i | \(0.900767\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.48928 | −0.736114 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.99075 | 0.171336 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.9167 | −1.61616 | −0.808081 | − | 0.589071i | \(-0.799494\pi\) | ||||
−0.808081 | + | 0.589071i | \(0.799494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.9664 | 1.94798 | 0.973991 | − | 0.226588i | \(-0.0727572\pi\) | ||||
0.973991 | + | 0.226588i | \(0.0727572\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.25224 | 0.189673 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.89751 | −0.157580 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.54918 | 0.127775 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.37265 | −0.767837 | −0.383919 | − | 0.923367i | \(-0.625426\pi\) | ||||
−0.383919 | + | 0.923367i | \(0.625426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.64898 | 0.134192 | 0.0670961 | − | 0.997747i | \(-0.478627\pi\) | ||||
0.0670961 | + | 0.997747i | \(0.478627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.62944 | 0.293423 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.48763 | 0.280133 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.7041 | −1.17352 | −0.586759 | − | 0.809761i | \(-0.699597\pi\) | ||||
−0.586759 | + | 0.809761i | \(0.699597\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.65482 | −0.210541 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.98257 | −0.629115 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.5583 | −1.14029 | −0.570147 | − | 0.821543i | \(-0.693114\pi\) | ||||
−0.570147 | + | 0.821543i | \(0.693114\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.552981 | 0.0430495 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.80194 | −0.139438 | −0.0697192 | − | 0.997567i | \(-0.522210\pi\) | ||||
−0.0697192 | + | 0.997567i | \(0.522210\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.09381 | −0.389533 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.4645 | 1.02369 | 0.511845 | − | 0.859078i | \(-0.328962\pi\) | ||||
0.511845 | + | 0.859078i | \(0.328962\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.87259 | 0.368333 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.21051 | −0.0909872 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.43106 | 0.630167 | 0.315083 | − | 0.949064i | \(-0.397968\pi\) | ||||
0.315083 | + | 0.949064i | \(0.397968\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.4436 | −1.66822 | −0.834109 | − | 0.551599i | \(-0.814018\pi\) | ||||
−0.834109 | + | 0.551599i | \(0.814018\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.22832 | −0.608255 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.76112 | −0.276523 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.04878 | 0.442331 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.57711 | 0.405675 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.38303 | −0.606574 | −0.303287 | − | 0.952899i | \(-0.598084\pi\) | ||||
−0.303287 | + | 0.952899i | \(0.598084\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.19008 | −0.589535 | −0.294767 | − | 0.955569i | \(-0.595242\pi\) | ||||
−0.294767 | + | 0.955569i | \(0.595242\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.552981 | 0.0395998 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.1023 | −0.862252 | −0.431126 | − | 0.902292i | \(-0.641884\pi\) | ||||
−0.431126 | + | 0.902292i | \(0.641884\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.8646 | 1.76261 | 0.881303 | − | 0.472551i | \(-0.156667\pi\) | ||||
0.881303 | + | 0.472551i | \(0.156667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.60072 | −0.677182 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.31591 | −0.373104 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.11343 | −0.217451 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.78977 | −0.332912 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.48928 | −0.587216 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.7697 | −1.77406 | −0.887030 | − | 0.461713i | \(-0.847235\pi\) | ||||
−0.887030 | + | 0.461713i | \(0.847235\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.8557 | −0.812341 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.66332 | 0.181637 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.77065 | 0.663275 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.79185 | −0.256229 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.04878 | 0.406885 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.74588 | 0.518703 | 0.259351 | − | 0.965783i | \(-0.416491\pi\) | ||||
0.259351 | + | 0.965783i | \(0.416491\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.92369 | 0.194913 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.51314 | −0.498665 | −0.249332 | − | 0.968418i | \(-0.580211\pi\) | ||||
−0.249332 | + | 0.968418i | \(0.580211\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.0839 | −1.39326 | −0.696630 | − | 0.717430i | \(-0.745318\pi\) | ||||
−0.696630 | + | 0.717430i | \(0.745318\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.54918 | 0.101929 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.3809 | 1.53173 | 0.765866 | − | 0.643001i | \(-0.222311\pi\) | ||||
0.765866 | + | 0.643001i | \(0.222311\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.518941 | −0.0338520 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.3712 | −1.19334 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.42839 | 0.351133 | 0.175567 | − | 0.984468i | \(-0.443824\pi\) | ||||
0.175567 | + | 0.984468i | \(0.443824\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.9194 | −1.15429 | −0.577145 | − | 0.816641i | \(-0.695833\pi\) | ||||
−0.577145 | + | 0.816641i | \(0.695833\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.13508 | 0.393566 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.356949 | −0.0228047 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.48928 | −0.540160 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.41757 | −0.533442 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.32837 | 0.273204 | 0.136602 | − | 0.990626i | \(-0.456382\pi\) | ||||
0.136602 | + | 0.990626i | \(0.456382\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.98257 | −0.501860 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.34486 | 0.209463 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.9892 | −0.747866 | −0.373933 | − | 0.927456i | \(-0.621991\pi\) | ||||
−0.373933 | + | 0.927456i | \(0.621991\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.5368 | −0.654727 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.18970 | −0.197437 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.00402 | −0.431886 | −0.215943 | − | 0.976406i | \(-0.569283\pi\) | ||||
−0.215943 | + | 0.976406i | \(0.569283\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.611699 | 0.0375764 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.3414 | 0.877680 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.2468 | −0.807672 | −0.403836 | − | 0.914831i | \(-0.632323\pi\) | ||||
−0.403836 | + | 0.914831i | \(0.632323\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.5661 | 1.24930 | 0.624650 | − | 0.780905i | \(-0.285242\pi\) | ||||
0.624650 | + | 0.780905i | \(0.285242\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.54918 | 0.0937609 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.87259 | 0.293828 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.45404 | 0.568038 | 0.284019 | − | 0.958819i | \(-0.408332\pi\) | ||||
0.284019 | + | 0.958819i | \(0.408332\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.86266 | 0.350988 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.798874 | 0.0476568 | 0.0238284 | − | 0.999716i | \(-0.492414\pi\) | ||||
0.0238284 | + | 0.999716i | \(0.492414\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.4553 | 0.918719 | 0.459360 | − | 0.888250i | \(-0.348079\pi\) | ||||
0.459360 | + | 0.888250i | \(0.348079\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.69441 | −0.278073 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.72233 | −0.514863 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.5877 | 1.15222 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.92384 | 0.347261 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.5721 | −1.43552 | −0.717759 | − | 0.696292i | \(-0.754832\pi\) | ||||
−0.717759 | + | 0.696292i | \(0.754832\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.278914 | 0.0162390 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.57711 | 0.323617 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.98257 | −0.461644 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.46133 | 0.430064 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.2925 | −0.591288 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.89590 | 0.108559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.47883 | −0.141474 | −0.0707371 | − | 0.997495i | \(-0.522535\pi\) | ||||
−0.0707371 | + | 0.997495i | \(0.522535\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.2959 | −0.813265 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.8260 | −1.74798 | −0.873992 | − | 0.485941i | \(-0.838477\pi\) | ||||
−0.873992 | + | 0.485941i | \(0.838477\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.2593 | 1.25817 | 0.629086 | − | 0.777336i | \(-0.283429\pi\) | ||||
0.629086 | + | 0.777336i | \(0.283429\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.214180 | −0.0120677 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.10203 | 0.118062 | 0.0590310 | − | 0.998256i | \(-0.481199\pi\) | ||||
0.0590310 | + | 0.998256i | \(0.481199\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.31591 | −0.297634 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.1649 | −0.958049 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −51.3498 | −2.85718 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.87259 | 0.270283 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.3578 | −1.51289 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.45382 | −0.0801519 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.4137 | 1.67169 | 0.835845 | − | 0.548966i | \(-0.184978\pi\) | ||||
0.835845 | + | 0.548966i | \(0.184978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.32240 | −0.346465 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.21211 | 0.120861 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.11263 | 0.278503 | 0.139251 | − | 0.990257i | \(-0.455530\pi\) | ||||
0.139251 | + | 0.990257i | \(0.455530\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.41907 | −0.185698 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.77065 | 0.529110 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.41421 | −0.237653 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.2330 | 1.83773 | 0.918863 | − | 0.394576i | \(-0.129109\pi\) | ||||
0.918863 | + | 0.394576i | \(0.129109\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.2630 | 1.78053 | 0.890263 | − | 0.455446i | \(-0.150520\pi\) | ||||
0.890263 | + | 0.455446i | \(0.150520\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.57711 | 0.297684 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.7880 | −0.999987 | −0.499993 | − | 0.866029i | \(-0.666664\pi\) | ||||
−0.499993 | + | 0.866029i | \(0.666664\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.73169 | 0.144983 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.37067 | 0.495949 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.76999 | 0.146195 | 0.0730973 | − | 0.997325i | \(-0.476712\pi\) | ||||
0.0730973 | + | 0.997325i | \(0.476712\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 53.0678 | 2.79304 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.54918 | 0.0813111 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.873685 | 0.0457308 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.6481 | 1.13002 | 0.565012 | − | 0.825083i | \(-0.308872\pi\) | ||||
0.565012 | + | 0.825083i | \(0.308872\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.23364 | −0.272453 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.71369 | 0.0889702 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.47631 | 0.438887 | 0.219443 | − | 0.975625i | \(-0.429576\pi\) | ||||
0.219443 | + | 0.975625i | \(0.429576\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.45935 | 0.281920 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.31591 | −0.273783 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.1315 | 0.623152 | 0.311576 | − | 0.950221i | \(-0.399143\pi\) | ||||
0.311576 | + | 0.950221i | \(0.399143\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.36022 | 0.479539 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.1500 | −1.48950 | −0.744748 | − | 0.667346i | \(-0.767430\pi\) | ||||
−0.744748 | + | 0.667346i | \(0.767430\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.356949 | −0.0181918 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.47701 | 0.227579 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.15489 | −0.413469 | −0.206735 | − | 0.978397i | \(-0.566284\pi\) | ||||
−0.206735 | + | 0.978397i | \(0.566284\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −48.2848 | −2.44187 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −33.7531 | −1.70262 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.23293 | 0.212982 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.6320 | −1.48719 | −0.743595 | − | 0.668631i | \(-0.766881\pi\) | ||||
−0.743595 | + | 0.668631i | \(0.766881\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.1515 | −0.658396 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.0032 | 1.04885 | 0.524424 | − | 0.851457i | \(-0.324281\pi\) | ||||
0.524424 | + | 0.851457i | \(0.324281\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.77065 | 0.486711 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.44149 | 0.121319 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.5368 | −0.522292 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.66645 | −0.477975 | −0.238988 | − | 0.971023i | \(-0.576816\pi\) | ||||
−0.238988 | + | 0.971023i | \(0.576816\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −29.3054 | −1.44553 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.781383 | 0.0384493 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.93950 | 0.0952064 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 35.5791 | 1.74232 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.0140 | −0.684628 | −0.342314 | − | 0.939586i | \(-0.611211\pi\) | ||||
−0.342314 | + | 0.939586i | \(0.611211\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.94209 | −0.484548 | −0.242274 | − | 0.970208i | \(-0.577893\pi\) | ||||
−0.242274 | + | 0.970208i | \(0.577893\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.872335 | −0.0424144 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29.4732 | 1.42966 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.31139 | 0.257036 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.54918 | 0.0747953 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.12683 | −0.295119 | −0.147559 | − | 0.989053i | \(-0.547142\pi\) | ||||
−0.147559 | + | 0.989053i | \(0.547142\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.4768 | 1.08017 | 0.540083 | − | 0.841612i | \(-0.318393\pi\) | ||||
0.540083 | + | 0.841612i | \(0.318393\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.93960 | −0.140943 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 67.7663 | 3.24170 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.1531 | 1.20049 | 0.600247 | − | 0.799815i | \(-0.295069\pi\) | ||||
0.600247 | + | 0.799815i | \(0.295069\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.600028 | −0.0285728 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.5891 | 0.693147 | 0.346574 | − | 0.938023i | \(-0.387345\pi\) | ||||
0.346574 | + | 0.938023i | \(0.387345\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.30442 | −0.156645 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.5200 | −0.686771 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.3003 | −0.769257 | −0.384629 | − | 0.923071i | \(-0.625670\pi\) | ||||
−0.384629 | + | 0.923071i | \(0.625670\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.72233 | −0.410718 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.55458 | 0.120024 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.356949 | −0.0167341 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.10112 | 0.145064 | 0.0725321 | − | 0.997366i | \(-0.476892\pi\) | ||||
0.0725321 | + | 0.997366i | \(0.476892\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 33.7347 | 1.57460 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.5437 | 1.23626 | 0.618131 | − | 0.786075i | \(-0.287890\pi\) | ||||
0.618131 | + | 0.786075i | \(0.287890\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.2201 | −0.707340 | −0.353670 | − | 0.935370i | \(-0.615066\pi\) | ||||
−0.353670 | + | 0.935370i | \(0.615066\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.40298 | 0.250557 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.6005 | 0.675631 | 0.337815 | − | 0.941212i | \(-0.390312\pi\) | ||||
0.337815 | + | 0.941212i | \(0.390312\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.19727 | 0.286163 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.7794 | −1.04962 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.46133 | 0.343072 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −41.3647 | −1.89794 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.02826 | 0.0470808 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.2842 | 1.01819 | 0.509095 | − | 0.860711i | \(-0.329980\pi\) | ||||
0.509095 | + | 0.860711i | \(0.329980\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5368 | −0.480438 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.3665 | −0.562694 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.36492 | −0.0619778 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.2685 | −1.64348 | −0.821742 | − | 0.569860i | \(-0.806997\pi\) | ||||
−0.821742 | + | 0.569860i | \(0.806997\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.5535 | −1.01990 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.21894 | 0.235528 | 0.117764 | − | 0.993042i | \(-0.462427\pi\) | ||||
0.117764 | + | 0.993042i | \(0.462427\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.1548 | −1.44818 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.214180 | −0.00962666 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.65289 | 0.343279 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.5188 | 0.739482 | 0.369741 | − | 0.929135i | \(-0.379446\pi\) | ||||
0.369741 | + | 0.929135i | \(0.379446\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.79154 | −0.124717 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.4935 | −1.58258 | −0.791288 | − | 0.611444i | \(-0.790589\pi\) | ||||
−0.791288 | + | 0.611444i | \(0.790589\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.37151 | 0.105531 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.54918 | 0.0688017 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −43.8652 | −1.94429 | −0.972146 | − | 0.234376i | \(-0.924695\pi\) | ||||
−0.972146 | + | 0.234376i | \(0.924695\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.44764 | 0.108277 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −47.3456 | −2.09036 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.29394 | 0.145148 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.45382 | −0.0639391 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.8591 | 0.915611 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.9666 | −0.524264 | −0.262132 | − | 0.965032i | \(-0.584426\pi\) | ||||
−0.262132 | + | 0.965032i | \(0.584426\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.6990 | 0.686470 | 0.343235 | − | 0.939249i | \(-0.388477\pi\) | ||||
0.343235 | + | 0.939249i | \(0.388477\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.54854 | 0.329445 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 59.1005 | 2.57446 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 40.7215 | 1.77050 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.468852 | 0.0203464 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.72233 | −0.377806 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.95498 | 0.170988 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.0613 | 0.563635 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.7880 | 1.15171 | 0.575854 | − | 0.817553i | \(-0.304670\pi\) | ||||
0.575854 | + | 0.817553i | \(0.304670\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −34.7692 | −1.49209 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.30354 | 0.270014 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.09563 | −0.388901 | −0.194450 | − | 0.980912i | \(-0.562292\pi\) | ||||
−0.194450 | + | 0.980912i | \(0.562292\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.18698 | 0.136017 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 45.1283 | 1.92253 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.8586 | 0.504280 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.82667 | −0.247328 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.5695 | −0.574958 | −0.287479 | − | 0.957787i | \(-0.592817\pi\) | ||||
−0.287479 | + | 0.957787i | \(0.592817\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.46133 | 0.315581 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.37067 | 0.395630 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.20690 | −0.261590 | −0.130795 | − | 0.991409i | \(-0.541753\pi\) | ||||
−0.130795 | + | 0.991409i | \(0.541753\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.787791 | 0.0331426 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.83988 | 0.287248 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.4433 | −1.23433 | −0.617164 | − | 0.786834i | \(-0.711719\pi\) | ||||
−0.617164 | + | 0.786834i | \(0.711719\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.8202 | 1.24794 | 0.623968 | − | 0.781450i | \(-0.285519\pi\) | ||||
0.623968 | + | 0.781450i | \(0.285519\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.9869 | −0.542533 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.8958 | −1.62207 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5995 | 0.524524 | 0.262262 | − | 0.964997i | \(-0.415531\pi\) | ||||
0.262262 | + | 0.964997i | \(0.415531\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.6879 | −0.527293 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.43355 | 0.225422 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.71369 | 0.0709736 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.214180 | −0.00885524 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.3278 | 1.29303 | 0.646517 | − | 0.762899i | \(-0.276225\pi\) | ||||
0.646517 | + | 0.762899i | \(0.276225\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −82.9457 | −3.41772 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.7487 | −0.771217 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.1972 | 0.583010 | 0.291505 | − | 0.956569i | \(-0.405844\pi\) | ||||
0.291505 | + | 0.956569i | \(0.405844\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.15911 | −0.0885148 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 38.5199 | 1.57651 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.9027 | −1.46694 | −0.733472 | − | 0.679720i | \(-0.762101\pi\) | ||||
−0.733472 | + | 0.679720i | \(0.762101\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.89109 | 0.281094 | 0.140547 | − | 0.990074i | \(-0.455114\pi\) | ||||
0.140547 | + | 0.990074i | \(0.455114\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.71854 | 0.151431 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.356949 | −0.0145121 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.0947 | −0.775032 | −0.387516 | − | 0.921863i | \(-0.626667\pi\) | ||||
−0.387516 | + | 0.921863i | \(0.626667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.23533 | −0.333712 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.45382 | −0.0588154 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.4928 | 0.464189 | 0.232095 | − | 0.972693i | \(-0.425442\pi\) | ||||
0.232095 | + | 0.972693i | \(0.425442\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.82328 | −0.194493 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.1261 | −1.29335 | −0.646674 | − | 0.762767i | \(-0.723841\pi\) | ||||
−0.646674 | + | 0.762767i | \(0.723841\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.8651 | 0.999411 | 0.499706 | − | 0.866195i | \(-0.333442\pi\) | ||||
0.499706 | + | 0.866195i | \(0.333442\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −44.5197 | −1.78651 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.25740 | −0.370890 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.1050 | 0.924202 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.1515 | −0.525219 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −63.7350 | −2.54128 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.4588 | 0.575595 | 0.287797 | − | 0.957691i | \(-0.407077\pi\) | ||||
0.287797 | + | 0.957691i | \(0.407077\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −39.9220 | −1.58676 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.15670 | −0.0855860 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.59195 | 0.181655 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −46.4826 | −1.83595 | −0.917976 | − | 0.396637i | \(-0.870177\pi\) | ||||
−0.917976 | + | 0.396637i | \(0.870177\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.9147 | −0.903666 | −0.451833 | − | 0.892102i | \(-0.649230\pi\) | ||||
−0.451833 | + | 0.892102i | \(0.649230\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.12597 | 0.162460 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.93310 | 0.390511 | 0.195255 | − | 0.980752i | \(-0.437446\pi\) | ||||
0.195255 | + | 0.980752i | \(0.437446\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.781383 | 0.0306720 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.1365 | 0.593247 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.8734 | 0.934238 | 0.467119 | − | 0.884195i | \(-0.345292\pi\) | ||||
0.467119 | + | 0.884195i | \(0.345292\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.77710 | 0.303876 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.46865 | 0.0572977 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.9548 | 1.05001 | 0.525004 | − | 0.851100i | \(-0.324064\pi\) | ||||
0.525004 | + | 0.851100i | \(0.324064\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.9740 | −0.893586 | −0.446793 | − | 0.894637i | \(-0.647434\pi\) | ||||
−0.446793 | + | 0.894637i | \(0.647434\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.37067 | 0.363927 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.03024 | 0.117508 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42.4347 | 1.64308 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.9998 | 0.463939 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.31139 | 0.205044 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.05070 | −0.233237 | −0.116619 | − | 0.993177i | \(-0.537206\pi\) | ||||
−0.116619 | + | 0.993177i | \(0.537206\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 27.1749 | 1.04596 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.1842 | 1.12164 | 0.560820 | − | 0.827938i | \(-0.310486\pi\) | ||||
0.560820 | + | 0.827938i | \(0.310486\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.82384 | −0.146746 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.6392 | −0.446017 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.6520 | −1.09634 | −0.548169 | − | 0.836367i | \(-0.684675\pi\) | ||||
−0.548169 | + | 0.836367i | \(0.684675\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.75230 | 0.257992 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −32.6628 | −1.24616 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.71369 | 0.0652862 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.0755 | −0.497416 | −0.248708 | − | 0.968579i | \(-0.580006\pi\) | ||||
−0.248708 | + | 0.968579i | \(0.580006\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.600028 | −0.0227932 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.19783 | −0.310961 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −52.7594 | −1.99841 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 36.2213 | 1.37001 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.91478 | 0.374476 | 0.187238 | − | 0.982315i | \(-0.440046\pi\) | ||||
0.187238 | + | 0.982315i | \(0.440046\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 89.4501 | 3.37368 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.803936 | −0.0302780 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.64381 | 0.249866 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.4122 | −1.40504 | −0.702522 | − | 0.711662i | \(-0.747943\pi\) | ||||
−0.702522 | + | 0.711662i | \(0.747943\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.11551 | 0.266853 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −77.9949 | −2.92093 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.356949 | −0.0133492 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.40957 | 0.314061 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.1404 | 0.974872 | 0.487436 | − | 0.873159i | \(-0.337932\pi\) | ||||
0.487436 | + | 0.873159i | \(0.337932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.22802 | 0.343669 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −27.7605 | −1.03242 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −25.9023 | −0.961985 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.2363 | 0.713435 | 0.356717 | − | 0.934212i | \(-0.383896\pi\) | ||||
0.356717 | + | 0.934212i | \(0.383896\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 30.0240 | 1.11200 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.1319 | 1.66926 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.8790 | −0.660378 | −0.330189 | − | 0.943915i | \(-0.607112\pi\) | ||||
−0.330189 | + | 0.943915i | \(0.607112\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.552981 | −0.0203970 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.19727 | 0.228279 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.4069 | 0.750681 | 0.375341 | − | 0.926887i | \(-0.377526\pi\) | ||||
0.375341 | + | 0.926887i | \(0.377526\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.1515 | −0.483131 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.3952 | −0.748226 | −0.374113 | − | 0.927383i | \(-0.622053\pi\) | ||||
−0.374113 | + | 0.927383i | \(0.622053\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.34556 | 0.122572 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.26028 | 0.119287 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.0799 | 0.404852 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.5747 | 1.29814 | 0.649070 | − | 0.760728i | \(-0.275158\pi\) | ||||
0.649070 | + | 0.760728i | \(0.275158\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.70544 | 0.244360 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.588603 | −0.0214215 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.55291 | −0.274515 | −0.137258 | − | 0.990535i | \(-0.543829\pi\) | ||||
−0.137258 | + | 0.990535i | \(0.543829\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.3665 | −0.448875 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.6862 | 1.07612 | 0.538062 | − | 0.842906i | \(-0.319157\pi\) | ||||
0.538062 | + | 0.842906i | \(0.319157\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.6595 | 0.639316 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.29553 | −0.0468398 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.781383 | 0.0282141 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.3335 | 1.77901 | 0.889506 | − | 0.456924i | \(-0.151049\pi\) | ||||
0.889506 | + | 0.456924i | \(0.151049\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.5735 | −0.668907 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −50.8325 | −1.82832 | −0.914160 | − | 0.405354i | \(-0.867148\pi\) | ||||
−0.914160 | + | 0.405354i | \(0.867148\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 47.6083 | 1.71014 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.3235 | −0.585602 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 74.0463 | 2.65298 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.65289 | 0.273842 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29.6474 | −1.05951 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.24864 | 0.187332 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.7664 | 1.73833 | 0.869167 | − | 0.494518i | \(-0.164655\pi\) | ||||
0.869167 | + | 0.494518i | \(0.164655\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.8505 | −0.386289 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.20701 | 0.0784723 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.31139 | 0.188613 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.947635 | 0.0336092 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.3353 | 0.861999 | 0.431000 | − | 0.902352i | \(-0.358161\pi\) | ||||
0.431000 | + | 0.902352i | \(0.358161\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.79385 | −0.311104 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.55470 | −0.196266 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.44764 | 0.0863754 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.84938 | 0.100427 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.5218 | −0.722400 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.2803 | 1.45134 | 0.725668 | − | 0.688045i | \(-0.241531\pi\) | ||||
0.725668 | + | 0.688045i | \(0.241531\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.5033 | 0.684855 | 0.342428 | − | 0.939544i | \(-0.388751\pi\) | ||||
0.342428 | + | 0.939544i | \(0.388751\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31.8606 | 1.11740 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.19658 | 0.182028 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −63.3413 | −2.21603 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.600028 | −0.0209667 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.3464 | 0.605392 | 0.302696 | − | 0.953087i | \(-0.402113\pi\) | ||||
0.302696 | + | 0.953087i | \(0.402113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.1458 | −1.01596 | −0.507980 | − | 0.861369i | \(-0.669608\pi\) | ||||
−0.507980 | + | 0.861369i | \(0.669608\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.54854 | 0.262806 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.7663 | 0.791661 | 0.395830 | − | 0.918324i | \(-0.370457\pi\) | ||||
0.395830 | + | 0.918324i | \(0.370457\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.2238 | 0.598206 | 0.299103 | − | 0.954221i | \(-0.403313\pi\) | ||||
0.299103 | + | 0.954221i | \(0.403313\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.6460 | 0.508066 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.04878 | −0.209578 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.643202 | 0.0222589 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 54.4919 | 1.88352 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.2951 | 1.04590 | 0.522952 | − | 0.852362i | \(-0.324831\pi\) | ||||
0.522952 | + | 0.852362i | \(0.324831\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.741062 | −0.0255539 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.23760 | 0.0426253 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.356949 | −0.0122794 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.9430 | 0.821723 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 84.1111 | 2.88329 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.4519 | 1.14537 | 0.572686 | − | 0.819775i | \(-0.305901\pi\) | ||||
0.572686 | + | 0.819775i | \(0.305901\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.81823 | 0.0621822 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.70378 | 0.160678 | 0.0803391 | − | 0.996768i | \(-0.474400\pi\) | ||||
0.0803391 | + | 0.996768i | \(0.474400\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.7030 | −1.08169 | −0.540846 | − | 0.841122i | \(-0.681896\pi\) | ||||
−0.540846 | + | 0.841122i | \(0.681896\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.5125 | −0.460505 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.32286 | 0.249273 | 0.124636 | − | 0.992202i | \(-0.460224\pi\) | ||||
0.124636 | + | 0.992202i | \(0.460224\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.80616 | −0.163414 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 30.3450 | 1.03057 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.8586 | 0.402277 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.19727 | 0.209987 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.29441 | −0.0776541 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.52401 | −0.119133 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.9628 | −1.45075 | −0.725375 | − | 0.688354i | \(-0.758334\pi\) | ||||
−0.725375 | + | 0.688354i | \(0.758334\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −38.0667 | −1.28396 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.65959 | 0.123295 | 0.0616474 | − | 0.998098i | \(-0.480365\pi\) | ||||
0.0616474 | + | 0.998098i | \(0.480365\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.2488 | −0.748731 | −0.374366 | − | 0.927281i | \(-0.622140\pi\) | ||||
−0.374366 | + | 0.927281i | \(0.622140\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.432089 | 0.0145245 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.2501 | −0.579202 | −0.289601 | − | 0.957147i | \(-0.593523\pi\) | ||||
−0.289601 | + | 0.957147i | \(0.593523\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.04203 | −0.202643 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.83988 | 0.229145 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.3419 | 0.413006 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.00946 | −0.100595 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.3665 | −0.412905 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −51.9399 | −1.73229 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.3657 | 0.345332 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.5590 | 0.384659 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.01122 | 0.266302 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.7320 | −0.356349 | −0.178175 | − | 0.983999i | \(-0.557019\pi\) | ||||
−0.178175 | + | 0.983999i | \(0.557019\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.98648 | 0.132223 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.3482 | 0.574771 | 0.287386 | − | 0.957815i | \(-0.407214\pi\) | ||||
0.287386 | + | 0.957815i | \(0.407214\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.43355 | 0.179824 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.93709 | 0.0970973 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.7877 | 0.719492 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.9821 | −1.41785 | −0.708924 | − | 0.705285i | \(-0.750819\pi\) | ||||
−0.708924 | + | 0.705285i | \(0.750819\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.84016 | −0.126538 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.65289 | 0.251898 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −51.3417 | −1.68810 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.53707 | 0.181861 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.4507 | −1.58962 | −0.794808 | − | 0.606861i | \(-0.792428\pi\) | ||||
−0.794808 | + | 0.606861i | \(0.792428\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.48928 | 0.278225 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −47.7552 | −1.56343 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.15911 | −0.0706104 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.0939 | −1.08113 | −0.540565 | − | 0.841302i | \(-0.681789\pi\) | ||||
−0.540565 | + | 0.841302i | \(0.681789\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 34.4838 | 1.12534 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.8501 | 0.451499 | 0.225750 | − | 0.974185i | \(-0.427517\pi\) | ||||
0.225750 | + | 0.974185i | \(0.427517\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 69.6266 | 2.26735 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.99075 | −0.0647590 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.457427 | −0.0148644 | −0.00743219 | − | 0.999972i | \(-0.502366\pi\) | ||||
−0.00743219 | + | 0.999972i | \(0.502366\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.44764 | 0.0794539 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.25644 | 0.105597 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.5821 | −1.08783 | −0.543915 | − | 0.839140i | \(-0.683059\pi\) | ||||
−0.543915 | + | 0.839140i | \(0.683059\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.99232 | 0.0968291 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.23533 | −0.266210 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.9167 | 0.610852 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 64.4655 | 2.07953 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.64827 | 0.214238 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.92345 | 0.0941090 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.2960 | −1.64957 | −0.824784 | − | 0.565448i | \(-0.808703\pi\) | ||||
−0.824784 | + | 0.565448i | \(0.808703\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −79.5503 | −2.55552 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57.5395 | −1.84653 | −0.923265 | − | 0.384163i | \(-0.874490\pi\) | ||||
−0.923265 | + | 0.384163i | \(0.874490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.9664 | −0.736268 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.54854 | 0.241747 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.89398 | 0.124579 | 0.0622897 | − | 0.998058i | \(-0.480160\pi\) | ||||
0.0622897 | + | 0.998058i | \(0.480160\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.25740 | −0.295868 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.5962 | 0.338310 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.9979 | 0.733519 | 0.366760 | − | 0.930316i | \(-0.380467\pi\) | ||||
0.366760 | + | 0.930316i | \(0.380467\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.31991 | 0.137644 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.25224 | −0.0716896 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −59.5606 | −1.89392 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.3704 | −0.964749 | −0.482375 | − | 0.875965i | \(-0.660226\pi\) | ||||
−0.482375 | + | 0.875965i | \(0.660226\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 47.1165 | 1.49520 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.87541 | −0.281370 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.31661 | 0.105038 | 0.0525190 | − | 0.998620i | \(-0.483275\pi\) | ||||
0.0525190 | + | 0.998620i | \(0.483275\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −58.7651 | −1.85924 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8008.2.a.u.1.7 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.u.1.7 | ✓ | 10 | 1.1 | even | 1 | trivial |