Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 15x^{7} + 45x^{6} + 64x^{5} - 201x^{4} - 63x^{3} + 282x^{2} + 3x - 116 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.07040\) 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 | ||||||||
\(3\) | −3.07040 | −1.77270 | −0.886348 | − | 0.463020i | \(-0.846766\pi\) | ||||
−0.886348 | + | 0.463020i | \(0.846766\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.53994 | −1.58311 | −0.791554 | − | 0.611099i | \(-0.790728\pi\) | ||||
−0.791554 | + | 0.611099i | \(0.790728\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.42735 | 2.14245 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.8690 | 2.80637 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.83553 | 0.445181 | 0.222590 | − | 0.974912i | \(-0.428549\pi\) | ||||
0.222590 | + | 0.974912i | \(0.428549\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.318127 | −0.0729833 | −0.0364916 | − | 0.999334i | \(-0.511618\pi\) | ||||
−0.0364916 | + | 0.999334i | \(0.511618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.07040 | 0.670016 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.10506 | 0.230421 | 0.115210 | − | 0.993341i | \(-0.463246\pi\) | ||||
0.115210 | + | 0.993341i | \(0.463246\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.53117 | 1.50623 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −10.5233 | −2.02522 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.36170 | −0.252862 | −0.126431 | − | 0.991975i | \(-0.540352\pi\) | ||||
−0.126431 | + | 0.991975i | \(0.540352\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.34508 | −0.241583 | −0.120791 | − | 0.992678i | \(-0.538543\pi\) | ||||
−0.120791 | + | 0.992678i | \(0.538543\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.07040 | −0.534488 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.53994 | 0.598359 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.6497 | 1.75080 | 0.875399 | − | 0.483400i | \(-0.160598\pi\) | ||||
0.875399 | + | 0.483400i | \(0.160598\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.07040 | 0.491657 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.852734 | 0.133175 | 0.0665874 | − | 0.997781i | \(-0.478789\pi\) | ||||
0.0665874 | + | 0.997781i | \(0.478789\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.13797 | −0.326037 | −0.163018 | − | 0.986623i | \(-0.552123\pi\) | ||||
−0.163018 | + | 0.986623i | \(0.552123\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −22.7524 | −3.39173 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.5005 | 1.53166 | 0.765831 | − | 0.643042i | \(-0.222328\pi\) | ||||
0.765831 | + | 0.643042i | \(0.222328\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.63580 | −0.789170 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.45473 | −0.199823 | −0.0999115 | − | 0.994996i | \(-0.531856\pi\) | ||||
−0.0999115 | + | 0.994996i | \(0.531856\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.53994 | −0.477325 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.976776 | 0.129377 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.50546 | −0.716750 | −0.358375 | − | 0.933578i | \(-0.616669\pi\) | ||||
−0.358375 | + | 0.933578i | \(0.616669\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.79694 | −0.614185 | −0.307093 | − | 0.951680i | \(-0.599356\pi\) | ||||
−0.307093 | + | 0.951680i | \(0.599356\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.42735 | −0.809770 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.53994 | 0.439075 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.55735 | 0.190260 | 0.0951302 | − | 0.995465i | \(-0.469673\pi\) | ||||
0.0951302 | + | 0.995465i | \(0.469673\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.39297 | −0.408466 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.673836 | 0.0799696 | 0.0399848 | − | 0.999200i | \(-0.487269\pi\) | ||||
0.0399848 | + | 0.999200i | \(0.487269\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.83968 | 0.332359 | 0.166179 | − | 0.986096i | \(-0.446857\pi\) | ||||
0.166179 | + | 0.986096i | \(0.446857\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −23.1237 | −2.67009 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.33566 | −0.712818 | −0.356409 | − | 0.934330i | \(-0.615999\pi\) | ||||
−0.356409 | + | 0.934330i | \(0.615999\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 13.0288 | 1.44764 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.51924 | −0.496051 | −0.248025 | − | 0.968754i | \(-0.579782\pi\) | ||||
−0.248025 | + | 0.968754i | \(0.579782\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.49766 | −0.704770 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.18097 | 0.448247 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.3709 | −1.41731 | −0.708654 | − | 0.705556i | \(-0.750697\pi\) | ||||
−0.708654 | + | 0.705556i | \(0.750697\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.12992 | 0.428253 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.12615 | 0.115540 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.08525 | −0.313260 | −0.156630 | − | 0.987657i | \(-0.550063\pi\) | ||||
−0.156630 | + | 0.987657i | \(0.550063\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.42735 | 0.645973 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.2620 | 1.41912 | 0.709559 | − | 0.704646i | \(-0.248894\pi\) | ||||
0.709559 | + | 0.704646i | \(0.248894\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.8325 | −1.56002 | −0.780010 | − | 0.625767i | \(-0.784786\pi\) | ||||
−0.780010 | + | 0.625767i | \(0.784786\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.8690 | −1.06071 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.7426 | −1.42522 | −0.712612 | − | 0.701558i | \(-0.752488\pi\) | ||||
−0.712612 | + | 0.701558i | \(0.752488\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.4349 | −0.999480 | −0.499740 | − | 0.866176i | \(-0.666571\pi\) | ||||
−0.499740 | + | 0.866176i | \(0.666571\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −32.6988 | −3.10363 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.85354 | 0.926943 | 0.463472 | − | 0.886112i | \(-0.346604\pi\) | ||||
0.463472 | + | 0.886112i | \(0.346604\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.91184 | −0.364781 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.42735 | −0.594209 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.83553 | −0.168263 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.61824 | −0.236078 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.96018 | −0.801423 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.56257 | 0.227391 | 0.113696 | − | 0.993516i | \(-0.463731\pi\) | ||||
0.113696 | + | 0.993516i | \(0.463731\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.56441 | 0.577964 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.39260 | −0.558524 | −0.279262 | − | 0.960215i | \(-0.590090\pi\) | ||||
−0.279262 | + | 0.960215i | \(0.590090\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.318127 | 0.0275851 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 37.2520 | 3.20614 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.06708 | 0.432910 | 0.216455 | − | 0.976293i | \(-0.430551\pi\) | ||||
0.216455 | + | 0.976293i | \(0.430551\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.7171 | −1.07865 | −0.539325 | − | 0.842098i | \(-0.681321\pi\) | ||||
−0.539325 | + | 0.842098i | \(0.681321\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −32.2409 | −2.71517 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.82034 | 0.400307 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.07040 | −0.253242 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.4741 | −1.10384 | −0.551921 | − | 0.833896i | \(-0.686105\pi\) | ||||
−0.551921 | + | 0.833896i | \(0.686105\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.3013 | 1.89623 | 0.948117 | − | 0.317922i | \(-0.102985\pi\) | ||||
0.948117 | + | 0.317922i | \(0.102985\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.7976 | 0.953778 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.76148 | 0.382452 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.46455 | −0.515927 | −0.257964 | − | 0.966155i | \(-0.583051\pi\) | ||||
−0.257964 | + | 0.966155i | \(0.583051\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.46661 | 0.354225 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.10506 | −0.0870908 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.0285 | −1.72540 | −0.862702 | − | 0.505713i | \(-0.831230\pi\) | ||||
−0.862702 | + | 0.505713i | \(0.831230\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.8690 | 0.846153 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.8268 | −0.992566 | −0.496283 | − | 0.868161i | \(-0.665302\pi\) | ||||
−0.496283 | + | 0.868161i | \(0.665302\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.04471 | −0.156363 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.896457 | 0.0681564 | 0.0340782 | − | 0.999419i | \(-0.489150\pi\) | ||||
0.0340782 | + | 0.999419i | \(0.489150\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.53117 | −0.569303 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.9040 | 1.27058 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.6403 | 1.09427 | 0.547134 | − | 0.837045i | \(-0.315719\pi\) | ||||
0.547134 | + | 0.837045i | \(0.315719\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.12159 | 0.529344 | 0.264672 | − | 0.964339i | \(-0.414736\pi\) | ||||
0.264672 | + | 0.964339i | \(0.414736\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.7285 | 1.08876 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −37.6993 | −2.77171 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.83553 | 0.134227 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.5233 | 0.765460 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.81282 | 0.348244 | 0.174122 | − | 0.984724i | \(-0.444291\pi\) | ||||
0.174122 | + | 0.984724i | \(0.444291\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.49734 | 0.107781 | 0.0538903 | − | 0.998547i | \(-0.482838\pi\) | ||||
0.0538903 | + | 0.998547i | \(0.482838\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.8690 | −0.778347 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.5736 | −0.824582 | −0.412291 | − | 0.911052i | \(-0.635271\pi\) | ||||
−0.412291 | + | 0.911052i | \(0.635271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.1145 | −1.07144 | −0.535718 | − | 0.844397i | \(-0.679959\pi\) | ||||
−0.535718 | + | 0.844397i | \(0.679959\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.78168 | −0.337274 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.36170 | 0.0955727 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.01863 | −0.210830 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.10260 | 0.493665 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.318127 | −0.0220053 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.20348 | −0.427065 | −0.213532 | − | 0.976936i | \(-0.568497\pi\) | ||||
−0.213532 | + | 0.976936i | \(0.568497\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.06895 | −0.141762 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.56827 | 0.516151 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.34508 | 0.0913097 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.71894 | −0.589171 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.83553 | −0.123471 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.9688 | −0.935421 | −0.467711 | − | 0.883882i | \(-0.654921\pi\) | ||||
−0.467711 | + | 0.883882i | \(0.654921\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 48.4055 | 3.22703 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.25786 | −0.282604 | −0.141302 | − | 0.989967i | \(-0.545129\pi\) | ||||
−0.141302 | + | 0.989967i | \(0.545129\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.43864 | 0.161150 | 0.0805751 | − | 0.996749i | \(-0.474324\pi\) | ||||
0.0805751 | + | 0.996749i | \(0.474324\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.07040 | 0.202017 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.0686 | 1.57678 | 0.788392 | − | 0.615173i | \(-0.210914\pi\) | ||||
0.788392 | + | 0.615173i | \(0.210914\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −37.1713 | −2.42479 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.4530 | 1.26361 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0385 | 0.778703 | 0.389351 | − | 0.921089i | \(-0.372699\pi\) | ||||
0.389351 | + | 0.921089i | \(0.372699\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.3026 | 0.985730 | 0.492865 | − | 0.870106i | \(-0.335950\pi\) | ||||
0.492865 | + | 0.870106i | \(0.335950\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.43361 | −0.541016 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.53994 | −0.226158 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.318127 | 0.0202419 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.8759 | 0.879347 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.800260 | −0.0505120 | −0.0252560 | − | 0.999681i | \(-0.508040\pi\) | ||||
−0.0252560 | + | 0.999681i | \(0.508040\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.10506 | 0.0694744 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 19.9504 | 1.24934 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.3486 | 1.20693 | 0.603467 | − | 0.797388i | \(-0.293786\pi\) | ||||
0.603467 | + | 0.797388i | \(0.293786\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.6497 | −0.661740 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.75213 | −0.541743 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.4405 | 1.19876 | 0.599378 | − | 0.800466i | \(-0.295415\pi\) | ||||
0.599378 | + | 0.800466i | \(0.295415\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.14967 | 0.316341 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 41.0539 | 2.51246 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.2124 | 1.04946 | 0.524731 | − | 0.851268i | \(-0.324166\pi\) | ||||
0.524731 | + | 0.851268i | \(0.324166\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.5128 | 0.638609 | 0.319304 | − | 0.947652i | \(-0.396551\pi\) | ||||
0.319304 | + | 0.947652i | \(0.396551\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.07040 | −0.185829 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.53117 | 0.454146 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.6416 | 1.54065 | 0.770327 | − | 0.637649i | \(-0.220093\pi\) | ||||
0.770327 | + | 0.637649i | \(0.220093\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.64527 | −0.517579 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.0875 | 0.900045 | 0.450022 | − | 0.893017i | \(-0.351416\pi\) | ||||
0.450022 | + | 0.893017i | \(0.351416\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.7746 | −0.759373 | −0.379686 | − | 0.925115i | \(-0.623968\pi\) | ||||
−0.379686 | + | 0.925115i | \(0.623968\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.45773 | −0.204818 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.852734 | −0.0503353 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6308 | −0.801814 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.47296 | 0.555315 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.45302 | 0.260148 | 0.130074 | − | 0.991504i | \(-0.458478\pi\) | ||||
0.130074 | + | 0.991504i | \(0.458478\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.4890 | 1.13469 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.5233 | −0.610626 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.10506 | −0.0639072 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.13797 | 0.123230 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −43.7899 | −2.51567 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.9809 | 0.972322 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.92416 | −0.166890 | −0.0834452 | − | 0.996512i | \(-0.526592\pi\) | ||||
−0.0834452 | + | 0.996512i | \(0.526592\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 48.6120 | 2.76544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.81577 | 0.273077 | 0.136539 | − | 0.990635i | \(-0.456402\pi\) | ||||
0.136539 | + | 0.990635i | \(0.456402\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.6350 | −0.657652 | −0.328826 | − | 0.944391i | \(-0.606653\pi\) | ||||
−0.328826 | + | 0.944391i | \(0.606653\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 22.7524 | 1.28195 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.568439 | −0.0319267 | −0.0159634 | − | 0.999873i | \(-0.505082\pi\) | ||||
−0.0159634 | + | 0.999873i | \(0.505082\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.36170 | −0.0762406 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 45.2658 | 2.52649 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.583930 | −0.0324908 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.53117 | −0.417754 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 32.0392 | 1.77177 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.5005 | −0.578914 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.42000 | −0.187980 | −0.0939901 | − | 0.995573i | \(-0.529962\pi\) | ||||
−0.0939901 | + | 0.995573i | \(0.529962\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 68.4493 | 3.75100 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.51292 | −0.301203 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.4942 | 0.680601 | 0.340300 | − | 0.940317i | \(-0.389471\pi\) | ||||
0.340300 | + | 0.940317i | \(0.389471\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −30.2543 | −1.64319 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.34508 | −0.0728399 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.0109 | 0.646646 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.94152 | 0.426323 | 0.213161 | − | 0.977017i | \(-0.431624\pi\) | ||||
0.213161 | + | 0.977017i | \(0.431624\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.6625 | 1.85544 | 0.927719 | − | 0.373278i | \(-0.121766\pi\) | ||||
0.927719 | + | 0.373278i | \(0.121766\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.5233 | 0.561694 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.488574 | 0.0260041 | 0.0130021 | − | 0.999915i | \(-0.495861\pi\) | ||||
0.0130021 | + | 0.999915i | \(0.495861\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.38534 | −0.126601 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.63580 | 0.298278 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.8639 | −1.52338 | −0.761688 | − | 0.647944i | \(-0.775629\pi\) | ||||
−0.761688 | + | 0.647944i | \(0.775629\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8988 | −0.994673 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.07040 | −0.161154 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.0523 | −0.526160 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.96410 | −0.102525 | −0.0512625 | − | 0.998685i | \(-0.516325\pi\) | ||||
−0.0512625 | + | 0.998685i | \(0.516325\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.48083 | 0.285320 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.45473 | 0.0755260 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.7295 | 0.866219 | 0.433109 | − | 0.901341i | \(-0.357416\pi\) | ||||
0.433109 | + | 0.901341i | \(0.357416\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 27.5113 | 1.42068 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.36170 | 0.0701312 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.4701 | −0.897380 | −0.448690 | − | 0.893687i | \(-0.648109\pi\) | ||||
−0.448690 | + | 0.893687i | \(0.648109\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.86812 | −0.403096 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.87459 | −0.453471 | −0.226735 | − | 0.973956i | \(-0.572805\pi\) | ||||
−0.226735 | + | 0.973956i | \(0.572805\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.53994 | 0.180412 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.7415 | −0.698517 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.8454 | −0.752691 | −0.376346 | − | 0.926479i | \(-0.622820\pi\) | ||||
−0.376346 | + | 0.926479i | \(0.622820\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.02837 | 0.102579 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.6278 | 0.990093 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.4279 | 1.12847 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.4087 | 1.02428 | 0.512142 | − | 0.858901i | \(-0.328852\pi\) | ||||
0.512142 | + | 0.858901i | \(0.328852\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.976776 | −0.0489000 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.1461 | −0.656485 | −0.328242 | − | 0.944594i | \(-0.606456\pi\) | ||||
−0.328242 | + | 0.944594i | \(0.606456\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.34508 | 0.0670030 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −46.1212 | −2.29178 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.6497 | 0.527886 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.67209 | −0.0826796 | −0.0413398 | − | 0.999145i | \(-0.513163\pi\) | ||||
−0.0413398 | + | 0.999145i | \(0.513163\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.5580 | −0.767418 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.50546 | 0.270906 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.9978 | 0.785302 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 39.0466 | 1.91212 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.99163 | −0.488123 | −0.244061 | − | 0.969760i | \(-0.578480\pi\) | ||||
−0.244061 | + | 0.969760i | \(0.578480\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.2254 | 1.13194 | 0.565969 | − | 0.824426i | \(-0.308502\pi\) | ||||
0.565969 | + | 0.824426i | \(0.308502\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 67.4907 | 3.28151 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.8237 | 0.670546 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.79694 | 0.232140 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.07040 | 0.148240 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.7865 | 1.14576 | 0.572878 | − | 0.819640i | \(-0.305827\pi\) | ||||
0.572878 | + | 0.819640i | \(0.305827\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.6525 | 0.896382 | 0.448191 | − | 0.893938i | \(-0.352068\pi\) | ||||
0.448191 | + | 0.893938i | \(0.352068\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.8004 | −0.709623 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.351549 | −0.0168169 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.4711 | −0.929306 | −0.464653 | − | 0.885493i | \(-0.653821\pi\) | ||||
−0.464653 | + | 0.885493i | \(0.653821\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.42735 | 0.306064 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.0959 | 1.47741 | 0.738706 | − | 0.674028i | \(-0.235437\pi\) | ||||
0.738706 | + | 0.674028i | \(0.235437\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 47.3320 | 2.24375 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 41.3709 | 1.95678 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.6766 | −0.739823 | −0.369911 | − | 0.929067i | \(-0.620612\pi\) | ||||
−0.369911 | + | 0.929067i | \(0.620612\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.852734 | 0.0401537 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −71.5443 | −3.36145 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.53994 | −0.165955 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.4595 | 1.14417 | 0.572084 | − | 0.820195i | \(-0.306135\pi\) | ||||
0.572084 | + | 0.820195i | \(0.306135\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.3159 | −0.901588 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.5634 | −1.00431 | −0.502154 | − | 0.864778i | \(-0.667459\pi\) | ||||
−0.502154 | + | 0.864778i | \(0.667459\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.6525 | −0.866856 | −0.433428 | − | 0.901188i | \(-0.642696\pi\) | ||||
−0.433428 | + | 0.901188i | \(0.642696\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.6197 | −0.677970 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.7416 | −0.913532 | −0.456766 | − | 0.889587i | \(-0.650992\pi\) | ||||
−0.456766 | + | 0.889587i | \(0.650992\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.55735 | −0.0719117 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.8487 | 0.914582 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.13797 | −0.0983037 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.39587 | −0.109930 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.35008 | −0.428111 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.5165 | 1.02880 | 0.514402 | − | 0.857549i | \(-0.328014\pi\) | ||||
0.514402 | + | 0.857549i | \(0.328014\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.6497 | −0.485584 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.39297 | 0.154386 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.9216 | 0.495925 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.47178 | 0.0666929 | 0.0333464 | − | 0.999444i | \(-0.489384\pi\) | ||||
0.0333464 | + | 0.999444i | \(0.489384\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 67.6362 | 3.05862 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.8596 | −1.25729 | −0.628644 | − | 0.777693i | \(-0.716390\pi\) | ||||
−0.628644 | + | 0.777693i | \(0.716390\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.49944 | −0.112569 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −22.7524 | −1.02265 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.673836 | −0.0302257 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.6808 | −1.06010 | −0.530048 | − | 0.847967i | \(-0.677826\pi\) | ||||
−0.530048 | + | 0.847967i | \(0.677826\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 39.3833 | 1.75952 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.7351 | 1.05829 | 0.529147 | − | 0.848530i | \(-0.322512\pi\) | ||||
0.529147 | + | 0.848530i | \(0.322512\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −50.4865 | −2.24662 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.07040 | −0.136361 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.0502 | −0.933032 | −0.466516 | − | 0.884513i | \(-0.654491\pi\) | ||||
−0.466516 | + | 0.884513i | \(0.654491\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.83968 | −0.125620 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.34776 | 0.147807 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 56.0460 | 2.46968 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.5005 | 0.461813 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.75248 | −0.120821 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.2797 | −0.581795 | −0.290897 | − | 0.956754i | \(-0.593954\pi\) | ||||
−0.290897 | + | 0.956754i | \(0.593954\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.0330 | 1.53189 | 0.765944 | − | 0.642907i | \(-0.222272\pi\) | ||||
0.765944 | + | 0.642907i | \(0.222272\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 23.1237 | 1.00920 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.46892 | −0.107548 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7788 | −0.946906 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.3856 | −1.53560 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.852734 | −0.0369360 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 52.1880 | 2.25628 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −44.9516 | −1.93980 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.0767 | −0.476224 | −0.238112 | − | 0.971238i | \(-0.576529\pi\) | ||||
−0.238112 | + | 0.971238i | \(0.576529\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.8661 | −0.938365 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 36.9388 | 1.58228 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.4467 | −1.90040 | −0.950202 | − | 0.311634i | \(-0.899124\pi\) | ||||
−0.950202 | + | 0.311634i | \(0.899124\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −30.8316 | −1.31586 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.433193 | 0.0184547 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.33566 | 0.269420 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 115.752 | 4.91339 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.34468 | 0.0993473 | 0.0496736 | − | 0.998766i | \(-0.484182\pi\) | ||||
0.0496736 | + | 0.998766i | \(0.484182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.13797 | 0.0904263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.63580 | −0.237944 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.2348 | 1.06352 | 0.531760 | − | 0.846895i | \(-0.321531\pi\) | ||||
0.531760 | + | 0.846895i | \(0.321531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.8809 | −1.46745 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.0288 | −0.547158 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −39.5541 | −1.65819 | −0.829097 | − | 0.559105i | \(-0.811145\pi\) | ||||
−0.829097 | + | 0.559105i | \(0.811145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.28447 | 0.0537532 | 0.0268766 | − | 0.999639i | \(-0.491444\pi\) | ||||
0.0268766 | + | 0.999639i | \(0.491444\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.7773 | −0.617330 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.32238 | 0.347067 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.5395 | −0.605288 | −0.302644 | − | 0.953104i | \(-0.597869\pi\) | ||||
−0.302644 | + | 0.953104i | \(0.597869\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.59742 | −0.191062 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.51924 | 0.187490 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.45473 | −0.0602489 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 22.7524 | 0.940697 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.1511 | −1.32702 | −0.663510 | − | 0.748168i | \(-0.730934\pi\) | ||||
−0.663510 | + | 0.748168i | \(0.730934\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.427904 | 0.0176315 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 35.5355 | 1.46173 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.1241 | 1.27811 | 0.639057 | − | 0.769159i | \(-0.279325\pi\) | ||||
0.639057 | + | 0.769159i | \(0.279325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.49766 | 0.266378 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 46.4074 | 1.89933 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.8698 | 1.13873 | 0.569364 | − | 0.822085i | \(-0.307189\pi\) | ||||
0.569364 | + | 0.822085i | \(0.307189\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.7458 | −1.00940 | −0.504701 | − | 0.863294i | \(-0.668397\pi\) | ||||
−0.504701 | + | 0.863294i | \(0.668397\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.0096 | 0.407624 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.53994 | −0.143919 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.0137 | 1.05586 | 0.527931 | − | 0.849287i | \(-0.322968\pi\) | ||||
0.527931 | + | 0.849287i | \(0.322968\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.18097 | −0.169421 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.5005 | −0.424806 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.72789 | −0.190958 | −0.0954788 | − | 0.995431i | \(-0.530438\pi\) | ||||
−0.0954788 | + | 0.995431i | \(0.530438\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.26839 | 0.373738 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.5562 | 1.39118 | 0.695591 | − | 0.718438i | \(-0.255143\pi\) | ||||
0.695591 | + | 0.718438i | \(0.255143\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.3735 | 0.899268 | 0.449634 | − | 0.893213i | \(-0.351554\pi\) | ||||
0.449634 | + | 0.893213i | \(0.351554\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.6289 | −0.466652 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.3709 | 0.535692 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.93735 | −0.237494 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.976776 | 0.0390087 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.5478 | 0.779422 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.63999 | 0.304143 | 0.152072 | − | 0.988369i | \(-0.451406\pi\) | ||||
0.152072 | + | 0.988369i | \(0.451406\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.0471 | 0.757056 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.07135 | −0.359985 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.33098 | 0.171331 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.2348 | 1.07571 | 0.537855 | − | 0.843037i | \(-0.319235\pi\) | ||||
0.537855 | + | 0.843037i | \(0.319235\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.4951 | 1.47866 | 0.739331 | − | 0.673342i | \(-0.235142\pi\) | ||||
0.739331 | + | 0.673342i | \(0.235142\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.2376 | −0.914980 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.2852 | 1.15132 | 0.575660 | − | 0.817689i | \(-0.304745\pi\) | ||||
0.575660 | + | 0.817689i | \(0.304745\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.50546 | −0.216108 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.12992 | −0.161864 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.97367 | 0.155502 | 0.0777509 | − | 0.996973i | \(-0.475226\pi\) | ||||
0.0777509 | + | 0.996973i | \(0.475226\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.6294 | 0.884204 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.2516 | 0.712063 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.6580 | −1.27218 | −0.636088 | − | 0.771617i | \(-0.719448\pi\) | ||||
−0.636088 | + | 0.771617i | \(0.719448\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.9618 | 1.51544 | 0.757718 | − | 0.652582i | \(-0.226314\pi\) | ||||
0.757718 | + | 0.652582i | \(0.226314\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.63580 | 0.218877 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.12615 | −0.0436702 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.50476 | −0.0582645 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 42.8899 | 1.65822 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.79694 | −0.185184 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.12969 | −0.313376 | −0.156688 | − | 0.987648i | \(-0.550082\pi\) | ||||
−0.156688 | + | 0.987648i | \(0.550082\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −79.2530 | −3.05045 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.3465 | 0.666682 | 0.333341 | − | 0.942806i | \(-0.391824\pi\) | ||||
0.333341 | + | 0.942806i | \(0.391824\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.08525 | 0.118401 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.0733 | 0.500971 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.1608 | 1.00101 | 0.500507 | − | 0.865733i | \(-0.333147\pi\) | ||||
0.500507 | + | 0.865733i | \(0.333147\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.9372 | −0.685344 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.48761 | −0.285670 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.45473 | 0.0554209 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.7575 | −1.39832 | −0.699161 | − | 0.714964i | \(-0.746443\pi\) | ||||
−0.699161 | + | 0.714964i | \(0.746443\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.42735 | −0.244155 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 45.0178 | 1.70762 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.56522 | 0.0592869 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −73.9001 | −2.79516 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.2156 | 1.85885 | 0.929424 | − | 0.369014i | \(-0.120305\pi\) | ||||
0.929424 | + | 0.369014i | \(0.120305\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.38795 | −0.127779 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 114.131 | 4.29841 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.2620 | −0.536376 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.0710 | −1.58001 | −0.790004 | − | 0.613102i | \(-0.789922\pi\) | ||||
−0.790004 | + | 0.613102i | \(0.789922\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −40.7215 | −1.52718 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.48639 | −0.0556656 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.53994 | 0.132386 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −36.9629 | −1.38040 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.9972 | −1.15600 | −0.578001 | − | 0.816036i | \(-0.696167\pi\) | ||||
−0.578001 | + | 0.816036i | \(0.696167\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.8325 | 0.589632 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −46.9852 | −1.74740 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.2552 | −0.380869 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.4255 | −1.79600 | −0.898002 | − | 0.439991i | \(-0.854981\pi\) | ||||
−0.898002 | + | 0.439991i | \(0.854981\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.1919 | −0.488588 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.92430 | −0.145145 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.8393 | 1.47150 | 0.735748 | − | 0.677255i | \(-0.236831\pi\) | ||||
0.735748 | + | 0.677255i | \(0.236831\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.8690 | 0.400910 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.55735 | 0.0573657 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.50888 | −0.202647 | −0.101324 | − | 0.994854i | \(-0.532308\pi\) | ||||
−0.101324 | + | 0.994854i | \(0.532308\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.976776 | −0.0358828 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.63743 | 0.170131 | 0.0850653 | − | 0.996375i | \(-0.472890\pi\) | ||||
0.0850653 | + | 0.996375i | \(0.472890\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 47.6975 | 1.74750 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29.0467 | −1.06276 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.7426 | 0.538684 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0160 | 0.438469 | 0.219235 | − | 0.975672i | \(-0.429644\pi\) | ||||
0.219235 | + | 0.975672i | \(0.429644\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.45712 | 0.0895424 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −82.4852 | −3.00194 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.2755 | −1.64557 | −0.822783 | − | 0.568355i | \(-0.807580\pi\) | ||||
−0.822783 | + | 0.568355i | \(0.807580\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.39297 | −0.123157 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.6581 | −0.603854 | −0.301927 | − | 0.953331i | \(-0.597630\pi\) | ||||
−0.301927 | + | 0.953331i | \(0.597630\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.4349 | 0.377768 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −41.7627 | −1.50993 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.50546 | 0.198791 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.4831 | −1.24349 | −0.621746 | − | 0.783219i | \(-0.713576\pi\) | ||||
−0.621746 | + | 0.783219i | \(0.713576\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −59.4080 | −2.13953 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.4753 | 0.484672 | 0.242336 | − | 0.970192i | \(-0.422086\pi\) | ||||
0.242336 | + | 0.970192i | \(0.422086\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.1300 | −0.363880 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32.6988 | 1.17306 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.271278 | −0.00971953 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.673836 | 0.0241117 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.3296 | 0.512100 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.8841 | 0.816769 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.7684 | 1.41759 | 0.708795 | − | 0.705414i | \(-0.249239\pi\) | ||||
0.708795 | + | 0.705414i | \(0.249239\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −59.6902 | −2.12503 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.85354 | −0.350352 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.79694 | 0.170344 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.8115 | −0.560777 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.5289 | 1.50645 | 0.753226 | − | 0.657762i | \(-0.228497\pi\) | ||||
0.753226 | + | 0.657762i | \(0.228497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.2740 | 0.681866 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −85.9393 | −3.03651 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.83968 | 0.100210 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.91184 | 0.137874 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −52.8491 | −1.86038 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.59554 | 0.0560963 | 0.0280481 | − | 0.999607i | \(-0.491071\pi\) | ||||
0.0280481 | + | 0.999607i | \(0.491071\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.0024 | 0.842837 | 0.421418 | − | 0.906866i | \(-0.361532\pi\) | ||||
0.421418 | + | 0.906866i | \(0.361532\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −32.2786 | −1.13206 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 77.9795 | 2.73150 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.680144 | 0.0237952 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.42735 | 0.224590 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.6833 | 1.17556 | 0.587778 | − | 0.809022i | \(-0.300003\pi\) | ||||
0.587778 | + | 0.809022i | \(0.300003\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.5993 | 0.439185 | 0.219592 | − | 0.975592i | \(-0.429527\pi\) | ||||
0.219592 | + | 0.975592i | \(0.429527\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −23.1237 | −0.805064 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.2424 | −0.982084 | −0.491042 | − | 0.871136i | \(-0.663384\pi\) | ||||
−0.491042 | + | 0.871136i | \(0.663384\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.7396 | 1.06763 | 0.533816 | − | 0.845601i | \(-0.320758\pi\) | ||||
0.533816 | + | 0.845601i | \(0.320758\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −78.7299 | −2.73111 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.83553 | 0.0635973 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.4060 | 1.57134 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.1547 | 0.489258 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.8066 | 1.02904 | 0.514518 | − | 0.857479i | \(-0.327971\pi\) | ||||
0.514518 | + | 0.857479i | \(0.327971\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.1458 | −0.936061 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −46.3247 | −1.59551 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.53994 | −0.121778 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 39.2232 | 1.34614 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.7685 | 0.403420 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.99204 | 0.170924 | 0.0854620 | − | 0.996341i | \(-0.472763\pi\) | ||||
0.0854620 | + | 0.996341i | \(0.472763\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.23816 | 0.247540 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.1557 | −0.961779 | −0.480889 | − | 0.876781i | \(-0.659686\pi\) | ||||
−0.480889 | + | 0.876781i | \(0.659686\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −51.0735 | −1.74260 | −0.871302 | − | 0.490747i | \(-0.836724\pi\) | ||||
−0.871302 | + | 0.490747i | \(0.836724\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.61824 | 0.0892292 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.1643 | 0.958723 | 0.479362 | − | 0.877617i | \(-0.340868\pi\) | ||||
0.479362 | + | 0.877617i | \(0.340868\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.17340 | −0.107899 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 41.8521 | 1.42137 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.33566 | −0.214923 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.55735 | −0.0527687 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.8300 | −0.671144 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.96018 | 0.302909 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.4567 | −1.16352 | −0.581760 | − | 0.813361i | \(-0.697636\pi\) | ||||
−0.581760 | + | 0.813361i | \(0.697636\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.6726 | −0.461164 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.8794 | −0.770828 | −0.385414 | − | 0.922744i | \(-0.625941\pi\) | ||||
−0.385414 | + | 0.922744i | \(0.625941\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.3514 | −0.348353 | −0.174176 | − | 0.984714i | \(-0.555726\pi\) | ||||
−0.174176 | + | 0.984714i | \(0.555726\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −59.8390 | −2.01147 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −57.3639 | −1.92609 | −0.963046 | − | 0.269337i | \(-0.913195\pi\) | ||||
−0.963046 | + | 0.269337i | \(0.913195\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.56257 | −0.0859459 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.0288 | 0.436481 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.34050 | −0.111786 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −51.8258 | −1.73234 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.39297 | 0.113288 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.83159 | 0.0610870 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.67020 | −0.0889574 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.56441 | −0.218450 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.2100 | −0.838008 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.9637 | 0.629681 | 0.314840 | − | 0.949145i | \(-0.398049\pi\) | ||||
0.314840 | + | 0.949145i | \(0.398049\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 91.6667 | 3.04039 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.91143 | −0.162723 | −0.0813615 | − | 0.996685i | \(-0.525927\pi\) | ||||
−0.0813615 | + | 0.996685i | \(0.525927\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.51924 | −0.149565 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −52.1381 | −1.72363 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.39260 | 0.211102 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.8744 | −0.589622 | −0.294811 | − | 0.955556i | \(-0.595257\pi\) | ||||
−0.294811 | + | 0.955556i | \(0.595257\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.97833 | 0.295846 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.673836 | −0.0221796 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 80.2046 | 2.63711 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −101.761 | −3.34227 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.43045 | −0.210976 | −0.105488 | − | 0.994421i | \(-0.533640\pi\) | ||||
−0.105488 | + | 0.994421i | \(0.533640\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.318127 | −0.0104262 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.7863 | −0.484083 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.49766 | −0.212496 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.8778 | 0.584041 | 0.292021 | − | 0.956412i | \(-0.405672\pi\) | ||||
0.292021 | + | 0.956412i | \(0.405672\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35.7242 | 1.16582 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.3162 | 0.564493 | 0.282246 | − | 0.959342i | \(-0.408920\pi\) | ||||
0.282246 | + | 0.959342i | \(0.408920\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.942322 | 0.0306862 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −37.2520 | −1.21181 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.4657 | 1.41245 | 0.706223 | − | 0.707990i | \(-0.250398\pi\) | ||||
0.706223 | + | 0.707990i | \(0.250398\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.83968 | −0.0921798 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.74533 | 0.0565964 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.13801 | 0.101650 | 0.0508251 | − | 0.998708i | \(-0.483815\pi\) | ||||
0.0508251 | + | 0.998708i | \(0.483815\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.0371 | −0.551308 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.18097 | 0.135151 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.06708 | −0.163625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1908 | −0.941638 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −94.7561 | −3.05347 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.30048 | −0.170628 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.4418 | 1.75073 | 0.875366 | − | 0.483462i | \(-0.160621\pi\) | ||||
0.875366 | + | 0.483462i | \(0.160621\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.79290 | 0.0575962 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.2136 | 1.64352 | 0.821761 | − | 0.569832i | \(-0.192992\pi\) | ||||
0.821761 | + | 0.569832i | \(0.192992\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.7171 | 0.407692 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.1237 | 0.740551 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.2400 | 0.967462 | 0.483731 | − | 0.875217i | \(-0.339281\pi\) | ||||
0.483731 | + | 0.875217i | \(0.339281\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.3709 | −0.427335 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −67.0686 | −2.14134 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.54306 | −0.208691 | −0.104346 | − | 0.994541i | \(-0.533275\pi\) | ||||
−0.104346 | + | 0.994541i | \(0.533275\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 40.9697 | 1.30540 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 32.2409 | 1.02624 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.36258 | −0.0751256 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.3945 | −1.66437 | −0.832183 | − | 0.554501i | \(-0.812909\pi\) | ||||
−0.832183 | + | 0.554501i | \(0.812909\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.5008 | 0.333232 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 53.5043 | 1.69620 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.6151 | 1.38130 | 0.690652 | − | 0.723188i | \(-0.257324\pi\) | ||||
0.690652 | + | 0.723188i | \(0.257324\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −112.070 | −3.54575 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8008.2.a.n.1.1 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.n.1.1 | ✓ | 9 | 1.1 | even | 1 | trivial |