Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3762,2,Mod(1,3762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3762, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3762.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: | \(30.0397212404\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - 6x - 3 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 418) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.523976\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3762.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.72545 | −1.21886 | −0.609429 | − | 0.792841i | \(-0.708601\pi\) | ||||
−0.609429 | + | 0.792841i | \(0.708601\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.67750 | −1.76793 | −0.883964 | − | 0.467556i | \(-0.845135\pi\) | ||||
−0.883964 | + | 0.467556i | \(0.845135\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.72545 | −0.861863 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.67750 | −0.742604 | −0.371302 | − | 0.928512i | \(-0.621089\pi\) | ||||
−0.371302 | + | 0.928512i | \(0.621089\pi\) | |||||||
\(14\) | −4.67750 | −1.25011 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.201472 | −0.0488642 | −0.0244321 | − | 0.999701i | \(-0.507778\pi\) | ||||
−0.0244321 | + | 0.999701i | \(0.507778\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −2.72545 | −0.609429 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 1.79853 | 0.375019 | 0.187509 | − | 0.982263i | \(-0.439958\pi\) | ||||
0.187509 | + | 0.982263i | \(0.439958\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.42807 | 0.485614 | ||||||||
\(26\) | −2.67750 | −0.525100 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.67750 | −0.883964 | ||||||||
\(29\) | 4.92692 | 0.914906 | 0.457453 | − | 0.889234i | \(-0.348762\pi\) | ||||
0.457453 | + | 0.889234i | \(0.348762\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.57193 | −0.461932 | −0.230966 | − | 0.972962i | \(-0.574189\pi\) | ||||
−0.230966 | + | 0.972962i | \(0.574189\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.201472 | −0.0345522 | ||||||||
\(35\) | 12.7483 | 2.15485 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.40294 | 0.723840 | 0.361920 | − | 0.932209i | \(-0.382121\pi\) | ||||
0.361920 | + | 0.932209i | \(0.382121\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.72545 | −0.430931 | ||||||||
\(41\) | −4.97487 | −0.776945 | −0.388472 | − | 0.921460i | \(-0.626997\pi\) | ||||
−0.388472 | + | 0.921460i | \(0.626997\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.7734 | −1.79543 | −0.897713 | − | 0.440580i | \(-0.854773\pi\) | ||||
−0.897713 | + | 0.440580i | \(0.854773\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.79853 | 0.265178 | ||||||||
\(47\) | 12.4989 | 1.82314 | 0.911572 | − | 0.411140i | \(-0.134869\pi\) | ||||
0.911572 | + | 0.411140i | \(0.134869\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.8790 | 2.12557 | ||||||||
\(50\) | 2.42807 | 0.343381 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.67750 | −0.371302 | ||||||||
\(53\) | 4.10557 | 0.563943 | 0.281971 | − | 0.959423i | \(-0.409012\pi\) | ||||
0.281971 | + | 0.959423i | \(0.409012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.72545 | −0.367499 | ||||||||
\(56\) | −4.67750 | −0.625057 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.92692 | 0.646936 | ||||||||
\(59\) | 5.24943 | 0.683417 | 0.341708 | − | 0.939806i | \(-0.388994\pi\) | ||||
0.341708 | + | 0.939806i | \(0.388994\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.59706 | 0.204482 | 0.102241 | − | 0.994760i | \(-0.467399\pi\) | ||||
0.102241 | + | 0.994760i | \(0.467399\pi\) | |||||||
\(62\) | −2.57193 | −0.326635 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.29738 | 0.905128 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.08044 | 1.10935 | 0.554676 | − | 0.832066i | \(-0.312842\pi\) | ||||
0.554676 | + | 0.832066i | \(0.312842\pi\) | |||||||
\(68\) | −0.201472 | −0.0244321 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 12.7483 | 1.52371 | ||||||||
\(71\) | −12.8214 | −1.52161 | −0.760807 | − | 0.648978i | \(-0.775197\pi\) | ||||
−0.760807 | + | 0.648978i | \(0.775197\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.20147 | 0.257663 | 0.128831 | − | 0.991667i | \(-0.458877\pi\) | ||||
0.128831 | + | 0.991667i | \(0.458877\pi\) | |||||||
\(74\) | 4.40294 | 0.511832 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −4.67750 | −0.533050 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.8538 | 1.33366 | 0.666831 | − | 0.745209i | \(-0.267650\pi\) | ||||
0.666831 | + | 0.745209i | \(0.267650\pi\) | |||||||
\(80\) | −2.72545 | −0.304714 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.97487 | −0.549383 | ||||||||
\(83\) | 13.6775 | 1.50130 | 0.750650 | − | 0.660700i | \(-0.229740\pi\) | ||||
0.750650 | + | 0.660700i | \(0.229740\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.549103 | 0.0595585 | ||||||||
\(86\) | −11.7734 | −1.26956 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 5.45090 | 0.577794 | 0.288897 | − | 0.957360i | \(-0.406711\pi\) | ||||
0.288897 | + | 0.957360i | \(0.406711\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.5240 | 1.31287 | ||||||||
\(92\) | 1.79853 | 0.187509 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.4989 | 1.28916 | ||||||||
\(95\) | 2.72545 | 0.279625 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.8059 | 1.70638 | 0.853190 | − | 0.521601i | \(-0.174665\pi\) | ||||
0.853190 | + | 0.521601i | \(0.174665\pi\) | |||||||
\(98\) | 14.8790 | 1.50300 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.42807 | 0.242807 | ||||||||
\(101\) | −7.45090 | −0.741392 | −0.370696 | − | 0.928754i | \(-0.620881\pi\) | ||||
−0.370696 | + | 0.928754i | \(0.620881\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.4834 | −1.42709 | −0.713545 | − | 0.700609i | \(-0.752912\pi\) | ||||
−0.713545 | + | 0.700609i | \(0.752912\pi\) | |||||||
\(104\) | −2.67750 | −0.262550 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.10557 | 0.398768 | ||||||||
\(107\) | −1.15352 | −0.111515 | −0.0557575 | − | 0.998444i | \(-0.517757\pi\) | ||||
−0.0557575 | + | 0.998444i | \(0.517757\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.55646 | −0.915343 | −0.457672 | − | 0.889121i | \(-0.651316\pi\) | ||||
−0.457672 | + | 0.889121i | \(0.651316\pi\) | |||||||
\(110\) | −2.72545 | −0.259861 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.67750 | −0.441982 | ||||||||
\(113\) | 8.00000 | 0.752577 | 0.376288 | − | 0.926503i | \(-0.377200\pi\) | ||||
0.376288 | + | 0.926503i | \(0.377200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.90179 | −0.457095 | ||||||||
\(116\) | 4.92692 | 0.457453 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.24943 | 0.483249 | ||||||||
\(119\) | 0.942386 | 0.0863884 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.59706 | 0.144591 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.57193 | −0.230966 | ||||||||
\(125\) | 7.00966 | 0.626963 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.75794 | 0.510934 | 0.255467 | − | 0.966818i | \(-0.417771\pi\) | ||||
0.255467 | + | 0.966818i | \(0.417771\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.29738 | 0.640022 | ||||||||
\(131\) | −1.42807 | −0.124771 | −0.0623856 | − | 0.998052i | \(-0.519871\pi\) | ||||
−0.0623856 | + | 0.998052i | \(0.519871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.67750 | 0.405590 | ||||||||
\(134\) | 9.08044 | 0.784431 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.201472 | −0.0172761 | ||||||||
\(137\) | 14.5313 | 1.24150 | 0.620748 | − | 0.784010i | \(-0.286829\pi\) | ||||
0.620748 | + | 0.784010i | \(0.286829\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.1763 | 1.37206 | 0.686030 | − | 0.727573i | \(-0.259352\pi\) | ||||
0.686030 | + | 0.727573i | \(0.259352\pi\) | |||||||
\(140\) | 12.7483 | 1.07743 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.8214 | −1.07594 | ||||||||
\(143\) | −2.67750 | −0.223903 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.4281 | −1.11514 | ||||||||
\(146\) | 2.20147 | 0.182195 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.40294 | 0.361920 | ||||||||
\(149\) | −6.30704 | −0.516693 | −0.258346 | − | 0.966052i | \(-0.583178\pi\) | ||||
−0.258346 | + | 0.966052i | \(0.583178\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.498850 | 0.0405959 | 0.0202979 | − | 0.999794i | \(-0.493539\pi\) | ||||
0.0202979 | + | 0.999794i | \(0.493539\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.67750 | −0.376923 | ||||||||
\(155\) | 7.00966 | 0.563030 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.6272 | −1.08757 | −0.543786 | − | 0.839224i | \(-0.683010\pi\) | ||||
−0.543786 | + | 0.839224i | \(0.683010\pi\) | |||||||
\(158\) | 11.8538 | 0.943041 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.72545 | −0.215466 | ||||||||
\(161\) | −8.41261 | −0.663006 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.9497 | 1.24928 | 0.624640 | − | 0.780913i | \(-0.285246\pi\) | ||||
0.624640 | + | 0.780913i | \(0.285246\pi\) | |||||||
\(164\) | −4.97487 | −0.388472 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.6775 | 1.06158 | ||||||||
\(167\) | −18.8059 | −1.45524 | −0.727622 | − | 0.685979i | \(-0.759374\pi\) | ||||
−0.727622 | + | 0.685979i | \(0.759374\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.83102 | −0.448540 | ||||||||
\(170\) | 0.549103 | 0.0421142 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.7734 | −0.897713 | ||||||||
\(173\) | 3.22430 | 0.245139 | 0.122569 | − | 0.992460i | \(-0.460887\pi\) | ||||
0.122569 | + | 0.992460i | \(0.460887\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.3573 | −0.858531 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.45090 | 0.408562 | ||||||||
\(179\) | −13.3778 | −0.999905 | −0.499953 | − | 0.866053i | \(-0.666649\pi\) | ||||
−0.499953 | + | 0.866053i | \(0.666649\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.9497 | 1.18554 | 0.592768 | − | 0.805373i | \(-0.298035\pi\) | ||||
0.592768 | + | 0.805373i | \(0.298035\pi\) | |||||||
\(182\) | 12.5240 | 0.928339 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.79853 | 0.132589 | ||||||||
\(185\) | −12.0000 | −0.882258 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.201472 | −0.0147331 | ||||||||
\(188\) | 12.4989 | 0.911572 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.72545 | 0.197725 | ||||||||
\(191\) | 24.0553 | 1.74058 | 0.870291 | − | 0.492538i | \(-0.163931\pi\) | ||||
0.870291 | + | 0.492538i | \(0.163931\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0325 | 0.938099 | 0.469050 | − | 0.883172i | \(-0.344597\pi\) | ||||
0.469050 | + | 0.883172i | \(0.344597\pi\) | |||||||
\(194\) | 16.8059 | 1.20659 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.8790 | 1.06278 | ||||||||
\(197\) | 5.59706 | 0.398774 | 0.199387 | − | 0.979921i | \(-0.436105\pi\) | ||||
0.199387 | + | 0.979921i | \(0.436105\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.39558 | −0.524259 | −0.262129 | − | 0.965033i | \(-0.584425\pi\) | ||||
−0.262129 | + | 0.965033i | \(0.584425\pi\) | |||||||
\(200\) | 2.42807 | 0.171691 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.45090 | −0.524243 | ||||||||
\(203\) | −23.0457 | −1.61749 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.5588 | 0.946985 | ||||||||
\(206\) | −14.4834 | −1.00911 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.67750 | −0.185651 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.2974 | −0.984272 | −0.492136 | − | 0.870518i | \(-0.663784\pi\) | ||||
−0.492136 | + | 0.870518i | \(0.663784\pi\) | |||||||
\(212\) | 4.10557 | 0.281971 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.15352 | −0.0788530 | ||||||||
\(215\) | 32.0878 | 2.18837 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0302 | 0.816662 | ||||||||
\(218\) | −9.55646 | −0.647245 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.72545 | −0.183750 | ||||||||
\(221\) | 0.539441 | 0.0362868 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.402945 | −0.0269832 | −0.0134916 | − | 0.999909i | \(-0.504295\pi\) | ||||
−0.0134916 | + | 0.999909i | \(0.504295\pi\) | |||||||
\(224\) | −4.67750 | −0.312528 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.00000 | 0.532152 | ||||||||
\(227\) | 21.0074 | 1.39431 | 0.697154 | − | 0.716922i | \(-0.254449\pi\) | ||||
0.697154 | + | 0.716922i | \(0.254449\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.3299 | −0.946944 | −0.473472 | − | 0.880809i | \(-0.657000\pi\) | ||||
−0.473472 | + | 0.880809i | \(0.657000\pi\) | |||||||
\(230\) | −4.90179 | −0.323215 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.92692 | 0.323468 | ||||||||
\(233\) | 24.4029 | 1.59869 | 0.799345 | − | 0.600872i | \(-0.205180\pi\) | ||||
0.799345 | + | 0.600872i | \(0.205180\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −34.0650 | −2.22215 | ||||||||
\(236\) | 5.24943 | 0.341708 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.942386 | 0.0610858 | ||||||||
\(239\) | 12.6849 | 0.820515 | 0.410258 | − | 0.911970i | \(-0.365439\pi\) | ||||
0.410258 | + | 0.911970i | \(0.365439\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.9343 | −1.54174 | −0.770871 | − | 0.636991i | \(-0.780179\pi\) | ||||
−0.770871 | + | 0.636991i | \(0.780179\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.59706 | 0.102241 | ||||||||
\(245\) | −40.5519 | −2.59076 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.67750 | 0.170365 | ||||||||
\(248\) | −2.57193 | −0.163318 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.00966 | 0.443330 | ||||||||
\(251\) | −18.4989 | −1.16764 | −0.583819 | − | 0.811884i | \(-0.698442\pi\) | ||||
−0.583819 | + | 0.811884i | \(0.698442\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.79853 | 0.113072 | ||||||||
\(254\) | 5.75794 | 0.361285 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −27.7579 | −1.73149 | −0.865746 | − | 0.500483i | \(-0.833156\pi\) | ||||
−0.865746 | + | 0.500483i | \(0.833156\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.5948 | −1.27970 | ||||||||
\(260\) | 7.29738 | 0.452564 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.42807 | −0.0882265 | ||||||||
\(263\) | −20.2723 | −1.25004 | −0.625020 | − | 0.780608i | \(-0.714909\pi\) | ||||
−0.625020 | + | 0.780608i | \(0.714909\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.1895 | −0.687366 | ||||||||
\(266\) | 4.67750 | 0.286796 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.08044 | 0.554676 | ||||||||
\(269\) | 15.6427 | 0.953753 | 0.476876 | − | 0.878970i | \(-0.341769\pi\) | ||||
0.476876 | + | 0.878970i | \(0.341769\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.3395 | −0.749573 | −0.374786 | − | 0.927111i | \(-0.622284\pi\) | ||||
−0.374786 | + | 0.927111i | \(0.622284\pi\) | |||||||
\(272\) | −0.201472 | −0.0122161 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.5313 | 0.877870 | ||||||||
\(275\) | 2.42807 | 0.146418 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.49885 | 0.510646 | 0.255323 | − | 0.966856i | \(-0.417818\pi\) | ||||
0.255323 | + | 0.966856i | \(0.417818\pi\) | |||||||
\(278\) | 16.1763 | 0.970193 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.7483 | 0.761855 | ||||||||
\(281\) | 7.12839 | 0.425244 | 0.212622 | − | 0.977134i | \(-0.431800\pi\) | ||||
0.212622 | + | 0.977134i | \(0.431800\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.5240 | 0.685029 | 0.342515 | − | 0.939512i | \(-0.388721\pi\) | ||||
0.342515 | + | 0.939512i | \(0.388721\pi\) | |||||||
\(284\) | −12.8214 | −0.760807 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.67750 | −0.158324 | ||||||||
\(287\) | 23.2700 | 1.37358 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9594 | −0.997612 | ||||||||
\(290\) | −13.4281 | −0.788523 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.20147 | 0.128831 | ||||||||
\(293\) | −10.6775 | −0.623786 | −0.311893 | − | 0.950117i | \(-0.600963\pi\) | ||||
−0.311893 | + | 0.950117i | \(0.600963\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.3070 | −0.832988 | ||||||||
\(296\) | 4.40294 | 0.255916 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.30704 | −0.365357 | ||||||||
\(299\) | −4.81555 | −0.278490 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 55.0700 | 3.17418 | ||||||||
\(302\) | 0.498850 | 0.0287056 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −4.35269 | −0.249234 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.2568 | −1.72685 | −0.863423 | − | 0.504481i | \(-0.831684\pi\) | ||||
−0.863423 | + | 0.504481i | \(0.831684\pi\) | |||||||
\(308\) | −4.67750 | −0.266525 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.00966 | 0.398122 | ||||||||
\(311\) | −8.79623 | −0.498788 | −0.249394 | − | 0.968402i | \(-0.580231\pi\) | ||||
−0.249394 | + | 0.968402i | \(0.580231\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.1860 | 0.575747 | 0.287874 | − | 0.957668i | \(-0.407052\pi\) | ||||
0.287874 | + | 0.957668i | \(0.407052\pi\) | |||||||
\(314\) | −13.6272 | −0.769030 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.8538 | 0.666831 | ||||||||
\(317\) | 12.0097 | 0.674530 | 0.337265 | − | 0.941410i | \(-0.390498\pi\) | ||||
0.337265 | + | 0.941410i | \(0.390498\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.92692 | 0.275855 | ||||||||
\(320\) | −2.72545 | −0.152357 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.41261 | −0.468816 | ||||||||
\(323\) | 0.201472 | 0.0112102 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.50115 | −0.360619 | ||||||||
\(326\) | 15.9497 | 0.883375 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.97487 | −0.274691 | ||||||||
\(329\) | −58.4633 | −3.22319 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.1667 | 1.43825 | 0.719126 | − | 0.694880i | \(-0.244543\pi\) | ||||
0.719126 | + | 0.694880i | \(0.244543\pi\) | |||||||
\(332\) | 13.6775 | 0.750650 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.8059 | −1.02901 | ||||||||
\(335\) | −24.7483 | −1.35214 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.3778 | 0.946630 | 0.473315 | − | 0.880893i | \(-0.343057\pi\) | ||||
0.473315 | + | 0.880893i | \(0.343057\pi\) | |||||||
\(338\) | −5.83102 | −0.317165 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.549103 | 0.0297793 | ||||||||
\(341\) | −2.57193 | −0.139278 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −36.8538 | −1.98992 | ||||||||
\(344\) | −11.7734 | −0.634779 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.22430 | 0.173339 | ||||||||
\(347\) | 12.4029 | 0.665825 | 0.332912 | − | 0.942958i | \(-0.391969\pi\) | ||||
0.332912 | + | 0.942958i | \(0.391969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.8036 | −1.27418 | −0.637088 | − | 0.770791i | \(-0.719861\pi\) | ||||
−0.637088 | + | 0.770791i | \(0.719861\pi\) | |||||||
\(350\) | −11.3573 | −0.607073 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 24.2664 | 1.29157 | 0.645786 | − | 0.763518i | \(-0.276530\pi\) | ||||
0.645786 | + | 0.763518i | \(0.276530\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 34.9439 | 1.85463 | ||||||||
\(356\) | 5.45090 | 0.288897 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.3778 | −0.707040 | ||||||||
\(359\) | −20.3395 | −1.07348 | −0.536740 | − | 0.843748i | \(-0.680344\pi\) | ||||
−0.536740 | + | 0.843748i | \(0.680344\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 15.9497 | 0.838300 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.5240 | 0.656435 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.0170 | −1.20148 | −0.600739 | − | 0.799445i | \(-0.705127\pi\) | ||||
−0.600739 | + | 0.799445i | \(0.705127\pi\) | |||||||
\(368\) | 1.79853 | 0.0937547 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.0000 | −0.623850 | ||||||||
\(371\) | −19.2038 | −0.997010 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.5890 | −0.962499 | −0.481250 | − | 0.876584i | \(-0.659817\pi\) | ||||
−0.481250 | + | 0.876584i | \(0.659817\pi\) | |||||||
\(374\) | −0.201472 | −0.0104179 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.4989 | 0.644579 | ||||||||
\(377\) | −13.1918 | −0.679413 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.5816 | −0.543540 | −0.271770 | − | 0.962362i | \(-0.587609\pi\) | ||||
−0.271770 | + | 0.962362i | \(0.587609\pi\) | |||||||
\(380\) | 2.72545 | 0.139813 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 24.0553 | 1.23078 | ||||||||
\(383\) | 26.0878 | 1.33302 | 0.666512 | − | 0.745494i | \(-0.267786\pi\) | ||||
0.666512 | + | 0.745494i | \(0.267786\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.7483 | 0.649712 | ||||||||
\(386\) | 13.0325 | 0.663336 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.8059 | 0.853190 | ||||||||
\(389\) | 9.46636 | 0.479964 | 0.239982 | − | 0.970777i | \(-0.422859\pi\) | ||||
0.239982 | + | 0.970777i | \(0.422859\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.362354 | −0.0183250 | ||||||||
\(392\) | 14.8790 | 0.751501 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.59706 | 0.281976 | ||||||||
\(395\) | −32.3070 | −1.62554 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.1667 | −1.26308 | −0.631540 | − | 0.775343i | \(-0.717577\pi\) | ||||
−0.631540 | + | 0.775343i | \(0.717577\pi\) | |||||||
\(398\) | −7.39558 | −0.370707 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.42807 | 0.121404 | ||||||||
\(401\) | 16.0650 | 0.802247 | 0.401123 | − | 0.916024i | \(-0.368620\pi\) | ||||
0.401123 | + | 0.916024i | \(0.368620\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.88633 | 0.343033 | ||||||||
\(404\) | −7.45090 | −0.370696 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −23.0457 | −1.14374 | ||||||||
\(407\) | 4.40294 | 0.218246 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.5313 | −0.965763 | −0.482881 | − | 0.875686i | \(-0.660410\pi\) | ||||
−0.482881 | + | 0.875686i | \(0.660410\pi\) | |||||||
\(410\) | 13.5588 | 0.669620 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.4834 | −0.713545 | ||||||||
\(413\) | −24.5542 | −1.20823 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −37.2773 | −1.82987 | ||||||||
\(416\) | −2.67750 | −0.131275 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.00000 | −0.0489116 | ||||||||
\(419\) | −24.9018 | −1.21653 | −0.608266 | − | 0.793733i | \(-0.708135\pi\) | ||||
−0.608266 | + | 0.793733i | \(0.708135\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.6044 | 1.29662 | 0.648310 | − | 0.761377i | \(-0.275476\pi\) | ||||
0.648310 | + | 0.761377i | \(0.275476\pi\) | |||||||
\(422\) | −14.2974 | −0.695985 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.10557 | 0.199384 | ||||||||
\(425\) | −0.489189 | −0.0237292 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.47022 | −0.361509 | ||||||||
\(428\) | −1.15352 | −0.0557575 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 32.0878 | 1.54741 | ||||||||
\(431\) | 32.5948 | 1.57003 | 0.785017 | − | 0.619474i | \(-0.212654\pi\) | ||||
0.785017 | + | 0.619474i | \(0.212654\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.7386 | 0.948577 | 0.474289 | − | 0.880369i | \(-0.342705\pi\) | ||||
0.474289 | + | 0.880369i | \(0.342705\pi\) | |||||||
\(434\) | 12.0302 | 0.577468 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.55646 | −0.457672 | ||||||||
\(437\) | −1.79853 | −0.0860352 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.4029 | −1.16469 | −0.582345 | − | 0.812942i | \(-0.697865\pi\) | ||||
−0.582345 | + | 0.812942i | \(0.697865\pi\) | |||||||
\(440\) | −2.72545 | −0.129931 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.539441 | 0.0256586 | ||||||||
\(443\) | 16.5948 | 0.788441 | 0.394220 | − | 0.919016i | \(-0.371015\pi\) | ||||
0.394220 | + | 0.919016i | \(0.371015\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.8561 | −0.704249 | ||||||||
\(446\) | −0.402945 | −0.0190800 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.67750 | −0.220991 | ||||||||
\(449\) | 20.9520 | 0.988788 | 0.494394 | − | 0.869238i | \(-0.335390\pi\) | ||||
0.494394 | + | 0.869238i | \(0.335390\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.97487 | −0.234258 | ||||||||
\(452\) | 8.00000 | 0.376288 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.0074 | 0.985924 | ||||||||
\(455\) | −34.1335 | −1.60020 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.3144 | 1.09060 | 0.545301 | − | 0.838240i | \(-0.316415\pi\) | ||||
0.545301 | + | 0.838240i | \(0.316415\pi\) | |||||||
\(458\) | −14.3299 | −0.669591 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.90179 | −0.228547 | ||||||||
\(461\) | −20.8059 | −0.969027 | −0.484513 | − | 0.874784i | \(-0.661003\pi\) | ||||
−0.484513 | + | 0.874784i | \(0.661003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.29002 | −0.431744 | −0.215872 | − | 0.976422i | \(-0.569259\pi\) | ||||
−0.215872 | + | 0.976422i | \(0.569259\pi\) | |||||||
\(464\) | 4.92692 | 0.228727 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.4029 | 1.13044 | ||||||||
\(467\) | −12.0457 | −0.557406 | −0.278703 | − | 0.960377i | \(-0.589905\pi\) | ||||
−0.278703 | + | 0.960377i | \(0.589905\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −42.4737 | −1.96125 | ||||||||
\(470\) | −34.0650 | −1.57130 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.24943 | 0.241624 | ||||||||
\(473\) | −11.7734 | −0.541342 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.42807 | −0.111408 | ||||||||
\(476\) | 0.942386 | 0.0431942 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.6849 | 0.580192 | ||||||||
\(479\) | −0.188307 | −0.00860396 | −0.00430198 | − | 0.999991i | \(-0.501369\pi\) | ||||
−0.00430198 | + | 0.999991i | \(0.501369\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.7889 | −0.537526 | ||||||||
\(482\) | −23.9343 | −1.09018 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −45.8036 | −2.07983 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.3852 | −1.51283 | −0.756413 | − | 0.654094i | \(-0.773050\pi\) | ||||
−0.756413 | + | 0.654094i | \(0.773050\pi\) | |||||||
\(488\) | 1.59706 | 0.0722953 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −40.5519 | −1.83195 | ||||||||
\(491\) | −12.5217 | −0.565095 | −0.282548 | − | 0.959253i | \(-0.591180\pi\) | ||||
−0.282548 | + | 0.959253i | \(0.591180\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.992638 | −0.0447062 | ||||||||
\(494\) | 2.67750 | 0.120466 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.57193 | −0.115483 | ||||||||
\(497\) | 59.9718 | 2.69010 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.3070 | 0.730003 | 0.365002 | − | 0.931007i | \(-0.381068\pi\) | ||||
0.365002 | + | 0.931007i | \(0.381068\pi\) | |||||||
\(500\) | 7.00966 | 0.313482 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.4989 | −0.825644 | ||||||||
\(503\) | 18.9726 | 0.845945 | 0.422973 | − | 0.906142i | \(-0.360987\pi\) | ||||
0.422973 | + | 0.906142i | \(0.360987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.3070 | 0.903651 | ||||||||
\(506\) | 1.79853 | 0.0799543 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.75794 | 0.255467 | ||||||||
\(509\) | 30.6907 | 1.36034 | 0.680170 | − | 0.733055i | \(-0.261906\pi\) | ||||
0.680170 | + | 0.733055i | \(0.261906\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.2974 | −0.455529 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27.7579 | −1.22435 | ||||||||
\(515\) | 39.4737 | 1.73942 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.4989 | 0.549699 | ||||||||
\(518\) | −20.5948 | −0.904882 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.29738 | 0.320011 | ||||||||
\(521\) | 42.1106 | 1.84490 | 0.922450 | − | 0.386116i | \(-0.126184\pi\) | ||||
0.922450 | + | 0.386116i | \(0.126184\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.8133 | 1.65346 | 0.826729 | − | 0.562600i | \(-0.190199\pi\) | ||||
0.826729 | + | 0.562600i | \(0.190199\pi\) | |||||||
\(524\) | −1.42807 | −0.0623856 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.2723 | −0.883912 | ||||||||
\(527\) | 0.518173 | 0.0225720 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.7653 | −0.859361 | ||||||||
\(530\) | −11.1895 | −0.486041 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.67750 | 0.202795 | ||||||||
\(533\) | 13.3202 | 0.576962 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.14386 | 0.135921 | ||||||||
\(536\) | 9.08044 | 0.392215 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.6427 | 0.674405 | ||||||||
\(539\) | 14.8790 | 0.640883 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.5661 | 0.583253 | 0.291627 | − | 0.956532i | \(-0.405804\pi\) | ||||
0.291627 | + | 0.956532i | \(0.405804\pi\) | |||||||
\(542\) | −12.3395 | −0.530028 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.201472 | −0.00863806 | ||||||||
\(545\) | 26.0457 | 1.11567 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 46.4177 | 1.98468 | 0.992338 | − | 0.123552i | \(-0.0394286\pi\) | ||||
0.992338 | + | 0.123552i | \(0.0394286\pi\) | |||||||
\(548\) | 14.5313 | 0.620748 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.42807 | 0.103533 | ||||||||
\(551\) | −4.92692 | −0.209894 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −55.4463 | −2.35782 | ||||||||
\(554\) | 8.49885 | 0.361082 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.1763 | 0.686030 | ||||||||
\(557\) | 38.2065 | 1.61886 | 0.809431 | − | 0.587214i | \(-0.199775\pi\) | ||||
0.809431 | + | 0.587214i | \(0.199775\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.5232 | 1.33329 | ||||||||
\(560\) | 12.7483 | 0.538713 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.12839 | 0.300693 | ||||||||
\(563\) | 7.01702 | 0.295732 | 0.147866 | − | 0.989007i | \(-0.452760\pi\) | ||||
0.147866 | + | 0.989007i | \(0.452760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.8036 | −0.917284 | ||||||||
\(566\) | 11.5240 | 0.484389 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.8214 | −0.537972 | ||||||||
\(569\) | 41.4235 | 1.73656 | 0.868281 | − | 0.496072i | \(-0.165225\pi\) | ||||
0.868281 | + | 0.496072i | \(0.165225\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.1381 | 0.507962 | 0.253981 | − | 0.967209i | \(-0.418260\pi\) | ||||
0.253981 | + | 0.967209i | \(0.418260\pi\) | |||||||
\(572\) | −2.67750 | −0.111952 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 23.2700 | 0.971269 | ||||||||
\(575\) | 4.36695 | 0.182115 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.8384 | 0.534469 | 0.267234 | − | 0.963632i | \(-0.413890\pi\) | ||||
0.267234 | + | 0.963632i | \(0.413890\pi\) | |||||||
\(578\) | −16.9594 | −0.705418 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13.4281 | −0.557570 | ||||||||
\(581\) | −63.9764 | −2.65419 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.10557 | 0.170035 | ||||||||
\(584\) | 2.20147 | 0.0910976 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.6775 | −0.441083 | ||||||||
\(587\) | −4.00000 | −0.165098 | −0.0825488 | − | 0.996587i | \(-0.526306\pi\) | ||||
−0.0825488 | + | 0.996587i | \(0.526306\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.57193 | 0.105974 | ||||||||
\(590\) | −14.3070 | −0.589011 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.40294 | 0.180960 | ||||||||
\(593\) | −40.4177 | −1.65975 | −0.829877 | − | 0.557946i | \(-0.811590\pi\) | ||||
−0.829877 | + | 0.557946i | \(0.811590\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.56842 | −0.105295 | ||||||||
\(596\) | −6.30704 | −0.258346 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.81555 | −0.196923 | ||||||||
\(599\) | −0.679795 | −0.0277757 | −0.0138878 | − | 0.999904i | \(-0.504421\pi\) | ||||
−0.0138878 | + | 0.999904i | \(0.504421\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.5240 | 0.877981 | 0.438991 | − | 0.898492i | \(-0.355336\pi\) | ||||
0.438991 | + | 0.898492i | \(0.355336\pi\) | |||||||
\(602\) | 55.0700 | 2.24449 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.498850 | 0.0202979 | ||||||||
\(605\) | −2.72545 | −0.110805 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.3550 | 0.542062 | 0.271031 | − | 0.962571i | \(-0.412635\pi\) | ||||
0.271031 | + | 0.962571i | \(0.412635\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.35269 | −0.176235 | ||||||||
\(611\) | −33.4656 | −1.35387 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.11293 | 0.368068 | 0.184034 | − | 0.982920i | \(-0.441084\pi\) | ||||
0.184034 | + | 0.982920i | \(0.441084\pi\) | |||||||
\(614\) | −30.2568 | −1.22106 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.67750 | −0.188462 | ||||||||
\(617\) | −0.329866 | −0.0132799 | −0.00663995 | − | 0.999978i | \(-0.502114\pi\) | ||||
−0.00663995 | + | 0.999978i | \(0.502114\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.92112 | 0.358570 | 0.179285 | − | 0.983797i | \(-0.442622\pi\) | ||||
0.179285 | + | 0.983797i | \(0.442622\pi\) | |||||||
\(620\) | 7.00966 | 0.281515 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.79623 | −0.352697 | ||||||||
\(623\) | −25.4966 | −1.02150 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2448 | −1.24979 | ||||||||
\(626\) | 10.1860 | 0.407115 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.6272 | −0.543786 | ||||||||
\(629\) | −0.887072 | −0.0353699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.6597 | 1.77788 | 0.888938 | − | 0.458028i | \(-0.151444\pi\) | ||||
0.888938 | + | 0.458028i | \(0.151444\pi\) | |||||||
\(632\) | 11.8538 | 0.471521 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.0097 | 0.476965 | ||||||||
\(635\) | −15.6930 | −0.622756 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −39.8384 | −1.57845 | ||||||||
\(638\) | 4.92692 | 0.195059 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.72545 | −0.107733 | ||||||||
\(641\) | 6.93272 | 0.273826 | 0.136913 | − | 0.990583i | \(-0.456282\pi\) | ||||
0.136913 | + | 0.990583i | \(0.456282\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.4966 | 0.926614 | 0.463307 | − | 0.886198i | \(-0.346663\pi\) | ||||
0.463307 | + | 0.886198i | \(0.346663\pi\) | |||||||
\(644\) | −8.41261 | −0.331503 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.201472 | 0.00792682 | ||||||||
\(647\) | −20.9880 | −0.825125 | −0.412562 | − | 0.910929i | \(-0.635366\pi\) | ||||
−0.412562 | + | 0.910929i | \(0.635366\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.24943 | 0.206058 | ||||||||
\(650\) | −6.50115 | −0.254996 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.9497 | 0.624640 | ||||||||
\(653\) | 44.1335 | 1.72708 | 0.863538 | − | 0.504284i | \(-0.168244\pi\) | ||||
0.863538 | + | 0.504284i | \(0.168244\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.89213 | 0.152078 | ||||||||
\(656\) | −4.97487 | −0.194236 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −58.4633 | −2.27914 | ||||||||
\(659\) | −24.0862 | −0.938267 | −0.469133 | − | 0.883127i | \(-0.655434\pi\) | ||||
−0.469133 | + | 0.883127i | \(0.655434\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.65237 | −0.375434 | −0.187717 | − | 0.982223i | \(-0.560109\pi\) | ||||
−0.187717 | + | 0.982223i | \(0.560109\pi\) | |||||||
\(662\) | 26.1667 | 1.01700 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.6775 | 0.530790 | ||||||||
\(665\) | −12.7483 | −0.494357 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.86120 | 0.343107 | ||||||||
\(668\) | −18.8059 | −0.727622 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −24.7483 | −0.956109 | ||||||||
\(671\) | 1.59706 | 0.0616536 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.6176 | 0.948938 | 0.474469 | − | 0.880272i | \(-0.342640\pi\) | ||||
0.474469 | + | 0.880272i | \(0.342640\pi\) | |||||||
\(674\) | 17.3778 | 0.669369 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.83102 | −0.224270 | ||||||||
\(677\) | −21.5719 | −0.829077 | −0.414538 | − | 0.910032i | \(-0.636057\pi\) | ||||
−0.414538 | + | 0.910032i | \(0.636057\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −78.6095 | −3.01675 | ||||||||
\(680\) | 0.549103 | 0.0210571 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.57193 | −0.0984843 | ||||||||
\(683\) | 0.997701 | 0.0381759 | 0.0190880 | − | 0.999818i | \(-0.493924\pi\) | ||||
0.0190880 | + | 0.999818i | \(0.493924\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −39.6044 | −1.51321 | ||||||||
\(686\) | −36.8538 | −1.40709 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11.7734 | −0.448857 | ||||||||
\(689\) | −10.9926 | −0.418786 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.00230 | −0.342464 | −0.171232 | − | 0.985231i | \(-0.554775\pi\) | ||||
−0.171232 | + | 0.985231i | \(0.554775\pi\) | |||||||
\(692\) | 3.22430 | 0.122569 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.4029 | 0.470809 | ||||||||
\(695\) | −44.0878 | −1.67235 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.00230 | 0.0379648 | ||||||||
\(698\) | −23.8036 | −0.900979 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.3573 | −0.429265 | ||||||||
\(701\) | 15.0936 | 0.570078 | 0.285039 | − | 0.958516i | \(-0.407994\pi\) | ||||
0.285039 | + | 0.958516i | \(0.407994\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.40294 | −0.166060 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.2664 | 0.913280 | ||||||||
\(707\) | 34.8515 | 1.31073 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.9246 | −0.860952 | −0.430476 | − | 0.902602i | \(-0.641654\pi\) | ||||
−0.430476 | + | 0.902602i | \(0.641654\pi\) | |||||||
\(710\) | 34.9439 | 1.31142 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.45090 | 0.204281 | ||||||||
\(713\) | −4.62569 | −0.173233 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.29738 | 0.272906 | ||||||||
\(716\) | −13.3778 | −0.499953 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20.3395 | −0.759064 | ||||||||
\(719\) | −6.70032 | −0.249880 | −0.124940 | − | 0.992164i | \(-0.539874\pi\) | ||||
−0.124940 | + | 0.992164i | \(0.539874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 67.7460 | 2.52299 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.9497 | 0.592768 | ||||||||
\(725\) | 11.9629 | 0.444291 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.4583 | −0.684579 | −0.342289 | − | 0.939595i | \(-0.611202\pi\) | ||||
−0.342289 | + | 0.939595i | \(0.611202\pi\) | |||||||
\(728\) | 12.5240 | 0.464169 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.00000 | −0.222070 | ||||||||
\(731\) | 2.37201 | 0.0877321 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.8995 | 1.54759 | 0.773797 | − | 0.633434i | \(-0.218355\pi\) | ||||
0.773797 | + | 0.633434i | \(0.218355\pi\) | |||||||
\(734\) | −23.0170 | −0.849574 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.79853 | 0.0662946 | ||||||||
\(737\) | 9.08044 | 0.334482 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.8361 | −1.28147 | −0.640733 | − | 0.767764i | \(-0.721369\pi\) | ||||
−0.640733 | + | 0.767764i | \(0.721369\pi\) | |||||||
\(740\) | −12.0000 | −0.441129 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.2038 | −0.704993 | ||||||||
\(743\) | 25.7889 | 0.946102 | 0.473051 | − | 0.881035i | \(-0.343153\pi\) | ||||
0.473051 | + | 0.881035i | \(0.343153\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.1895 | 0.629775 | ||||||||
\(746\) | −18.5890 | −0.680590 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.201472 | −0.00736656 | ||||||||
\(749\) | 5.39558 | 0.197150 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.5011 | −1.22247 | −0.611237 | − | 0.791447i | \(-0.709328\pi\) | ||||
−0.611237 | + | 0.791447i | \(0.709328\pi\) | |||||||
\(752\) | 12.4989 | 0.455786 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.1918 | −0.480417 | ||||||||
\(755\) | −1.35959 | −0.0494806 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.53134 | 0.273731 | 0.136866 | − | 0.990590i | \(-0.456297\pi\) | ||||
0.136866 | + | 0.990590i | \(0.456297\pi\) | |||||||
\(758\) | −10.5816 | −0.384341 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.72545 | 0.0988624 | ||||||||
\(761\) | −38.1969 | −1.38464 | −0.692318 | − | 0.721593i | \(-0.743410\pi\) | ||||
−0.692318 | + | 0.721593i | \(0.743410\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44.7003 | 1.61826 | ||||||||
\(764\) | 24.0553 | 0.870291 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.0878 | 0.942591 | ||||||||
\(767\) | −14.0553 | −0.507508 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.6501 | 0.600417 | 0.300208 | − | 0.953874i | \(-0.402944\pi\) | ||||
0.300208 | + | 0.953874i | \(0.402944\pi\) | |||||||
\(770\) | 12.7483 | 0.459416 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.0325 | 0.469050 | ||||||||
\(773\) | 23.6330 | 0.850022 | 0.425011 | − | 0.905188i | \(-0.360270\pi\) | ||||
0.425011 | + | 0.905188i | \(0.360270\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.24483 | −0.224321 | ||||||||
\(776\) | 16.8059 | 0.603296 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.46636 | 0.339386 | ||||||||
\(779\) | 4.97487 | 0.178243 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.8214 | −0.458784 | ||||||||
\(782\) | −0.362354 | −0.0129577 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 14.8790 | 0.531392 | ||||||||
\(785\) | 37.1404 | 1.32560 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.3933 | −0.726942 | −0.363471 | − | 0.931606i | \(-0.618408\pi\) | ||||
−0.363471 | + | 0.931606i | \(0.618408\pi\) | |||||||
\(788\) | 5.59706 | 0.199387 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.3070 | −1.14943 | ||||||||
\(791\) | −37.4200 | −1.33050 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.27611 | −0.151849 | ||||||||
\(794\) | −25.1667 | −0.893132 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.39558 | −0.262129 | ||||||||
\(797\) | 9.70262 | 0.343685 | 0.171842 | − | 0.985124i | \(-0.445028\pi\) | ||||
0.171842 | + | 0.985124i | \(0.445028\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.51817 | −0.0890865 | ||||||||
\(800\) | 2.42807 | 0.0858453 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.0650 | 0.567274 | ||||||||
\(803\) | 2.20147 | 0.0776883 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.9281 | 0.808110 | ||||||||
\(806\) | 6.88633 | 0.242561 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.45090 | −0.262122 | ||||||||
\(809\) | 27.0723 | 0.951813 | 0.475906 | − | 0.879496i | \(-0.342120\pi\) | ||||
0.475906 | + | 0.879496i | \(0.342120\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.9548 | 1.82438 | 0.912190 | − | 0.409767i | \(-0.134390\pi\) | ||||
0.912190 | + | 0.409767i | \(0.134390\pi\) | |||||||
\(812\) | −23.0457 | −0.808744 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.40294 | 0.154323 | ||||||||
\(815\) | −43.4702 | −1.52270 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.7734 | 0.411899 | ||||||||
\(818\) | −19.5313 | −0.682897 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.5588 | 0.473493 | ||||||||
\(821\) | 25.6574 | 0.895451 | 0.447725 | − | 0.894171i | \(-0.352234\pi\) | ||||
0.447725 | + | 0.894171i | \(0.352234\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.8635 | −1.45927 | −0.729635 | − | 0.683837i | \(-0.760310\pi\) | ||||
−0.729635 | + | 0.683837i | \(0.760310\pi\) | |||||||
\(824\) | −14.4834 | −0.504553 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.5542 | −0.854349 | ||||||||
\(827\) | −6.15582 | −0.214059 | −0.107029 | − | 0.994256i | \(-0.534134\pi\) | ||||
−0.107029 | + | 0.994256i | \(0.534134\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.247126 | −0.00858303 | −0.00429151 | − | 0.999991i | \(-0.501366\pi\) | ||||
−0.00429151 | + | 0.999991i | \(0.501366\pi\) | |||||||
\(830\) | −37.2773 | −1.29391 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.67750 | −0.0928255 | ||||||||
\(833\) | −2.99770 | −0.103864 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 51.2545 | 1.77373 | ||||||||
\(836\) | −1.00000 | −0.0345857 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.9018 | −0.860218 | ||||||||
\(839\) | −16.9320 | −0.584557 | −0.292278 | − | 0.956333i | \(-0.594413\pi\) | ||||
−0.292278 | + | 0.956333i | \(0.594413\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.72545 | −0.162947 | ||||||||
\(842\) | 26.6044 | 0.916849 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14.2974 | −0.492136 | ||||||||
\(845\) | 15.8921 | 0.546706 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.67750 | −0.160721 | ||||||||
\(848\) | 4.10557 | 0.140986 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.489189 | −0.0167790 | ||||||||
\(851\) | 7.91882 | 0.271454 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.6930 | 0.742753 | 0.371376 | − | 0.928482i | \(-0.378886\pi\) | ||||
0.371376 | + | 0.928482i | \(0.378886\pi\) | |||||||
\(854\) | −7.47022 | −0.255626 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.15352 | −0.0394265 | ||||||||
\(857\) | −34.7328 | −1.18645 | −0.593225 | − | 0.805037i | \(-0.702146\pi\) | ||||
−0.593225 | + | 0.805037i | \(0.702146\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.3047 | −0.522191 | −0.261095 | − | 0.965313i | \(-0.584084\pi\) | ||||
−0.261095 | + | 0.965313i | \(0.584084\pi\) | |||||||
\(860\) | 32.0878 | 1.09418 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 32.5948 | 1.11018 | ||||||||
\(863\) | −35.8457 | −1.22020 | −0.610102 | − | 0.792323i | \(-0.708871\pi\) | ||||
−0.610102 | + | 0.792323i | \(0.708871\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.78766 | −0.298789 | ||||||||
\(866\) | 19.7386 | 0.670745 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.0302 | 0.408331 | ||||||||
\(869\) | 11.8538 | 0.402114 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.3128 | −0.823809 | ||||||||
\(872\) | −9.55646 | −0.323623 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.79853 | −0.0608361 | ||||||||
\(875\) | −32.7877 | −1.10843 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.4907 | −1.53611 | −0.768057 | − | 0.640382i | \(-0.778776\pi\) | ||||
−0.768057 | + | 0.640382i | \(0.778776\pi\) | |||||||
\(878\) | −24.4029 | −0.823559 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.72545 | −0.0918749 | ||||||||
\(881\) | −31.3322 | −1.05561 | −0.527804 | − | 0.849366i | \(-0.676984\pi\) | ||||
−0.527804 | + | 0.849366i | \(0.676984\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.3550 | 1.18979 | 0.594895 | − | 0.803803i | \(-0.297194\pi\) | ||||
0.594895 | + | 0.803803i | \(0.297194\pi\) | |||||||
\(884\) | 0.539441 | 0.0181434 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.5948 | 0.557512 | ||||||||
\(887\) | 16.6141 | 0.557846 | 0.278923 | − | 0.960313i | \(-0.410023\pi\) | ||||
0.278923 | + | 0.960313i | \(0.410023\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.9327 | −0.903295 | ||||||||
\(890\) | −14.8561 | −0.497979 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.402945 | −0.0134916 | ||||||||
\(893\) | −12.4989 | −0.418258 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.4606 | 1.21874 | ||||||||
\(896\) | −4.67750 | −0.156264 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.9520 | 0.699179 | ||||||||
\(899\) | −12.6717 | −0.422625 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.827158 | −0.0275566 | ||||||||
\(902\) | −4.97487 | −0.165645 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.00000 | 0.266076 | ||||||||
\(905\) | −43.4702 | −1.44500 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 54.8612 | 1.82164 | 0.910818 | − | 0.412808i | \(-0.135452\pi\) | ||||
0.910818 | + | 0.412808i | \(0.135452\pi\) | |||||||
\(908\) | 21.0074 | 0.697154 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −34.1335 | −1.13151 | ||||||||
\(911\) | −2.98298 | −0.0988304 | −0.0494152 | − | 0.998778i | \(-0.515736\pi\) | ||||
−0.0494152 | + | 0.998778i | \(0.515736\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.6775 | 0.452659 | ||||||||
\(914\) | 23.3144 | 0.771172 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.3299 | −0.473472 | ||||||||
\(917\) | 6.67980 | 0.220586 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.6701 | −0.879767 | −0.439883 | − | 0.898055i | \(-0.644980\pi\) | ||||
−0.439883 | + | 0.898055i | \(0.644980\pi\) | |||||||
\(920\) | −4.90179 | −0.161607 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.8059 | −0.685205 | ||||||||
\(923\) | 34.3291 | 1.12996 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.6907 | 0.351507 | ||||||||
\(926\) | −9.29002 | −0.305289 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.92692 | 0.161734 | ||||||||
\(929\) | −43.7595 | −1.43570 | −0.717851 | − | 0.696197i | \(-0.754874\pi\) | ||||
−0.717851 | + | 0.696197i | \(0.754874\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.8790 | −0.487638 | ||||||||
\(932\) | 24.4029 | 0.799345 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.0457 | −0.394146 | ||||||||
\(935\) | 0.549103 | 0.0179576 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.7823 | 1.56098 | 0.780490 | − | 0.625168i | \(-0.214970\pi\) | ||||
0.780490 | + | 0.625168i | \(0.214970\pi\) | |||||||
\(938\) | −42.4737 | −1.38682 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −34.0650 | −1.11108 | ||||||||
\(941\) | −36.2664 | −1.18225 | −0.591126 | − | 0.806579i | \(-0.701316\pi\) | ||||
−0.591126 | + | 0.806579i | \(0.701316\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.94745 | −0.291369 | ||||||||
\(944\) | 5.24943 | 0.170854 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.7734 | −0.382786 | ||||||||
\(947\) | −35.5468 | −1.15512 | −0.577558 | − | 0.816350i | \(-0.695994\pi\) | ||||
−0.577558 | + | 0.816350i | \(0.695994\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.89443 | −0.191341 | ||||||||
\(950\) | −2.42807 | −0.0787770 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.942386 | 0.0305429 | ||||||||
\(953\) | −23.2088 | −0.751808 | −0.375904 | − | 0.926659i | \(-0.622668\pi\) | ||||
−0.375904 | + | 0.926659i | \(0.622668\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −65.5615 | −2.12152 | ||||||||
\(956\) | 12.6849 | 0.410258 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.188307 | −0.00608392 | ||||||||
\(959\) | −67.9703 | −2.19487 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.3852 | −0.786619 | ||||||||
\(962\) | −11.7889 | −0.380088 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23.9343 | −0.770871 | ||||||||
\(965\) | −35.5194 | −1.14341 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.09591 | −0.196031 | −0.0980156 | − | 0.995185i | \(-0.531249\pi\) | ||||
−0.0980156 | + | 0.995185i | \(0.531249\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −45.8036 | −1.47066 | ||||||||
\(971\) | −34.9822 | −1.12263 | −0.561317 | − | 0.827601i | \(-0.689705\pi\) | ||||
−0.561317 | + | 0.827601i | \(0.689705\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −75.6648 | −2.42570 | ||||||||
\(974\) | −33.3852 | −1.06973 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.59706 | 0.0511205 | ||||||||
\(977\) | 10.9018 | 0.348779 | 0.174390 | − | 0.984677i | \(-0.444205\pi\) | ||||
0.174390 | + | 0.984677i | \(0.444205\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.45090 | 0.174211 | ||||||||
\(980\) | −40.5519 | −1.29538 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.5217 | −0.399583 | ||||||||
\(983\) | 25.4281 | 0.811030 | 0.405515 | − | 0.914089i | \(-0.367092\pi\) | ||||
0.405515 | + | 0.914089i | \(0.367092\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.2545 | −0.486048 | ||||||||
\(986\) | −0.992638 | −0.0316120 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.67750 | 0.0851825 | ||||||||
\(989\) | −21.1748 | −0.673319 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.3925 | 1.56901 | 0.784503 | − | 0.620125i | \(-0.212918\pi\) | ||||
0.784503 | + | 0.620125i | \(0.212918\pi\) | |||||||
\(992\) | −2.57193 | −0.0816588 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 59.9718 | 1.90219 | ||||||||
\(995\) | 20.1563 | 0.638997 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.7409 | 0.656871 | 0.328436 | − | 0.944526i | \(-0.393479\pi\) | ||||
0.328436 | + | 0.944526i | \(0.393479\pi\) | |||||||
\(998\) | 16.3070 | 0.516190 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3762.2.a.bg.1.1 | 3 | ||
3.2 | odd | 2 | 418.2.a.g.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 3344.2.a.q.1.2 | 3 | |||
33.32 | even | 2 | 4598.2.a.bo.1.2 | 3 | |||
57.56 | even | 2 | 7942.2.a.bi.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.a.g.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
3344.2.a.q.1.2 | 3 | 12.11 | even | 2 | |||
3762.2.a.bg.1.1 | 3 | 1.1 | even | 1 | trivial | ||
4598.2.a.bo.1.2 | 3 | 33.32 | even | 2 | |||
7942.2.a.bi.1.2 | 3 | 57.56 | even | 2 |