Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(1,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.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: | \(35.1341768894\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2200) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.61803 | −0.934172 | −0.467086 | − | 0.884212i | \(-0.654696\pi\) | ||||
−0.467086 | + | 0.884212i | \(0.654696\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.618034 | −0.233595 | −0.116797 | − | 0.993156i | \(-0.537263\pi\) | ||||
−0.116797 | + | 0.993156i | \(0.537263\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.23607 | −0.620174 | −0.310087 | − | 0.950708i | \(-0.600358\pi\) | ||||
−0.310087 | + | 0.950708i | \(0.600358\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.85410 | −1.17729 | −0.588646 | − | 0.808391i | \(-0.700339\pi\) | ||||
−0.588646 | + | 0.808391i | \(0.700339\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.47214 | 1.25539 | 0.627697 | − | 0.778458i | \(-0.283998\pi\) | ||||
0.627697 | + | 0.778458i | \(0.283998\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.32624 | 1.31911 | 0.659556 | − | 0.751656i | \(-0.270744\pi\) | ||||
0.659556 | + | 0.751656i | \(0.270744\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.47214 | 1.05311 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.38197 | −0.813711 | −0.406855 | − | 0.913493i | \(-0.633375\pi\) | ||||
−0.406855 | + | 0.913493i | \(0.633375\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.23607 | 0.760820 | 0.380410 | − | 0.924818i | \(-0.375783\pi\) | ||||
0.380410 | + | 0.924818i | \(0.375783\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.61803 | −0.281664 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.76393 | −0.289989 | −0.144994 | − | 0.989432i | \(-0.546316\pi\) | ||||
−0.144994 | + | 0.989432i | \(0.546316\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.61803 | 0.579349 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.94427 | 1.24069 | 0.620343 | − | 0.784330i | \(-0.286993\pi\) | ||||
0.620343 | + | 0.784330i | \(0.286993\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.47214 | −1.29199 | −0.645994 | − | 0.763342i | \(-0.723557\pi\) | ||||
−0.645994 | + | 0.763342i | \(0.723557\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.70820 | −0.686762 | −0.343381 | − | 0.939196i | \(-0.611572\pi\) | ||||
−0.343381 | + | 0.939196i | \(0.611572\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.61803 | −0.945433 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.85410 | 1.09979 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.85410 | 0.529402 | 0.264701 | − | 0.964331i | \(-0.414727\pi\) | ||||
0.264701 | + | 0.964331i | \(0.414727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.85410 | −1.17275 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.76393 | 0.490022 | 0.245011 | − | 0.969520i | \(-0.421208\pi\) | ||||
0.245011 | + | 0.969520i | \(0.421208\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.09017 | 0.907803 | 0.453902 | − | 0.891052i | \(-0.350032\pi\) | ||||
0.453902 | + | 0.891052i | \(0.350032\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.236068 | 0.0297418 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.2361 | −1.23228 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.291796 | 0.0346298 | 0.0173149 | − | 0.999850i | \(-0.494488\pi\) | ||||
0.0173149 | + | 0.999850i | \(0.494488\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.09017 | 0.829842 | 0.414921 | − | 0.909858i | \(-0.363809\pi\) | ||||
0.414921 | + | 0.909858i | \(0.363809\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.618034 | −0.0704315 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.85410 | −0.321112 | −0.160556 | − | 0.987027i | \(-0.551329\pi\) | ||||
−0.160556 | + | 0.987027i | \(0.551329\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.14590 | −0.125779 | −0.0628893 | − | 0.998021i | \(-0.520032\pi\) | ||||
−0.0628893 | + | 0.998021i | \(0.520032\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.09017 | 0.760146 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.5623 | −1.33160 | −0.665801 | − | 0.746129i | \(-0.731910\pi\) | ||||
−0.665801 | + | 0.746129i | \(0.731910\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.38197 | 0.144869 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.85410 | −0.710737 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.90983 | −0.498518 | −0.249259 | − | 0.968437i | \(-0.580187\pi\) | ||||
−0.249259 | + | 0.968437i | \(0.580187\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.381966 | −0.0383890 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.56231 | −0.752478 | −0.376239 | − | 0.926523i | \(-0.622783\pi\) | ||||
−0.376239 | + | 0.926523i | \(0.622783\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.8541 | −1.66068 | −0.830342 | − | 0.557254i | \(-0.811855\pi\) | ||||
−0.830342 | + | 0.557254i | \(0.811855\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.9443 | −1.15470 | −0.577348 | − | 0.816498i | \(-0.695912\pi\) | ||||
−0.577348 | + | 0.816498i | \(0.695912\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.79837 | 0.555383 | 0.277692 | − | 0.960670i | \(-0.410431\pi\) | ||||
0.277692 | + | 0.960670i | \(0.410431\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.85410 | 0.270899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.236068 | −0.0222074 | −0.0111037 | − | 0.999938i | \(-0.503534\pi\) | ||||
−0.0111037 | + | 0.999938i | \(0.503534\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.854102 | 0.0789618 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.00000 | 0.275010 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.8541 | −1.15902 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.381966 | 0.0338940 | 0.0169470 | − | 0.999856i | \(-0.494605\pi\) | ||||
0.0169470 | + | 0.999856i | \(0.494605\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.7082 | 1.20694 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.0902 | 1.31843 | 0.659217 | − | 0.751953i | \(-0.270888\pi\) | ||||
0.659217 | + | 0.751953i | \(0.270888\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.38197 | −0.293254 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.38197 | −0.545248 | −0.272624 | − | 0.962121i | \(-0.587892\pi\) | ||||
−0.272624 | + | 0.962121i | \(0.587892\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.00000 | 0.593732 | 0.296866 | − | 0.954919i | \(-0.404058\pi\) | ||||
0.296866 | + | 0.954919i | \(0.404058\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.61803 | 0.641554 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.23607 | −0.186989 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.7082 | 0.883198 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.0000 | −0.983078 | −0.491539 | − | 0.870855i | \(-0.663566\pi\) | ||||
−0.491539 | + | 0.870855i | \(0.663566\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.6525 | 1.11102 | 0.555511 | − | 0.831509i | \(-0.312523\pi\) | ||||
0.555511 | + | 0.831509i | \(0.312523\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.85410 | 0.149895 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.4164 | −1.38998 | −0.694990 | − | 0.719019i | \(-0.744591\pi\) | ||||
−0.694990 | + | 0.719019i | \(0.744591\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.23607 | −0.494552 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.90983 | −0.308138 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.3820 | −1.20481 | −0.602404 | − | 0.798191i | \(-0.705790\pi\) | ||||
−0.602404 | + | 0.798191i | \(0.705790\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.00000 | −0.696441 | −0.348220 | − | 0.937413i | \(-0.613214\pi\) | ||||
−0.348220 | + | 0.937413i | \(0.613214\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.00000 | −0.615385 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.09017 | −0.159839 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.8885 | 1.13196 | 0.565978 | − | 0.824421i | \(-0.308499\pi\) | ||||
0.565978 | + | 0.824421i | \(0.308499\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.09017 | −0.457765 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.0902 | 0.978405 | 0.489203 | − | 0.872170i | \(-0.337288\pi\) | ||||
0.489203 | + | 0.872170i | \(0.337288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0902 | 0.972985 | 0.486492 | − | 0.873685i | \(-0.338276\pi\) | ||||
0.486492 | + | 0.873685i | \(0.338276\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.4721 | −0.848045 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.85410 | −0.354967 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.38197 | −0.246002 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3820 | 0.751213 | 0.375606 | − | 0.926779i | \(-0.377434\pi\) | ||||
0.375606 | + | 0.926779i | \(0.377434\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9443 | −0.931749 | −0.465875 | − | 0.884851i | \(-0.654260\pi\) | ||||
−0.465875 | + | 0.884851i | \(0.654260\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.5623 | 1.53625 | 0.768125 | − | 0.640300i | \(-0.221190\pi\) | ||||
0.768125 | + | 0.640300i | \(0.221190\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.5623 | −1.45762 | −0.728812 | − | 0.684714i | \(-0.759927\pi\) | ||||
−0.728812 | + | 0.684714i | \(0.759927\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.70820 | 0.190079 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.41641 | −0.167952 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.47214 | 0.378516 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.70820 | −0.461812 | −0.230906 | − | 0.972976i | \(-0.574169\pi\) | ||||
−0.230906 | + | 0.972976i | \(0.574169\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.472136 | −0.0323502 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.61803 | −0.177724 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.4721 | −0.775215 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.8541 | 0.730126 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.18034 | 0.346901 | 0.173451 | − | 0.984843i | \(-0.444508\pi\) | ||||
0.173451 | + | 0.984843i | \(0.444508\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.79837 | 0.517596 | 0.258798 | − | 0.965931i | \(-0.416674\pi\) | ||||
0.258798 | + | 0.965931i | \(0.416674\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.5066 | −1.81769 | −0.908843 | − | 0.417139i | \(-0.863033\pi\) | ||||
−0.908843 | + | 0.417139i | \(0.863033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.1459 | −1.18878 | −0.594389 | − | 0.804178i | \(-0.702606\pi\) | ||||
−0.594389 | + | 0.804178i | \(0.702606\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.61803 | 0.299974 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.0902 | −1.36421 | −0.682105 | − | 0.731254i | \(-0.738935\pi\) | ||||
−0.682105 | + | 0.731254i | \(0.738935\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.0344 | −1.09728 | −0.548642 | − | 0.836057i | \(-0.684855\pi\) | ||||
−0.548642 | + | 0.836057i | \(0.684855\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.2361 | −0.778562 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.85410 | 0.117499 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.14590 | 0.451045 | 0.225523 | − | 0.974238i | \(-0.427591\pi\) | ||||
0.225523 | + | 0.974238i | \(0.427591\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.32624 | 0.397727 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.05573 | −0.0658545 | −0.0329273 | − | 0.999458i | \(-0.510483\pi\) | ||||
−0.0329273 | + | 0.999458i | \(0.510483\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.09017 | 0.0677399 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.67376 | 0.103603 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.1246 | −1.61091 | −0.805456 | − | 0.592655i | \(-0.798080\pi\) | ||||
−0.805456 | + | 0.592655i | \(0.798080\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.3262 | 1.24395 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.7984 | −1.45101 | −0.725506 | − | 0.688216i | \(-0.758394\pi\) | ||||
−0.725506 | + | 0.688216i | \(0.758394\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.4164 | −1.11872 | −0.559359 | − | 0.828926i | \(-0.688952\pi\) | ||||
−0.559359 | + | 0.828926i | \(0.688952\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.23607 | −0.135333 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.9443 | 0.957998 | 0.478999 | − | 0.877815i | \(-0.341000\pi\) | ||||
0.478999 | + | 0.877815i | \(0.341000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.61803 | −0.0968692 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.3607 | −1.87082 | −0.935411 | − | 0.353563i | \(-0.884970\pi\) | ||||
−0.935411 | + | 0.353563i | \(0.884970\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.1459 | 0.781443 | 0.390721 | − | 0.920509i | \(-0.372226\pi\) | ||||
0.390721 | + | 0.920509i | \(0.372226\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.90983 | −0.289818 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.56231 | 0.386018 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.94427 | 0.465701 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.8885 | −1.16190 | −0.580951 | − | 0.813939i | \(-0.697319\pi\) | ||||
−0.580951 | + | 0.813939i | \(0.697319\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.47214 | 0.317526 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.1459 | −0.818078 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.23607 | 0.301802 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.2361 | 0.702944 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.85410 | −0.277038 | −0.138519 | − | 0.990360i | \(-0.544234\pi\) | ||||
−0.138519 | + | 0.990360i | \(0.544234\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.2705 | 1.55137 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.8885 | −0.617433 | −0.308716 | − | 0.951154i | \(-0.599899\pi\) | ||||
−0.308716 | + | 0.951154i | \(0.599899\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.7082 | −1.56616 | −0.783080 | − | 0.621921i | \(-0.786353\pi\) | ||||
−0.783080 | + | 0.621921i | \(0.786353\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.27051 | −0.239856 | −0.119928 | − | 0.992783i | \(-0.538266\pi\) | ||||
−0.119928 | + | 0.992783i | \(0.538266\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.38197 | −0.245343 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.3262 | 1.07869 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −26.5623 | −1.47797 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.38197 | −0.518824 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.90983 | 0.160424 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.4164 | −1.56191 | −0.780954 | − | 0.624589i | \(-0.785266\pi\) | ||||
−0.780954 | + | 0.624589i | \(0.785266\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.673762 | 0.0369219 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.5279 | −0.845857 | −0.422928 | − | 0.906163i | \(-0.638998\pi\) | ||||
−0.422928 | + | 0.906163i | \(0.638998\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.381966 | 0.0207455 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.23607 | 0.229396 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.41641 | 0.454443 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.2705 | 0.927130 | 0.463565 | − | 0.886063i | \(-0.346570\pi\) | ||||
0.463565 | + | 0.886063i | \(0.346570\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.5279 | 1.42000 | 0.710002 | − | 0.704200i | \(-0.248694\pi\) | ||||
0.710002 | + | 0.704200i | \(0.248694\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.2361 | −0.653113 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.4164 | −1.93825 | −0.969125 | − | 0.246570i | \(-0.920696\pi\) | ||||
−0.969125 | + | 0.246570i | \(0.920696\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.85410 | −0.256906 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.00000 | 0.316668 | 0.158334 | − | 0.987386i | \(-0.449388\pi\) | ||||
0.158334 | + | 0.987386i | \(0.449388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.9443 | 0.576014 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.61803 | −0.0849248 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.7984 | −0.876868 | −0.438434 | − | 0.898763i | \(-0.644467\pi\) | ||||
−0.438434 | + | 0.898763i | \(0.644467\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.03444 | −0.157967 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.38197 | −0.123666 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.70820 | −0.243782 | −0.121891 | − | 0.992544i | \(-0.538896\pi\) | ||||
−0.121891 | + | 0.992544i | \(0.538896\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.79837 | 0.504642 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.3050 | 1.35119 | 0.675597 | − | 0.737271i | \(-0.263886\pi\) | ||||
0.675597 | + | 0.737271i | \(0.263886\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.618034 | −0.0316628 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.4164 | 1.50311 | 0.751554 | − | 0.659671i | \(-0.229305\pi\) | ||||
0.751554 | + | 0.659671i | \(0.229305\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.23607 | 0.164499 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.5279 | −0.888698 | −0.444349 | − | 0.895854i | \(-0.646565\pi\) | ||||
−0.444349 | + | 0.895854i | \(0.646565\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.7082 | −1.55298 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.4164 | −1.23164 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.8541 | 1.34777 | 0.673884 | − | 0.738837i | \(-0.264625\pi\) | ||||
0.673884 | + | 0.738837i | \(0.264625\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.47214 | 0.273949 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.3607 | 1.31639 | 0.658195 | − | 0.752848i | \(-0.271320\pi\) | ||||
0.658195 | + | 0.752848i | \(0.271320\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.47214 | −0.471841 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.76393 | −0.0874349 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.12461 | −0.302843 | −0.151421 | − | 0.988469i | \(-0.548385\pi\) | ||||
−0.151421 | + | 0.988469i | \(0.548385\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.3262 | 0.509356 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.32624 | −0.114467 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.3262 | −0.554648 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.888544 | 0.0434082 | 0.0217041 | − | 0.999764i | \(-0.493091\pi\) | ||||
0.0217041 | + | 0.999764i | \(0.493091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.09017 | −0.150606 | −0.0753028 | − | 0.997161i | \(-0.523992\pi\) | ||||
−0.0753028 | + | 0.997161i | \(0.523992\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.79837 | 0.0874399 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.38197 | −0.212058 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.61803 | 0.174680 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.00000 | 0.0481683 | 0.0240842 | − | 0.999710i | \(-0.492333\pi\) | ||||
0.0240842 | + | 0.999710i | \(0.492333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.7771 | 1.57517 | 0.787583 | − | 0.616208i | \(-0.211332\pi\) | ||||
0.787583 | + | 0.616208i | \(0.211332\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.6180 | 1.65601 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.3262 | −1.11330 | −0.556650 | − | 0.830747i | \(-0.687914\pi\) | ||||
−0.556650 | + | 0.830747i | \(0.687914\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.52786 | 0.120374 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.2918 | 0.679024 | 0.339512 | − | 0.940602i | \(-0.389738\pi\) | ||||
0.339512 | + | 0.940602i | \(0.389738\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.4164 | 0.918365 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.1591 | 1.47049 | 0.735243 | − | 0.677803i | \(-0.237068\pi\) | ||||
0.735243 | + | 0.677803i | \(0.237068\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.94427 | 0.374081 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.0902 | −1.03789 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.43769 | −0.207587 | −0.103793 | − | 0.994599i | \(-0.533098\pi\) | ||||
−0.103793 | + | 0.994599i | \(0.533098\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −26.5623 | −1.23982 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.1246 | −0.844147 | −0.422074 | − | 0.906562i | \(-0.638698\pi\) | ||||
−0.422074 | + | 0.906562i | \(0.638698\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.7082 | 0.869444 | 0.434722 | − | 0.900565i | \(-0.356847\pi\) | ||||
0.434722 | + | 0.900565i | \(0.356847\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.6525 | −1.55725 | −0.778625 | − | 0.627489i | \(-0.784083\pi\) | ||||
−0.778625 | + | 0.627489i | \(0.784083\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28.1803 | 1.29848 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.47214 | −0.389549 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.47214 | −0.0674045 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.5967 | −0.575560 | −0.287780 | − | 0.957697i | \(-0.592917\pi\) | ||||
−0.287780 | + | 0.957697i | \(0.592917\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.94427 | 0.179843 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.32624 | 0.287854 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.1803 | 0.687887 | 0.343943 | − | 0.938990i | \(-0.388237\pi\) | ||||
0.343943 | + | 0.938990i | \(0.388237\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.8885 | 1.12550 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.8328 | 1.07556 | 0.537780 | − | 0.843085i | \(-0.319263\pi\) | ||||
0.537780 | + | 0.843085i | \(0.319263\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.2705 | 0.957976 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.180340 | −0.00808935 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.6869 | −1.01561 | −0.507803 | − | 0.861473i | \(-0.669542\pi\) | ||||
−0.507803 | + | 0.861473i | \(0.669542\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.5623 | 0.650596 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.2361 | 1.66027 | 0.830137 | − | 0.557559i | \(-0.188262\pi\) | ||||
0.830137 | + | 0.557559i | \(0.188262\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9443 | 0.574875 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.2148 | −1.60519 | −0.802596 | − | 0.596523i | \(-0.796548\pi\) | ||||
−0.802596 | + | 0.596523i | \(0.796548\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.38197 | −0.193847 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 29.9443 | 1.32207 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.70820 | −0.207067 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.0902 | −1.05744 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.6525 | −1.69340 | −0.846698 | − | 0.532074i | \(-0.821413\pi\) | ||||
−0.846698 | + | 0.532074i | \(0.821413\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.472136 | −0.0206451 | −0.0103225 | − | 0.999947i | \(-0.503286\pi\) | ||||
−0.0103225 | + | 0.999947i | \(0.503286\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.5623 | −0.895708 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.0213 | 0.740056 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.43769 | −0.0623906 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.7639 | −0.769441 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.1803 | −0.913999 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.61803 | −0.285059 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.5066 | 1.22559 | 0.612797 | − | 0.790241i | \(-0.290044\pi\) | ||||
0.612797 | + | 0.790241i | \(0.290044\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.1803 | −0.908935 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.4377 | −0.959367 | −0.479683 | − | 0.877442i | \(-0.659248\pi\) | ||||
−0.479683 | + | 0.877442i | \(0.659248\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.70820 | −0.115583 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.9787 | −1.02153 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.76393 | 0.0750100 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.7082 | 0.623207 | 0.311603 | − | 0.950212i | \(-0.399134\pi\) | ||||
0.311603 | + | 0.950212i | \(0.399134\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.9443 | 0.801257 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.85410 | 0.331600 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.61803 | 0.278917 | 0.139458 | − | 0.990228i | \(-0.455464\pi\) | ||||
0.139458 | + | 0.990228i | \(0.455464\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.76393 | 0.200066 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.9098 | 1.37965 | 0.689826 | − | 0.723975i | \(-0.257687\pi\) | ||||
0.689826 | + | 0.723975i | \(0.257687\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.4508 | −1.73466 | −0.867332 | − | 0.497730i | \(-0.834167\pi\) | ||||
−0.867332 | + | 0.497730i | \(0.834167\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.7984 | −0.701762 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.7984 | −1.32378 | −0.661892 | − | 0.749599i | \(-0.730246\pi\) | ||||
−0.661892 | + | 0.749599i | \(0.730246\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.9443 | 0.870414 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.708204 | 0.0293812 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.85410 | 0.159621 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.27051 | −0.0937140 | −0.0468570 | − | 0.998902i | \(-0.514921\pi\) | ||||
−0.0468570 | + | 0.998902i | \(0.514921\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.1803 | 0.955129 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −34.8885 | −1.43512 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.88854 | 0.282879 | 0.141439 | − | 0.989947i | \(-0.454827\pi\) | ||||
0.141439 | + | 0.989947i | \(0.454827\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 33.2705 | 1.36167 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.0902 | −1.06602 | −0.533008 | − | 0.846110i | \(-0.678938\pi\) | ||||
−0.533008 | + | 0.846110i | \(0.678938\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.7426 | −1.05006 | −0.525032 | − | 0.851082i | \(-0.675947\pi\) | ||||
−0.525032 | + | 0.851082i | \(0.675947\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.05573 | −0.367561 | −0.183780 | − | 0.982967i | \(-0.558834\pi\) | ||||
−0.183780 | + | 0.982967i | \(0.558834\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.38197 | −0.177566 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.5279 | 0.425912 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.0902 | 0.972993 | 0.486496 | − | 0.873683i | \(-0.338275\pi\) | ||||
0.486496 | + | 0.873683i | \(0.338275\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.2361 | 0.774415 | 0.387207 | − | 0.921993i | \(-0.373440\pi\) | ||||
0.387207 | + | 0.921993i | \(0.373440\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.2918 | 0.855790 | 0.427895 | − | 0.903829i | \(-0.359255\pi\) | ||||
0.427895 | + | 0.903829i | \(0.359255\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.6180 | 1.38917 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.76393 | 0.311055 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.85410 | −0.353599 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.56231 | 0.341401 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.5066 | 1.29407 | 0.647033 | − | 0.762462i | \(-0.276009\pi\) | ||||
0.647033 | + | 0.762462i | \(0.276009\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.8541 | 0.431412 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.7984 | 0.586333 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.111456 | −0.00440914 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.11146 | −0.0438999 | −0.0219499 | − | 0.999759i | \(-0.506987\pi\) | ||||
−0.0219499 | + | 0.999759i | \(0.506987\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.05573 | −0.357123 | −0.178562 | − | 0.983929i | \(-0.557144\pi\) | ||||
−0.178562 | + | 0.983929i | \(0.557144\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.9443 | −0.548206 | −0.274103 | − | 0.961700i | \(-0.588381\pi\) | ||||
−0.274103 | + | 0.961700i | \(0.588381\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.76393 | 0.147747 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.23607 | 0.166025 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.3262 | 0.756294 | 0.378147 | − | 0.925746i | \(-0.376561\pi\) | ||||
0.378147 | + | 0.925746i | \(0.376561\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.70820 | −0.105657 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.7984 | −1.23869 | −0.619344 | − | 0.785119i | \(-0.712602\pi\) | ||||
−0.619344 | + | 0.785119i | \(0.712602\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.5967 | −1.03449 | −0.517247 | − | 0.855836i | \(-0.673043\pi\) | ||||
−0.517247 | + | 0.855836i | \(0.673043\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.5623 | −0.682063 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27.7214 | −1.07338 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.38197 | −0.324066 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.09017 | 0.273713 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.4721 | −0.596407 | −0.298204 | − | 0.954502i | \(-0.596387\pi\) | ||||
−0.298204 | + | 0.954502i | \(0.596387\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.7639 | 1.25922 | 0.629610 | − | 0.776911i | \(-0.283215\pi\) | ||||
0.629610 | + | 0.776911i | \(0.283215\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.03444 | 0.116451 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.6180 | −0.483524 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.7639 | 1.36847 | 0.684234 | − | 0.729262i | \(-0.260137\pi\) | ||||
0.684234 | + | 0.729262i | \(0.260137\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 44.5066 | 1.69803 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.61803 | −0.328321 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.20163 | −0.0457120 | −0.0228560 | − | 0.999739i | \(-0.507276\pi\) | ||||
−0.0228560 | + | 0.999739i | \(0.507276\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.236068 | 0.00896748 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −38.5623 | −1.46065 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.3607 | 1.11052 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.52786 | 0.208785 | 0.104392 | − | 0.994536i | \(-0.466710\pi\) | ||||
0.104392 | + | 0.994536i | \(0.466710\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.65248 | −0.364050 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.67376 | 0.175775 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.3607 | 0.614438 | 0.307219 | − | 0.951639i | \(-0.400602\pi\) | ||||
0.307219 | + | 0.951639i | \(0.400602\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.09017 | 0.0408846 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.7984 | 1.00361 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 34.1246 | 1.27441 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 41.9443 | 1.56426 | 0.782129 | − | 0.623117i | \(-0.214134\pi\) | ||||
0.782129 | + | 0.623117i | \(0.214134\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.4164 | 0.387927 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.5623 | 1.02505 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.5066 | −1.53939 | −0.769697 | − | 0.638410i | \(-0.779593\pi\) | ||||
−0.769697 | + | 0.638410i | \(0.779593\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 41.1246 | 1.52105 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.4721 | 1.67955 | 0.839776 | − | 0.542933i | \(-0.182686\pi\) | ||||
0.839776 | + | 0.542933i | \(0.182686\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.0344 | −1.32555 | −0.662774 | − | 0.748819i | \(-0.730621\pi\) | ||||
−0.662774 | + | 0.748819i | \(0.730621\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19.7984 | 0.727311 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.9656 | 0.438974 | 0.219487 | − | 0.975615i | \(-0.429562\pi\) | ||||
0.219487 | + | 0.975615i | \(0.429562\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.437694 | 0.0160144 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.38197 | 0.269731 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.1591 | 1.24648 | 0.623241 | − | 0.782030i | \(-0.285816\pi\) | ||||
0.623241 | + | 0.782030i | \(0.285816\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.5623 | −0.421354 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.8328 | −1.88390 | −0.941948 | − | 0.335759i | \(-0.891007\pi\) | ||||
−0.941948 | + | 0.335759i | \(0.891007\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.2361 | −0.371546 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.8885 | −1.37346 | −0.686729 | − | 0.726913i | \(-0.740954\pi\) | ||||
−0.686729 | + | 0.726913i | \(0.740954\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.58359 | −0.129735 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.41641 | −0.303899 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.9443 | 1.07982 | 0.539909 | − | 0.841723i | \(-0.318459\pi\) | ||||
0.539909 | + | 0.841723i | \(0.318459\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.70820 | 0.0615195 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.9098 | 1.18368 | 0.591842 | − | 0.806054i | \(-0.298401\pi\) | ||||
0.591842 | + | 0.806054i | \(0.298401\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.76393 | −0.0632807 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 43.4721 | 1.55755 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.291796 | 0.0104413 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23.9787 | −0.856929 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.5279 | 0.517862 | 0.258931 | − | 0.965896i | \(-0.416630\pi\) | ||||
0.258931 | + | 0.965896i | \(0.416630\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 42.2705 | 1.50487 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.145898 | 0.00518754 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.8541 | −0.562996 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.20163 | 0.148829 | 0.0744146 | − | 0.997227i | \(-0.476291\pi\) | ||||
0.0744146 | + | 0.997227i | \(0.476291\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.8541 | 0.808520 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.79837 | 0.169542 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.09017 | 0.250207 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 38.5066 | 1.35550 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.4164 | −0.401380 | −0.200690 | − | 0.979655i | \(-0.564318\pi\) | ||||
−0.200690 | + | 0.979655i | \(0.564318\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.8197 | −1.15245 | −0.576227 | − | 0.817290i | \(-0.695476\pi\) | ||||
−0.576227 | + | 0.817290i | \(0.695476\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.7984 | 1.04507 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −46.3607 | −1.62195 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.527864 | −0.0184451 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.36068 | 0.291790 | 0.145895 | − | 0.989300i | \(-0.453394\pi\) | ||||
0.145895 | + | 0.989300i | \(0.453394\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.5279 | −0.750414 | −0.375207 | − | 0.926941i | \(-0.622428\pi\) | ||||
−0.375207 | + | 0.926941i | \(0.622428\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.5967 | 0.820539 | 0.410270 | − | 0.911964i | \(-0.365435\pi\) | ||||
0.410270 | + | 0.911964i | \(0.365435\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.6180 | −1.16760 | −0.583801 | − | 0.811897i | \(-0.698435\pi\) | ||||
−0.583801 | + | 0.811897i | \(0.698435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.7984 | −0.894936 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32.1246 | 1.11305 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23.1803 | 0.801230 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.6738 | 0.817309 | 0.408655 | − | 0.912689i | \(-0.365998\pi\) | ||||
0.408655 | + | 0.912689i | \(0.365998\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.79837 | −0.337875 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 50.7426 | 1.74767 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.618034 | −0.0212359 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.2705 | −0.730002 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.1591 | −0.382527 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.6180 | 1.01410 | 0.507051 | − | 0.861916i | \(-0.330736\pi\) | ||||
0.507051 | + | 0.861916i | \(0.330736\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.6525 | 0.671316 | 0.335658 | − | 0.941984i | \(-0.391041\pi\) | ||||
0.335658 | + | 0.941984i | \(0.391041\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.4853 | −1.48370 | −0.741850 | − | 0.670566i | \(-0.766051\pi\) | ||||
−0.741850 | + | 0.670566i | \(0.766051\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.94427 | 0.270740 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.94427 | −0.338507 | −0.169253 | − | 0.985573i | \(-0.554136\pi\) | ||||
−0.169253 | + | 0.985573i | \(0.554136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.6180 | −0.360607 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.85410 | −0.0968188 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.87539 | 0.0634723 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.5279 | 0.997085 | 0.498543 | − | 0.866865i | \(-0.333869\pi\) | ||||
0.498543 | + | 0.866865i | \(0.333869\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32.1803 | 1.08542 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.6738 | −0.460681 | −0.230340 | − | 0.973110i | \(-0.573984\pi\) | ||||
−0.230340 | + | 0.973110i | \(0.573984\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.3607 | 0.651539 | 0.325769 | − | 0.945449i | \(-0.394377\pi\) | ||||
0.325769 | + | 0.945449i | \(0.394377\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.2361 | 0.948074 | 0.474037 | − | 0.880505i | \(-0.342796\pi\) | ||||
0.474037 | + | 0.880505i | \(0.342796\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.236068 | −0.00791747 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.70820 | −0.258235 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.7639 | −0.862157 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.8885 | 0.764226 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.5623 | −0.619088 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.7082 | −0.623261 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.47214 | −0.281935 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.8328 | 0.492516 | 0.246258 | − | 0.969204i | \(-0.420799\pi\) | ||||
0.246258 | + | 0.969204i | \(0.420799\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.88854 | 0.0958070 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.3050 | 1.83233 | 0.916167 | − | 0.400796i | \(-0.131266\pi\) | ||||
0.916167 | + | 0.400796i | \(0.131266\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.14590 | −0.0379237 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.32624 | −0.307980 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.3607 | 1.72722 | 0.863610 | − | 0.504161i | \(-0.168198\pi\) | ||||
0.863610 | + | 0.504161i | \(0.168198\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.85410 | 0.258801 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.652476 | −0.0214765 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.43769 | 0.211442 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.1803 | −0.760522 | −0.380261 | − | 0.924879i | \(-0.624166\pi\) | ||||
−0.380261 | + | 0.924879i | \(0.624166\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.2148 | −1.18689 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.6180 | 0.576789 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.0557 | −1.14522 | −0.572610 | − | 0.819828i | \(-0.694069\pi\) | ||||
−0.572610 | + | 0.819828i | \(0.694069\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 44.8328 | 1.46306 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.5836 | −0.703605 | −0.351802 | − | 0.936074i | \(-0.614431\pi\) | ||||
−0.351802 | + | 0.936074i | \(0.614431\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50.2574 | 1.63660 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.2918 | −0.366934 | −0.183467 | − | 0.983026i | \(-0.558732\pi\) | ||||
−0.183467 | + | 0.983026i | \(0.558732\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.8541 | −0.514646 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.90983 | 0.224067 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.5279 | 0.632570 | 0.316285 | − | 0.948664i | \(-0.397564\pi\) | ||||
0.316285 | + | 0.948664i | \(0.397564\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.09017 | 0.229193 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.94427 | 0.127367 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.0557 | −0.421153 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.56231 | 0.147018 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.1591 | 0.776903 | 0.388451 | − | 0.921469i | \(-0.373010\pi\) | ||||
0.388451 | + | 0.921469i | \(0.373010\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 42.9787 | 1.38068 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.85410 | −0.123684 | −0.0618420 | − | 0.998086i | \(-0.519697\pi\) | ||||
−0.0618420 | + | 0.998086i | \(0.519697\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.32624 | −0.138693 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.5967 | 0.339020 | 0.169510 | − | 0.985528i | \(-0.445781\pi\) | ||||
0.169510 | + | 0.985528i | \(0.445781\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.5623 | −0.401493 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.21478 | −0.0707125 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.2492 | 0.964800 | 0.482400 | − | 0.875951i | \(-0.339765\pi\) | ||||
0.482400 | + | 0.875951i | \(0.339765\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.70820 | −0.149864 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −53.5967 | −1.70428 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.5623 | −1.54263 | −0.771316 | − | 0.636452i | \(-0.780401\pi\) | ||||
−0.771316 | + | 0.636452i | \(0.780401\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.9787 | 1.45909 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.97871 | −0.252688 | −0.126344 | − | 0.991986i | \(-0.540324\pi\) | ||||
−0.126344 | + | 0.991986i | \(0.540324\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.65248 | −0.305391 |
(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 | 4400.2.a.bk.1.1 | 2 | ||
4.3 | odd | 2 | 2200.2.a.r.1.2 | yes | 2 | ||
5.2 | odd | 4 | 4400.2.b.ba.4049.4 | 4 | |||
5.3 | odd | 4 | 4400.2.b.ba.4049.1 | 4 | |||
5.4 | even | 2 | 4400.2.a.bq.1.2 | 2 | |||
20.3 | even | 4 | 2200.2.b.j.1849.4 | 4 | |||
20.7 | even | 4 | 2200.2.b.j.1849.1 | 4 | |||
20.19 | odd | 2 | 2200.2.a.n.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2200.2.a.n.1.1 | ✓ | 2 | 20.19 | odd | 2 | ||
2200.2.a.r.1.2 | yes | 2 | 4.3 | odd | 2 | ||
2200.2.b.j.1849.1 | 4 | 20.7 | even | 4 | |||
2200.2.b.j.1849.4 | 4 | 20.3 | even | 4 | |||
4400.2.a.bk.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4400.2.a.bq.1.2 | 2 | 5.4 | even | 2 | |||
4400.2.b.ba.4049.1 | 4 | 5.3 | odd | 4 | |||
4400.2.b.ba.4049.4 | 4 | 5.2 | odd | 4 |