Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 15x^{7} + 15x^{6} + 66x^{5} - 59x^{4} - 77x^{3} + 34x^{2} + 11x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.00974\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00974 | −0.582974 | −0.291487 | − | 0.956575i | \(-0.594150\pi\) | ||||
−0.291487 | + | 0.956575i | \(0.594150\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.49743 | 1.11689 | 0.558443 | − | 0.829543i | \(-0.311399\pi\) | ||||
0.558443 | + | 0.829543i | \(0.311399\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.98043 | −0.660142 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.52176 | −0.651115 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.53427 | −1.09972 | −0.549861 | − | 0.835256i | \(-0.685319\pi\) | ||||
−0.549861 | + | 0.835256i | \(0.685319\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.365921 | −0.0839481 | −0.0419740 | − | 0.999119i | \(-0.513365\pi\) | ||||
−0.0419740 | + | 0.999119i | \(0.513365\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00974 | 0.220343 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.18456 | 0.455513 | 0.227757 | − | 0.973718i | \(-0.426861\pi\) | ||||
0.227757 | + | 0.973718i | \(0.426861\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.23718 | 0.247436 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.02893 | 0.967819 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.70380 | 1.43056 | 0.715280 | − | 0.698838i | \(-0.246299\pi\) | ||||
0.715280 | + | 0.698838i | \(0.246299\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.21949 | −1.11705 | −0.558527 | − | 0.829486i | \(-0.688633\pi\) | ||||
−0.558527 | + | 0.829486i | \(0.688633\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00974 | −0.175773 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.49743 | −0.422144 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.41650 | −1.05487 | −0.527433 | − | 0.849596i | \(-0.676846\pi\) | ||||
−0.527433 | + | 0.849596i | \(0.676846\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00974 | −0.161688 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.881703 | −0.137699 | −0.0688495 | − | 0.997627i | \(-0.521933\pi\) | ||||
−0.0688495 | + | 0.997627i | \(0.521933\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.18214 | −0.332773 | −0.166386 | − | 0.986061i | \(-0.553210\pi\) | ||||
−0.166386 | + | 0.986061i | \(0.553210\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.94598 | −0.737304 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.5382 | 1.97475 | 0.987373 | − | 0.158415i | \(-0.0506384\pi\) | ||||
0.987373 | + | 0.158415i | \(0.0506384\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.57843 | 0.641109 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.98388 | −0.821949 | −0.410974 | − | 0.911647i | \(-0.634811\pi\) | ||||
−0.410974 | + | 0.911647i | \(0.634811\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.49743 | 0.336754 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.369485 | 0.0489395 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.1921 | 1.45709 | 0.728544 | − | 0.684999i | \(-0.240197\pi\) | ||||
0.728544 | + | 0.684999i | \(0.240197\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.84106 | −0.619835 | −0.309917 | − | 0.950764i | \(-0.600301\pi\) | ||||
−0.309917 | + | 0.950764i | \(0.600301\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.98043 | 0.249510 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.49743 | 0.309769 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.801261 | −0.0978897 | −0.0489448 | − | 0.998801i | \(-0.515586\pi\) | ||||
−0.0489448 | + | 0.998801i | \(0.515586\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.20584 | −0.265552 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5313 | 1.24984 | 0.624921 | − | 0.780688i | \(-0.285131\pi\) | ||||
0.624921 | + | 0.780688i | \(0.285131\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.0437 | −1.76073 | −0.880367 | − | 0.474294i | \(-0.842703\pi\) | ||||
−0.880367 | + | 0.474294i | \(0.842703\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.24923 | −0.144249 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.8318 | −1.21868 | −0.609339 | − | 0.792910i | \(-0.708565\pi\) | ||||
−0.609339 | + | 0.792910i | \(0.708565\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.863362 | 0.0959291 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.4116 | −1.25259 | −0.626294 | − | 0.779587i | \(-0.715429\pi\) | ||||
−0.626294 | + | 0.779587i | \(0.715429\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.3240 | −1.22826 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.77884 | −0.833979 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.15030 | 0.227931 | 0.113965 | − | 0.993485i | \(-0.463645\pi\) | ||||
0.113965 | + | 0.993485i | \(0.463645\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.28007 | 0.651213 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.913864 | −0.0937605 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.92908 | −0.500473 | −0.250236 | − | 0.968185i | \(-0.580508\pi\) | ||||
−0.250236 | + | 0.968185i | \(0.580508\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.98043 | −0.199040 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.302490 | 0.0300989 | 0.0150495 | − | 0.999887i | \(-0.495209\pi\) | ||||
0.0150495 | + | 0.999887i | \(0.495209\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4841 | 1.23010 | 0.615048 | − | 0.788489i | \(-0.289136\pi\) | ||||
0.615048 | + | 0.788489i | \(0.289136\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.52176 | 0.246099 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.3796 | −1.87350 | −0.936750 | − | 0.349998i | \(-0.886182\pi\) | ||||
−0.936750 | + | 0.349998i | \(0.886182\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6608 | −1.02112 | −0.510561 | − | 0.859842i | \(-0.670562\pi\) | ||||
−0.510561 | + | 0.859842i | \(0.670562\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.47900 | 0.614959 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.85865 | 0.268919 | 0.134459 | − | 0.990919i | \(-0.457070\pi\) | ||||
0.134459 | + | 0.990919i | \(0.457070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.45581 | 0.508757 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.98043 | −0.183090 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.53427 | 0.415656 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.890291 | 0.0802748 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.39740 | −0.840529 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.74502 | 0.598523 | 0.299262 | − | 0.954171i | \(-0.403260\pi\) | ||||
0.299262 | + | 0.954171i | \(0.403260\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.20339 | 0.193998 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.19971 | 0.366930 | 0.183465 | − | 0.983026i | \(-0.441269\pi\) | ||||
0.183465 | + | 0.983026i | \(0.441269\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.365921 | 0.0317294 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12.5594 | 1.08094 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.91501 | −0.163610 | −0.0818051 | − | 0.996648i | \(-0.526068\pi\) | ||||
−0.0818051 | + | 0.996648i | \(0.526068\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.7175 | −0.909044 | −0.454522 | − | 0.890735i | \(-0.650190\pi\) | ||||
−0.454522 | + | 0.890735i | \(0.650190\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.6700 | −1.15122 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.2397 | 1.59777 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00974 | −0.0832819 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.1801 | 0.915912 | 0.457956 | − | 0.888975i | \(-0.348582\pi\) | ||||
0.457956 | + | 0.888975i | \(0.348582\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.960122 | −0.0781336 | −0.0390668 | − | 0.999237i | \(-0.512439\pi\) | ||||
−0.0390668 | + | 0.999237i | \(0.512439\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.97978 | 0.725972 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.5328 | −1.24762 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.2642 | −1.21822 | −0.609109 | − | 0.793086i | \(-0.708473\pi\) | ||||
−0.609109 | + | 0.793086i | \(0.708473\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.04216 | 0.479174 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.18456 | −0.172168 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.9718 | −1.17268 | −0.586341 | − | 0.810064i | \(-0.699432\pi\) | ||||
−0.586341 | + | 0.810064i | \(0.699432\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.52176 | −0.196319 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.94970 | 0.383020 | 0.191510 | − | 0.981491i | \(-0.438662\pi\) | ||||
0.191510 | + | 0.981491i | \(0.438662\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.724680 | 0.0554176 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.24942 | −0.171020 | −0.0855101 | − | 0.996337i | \(-0.527252\pi\) | ||||
−0.0855101 | + | 0.996337i | \(0.527252\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.23718 | −0.0935221 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.3011 | −0.849444 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.92785 | −0.517812 | −0.258906 | − | 0.965903i | \(-0.583362\pi\) | ||||
−0.258906 | + | 0.965903i | \(0.583362\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.74336 | −0.426900 | −0.213450 | − | 0.976954i | \(-0.568470\pi\) | ||||
−0.213450 | + | 0.976954i | \(0.568470\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.88821 | 0.361347 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.0248 | −1.17817 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.53427 | −0.331579 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.02893 | −0.365801 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.4151 | −1.18775 | −0.593877 | − | 0.804556i | \(-0.702403\pi\) | ||||
−0.593877 | + | 0.804556i | \(0.702403\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7374 | −0.844878 | −0.422439 | − | 0.906391i | \(-0.638826\pi\) | ||||
−0.422439 | + | 0.906391i | \(0.638826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.52176 | −0.180587 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.58716 | 0.540563 | 0.270281 | − | 0.962781i | \(-0.412883\pi\) | ||||
0.270281 | + | 0.962781i | \(0.412883\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.79733 | −0.694514 | −0.347257 | − | 0.937770i | \(-0.612887\pi\) | ||||
−0.347257 | + | 0.937770i | \(0.612887\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.809066 | 0.0570671 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.70380 | −0.540701 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.20200 | −0.153794 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.32637 | −0.300703 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.365921 | −0.0253113 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.3422 | 1.81347 | 0.906736 | − | 0.421698i | \(-0.138566\pi\) | ||||
0.906736 | + | 0.421698i | \(0.138566\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.6339 | −0.728624 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.44975 | −0.371670 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.21949 | 0.422207 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.1902 | 1.02646 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.53427 | −0.305008 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.3050 | −0.824007 | −0.412003 | − | 0.911182i | \(-0.635171\pi\) | ||||
−0.412003 | + | 0.911182i | \(0.635171\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.45014 | −0.163343 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.54237 | 0.102371 | 0.0511855 | − | 0.998689i | \(-0.483700\pi\) | ||||
0.0511855 | + | 0.998689i | \(0.483700\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.9995 | −1.18944 | −0.594720 | − | 0.803933i | \(-0.702737\pi\) | ||||
−0.594720 | + | 0.803933i | \(0.702737\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00974 | 0.0664360 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.9375 | −1.04410 | −0.522050 | − | 0.852915i | \(-0.674833\pi\) | ||||
−0.522050 | + | 0.852915i | \(0.674833\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.8107 | 2.20557 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.9373 | 0.710457 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.3433 | 1.18653 | 0.593266 | − | 0.805006i | \(-0.297838\pi\) | ||||
0.593266 | + | 0.805006i | \(0.297838\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.61217 | −0.554758 | −0.277379 | − | 0.960761i | \(-0.589466\pi\) | ||||
−0.277379 | + | 0.960761i | \(0.589466\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.9586 | −1.02374 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.49743 | 0.159555 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.365921 | −0.0232830 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.5228 | 0.730226 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.4344 | −0.721734 | −0.360867 | − | 0.932617i | \(-0.617519\pi\) | ||||
−0.360867 | + | 0.932617i | \(0.617519\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.18456 | 0.137342 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.4343 | 0.716046 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.8208 | −1.04925 | −0.524625 | − | 0.851333i | \(-0.675795\pi\) | ||||
−0.524625 | + | 0.851333i | \(0.675795\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.41650 | 0.398702 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.2568 | −0.944373 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.2677 | 1.12644 | 0.563218 | − | 0.826308i | \(-0.309563\pi\) | ||||
0.563218 | + | 0.826308i | \(0.309563\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.9443 | −0.918023 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.17124 | −0.132878 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.3169 | −0.750975 | −0.375487 | − | 0.926828i | \(-0.622525\pi\) | ||||
−0.375487 | + | 0.926828i | \(0.622525\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.3006 | 1.47616 | 0.738079 | − | 0.674714i | \(-0.235733\pi\) | ||||
0.738079 | + | 0.674714i | \(0.235733\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.00974 | 0.0611122 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.23718 | 0.0746048 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.14292 | −0.248924 | −0.124462 | − | 0.992224i | \(-0.539720\pi\) | ||||
−0.124462 | + | 0.992224i | \(0.539720\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.3172 | 0.737414 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.2332 | −1.86321 | −0.931607 | − | 0.363467i | \(-0.881593\pi\) | ||||
−0.931607 | + | 0.363467i | \(0.881593\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.6563 | 0.990112 | 0.495056 | − | 0.868861i | \(-0.335148\pi\) | ||||
0.495056 | + | 0.868861i | \(0.335148\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.922765 | 0.0546599 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.881703 | 0.0520453 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.55959 | 0.209388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.97709 | 0.291762 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.0128 | 1.57810 | 0.789052 | − | 0.614327i | \(-0.210572\pi\) | ||||
0.789052 | + | 0.614327i | \(0.210572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.9516 | 1.62740 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.02893 | 0.291808 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.18456 | 0.126337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.18214 | 0.125776 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.305437 | −0.0175469 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.0902 | −0.692285 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.7935 | −0.901382 | −0.450691 | − | 0.892680i | \(-0.648822\pi\) | ||||
−0.450691 | + | 0.892680i | \(0.648822\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.6057 | −0.717114 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.3795 | 0.985501 | 0.492750 | − | 0.870171i | \(-0.335992\pi\) | ||||
0.492750 | + | 0.870171i | \(0.335992\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.0958 | 0.740220 | 0.370110 | − | 0.928988i | \(-0.379320\pi\) | ||||
0.370110 | + | 0.928988i | \(0.379320\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.94598 | 0.278675 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.9025 | 1.90416 | 0.952078 | − | 0.305857i | \(-0.0989429\pi\) | ||||
0.952078 | + | 0.305857i | \(0.0989429\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.70380 | 0.431330 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.5684 | 1.09220 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.65918 | 0.0923195 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.23718 | 0.0686264 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.7647 | 0.595287 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.5382 | −0.746384 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.4390 | −0.958531 | −0.479266 | − | 0.877670i | \(-0.659097\pi\) | ||||
−0.479266 | + | 0.877670i | \(0.659097\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.7074 | 0.696362 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00110 | −0.109332 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.3030 | −0.615711 | −0.307856 | − | 0.951433i | \(-0.599611\pi\) | ||||
−0.307856 | + | 0.951433i | \(0.599611\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.88649 | −0.156773 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.21949 | −0.336805 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.50895 | −0.296592 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.4541 | −0.561205 | −0.280603 | − | 0.959824i | \(-0.590534\pi\) | ||||
−0.280603 | + | 0.959824i | \(0.590534\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.67327 | 0.196626 | 0.0983129 | − | 0.995156i | \(-0.468655\pi\) | ||||
0.0983129 | + | 0.995156i | \(0.468655\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.02893 | 0.268425 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.58978 | 0.297514 | 0.148757 | − | 0.988874i | \(-0.452473\pi\) | ||||
0.148757 | + | 0.988874i | \(0.452473\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.3014 | 1.39593 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.57843 | −0.242316 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.9758 | −1.00150 | −0.500751 | − | 0.865591i | \(-0.666943\pi\) | ||||
−0.500751 | + | 0.865591i | \(0.666943\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8661 | −0.992953 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00974 | −0.0529976 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −37.5707 | −1.96654 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.649035 | 0.0338794 | 0.0169397 | − | 0.999857i | \(-0.494608\pi\) | ||||
0.0169397 | + | 0.999857i | \(0.494608\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.74615 | 0.0909008 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.98388 | 0.310667 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.93989 | −0.359334 | −0.179667 | − | 0.983727i | \(-0.557502\pi\) | ||||
−0.179667 | + | 0.983727i | \(0.557502\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.48893 | 0.490006 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.70380 | 0.396766 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.5005 | −0.950309 | −0.475155 | − | 0.879902i | \(-0.657608\pi\) | ||||
−0.475155 | + | 0.879902i | \(0.657608\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.81071 | −0.348923 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.2993 | −0.577367 | −0.288683 | − | 0.957425i | \(-0.593217\pi\) | ||||
−0.288683 | + | 0.957425i | \(0.593217\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.49743 | −0.127281 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.32156 | 0.219677 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0292 | 0.762012 | 0.381006 | − | 0.924572i | \(-0.375578\pi\) | ||||
0.381006 | + | 0.924572i | \(0.375578\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.90540 | −0.500938 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.24061 | −0.213911 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.0518 | −1.36112 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.95471 | −0.499613 | −0.249806 | − | 0.968296i | \(-0.580367\pi\) | ||||
−0.249806 | + | 0.968296i | \(0.580367\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.369485 | −0.0184974 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.4612 | 0.822035 | 0.411017 | − | 0.911627i | \(-0.365174\pi\) | ||||
0.411017 | + | 0.911627i | \(0.365174\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.21949 | −0.309815 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.15619 | 0.107142 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.41650 | −0.318054 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.2681 | −0.952747 | −0.476373 | − | 0.879243i | \(-0.658049\pi\) | ||||
−0.476373 | + | 0.879243i | \(0.658049\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.93366 | 0.0953804 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.1921 | −0.550728 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.4998 | −1.39900 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.8219 | 0.529949 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.68072 | 0.277522 | 0.138761 | − | 0.990326i | \(-0.455688\pi\) | ||||
0.138761 | + | 0.990326i | \(0.455688\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.71031 | 0.278303 | 0.139152 | − | 0.990271i | \(-0.455562\pi\) | ||||
0.139152 | + | 0.990271i | \(0.455562\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −26.8113 | −1.30361 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.60971 | −0.272111 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.84106 | 0.234275 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.00974 | −0.0487507 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.3081 | −0.978208 | −0.489104 | − | 0.872226i | \(-0.662676\pi\) | ||||
−0.489104 | + | 0.872226i | \(0.662676\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.63239 | 0.462903 | 0.231452 | − | 0.972846i | \(-0.425653\pi\) | ||||
0.231452 | + | 0.972846i | \(0.425653\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −19.4271 | −0.931460 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.799378 | −0.0382395 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.3622 | 1.87865 | 0.939327 | − | 0.343024i | \(-0.111451\pi\) | ||||
0.939327 | + | 0.343024i | \(0.111451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.98043 | −0.0943060 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.88885 | −0.327299 | −0.163650 | − | 0.986519i | \(-0.552327\pi\) | ||||
−0.163650 | + | 0.986519i | \(0.552327\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.37022 | 0.254573 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.2890 | −0.533953 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.8660 | 1.26789 | 0.633943 | − | 0.773380i | \(-0.281435\pi\) | ||||
0.633943 | + | 0.773380i | \(0.281435\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.881703 | −0.0415178 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.969473 | 0.0455498 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.49743 | −0.117082 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.9684 | −0.934082 | −0.467041 | − | 0.884236i | \(-0.654680\pi\) | ||||
−0.467041 | + | 0.884236i | \(0.654680\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.8025 | −1.06433 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.3256 | −1.64528 | −0.822639 | − | 0.568563i | \(-0.807499\pi\) | ||||
−0.822639 | + | 0.568563i | \(0.807499\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.15838 | −0.332678 | −0.166339 | − | 0.986069i | \(-0.553195\pi\) | ||||
−0.166339 | + | 0.986069i | \(0.553195\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.6841 | 0.727331 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −40.7593 | −1.88611 | −0.943057 | − | 0.332632i | \(-0.892063\pi\) | ||||
−0.943057 | + | 0.332632i | \(0.892063\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.801261 | 0.0369988 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.4129 | 0.710189 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.18214 | −0.100335 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.452711 | −0.0207718 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.8506 | 0.542603 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.3387 | −1.15776 | −0.578878 | − | 0.815414i | \(-0.696509\pi\) | ||||
−0.578878 | + | 0.815414i | \(0.696509\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.41650 | −0.292567 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.20584 | 0.100369 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.3101 | −0.558971 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.73856 | −0.214725 | −0.107362 | − | 0.994220i | \(-0.534240\pi\) | ||||
−0.107362 | + | 0.994220i | \(0.534240\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.1176 | 0.683643 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.7755 | 0.576551 | 0.288276 | − | 0.957547i | \(-0.406918\pi\) | ||||
0.288276 | + | 0.957547i | \(0.406918\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.9311 | −1.57322 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.94598 | −0.222305 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.5313 | −0.472396 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.2772 | 1.08680 | 0.543398 | − | 0.839475i | \(-0.317138\pi\) | ||||
0.543398 | + | 0.839475i | \(0.317138\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.99791 | −0.223290 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.5036 | 1.53844 | 0.769220 | − | 0.638984i | \(-0.220645\pi\) | ||||
0.769220 | + | 0.638984i | \(0.220645\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.755450 | 0.0336171 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00974 | −0.0448441 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.3212 | −1.29964 | −0.649820 | − | 0.760089i | \(-0.725156\pi\) | ||||
−0.649820 | + | 0.760089i | \(0.725156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.0437 | 0.665495 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.84019 | −0.0812465 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.1783 | 1.37388 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.5382 | 0.595408 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.27133 | 0.0997002 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.7854 | 0.516328 | 0.258164 | − | 0.966101i | \(-0.416883\pi\) | ||||
0.258164 | + | 0.966101i | \(0.416883\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.6854 | −1.16687 | −0.583435 | − | 0.812160i | \(-0.698292\pi\) | ||||
−0.583435 | + | 0.812160i | \(0.698292\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.24923 | 0.0545209 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.2009 | 1.22845 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.2277 | −0.792508 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.1651 | −0.961885 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.881703 | −0.0381908 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −48.3994 | −2.09249 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.99533 | 0.301871 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.7426 | −1.36472 | −0.682360 | − | 0.731017i | \(-0.739046\pi\) | ||||
−0.682360 | + | 0.731017i | \(0.739046\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.79930 | 0.248872 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.6247 | −1.14048 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.11542 | −0.0904488 | −0.0452244 | − | 0.998977i | \(-0.514400\pi\) | ||||
−0.0452244 | + | 0.998977i | \(0.514400\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.58736 | 0.409179 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.81898 | −0.120093 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.8318 | 0.460617 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.1809 | 0.686840 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.5878 | 0.490992 | 0.245496 | − | 0.969398i | \(-0.421049\pi\) | ||||
0.245496 | + | 0.969398i | \(0.421049\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.18214 | −0.0922946 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.57843 | 0.193302 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.4621 | 0.988811 | 0.494405 | − | 0.869231i | \(-0.335386\pi\) | ||||
0.494405 | + | 0.869231i | \(0.335386\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.13928 | 0.300352 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.863362 | −0.0362578 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.2729 | −0.807963 | −0.403982 | − | 0.914767i | \(-0.632374\pi\) | ||||
−0.403982 | + | 0.914767i | \(0.632374\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.71626 | −0.197369 | −0.0986847 | − | 0.995119i | \(-0.531464\pi\) | ||||
−0.0986847 | + | 0.995119i | \(0.531464\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.5750 | 0.692429 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.70270 | 0.112710 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.74840 | 0.0727866 | 0.0363933 | − | 0.999338i | \(-0.488413\pi\) | ||||
0.0363933 | + | 0.999338i | \(0.488413\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.8517 | 0.492541 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.4116 | 0.473434 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.98388 | −0.247827 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.94598 | −0.204491 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.22227 | 0.256821 | 0.128410 | − | 0.991721i | \(-0.459013\pi\) | ||||
0.128410 | + | 0.991721i | \(0.459013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.27584 | 0.0937745 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.66105 | −0.315134 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.2842 | −1.61321 | −0.806604 | − | 0.591092i | \(-0.798697\pi\) | ||||
−0.806604 | + | 0.591092i | \(0.798697\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.3240 | 0.464240 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.89275 | 0.404883 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.9615 | 0.652169 | 0.326084 | − | 0.945341i | \(-0.394271\pi\) | ||||
0.326084 | + | 0.945341i | \(0.394271\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.3564 | 0.544820 | 0.272410 | − | 0.962181i | \(-0.412179\pi\) | ||||
0.272410 | + | 0.962181i | \(0.412179\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.58684 | 0.0646211 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.49743 | 0.101535 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.2807 | −1.79730 | −0.898649 | − | 0.438669i | \(-0.855450\pi\) | ||||
−0.898649 | + | 0.438669i | \(0.855450\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.77884 | 0.315214 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.5382 | 0.547696 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.6381 | 0.429670 | 0.214835 | − | 0.976650i | \(-0.431079\pi\) | ||||
0.214835 | + | 0.976650i | \(0.431079\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.22344 | 0.0896579 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.79544 | −0.152799 | −0.0763994 | − | 0.997077i | \(-0.524342\pi\) | ||||
−0.0763994 | + | 0.997077i | \(0.524342\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.1177 | −1.33111 | −0.665556 | − | 0.746348i | \(-0.731806\pi\) | ||||
−0.665556 | + | 0.746348i | \(0.731806\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.9860 | 0.440854 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.15030 | −0.0861498 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.6553 | −1.18621 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.369485 | 0.0147558 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.0942 | 1.16006 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.6084 | −0.621360 | −0.310680 | − | 0.950515i | \(-0.600557\pi\) | ||||
−0.310680 | + | 0.950515i | \(0.600557\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.5988 | −1.05721 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.8452 | 0.668483 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −20.8566 | −0.825072 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.1102 | −0.438825 | −0.219413 | − | 0.975632i | \(-0.570414\pi\) | ||||
−0.219413 | + | 0.975632i | \(0.570414\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.12970 | −0.0445510 | −0.0222755 | − | 0.999752i | \(-0.507091\pi\) | ||||
−0.0222755 | + | 0.999752i | \(0.507091\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.50283 | 0.216674 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.67659 | 0.0659134 | 0.0329567 | − | 0.999457i | \(-0.489508\pi\) | ||||
0.0329567 | + | 0.999457i | \(0.489508\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.1921 | 0.439329 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.28007 | −0.246135 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.4887 | 1.58445 | 0.792224 | − | 0.610231i | \(-0.208923\pi\) | ||||
0.792224 | + | 0.610231i | \(0.208923\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.4885 | 0.409820 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.7929 | 1.16233 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.6442 | 0.609411 | 0.304706 | − | 0.952447i | \(-0.401442\pi\) | ||||
0.304706 | + | 0.952447i | \(0.401442\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.38907 | 0.326297 | 0.163149 | − | 0.986602i | \(-0.447835\pi\) | ||||
0.163149 | + | 0.986602i | \(0.447835\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.57843 | 0.177812 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.913864 | 0.0354381 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.8295 | 0.651639 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.4249 | 0.480374 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.84106 | −0.186887 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.1583 | −1.43235 | −0.716173 | − | 0.697923i | \(-0.754108\pi\) | ||||
−0.716173 | + | 0.697923i | \(0.754108\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.22170 | 0.239473 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.5564 | 0.828479 | 0.414239 | − | 0.910168i | \(-0.364048\pi\) | ||||
0.414239 | + | 0.910168i | \(0.364048\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.92908 | 0.189161 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.55740 | −0.0596795 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.5299 | −0.402917 | −0.201458 | − | 0.979497i | \(-0.564568\pi\) | ||||
−0.201458 | + | 0.979497i | \(0.564568\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.78261 | −0.182734 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.1748 | 0.693412 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.98388 | −0.227968 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 52.3175 | 1.99025 | 0.995125 | − | 0.0986202i | \(-0.0314429\pi\) | ||||
0.995125 | + | 0.0986202i | \(0.0314429\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.98043 | 0.0752301 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.7662 | −1.01530 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.99788 | 0.151431 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.0927 | 0.608683 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.79701 | −0.218950 | −0.109475 | − | 0.993990i | \(-0.534917\pi\) | ||||
−0.109475 | + | 0.993990i | \(0.534917\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.34793 | 0.0885540 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −34.1400 | −1.28579 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.302490 | −0.0113763 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.5275 | −1.03382 | −0.516908 | − | 0.856041i | \(-0.672917\pi\) | ||||
−0.516908 | + | 0.856041i | \(0.672917\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.4517 | 0.804500 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.5869 | −0.508833 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.49743 | 0.0933988 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.5220 | −0.691717 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.2588 | −0.867408 | −0.433704 | − | 0.901055i | \(-0.642794\pi\) | ||||
−0.433704 | + | 0.901055i | \(0.642794\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.4841 | −0.464933 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.69605 | 0.323410 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.53099 | 0.353972 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.9978 | −1.29800 | −0.648999 | − | 0.760790i | \(-0.724812\pi\) | ||||
−0.648999 | + | 0.760790i | \(0.724812\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5239 | 0.500886 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.89440 | 0.365958 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.1423 | 0.817845 | 0.408922 | − | 0.912569i | \(-0.365905\pi\) | ||||
0.408922 | + | 0.912569i | \(0.365905\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.52176 | −0.0930165 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.801261 | −0.0295148 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.3036 | −1.11474 | −0.557368 | − | 0.830266i | \(-0.688189\pi\) | ||||
−0.557368 | + | 0.830266i | \(0.688189\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.369485 | 0.0135734 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.5396 | −1.26714 | −0.633568 | − | 0.773687i | \(-0.718410\pi\) | ||||
−0.633568 | + | 0.773687i | \(0.718410\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.9217 | 1.02297 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.5999 | 0.826886 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.3796 | 0.708117 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.4273 | 1.73065 | 0.865323 | − | 0.501214i | \(-0.167113\pi\) | ||||
0.865323 | + | 0.501214i | \(0.167113\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.5458 | 0.420752 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.39784 | −0.0872664 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.64799 | −0.241625 | −0.120813 | − | 0.992675i | \(-0.538550\pi\) | ||||
−0.120813 | + | 0.992675i | \(0.538550\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.20584 | −0.0800670 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.9591 | 1.30352 | 0.651758 | − | 0.758427i | \(-0.274032\pi\) | ||||
0.651758 | + | 0.758427i | \(0.274032\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.6608 | 0.385948 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22.4264 | 0.810829 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.1921 | 0.404124 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.7818 | −0.460924 | −0.230462 | − | 0.973081i | \(-0.574024\pi\) | ||||
−0.230462 | + | 0.973081i | \(0.574024\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.9846 | 0.611685 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.0166 | −1.07962 | −0.539812 | − | 0.841786i | \(-0.681505\pi\) | ||||
−0.539812 | + | 0.841786i | \(0.681505\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.69464 | −0.276400 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.47900 | −0.232433 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.322634 | 0.0115596 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.5313 | 0.376841 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 38.7419 | 1.38452 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.1214 | −1.36061 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.4408 | −1.26333 | −0.631664 | − | 0.775242i | \(-0.717628\pi\) | ||||
−0.631664 | + | 0.775242i | \(0.717628\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.4457 | −0.656683 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.85865 | −0.101642 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.84106 | −0.171911 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.0899 | 0.535183 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.5538 | 1.54275 | 0.771377 | − | 0.636379i | \(-0.219568\pi\) | ||||
0.771377 | + | 0.636379i | \(0.219568\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −61.3857 | −2.17167 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.25850 | −0.150467 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.0437 | −0.530881 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.45581 | −0.192292 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.4369 | 0.437798 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.7702 | −1.01151 | −0.505753 | − | 0.862678i | \(-0.668785\pi\) | ||||
−0.505753 | + | 0.862678i | \(0.668785\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.53736 | 0.229558 | 0.114779 | − | 0.993391i | \(-0.463384\pi\) | ||||
0.114779 | + | 0.993391i | \(0.463384\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.5373 | −0.860561 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −37.3911 | −1.30975 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.798491 | 0.0279356 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.98043 | 0.0692017 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.3259 | −1.89599 | −0.947994 | − | 0.318287i | \(-0.896892\pi\) | ||||
−0.947994 | + | 0.318287i | \(0.896892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.7051 | −0.617161 | −0.308580 | − | 0.951198i | \(-0.599854\pi\) | ||||
−0.308580 | + | 0.951198i | \(0.599854\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.24923 | −0.0434926 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.06631 | 0.176173 | 0.0880865 | − | 0.996113i | \(-0.471925\pi\) | ||||
0.0880865 | + | 0.996113i | \(0.471925\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.1760 | −1.36064 | −0.680319 | − | 0.732916i | \(-0.738159\pi\) | ||||
−0.680319 | + | 0.732916i | \(0.738159\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.18327 | 0.145116 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.53427 | −0.157103 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.3616 | 0.427790 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −31.2774 | −1.08111 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.3925 | 0.496884 | 0.248442 | − | 0.968647i | \(-0.420082\pi\) | ||||
0.248442 | + | 0.968647i | \(0.420082\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.3486 | 1.04650 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.5374 | 1.08620 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.49743 | 0.0859144 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.8185 | −0.577209 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.0173 | −0.480506 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.5823 | −0.773202 | −0.386601 | − | 0.922247i | \(-0.626351\pi\) | ||||
−0.386601 | + | 0.922247i | \(0.626351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.80984 | 0.0618952 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.3719 | −0.866688 | −0.433344 | − | 0.901229i | \(-0.642666\pi\) | ||||
−0.433344 | + | 0.901229i | \(0.642666\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.2873 | 0.385117 | 0.192558 | − | 0.981286i | \(-0.438322\pi\) | ||||
0.192558 | + | 0.981286i | \(0.438322\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.890291 | −0.0303410 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48.2809 | −1.64350 | −0.821750 | − | 0.569848i | \(-0.807002\pi\) | ||||
−0.821750 | + | 0.569848i | \(0.807002\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.61778 | −0.191010 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.59426 | −0.122068 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.8318 | −0.367445 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.801261 | −0.0271497 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.76168 | 0.330383 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.39740 | 0.317690 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.8479 | 1.85208 | 0.926040 | − | 0.377425i | \(-0.123190\pi\) | ||||
0.926040 | + | 0.377425i | \(0.123190\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.2759 | −0.919993 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.6520 | 0.594710 | 0.297355 | − | 0.954767i | \(-0.403896\pi\) | ||||
0.297355 | + | 0.954767i | \(0.403896\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.7267 | −1.60613 | −0.803065 | − | 0.595891i | \(-0.796799\pi\) | ||||
−0.803065 | + | 0.595891i | \(0.796799\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −28.2238 | −0.948733 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.0401 | 0.437843 | 0.218922 | − | 0.975742i | \(-0.429746\pi\) | ||||
0.218922 | + | 0.975742i | \(0.429746\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.74502 | −0.226221 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.863362 | 0.0289237 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.95390 | −0.165776 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.3019 | −0.578337 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.20584 | −0.0736509 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −47.9138 | −1.59801 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.1325 | 0.903915 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.20339 | −0.0733243 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.3437 | −0.476799 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.4071 | −0.345563 | −0.172782 | − | 0.984960i | \(-0.555275\pi\) | ||||
−0.172782 | + | 0.984960i | \(0.555275\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.599060 | −0.0198696 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.38463 | 0.277795 | 0.138898 | − | 0.990307i | \(-0.455644\pi\) | ||||
0.138898 | + | 0.990307i | \(0.455644\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.4116 | −0.377670 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.2080 | 0.403584 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.19971 | −0.138687 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.9995 | 1.35245 | 0.676224 | − | 0.736696i | \(-0.263615\pi\) | ||||
0.676224 | + | 0.736696i | \(0.263615\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.9473 | 0.525482 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.5313 | 0.346644 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.93837 | −0.261012 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.7239 | −0.812038 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.83579 | −0.257084 | −0.128542 | − | 0.991704i | \(-0.541030\pi\) | ||||
−0.128542 | + | 0.991704i | \(0.541030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.365921 | −0.0119926 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.5488 | −0.574521 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.3240 | −0.370336 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.1617 | −0.593317 | −0.296659 | − | 0.954984i | \(-0.595872\pi\) | ||||
−0.296659 | + | 0.954984i | \(0.595872\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.2234 | −0.431529 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.5504 | −1.02851 | −0.514257 | − | 0.857636i | \(-0.671932\pi\) | ||||
−0.514257 | + | 0.857636i | \(0.671932\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.92614 | −0.0627237 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.5594 | −0.408558 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.3514 | 0.888802 | 0.444401 | − | 0.895828i | \(-0.353417\pi\) | ||||
0.444401 | + | 0.895828i | \(0.353417\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.0437 | −0.488339 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −34.2327 | −1.11007 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.2584 | 0.397088 | 0.198544 | − | 0.980092i | \(-0.436379\pi\) | ||||
0.198544 | + | 0.980092i | \(0.436379\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.9956 | −1.32659 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.77884 | −0.251454 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.91501 | 0.0618388 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.68211 | 0.247810 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 38.3799 | 1.23678 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29.3134 | −0.943633 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.2786 | 0.362697 | 0.181348 | − | 0.983419i | \(-0.441954\pi\) | ||||
0.181348 | + | 0.983419i | \(0.441954\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.67535 | −0.0538198 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.8741 | 1.31171 | 0.655856 | − | 0.754886i | \(-0.272308\pi\) | ||||
0.655856 | + | 0.754886i | \(0.272308\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.7175 | 0.343586 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.24923 | −0.0400074 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.3903 | 1.22821 | 0.614107 | − | 0.789223i | \(-0.289516\pi\) | ||||
0.614107 | + | 0.789223i | \(0.289516\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.15030 | 0.0687238 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.1130 | 0.674085 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.4016 | 0.491233 | 0.245617 | − | 0.969367i | \(-0.421010\pi\) | ||||
0.245617 | + | 0.969367i | \(0.421010\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.9484 | 0.603747 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.6700 | 0.435122 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.76702 | −0.151582 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.0694 | −0.605759 | −0.302879 | − | 0.953029i | \(-0.597948\pi\) | ||||
−0.302879 | + | 0.953029i | \(0.597948\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.6088 | 0.558798 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.4682 | −0.775694 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 62.7971 | 1.98881 | 0.994403 | − | 0.105656i | \(-0.0336944\pi\) | ||||
0.994403 | + | 0.105656i | \(0.0336944\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −32.2682 | −1.02092 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8008.2.a.p.1.3 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.p.1.3 | ✓ | 9 | 1.1 | even | 1 | trivial |