Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 26x^{8} - 3x^{7} + 220x^{6} + 42x^{5} - 675x^{4} - 67x^{3} + 628x^{2} - 48x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-2.25873\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.25873 | 0.562920 | 0.281460 | − | 0.959573i | \(-0.409181\pi\) | ||||
0.281460 | + | 0.959573i | \(0.409181\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.924269 | 0.349341 | 0.174670 | − | 0.984627i | \(-0.444114\pi\) | ||||
0.174670 | + | 0.984627i | \(0.444114\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.02540 | −1.21370 | −0.606852 | − | 0.794815i | \(-0.707568\pi\) | ||||
−0.606852 | + | 0.794815i | \(0.707568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.29130 | 0.635493 | 0.317746 | − | 0.948176i | \(-0.397074\pi\) | ||||
0.317746 | + | 0.948176i | \(0.397074\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.25873 | 0.325002 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.17080 | −1.49664 | −0.748319 | − | 0.663339i | \(-0.769139\pi\) | ||||
−0.748319 | + | 0.663339i | \(0.769139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.46836 | −0.336864 | −0.168432 | − | 0.985713i | \(-0.553870\pi\) | ||||
−0.168432 | + | 0.985713i | \(0.553870\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.924269 | 0.201692 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.97565 | 1.45452 | 0.727262 | − | 0.686360i | \(-0.240793\pi\) | ||||
0.727262 | + | 0.686360i | \(0.240793\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.41561 | −0.683122 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00626 | −1.11533 | −0.557667 | − | 0.830065i | \(-0.688304\pi\) | ||||
−0.557667 | + | 0.830065i | \(0.688304\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.16677 | 0.209559 | 0.104779 | − | 0.994495i | \(-0.466586\pi\) | ||||
0.104779 | + | 0.994495i | \(0.466586\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.02540 | −0.700732 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.16340 | 0.196651 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.20171 | −0.855156 | −0.427578 | − | 0.903978i | \(-0.640633\pi\) | ||||
−0.427578 | + | 0.903978i | \(0.640633\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.29130 | 0.366902 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.15702 | −0.961565 | −0.480783 | − | 0.876840i | \(-0.659647\pi\) | ||||
−0.480783 | + | 0.876840i | \(0.659647\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.36680 | −0.513432 | −0.256716 | − | 0.966487i | \(-0.582640\pi\) | ||||
−0.256716 | + | 0.966487i | \(0.582640\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.25873 | 0.187640 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.22930 | −0.325177 | −0.162588 | − | 0.986694i | \(-0.551984\pi\) | ||||
−0.162588 | + | 0.986694i | \(0.551984\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.14573 | −0.877961 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.17080 | −0.864084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.66585 | 0.778264 | 0.389132 | − | 0.921182i | \(-0.372775\pi\) | ||||
0.389132 | + | 0.921182i | \(0.372775\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.06688 | −0.683217 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.46836 | −0.194489 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.30823 | −0.430694 | −0.215347 | − | 0.976538i | \(-0.569088\pi\) | ||||
−0.215347 | + | 0.976538i | \(0.569088\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.09227 | 0.908073 | 0.454036 | − | 0.890983i | \(-0.349984\pi\) | ||||
0.454036 | + | 0.890983i | \(0.349984\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.924269 | 0.116447 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.88412 | 0.357731 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.27623 | −0.155916 | −0.0779582 | − | 0.996957i | \(-0.524840\pi\) | ||||
−0.0779582 | + | 0.996957i | \(0.524840\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.97565 | 0.839769 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.32478 | −1.10665 | −0.553324 | − | 0.832966i | \(-0.686641\pi\) | ||||
−0.553324 | + | 0.832966i | \(0.686641\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.24728 | −0.614148 | −0.307074 | − | 0.951686i | \(-0.599350\pi\) | ||||
−0.307074 | + | 0.951686i | \(0.599350\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.41561 | −0.394400 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.72055 | −0.423996 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.42969 | 0.723397 | 0.361698 | − | 0.932295i | \(-0.382197\pi\) | ||||
0.361698 | + | 0.932295i | \(0.382197\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.18422 | −0.569042 | −0.284521 | − | 0.958670i | \(-0.591835\pi\) | ||||
−0.284521 | + | 0.958670i | \(0.591835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.76735 | −0.842487 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.00626 | −0.643939 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.24526 | −0.449997 | −0.224998 | − | 0.974359i | \(-0.572238\pi\) | ||||
−0.224998 | + | 0.974359i | \(0.572238\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.11778 | 0.222004 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.16677 | 0.120989 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.84826 | −0.189628 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.704554 | 0.0715366 | 0.0357683 | − | 0.999360i | \(-0.488612\pi\) | ||||
0.0357683 | + | 0.999360i | \(0.488612\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.02540 | −0.404568 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.74152 | −0.770310 | −0.385155 | − | 0.922852i | \(-0.625852\pi\) | ||||
−0.385155 | + | 0.922852i | \(0.625852\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.3637 | 1.31677 | 0.658384 | − | 0.752682i | \(-0.271240\pi\) | ||||
0.658384 | + | 0.752682i | \(0.271240\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.16340 | 0.113536 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.75302 | −0.556165 | −0.278083 | − | 0.960557i | \(-0.589699\pi\) | ||||
−0.278083 | + | 0.960557i | \(0.589699\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.708744 | −0.0678854 | −0.0339427 | − | 0.999424i | \(-0.510806\pi\) | ||||
−0.0339427 | + | 0.999424i | \(0.510806\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.20171 | −0.493725 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.18223 | −0.675648 | −0.337824 | − | 0.941209i | \(-0.609691\pi\) | ||||
−0.337824 | + | 0.941209i | \(0.609691\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.78043 | 0.818779 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.29130 | 0.211831 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.70348 | −0.522837 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.20383 | 0.473076 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.15702 | −0.555160 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.5929 | −0.947462 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.4966 | 1.10890 | 0.554449 | − | 0.832218i | \(-0.312929\pi\) | ||||
0.554449 | + | 0.832218i | \(0.312929\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.36680 | −0.296430 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.96532 | 0.783304 | 0.391652 | − | 0.920113i | \(-0.371904\pi\) | ||||
0.391652 | + | 0.920113i | \(0.371904\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.35716 | −0.117680 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.25873 | 0.108334 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.4263 | −1.14709 | −0.573543 | − | 0.819176i | \(-0.694431\pi\) | ||||
−0.573543 | + | 0.819176i | \(0.694431\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.23934 | 0.783670 | 0.391835 | − | 0.920035i | \(-0.371840\pi\) | ||||
0.391835 | + | 0.920035i | \(0.371840\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.22930 | −0.187741 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.22340 | −0.771300 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.56024 | −0.627844 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.14573 | −0.506891 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.36657 | 0.357724 | 0.178862 | − | 0.983874i | \(-0.442758\pi\) | ||||
0.178862 | + | 0.983874i | \(0.442758\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.7855 | −1.28461 | −0.642305 | − | 0.766449i | \(-0.722022\pi\) | ||||
−0.642305 | + | 0.766449i | \(0.722022\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.17080 | −0.498879 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.46865 | 0.117965 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.5938 | 1.00510 | 0.502548 | − | 0.864549i | \(-0.332396\pi\) | ||||
0.502548 | + | 0.864549i | \(0.332396\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.66585 | 0.449331 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.44737 | 0.508124 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.1877 | −1.03294 | −0.516470 | − | 0.856305i | \(-0.672754\pi\) | ||||
−0.516470 | + | 0.856305i | \(0.672754\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.06688 | −0.394456 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.74994 | −0.596149 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.46836 | −0.112288 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.2493 | −1.23541 | −0.617704 | − | 0.786411i | \(-0.711937\pi\) | ||||
−0.617704 | + | 0.786411i | \(0.711937\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.15694 | −0.238642 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.30823 | −0.248661 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.4410 | 1.15412 | 0.577058 | − | 0.816703i | \(-0.304201\pi\) | ||||
0.577058 | + | 0.816703i | \(0.304201\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.6250 | −0.864082 | −0.432041 | − | 0.901854i | \(-0.642206\pi\) | ||||
−0.432041 | + | 0.901854i | \(0.642206\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.09227 | 0.524276 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.54753 | −0.481384 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.8399 | 1.81647 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.924269 | 0.0672307 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.00126 | −0.651308 | −0.325654 | − | 0.945489i | \(-0.605584\pi\) | ||||
−0.325654 | + | 0.945489i | \(0.605584\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.5296 | −1.83766 | −0.918829 | − | 0.394656i | \(-0.870864\pi\) | ||||
−0.918829 | + | 0.394656i | \(0.870864\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.88412 | 0.206536 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.39532 | −0.384401 | −0.192200 | − | 0.981356i | \(-0.561562\pi\) | ||||
−0.192200 | + | 0.981356i | \(0.561562\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.23920 | −0.442285 | −0.221143 | − | 0.975241i | \(-0.570979\pi\) | ||||
−0.221143 | + | 0.975241i | \(0.570979\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.27623 | −0.0900184 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.55140 | −0.389632 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.75001 | −0.541284 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.97565 | 0.484841 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.91072 | 0.408853 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9201 | −1.09598 | −0.547992 | − | 0.836484i | \(-0.684608\pi\) | ||||
−0.547992 | + | 0.836484i | \(0.684608\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.32478 | −0.638923 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.23788 | −0.289021 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.07841 | 0.0732075 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.24728 | −0.354578 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.1392 | −0.951103 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.48274 | −0.0992919 | −0.0496459 | − | 0.998767i | \(-0.515809\pi\) | ||||
−0.0496459 | + | 0.998767i | \(0.515809\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.41561 | −0.227707 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.1543 | 1.27132 | 0.635659 | − | 0.771970i | \(-0.280728\pi\) | ||||
0.635659 | + | 0.771970i | \(0.280728\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.2564 | 1.93332 | 0.966659 | − | 0.256069i | \(-0.0824273\pi\) | ||||
0.966659 | + | 0.256069i | \(0.0824273\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.72055 | −0.244794 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.59781 | −0.104676 | −0.0523380 | − | 0.998629i | \(-0.516667\pi\) | ||||
−0.0523380 | + | 0.998629i | \(0.516667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.80608 | −0.183048 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.42969 | 0.417653 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.9614 | 1.54994 | 0.774968 | − | 0.632000i | \(-0.217766\pi\) | ||||
0.774968 | + | 0.632000i | \(0.217766\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.7232 | 1.20607 | 0.603033 | − | 0.797716i | \(-0.293959\pi\) | ||||
0.603033 | + | 0.797716i | \(0.293959\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.73579 | −0.494221 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.36445 | −0.214075 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.18422 | −0.328537 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.14508 | −0.0722770 | −0.0361385 | − | 0.999347i | \(-0.511506\pi\) | ||||
−0.0361385 | + | 0.999347i | \(0.511506\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.0798 | −1.76536 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.76735 | −0.486410 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.8857 | −1.11568 | −0.557839 | − | 0.829949i | \(-0.688370\pi\) | ||||
−0.557839 | + | 0.829949i | \(0.688370\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.80778 | −0.298741 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00626 | −0.371778 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.9904 | 1.23266 | 0.616332 | − | 0.787487i | \(-0.288618\pi\) | ||||
0.616332 | + | 0.787487i | \(0.288618\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.13175 | 0.438100 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.24526 | −0.259806 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.77209 | 0.169017 | 0.0845087 | − | 0.996423i | \(-0.473068\pi\) | ||||
0.0845087 | + | 0.996423i | \(0.473068\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4690 | 1.00042 | 0.500210 | − | 0.865904i | \(-0.333256\pi\) | ||||
0.500210 | + | 0.865904i | \(0.333256\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.11778 | 0.128174 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.7492 | 0.829107 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.17136 | 0.130465 | 0.0652323 | − | 0.997870i | \(-0.479221\pi\) | ||||
0.0652323 | + | 0.997870i | \(0.479221\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.16677 | 0.0698530 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0134 | 0.955280 | 0.477640 | − | 0.878556i | \(-0.341492\pi\) | ||||
0.477640 | + | 0.878556i | \(0.341492\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.56836 | −0.449892 | −0.224946 | − | 0.974371i | \(-0.572221\pi\) | ||||
−0.224946 | + | 0.974371i | \(0.572221\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.84826 | −0.109481 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.69074 | −0.335914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.0787 | 1.23993 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.704554 | 0.0413017 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.162963 | 0.00952040 | 0.00476020 | − | 0.999989i | \(-0.498485\pi\) | ||||
0.00476020 | + | 0.999989i | \(0.498485\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.16415 | −0.242446 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.02540 | −0.233577 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.9833 | 0.924339 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.11183 | −0.179363 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.74152 | −0.444739 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.92723 | 0.511172 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.2883 | −0.644256 | −0.322128 | − | 0.946696i | \(-0.604398\pi\) | ||||
−0.322128 | + | 0.946696i | \(0.604398\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.3637 | 0.760236 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.4293 | −0.931620 | −0.465810 | − | 0.884885i | \(-0.654237\pi\) | ||||
−0.465810 | + | 0.884885i | \(0.654237\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.7975 | 0.779880 | 0.389940 | − | 0.920840i | \(-0.372496\pi\) | ||||
0.389940 | + | 0.920840i | \(0.372496\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.16340 | 0.0655503 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.8536 | −0.946592 | −0.473296 | − | 0.880903i | \(-0.656936\pi\) | ||||
−0.473296 | + | 0.880903i | \(0.656936\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.1776 | 1.35369 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.75302 | −0.321102 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.06094 | 0.504164 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.82619 | −0.434119 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.708744 | −0.0391937 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.06047 | −0.113597 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.37132 | −0.515094 | −0.257547 | − | 0.966266i | \(-0.582914\pi\) | ||||
−0.257547 | + | 0.966266i | \(0.582914\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.20171 | −0.285052 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.60642 | −0.0877684 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.6222 | 1.39573 | 0.697865 | − | 0.716230i | \(-0.254134\pi\) | ||||
0.697865 | + | 0.716230i | \(0.254134\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.18223 | −0.390085 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.69673 | −0.254342 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.1502 | −0.656048 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.78043 | 0.472723 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.60728 | 0.515746 | 0.257873 | − | 0.966179i | \(-0.416978\pi\) | ||||
0.257873 | + | 0.966179i | \(0.416978\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.14376 | 0.221810 | 0.110905 | − | 0.993831i | \(-0.464625\pi\) | ||||
0.110905 | + | 0.993831i | \(0.464625\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.29130 | 0.122301 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −33.8224 | −1.80019 | −0.900093 | − | 0.435699i | \(-0.856501\pi\) | ||||
−0.900093 | + | 0.435699i | \(0.856501\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.7373 | −0.622953 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.70348 | −0.301860 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.31577 | −0.333334 | −0.166667 | − | 0.986013i | \(-0.553300\pi\) | ||||
−0.166667 | + | 0.986013i | \(0.553300\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8439 | −0.886522 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.20383 | 0.273130 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.60489 | −0.345716 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.633071 | 0.0330461 | 0.0165230 | − | 0.999863i | \(-0.494740\pi\) | ||||
0.0165230 | + | 0.999863i | \(0.494740\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.15702 | −0.320522 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.23677 | 0.271879 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.8217 | 1.18166 | 0.590830 | − | 0.806796i | \(-0.298800\pi\) | ||||
0.590830 | + | 0.806796i | \(0.298800\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.5929 | −0.547017 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.7622 | −0.708787 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.2141 | 0.678765 | 0.339383 | − | 0.940648i | \(-0.389782\pi\) | ||||
0.339383 | + | 0.940648i | \(0.389782\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.4966 | 0.640223 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.41509 | 0.429991 | 0.214996 | − | 0.976615i | \(-0.431026\pi\) | ||||
0.214996 | + | 0.976615i | \(0.431026\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.68316 | −0.238676 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.36680 | −0.171144 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.7742 | −0.850487 | −0.425243 | − | 0.905079i | \(-0.639812\pi\) | ||||
−0.425243 | + | 0.905079i | \(0.639812\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −43.0453 | −2.17689 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.96532 | 0.452241 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.09322 | 0.407214 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.00677 | 0.0505284 | 0.0252642 | − | 0.999681i | \(-0.491957\pi\) | ||||
0.0252642 | + | 0.999681i | \(0.491957\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.35716 | −0.0679428 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.8498 | 1.49063 | 0.745313 | − | 0.666715i | \(-0.232300\pi\) | ||||
0.745313 | + | 0.666715i | \(0.232300\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.67343 | 0.133173 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.25873 | 0.0625466 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.9390 | 1.03791 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.88612 | −0.192156 | −0.0960782 | − | 0.995374i | \(-0.530630\pi\) | ||||
−0.0960782 | + | 0.995374i | \(0.530630\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.4263 | −0.662270 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.05769 | −0.150459 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.52551 | −0.320325 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.23934 | 0.452452 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.80320 | 0.0880923 | 0.0440461 | − | 0.999029i | \(-0.485975\pi\) | ||||
0.0440461 | + | 0.999029i | \(0.485975\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.4419 | −0.508906 | −0.254453 | − | 0.967085i | \(-0.581895\pi\) | ||||
−0.254453 | + | 0.967085i | \(0.581895\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.22930 | −0.108392 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.0770 | 1.02239 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.55517 | 0.317227 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.22340 | −0.445310 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.78927 | −0.182523 | −0.0912614 | − | 0.995827i | \(-0.529090\pi\) | ||||
−0.0912614 | + | 0.995827i | \(0.529090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.59660 | −0.172841 | −0.0864207 | − | 0.996259i | \(-0.527543\pi\) | ||||
−0.0864207 | + | 0.996259i | \(0.527543\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.56024 | −0.362486 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.2427 | −0.489977 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.8265 | −0.850814 | −0.425407 | − | 0.905002i | \(-0.639869\pi\) | ||||
−0.425407 | + | 0.905002i | \(0.639869\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.14573 | −0.292654 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.9794 | 1.28183 | 0.640916 | − | 0.767611i | \(-0.278555\pi\) | ||||
0.640916 | + | 0.767611i | \(0.278555\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.34362 | −0.253312 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.36657 | 0.206532 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.4172 | 0.586002 | 0.293001 | − | 0.956112i | \(-0.405346\pi\) | ||||
0.293001 | + | 0.956112i | \(0.405346\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.7845 | 1.16706 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.7855 | −0.741669 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.66570 | 0.124970 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.8660 | −1.16318 | −0.581591 | − | 0.813481i | \(-0.697570\pi\) | ||||
−0.581591 | + | 0.813481i | \(0.697570\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.17080 | −0.288028 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.3987 | −0.903488 | −0.451744 | − | 0.892148i | \(-0.649198\pi\) | ||||
−0.451744 | + | 0.892148i | \(0.649198\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.50627 | 0.116476 | 0.0582381 | − | 0.998303i | \(-0.481452\pi\) | ||||
0.0582381 | + | 0.998303i | \(0.481452\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.46865 | 0.0681070 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.79530 | −0.268175 | −0.134087 | − | 0.990970i | \(-0.542810\pi\) | ||||
−0.134087 | + | 0.990970i | \(0.542810\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.17958 | −0.0544679 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.5938 | 0.580293 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.5527 | 0.623154 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.01533 | 0.230119 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.66585 | 0.259421 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.7100 | −1.03765 | −0.518824 | − | 0.854881i | \(-0.673630\pi\) | ||||
−0.518824 | + | 0.854881i | \(0.673630\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.9187 | −0.543446 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.44737 | 0.293366 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.886841 | 0.0402694 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.6439 | −0.935464 | −0.467732 | − | 0.883870i | \(-0.654929\pi\) | ||||
−0.467732 | + | 0.883870i | \(0.654929\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.1877 | −0.596368 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.38185 | −0.242879 | −0.121440 | − | 0.992599i | \(-0.538751\pi\) | ||||
−0.121440 | + | 0.992599i | \(0.538751\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.0634 | 1.66925 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.06688 | −0.227739 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.61860 | −0.386597 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.0040 | 0.447838 | 0.223919 | − | 0.974608i | \(-0.428115\pi\) | ||||
0.223919 | + | 0.974608i | \(0.428115\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.60290 | −0.338996 | −0.169498 | − | 0.985530i | \(-0.554215\pi\) | ||||
−0.169498 | + | 0.985530i | \(0.554215\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.74445 | −0.433622 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.74994 | −0.344187 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.0764 | −0.934196 | −0.467098 | − | 0.884206i | \(-0.654700\pi\) | ||||
−0.467098 | + | 0.884206i | \(0.654700\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.84990 | −0.214547 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.46836 | −0.0648296 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.8213 | 0.741235 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.97382 | 0.394668 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.2493 | −0.713263 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.90786 | 0.215017 | 0.107509 | − | 0.994204i | \(-0.465713\pi\) | ||||
0.107509 | + | 0.994204i | \(0.465713\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.87433 | −0.125686 | −0.0628428 | − | 0.998023i | \(-0.520017\pi\) | ||||
−0.0628428 | + | 0.998023i | \(0.520017\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.15694 | −0.137780 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.19993 | −0.313634 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.6597 | 1.11564 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.30823 | −0.143565 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.1076 | −0.611068 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.24148 | −0.313076 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.4410 | 0.666330 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.7390 | 1.06558 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.16539 | −0.308064 | −0.154032 | − | 0.988066i | \(-0.549226\pi\) | ||||
−0.154032 | + | 0.988066i | \(0.549226\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.6250 | −0.498878 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.892115 | −0.0382140 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.4816 | 1.51708 | 0.758541 | − | 0.651625i | \(-0.225913\pi\) | ||||
0.758541 | + | 0.651625i | \(0.225913\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.09227 | 0.302691 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.81934 | 0.375716 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.94276 | 0.252712 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.54753 | −0.277927 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.1731 | −0.812388 | −0.406194 | − | 0.913787i | \(-0.633144\pi\) | ||||
−0.406194 | + | 0.913787i | \(0.633144\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.71435 | −0.326282 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.8399 | 1.04874 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.7702 | 1.08608 | 0.543041 | − | 0.839706i | \(-0.317273\pi\) | ||||
0.543041 | + | 0.839706i | \(0.317273\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.04046 | −0.380335 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.924269 | 0.0388156 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.80775 | 0.0757846 | 0.0378923 | − | 0.999282i | \(-0.487936\pi\) | ||||
0.0378923 | + | 0.999282i | \(0.487936\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.2976 | 0.682035 | 0.341018 | − | 0.940057i | \(-0.389228\pi\) | ||||
0.341018 | + | 0.940057i | \(0.389228\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.00126 | −0.376033 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.8261 | −0.993616 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.1705 | −0.714817 | −0.357408 | − | 0.933948i | \(-0.616340\pi\) | ||||
−0.357408 | + | 0.933948i | \(0.616340\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.5296 | −1.06097 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.79161 | −0.198790 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.8073 | −0.944582 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.88412 | 0.119244 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.3725 | −0.634491 | −0.317245 | − | 0.948343i | \(-0.602758\pi\) | ||||
−0.317245 | + | 0.948343i | \(0.602758\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.71324 | −0.0705929 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.39532 | −0.221934 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.2488 | −1.16004 | −0.580020 | − | 0.814602i | \(-0.696955\pi\) | ||||
−0.580020 | + | 0.814602i | \(0.696955\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.17912 | −0.294315 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.23920 | −0.255354 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.09056 | 0.289712 | 0.144856 | − | 0.989453i | \(-0.453728\pi\) | ||||
0.144856 | + | 0.989453i | \(0.453728\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.79310 | 0.0731421 | 0.0365711 | − | 0.999331i | \(-0.488356\pi\) | ||||
0.0365711 | + | 0.999331i | \(0.488356\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.27623 | −0.0519721 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.55020 | 0.266304 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.1278 | 1.14167 | 0.570837 | − | 0.821064i | \(-0.306619\pi\) | ||||
0.570837 | + | 0.821064i | \(0.306619\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.55140 | −0.224954 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.10800 | −0.206647 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.3696 | −0.620772 | −0.310386 | − | 0.950611i | \(-0.600458\pi\) | ||||
−0.310386 | + | 0.950611i | \(0.600458\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.75001 | −0.312510 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.99630 | −0.241402 | −0.120701 | − | 0.992689i | \(-0.538514\pi\) | ||||
−0.120701 | + | 0.992689i | \(0.538514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.5726 | −0.465143 | −0.232571 | − | 0.972579i | \(-0.574714\pi\) | ||||
−0.232571 | + | 0.972579i | \(0.574714\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.97565 | 0.279923 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.92376 | −0.157202 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.74442 | 0.149777 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.91072 | 0.236052 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.0987 | 1.27986 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.07385 | −0.122368 | −0.0611839 | − | 0.998127i | \(-0.519488\pi\) | ||||
−0.0611839 | + | 0.998127i | \(0.519488\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.9201 | −0.632767 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.7299 | 0.624220 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.0817 | −0.557938 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.32478 | −0.368882 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.2065 | 0.679615 | 0.339807 | − | 0.940495i | \(-0.389638\pi\) | ||||
0.339807 | + | 0.940495i | \(0.389638\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.06653 | 0.199804 | 0.0999022 | − | 0.994997i | \(-0.468147\pi\) | ||||
0.0999022 | + | 0.994997i | \(0.468147\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.23788 | −0.166866 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.4037 | −1.35255 | −0.676275 | − | 0.736649i | \(-0.736407\pi\) | ||||
−0.676275 | + | 0.736649i | \(0.736407\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.3169 | 0.522735 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.07841 | 0.0422664 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.0747 | −0.433388 | −0.216694 | − | 0.976240i | \(-0.569527\pi\) | ||||
−0.216694 | + | 0.976240i | \(0.569527\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.2849 | 0.440937 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.24728 | −0.204716 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.94707 | −0.387483 | −0.193741 | − | 0.981053i | \(-0.562062\pi\) | ||||
−0.193741 | + | 0.981053i | \(0.562062\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.5451 | 0.526844 | 0.263422 | − | 0.964681i | \(-0.415149\pi\) | ||||
0.263422 | + | 0.964681i | \(0.415149\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.1392 | −0.549119 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.70829 | −0.0662446 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −41.8976 | −1.62228 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.48274 | −0.0573262 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.5492 | −1.10213 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.8773 | 0.766213 | 0.383107 | − | 0.923704i | \(-0.374854\pi\) | ||||
0.383107 | + | 0.923704i | \(0.374854\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.41561 | −0.131467 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.72306 | −0.143089 | −0.0715444 | − | 0.997437i | \(-0.522793\pi\) | ||||
−0.0715444 | + | 0.997437i | \(0.522793\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.651197 | 0.0249907 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.1543 | 0.733996 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −48.5781 | −1.85879 | −0.929395 | − | 0.369087i | \(-0.879671\pi\) | ||||
−0.929395 | + | 0.369087i | \(0.879671\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.9000 | −0.645717 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.2564 | 1.11620 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.9822 | 0.494581 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.48333 | −0.0564284 | −0.0282142 | − | 0.999602i | \(-0.508982\pi\) | ||||
−0.0282142 | + | 0.999602i | \(0.508982\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.72055 | −0.141332 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.6298 | 0.441143 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.9937 | 1.43912 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.59781 | −0.0604347 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.9473 | 1.13110 | 0.565548 | − | 0.824716i | \(-0.308665\pi\) | ||||
0.565548 | + | 0.824716i | \(0.308665\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.63798 | 0.288072 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.80608 | −0.105683 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.15524 | −0.269101 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.3277 | 1.85254 | 0.926271 | − | 0.376859i | \(-0.122996\pi\) | ||||
0.926271 | + | 0.376859i | \(0.122996\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.42969 | 0.241132 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.13901 | 0.304808 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.6097 | −0.434180 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.9614 | 0.894856 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 46.8935 | 1.74883 | 0.874416 | − | 0.485177i | \(-0.161245\pi\) | ||||
0.874416 | + | 0.485177i | \(0.161245\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.3517 | 0.460001 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.7232 | 0.696322 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.5150 | 0.761909 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.320341 | 0.0118808 | 0.00594040 | − | 0.999982i | \(-0.498109\pi\) | ||||
0.00594040 | + | 0.999982i | \(0.498109\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.7758 | 0.768422 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.4025 | 0.790521 | 0.395260 | − | 0.918569i | \(-0.370654\pi\) | ||||
0.395260 | + | 0.918569i | \(0.370654\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.73579 | −0.285339 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.13734 | 0.189236 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.54071 | −0.277389 | −0.138695 | − | 0.990335i | \(-0.544291\pi\) | ||||
−0.138695 | + | 0.990335i | \(0.544291\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.36445 | −0.123596 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −50.7691 | −1.86254 | −0.931268 | − | 0.364335i | \(-0.881296\pi\) | ||||
−0.931268 | + | 0.364335i | \(0.881296\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.49632 | 0.201370 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.18422 | −0.189681 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.31734 | −0.194291 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.4763 | −1.69594 | −0.847972 | − | 0.530041i | \(-0.822176\pi\) | ||||
−0.847972 | + | 0.530041i | \(0.822176\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.14508 | −0.0417292 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.8697 | −0.723132 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.1990 | −1.35202 | −0.676010 | − | 0.736892i | \(-0.736292\pi\) | ||||
−0.676010 | + | 0.736892i | \(0.736292\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28.0798 | −1.01923 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.0795 | 0.437883 | 0.218941 | − | 0.975738i | \(-0.429740\pi\) | ||||
0.218941 | + | 0.975738i | \(0.429740\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.655070 | −0.0237151 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.76735 | −0.280829 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.58014 | −0.273703 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.95765 | 0.286960 | 0.143480 | − | 0.989653i | \(-0.454171\pi\) | ||||
0.143480 | + | 0.989653i | \(0.454171\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.8857 | −0.644138 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.1855 | −1.62521 | −0.812605 | − | 0.582814i | \(-0.801952\pi\) | ||||
−0.812605 | + | 0.582814i | \(0.801952\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.98524 | −0.143154 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.80778 | −0.172478 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.04071 | 0.323917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37.5359 | 1.34314 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.00626 | −0.214646 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.8522 | 0.565789 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.6981 | 1.16556 | 0.582780 | − | 0.812630i | \(-0.301965\pi\) | ||||
0.582780 | + | 0.812630i | \(0.301965\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.9904 | 0.711679 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.63831 | −0.236031 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.2505 | 0.577074 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.13175 | 0.252937 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.6866 | −0.768180 | −0.384090 | − | 0.923296i | \(-0.625485\pi\) | ||||
−0.384090 | + | 0.923296i | \(0.625485\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.7566 | 0.486672 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.24526 | −0.149999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.1224 | 0.745393 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.11548 | 0.286033 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.77209 | 0.0975822 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.0601 | 0.634958 | 0.317479 | − | 0.948265i | \(-0.397164\pi\) | ||||
0.317479 | + | 0.948265i | \(0.397164\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.0712 | −0.704797 | −0.352398 | − | 0.935850i | \(-0.614634\pi\) | ||||
−0.352398 | + | 0.935850i | \(0.614634\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.4690 | 0.577593 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.5997 | −0.581462 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.94366 | 0.172957 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.11778 | 0.0740012 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.3675 | 1.65314 | 0.826569 | − | 0.562836i | \(-0.190290\pi\) | ||||
0.826569 | + | 0.562836i | \(0.190290\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.11295 | −0.247942 | −0.123971 | − | 0.992286i | \(-0.539563\pi\) | ||||
−0.123971 | + | 0.992286i | \(0.539563\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.7492 | 0.478685 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −53.6924 | −1.86707 | −0.933535 | − | 0.358487i | \(-0.883293\pi\) | ||||
−0.933535 | + | 0.358487i | \(0.883293\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.44695 | −0.223912 | −0.111956 | − | 0.993713i | \(-0.535712\pi\) | ||||
−0.111956 | + | 0.993713i | \(0.535712\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.17136 | 0.0753238 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37.9240 | 1.31399 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.25873 | 0.0435600 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.16677 | 0.0403296 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.84289 | −0.167195 | −0.0835976 | − | 0.996500i | \(-0.526641\pi\) | ||||
−0.0835976 | + | 0.996500i | \(0.526641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.07517 | 0.243972 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.0134 | 0.551531 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.75505 | −0.335584 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.80974 | 0.165265 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.56836 | −0.259745 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.2853 | −1.24384 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.8311 | 0.884442 | 0.442221 | − | 0.896906i | \(-0.354191\pi\) | ||||
0.442221 | + | 0.896906i | \(0.354191\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.84826 | −0.0632092 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.2860 | −0.624636 | −0.312318 | − | 0.949978i | \(-0.601105\pi\) | ||||
−0.312318 | + | 0.949978i | \(0.601105\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.22747 | −0.144240 | −0.0721198 | − | 0.997396i | \(-0.522976\pi\) | ||||
−0.0721198 | + | 0.997396i | \(0.522976\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.69074 | −0.193940 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.28826 | −0.111934 | −0.0559668 | − | 0.998433i | \(-0.517824\pi\) | ||||
−0.0559668 | + | 0.998433i | \(0.517824\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.4534 | −0.695435 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.0787 | 0.715872 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.8821 | −0.877989 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.92423 | −0.0990837 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.704554 | 0.0238455 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.79073 | −0.330987 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.7933 | 1.68140 | 0.840700 | − | 0.541502i | \(-0.182144\pi\) | ||||
0.840700 | + | 0.541502i | \(0.182144\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.162963 | 0.00549660 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.4710 | −0.622305 | −0.311152 | − | 0.950360i | \(-0.600715\pi\) | ||||
−0.311152 | + | 0.950360i | \(0.600715\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.81892 | 0.330433 | 0.165216 | − | 0.986257i | \(-0.447168\pi\) | ||||
0.165216 | + | 0.986257i | \(0.447168\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.16415 | −0.139976 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.8390 | 1.23693 | 0.618466 | − | 0.785812i | \(-0.287754\pi\) | ||||
0.618466 | + | 0.785812i | \(0.287754\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.5503 | 0.387383 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.02540 | −0.134856 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.27341 | 0.109540 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.4360 | 0.649675 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.9833 | 0.533667 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.00795 | −0.233728 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.9628 | −1.16478 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.11183 | −0.103555 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.6327 | −0.486408 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.9366 | −0.894416 | −0.447208 | − | 0.894430i | \(-0.647582\pi\) | ||||
−0.447208 | + | 0.894430i | \(0.647582\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.74152 | −0.256770 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.4770 | −1.04288 | −0.521440 | − | 0.853288i | \(-0.674605\pi\) | ||||
−0.521440 | + | 0.853288i | \(0.674605\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.8685 | 0.690648 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.92723 | 0.295125 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.28637 | 0.273640 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.5782 | −0.447903 | −0.223951 | − | 0.974600i | \(-0.571896\pi\) | ||||
−0.223951 | + | 0.974600i | \(0.571896\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.2883 | −0.371961 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.3659 | −0.703266 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.7670 | 0.584176 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.3637 | 0.438923 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −49.0061 | −1.60784 | −0.803919 | − | 0.594739i | \(-0.797255\pi\) | ||||
−0.803919 | + | 0.594739i | \(0.797255\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.02412 | 0.295754 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.4293 | −0.537871 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.2667 | 1.02253 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.3744 | 1.87434 | 0.937170 | − | 0.348873i | \(-0.113436\pi\) | ||||
0.937170 | + | 0.348873i | \(0.113436\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.7975 | 0.450264 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.1730 | −0.755418 | −0.377709 | − | 0.925924i | \(-0.623288\pi\) | ||||
−0.377709 | + | 0.925924i | \(0.623288\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −42.9492 | −1.39862 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.16340 | 0.0378455 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.5177 | −1.02419 | −0.512094 | − | 0.858929i | \(-0.671130\pi\) | ||||
−0.512094 | + | 0.858929i | \(0.671130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0231 | −0.390286 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.8536 | −0.546515 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.7674 | −1.41777 | −0.708883 | − | 0.705326i | \(-0.750800\pi\) | ||||
−0.708883 | + | 0.705326i | \(0.750800\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.3301 | −0.366634 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.1776 | 0.781551 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.4095 | −0.400724 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6386 | −0.956085 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.75302 | −0.185388 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.1347 | −1.03445 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.4549 | 1.39741 | 0.698707 | − | 0.715408i | \(-0.253759\pi\) | ||||
0.698707 | + | 0.715408i | \(0.253759\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.06094 | 0.291079 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.6119 | −1.07866 | −0.539329 | − | 0.842095i | \(-0.681322\pi\) | ||||
−0.539329 | + | 0.842095i | \(0.681322\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.53963 | 0.273768 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.82619 | −0.250639 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.2399 | −0.935466 | −0.467733 | − | 0.883870i | \(-0.654929\pi\) | ||||
−0.467733 | + | 0.883870i | \(0.654929\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.0889 | 0.546163 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.708744 | −0.0226285 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.3377 | 1.60552 | 0.802762 | − | 0.596300i | \(-0.203363\pi\) | ||||
0.802762 | + | 0.596300i | \(0.203363\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.79124 | −0.216387 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.06047 | −0.0655855 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.4856 | −0.746798 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.95825 | −0.125738 | −0.0628690 | − | 0.998022i | \(-0.520025\pi\) | ||||
−0.0628690 | + | 0.998022i | \(0.520025\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.37132 | −0.297390 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.85345 | −0.248971 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.8077 | 1.48242 | 0.741208 | − | 0.671276i | \(-0.234253\pi\) | ||||
0.741208 | + | 0.671276i | \(0.234253\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.20171 | −0.164575 |
(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 | 8016.2.a.bd.1.8 | 10 | ||
4.3 | odd | 2 | 4008.2.a.j.1.8 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.j.1.8 | ✓ | 10 | 4.3 | odd | 2 | ||
8016.2.a.bd.1.8 | 10 | 1.1 | even | 1 | trivial |