Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50508 | −1.06425 | −0.532127 | − | 0.846665i | \(-0.678607\pi\) | ||||
−0.532127 | + | 0.846665i | \(0.678607\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.265269 | 0.132634 | ||||||||
\(5\) | 2.12799 | 0.951666 | 0.475833 | − | 0.879536i | \(-0.342147\pi\) | ||||
0.475833 | + | 0.879536i | \(0.342147\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.61091 | 0.923096 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.20280 | −1.01281 | ||||||||
\(11\) | −1.63093 | −0.491744 | −0.245872 | − | 0.969302i | \(-0.579074\pi\) | ||||
−0.245872 | + | 0.969302i | \(0.579074\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.77338 | 0.769198 | 0.384599 | − | 0.923084i | \(-0.374340\pi\) | ||||
0.384599 | + | 0.923084i | \(0.374340\pi\) | |||||||
\(14\) | −1.50508 | −0.402250 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.46017 | −1.11504 | ||||||||
\(17\) | 4.81311 | 1.16735 | 0.583675 | − | 0.811988i | \(-0.301614\pi\) | ||||
0.583675 | + | 0.811988i | \(0.301614\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.82102 | 0.417771 | 0.208885 | − | 0.977940i | \(-0.433016\pi\) | ||||
0.208885 | + | 0.977940i | \(0.433016\pi\) | |||||||
\(20\) | 0.564490 | 0.126224 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.45468 | 0.523340 | ||||||||
\(23\) | −4.21796 | −0.879505 | −0.439752 | − | 0.898119i | \(-0.644934\pi\) | ||||
−0.439752 | + | 0.898119i | \(0.644934\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.471655 | −0.0943311 | ||||||||
\(26\) | −4.17416 | −0.818621 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.265269 | 0.0501311 | ||||||||
\(29\) | 2.17542 | 0.403965 | 0.201983 | − | 0.979389i | \(-0.435262\pi\) | ||||
0.201983 | + | 0.979389i | \(0.435262\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.01640 | −0.900972 | −0.450486 | − | 0.892784i | \(-0.648749\pi\) | ||||
−0.450486 | + | 0.892784i | \(0.648749\pi\) | |||||||
\(32\) | 1.49110 | 0.263591 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.24411 | −1.24236 | ||||||||
\(35\) | 2.12799 | 0.359696 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.80716 | −0.790292 | −0.395146 | − | 0.918618i | \(-0.629306\pi\) | ||||
−0.395146 | + | 0.918618i | \(0.629306\pi\) | |||||||
\(38\) | −2.74078 | −0.444614 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.55599 | 0.878480 | ||||||||
\(41\) | 0.803009 | 0.125409 | 0.0627044 | − | 0.998032i | \(-0.480027\pi\) | ||||
0.0627044 | + | 0.998032i | \(0.480027\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.2895 | 1.72164 | 0.860818 | − | 0.508913i | \(-0.169953\pi\) | ||||
0.860818 | + | 0.508913i | \(0.169953\pi\) | |||||||
\(44\) | −0.432635 | −0.0652223 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.34837 | 0.936016 | ||||||||
\(47\) | 7.13834 | 1.04123 | 0.520617 | − | 0.853790i | \(-0.325702\pi\) | ||||
0.520617 | + | 0.853790i | \(0.325702\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.709880 | 0.100392 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.735692 | 0.102022 | ||||||||
\(53\) | −7.35769 | −1.01066 | −0.505328 | − | 0.862927i | \(-0.668629\pi\) | ||||
−0.505328 | + | 0.862927i | \(0.668629\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.47061 | −0.467977 | ||||||||
\(56\) | 2.61091 | 0.348898 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.27418 | −0.429921 | ||||||||
\(59\) | −1.99972 | −0.260341 | −0.130170 | − | 0.991492i | \(-0.541552\pi\) | ||||
−0.130170 | + | 0.991492i | \(0.541552\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.64713 | 0.210893 | 0.105447 | − | 0.994425i | \(-0.466373\pi\) | ||||
0.105447 | + | 0.994425i | \(0.466373\pi\) | |||||||
\(62\) | 7.55008 | 0.958862 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.67612 | 0.834515 | ||||||||
\(65\) | 5.90173 | 0.732019 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.7832 | 1.31737 | 0.658687 | − | 0.752417i | \(-0.271112\pi\) | ||||
0.658687 | + | 0.752417i | \(0.271112\pi\) | |||||||
\(68\) | 1.27677 | 0.154831 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.20280 | −0.382808 | ||||||||
\(71\) | −4.48471 | −0.532238 | −0.266119 | − | 0.963940i | \(-0.585741\pi\) | ||||
−0.266119 | + | 0.963940i | \(0.585741\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.53294 | 0.647582 | 0.323791 | − | 0.946129i | \(-0.395043\pi\) | ||||
0.323791 | + | 0.946129i | \(0.395043\pi\) | |||||||
\(74\) | 7.23516 | 0.841070 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.483060 | 0.0554108 | ||||||||
\(77\) | −1.63093 | −0.185862 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.583282 | −0.0656244 | −0.0328122 | − | 0.999462i | \(-0.510446\pi\) | ||||
−0.0328122 | + | 0.999462i | \(0.510446\pi\) | |||||||
\(80\) | −9.49120 | −1.06115 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.20859 | −0.133467 | ||||||||
\(83\) | 4.31083 | 0.473175 | 0.236588 | − | 0.971610i | \(-0.423971\pi\) | ||||
0.236588 | + | 0.971610i | \(0.423971\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.2422 | 1.11093 | ||||||||
\(86\) | −16.9916 | −1.83226 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.25822 | −0.453927 | ||||||||
\(89\) | 0.157199 | 0.0166630 | 0.00833151 | − | 0.999965i | \(-0.497348\pi\) | ||||
0.00833151 | + | 0.999965i | \(0.497348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.77338 | 0.290729 | ||||||||
\(92\) | −1.11889 | −0.116653 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.7438 | −1.10814 | ||||||||
\(95\) | 3.87512 | 0.397579 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.33005 | 0.236581 | 0.118290 | − | 0.992979i | \(-0.462259\pi\) | ||||
0.118290 | + | 0.992979i | \(0.462259\pi\) | |||||||
\(98\) | −1.50508 | −0.152036 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.125116 | −0.0125116 | ||||||||
\(101\) | −5.25621 | −0.523013 | −0.261506 | − | 0.965202i | \(-0.584219\pi\) | ||||
−0.261506 | + | 0.965202i | \(0.584219\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.1853 | 1.20066 | 0.600328 | − | 0.799754i | \(-0.295037\pi\) | ||||
0.600328 | + | 0.799754i | \(0.295037\pi\) | |||||||
\(104\) | 7.24105 | 0.710044 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.0739 | 1.07559 | ||||||||
\(107\) | 10.1443 | 0.980690 | 0.490345 | − | 0.871528i | \(-0.336871\pi\) | ||||
0.490345 | + | 0.871528i | \(0.336871\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.63005 | 0.539261 | 0.269630 | − | 0.962964i | \(-0.413098\pi\) | ||||
0.269630 | + | 0.962964i | \(0.413098\pi\) | |||||||
\(110\) | 5.22355 | 0.498046 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.46017 | −0.421446 | ||||||||
\(113\) | 10.0500 | 0.945425 | 0.472713 | − | 0.881217i | \(-0.343275\pi\) | ||||
0.472713 | + | 0.881217i | \(0.343275\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.97577 | −0.836995 | ||||||||
\(116\) | 0.577071 | 0.0535797 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.00973 | 0.277069 | ||||||||
\(119\) | 4.81311 | 0.441217 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.34006 | −0.758187 | ||||||||
\(122\) | −2.47906 | −0.224444 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.33069 | −0.119500 | ||||||||
\(125\) | −11.6436 | −1.04144 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −13.0303 | −1.15173 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.88258 | −0.779054 | ||||||||
\(131\) | 1.48299 | 0.129570 | 0.0647848 | − | 0.997899i | \(-0.479364\pi\) | ||||
0.0647848 | + | 0.997899i | \(0.479364\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.82102 | 0.157903 | ||||||||
\(134\) | −16.2296 | −1.40202 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.5666 | 1.07758 | ||||||||
\(137\) | −11.8958 | −1.01633 | −0.508164 | − | 0.861261i | \(-0.669675\pi\) | ||||
−0.508164 | + | 0.861261i | \(0.669675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.572818 | −0.0485858 | −0.0242929 | − | 0.999705i | \(-0.507733\pi\) | ||||
−0.0242929 | + | 0.999705i | \(0.507733\pi\) | |||||||
\(140\) | 0.564490 | 0.0477081 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.74986 | 0.566435 | ||||||||
\(143\) | −4.52320 | −0.378249 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.62927 | 0.384440 | ||||||||
\(146\) | −8.32752 | −0.689191 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.27519 | −0.104820 | ||||||||
\(149\) | −1.43612 | −0.117651 | −0.0588256 | − | 0.998268i | \(-0.518736\pi\) | ||||
−0.0588256 | + | 0.998268i | \(0.518736\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.2726 | −1.16149 | −0.580745 | − | 0.814085i | \(-0.697239\pi\) | ||||
−0.580745 | + | 0.814085i | \(0.697239\pi\) | |||||||
\(152\) | 4.75452 | 0.385643 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.45468 | 0.197804 | ||||||||
\(155\) | −10.6748 | −0.857424 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.4735 | 1.79358 | 0.896791 | − | 0.442453i | \(-0.145892\pi\) | ||||
0.896791 | + | 0.442453i | \(0.145892\pi\) | |||||||
\(158\) | 0.877887 | 0.0698409 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.17304 | 0.250851 | ||||||||
\(161\) | −4.21796 | −0.332422 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.6555 | 0.834604 | 0.417302 | − | 0.908768i | \(-0.362976\pi\) | ||||
0.417302 | + | 0.908768i | \(0.362976\pi\) | |||||||
\(164\) | 0.213013 | 0.0166335 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.48815 | −0.503578 | ||||||||
\(167\) | 20.1342 | 1.55803 | 0.779015 | − | 0.627006i | \(-0.215720\pi\) | ||||
0.779015 | + | 0.627006i | \(0.215720\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.30836 | −0.408335 | ||||||||
\(170\) | −15.4154 | −1.18231 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.99476 | 0.228348 | ||||||||
\(173\) | −7.40946 | −0.563331 | −0.281665 | − | 0.959513i | \(-0.590887\pi\) | ||||
−0.281665 | + | 0.959513i | \(0.590887\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.471655 | −0.0356538 | ||||||||
\(176\) | 7.27423 | 0.548316 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.236597 | −0.0177337 | ||||||||
\(179\) | −13.2628 | −0.991306 | −0.495653 | − | 0.868521i | \(-0.665071\pi\) | ||||
−0.495653 | + | 0.868521i | \(0.665071\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.2421 | 0.984281 | 0.492140 | − | 0.870516i | \(-0.336215\pi\) | ||||
0.492140 | + | 0.870516i | \(0.336215\pi\) | |||||||
\(182\) | −4.17416 | −0.309410 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.0127 | −0.811868 | ||||||||
\(185\) | −10.2296 | −0.752094 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.84985 | −0.574038 | ||||||||
\(188\) | 1.89358 | 0.138103 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.83236 | −0.423124 | ||||||||
\(191\) | 6.93155 | 0.501549 | 0.250775 | − | 0.968046i | \(-0.419315\pi\) | ||||
0.250775 | + | 0.968046i | \(0.419315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.9826 | 0.934510 | 0.467255 | − | 0.884123i | \(-0.345243\pi\) | ||||
0.467255 | + | 0.884123i | \(0.345243\pi\) | |||||||
\(194\) | −3.50692 | −0.251782 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.265269 | 0.0189478 | ||||||||
\(197\) | −0.943824 | −0.0672446 | −0.0336223 | − | 0.999435i | \(-0.510704\pi\) | ||||
−0.0336223 | + | 0.999435i | \(0.510704\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.1662 | 1.07511 | 0.537553 | − | 0.843230i | \(-0.319349\pi\) | ||||
0.537553 | + | 0.843230i | \(0.319349\pi\) | |||||||
\(200\) | −1.23145 | −0.0870767 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.91102 | 0.556618 | ||||||||
\(203\) | 2.17542 | 0.152685 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.70879 | 0.119347 | ||||||||
\(206\) | −18.3399 | −1.27780 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.3698 | −0.857688 | ||||||||
\(209\) | −2.96996 | −0.205437 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.1654 | 1.38824 | 0.694122 | − | 0.719857i | \(-0.255793\pi\) | ||||
0.694122 | + | 0.719857i | \(0.255793\pi\) | |||||||
\(212\) | −1.95177 | −0.134048 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.2680 | −1.04370 | ||||||||
\(215\) | 24.0240 | 1.63842 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.01640 | −0.340535 | ||||||||
\(218\) | −8.47368 | −0.573910 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.920644 | −0.0620698 | ||||||||
\(221\) | 13.3486 | 0.897923 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.2773 | 1.69269 | 0.846346 | − | 0.532633i | \(-0.178798\pi\) | ||||
0.846346 | + | 0.532633i | \(0.178798\pi\) | |||||||
\(224\) | 1.49110 | 0.0996280 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.1261 | −1.00617 | ||||||||
\(227\) | −5.94333 | −0.394473 | −0.197236 | − | 0.980356i | \(-0.563197\pi\) | ||||
−0.197236 | + | 0.980356i | \(0.563197\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.5825 | 1.09580 | 0.547902 | − | 0.836542i | \(-0.315427\pi\) | ||||
0.547902 | + | 0.836542i | \(0.315427\pi\) | |||||||
\(230\) | 13.5093 | 0.890775 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.67983 | 0.372899 | ||||||||
\(233\) | −26.7788 | −1.75434 | −0.877168 | − | 0.480183i | \(-0.840570\pi\) | ||||
−0.877168 | + | 0.480183i | \(0.840570\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.1903 | 0.990907 | ||||||||
\(236\) | −0.530463 | −0.0345302 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.24411 | −0.469566 | ||||||||
\(239\) | −7.15117 | −0.462571 | −0.231285 | − | 0.972886i | \(-0.574293\pi\) | ||||
−0.231285 | + | 0.972886i | \(0.574293\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.1647 | 1.04126 | 0.520630 | − | 0.853783i | \(-0.325697\pi\) | ||||
0.520630 | + | 0.853783i | \(0.325697\pi\) | |||||||
\(242\) | 12.5525 | 0.806903 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.436932 | 0.0279717 | ||||||||
\(245\) | 2.12799 | 0.135952 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.05039 | 0.321348 | ||||||||
\(248\) | −13.0974 | −0.831684 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 17.5246 | 1.10835 | ||||||||
\(251\) | 10.5416 | 0.665382 | 0.332691 | − | 0.943036i | \(-0.392043\pi\) | ||||
0.332691 | + | 0.943036i | \(0.392043\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.87920 | 0.432492 | ||||||||
\(254\) | 1.50508 | 0.0944372 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.25941 | 0.391213 | ||||||||
\(257\) | 8.14743 | 0.508222 | 0.254111 | − | 0.967175i | \(-0.418217\pi\) | ||||
0.254111 | + | 0.967175i | \(0.418217\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.80716 | −0.298702 | ||||||||
\(260\) | 1.56555 | 0.0970910 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.23202 | −0.137895 | ||||||||
\(263\) | −13.8490 | −0.853963 | −0.426982 | − | 0.904260i | \(-0.640423\pi\) | ||||
−0.426982 | + | 0.904260i | \(0.640423\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.6571 | −0.961808 | ||||||||
\(266\) | −2.74078 | −0.168048 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.86044 | 0.174729 | ||||||||
\(269\) | −8.14970 | −0.496896 | −0.248448 | − | 0.968645i | \(-0.579921\pi\) | ||||
−0.248448 | + | 0.968645i | \(0.579921\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.7842 | −0.776583 | −0.388291 | − | 0.921537i | \(-0.626935\pi\) | ||||
−0.388291 | + | 0.921537i | \(0.626935\pi\) | |||||||
\(272\) | −21.4673 | −1.30164 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.9042 | 1.08163 | ||||||||
\(275\) | 0.769238 | 0.0463868 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.03321 | 0.182248 | 0.0911240 | − | 0.995840i | \(-0.470954\pi\) | ||||
0.0911240 | + | 0.995840i | \(0.470954\pi\) | |||||||
\(278\) | 0.862138 | 0.0517076 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.55599 | 0.332034 | ||||||||
\(281\) | −33.1775 | −1.97920 | −0.989602 | − | 0.143832i | \(-0.954057\pi\) | ||||
−0.989602 | + | 0.143832i | \(0.954057\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.84353 | −0.109587 | −0.0547933 | − | 0.998498i | \(-0.517450\pi\) | ||||
−0.0547933 | + | 0.998498i | \(0.517450\pi\) | |||||||
\(284\) | −1.18966 | −0.0705930 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.80778 | 0.402552 | ||||||||
\(287\) | 0.803009 | 0.0474001 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.16599 | 0.362705 | ||||||||
\(290\) | −6.96743 | −0.409142 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.46772 | 0.0858917 | ||||||||
\(293\) | −19.4459 | −1.13604 | −0.568021 | − | 0.823014i | \(-0.692291\pi\) | ||||
−0.568021 | + | 0.823014i | \(0.692291\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.25538 | −0.247758 | ||||||||
\(296\) | −12.5511 | −0.729516 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.16147 | 0.125211 | ||||||||
\(299\) | −11.6980 | −0.676513 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.2895 | 0.650717 | ||||||||
\(302\) | 21.4815 | 1.23612 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.12206 | −0.465832 | ||||||||
\(305\) | 3.50507 | 0.200700 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.861448 | −0.0491654 | −0.0245827 | − | 0.999698i | \(-0.507826\pi\) | ||||
−0.0245827 | + | 0.999698i | \(0.507826\pi\) | |||||||
\(308\) | −0.432635 | −0.0246517 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 16.0665 | 0.912516 | ||||||||
\(311\) | 5.78371 | 0.327964 | 0.163982 | − | 0.986463i | \(-0.447566\pi\) | ||||
0.163982 | + | 0.986463i | \(0.447566\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.3373 | −1.43215 | −0.716074 | − | 0.698024i | \(-0.754063\pi\) | ||||
−0.716074 | + | 0.698024i | \(0.754063\pi\) | |||||||
\(314\) | −33.8245 | −1.90883 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.154727 | −0.00870405 | ||||||||
\(317\) | −12.8867 | −0.723791 | −0.361896 | − | 0.932219i | \(-0.617870\pi\) | ||||
−0.361896 | + | 0.932219i | \(0.617870\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.54796 | −0.198648 | ||||||||
\(320\) | 14.2067 | 0.794180 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.34837 | 0.353781 | ||||||||
\(323\) | 8.76477 | 0.487685 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.30808 | −0.0725592 | ||||||||
\(326\) | −16.0374 | −0.888230 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.09658 | 0.115764 | ||||||||
\(329\) | 7.13834 | 0.393549 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.4461 | −0.739062 | −0.369531 | − | 0.929218i | \(-0.620482\pi\) | ||||
−0.369531 | + | 0.929218i | \(0.620482\pi\) | |||||||
\(332\) | 1.14353 | 0.0627594 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −30.3036 | −1.65814 | ||||||||
\(335\) | 22.9465 | 1.25370 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.39436 | 0.402796 | 0.201398 | − | 0.979509i | \(-0.435451\pi\) | ||||
0.201398 | + | 0.979509i | \(0.435451\pi\) | |||||||
\(338\) | 7.98951 | 0.434572 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.71695 | 0.147347 | ||||||||
\(341\) | 8.18140 | 0.443048 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 29.4759 | 1.58924 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.1518 | 0.599527 | ||||||||
\(347\) | −5.77786 | −0.310172 | −0.155086 | − | 0.987901i | \(-0.549565\pi\) | ||||
−0.155086 | + | 0.987901i | \(0.549565\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.3767 | −0.930155 | −0.465078 | − | 0.885270i | \(-0.653974\pi\) | ||||
−0.465078 | + | 0.885270i | \(0.653974\pi\) | |||||||
\(350\) | 0.709880 | 0.0379447 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.43188 | −0.129619 | ||||||||
\(353\) | 20.2089 | 1.07561 | 0.537805 | − | 0.843069i | \(-0.319254\pi\) | ||||
0.537805 | + | 0.843069i | \(0.319254\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.54343 | −0.506513 | ||||||||
\(356\) | 0.0416999 | 0.00221009 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.9615 | 1.05500 | ||||||||
\(359\) | −23.5996 | −1.24554 | −0.622769 | − | 0.782406i | \(-0.713992\pi\) | ||||
−0.622769 | + | 0.782406i | \(0.713992\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6839 | −0.825467 | ||||||||
\(362\) | −19.9305 | −1.04752 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.735692 | 0.0385607 | ||||||||
\(365\) | 11.7740 | 0.616282 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.3692 | 0.541266 | 0.270633 | − | 0.962683i | \(-0.412767\pi\) | ||||
0.270633 | + | 0.962683i | \(0.412767\pi\) | |||||||
\(368\) | 18.8128 | 0.980685 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 15.3964 | 0.800418 | ||||||||
\(371\) | −7.35769 | −0.381992 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.7799 | −1.33483 | −0.667415 | − | 0.744686i | \(-0.732599\pi\) | ||||
−0.667415 | + | 0.744686i | \(0.732599\pi\) | |||||||
\(374\) | 11.8147 | 0.610921 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.6376 | 0.961159 | ||||||||
\(377\) | 6.03327 | 0.310729 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.5474 | 1.56912 | 0.784558 | − | 0.620056i | \(-0.212890\pi\) | ||||
0.784558 | + | 0.620056i | \(0.212890\pi\) | |||||||
\(380\) | 1.02795 | 0.0527326 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.4325 | −0.533775 | ||||||||
\(383\) | 29.0438 | 1.48407 | 0.742034 | − | 0.670362i | \(-0.233861\pi\) | ||||
0.742034 | + | 0.670362i | \(0.233861\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.47061 | −0.176879 | ||||||||
\(386\) | −19.5399 | −0.994555 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.618090 | 0.0313788 | ||||||||
\(389\) | −25.0195 | −1.26854 | −0.634270 | − | 0.773111i | \(-0.718699\pi\) | ||||
−0.634270 | + | 0.773111i | \(0.718699\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.3015 | −1.02669 | ||||||||
\(392\) | 2.61091 | 0.131871 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.42053 | 0.0715653 | ||||||||
\(395\) | −1.24122 | −0.0624525 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.8034 | 1.69654 | 0.848272 | − | 0.529561i | \(-0.177643\pi\) | ||||
0.848272 | + | 0.529561i | \(0.177643\pi\) | |||||||
\(398\) | −22.8264 | −1.14418 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.10366 | 0.105183 | ||||||||
\(401\) | −16.5983 | −0.828877 | −0.414439 | − | 0.910077i | \(-0.636022\pi\) | ||||
−0.414439 | + | 0.910077i | \(0.636022\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.9124 | −0.693025 | ||||||||
\(404\) | −1.39431 | −0.0693695 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.27418 | −0.162495 | ||||||||
\(407\) | 7.84015 | 0.388622 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.6138 | −0.870944 | −0.435472 | − | 0.900202i | \(-0.643419\pi\) | ||||
−0.435472 | + | 0.900202i | \(0.643419\pi\) | |||||||
\(410\) | −2.57187 | −0.127016 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.23239 | 0.159248 | ||||||||
\(413\) | −1.99972 | −0.0983996 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.17341 | 0.450305 | ||||||||
\(416\) | 4.13538 | 0.202754 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.47003 | 0.218636 | ||||||||
\(419\) | 31.9337 | 1.56007 | 0.780033 | − | 0.625739i | \(-0.215202\pi\) | ||||
0.780033 | + | 0.625739i | \(0.215202\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.7893 | −1.30563 | −0.652816 | − | 0.757517i | \(-0.726412\pi\) | ||||
−0.652816 | + | 0.757517i | \(0.726412\pi\) | |||||||
\(422\) | −30.3506 | −1.47744 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −19.2103 | −0.932933 | ||||||||
\(425\) | −2.27013 | −0.110117 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.64713 | 0.0797101 | ||||||||
\(428\) | 2.69098 | 0.130073 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −36.1581 | −1.74370 | ||||||||
\(431\) | −3.12430 | −0.150492 | −0.0752462 | − | 0.997165i | \(-0.523974\pi\) | ||||
−0.0752462 | + | 0.997165i | \(0.523974\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.7813 | 0.806456 | 0.403228 | − | 0.915100i | \(-0.367888\pi\) | ||||
0.403228 | + | 0.915100i | \(0.367888\pi\) | |||||||
\(434\) | 7.55008 | 0.362416 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.49348 | 0.0715245 | ||||||||
\(437\) | −7.68099 | −0.367432 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.99581 | −0.0952548 | −0.0476274 | − | 0.998865i | \(-0.515166\pi\) | ||||
−0.0476274 | + | 0.998865i | \(0.515166\pi\) | |||||||
\(440\) | −9.06145 | −0.431988 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −20.0907 | −0.955617 | ||||||||
\(443\) | −5.38599 | −0.255896 | −0.127948 | − | 0.991781i | \(-0.540839\pi\) | ||||
−0.127948 | + | 0.991781i | \(0.540839\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.334517 | 0.0158576 | ||||||||
\(446\) | −38.0444 | −1.80145 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.67612 | 0.315417 | ||||||||
\(449\) | −3.18246 | −0.150190 | −0.0750948 | − | 0.997176i | \(-0.523926\pi\) | ||||
−0.0750948 | + | 0.997176i | \(0.523926\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.30965 | −0.0616691 | ||||||||
\(452\) | 2.66595 | 0.125396 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.94519 | 0.419819 | ||||||||
\(455\) | 5.90173 | 0.276677 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.3721 | 0.859409 | 0.429704 | − | 0.902970i | \(-0.358618\pi\) | ||||
0.429704 | + | 0.902970i | \(0.358618\pi\) | |||||||
\(458\) | −24.9581 | −1.16621 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.38099 | −0.111014 | ||||||||
\(461\) | 2.21772 | 0.103289 | 0.0516447 | − | 0.998666i | \(-0.483554\pi\) | ||||
0.0516447 | + | 0.998666i | \(0.483554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.10883 | 0.376849 | 0.188425 | − | 0.982088i | \(-0.439662\pi\) | ||||
0.188425 | + | 0.982088i | \(0.439662\pi\) | |||||||
\(464\) | −9.70274 | −0.450438 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 40.3042 | 1.86706 | ||||||||
\(467\) | −15.3655 | −0.711029 | −0.355514 | − | 0.934671i | \(-0.615694\pi\) | ||||
−0.355514 | + | 0.934671i | \(0.615694\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.7832 | 0.497921 | ||||||||
\(470\) | −22.8627 | −1.05458 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.22108 | −0.240320 | ||||||||
\(473\) | −18.4124 | −0.846605 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.858894 | −0.0394088 | ||||||||
\(476\) | 1.27677 | 0.0585205 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.7631 | 0.492292 | ||||||||
\(479\) | 39.2875 | 1.79509 | 0.897545 | − | 0.440922i | \(-0.145348\pi\) | ||||
0.897545 | + | 0.440922i | \(0.145348\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.3321 | −0.607891 | ||||||||
\(482\) | −24.3292 | −1.10816 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.21236 | −0.100562 | ||||||||
\(485\) | 4.95833 | 0.225146 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.7758 | 0.624243 | 0.312121 | − | 0.950042i | \(-0.398960\pi\) | ||||
0.312121 | + | 0.950042i | \(0.398960\pi\) | |||||||
\(488\) | 4.30051 | 0.194675 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.20280 | −0.144688 | ||||||||
\(491\) | 4.77600 | 0.215538 | 0.107769 | − | 0.994176i | \(-0.465629\pi\) | ||||
0.107769 | + | 0.994176i | \(0.465629\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.4705 | 0.471569 | ||||||||
\(494\) | −7.60124 | −0.341996 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 22.3740 | 1.00462 | ||||||||
\(497\) | −4.48471 | −0.201167 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.9600 | 0.893533 | 0.446767 | − | 0.894651i | \(-0.352575\pi\) | ||||
0.446767 | + | 0.894651i | \(0.352575\pi\) | |||||||
\(500\) | −3.08869 | −0.138131 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.8660 | −0.708134 | ||||||||
\(503\) | 18.5831 | 0.828581 | 0.414290 | − | 0.910145i | \(-0.364030\pi\) | ||||
0.414290 | + | 0.910145i | \(0.364030\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.1852 | −0.497733 | ||||||||
\(506\) | −10.3538 | −0.460280 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.265269 | −0.0117694 | ||||||||
\(509\) | 38.2223 | 1.69417 | 0.847086 | − | 0.531455i | \(-0.178355\pi\) | ||||
0.847086 | + | 0.531455i | \(0.178355\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.53294 | 0.244763 | ||||||||
\(512\) | 16.6397 | 0.735377 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.2625 | −0.540877 | ||||||||
\(515\) | 25.9303 | 1.14262 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.6421 | −0.512021 | ||||||||
\(518\) | 7.23516 | 0.317895 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 15.4089 | 0.675725 | ||||||||
\(521\) | 4.27005 | 0.187074 | 0.0935371 | − | 0.995616i | \(-0.470183\pi\) | ||||
0.0935371 | + | 0.995616i | \(0.470183\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.89861 | −0.126747 | −0.0633736 | − | 0.997990i | \(-0.520186\pi\) | ||||
−0.0633736 | + | 0.997990i | \(0.520186\pi\) | |||||||
\(524\) | 0.393392 | 0.0171854 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.8438 | 0.908833 | ||||||||
\(527\) | −24.1444 | −1.05175 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.20884 | −0.226471 | ||||||||
\(530\) | 23.5652 | 1.02361 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.483060 | 0.0209433 | ||||||||
\(533\) | 2.22705 | 0.0964642 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.5871 | 0.933290 | ||||||||
\(536\) | 28.1539 | 1.21606 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.2660 | 0.528823 | ||||||||
\(539\) | −1.63093 | −0.0702492 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.8368 | 0.809856 | 0.404928 | − | 0.914349i | \(-0.367297\pi\) | ||||
0.404928 | + | 0.914349i | \(0.367297\pi\) | |||||||
\(542\) | 19.2412 | 0.826480 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.17680 | 0.307703 | ||||||||
\(545\) | 11.9807 | 0.513196 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.4065 | 1.25733 | 0.628665 | − | 0.777676i | \(-0.283602\pi\) | ||||
0.628665 | + | 0.777676i | \(0.283602\pi\) | |||||||
\(548\) | −3.15559 | −0.134800 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.15777 | −0.0493673 | ||||||||
\(551\) | 3.96148 | 0.168765 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.583282 | −0.0248037 | ||||||||
\(554\) | −4.56523 | −0.193958 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.151951 | −0.00644415 | ||||||||
\(557\) | 45.9015 | 1.94491 | 0.972455 | − | 0.233090i | \(-0.0748835\pi\) | ||||
0.972455 | + | 0.233090i | \(0.0748835\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.3101 | 1.32428 | ||||||||
\(560\) | −9.49120 | −0.401076 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 49.9348 | 2.10637 | ||||||||
\(563\) | −8.87157 | −0.373892 | −0.186946 | − | 0.982370i | \(-0.559859\pi\) | ||||
−0.186946 | + | 0.982370i | \(0.559859\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.3863 | 0.899729 | ||||||||
\(566\) | 2.77466 | 0.116628 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.7092 | −0.491307 | ||||||||
\(569\) | −16.3396 | −0.684991 | −0.342495 | − | 0.939520i | \(-0.611272\pi\) | ||||
−0.342495 | + | 0.939520i | \(0.611272\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.9875 | 0.752754 | 0.376377 | − | 0.926467i | \(-0.377170\pi\) | ||||
0.376377 | + | 0.926467i | \(0.377170\pi\) | |||||||
\(572\) | −1.19986 | −0.0501688 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.20859 | −0.0504457 | ||||||||
\(575\) | 1.98942 | 0.0829646 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.6836 | −0.777808 | −0.388904 | − | 0.921278i | \(-0.627146\pi\) | ||||
−0.388904 | + | 0.921278i | \(0.627146\pi\) | |||||||
\(578\) | −9.28031 | −0.386010 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.22800 | 0.0509900 | ||||||||
\(581\) | 4.31083 | 0.178844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.9999 | 0.496985 | ||||||||
\(584\) | 14.4460 | 0.597780 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 29.2677 | 1.20904 | ||||||||
\(587\) | 20.4150 | 0.842617 | 0.421309 | − | 0.906917i | \(-0.361571\pi\) | ||||
0.421309 | + | 0.906917i | \(0.361571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.13496 | −0.376400 | ||||||||
\(590\) | 6.40469 | 0.263677 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 21.4407 | 0.881209 | ||||||||
\(593\) | 38.0384 | 1.56205 | 0.781025 | − | 0.624500i | \(-0.214697\pi\) | ||||
0.781025 | + | 0.624500i | \(0.214697\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.2422 | 0.419891 | ||||||||
\(596\) | −0.380957 | −0.0156046 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 17.6064 | 0.719981 | ||||||||
\(599\) | 35.1546 | 1.43638 | 0.718189 | − | 0.695848i | \(-0.244971\pi\) | ||||
0.718189 | + | 0.695848i | \(0.244971\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.5758 | −1.41038 | −0.705189 | − | 0.709020i | \(-0.749138\pi\) | ||||
−0.705189 | + | 0.709020i | \(0.749138\pi\) | |||||||
\(602\) | −16.9916 | −0.692528 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.78609 | −0.154054 | ||||||||
\(605\) | −17.7476 | −0.721541 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.0631932 | −0.00256493 | −0.00128247 | − | 0.999999i | \(-0.500408\pi\) | ||||
−0.00128247 | + | 0.999999i | \(0.500408\pi\) | |||||||
\(608\) | 2.71532 | 0.110121 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.27542 | −0.213596 | ||||||||
\(611\) | 19.7973 | 0.800914 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.0028 | 0.969466 | 0.484733 | − | 0.874662i | \(-0.338917\pi\) | ||||
0.484733 | + | 0.874662i | \(0.338917\pi\) | |||||||
\(614\) | 1.29655 | 0.0523245 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.25822 | −0.171568 | ||||||||
\(617\) | −8.66784 | −0.348954 | −0.174477 | − | 0.984661i | \(-0.555823\pi\) | ||||
−0.174477 | + | 0.984661i | \(0.555823\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.2979 | −1.01681 | −0.508404 | − | 0.861119i | \(-0.669764\pi\) | ||||
−0.508404 | + | 0.861119i | \(0.669764\pi\) | |||||||
\(620\) | −2.83170 | −0.113724 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.70496 | −0.349037 | ||||||||
\(623\) | 0.157199 | 0.00629803 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4193 | −0.896771 | ||||||||
\(626\) | 38.1347 | 1.52417 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.96153 | 0.237891 | ||||||||
\(629\) | −23.1374 | −0.922547 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.28821 | −0.130901 | −0.0654507 | − | 0.997856i | \(-0.520849\pi\) | ||||
−0.0654507 | + | 0.997856i | \(0.520849\pi\) | |||||||
\(632\) | −1.52290 | −0.0605776 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19.3956 | 0.770297 | ||||||||
\(635\) | −2.12799 | −0.0844467 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.77338 | 0.109885 | ||||||||
\(638\) | 5.33997 | 0.211411 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −27.7283 | −1.09606 | ||||||||
\(641\) | −31.2786 | −1.23543 | −0.617716 | − | 0.786401i | \(-0.711942\pi\) | ||||
−0.617716 | + | 0.786401i | \(0.711942\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.4185 | −1.08128 | −0.540640 | − | 0.841254i | \(-0.681818\pi\) | ||||
−0.540640 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(644\) | −1.11889 | −0.0440906 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.1917 | −0.519020 | ||||||||
\(647\) | 35.8863 | 1.41084 | 0.705418 | − | 0.708791i | \(-0.250759\pi\) | ||||
0.705418 | + | 0.708791i | \(0.250759\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.26140 | 0.128021 | ||||||||
\(650\) | 1.96877 | 0.0772214 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.82658 | 0.110697 | ||||||||
\(653\) | 20.9115 | 0.818329 | 0.409165 | − | 0.912461i | \(-0.365820\pi\) | ||||
0.409165 | + | 0.912461i | \(0.365820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.15579 | 0.123307 | ||||||||
\(656\) | −3.58155 | −0.139836 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.7438 | −0.418836 | ||||||||
\(659\) | −4.11845 | −0.160432 | −0.0802160 | − | 0.996778i | \(-0.525561\pi\) | ||||
−0.0802160 | + | 0.996778i | \(0.525561\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.1674 | 1.32896 | 0.664479 | − | 0.747307i | \(-0.268653\pi\) | ||||
0.664479 | + | 0.747307i | \(0.268653\pi\) | |||||||
\(662\) | 20.2374 | 0.786549 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.2552 | 0.436787 | ||||||||
\(665\) | 3.87512 | 0.150271 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.17583 | −0.355289 | ||||||||
\(668\) | 5.34097 | 0.206648 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −34.5363 | −1.33426 | ||||||||
\(671\) | −2.68635 | −0.103706 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.60403 | −0.216020 | −0.108010 | − | 0.994150i | \(-0.534448\pi\) | ||||
−0.108010 | + | 0.994150i | \(0.534448\pi\) | |||||||
\(674\) | −11.1291 | −0.428677 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.40814 | −0.0541593 | ||||||||
\(677\) | −7.27308 | −0.279527 | −0.139764 | − | 0.990185i | \(-0.544634\pi\) | ||||
−0.139764 | + | 0.990185i | \(0.544634\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.33005 | 0.0894192 | ||||||||
\(680\) | 26.7416 | 1.02549 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.3137 | −0.471515 | ||||||||
\(683\) | 25.5922 | 0.979259 | 0.489630 | − | 0.871930i | \(-0.337132\pi\) | ||||
0.489630 | + | 0.871930i | \(0.337132\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.3142 | −0.967204 | ||||||||
\(686\) | −1.50508 | −0.0574643 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −50.3532 | −1.91970 | ||||||||
\(689\) | −20.4057 | −0.777395 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.6598 | −0.557686 | −0.278843 | − | 0.960337i | \(-0.589951\pi\) | ||||
−0.278843 | + | 0.960337i | \(0.589951\pi\) | |||||||
\(692\) | −1.96550 | −0.0747171 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.69615 | 0.330102 | ||||||||
\(695\) | −1.21895 | −0.0462375 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.86497 | 0.146396 | ||||||||
\(698\) | 26.1534 | 0.989920 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.125116 | −0.00472892 | ||||||||
\(701\) | 27.0381 | 1.02122 | 0.510608 | − | 0.859814i | \(-0.329420\pi\) | ||||
0.510608 | + | 0.859814i | \(0.329420\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.75394 | −0.330161 | ||||||||
\(704\) | −10.8883 | −0.410368 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.4160 | −1.14472 | ||||||||
\(707\) | −5.25621 | −0.197680 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.6488 | −1.75193 | −0.875966 | − | 0.482372i | \(-0.839775\pi\) | ||||
−0.875966 | + | 0.482372i | \(0.839775\pi\) | |||||||
\(710\) | 14.3636 | 0.539058 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.410431 | 0.0153816 | ||||||||
\(713\) | 21.1589 | 0.792409 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.62532 | −0.359966 | ||||||||
\(716\) | −3.51820 | −0.131481 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 35.5193 | 1.32557 | ||||||||
\(719\) | 33.5776 | 1.25224 | 0.626118 | − | 0.779729i | \(-0.284643\pi\) | ||||
0.626118 | + | 0.779729i | \(0.284643\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.1853 | 0.453805 | ||||||||
\(722\) | 23.6055 | 0.878506 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.51273 | 0.130550 | ||||||||
\(725\) | −1.02605 | −0.0381065 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.6696 | 1.13747 | 0.568737 | − | 0.822520i | \(-0.307432\pi\) | ||||
0.568737 | + | 0.822520i | \(0.307432\pi\) | |||||||
\(728\) | 7.24105 | 0.268371 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17.7209 | −0.655880 | ||||||||
\(731\) | 54.3376 | 2.00975 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0914 | 0.963706 | 0.481853 | − | 0.876252i | \(-0.339964\pi\) | ||||
0.481853 | + | 0.876252i | \(0.339964\pi\) | |||||||
\(734\) | −15.6064 | −0.576043 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.28938 | −0.231830 | ||||||||
\(737\) | −17.5866 | −0.647812 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.6632 | −0.539396 | −0.269698 | − | 0.962945i | \(-0.586924\pi\) | ||||
−0.269698 | + | 0.962945i | \(0.586924\pi\) | |||||||
\(740\) | −2.71359 | −0.0997536 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.0739 | 0.406536 | ||||||||
\(743\) | 7.35661 | 0.269888 | 0.134944 | − | 0.990853i | \(-0.456915\pi\) | ||||
0.134944 | + | 0.990853i | \(0.456915\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.05604 | −0.111965 | ||||||||
\(746\) | 38.8008 | 1.42060 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.08232 | −0.0761372 | ||||||||
\(749\) | 10.1443 | 0.370666 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.6001 | −0.934161 | −0.467081 | − | 0.884215i | \(-0.654694\pi\) | ||||
−0.467081 | + | 0.884215i | \(0.654694\pi\) | |||||||
\(752\) | −31.8382 | −1.16102 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.08056 | −0.330694 | ||||||||
\(755\) | −30.3720 | −1.10535 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.8028 | 0.683401 | 0.341700 | − | 0.939809i | \(-0.388997\pi\) | ||||
0.341700 | + | 0.939809i | \(0.388997\pi\) | |||||||
\(758\) | −45.9763 | −1.66994 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.1176 | 0.367003 | ||||||||
\(761\) | 45.6268 | 1.65397 | 0.826985 | − | 0.562224i | \(-0.190054\pi\) | ||||
0.826985 | + | 0.562224i | \(0.190054\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.63005 | 0.203821 | ||||||||
\(764\) | 1.83872 | 0.0665227 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −43.7133 | −1.57942 | ||||||||
\(767\) | −5.54598 | −0.200254 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.98470 | −0.0715699 | −0.0357850 | − | 0.999360i | \(-0.511393\pi\) | ||||
−0.0357850 | + | 0.999360i | \(0.511393\pi\) | |||||||
\(770\) | 5.22355 | 0.188244 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.44389 | 0.123948 | ||||||||
\(773\) | 10.7260 | 0.385789 | 0.192894 | − | 0.981220i | \(-0.438213\pi\) | ||||
0.192894 | + | 0.981220i | \(0.438213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.36601 | 0.0849896 | ||||||||
\(776\) | 6.08356 | 0.218387 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.6564 | 1.35005 | ||||||||
\(779\) | 1.46230 | 0.0523922 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.31426 | 0.261725 | ||||||||
\(782\) | 30.5554 | 1.09266 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.46017 | −0.159292 | ||||||||
\(785\) | 47.8235 | 1.70689 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.4882 | −1.30067 | −0.650333 | − | 0.759650i | \(-0.725370\pi\) | ||||
−0.650333 | + | 0.759650i | \(0.725370\pi\) | |||||||
\(788\) | −0.250367 | −0.00891896 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.86814 | 0.0664653 | ||||||||
\(791\) | 10.0500 | 0.357337 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.56812 | 0.162219 | ||||||||
\(794\) | −50.8768 | −1.80555 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.02313 | 0.142596 | ||||||||
\(797\) | 17.3175 | 0.613416 | 0.306708 | − | 0.951804i | \(-0.400773\pi\) | ||||
0.306708 | + | 0.951804i | \(0.400773\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.3576 | 1.21548 | ||||||||
\(800\) | −0.703283 | −0.0248648 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.9817 | 0.882135 | ||||||||
\(803\) | −9.02385 | −0.318445 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.97577 | −0.316354 | ||||||||
\(806\) | 20.9393 | 0.737554 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.7235 | −0.482791 | ||||||||
\(809\) | −34.3146 | −1.20644 | −0.603219 | − | 0.797575i | \(-0.706116\pi\) | ||||
−0.603219 | + | 0.797575i | \(0.706116\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.0816467 | 0.00286700 | 0.00143350 | − | 0.999999i | \(-0.499544\pi\) | ||||
0.00143350 | + | 0.999999i | \(0.499544\pi\) | |||||||
\(812\) | 0.577071 | 0.0202512 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.8001 | −0.413592 | ||||||||
\(815\) | 22.6748 | 0.794264 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.5585 | 0.719249 | ||||||||
\(818\) | 26.5101 | 0.926905 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.453290 | 0.0158296 | ||||||||
\(821\) | −43.5520 | −1.51997 | −0.759987 | − | 0.649938i | \(-0.774795\pi\) | ||||
−0.759987 | + | 0.649938i | \(0.774795\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.81861 | 0.0633928 | 0.0316964 | − | 0.999498i | \(-0.489909\pi\) | ||||
0.0316964 | + | 0.999498i | \(0.489909\pi\) | |||||||
\(824\) | 31.8148 | 1.10832 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.00973 | 0.104722 | ||||||||
\(827\) | 2.64469 | 0.0919649 | 0.0459824 | − | 0.998942i | \(-0.485358\pi\) | ||||
0.0459824 | + | 0.998942i | \(0.485358\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.9868 | −1.28461 | −0.642303 | − | 0.766451i | \(-0.722021\pi\) | ||||
−0.642303 | + | 0.766451i | \(0.722021\pi\) | |||||||
\(830\) | −13.8067 | −0.479239 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 18.5154 | 0.641907 | ||||||||
\(833\) | 4.81311 | 0.166764 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 42.8453 | 1.48272 | ||||||||
\(836\) | −0.787838 | −0.0272480 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −48.0629 | −1.66030 | ||||||||
\(839\) | −35.5013 | −1.22564 | −0.612820 | − | 0.790223i | \(-0.709965\pi\) | ||||
−0.612820 | + | 0.790223i | \(0.709965\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.2676 | −0.836812 | ||||||||
\(842\) | 40.3201 | 1.38952 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.34926 | 0.184129 | ||||||||
\(845\) | −11.2961 | −0.388599 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.34006 | −0.286568 | ||||||||
\(848\) | 32.8166 | 1.12693 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.41673 | 0.117193 | ||||||||
\(851\) | 20.2764 | 0.695065 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.0930 | 1.47548 | 0.737738 | − | 0.675087i | \(-0.235894\pi\) | ||||
0.737738 | + | 0.675087i | \(0.235894\pi\) | |||||||
\(854\) | −2.47906 | −0.0848318 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 26.4860 | 0.905271 | ||||||||
\(857\) | −38.6248 | −1.31940 | −0.659700 | − | 0.751529i | \(-0.729317\pi\) | ||||
−0.659700 | + | 0.751529i | \(0.729317\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.37477 | 0.183385 | 0.0916924 | − | 0.995787i | \(-0.470772\pi\) | ||||
0.0916924 | + | 0.995787i | \(0.470772\pi\) | |||||||
\(860\) | 6.37282 | 0.217311 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.70233 | 0.160162 | ||||||||
\(863\) | 40.1594 | 1.36704 | 0.683520 | − | 0.729932i | \(-0.260448\pi\) | ||||
0.683520 | + | 0.729932i | \(0.260448\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.7673 | −0.536103 | ||||||||
\(866\) | −25.2571 | −0.858273 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.33069 | −0.0451667 | ||||||||
\(869\) | 0.951293 | 0.0322704 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.9059 | 1.01332 | ||||||||
\(872\) | 14.6995 | 0.497790 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.5605 | 0.391040 | ||||||||
\(875\) | −11.6436 | −0.393627 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.6508 | 0.933702 | 0.466851 | − | 0.884336i | \(-0.345388\pi\) | ||||
0.466851 | + | 0.884336i | \(0.345388\pi\) | |||||||
\(878\) | 3.00385 | 0.101375 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 15.4795 | 0.521814 | ||||||||
\(881\) | 6.15905 | 0.207504 | 0.103752 | − | 0.994603i | \(-0.466915\pi\) | ||||
0.103752 | + | 0.994603i | \(0.466915\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.7955 | 0.767130 | 0.383565 | − | 0.923514i | \(-0.374696\pi\) | ||||
0.383565 | + | 0.923514i | \(0.374696\pi\) | |||||||
\(884\) | 3.54096 | 0.119095 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.10635 | 0.272338 | ||||||||
\(887\) | −10.9460 | −0.367531 | −0.183765 | − | 0.982970i | \(-0.558829\pi\) | ||||
−0.183765 | + | 0.982970i | \(0.558829\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −0.503475 | −0.0168765 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.70528 | 0.224509 | ||||||||
\(893\) | 12.9991 | 0.434997 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28.2231 | −0.943393 | ||||||||
\(896\) | −13.0303 | −0.435312 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.78986 | 0.159840 | ||||||||
\(899\) | −10.9128 | −0.363961 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −35.4133 | −1.17979 | ||||||||
\(902\) | 1.97113 | 0.0656315 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.2397 | 0.872718 | ||||||||
\(905\) | 28.1792 | 0.936707 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.1632 | 0.603099 | 0.301550 | − | 0.953450i | \(-0.402496\pi\) | ||||
0.301550 | + | 0.953450i | \(0.402496\pi\) | |||||||
\(908\) | −1.57658 | −0.0523207 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.88258 | −0.294455 | ||||||||
\(911\) | 2.71351 | 0.0899024 | 0.0449512 | − | 0.998989i | \(-0.485687\pi\) | ||||
0.0449512 | + | 0.998989i | \(0.485687\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.03068 | −0.232681 | ||||||||
\(914\) | −27.6514 | −0.914628 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.39883 | 0.145341 | ||||||||
\(917\) | 1.48299 | 0.0489727 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.2240 | 1.06297 | 0.531486 | − | 0.847067i | \(-0.321634\pi\) | ||||
0.531486 | + | 0.847067i | \(0.321634\pi\) | |||||||
\(920\) | −23.4349 | −0.772627 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.33784 | −0.109926 | ||||||||
\(923\) | −12.4378 | −0.409396 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.26732 | 0.0745491 | ||||||||
\(926\) | −12.2044 | −0.401063 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.24376 | 0.106482 | ||||||||
\(929\) | −9.80980 | −0.321849 | −0.160925 | − | 0.986967i | \(-0.551448\pi\) | ||||
−0.160925 | + | 0.986967i | \(0.551448\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.82102 | 0.0596816 | ||||||||
\(932\) | −7.10358 | −0.232685 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.1263 | 0.756714 | ||||||||
\(935\) | −16.7044 | −0.546292 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.87596 | 0.0612850 | 0.0306425 | − | 0.999530i | \(-0.490245\pi\) | ||||
0.0306425 | + | 0.999530i | \(0.490245\pi\) | |||||||
\(938\) | −16.2296 | −0.529914 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.02952 | 0.131428 | ||||||||
\(941\) | 9.37897 | 0.305746 | 0.152873 | − | 0.988246i | \(-0.451147\pi\) | ||||
0.152873 | + | 0.988246i | \(0.451147\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.38706 | −0.110298 | ||||||||
\(944\) | 8.91907 | 0.290291 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27.7122 | 0.901001 | ||||||||
\(947\) | 13.5267 | 0.439559 | 0.219779 | − | 0.975550i | \(-0.429466\pi\) | ||||
0.219779 | + | 0.975550i | \(0.429466\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.3450 | 0.498118 | ||||||||
\(950\) | 1.29271 | 0.0419409 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.5666 | 0.407286 | ||||||||
\(953\) | 38.8476 | 1.25840 | 0.629199 | − | 0.777244i | \(-0.283383\pi\) | ||||
0.629199 | + | 0.777244i | \(0.283383\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.7503 | 0.477307 | ||||||||
\(956\) | −1.89698 | −0.0613528 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −59.1308 | −1.91043 | ||||||||
\(959\) | −11.8958 | −0.384136 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.83576 | −0.188250 | ||||||||
\(962\) | 20.0659 | 0.646949 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.28799 | 0.138107 | ||||||||
\(965\) | 27.6269 | 0.889341 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.4337 | −1.49321 | −0.746604 | − | 0.665268i | \(-0.768317\pi\) | ||||
−0.746604 | + | 0.665268i | \(0.768317\pi\) | |||||||
\(968\) | −21.7752 | −0.699880 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.46269 | −0.239612 | ||||||||
\(971\) | 17.6091 | 0.565104 | 0.282552 | − | 0.959252i | \(-0.408819\pi\) | ||||
0.282552 | + | 0.959252i | \(0.408819\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.572818 | −0.0183637 | ||||||||
\(974\) | −20.7338 | −0.664352 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.34647 | −0.235155 | ||||||||
\(977\) | −7.43882 | −0.237989 | −0.118995 | − | 0.992895i | \(-0.537967\pi\) | ||||
−0.118995 | + | 0.992895i | \(0.537967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.256380 | −0.00819394 | ||||||||
\(980\) | 0.564490 | 0.0180320 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.18826 | −0.229387 | ||||||||
\(983\) | −32.9210 | −1.05002 | −0.525008 | − | 0.851097i | \(-0.675938\pi\) | ||||
−0.525008 | + | 0.851097i | \(0.675938\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.00845 | −0.0639945 | ||||||||
\(986\) | −15.7590 | −0.501868 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.33971 | 0.0426219 | ||||||||
\(989\) | −47.6187 | −1.51419 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.9537 | 1.23741 | 0.618703 | − | 0.785625i | \(-0.287658\pi\) | ||||
0.618703 | + | 0.785625i | \(0.287658\pi\) | |||||||
\(992\) | −7.47993 | −0.237488 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.74986 | 0.214092 | ||||||||
\(995\) | 32.2736 | 1.02314 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.7715 | 0.436149 | 0.218075 | − | 0.975932i | \(-0.430022\pi\) | ||||
0.218075 | + | 0.975932i | \(0.430022\pi\) | |||||||
\(998\) | −30.0414 | −0.950945 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.ba.1.11 | ✓ | 40 | |
3.2 | odd | 2 | inner | 8001.2.a.ba.1.30 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.ba.1.11 | ✓ | 40 | 1.1 | even | 1 | trivial | |
8001.2.a.ba.1.30 | yes | 40 | 3.2 | odd | 2 | inner |