Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(1,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.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: | \(52.0396846251\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 882.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −22.0000 | −1.96774 | −0.983870 | − | 0.178885i | \(-0.942751\pi\) | ||||
−0.983870 | + | 0.178885i | \(0.942751\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 44.0000 | 1.39140 | ||||||||
\(11\) | 26.0000 | 0.712663 | 0.356332 | − | 0.934360i | \(-0.384027\pi\) | ||||
0.356332 | + | 0.934360i | \(0.384027\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 54.0000 | 1.15207 | 0.576035 | − | 0.817425i | \(-0.304599\pi\) | ||||
0.576035 | + | 0.817425i | \(0.304599\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −74.0000 | −1.05574 | −0.527872 | − | 0.849324i | \(-0.677010\pi\) | ||||
−0.527872 | + | 0.849324i | \(0.677010\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −116.000 | −1.40064 | −0.700322 | − | 0.713827i | \(-0.746960\pi\) | ||||
−0.700322 | + | 0.713827i | \(0.746960\pi\) | |||||||
\(20\) | −88.0000 | −0.983870 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −52.0000 | −0.503929 | ||||||||
\(23\) | −58.0000 | −0.525819 | −0.262909 | − | 0.964821i | \(-0.584682\pi\) | ||||
−0.262909 | + | 0.964821i | \(0.584682\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 359.000 | 2.87200 | ||||||||
\(26\) | −108.000 | −0.814636 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 208.000 | 1.33188 | 0.665942 | − | 0.746004i | \(-0.268030\pi\) | ||||
0.665942 | + | 0.746004i | \(0.268030\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 252.000 | 1.46002 | 0.730009 | − | 0.683438i | \(-0.239516\pi\) | ||||
0.730009 | + | 0.683438i | \(0.239516\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 148.000 | 0.746523 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 50.0000 | 0.222161 | 0.111080 | − | 0.993811i | \(-0.464569\pi\) | ||||
0.111080 | + | 0.993811i | \(0.464569\pi\) | |||||||
\(38\) | 232.000 | 0.990404 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 176.000 | 0.695701 | ||||||||
\(41\) | −126.000 | −0.479949 | −0.239974 | − | 0.970779i | \(-0.577139\pi\) | ||||
−0.239974 | + | 0.970779i | \(0.577139\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 164.000 | 0.581622 | 0.290811 | − | 0.956780i | \(-0.406075\pi\) | ||||
0.290811 | + | 0.956780i | \(0.406075\pi\) | |||||||
\(44\) | 104.000 | 0.356332 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 116.000 | 0.371810 | ||||||||
\(47\) | 444.000 | 1.37796 | 0.688979 | − | 0.724781i | \(-0.258059\pi\) | ||||
0.688979 | + | 0.724781i | \(0.258059\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −718.000 | −2.03081 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 216.000 | 0.576035 | ||||||||
\(53\) | 12.0000 | 0.0311005 | 0.0155503 | − | 0.999879i | \(-0.495050\pi\) | ||||
0.0155503 | + | 0.999879i | \(0.495050\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −572.000 | −1.40234 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −416.000 | −0.941784 | ||||||||
\(59\) | −124.000 | −0.273617 | −0.136809 | − | 0.990597i | \(-0.543685\pi\) | ||||
−0.136809 | + | 0.990597i | \(0.543685\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 162.000 | 0.340032 | 0.170016 | − | 0.985441i | \(-0.445618\pi\) | ||||
0.170016 | + | 0.985441i | \(0.445618\pi\) | |||||||
\(62\) | −504.000 | −1.03239 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −1188.00 | −2.26697 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −860.000 | −1.56815 | −0.784073 | − | 0.620669i | \(-0.786861\pi\) | ||||
−0.784073 | + | 0.620669i | \(0.786861\pi\) | |||||||
\(68\) | −296.000 | −0.527872 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −238.000 | −0.397823 | −0.198911 | − | 0.980017i | \(-0.563741\pi\) | ||||
−0.198911 | + | 0.980017i | \(0.563741\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 146.000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | −100.000 | −0.157091 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −464.000 | −0.700322 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −984.000 | −1.40138 | −0.700688 | − | 0.713468i | \(-0.747123\pi\) | ||||
−0.700688 | + | 0.713468i | \(0.747123\pi\) | |||||||
\(80\) | −352.000 | −0.491935 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 252.000 | 0.339375 | ||||||||
\(83\) | −656.000 | −0.867534 | −0.433767 | − | 0.901025i | \(-0.642816\pi\) | ||||
−0.433767 | + | 0.901025i | \(0.642816\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1628.00 | 2.07743 | ||||||||
\(86\) | −328.000 | −0.411269 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −208.000 | −0.251964 | ||||||||
\(89\) | 954.000 | 1.13622 | 0.568111 | − | 0.822952i | \(-0.307674\pi\) | ||||
0.568111 | + | 0.822952i | \(0.307674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −232.000 | −0.262909 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −888.000 | −0.974364 | ||||||||
\(95\) | 2552.00 | 2.75610 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −526.000 | −0.550590 | −0.275295 | − | 0.961360i | \(-0.588775\pi\) | ||||
−0.275295 | + | 0.961360i | \(0.588775\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1436.00 | 1.43600 | ||||||||
\(101\) | −1306.00 | −1.28665 | −0.643326 | − | 0.765592i | \(-0.722446\pi\) | ||||
−0.643326 | + | 0.765592i | \(0.722446\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 508.000 | 0.485968 | 0.242984 | − | 0.970030i | \(-0.421874\pi\) | ||||
0.242984 | + | 0.970030i | \(0.421874\pi\) | |||||||
\(104\) | −432.000 | −0.407318 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −24.0000 | −0.0219914 | ||||||||
\(107\) | 498.000 | 0.449939 | 0.224970 | − | 0.974366i | \(-0.427772\pi\) | ||||
0.224970 | + | 0.974366i | \(0.427772\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −614.000 | −0.539546 | −0.269773 | − | 0.962924i | \(-0.586949\pi\) | ||||
−0.269773 | + | 0.962924i | \(0.586949\pi\) | |||||||
\(110\) | 1144.00 | 0.991601 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1232.00 | −1.02564 | −0.512818 | − | 0.858498i | \(-0.671398\pi\) | ||||
−0.512818 | + | 0.858498i | \(0.671398\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1276.00 | 1.03467 | ||||||||
\(116\) | 832.000 | 0.665942 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 248.000 | 0.193477 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −655.000 | −0.492111 | ||||||||
\(122\) | −324.000 | −0.240439 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1008.00 | 0.730009 | ||||||||
\(125\) | −5148.00 | −3.68361 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2808.00 | −1.96197 | −0.980983 | − | 0.194093i | \(-0.937824\pi\) | ||||
−0.980983 | + | 0.194093i | \(0.937824\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2376.00 | 1.60299 | ||||||||
\(131\) | −520.000 | −0.346814 | −0.173407 | − | 0.984850i | \(-0.555478\pi\) | ||||
−0.173407 | + | 0.984850i | \(0.555478\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1720.00 | 1.10885 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 592.000 | 0.373262 | ||||||||
\(137\) | −2516.00 | −1.56902 | −0.784512 | − | 0.620113i | \(-0.787087\pi\) | ||||
−0.784512 | + | 0.620113i | \(0.787087\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2672.00 | 1.63048 | 0.815238 | − | 0.579126i | \(-0.196606\pi\) | ||||
0.815238 | + | 0.579126i | \(0.196606\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 476.000 | 0.281303 | ||||||||
\(143\) | 1404.00 | 0.821038 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4576.00 | −2.62080 | ||||||||
\(146\) | −292.000 | −0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 200.000 | 0.111080 | ||||||||
\(149\) | −1164.00 | −0.639991 | −0.319995 | − | 0.947419i | \(-0.603681\pi\) | ||||
−0.319995 | + | 0.947419i | \(0.603681\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1672.00 | 0.901096 | 0.450548 | − | 0.892752i | \(-0.351229\pi\) | ||||
0.450548 | + | 0.892752i | \(0.351229\pi\) | |||||||
\(152\) | 928.000 | 0.495202 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5544.00 | −2.87293 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −446.000 | −0.226718 | −0.113359 | − | 0.993554i | \(-0.536161\pi\) | ||||
−0.113359 | + | 0.993554i | \(0.536161\pi\) | |||||||
\(158\) | 1968.00 | 0.990922 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 704.000 | 0.347851 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 428.000 | 0.205666 | 0.102833 | − | 0.994699i | \(-0.467209\pi\) | ||||
0.102833 | + | 0.994699i | \(0.467209\pi\) | |||||||
\(164\) | −504.000 | −0.239974 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1312.00 | 0.613439 | ||||||||
\(167\) | −4.00000 | −0.00185347 | −0.000926734 | − | 1.00000i | \(-0.500295\pi\) | ||||
−0.000926734 | 1.00000i | \(0.500295\pi\) | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 719.000 | 0.327264 | ||||||||
\(170\) | −3256.00 | −1.46896 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 656.000 | 0.290811 | ||||||||
\(173\) | 590.000 | 0.259288 | 0.129644 | − | 0.991561i | \(-0.458617\pi\) | ||||
0.129644 | + | 0.991561i | \(0.458617\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 416.000 | 0.178166 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1908.00 | −0.803431 | ||||||||
\(179\) | 3534.00 | 1.47566 | 0.737831 | − | 0.674985i | \(-0.235850\pi\) | ||||
0.737831 | + | 0.674985i | \(0.235850\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1098.00 | −0.450904 | −0.225452 | − | 0.974254i | \(-0.572386\pi\) | ||||
−0.225452 | + | 0.974254i | \(0.572386\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 464.000 | 0.185905 | ||||||||
\(185\) | −1100.00 | −0.437155 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1924.00 | −0.752389 | ||||||||
\(188\) | 1776.00 | 0.688979 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5104.00 | −1.94886 | ||||||||
\(191\) | −4854.00 | −1.83886 | −0.919432 | − | 0.393248i | \(-0.871351\pi\) | ||||
−0.919432 | + | 0.393248i | \(0.871351\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1498.00 | −0.558696 | −0.279348 | − | 0.960190i | \(-0.590118\pi\) | ||||
−0.279348 | + | 0.960190i | \(0.590118\pi\) | |||||||
\(194\) | 1052.00 | 0.389326 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 620.000 | 0.224229 | 0.112115 | − | 0.993695i | \(-0.464238\pi\) | ||||
0.112115 | + | 0.993695i | \(0.464238\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −32.0000 | −0.0113991 | −0.00569955 | − | 0.999984i | \(-0.501814\pi\) | ||||
−0.00569955 | + | 0.999984i | \(0.501814\pi\) | |||||||
\(200\) | −2872.00 | −1.01541 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2612.00 | 0.909800 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2772.00 | 0.944414 | ||||||||
\(206\) | −1016.00 | −0.343631 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 864.000 | 0.288017 | ||||||||
\(209\) | −3016.00 | −0.998187 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4268.00 | 1.39252 | 0.696259 | − | 0.717791i | \(-0.254847\pi\) | ||||
0.696259 | + | 0.717791i | \(0.254847\pi\) | |||||||
\(212\) | 48.0000 | 0.0155503 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −996.000 | −0.318155 | ||||||||
\(215\) | −3608.00 | −1.14448 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1228.00 | 0.381517 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2288.00 | −0.701168 | ||||||||
\(221\) | −3996.00 | −1.21629 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3464.00 | −1.04021 | −0.520104 | − | 0.854103i | \(-0.674107\pi\) | ||||
−0.520104 | + | 0.854103i | \(0.674107\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2464.00 | 0.725234 | ||||||||
\(227\) | 3252.00 | 0.950849 | 0.475425 | − | 0.879756i | \(-0.342294\pi\) | ||||
0.475425 | + | 0.879756i | \(0.342294\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −418.000 | −0.120621 | −0.0603105 | − | 0.998180i | \(-0.519209\pi\) | ||||
−0.0603105 | + | 0.998180i | \(0.519209\pi\) | |||||||
\(230\) | −2552.00 | −0.731626 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1664.00 | −0.470892 | ||||||||
\(233\) | 2084.00 | 0.585954 | 0.292977 | − | 0.956119i | \(-0.405354\pi\) | ||||
0.292977 | + | 0.956119i | \(0.405354\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9768.00 | −2.71146 | ||||||||
\(236\) | −496.000 | −0.136809 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1662.00 | 0.449815 | 0.224908 | − | 0.974380i | \(-0.427792\pi\) | ||||
0.224908 | + | 0.974380i | \(0.427792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6182.00 | −1.65236 | −0.826178 | − | 0.563410i | \(-0.809489\pi\) | ||||
−0.826178 | + | 0.563410i | \(0.809489\pi\) | |||||||
\(242\) | 1310.00 | 0.347975 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 648.000 | 0.170016 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6264.00 | −1.61364 | ||||||||
\(248\) | −2016.00 | −0.516194 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10296.0 | 2.60470 | ||||||||
\(251\) | 996.000 | 0.250466 | 0.125233 | − | 0.992127i | \(-0.460032\pi\) | ||||
0.125233 | + | 0.992127i | \(0.460032\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1508.00 | −0.374732 | ||||||||
\(254\) | 5616.00 | 1.38732 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5994.00 | 1.45485 | 0.727423 | − | 0.686189i | \(-0.240718\pi\) | ||||
0.727423 | + | 0.686189i | \(0.240718\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4752.00 | −1.13349 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1040.00 | 0.245234 | ||||||||
\(263\) | 6414.00 | 1.50382 | 0.751909 | − | 0.659267i | \(-0.229133\pi\) | ||||
0.751909 | + | 0.659267i | \(0.229133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −264.000 | −0.0611977 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3440.00 | −0.784073 | ||||||||
\(269\) | −2686.00 | −0.608804 | −0.304402 | − | 0.952544i | \(-0.598457\pi\) | ||||
−0.304402 | + | 0.952544i | \(0.598457\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5100.00 | −1.14318 | −0.571592 | − | 0.820538i | \(-0.693674\pi\) | ||||
−0.571592 | + | 0.820538i | \(0.693674\pi\) | |||||||
\(272\) | −1184.00 | −0.263936 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5032.00 | 1.10947 | ||||||||
\(275\) | 9334.00 | 2.04677 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4426.00 | −0.960045 | −0.480023 | − | 0.877256i | \(-0.659372\pi\) | ||||
−0.480023 | + | 0.877256i | \(0.659372\pi\) | |||||||
\(278\) | −5344.00 | −1.15292 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7508.00 | 1.59391 | 0.796957 | − | 0.604036i | \(-0.206442\pi\) | ||||
0.796957 | + | 0.604036i | \(0.206442\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3412.00 | −0.716687 | −0.358343 | − | 0.933590i | \(-0.616658\pi\) | ||||
−0.358343 | + | 0.933590i | \(0.616658\pi\) | |||||||
\(284\) | −952.000 | −0.198911 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2808.00 | −0.580561 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 563.000 | 0.114594 | ||||||||
\(290\) | 9152.00 | 1.85319 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 584.000 | 0.117041 | ||||||||
\(293\) | 4734.00 | 0.943902 | 0.471951 | − | 0.881625i | \(-0.343550\pi\) | ||||
0.471951 | + | 0.881625i | \(0.343550\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2728.00 | 0.538408 | ||||||||
\(296\) | −400.000 | −0.0785457 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2328.00 | 0.452542 | ||||||||
\(299\) | −3132.00 | −0.605780 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3344.00 | −0.637171 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1856.00 | −0.350161 | ||||||||
\(305\) | −3564.00 | −0.669095 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5836.00 | −1.08494 | −0.542472 | − | 0.840074i | \(-0.682512\pi\) | ||||
−0.542472 | + | 0.840074i | \(0.682512\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11088.0 | 2.03147 | ||||||||
\(311\) | −5620.00 | −1.02470 | −0.512349 | − | 0.858777i | \(-0.671225\pi\) | ||||
−0.512349 | + | 0.858777i | \(0.671225\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6082.00 | −1.09832 | −0.549161 | − | 0.835716i | \(-0.685053\pi\) | ||||
−0.549161 | + | 0.835716i | \(0.685053\pi\) | |||||||
\(314\) | 892.000 | 0.160314 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3936.00 | −0.700688 | ||||||||
\(317\) | −7308.00 | −1.29482 | −0.647410 | − | 0.762142i | \(-0.724148\pi\) | ||||
−0.647410 | + | 0.762142i | \(0.724148\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5408.00 | 0.949185 | ||||||||
\(320\) | −1408.00 | −0.245967 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8584.00 | 1.47872 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19386.0 | 3.30874 | ||||||||
\(326\) | −856.000 | −0.145428 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1008.00 | 0.169687 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8020.00 | −1.33178 | −0.665890 | − | 0.746050i | \(-0.731948\pi\) | ||||
−0.665890 | + | 0.746050i | \(0.731948\pi\) | |||||||
\(332\) | −2624.00 | −0.433767 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.00000 | 0.00131060 | ||||||||
\(335\) | 18920.0 | 3.08570 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4590.00 | 0.741938 | 0.370969 | − | 0.928645i | \(-0.379026\pi\) | ||||
0.370969 | + | 0.928645i | \(0.379026\pi\) | |||||||
\(338\) | −1438.00 | −0.231411 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6512.00 | 1.03871 | ||||||||
\(341\) | 6552.00 | 1.04050 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1312.00 | −0.205635 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1180.00 | −0.183344 | ||||||||
\(347\) | −6546.00 | −1.01270 | −0.506351 | − | 0.862327i | \(-0.669006\pi\) | ||||
−0.506351 | + | 0.862327i | \(0.669006\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7994.00 | 1.22610 | 0.613050 | − | 0.790044i | \(-0.289942\pi\) | ||||
0.613050 | + | 0.790044i | \(0.289942\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −832.000 | −0.125982 | ||||||||
\(353\) | −4650.00 | −0.701118 | −0.350559 | − | 0.936541i | \(-0.614008\pi\) | ||||
−0.350559 | + | 0.936541i | \(0.614008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5236.00 | 0.782811 | ||||||||
\(356\) | 3816.00 | 0.568111 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7068.00 | −1.04345 | ||||||||
\(359\) | 346.000 | 0.0508668 | 0.0254334 | − | 0.999677i | \(-0.491903\pi\) | ||||
0.0254334 | + | 0.999677i | \(0.491903\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6597.00 | 0.961802 | ||||||||
\(362\) | 2196.00 | 0.318838 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3212.00 | −0.460613 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6784.00 | 0.964910 | 0.482455 | − | 0.875921i | \(-0.339745\pi\) | ||||
0.482455 | + | 0.875921i | \(0.339745\pi\) | |||||||
\(368\) | −928.000 | −0.131455 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2200.00 | 0.309115 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6098.00 | −0.846495 | −0.423247 | − | 0.906014i | \(-0.639110\pi\) | ||||
−0.423247 | + | 0.906014i | \(0.639110\pi\) | |||||||
\(374\) | 3848.00 | 0.532020 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3552.00 | −0.487182 | ||||||||
\(377\) | 11232.0 | 1.53442 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2660.00 | −0.360515 | −0.180257 | − | 0.983619i | \(-0.557693\pi\) | ||||
−0.180257 | + | 0.983619i | \(0.557693\pi\) | |||||||
\(380\) | 10208.0 | 1.37805 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9708.00 | 1.30027 | ||||||||
\(383\) | 760.000 | 0.101395 | 0.0506974 | − | 0.998714i | \(-0.483856\pi\) | ||||
0.0506974 | + | 0.998714i | \(0.483856\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2996.00 | 0.395058 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2104.00 | −0.275295 | ||||||||
\(389\) | −104.000 | −0.0135553 | −0.00677765 | − | 0.999977i | \(-0.502157\pi\) | ||||
−0.00677765 | + | 0.999977i | \(0.502157\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4292.00 | 0.555130 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1240.00 | −0.158554 | ||||||||
\(395\) | 21648.0 | 2.75754 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4398.00 | −0.555993 | −0.277997 | − | 0.960582i | \(-0.589670\pi\) | ||||
−0.277997 | + | 0.960582i | \(0.589670\pi\) | |||||||
\(398\) | 64.0000 | 0.00806038 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5744.00 | 0.718000 | ||||||||
\(401\) | 13236.0 | 1.64831 | 0.824157 | − | 0.566361i | \(-0.191649\pi\) | ||||
0.824157 | + | 0.566361i | \(0.191649\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13608.0 | 1.68204 | ||||||||
\(404\) | −5224.00 | −0.643326 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1300.00 | 0.158326 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9490.00 | 1.14731 | 0.573656 | − | 0.819097i | \(-0.305525\pi\) | ||||
0.573656 | + | 0.819097i | \(0.305525\pi\) | |||||||
\(410\) | −5544.00 | −0.667802 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2032.00 | 0.242984 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14432.0 | 1.70708 | ||||||||
\(416\) | −1728.00 | −0.203659 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6032.00 | 0.705825 | ||||||||
\(419\) | −4236.00 | −0.493895 | −0.246948 | − | 0.969029i | \(-0.579428\pi\) | ||||
−0.246948 | + | 0.969029i | \(0.579428\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 918.000 | 0.106272 | 0.0531361 | − | 0.998587i | \(-0.483078\pi\) | ||||
0.0531361 | + | 0.998587i | \(0.483078\pi\) | |||||||
\(422\) | −8536.00 | −0.984659 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −96.0000 | −0.0109957 | ||||||||
\(425\) | −26566.0 | −3.03209 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1992.00 | 0.224970 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7216.00 | 0.809271 | ||||||||
\(431\) | −11814.0 | −1.32033 | −0.660163 | − | 0.751123i | \(-0.729513\pi\) | ||||
−0.660163 | + | 0.751123i | \(0.729513\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8374.00 | 0.929397 | 0.464698 | − | 0.885469i | \(-0.346163\pi\) | ||||
0.464698 | + | 0.885469i | \(0.346163\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2456.00 | −0.269773 | ||||||||
\(437\) | 6728.00 | 0.736485 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3840.00 | −0.417479 | −0.208739 | − | 0.977971i | \(-0.566936\pi\) | ||||
−0.208739 | + | 0.977971i | \(0.566936\pi\) | |||||||
\(440\) | 4576.00 | 0.495801 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7992.00 | 0.860047 | ||||||||
\(443\) | 10166.0 | 1.09030 | 0.545148 | − | 0.838340i | \(-0.316473\pi\) | ||||
0.545148 | + | 0.838340i | \(0.316473\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20988.0 | −2.23579 | ||||||||
\(446\) | 6928.00 | 0.735539 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8200.00 | 0.861875 | 0.430938 | − | 0.902382i | \(-0.358183\pi\) | ||||
0.430938 | + | 0.902382i | \(0.358183\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3276.00 | −0.342042 | ||||||||
\(452\) | −4928.00 | −0.512818 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6504.00 | −0.672352 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6074.00 | −0.621728 | −0.310864 | − | 0.950454i | \(-0.600618\pi\) | ||||
−0.310864 | + | 0.950454i | \(0.600618\pi\) | |||||||
\(458\) | 836.000 | 0.0852920 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5104.00 | 0.517337 | ||||||||
\(461\) | 2006.00 | 0.202665 | 0.101333 | − | 0.994853i | \(-0.467689\pi\) | ||||
0.101333 | + | 0.994853i | \(0.467689\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3728.00 | −0.374201 | −0.187100 | − | 0.982341i | \(-0.559909\pi\) | ||||
−0.187100 | + | 0.982341i | \(0.559909\pi\) | |||||||
\(464\) | 3328.00 | 0.332971 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4168.00 | −0.414332 | ||||||||
\(467\) | 6380.00 | 0.632187 | 0.316093 | − | 0.948728i | \(-0.397629\pi\) | ||||
0.316093 | + | 0.948728i | \(0.397629\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 19536.0 | 1.91729 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 992.000 | 0.0967383 | ||||||||
\(473\) | 4264.00 | 0.414501 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −41644.0 | −4.02265 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3324.00 | −0.318067 | ||||||||
\(479\) | −17180.0 | −1.63878 | −0.819389 | − | 0.573239i | \(-0.805687\pi\) | ||||
−0.819389 | + | 0.573239i | \(0.805687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2700.00 | 0.255945 | ||||||||
\(482\) | 12364.0 | 1.16839 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2620.00 | −0.246056 | ||||||||
\(485\) | 11572.0 | 1.08342 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2728.00 | −0.253835 | −0.126917 | − | 0.991913i | \(-0.540508\pi\) | ||||
−0.126917 | + | 0.991913i | \(0.540508\pi\) | |||||||
\(488\) | −1296.00 | −0.120220 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2574.00 | 0.236585 | 0.118292 | − | 0.992979i | \(-0.462258\pi\) | ||||
0.118292 | + | 0.992979i | \(0.462258\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15392.0 | −1.40613 | ||||||||
\(494\) | 12528.0 | 1.14101 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4032.00 | 0.365004 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7484.00 | −0.671403 | −0.335701 | − | 0.941969i | \(-0.608973\pi\) | ||||
−0.335701 | + | 0.941969i | \(0.608973\pi\) | |||||||
\(500\) | −20592.0 | −1.84180 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1992.00 | −0.177106 | ||||||||
\(503\) | −7920.00 | −0.702058 | −0.351029 | − | 0.936365i | \(-0.614168\pi\) | ||||
−0.351029 | + | 0.936365i | \(0.614168\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28732.0 | 2.53180 | ||||||||
\(506\) | 3016.00 | 0.264975 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11232.0 | −0.980983 | ||||||||
\(509\) | −7254.00 | −0.631685 | −0.315843 | − | 0.948812i | \(-0.602287\pi\) | ||||
−0.315843 | + | 0.948812i | \(0.602287\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11988.0 | −1.02873 | ||||||||
\(515\) | −11176.0 | −0.956259 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11544.0 | 0.982020 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9504.00 | 0.801496 | ||||||||
\(521\) | 17862.0 | 1.50201 | 0.751006 | − | 0.660295i | \(-0.229569\pi\) | ||||
0.751006 | + | 0.660295i | \(0.229569\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 592.000 | 0.0494959 | 0.0247479 | − | 0.999694i | \(-0.492122\pi\) | ||||
0.0247479 | + | 0.999694i | \(0.492122\pi\) | |||||||
\(524\) | −2080.00 | −0.173407 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12828.0 | −1.06336 | ||||||||
\(527\) | −18648.0 | −1.54140 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8803.00 | −0.723514 | ||||||||
\(530\) | 528.000 | 0.0432733 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6804.00 | −0.552934 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10956.0 | −0.885363 | ||||||||
\(536\) | 6880.00 | 0.554423 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5372.00 | 0.430490 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6402.00 | −0.508768 | −0.254384 | − | 0.967103i | \(-0.581873\pi\) | ||||
−0.254384 | + | 0.967103i | \(0.581873\pi\) | |||||||
\(542\) | 10200.0 | 0.808353 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2368.00 | 0.186631 | ||||||||
\(545\) | 13508.0 | 1.06169 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8988.00 | −0.702558 | −0.351279 | − | 0.936271i | \(-0.614253\pi\) | ||||
−0.351279 | + | 0.936271i | \(0.614253\pi\) | |||||||
\(548\) | −10064.0 | −0.784512 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −18668.0 | −1.44728 | ||||||||
\(551\) | −24128.0 | −1.86549 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8852.00 | 0.678855 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10688.0 | 0.815238 | ||||||||
\(557\) | 3244.00 | 0.246773 | 0.123387 | − | 0.992359i | \(-0.460624\pi\) | ||||
0.123387 | + | 0.992359i | \(0.460624\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8856.00 | 0.670070 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15016.0 | −1.12707 | ||||||||
\(563\) | −9812.00 | −0.734505 | −0.367253 | − | 0.930121i | \(-0.619702\pi\) | ||||
−0.367253 | + | 0.930121i | \(0.619702\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27104.0 | 2.01818 | ||||||||
\(566\) | 6824.00 | 0.506774 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1904.00 | 0.140652 | ||||||||
\(569\) | −12156.0 | −0.895617 | −0.447808 | − | 0.894130i | \(-0.647795\pi\) | ||||
−0.447808 | + | 0.894130i | \(0.647795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6876.00 | 0.503943 | 0.251972 | − | 0.967735i | \(-0.418921\pi\) | ||||
0.251972 | + | 0.967735i | \(0.418921\pi\) | |||||||
\(572\) | 5616.00 | 0.410519 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20822.0 | −1.51015 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20002.0 | −1.44314 | −0.721572 | − | 0.692339i | \(-0.756580\pi\) | ||||
−0.721572 | + | 0.692339i | \(0.756580\pi\) | |||||||
\(578\) | −1126.00 | −0.0810301 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −18304.0 | −1.31040 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 312.000 | 0.0221642 | ||||||||
\(584\) | −1168.00 | −0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9468.00 | −0.667439 | ||||||||
\(587\) | −18404.0 | −1.29406 | −0.647031 | − | 0.762464i | \(-0.723990\pi\) | ||||
−0.647031 | + | 0.762464i | \(0.723990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29232.0 | −2.04496 | ||||||||
\(590\) | −5456.00 | −0.380712 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 800.000 | 0.0555402 | ||||||||
\(593\) | 9846.00 | 0.681833 | 0.340916 | − | 0.940094i | \(-0.389263\pi\) | ||||
0.340916 | + | 0.940094i | \(0.389263\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4656.00 | −0.319995 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6264.00 | 0.428351 | ||||||||
\(599\) | 9234.00 | 0.629868 | 0.314934 | − | 0.949114i | \(-0.398018\pi\) | ||||
0.314934 | + | 0.949114i | \(0.398018\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1510.00 | 0.102486 | 0.0512431 | − | 0.998686i | \(-0.483682\pi\) | ||||
0.0512431 | + | 0.998686i | \(0.483682\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6688.00 | 0.450548 | ||||||||
\(605\) | 14410.0 | 0.968347 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17544.0 | −1.17313 | −0.586564 | − | 0.809903i | \(-0.699520\pi\) | ||||
−0.586564 | + | 0.809903i | \(0.699520\pi\) | |||||||
\(608\) | 3712.00 | 0.247601 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7128.00 | 0.473122 | ||||||||
\(611\) | 23976.0 | 1.58750 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9246.00 | 0.609205 | 0.304602 | − | 0.952480i | \(-0.401476\pi\) | ||||
0.304602 | + | 0.952480i | \(0.401476\pi\) | |||||||
\(614\) | 11672.0 | 0.767172 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29212.0 | −1.90605 | −0.953023 | − | 0.302897i | \(-0.902046\pi\) | ||||
−0.953023 | + | 0.302897i | \(0.902046\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7096.00 | −0.460763 | −0.230382 | − | 0.973100i | \(-0.573997\pi\) | ||||
−0.230382 | + | 0.973100i | \(0.573997\pi\) | |||||||
\(620\) | −22176.0 | −1.43647 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11240.0 | 0.724571 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 68381.0 | 4.37638 | ||||||||
\(626\) | 12164.0 | 0.776631 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1784.00 | −0.113359 | ||||||||
\(629\) | −3700.00 | −0.234545 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 488.000 | 0.0307876 | 0.0153938 | − | 0.999882i | \(-0.495100\pi\) | ||||
0.0153938 | + | 0.999882i | \(0.495100\pi\) | |||||||
\(632\) | 7872.00 | 0.495461 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14616.0 | 0.915577 | ||||||||
\(635\) | 61776.0 | 3.86064 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10816.0 | −0.671175 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2816.00 | 0.173925 | ||||||||
\(641\) | 8756.00 | 0.539534 | 0.269767 | − | 0.962926i | \(-0.413053\pi\) | ||||
0.269767 | + | 0.962926i | \(0.413053\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3364.00 | 0.206319 | 0.103160 | − | 0.994665i | \(-0.467105\pi\) | ||||
0.103160 | + | 0.994665i | \(0.467105\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17168.0 | −1.04561 | ||||||||
\(647\) | −21804.0 | −1.32489 | −0.662445 | − | 0.749111i | \(-0.730481\pi\) | ||||
−0.662445 | + | 0.749111i | \(0.730481\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3224.00 | −0.194997 | ||||||||
\(650\) | −38772.0 | −2.33964 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1712.00 | 0.102833 | ||||||||
\(653\) | 13488.0 | 0.808310 | 0.404155 | − | 0.914691i | \(-0.367566\pi\) | ||||
0.404155 | + | 0.914691i | \(0.367566\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11440.0 | 0.682439 | ||||||||
\(656\) | −2016.00 | −0.119987 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28946.0 | 1.71104 | 0.855521 | − | 0.517769i | \(-0.173237\pi\) | ||||
0.855521 | + | 0.517769i | \(0.173237\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20642.0 | 1.21465 | 0.607323 | − | 0.794455i | \(-0.292243\pi\) | ||||
0.607323 | + | 0.794455i | \(0.292243\pi\) | |||||||
\(662\) | 16040.0 | 0.941710 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5248.00 | 0.306720 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12064.0 | −0.700330 | ||||||||
\(668\) | −16.0000 | −0.000926734 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −37840.0 | −2.18192 | ||||||||
\(671\) | 4212.00 | 0.242329 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17602.0 | −1.00818 | −0.504092 | − | 0.863650i | \(-0.668173\pi\) | ||||
−0.504092 | + | 0.863650i | \(0.668173\pi\) | |||||||
\(674\) | −9180.00 | −0.524630 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2876.00 | 0.163632 | ||||||||
\(677\) | −4266.00 | −0.242180 | −0.121090 | − | 0.992642i | \(-0.538639\pi\) | ||||
−0.121090 | + | 0.992642i | \(0.538639\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −13024.0 | −0.734482 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13104.0 | −0.735745 | ||||||||
\(683\) | −26874.0 | −1.50557 | −0.752786 | − | 0.658266i | \(-0.771290\pi\) | ||||
−0.752786 | + | 0.658266i | \(0.771290\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 55352.0 | 3.08743 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2624.00 | 0.145406 | ||||||||
\(689\) | 648.000 | 0.0358299 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17128.0 | 0.942952 | 0.471476 | − | 0.881879i | \(-0.343721\pi\) | ||||
0.471476 | + | 0.881879i | \(0.343721\pi\) | |||||||
\(692\) | 2360.00 | 0.129644 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13092.0 | 0.716089 | ||||||||
\(695\) | −58784.0 | −3.20835 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9324.00 | 0.506703 | ||||||||
\(698\) | −15988.0 | −0.866984 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11968.0 | 0.644829 | 0.322414 | − | 0.946599i | \(-0.395506\pi\) | ||||
0.322414 | + | 0.946599i | \(0.395506\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5800.00 | −0.311168 | ||||||||
\(704\) | 1664.00 | 0.0890829 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9300.00 | 0.495765 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5278.00 | −0.279576 | −0.139788 | − | 0.990181i | \(-0.544642\pi\) | ||||
−0.139788 | + | 0.990181i | \(0.544642\pi\) | |||||||
\(710\) | −10472.0 | −0.553531 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7632.00 | −0.401715 | ||||||||
\(713\) | −14616.0 | −0.767705 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −30888.0 | −1.61559 | ||||||||
\(716\) | 14136.0 | 0.737831 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −692.000 | −0.0359683 | ||||||||
\(719\) | −6720.00 | −0.348559 | −0.174279 | − | 0.984696i | \(-0.555760\pi\) | ||||
−0.174279 | + | 0.984696i | \(0.555760\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −13194.0 | −0.680097 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4392.00 | −0.225452 | ||||||||
\(725\) | 74672.0 | 3.82517 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16804.0 | −0.857257 | −0.428629 | − | 0.903481i | \(-0.641003\pi\) | ||||
−0.428629 | + | 0.903481i | \(0.641003\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6424.00 | 0.325703 | ||||||||
\(731\) | −12136.0 | −0.614044 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27522.0 | −1.38683 | −0.693416 | − | 0.720537i | \(-0.743895\pi\) | ||||
−0.693416 | + | 0.720537i | \(0.743895\pi\) | |||||||
\(734\) | −13568.0 | −0.682294 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1856.00 | 0.0929525 | ||||||||
\(737\) | −22360.0 | −1.11756 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21132.0 | 1.05190 | 0.525949 | − | 0.850516i | \(-0.323710\pi\) | ||||
0.525949 | + | 0.850516i | \(0.323710\pi\) | |||||||
\(740\) | −4400.00 | −0.218577 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.0000 | −0.00148128 | −0.000740641 | − | 1.00000i | \(-0.500236\pi\) | ||||
−0.000740641 | 1.00000i | \(0.500236\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25608.0 | 1.25933 | ||||||||
\(746\) | 12196.0 | 0.598562 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7696.00 | −0.376195 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15480.0 | −0.752161 | −0.376081 | − | 0.926587i | \(-0.622728\pi\) | ||||
−0.376081 | + | 0.926587i | \(0.622728\pi\) | |||||||
\(752\) | 7104.00 | 0.344490 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −22464.0 | −1.08500 | ||||||||
\(755\) | −36784.0 | −1.77312 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28770.0 | 1.38133 | 0.690663 | − | 0.723177i | \(-0.257319\pi\) | ||||
0.690663 | + | 0.723177i | \(0.257319\pi\) | |||||||
\(758\) | 5320.00 | 0.254922 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −20416.0 | −0.974429 | ||||||||
\(761\) | 12418.0 | 0.591527 | 0.295764 | − | 0.955261i | \(-0.404426\pi\) | ||||
0.295764 | + | 0.955261i | \(0.404426\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −19416.0 | −0.919432 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1520.00 | −0.0716969 | ||||||||
\(767\) | −6696.00 | −0.315226 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12346.0 | −0.578944 | −0.289472 | − | 0.957186i | \(-0.593480\pi\) | ||||
−0.289472 | + | 0.957186i | \(0.593480\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5992.00 | −0.279348 | ||||||||
\(773\) | −38098.0 | −1.77269 | −0.886345 | − | 0.463025i | \(-0.846764\pi\) | ||||
−0.886345 | + | 0.463025i | \(0.846764\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 90468.0 | 4.19317 | ||||||||
\(776\) | 4208.00 | 0.194663 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 208.000 | 0.00958504 | ||||||||
\(779\) | 14616.0 | 0.672237 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6188.00 | −0.283514 | ||||||||
\(782\) | −8584.00 | −0.392536 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9812.00 | 0.446121 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13824.0 | −0.626140 | −0.313070 | − | 0.949730i | \(-0.601357\pi\) | ||||
−0.313070 | + | 0.949730i | \(0.601357\pi\) | |||||||
\(788\) | 2480.00 | 0.112115 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −43296.0 | −1.94988 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8748.00 | 0.391741 | ||||||||
\(794\) | 8796.00 | 0.393147 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −128.000 | −0.00569955 | ||||||||
\(797\) | −22170.0 | −0.985322 | −0.492661 | − | 0.870221i | \(-0.663976\pi\) | ||||
−0.492661 | + | 0.870221i | \(0.663976\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32856.0 | −1.45477 | ||||||||
\(800\) | −11488.0 | −0.507703 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26472.0 | −1.16553 | ||||||||
\(803\) | 3796.00 | 0.166822 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −27216.0 | −1.18938 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10448.0 | 0.454900 | ||||||||
\(809\) | 16288.0 | 0.707856 | 0.353928 | − | 0.935273i | \(-0.384846\pi\) | ||||
0.353928 | + | 0.935273i | \(0.384846\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8720.00 | 0.377559 | 0.188780 | − | 0.982019i | \(-0.439547\pi\) | ||||
0.188780 | + | 0.982019i | \(0.439547\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2600.00 | −0.111953 | ||||||||
\(815\) | −9416.00 | −0.404697 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19024.0 | −0.814646 | ||||||||
\(818\) | −18980.0 | −0.811272 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11088.0 | 0.472207 | ||||||||
\(821\) | −31372.0 | −1.33361 | −0.666803 | − | 0.745234i | \(-0.732338\pi\) | ||||
−0.666803 | + | 0.745234i | \(0.732338\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17648.0 | −0.747473 | −0.373737 | − | 0.927535i | \(-0.621924\pi\) | ||||
−0.373737 | + | 0.927535i | \(0.621924\pi\) | |||||||
\(824\) | −4064.00 | −0.171816 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2382.00 | −0.100158 | −0.0500788 | − | 0.998745i | \(-0.515947\pi\) | ||||
−0.0500788 | + | 0.998745i | \(0.515947\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26650.0 | −1.11652 | −0.558259 | − | 0.829667i | \(-0.688530\pi\) | ||||
−0.558259 | + | 0.829667i | \(0.688530\pi\) | |||||||
\(830\) | −28864.0 | −1.20709 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3456.00 | 0.144009 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 88.0000 | 0.00364714 | ||||||||
\(836\) | −12064.0 | −0.499093 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8472.00 | 0.349237 | ||||||||
\(839\) | −24092.0 | −0.991357 | −0.495678 | − | 0.868506i | \(-0.665080\pi\) | ||||
−0.495678 | + | 0.868506i | \(0.665080\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18875.0 | 0.773914 | ||||||||
\(842\) | −1836.00 | −0.0751458 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17072.0 | 0.696259 | ||||||||
\(845\) | −15818.0 | −0.643971 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 192.000 | 0.00777513 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 53132.0 | 2.14401 | ||||||||
\(851\) | −2900.00 | −0.116816 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8194.00 | 0.328906 | 0.164453 | − | 0.986385i | \(-0.447414\pi\) | ||||
0.164453 | + | 0.986385i | \(0.447414\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3984.00 | −0.159077 | ||||||||
\(857\) | 16962.0 | 0.676092 | 0.338046 | − | 0.941130i | \(-0.390234\pi\) | ||||
0.338046 | + | 0.941130i | \(0.390234\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48556.0 | 1.92865 | 0.964324 | − | 0.264723i | \(-0.0852806\pi\) | ||||
0.964324 | + | 0.264723i | \(0.0852806\pi\) | |||||||
\(860\) | −14432.0 | −0.572241 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 23628.0 | 0.933611 | ||||||||
\(863\) | −34274.0 | −1.35191 | −0.675956 | − | 0.736942i | \(-0.736269\pi\) | ||||
−0.675956 | + | 0.736942i | \(0.736269\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12980.0 | −0.510212 | ||||||||
\(866\) | −16748.0 | −0.657183 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25584.0 | −0.998709 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46440.0 | −1.80661 | ||||||||
\(872\) | 4912.00 | 0.190758 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13456.0 | −0.520773 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7126.00 | 0.274376 | 0.137188 | − | 0.990545i | \(-0.456194\pi\) | ||||
0.137188 | + | 0.990545i | \(0.456194\pi\) | |||||||
\(878\) | 7680.00 | 0.295202 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9152.00 | −0.350584 | ||||||||
\(881\) | 9222.00 | 0.352664 | 0.176332 | − | 0.984331i | \(-0.443577\pi\) | ||||
0.176332 | + | 0.984331i | \(0.443577\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37652.0 | 1.43498 | 0.717492 | − | 0.696567i | \(-0.245290\pi\) | ||||
0.717492 | + | 0.696567i | \(0.245290\pi\) | |||||||
\(884\) | −15984.0 | −0.608145 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20332.0 | −0.770956 | ||||||||
\(887\) | 21996.0 | 0.832642 | 0.416321 | − | 0.909218i | \(-0.363319\pi\) | ||||
0.416321 | + | 0.909218i | \(0.363319\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 41976.0 | 1.58094 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13856.0 | −0.520104 | ||||||||
\(893\) | −51504.0 | −1.93003 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −77748.0 | −2.90372 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16400.0 | −0.609438 | ||||||||
\(899\) | 52416.0 | 1.94457 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −888.000 | −0.0328342 | ||||||||
\(902\) | 6552.00 | 0.241860 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9856.00 | 0.362617 | ||||||||
\(905\) | 24156.0 | 0.887263 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14844.0 | 0.543426 | 0.271713 | − | 0.962378i | \(-0.412410\pi\) | ||||
0.271713 | + | 0.962378i | \(0.412410\pi\) | |||||||
\(908\) | 13008.0 | 0.475425 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19446.0 | −0.707217 | −0.353609 | − | 0.935394i | \(-0.615045\pi\) | ||||
−0.353609 | + | 0.935394i | \(0.615045\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17056.0 | −0.618260 | ||||||||
\(914\) | 12148.0 | 0.439628 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1672.00 | −0.0603105 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39200.0 | −1.40706 | −0.703530 | − | 0.710665i | \(-0.748394\pi\) | ||||
−0.703530 | + | 0.710665i | \(0.748394\pi\) | |||||||
\(920\) | −10208.0 | −0.365813 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4012.00 | −0.143306 | ||||||||
\(923\) | −12852.0 | −0.458319 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17950.0 | 0.638046 | ||||||||
\(926\) | 7456.00 | 0.264600 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6656.00 | −0.235446 | ||||||||
\(929\) | 15954.0 | 0.563438 | 0.281719 | − | 0.959497i | \(-0.409095\pi\) | ||||
0.281719 | + | 0.959497i | \(0.409095\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8336.00 | 0.292977 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12760.0 | −0.447024 | ||||||||
\(935\) | 42328.0 | 1.48051 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2546.00 | −0.0887665 | −0.0443832 | − | 0.999015i | \(-0.514132\pi\) | ||||
−0.0443832 | + | 0.999015i | \(0.514132\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −39072.0 | −1.35573 | ||||||||
\(941\) | −430.000 | −0.0148965 | −0.00744825 | − | 0.999972i | \(-0.502371\pi\) | ||||
−0.00744825 | + | 0.999972i | \(0.502371\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7308.00 | 0.252366 | ||||||||
\(944\) | −1984.00 | −0.0684043 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8528.00 | −0.293096 | ||||||||
\(947\) | 38266.0 | 1.31307 | 0.656535 | − | 0.754295i | \(-0.272021\pi\) | ||||
0.656535 | + | 0.754295i | \(0.272021\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7884.00 | 0.269679 | ||||||||
\(950\) | 83288.0 | 2.84444 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28216.0 | −0.959083 | −0.479541 | − | 0.877519i | \(-0.659197\pi\) | ||||
−0.479541 | + | 0.877519i | \(0.659197\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 106788. | 3.61841 | ||||||||
\(956\) | 6648.00 | 0.224908 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 34360.0 | 1.15879 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33713.0 | 1.13165 | ||||||||
\(962\) | −5400.00 | −0.180980 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −24728.0 | −0.826178 | ||||||||
\(965\) | 32956.0 | 1.09937 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27712.0 | −0.921570 | −0.460785 | − | 0.887512i | \(-0.652432\pi\) | ||||
−0.460785 | + | 0.887512i | \(0.652432\pi\) | |||||||
\(968\) | 5240.00 | 0.173988 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23144.0 | −0.766092 | ||||||||
\(971\) | −32976.0 | −1.08986 | −0.544928 | − | 0.838483i | \(-0.683443\pi\) | ||||
−0.544928 | + | 0.838483i | \(0.683443\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5456.00 | 0.179488 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2592.00 | 0.0850081 | ||||||||
\(977\) | −8940.00 | −0.292749 | −0.146375 | − | 0.989229i | \(-0.546760\pi\) | ||||
−0.146375 | + | 0.989229i | \(0.546760\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24804.0 | 0.809744 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5148.00 | −0.167291 | ||||||||
\(983\) | 3288.00 | 0.106685 | 0.0533423 | − | 0.998576i | \(-0.483013\pi\) | ||||
0.0533423 | + | 0.998576i | \(0.483013\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13640.0 | −0.441225 | ||||||||
\(986\) | 30784.0 | 0.994282 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25056.0 | −0.806819 | ||||||||
\(989\) | −9512.00 | −0.305828 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33944.0 | 1.08806 | 0.544030 | − | 0.839066i | \(-0.316898\pi\) | ||||
0.544030 | + | 0.839066i | \(0.316898\pi\) | |||||||
\(992\) | −8064.00 | −0.258097 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 704.000 | 0.0224305 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54562.0 | 1.73320 | 0.866598 | − | 0.499007i | \(-0.166302\pi\) | ||||
0.866598 | + | 0.499007i | \(0.166302\pi\) | |||||||
\(998\) | 14968.0 | 0.474753 | ||||||||
\(999\) | 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 | 882.4.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 882.4.a.s.1.1 | 1 | |||
7.2 | even | 3 | 882.4.g.x.361.1 | 2 | |||
7.3 | odd | 6 | 882.4.g.n.667.1 | 2 | |||
7.4 | even | 3 | 882.4.g.x.667.1 | 2 | |||
7.5 | odd | 6 | 882.4.g.n.361.1 | 2 | |||
7.6 | odd | 2 | 126.4.a.e.1.1 | ✓ | 1 | ||
21.2 | odd | 6 | 882.4.g.a.361.1 | 2 | |||
21.5 | even | 6 | 882.4.g.m.361.1 | 2 | |||
21.11 | odd | 6 | 882.4.g.a.667.1 | 2 | |||
21.17 | even | 6 | 882.4.g.m.667.1 | 2 | |||
21.20 | even | 2 | 126.4.a.f.1.1 | yes | 1 | ||
28.27 | even | 2 | 1008.4.a.w.1.1 | 1 | |||
84.83 | odd | 2 | 1008.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.4.a.e.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
126.4.a.f.1.1 | yes | 1 | 21.20 | even | 2 | ||
882.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
882.4.a.s.1.1 | 1 | 3.2 | odd | 2 | |||
882.4.g.a.361.1 | 2 | 21.2 | odd | 6 | |||
882.4.g.a.667.1 | 2 | 21.11 | odd | 6 | |||
882.4.g.m.361.1 | 2 | 21.5 | even | 6 | |||
882.4.g.m.667.1 | 2 | 21.17 | even | 6 | |||
882.4.g.n.361.1 | 2 | 7.5 | odd | 6 | |||
882.4.g.n.667.1 | 2 | 7.3 | odd | 6 | |||
882.4.g.x.361.1 | 2 | 7.2 | even | 3 | |||
882.4.g.x.667.1 | 2 | 7.4 | even | 3 | |||
1008.4.a.a.1.1 | 1 | 84.83 | odd | 2 | |||
1008.4.a.w.1.1 | 1 | 28.27 | even | 2 |