Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2496,4,Mod(1,2496)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2496, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("2496.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2496 = 2^{6} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2496.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: | \(147.268767374\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 78) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2496.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.00000 | −0.536656 | −0.268328 | − | 0.963328i | \(-0.586471\pi\) | ||||
−0.268328 | + | 0.963328i | \(0.586471\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −20.0000 | −1.07990 | −0.539949 | − | 0.841698i | \(-0.681557\pi\) | ||||
−0.539949 | + | 0.841698i | \(0.681557\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 24.0000 | 0.657843 | 0.328921 | − | 0.944357i | \(-0.393315\pi\) | ||||
0.328921 | + | 0.944357i | \(0.393315\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 18.0000 | 0.309839 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −30.0000 | −0.428004 | −0.214002 | − | 0.976833i | \(-0.568650\pi\) | ||||
−0.214002 | + | 0.976833i | \(0.568650\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.0000 | −0.193192 | −0.0965961 | − | 0.995324i | \(-0.530796\pi\) | ||||
−0.0965961 | + | 0.995324i | \(0.530796\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 60.0000 | 0.623480 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 72.0000 | 0.652741 | 0.326370 | − | 0.945242i | \(-0.394174\pi\) | ||||
0.326370 | + | 0.945242i | \(0.394174\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −89.0000 | −0.712000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 282.000 | 1.80573 | 0.902864 | − | 0.429927i | \(-0.141461\pi\) | ||||
0.902864 | + | 0.429927i | \(0.141461\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −164.000 | −0.950170 | −0.475085 | − | 0.879940i | \(-0.657583\pi\) | ||||
−0.475085 | + | 0.879940i | \(0.657583\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −72.0000 | −0.379806 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 120.000 | 0.579534 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −110.000 | −0.488754 | −0.244377 | − | 0.969680i | \(-0.578583\pi\) | ||||
−0.244377 | + | 0.969680i | \(0.578583\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.0000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −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 | \(0.406075\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −54.0000 | −0.178885 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 204.000 | 0.633116 | 0.316558 | − | 0.948573i | \(-0.397473\pi\) | ||||
0.316558 | + | 0.948573i | \(0.397473\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 57.0000 | 0.166181 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 90.0000 | 0.247108 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 738.000 | 1.91268 | 0.956341 | − | 0.292255i | \(-0.0944055\pi\) | ||||
0.956341 | + | 0.292255i | \(0.0944055\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −144.000 | −0.353036 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 48.0000 | 0.111540 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 120.000 | 0.264791 | 0.132396 | − | 0.991197i | \(-0.457733\pi\) | ||||
0.132396 | + | 0.991197i | \(0.457733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −614.000 | −1.28876 | −0.644382 | − | 0.764703i | \(-0.722885\pi\) | ||||
−0.644382 | + | 0.764703i | \(0.722885\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −180.000 | −0.359966 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 78.0000 | 0.148842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 848.000 | 1.54626 | 0.773132 | − | 0.634245i | \(-0.218689\pi\) | ||||
0.773132 | + | 0.634245i | \(0.218689\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −216.000 | −0.376860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −132.000 | −0.220641 | −0.110321 | − | 0.993896i | \(-0.535188\pi\) | ||||
−0.110321 | + | 0.993896i | \(0.535188\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 218.000 | 0.349520 | 0.174760 | − | 0.984611i | \(-0.444085\pi\) | ||||
0.174760 | + | 0.984611i | \(0.444085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 267.000 | 0.411073 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −480.000 | −0.710404 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1096.00 | 1.56088 | 0.780441 | − | 0.625230i | \(-0.214995\pi\) | ||||
0.780441 | + | 0.625230i | \(0.214995\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 552.000 | 0.729998 | 0.364999 | − | 0.931008i | \(-0.381069\pi\) | ||||
0.364999 | + | 0.931008i | \(0.381069\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 180.000 | 0.229691 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −846.000 | −1.04254 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 210.000 | 0.250112 | 0.125056 | − | 0.992150i | \(-0.460089\pi\) | ||||
0.125056 | + | 0.992150i | \(0.460089\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 260.000 | 0.299510 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 492.000 | 0.548581 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 96.0000 | 0.103678 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1726.00 | −1.80669 | −0.903344 | − | 0.428917i | \(-0.858895\pi\) | ||||
−0.903344 | + | 0.428917i | \(0.858895\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 216.000 | 0.219281 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −798.000 | −0.786178 | −0.393089 | − | 0.919500i | \(-0.628594\pi\) | ||||
−0.393089 | + | 0.919500i | \(0.628594\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 520.000 | 0.497448 | 0.248724 | − | 0.968574i | \(-0.419989\pi\) | ||||
0.248724 | + | 0.968574i | \(0.419989\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −360.000 | −0.334594 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000 | 0.0108419 | 0.00542095 | − | 0.999985i | \(-0.498274\pi\) | ||||
0.00542095 | + | 0.999985i | \(0.498274\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1834.00 | 1.61161 | 0.805804 | − | 0.592182i | \(-0.201733\pi\) | ||||
0.805804 | + | 0.592182i | \(0.201733\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 330.000 | 0.282182 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −366.000 | −0.304694 | −0.152347 | − | 0.988327i | \(-0.548683\pi\) | ||||
−0.152347 | + | 0.988327i | \(0.548683\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −432.000 | −0.350297 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 600.000 | 0.462201 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −755.000 | −0.567243 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 378.000 | 0.277098 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1284.00 | 0.918756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2144.00 | −1.49803 | −0.749013 | − | 0.662556i | \(-0.769472\pi\) | ||||
−0.749013 | + | 0.662556i | \(0.769472\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −492.000 | −0.335800 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2748.00 | −1.83278 | −0.916389 | − | 0.400289i | \(-0.868910\pi\) | ||||
−0.916389 | + | 0.400289i | \(0.868910\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 320.000 | 0.208628 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 162.000 | 0.103280 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2754.00 | 1.71745 | 0.858723 | − | 0.512440i | \(-0.171258\pi\) | ||||
0.858723 | + | 0.512440i | \(0.171258\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2252.00 | 1.37419 | 0.687094 | − | 0.726568i | \(-0.258886\pi\) | ||||
0.687094 | + | 0.726568i | \(0.258886\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −612.000 | −0.365530 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −312.000 | −0.182453 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1692.00 | −0.969055 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −171.000 | −0.0959445 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1770.00 | 0.973182 | 0.486591 | − | 0.873630i | \(-0.338240\pi\) | ||||
0.486591 | + | 0.873630i | \(0.338240\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 988.000 | 0.532466 | 0.266233 | − | 0.963909i | \(-0.414221\pi\) | ||||
0.266233 | + | 0.963909i | \(0.414221\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −270.000 | −0.142668 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 984.000 | 0.509915 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −326.000 | −0.165717 | −0.0828587 | − | 0.996561i | \(-0.526405\pi\) | ||||
−0.0828587 | + | 0.996561i | \(0.526405\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2214.00 | −1.10429 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1440.00 | −0.704894 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1496.00 | 0.718870 | 0.359435 | − | 0.933170i | \(-0.382969\pi\) | ||||
0.359435 | + | 0.933170i | \(0.382969\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 432.000 | 0.203825 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1116.00 | −0.517118 | −0.258559 | − | 0.965995i | \(-0.583248\pi\) | ||||
−0.258559 | + | 0.965995i | \(0.583248\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −144.000 | −0.0643974 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4374.00 | −1.92225 | −0.961124 | − | 0.276116i | \(-0.910953\pi\) | ||||
−0.961124 | + | 0.276116i | \(0.910953\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1780.00 | 0.768888 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −360.000 | −0.152877 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.00501074 | 0.00250537 | − | 0.999997i | \(-0.499203\pi\) | ||||
0.00250537 | + | 0.999997i | \(0.499203\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4718.00 | −1.93749 | −0.968746 | − | 0.248053i | \(-0.920209\pi\) | ||||
−0.968746 | + | 0.248053i | \(0.920209\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1842.00 | 0.744069 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 660.000 | 0.262293 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −720.000 | −0.281559 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 540.000 | 0.207827 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1368.00 | 0.518246 | 0.259123 | − | 0.965844i | \(-0.416566\pi\) | ||||
0.259123 | + | 0.965844i | \(0.416566\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3310.00 | −1.23450 | −0.617251 | − | 0.786766i | \(-0.711754\pi\) | ||||
−0.617251 | + | 0.786766i | \(0.711754\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −234.000 | −0.0859338 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3126.00 | −1.13055 | −0.565275 | − | 0.824903i | \(-0.691230\pi\) | ||||
−0.565275 | + | 0.824903i | \(0.691230\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4664.00 | −1.66142 | −0.830709 | − | 0.556707i | \(-0.812065\pi\) | ||||
−0.830709 | + | 0.556707i | \(0.812065\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2544.00 | −0.892736 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5640.00 | −1.95000 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 756.000 | 0.257567 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 648.000 | 0.217580 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −384.000 | −0.127090 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −556.000 | −0.181406 | −0.0907029 | − | 0.995878i | \(-0.528911\pi\) | ||||
−0.0907029 | + | 0.995878i | \(0.528911\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 396.000 | 0.127387 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −984.000 | −0.312131 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3280.00 | 1.02609 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −654.000 | −0.201796 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 390.000 | 0.118707 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 268.000 | 0.0804781 | 0.0402390 | − | 0.999190i | \(-0.487188\pi\) | ||||
0.0402390 | + | 0.999190i | \(0.487188\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −801.000 | −0.237333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1800.00 | 0.526300 | 0.263150 | − | 0.964755i | \(-0.415239\pi\) | ||||
0.263150 | + | 0.964755i | \(0.415239\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2990.00 | −0.862816 | −0.431408 | − | 0.902157i | \(-0.641983\pi\) | ||||
−0.431408 | + | 0.902157i | \(0.641983\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1440.00 | 0.410152 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2826.00 | 0.794581 | 0.397291 | − | 0.917693i | \(-0.369951\pi\) | ||||
0.397291 | + | 0.917693i | \(0.369951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1224.00 | −0.339766 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3288.00 | −0.901175 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1812.00 | 0.490412 | 0.245206 | − | 0.969471i | \(-0.421144\pi\) | ||||
0.245206 | + | 0.969471i | \(0.421144\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1582.00 | −0.422845 | −0.211422 | − | 0.977395i | \(-0.567810\pi\) | ||||
−0.211422 | + | 0.977395i | \(0.567810\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −342.000 | −0.0891820 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 208.000 | 0.0535819 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1656.00 | −0.421465 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2148.00 | 0.540162 | 0.270081 | − | 0.962838i | \(-0.412950\pi\) | ||||
0.270081 | + | 0.962838i | \(0.412950\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1728.00 | 0.429401 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −540.000 | −0.132612 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −558.000 | −0.135436 | −0.0677181 | − | 0.997704i | \(-0.521572\pi\) | ||||
−0.0677181 | + | 0.997704i | \(0.521572\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2200.00 | 0.527804 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2538.00 | 0.601909 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2112.00 | −0.495177 | −0.247588 | − | 0.968865i | \(-0.579638\pi\) | ||||
−0.247588 | + | 0.968865i | \(0.579638\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4428.00 | −1.02645 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −630.000 | −0.144402 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5046.00 | −1.14372 | −0.571859 | − | 0.820352i | \(-0.693777\pi\) | ||||
−0.571859 | + | 0.820352i | \(0.693777\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3796.00 | 0.850888 | 0.425444 | − | 0.904985i | \(-0.360118\pi\) | ||||
0.425444 | + | 0.904985i | \(0.360118\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −780.000 | −0.172922 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2136.00 | −0.468384 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5582.00 | −1.21079 | −0.605397 | − | 0.795924i | \(-0.706986\pi\) | ||||
−0.605397 | + | 0.795924i | \(0.706986\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1476.00 | −0.316723 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1950.00 | −0.413976 | −0.206988 | − | 0.978343i | \(-0.566366\pi\) | ||||
−0.206988 | + | 0.978343i | \(0.566366\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4732.00 | −0.993951 | −0.496976 | − | 0.867765i | \(-0.665556\pi\) | ||||
−0.496976 | + | 0.867765i | \(0.665556\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −288.000 | −0.0598584 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2520.00 | 0.518296 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4013.00 | −0.816813 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5178.00 | 1.04309 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4998.00 | −0.996540 | −0.498270 | − | 0.867022i | \(-0.666031\pi\) | ||||
−0.498270 | + | 0.867022i | \(0.666031\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −720.000 | −0.142102 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −648.000 | −0.126602 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −936.000 | −0.181038 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3280.00 | −0.628093 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2394.00 | 0.453900 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3684.00 | 0.691624 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6824.00 | 1.26862 | 0.634310 | − | 0.773079i | \(-0.281284\pi\) | ||||
0.634310 | + | 0.773079i | \(0.281284\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1560.00 | −0.287202 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8760.00 | 1.59722 | 0.798608 | − | 0.601852i | \(-0.205570\pi\) | ||||
0.798608 | + | 0.601852i | \(0.205570\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3962.00 | 0.715481 | 0.357740 | − | 0.933821i | \(-0.383547\pi\) | ||||
0.357740 | + | 0.933821i | \(0.383547\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1080.00 | 0.193178 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7086.00 | −1.25549 | −0.627744 | − | 0.778420i | \(-0.716021\pi\) | ||||
−0.627744 | + | 0.778420i | \(0.716021\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6768.00 | 1.18788 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −36.0000 | −0.00625958 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 480.000 | 0.0826870 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1157.00 | 0.197473 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5502.00 | −0.930463 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4080.00 | −0.683701 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9016.00 | −1.49717 | −0.748586 | − | 0.663037i | \(-0.769267\pi\) | ||||
−0.748586 | + | 0.663037i | \(0.769267\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −990.000 | −0.162918 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5088.00 | −0.829812 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2306.00 | 0.372747 | 0.186374 | − | 0.982479i | \(-0.440327\pi\) | ||||
0.186374 | + | 0.982479i | \(0.440327\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1098.00 | 0.175915 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3936.00 | −0.625063 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5720.00 | 0.900440 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1296.00 | 0.202244 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11076.0 | −1.71352 | −0.856759 | − | 0.515717i | \(-0.827526\pi\) | ||||
−0.856759 | + | 0.515717i | \(0.827526\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2342.00 | −0.359210 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 351.000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4650.00 | 0.701118 | 0.350559 | − | 0.936541i | \(-0.385992\pi\) | ||||
0.350559 | + | 0.936541i | \(0.385992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 792.000 | 0.118408 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1800.00 | −0.266852 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11268.0 | 1.65655 | 0.828276 | − | 0.560320i | \(-0.189322\pi\) | ||||
0.828276 | + | 0.560320i | \(0.189322\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6603.00 | −0.962677 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2265.00 | 0.327498 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1308.00 | −0.187572 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7288.00 | 1.03660 | 0.518298 | − | 0.855200i | \(-0.326566\pi\) | ||||
0.518298 | + | 0.855200i | \(0.326566\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1134.00 | −0.159983 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14760.0 | −2.06550 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9970.00 | 1.38399 | 0.691993 | − | 0.721904i | \(-0.256733\pi\) | ||||
0.691993 | + | 0.721904i | \(0.256733\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3852.00 | −0.530444 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3666.00 | −0.500819 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13448.0 | 1.82263 | 0.911316 | − | 0.411708i | \(-0.135068\pi\) | ||||
0.911316 | + | 0.411708i | \(0.135068\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6432.00 | 0.864885 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11820.0 | −1.57696 | −0.788478 | − | 0.615064i | \(-0.789130\pi\) | ||||
−0.788478 | + | 0.615064i | \(0.789130\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2880.00 | 0.381243 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1476.00 | 0.193874 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −174.000 | −0.0226790 | −0.0113395 | − | 0.999936i | \(-0.503610\pi\) | ||||
−0.0113395 | + | 0.999936i | \(0.503610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2160.00 | −0.279376 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8244.00 | 1.05815 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6576.00 | −0.837657 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2986.00 | 0.377489 | 0.188744 | − | 0.982026i | \(-0.439558\pi\) | ||||
0.188744 | + | 0.982026i | \(0.439558\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −960.000 | −0.120451 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10566.0 | −1.31581 | −0.657906 | − | 0.753100i | \(-0.728558\pi\) | ||||
−0.657906 | + | 0.753100i | \(0.728558\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2132.00 | 0.263530 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −486.000 | −0.0596285 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2640.00 | −0.321523 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7270.00 | −0.878920 | −0.439460 | − | 0.898262i | \(-0.644830\pi\) | ||||
−0.439460 | + | 0.898262i | \(0.644830\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8262.00 | −0.991568 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2400.00 | −0.285947 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3312.00 | −0.391758 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6756.00 | −0.793388 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7308.00 | −0.852074 | −0.426037 | − | 0.904706i | \(-0.640091\pi\) | ||||
−0.426037 | + | 0.904706i | \(0.640091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5938.00 | 0.687412 | 0.343706 | − | 0.939077i | \(-0.388318\pi\) | ||||
0.343706 | + | 0.939077i | \(0.388318\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1836.00 | 0.211039 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2670.00 | 0.304739 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12280.0 | 1.39174 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 936.000 | 0.105339 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11532.0 | −1.28881 | −0.644405 | − | 0.764685i | \(-0.722895\pi\) | ||||
−0.644405 | + | 0.764685i | \(0.722895\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −718.000 | −0.0796879 | −0.0398440 | − | 0.999206i | \(-0.512686\pi\) | ||||
−0.0398440 | + | 0.999206i | \(0.512686\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5076.00 | 0.559484 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1152.00 | −0.126104 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8984.00 | −0.976726 | −0.488363 | − | 0.872640i | \(-0.662406\pi\) | ||||
−0.488363 | + | 0.872640i | \(0.662406\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 513.000 | 0.0553936 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2604.00 | 0.279277 | 0.139639 | − | 0.990203i | \(-0.455406\pi\) | ||||
0.139639 | + | 0.990203i | \(0.455406\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1260.00 | −0.134224 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5310.00 | −0.561867 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13206.0 | −1.38804 | −0.694020 | − | 0.719956i | \(-0.744162\pi\) | ||||
−0.694020 | + | 0.719956i | \(0.744162\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3024.00 | −0.315731 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2964.00 | −0.307419 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1560.00 | −0.160734 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8426.00 | 0.862476 | 0.431238 | − | 0.902238i | \(-0.358077\pi\) | ||||
0.431238 | + | 0.902238i | \(0.358077\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 810.000 | 0.0823694 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16686.0 | −1.68578 | −0.842890 | − | 0.538086i | \(-0.819148\pi\) | ||||
−0.842890 | + | 0.538086i | \(0.819148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15932.0 | −1.59919 | −0.799593 | − | 0.600543i | \(-0.794951\pi\) | ||||
−0.799593 | + | 0.600543i | \(0.794951\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2952.00 | −0.294399 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18540.0 | 1.83711 | 0.918553 | − | 0.395297i | \(-0.129358\pi\) | ||||
0.918553 | + | 0.395297i | \(0.129358\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16960.0 | −1.66981 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 978.000 | 0.0956770 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3936.00 | 0.382616 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1424.00 | 0.137553 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6642.00 | 0.637560 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6180.00 | −0.589502 | −0.294751 | − | 0.955574i | \(-0.595237\pi\) | ||||
−0.294751 | + | 0.955574i | \(0.595237\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1430.00 | 0.135556 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4320.00 | 0.406971 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10356.0 | 0.969571 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11756.0 | −1.09387 | −0.546936 | − | 0.837175i | \(-0.684206\pi\) | ||||
−0.546936 | + | 0.837175i | \(0.684206\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4488.00 | −0.415040 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1908.00 | 0.175370 | 0.0876852 | − | 0.996148i | \(-0.472053\pi\) | ||||
0.0876852 | + | 0.996148i | \(0.472053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8460.00 | −0.772858 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1296.00 | −0.117679 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2640.00 | 0.238270 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8944.00 | −0.802382 | −0.401191 | − | 0.915995i | \(-0.631404\pi\) | ||||
−0.401191 | + | 0.915995i | \(0.631404\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3348.00 | 0.298558 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6528.00 | 0.578666 | 0.289333 | − | 0.957228i | \(-0.406566\pi\) | ||||
0.289333 | + | 0.957228i | \(0.406566\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4788.00 | 0.421907 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −507.000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12114.0 | 1.05490 | 0.527450 | − | 0.849586i | \(-0.323148\pi\) | ||||
0.527450 | + | 0.849586i | \(0.323148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4360.00 | −0.377446 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 432.000 | 0.0371799 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3120.00 | −0.266958 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4896.00 | 0.416491 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13122.0 | 1.10981 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14310.0 | −1.20333 | −0.601663 | − | 0.798750i | \(-0.705495\pi\) | ||||
−0.601663 | + | 0.798750i | \(0.705495\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18340.0 | −1.53337 | −0.766685 | − | 0.642024i | \(-0.778095\pi\) | ||||
−0.766685 | + | 0.642024i | \(0.778095\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5340.00 | −0.443918 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4920.00 | 0.406677 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1080.00 | 0.0882637 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1638.00 | 0.133114 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −72.0000 | −0.00581838 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −36.0000 | −0.00289295 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1368.00 | 0.109321 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9254.00 | −0.735417 | −0.367708 | − | 0.929941i | \(-0.619858\pi\) | ||||
−0.367708 | + | 0.929941i | \(0.619858\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14154.0 | 1.11861 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11004.0 | −0.864880 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17444.0 | 1.36353 | 0.681766 | − | 0.731571i | \(-0.261212\pi\) | ||||
0.681766 | + | 0.731571i | \(0.261212\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5526.00 | −0.429588 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4512.00 | −0.348852 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21920.0 | −1.68559 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1980.00 | −0.151435 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3714.00 | 0.282526 | 0.141263 | − | 0.989972i | \(-0.454884\pi\) | ||||
0.141263 | + | 0.989972i | \(0.454884\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2132.00 | −0.161313 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2160.00 | 0.162558 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13812.0 | −1.03394 | −0.516968 | − | 0.856004i | \(-0.672940\pi\) | ||||
−0.516968 | + | 0.856004i | \(0.672940\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2196.00 | 0.163516 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1620.00 | −0.119989 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15942.0 | −1.17456 | −0.587279 | − | 0.809385i | \(-0.699801\pi\) | ||||
−0.587279 | + | 0.809385i | \(0.699801\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1604.00 | 0.117557 | 0.0587787 | − | 0.998271i | \(-0.481279\pi\) | ||||
0.0587787 | + | 0.998271i | \(0.481279\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4104.00 | −0.299210 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6408.00 | −0.464751 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10654.0 | −0.768686 | −0.384343 | − | 0.923190i | \(-0.625572\pi\) | ||||
−0.384343 | + | 0.923190i | \(0.625572\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9930.00 | 0.712740 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11040.0 | −0.788324 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17712.0 | 1.25824 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 702.000 | 0.0496139 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9984.00 | −0.702017 | −0.351008 | − | 0.936372i | \(-0.614161\pi\) | ||||
−0.351008 | + | 0.936372i | \(0.614161\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2624.00 | 0.183565 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9378.00 | 0.652723 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12618.0 | 0.873793 | 0.436896 | − | 0.899512i | \(-0.356078\pi\) | ||||
0.436896 | + | 0.899512i | \(0.356078\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3600.00 | −0.248043 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13992.0 | 0.959220 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11184.0 | −0.762881 | −0.381441 | − | 0.924393i | \(-0.624572\pi\) | ||||
−0.381441 | + | 0.924393i | \(0.624572\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2810.00 | 0.190719 | 0.0953596 | − | 0.995443i | \(-0.469600\pi\) | ||||
0.0953596 | + | 0.995443i | \(0.469600\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7632.00 | 0.515421 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4530.00 | 0.304414 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1064.00 | −0.0711473 | −0.0355737 | − | 0.999367i | \(-0.511326\pi\) | ||||
−0.0355737 | + | 0.999367i | \(0.511326\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16920.0 | 1.12583 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2652.00 | −0.175595 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20914.0 | 1.37799 | 0.688996 | − | 0.724766i | \(-0.258052\pi\) | ||||
0.688996 | + | 0.724766i | \(0.258052\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2268.00 | −0.148707 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9714.00 | 0.633826 | 0.316913 | − | 0.948455i | \(-0.397354\pi\) | ||||
0.316913 | + | 0.948455i | \(0.397354\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14848.0 | −0.964122 | −0.482061 | − | 0.876138i | \(-0.660112\pi\) | ||||
−0.482061 | + | 0.876138i | \(0.660112\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1944.00 | −0.125620 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4200.00 | −0.270095 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3421.00 | 0.218944 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1152.00 | 0.0733755 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3300.00 | 0.209189 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19172.0 | −1.20955 | −0.604774 | − | 0.796397i | \(-0.706737\pi\) | ||||
−0.604774 | + | 0.796397i | \(0.706737\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1668.00 | 0.104735 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12864.0 | 0.803925 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −741.000 | −0.0460902 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1188.00 | −0.0735470 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11502.0 | −0.708739 | −0.354369 | − | 0.935105i | \(-0.615304\pi\) | ||||
−0.354369 | + | 0.935105i | \(0.615304\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15568.0 | −0.954809 | −0.477404 | − | 0.878684i | \(-0.658422\pi\) | ||||
−0.477404 | + | 0.878684i | \(0.658422\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2952.00 | 0.180209 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1128.00 | −0.0685414 | −0.0342707 | − | 0.999413i | \(-0.510911\pi\) | ||||
−0.0342707 | + | 0.999413i | \(0.510911\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2880.00 | 0.174191 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9840.00 | −0.592412 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8118.00 | −0.486496 | −0.243248 | − | 0.969964i | \(-0.578213\pi\) | ||||
−0.243248 | + | 0.969964i | \(0.578213\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16488.0 | 0.983572 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1962.00 | 0.116507 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13572.0 | 0.802261 | 0.401131 | − | 0.916021i | \(-0.368617\pi\) | ||||
0.401131 | + | 0.916021i | \(0.368617\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13138.0 | 0.773085 | 0.386542 | − | 0.922272i | \(-0.373669\pi\) | ||||
0.386542 | + | 0.922272i | \(0.373669\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1170.00 | −0.0685355 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1920.00 | −0.111962 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20304.0 | 1.17867 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −804.000 | −0.0464640 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14736.0 | −0.847805 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −718.000 | −0.0411246 | −0.0205623 | − | 0.999789i | \(-0.506546\pi\) | ||||
−0.0205623 | + | 0.999789i | \(0.506546\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2403.00 | 0.137024 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2994.00 | 0.169969 | 0.0849843 | − | 0.996382i | \(-0.472916\pi\) | ||||
0.0849843 | + | 0.996382i | \(0.472916\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34520.0 | 1.95104 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5400.00 | −0.303860 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27384.0 | 1.53414 | 0.767071 | − | 0.641562i | \(-0.221713\pi\) | ||||
0.767071 | + | 0.641562i | \(0.221713\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16524.0 | −0.921678 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8970.00 | 0.498147 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9594.00 | −0.530482 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27632.0 | 1.52123 | 0.760616 | − | 0.649202i | \(-0.224897\pi\) | ||||
0.760616 | + | 0.649202i | \(0.224897\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4320.00 | −0.236801 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13512.0 | −0.737467 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3780.00 | 0.205420 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8478.00 | −0.458752 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19062.0 | −1.02705 | −0.513525 | − | 0.858075i | \(-0.671661\pi\) | ||||
−0.513525 | + | 0.858075i | \(0.671661\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1760.00 | 0.0944234 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3672.00 | 0.196164 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15960.0 | 0.848992 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3854.00 | −0.204147 | −0.102073 | − | 0.994777i | \(-0.532548\pi\) | ||||
−0.102073 | + | 0.994777i | \(0.532548\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9864.00 | 0.520294 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11808.0 | −0.620215 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1872.00 | 0.0979144 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5436.00 | −0.283140 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20976.0 | −1.08800 | −0.544001 | − | 0.839085i | \(-0.683091\pi\) | ||||
−0.544001 | + | 0.839085i | \(0.683091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10400.0 | −0.537193 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4746.00 | 0.244130 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −25098.0 | −1.28568 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29464.0 | 1.50311 | 0.751554 | − | 0.659672i | \(-0.229305\pi\) | ||||
0.751554 | + | 0.659672i | \(0.229305\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4920.00 | −0.248937 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2698.00 | 0.135952 | 0.0679761 | − | 0.997687i | \(-0.478346\pi\) | ||||
0.0679761 | + | 0.997687i | \(0.478346\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1026.00 | 0.0514892 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20352.0 | 1.01720 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 632.000 | 0.0314594 | 0.0157297 | − | 0.999876i | \(-0.494993\pi\) | ||||
0.0157297 | + | 0.999876i | \(0.494993\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −624.000 | −0.0309355 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20844.0 | 1.02920 | 0.514598 | − | 0.857432i | \(-0.327941\pi\) | ||||
0.514598 | + | 0.857432i | \(0.327941\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10620.0 | −0.522264 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4968.00 | 0.243333 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −240.000 | −0.0117082 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −272.000 | −0.0132163 | −0.00660814 | − | 0.999978i | \(-0.502103\pi\) | ||||
−0.00660814 | + | 0.999978i | \(0.502103\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6444.00 | −0.311862 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5928.00 | −0.285751 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37550.0 | −1.80288 | −0.901439 | − | 0.432907i | \(-0.857488\pi\) | ||||
−0.901439 | + | 0.432907i | \(0.857488\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5184.00 | −0.247915 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33330.0 | 1.58766 | 0.793832 | − | 0.608138i | \(-0.208083\pi\) | ||||
0.793832 | + | 0.608138i | \(0.208083\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36680.0 | −1.74037 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1620.00 | 0.0765637 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1560.00 | −0.0734398 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15406.0 | −0.722438 | −0.361219 | − | 0.932481i | \(-0.617639\pi\) | ||||
−0.361219 | + | 0.932481i | \(0.617639\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1674.00 | 0.0781941 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29514.0 | 1.37328 | 0.686640 | − | 0.726998i | \(-0.259085\pi\) | ||||
0.686640 | + | 0.726998i | \(0.259085\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14596.0 | 0.676521 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6600.00 | −0.304728 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2016.00 | 0.0927223 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3168.00 | −0.145147 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7614.00 | −0.347512 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1956.00 | 0.0889333 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33176.0 | 1.50266 | 0.751332 | − | 0.659924i | \(-0.229412\pi\) | ||||
0.751332 | + | 0.659924i | \(0.229412\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6336.00 | 0.285890 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7320.00 | 0.329038 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7982.00 | 0.357439 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13284.0 | 0.592623 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16746.0 | 0.744258 | 0.372129 | − | 0.928181i | \(-0.378628\pi\) | ||||
0.372129 | + | 0.928181i | \(0.378628\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6120.00 | −0.270976 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1890.00 | 0.0833706 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5232.00 | 0.229929 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8640.00 | 0.378286 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15138.0 | 0.660326 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15846.0 | −0.688647 | −0.344324 | − | 0.938851i | \(-0.611892\pi\) | ||||
−0.344324 | + | 0.938851i | \(0.611892\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22952.0 | 0.993778 | 0.496889 | − | 0.867814i | \(-0.334476\pi\) | ||||
0.496889 | + | 0.867814i | \(0.334476\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11388.0 | −0.491260 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8976.00 | −0.385786 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2624.00 | −0.112365 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2340.00 | 0.0998367 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37146.0 | 1.57906 | 0.789528 | − | 0.613715i | \(-0.210326\pi\) | ||||
0.789528 | + | 0.613715i | \(0.210326\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9592.00 | 0.406265 | 0.203133 | − | 0.979151i | \(-0.434888\pi\) | ||||
0.203133 | + | 0.979151i | \(0.434888\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6408.00 | 0.270422 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39960.0 | −1.68022 | −0.840112 | − | 0.542413i | \(-0.817511\pi\) | ||||
−0.840112 | + | 0.542413i | \(0.817511\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3706.00 | 0.155265 | 0.0776325 | − | 0.996982i | \(-0.475264\pi\) | ||||
0.0776325 | + | 0.996982i | \(0.475264\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16746.0 | 0.699052 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1710.00 | −0.0711260 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6696.00 | 0.277515 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4428.00 | 0.182860 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9756.00 | −0.401448 | −0.200724 | − | 0.979648i | \(-0.564329\pi\) | ||||
−0.200724 | + | 0.979648i | \(0.564329\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55135.0 | 2.26065 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5850.00 | 0.239009 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1014.00 | −0.0412813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15100.0 | 0.612565 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14196.0 | 0.573858 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7920.00 | −0.319029 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11342.0 | −0.455267 | −0.227633 | − | 0.973747i | \(-0.573099\pi\) | ||||
−0.227633 | + | 0.973747i | \(0.573099\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 864.000 | 0.0345593 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16134.0 | −0.643089 | −0.321544 | − | 0.946895i | \(-0.604202\pi\) | ||||
−0.321544 | + | 0.946895i | \(0.604202\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20932.0 | −0.831421 | −0.415710 | − | 0.909497i | \(-0.636467\pi\) | ||||
−0.415710 | + | 0.909497i | \(0.636467\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7560.00 | −0.299238 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10044.0 | −0.396178 | −0.198089 | − | 0.980184i | \(-0.563474\pi\) | ||||
−0.198089 | + | 0.980184i | \(0.563474\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26244.0 | 1.03159 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12039.0 | 0.471587 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26304.0 | 1.02681 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11024.0 | −0.428856 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15534.0 | −0.602229 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −25680.0 | −0.992163 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26314.0 | 1.01318 | 0.506591 | − | 0.862186i | \(-0.330905\pi\) | ||||
0.506591 | + | 0.862186i | \(0.330905\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14994.0 | 0.575353 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37506.0 | 1.43429 | 0.717145 | − | 0.696924i | \(-0.245449\pi\) | ||||
0.717145 | + | 0.696924i | \(0.245449\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6388.00 | −0.243458 | −0.121729 | − | 0.992563i | \(-0.538844\pi\) | ||||
−0.121729 | + | 0.992563i | \(0.538844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2160.00 | 0.0820425 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5472.00 | 0.207138 | 0.103569 | − | 0.994622i | \(-0.466974\pi\) | ||||
0.103569 | + | 0.994622i | \(0.466974\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42880.0 | 1.61772 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1944.00 | 0.0730937 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3264.00 | −0.122313 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −72.0000 | −0.00268904 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2808.00 | 0.104522 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −46248.0 | −1.71575 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22140.0 | −0.818635 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9840.00 | 0.362630 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28308.0 | 1.03977 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7180.00 | −0.262853 | −0.131427 | − | 0.991326i | \(-0.541956\pi\) | ||||
−0.131427 | + | 0.991326i | \(0.541956\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7182.00 | −0.262059 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27624.0 | −1.00464 | −0.502318 | − | 0.864683i | \(-0.667519\pi\) | ||||
−0.502318 | + | 0.864683i | \(0.667519\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13248.0 | 0.480224 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11052.0 | −0.399309 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 54960.0 | 1.97921 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30256.0 | 1.08602 | 0.543011 | − | 0.839726i | \(-0.317284\pi\) | ||||
0.543011 | + | 0.839726i | \(0.317284\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20472.0 | −0.732438 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1716.00 | 0.0611948 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9790.00 | 0.347993 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4680.00 | 0.165816 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1926.00 | −0.0680194 | −0.0340097 | − | 0.999422i | \(-0.510828\pi\) | ||||
−0.0340097 | + | 0.999422i | \(0.510828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −912.000 | −0.0321048 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26280.0 | −0.922153 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4320.00 | 0.151101 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3962.00 | 0.138135 | 0.0690677 | − | 0.997612i | \(-0.477998\pi\) | ||||
0.0690677 | + | 0.997612i | \(0.477998\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11886.0 | −0.413083 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1074.00 | 0.0372066 | 0.0186033 | − | 0.999827i | \(-0.494078\pi\) | ||||
0.0186033 | + | 0.999827i | \(0.494078\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9072.00 | −0.313282 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3240.00 | −0.111531 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4848.00 | 0.166356 | 0.0831778 | − | 0.996535i | \(-0.473493\pi\) | ||||
0.0831778 | + | 0.996535i | \(0.473493\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2834.00 | −0.0969394 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21258.0 | 0.724856 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 762.000 | 0.0259009 | 0.0129505 | − | 0.999916i | \(-0.495878\pi\) | ||||
0.0129505 | + | 0.999916i | \(0.495878\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8208.00 | −0.278120 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20304.0 | −0.685826 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −55080.0 | −1.85467 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2895.00 | −0.0971770 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 108.000 | 0.00361397 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19860.0 | 0.662504 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35804.0 | −1.19067 | −0.595336 | − | 0.803477i | \(-0.702981\pi\) | ||||
−0.595336 | + | 0.803477i | \(0.702981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1440.00 | −0.0477394 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4260.00 | −0.140793 | −0.0703964 | − | 0.997519i | \(-0.522426\pi\) | ||||
−0.0703964 | + | 0.997519i | \(0.522426\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45040.0 | −1.48398 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3471.00 | −0.114011 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28710.0 | −0.940137 | −0.470069 | − | 0.882630i | \(-0.655771\pi\) | ||||
−0.470069 | + | 0.882630i | \(0.655771\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5040.00 | 0.164534 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16506.0 | 0.537203 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49524.0 | 1.60689 | 0.803444 | − | 0.595381i | \(-0.202999\pi\) | ||||
0.803444 | + | 0.595381i | \(0.202999\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18756.0 | 0.606717 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12240.0 | 0.394735 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11808.0 | 0.379649 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44408.0 | −1.42348 | −0.711739 | − | 0.702444i | \(-0.752092\pi\) | ||||
−0.711739 | + | 0.702444i | \(0.752092\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27048.0 | 0.864393 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27984.0 | 0.891610 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18398.0 | −0.584424 | −0.292212 | − | 0.956354i | \(-0.594391\pi\) | ||||
−0.292212 | + | 0.956354i | \(0.594391\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2970.00 | 0.0940607 |
(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 | 2496.4.a.b.1.1 | 1 | ||
4.3 | odd | 2 | 2496.4.a.k.1.1 | 1 | |||
8.3 | odd | 2 | 78.4.a.e.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 624.4.a.i.1.1 | 1 | |||
24.5 | odd | 2 | 1872.4.a.e.1.1 | 1 | |||
24.11 | even | 2 | 234.4.a.b.1.1 | 1 | |||
40.19 | odd | 2 | 1950.4.a.c.1.1 | 1 | |||
104.51 | odd | 2 | 1014.4.a.b.1.1 | 1 | |||
104.83 | even | 4 | 1014.4.b.c.337.1 | 2 | |||
104.99 | even | 4 | 1014.4.b.c.337.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.4.a.e.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
234.4.a.b.1.1 | 1 | 24.11 | even | 2 | |||
624.4.a.i.1.1 | 1 | 8.5 | even | 2 | |||
1014.4.a.b.1.1 | 1 | 104.51 | odd | 2 | |||
1014.4.b.c.337.1 | 2 | 104.83 | even | 4 | |||
1014.4.b.c.337.2 | 2 | 104.99 | even | 4 | |||
1872.4.a.e.1.1 | 1 | 24.5 | odd | 2 | |||
1950.4.a.c.1.1 | 1 | 40.19 | odd | 2 | |||
2496.4.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2496.4.a.k.1.1 | 1 | 4.3 | odd | 2 |