Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,4,Mod(1,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1386.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.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: | \(81.7766472680\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 462) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1386.1 |
$q$-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 | ||||||||
\(5\) | −3.00000 | −0.268328 | −0.134164 | − | 0.990959i | \(-0.542835\pi\) | ||||
−0.134164 | + | 0.990959i | \(0.542835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.00000 | 0.189737 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 41.0000 | 0.874720 | 0.437360 | − | 0.899287i | \(-0.355914\pi\) | ||||
0.437360 | + | 0.899287i | \(0.355914\pi\) | |||||||
\(14\) | −14.0000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −6.00000 | −0.0856008 | −0.0428004 | − | 0.999084i | \(-0.513628\pi\) | ||||
−0.0428004 | + | 0.999084i | \(0.513628\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −43.0000 | −0.519204 | −0.259602 | − | 0.965716i | \(-0.583591\pi\) | ||||
−0.259602 | + | 0.965716i | \(0.583591\pi\) | |||||||
\(20\) | −12.0000 | −0.134164 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −22.0000 | −0.213201 | ||||||||
\(23\) | −120.000 | −1.08790 | −0.543951 | − | 0.839117i | \(-0.683072\pi\) | ||||
−0.543951 | + | 0.839117i | \(0.683072\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −116.000 | −0.928000 | ||||||||
\(26\) | −82.0000 | −0.618520 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | −111.000 | −0.710765 | −0.355382 | − | 0.934721i | \(-0.615649\pi\) | ||||
−0.355382 | + | 0.934721i | \(0.615649\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 266.000 | 1.54113 | 0.770565 | − | 0.637362i | \(-0.219974\pi\) | ||||
0.770565 | + | 0.637362i | \(0.219974\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.0000 | 0.0605289 | ||||||||
\(35\) | −21.0000 | −0.101419 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −79.0000 | −0.351014 | −0.175507 | − | 0.984478i | \(-0.556156\pi\) | ||||
−0.175507 | + | 0.984478i | \(0.556156\pi\) | |||||||
\(38\) | 86.0000 | 0.367133 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 24.0000 | 0.0948683 | ||||||||
\(41\) | −216.000 | −0.822769 | −0.411385 | − | 0.911462i | \(-0.634955\pi\) | ||||
−0.411385 | + | 0.911462i | \(0.634955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 284.000 | 1.00720 | 0.503600 | − | 0.863937i | \(-0.332009\pi\) | ||||
0.503600 | + | 0.863937i | \(0.332009\pi\) | |||||||
\(44\) | 44.0000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 240.000 | 0.769262 | ||||||||
\(47\) | −213.000 | −0.661048 | −0.330524 | − | 0.943798i | \(-0.607225\pi\) | ||||
−0.330524 | + | 0.943798i | \(0.607225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 232.000 | 0.656195 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 164.000 | 0.437360 | ||||||||
\(53\) | 216.000 | 0.559809 | 0.279905 | − | 0.960028i | \(-0.409697\pi\) | ||||
0.279905 | + | 0.960028i | \(0.409697\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −33.0000 | −0.0809040 | ||||||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 222.000 | 0.502587 | ||||||||
\(59\) | −393.000 | −0.867191 | −0.433595 | − | 0.901108i | \(-0.642755\pi\) | ||||
−0.433595 | + | 0.901108i | \(0.642755\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 350.000 | 0.734638 | 0.367319 | − | 0.930095i | \(-0.380276\pi\) | ||||
0.367319 | + | 0.930095i | \(0.380276\pi\) | |||||||
\(62\) | −532.000 | −1.08974 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −123.000 | −0.234712 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 821.000 | 1.49703 | 0.748516 | − | 0.663117i | \(-0.230767\pi\) | ||||
0.748516 | + | 0.663117i | \(0.230767\pi\) | |||||||
\(68\) | −24.0000 | −0.0428004 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 42.0000 | 0.0717137 | ||||||||
\(71\) | 264.000 | 0.441282 | 0.220641 | − | 0.975355i | \(-0.429185\pi\) | ||||
0.220641 | + | 0.975355i | \(0.429185\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −865.000 | −1.38686 | −0.693429 | − | 0.720525i | \(-0.743901\pi\) | ||||
−0.693429 | + | 0.720525i | \(0.743901\pi\) | |||||||
\(74\) | 158.000 | 0.248204 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −172.000 | −0.259602 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −484.000 | −0.689294 | −0.344647 | − | 0.938732i | \(-0.612001\pi\) | ||||
−0.344647 | + | 0.938732i | \(0.612001\pi\) | |||||||
\(80\) | −48.0000 | −0.0670820 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 432.000 | 0.581786 | ||||||||
\(83\) | −1158.00 | −1.53141 | −0.765705 | − | 0.643192i | \(-0.777610\pi\) | ||||
−0.765705 | + | 0.643192i | \(0.777610\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.0000 | 0.0229691 | ||||||||
\(86\) | −568.000 | −0.712198 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −88.0000 | −0.106600 | ||||||||
\(89\) | −330.000 | −0.393033 | −0.196516 | − | 0.980501i | \(-0.562963\pi\) | ||||
−0.196516 | + | 0.980501i | \(0.562963\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 287.000 | 0.330613 | ||||||||
\(92\) | −480.000 | −0.543951 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 426.000 | 0.467431 | ||||||||
\(95\) | 129.000 | 0.139317 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 980.000 | 1.02581 | 0.512907 | − | 0.858444i | \(-0.328569\pi\) | ||||
0.512907 | + | 0.858444i | \(0.328569\pi\) | |||||||
\(98\) | −98.0000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −464.000 | −0.464000 | ||||||||
\(101\) | −210.000 | −0.206889 | −0.103444 | − | 0.994635i | \(-0.532986\pi\) | ||||
−0.103444 | + | 0.994635i | \(0.532986\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1330.00 | −1.27232 | −0.636159 | − | 0.771558i | \(-0.719478\pi\) | ||||
−0.636159 | + | 0.771558i | \(0.719478\pi\) | |||||||
\(104\) | −328.000 | −0.309260 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −432.000 | −0.395845 | ||||||||
\(107\) | 1329.00 | 1.20074 | 0.600370 | − | 0.799722i | \(-0.295020\pi\) | ||||
0.600370 | + | 0.799722i | \(0.295020\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −94.0000 | −0.0826015 | −0.0413008 | − | 0.999147i | \(-0.513150\pi\) | ||||
−0.0413008 | + | 0.999147i | \(0.513150\pi\) | |||||||
\(110\) | 66.0000 | 0.0572078 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | −198.000 | −0.164834 | −0.0824171 | − | 0.996598i | \(-0.526264\pi\) | ||||
−0.0824171 | + | 0.996598i | \(0.526264\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 360.000 | 0.291915 | ||||||||
\(116\) | −444.000 | −0.355382 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 786.000 | 0.613196 | ||||||||
\(119\) | −42.0000 | −0.0323541 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −700.000 | −0.519467 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1064.00 | 0.770565 | ||||||||
\(125\) | 723.000 | 0.517337 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1066.00 | −0.744821 | −0.372410 | − | 0.928068i | \(-0.621469\pi\) | ||||
−0.372410 | + | 0.928068i | \(0.621469\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 246.000 | 0.165966 | ||||||||
\(131\) | 120.000 | 0.0800340 | 0.0400170 | − | 0.999199i | \(-0.487259\pi\) | ||||
0.0400170 | + | 0.999199i | \(0.487259\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −301.000 | −0.196241 | ||||||||
\(134\) | −1642.00 | −1.05856 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 48.0000 | 0.0302645 | ||||||||
\(137\) | 1938.00 | 1.20857 | 0.604287 | − | 0.796767i | \(-0.293458\pi\) | ||||
0.604287 | + | 0.796767i | \(0.293458\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1712.00 | 1.04468 | 0.522338 | − | 0.852739i | \(-0.325060\pi\) | ||||
0.522338 | + | 0.852739i | \(0.325060\pi\) | |||||||
\(140\) | −84.0000 | −0.0507093 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −528.000 | −0.312034 | ||||||||
\(143\) | 451.000 | 0.263738 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 333.000 | 0.190718 | ||||||||
\(146\) | 1730.00 | 0.980656 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −316.000 | −0.175507 | ||||||||
\(149\) | 1917.00 | 1.05401 | 0.527003 | − | 0.849864i | \(-0.323316\pi\) | ||||
0.527003 | + | 0.849864i | \(0.323316\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3022.00 | −1.62865 | −0.814327 | − | 0.580406i | \(-0.802894\pi\) | ||||
−0.814327 | + | 0.580406i | \(0.802894\pi\) | |||||||
\(152\) | 344.000 | 0.183566 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −154.000 | −0.0805823 | ||||||||
\(155\) | −798.000 | −0.413528 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2200.00 | −1.11834 | −0.559169 | − | 0.829054i | \(-0.688880\pi\) | ||||
−0.559169 | + | 0.829054i | \(0.688880\pi\) | |||||||
\(158\) | 968.000 | 0.487405 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 96.0000 | 0.0474342 | ||||||||
\(161\) | −840.000 | −0.411188 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3715.00 | −1.78516 | −0.892581 | − | 0.450888i | \(-0.851107\pi\) | ||||
−0.892581 | + | 0.450888i | \(0.851107\pi\) | |||||||
\(164\) | −864.000 | −0.411385 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2316.00 | 1.08287 | ||||||||
\(167\) | −84.0000 | −0.0389228 | −0.0194614 | − | 0.999811i | \(-0.506195\pi\) | ||||
−0.0194614 | + | 0.999811i | \(0.506195\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −516.000 | −0.234866 | ||||||||
\(170\) | −36.0000 | −0.0162416 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1136.00 | 0.503600 | ||||||||
\(173\) | −1812.00 | −0.796323 | −0.398161 | − | 0.917315i | \(-0.630352\pi\) | ||||
−0.398161 | + | 0.917315i | \(0.630352\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −812.000 | −0.350751 | ||||||||
\(176\) | 176.000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 660.000 | 0.277916 | ||||||||
\(179\) | −192.000 | −0.0801718 | −0.0400859 | − | 0.999196i | \(-0.512763\pi\) | ||||
−0.0400859 | + | 0.999196i | \(0.512763\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3148.00 | −1.29276 | −0.646378 | − | 0.763017i | \(-0.723717\pi\) | ||||
−0.646378 | + | 0.763017i | \(0.723717\pi\) | |||||||
\(182\) | −574.000 | −0.233779 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 960.000 | 0.384631 | ||||||||
\(185\) | 237.000 | 0.0941870 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −66.0000 | −0.0258096 | ||||||||
\(188\) | −852.000 | −0.330524 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −258.000 | −0.0985120 | ||||||||
\(191\) | −4554.00 | −1.72521 | −0.862607 | − | 0.505875i | \(-0.831170\pi\) | ||||
−0.862607 | + | 0.505875i | \(0.831170\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −940.000 | −0.350584 | −0.175292 | − | 0.984517i | \(-0.556087\pi\) | ||||
−0.175292 | + | 0.984517i | \(0.556087\pi\) | |||||||
\(194\) | −1960.00 | −0.725360 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 1122.00 | 0.405783 | 0.202891 | − | 0.979201i | \(-0.434966\pi\) | ||||
0.202891 | + | 0.979201i | \(0.434966\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3956.00 | 1.40921 | 0.704607 | − | 0.709598i | \(-0.251124\pi\) | ||||
0.704607 | + | 0.709598i | \(0.251124\pi\) | |||||||
\(200\) | 928.000 | 0.328098 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 420.000 | 0.146293 | ||||||||
\(203\) | −777.000 | −0.268644 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 648.000 | 0.220772 | ||||||||
\(206\) | 2660.00 | 0.899665 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 656.000 | 0.218680 | ||||||||
\(209\) | −473.000 | −0.156546 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 122.000 | 0.0398049 | 0.0199024 | − | 0.999802i | \(-0.493664\pi\) | ||||
0.0199024 | + | 0.999802i | \(0.493664\pi\) | |||||||
\(212\) | 864.000 | 0.279905 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2658.00 | −0.849052 | ||||||||
\(215\) | −852.000 | −0.270260 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1862.00 | 0.582492 | ||||||||
\(218\) | 188.000 | 0.0584081 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −132.000 | −0.0404520 | ||||||||
\(221\) | −246.000 | −0.0748767 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 602.000 | 0.180775 | 0.0903877 | − | 0.995907i | \(-0.471189\pi\) | ||||
0.0903877 | + | 0.995907i | \(0.471189\pi\) | |||||||
\(224\) | −224.000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 396.000 | 0.116555 | ||||||||
\(227\) | 426.000 | 0.124558 | 0.0622789 | − | 0.998059i | \(-0.480163\pi\) | ||||
0.0622789 | + | 0.998059i | \(0.480163\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4396.00 | −1.26854 | −0.634270 | − | 0.773111i | \(-0.718699\pi\) | ||||
−0.634270 | + | 0.773111i | \(0.718699\pi\) | |||||||
\(230\) | −720.000 | −0.206415 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 888.000 | 0.251293 | ||||||||
\(233\) | −3198.00 | −0.899176 | −0.449588 | − | 0.893236i | \(-0.648429\pi\) | ||||
−0.449588 | + | 0.893236i | \(0.648429\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 639.000 | 0.177378 | ||||||||
\(236\) | −1572.00 | −0.433595 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 84.0000 | 0.0228778 | ||||||||
\(239\) | −2997.00 | −0.811129 | −0.405564 | − | 0.914066i | \(-0.632925\pi\) | ||||
−0.405564 | + | 0.914066i | \(0.632925\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6235.00 | −1.66652 | −0.833261 | − | 0.552880i | \(-0.813529\pi\) | ||||
−0.833261 | + | 0.552880i | \(0.813529\pi\) | |||||||
\(242\) | −242.000 | −0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1400.00 | 0.367319 | ||||||||
\(245\) | −147.000 | −0.0383326 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1763.00 | −0.454158 | ||||||||
\(248\) | −2128.00 | −0.544872 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1446.00 | −0.365812 | ||||||||
\(251\) | −3735.00 | −0.939247 | −0.469624 | − | 0.882867i | \(-0.655610\pi\) | ||||
−0.469624 | + | 0.882867i | \(0.655610\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1320.00 | −0.328015 | ||||||||
\(254\) | 2132.00 | 0.526668 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −1515.00 | −0.367716 | −0.183858 | − | 0.982953i | \(-0.558859\pi\) | ||||
−0.183858 | + | 0.982953i | \(0.558859\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −553.000 | −0.132671 | ||||||||
\(260\) | −492.000 | −0.117356 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −240.000 | −0.0565926 | ||||||||
\(263\) | 4317.00 | 1.01216 | 0.506079 | − | 0.862487i | \(-0.331094\pi\) | ||||
0.506079 | + | 0.862487i | \(0.331094\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −648.000 | −0.150213 | ||||||||
\(266\) | 602.000 | 0.138763 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3284.00 | 0.748516 | ||||||||
\(269\) | 1434.00 | 0.325028 | 0.162514 | − | 0.986706i | \(-0.448040\pi\) | ||||
0.162514 | + | 0.986706i | \(0.448040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −943.000 | −0.211377 | −0.105689 | − | 0.994399i | \(-0.533705\pi\) | ||||
−0.105689 | + | 0.994399i | \(0.533705\pi\) | |||||||
\(272\) | −96.0000 | −0.0214002 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3876.00 | −0.854590 | ||||||||
\(275\) | −1276.00 | −0.279803 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5776.00 | −1.25287 | −0.626437 | − | 0.779472i | \(-0.715488\pi\) | ||||
−0.626437 | + | 0.779472i | \(0.715488\pi\) | |||||||
\(278\) | −3424.00 | −0.738697 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 168.000 | 0.0358569 | ||||||||
\(281\) | 1653.00 | 0.350924 | 0.175462 | − | 0.984486i | \(-0.443858\pi\) | ||||
0.175462 | + | 0.984486i | \(0.443858\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 677.000 | 0.142203 | 0.0711015 | − | 0.997469i | \(-0.477349\pi\) | ||||
0.0711015 | + | 0.997469i | \(0.477349\pi\) | |||||||
\(284\) | 1056.00 | 0.220641 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −902.000 | −0.186491 | ||||||||
\(287\) | −1512.00 | −0.310977 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4877.00 | −0.992673 | ||||||||
\(290\) | −666.000 | −0.134858 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3460.00 | −0.693429 | ||||||||
\(293\) | −4752.00 | −0.947491 | −0.473745 | − | 0.880662i | \(-0.657098\pi\) | ||||
−0.473745 | + | 0.880662i | \(0.657098\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1179.00 | 0.232692 | ||||||||
\(296\) | 632.000 | 0.124102 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3834.00 | −0.745294 | ||||||||
\(299\) | −4920.00 | −0.951609 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1988.00 | 0.380686 | ||||||||
\(302\) | 6044.00 | 1.15163 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −688.000 | −0.129801 | ||||||||
\(305\) | −1050.00 | −0.197124 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1676.00 | 0.311578 | 0.155789 | − | 0.987790i | \(-0.450208\pi\) | ||||
0.155789 | + | 0.987790i | \(0.450208\pi\) | |||||||
\(308\) | 308.000 | 0.0569803 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1596.00 | 0.292409 | ||||||||
\(311\) | 6288.00 | 1.14649 | 0.573247 | − | 0.819382i | \(-0.305683\pi\) | ||||
0.573247 | + | 0.819382i | \(0.305683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −430.000 | −0.0776519 | −0.0388259 | − | 0.999246i | \(-0.512362\pi\) | ||||
−0.0388259 | + | 0.999246i | \(0.512362\pi\) | |||||||
\(314\) | 4400.00 | 0.790785 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1936.00 | −0.344647 | ||||||||
\(317\) | −7176.00 | −1.27143 | −0.635717 | − | 0.771923i | \(-0.719295\pi\) | ||||
−0.635717 | + | 0.771923i | \(0.719295\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1221.00 | −0.214304 | ||||||||
\(320\) | −192.000 | −0.0335410 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1680.00 | 0.290754 | ||||||||
\(323\) | 258.000 | 0.0444443 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4756.00 | −0.811740 | ||||||||
\(326\) | 7430.00 | 1.26230 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1728.00 | 0.290893 | ||||||||
\(329\) | −1491.00 | −0.249853 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5360.00 | 0.890067 | 0.445034 | − | 0.895514i | \(-0.353192\pi\) | ||||
0.445034 | + | 0.895514i | \(0.353192\pi\) | |||||||
\(332\) | −4632.00 | −0.765705 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 168.000 | 0.0275226 | ||||||||
\(335\) | −2463.00 | −0.401696 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9376.00 | −1.51556 | −0.757779 | − | 0.652511i | \(-0.773716\pi\) | ||||
−0.757779 | + | 0.652511i | \(0.773716\pi\) | |||||||
\(338\) | 1032.00 | 0.166075 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 72.0000 | 0.0114846 | ||||||||
\(341\) | 2926.00 | 0.464668 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −2272.00 | −0.356099 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3624.00 | 0.563085 | ||||||||
\(347\) | −1608.00 | −0.248766 | −0.124383 | − | 0.992234i | \(-0.539695\pi\) | ||||
−0.124383 | + | 0.992234i | \(0.539695\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2477.00 | 0.379916 | 0.189958 | − | 0.981792i | \(-0.439165\pi\) | ||||
0.189958 | + | 0.981792i | \(0.439165\pi\) | |||||||
\(350\) | 1624.00 | 0.248018 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −352.000 | −0.0533002 | ||||||||
\(353\) | 975.000 | 0.147009 | 0.0735043 | − | 0.997295i | \(-0.476582\pi\) | ||||
0.0735043 | + | 0.997295i | \(0.476582\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −792.000 | −0.118408 | ||||||||
\(356\) | −1320.00 | −0.196516 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 384.000 | 0.0566900 | ||||||||
\(359\) | −4116.00 | −0.605109 | −0.302555 | − | 0.953132i | \(-0.597839\pi\) | ||||
−0.302555 | + | 0.953132i | \(0.597839\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5010.00 | −0.730427 | ||||||||
\(362\) | 6296.00 | 0.914117 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1148.00 | 0.165306 | ||||||||
\(365\) | 2595.00 | 0.372133 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2066.00 | 0.293854 | 0.146927 | − | 0.989147i | \(-0.453062\pi\) | ||||
0.146927 | + | 0.989147i | \(0.453062\pi\) | |||||||
\(368\) | −1920.00 | −0.271975 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −474.000 | −0.0666002 | ||||||||
\(371\) | 1512.00 | 0.211588 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1778.00 | 0.246813 | 0.123407 | − | 0.992356i | \(-0.460618\pi\) | ||||
0.123407 | + | 0.992356i | \(0.460618\pi\) | |||||||
\(374\) | 132.000 | 0.0182502 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1704.00 | 0.233716 | ||||||||
\(377\) | −4551.00 | −0.621720 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10717.0 | −1.45249 | −0.726247 | − | 0.687434i | \(-0.758737\pi\) | ||||
−0.726247 | + | 0.687434i | \(0.758737\pi\) | |||||||
\(380\) | 516.000 | 0.0696585 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9108.00 | 1.21991 | ||||||||
\(383\) | −9360.00 | −1.24876 | −0.624378 | − | 0.781122i | \(-0.714648\pi\) | ||||
−0.624378 | + | 0.781122i | \(0.714648\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −231.000 | −0.0305788 | ||||||||
\(386\) | 1880.00 | 0.247900 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3920.00 | 0.512907 | ||||||||
\(389\) | −8364.00 | −1.09016 | −0.545079 | − | 0.838385i | \(-0.683500\pi\) | ||||
−0.545079 | + | 0.838385i | \(0.683500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 720.000 | 0.0931252 | ||||||||
\(392\) | −392.000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2244.00 | −0.286932 | ||||||||
\(395\) | 1452.00 | 0.184957 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −646.000 | −0.0816670 | −0.0408335 | − | 0.999166i | \(-0.513001\pi\) | ||||
−0.0408335 | + | 0.999166i | \(0.513001\pi\) | |||||||
\(398\) | −7912.00 | −0.996464 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1856.00 | −0.232000 | ||||||||
\(401\) | −2808.00 | −0.349688 | −0.174844 | − | 0.984596i | \(-0.555942\pi\) | ||||
−0.174844 | + | 0.984596i | \(0.555942\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10906.0 | 1.34806 | ||||||||
\(404\) | −840.000 | −0.103444 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1554.00 | 0.189960 | ||||||||
\(407\) | −869.000 | −0.105835 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8750.00 | 1.05785 | 0.528924 | − | 0.848669i | \(-0.322596\pi\) | ||||
0.528924 | + | 0.848669i | \(0.322596\pi\) | |||||||
\(410\) | −1296.00 | −0.156109 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5320.00 | −0.636159 | ||||||||
\(413\) | −2751.00 | −0.327767 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3474.00 | 0.410920 | ||||||||
\(416\) | −1312.00 | −0.154630 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 946.000 | 0.110695 | ||||||||
\(419\) | −13263.0 | −1.54640 | −0.773198 | − | 0.634165i | \(-0.781344\pi\) | ||||
−0.773198 | + | 0.634165i | \(0.781344\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5785.00 | −0.669700 | −0.334850 | − | 0.942271i | \(-0.608686\pi\) | ||||
−0.334850 | + | 0.942271i | \(0.608686\pi\) | |||||||
\(422\) | −244.000 | −0.0281463 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1728.00 | −0.197922 | ||||||||
\(425\) | 696.000 | 0.0794376 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2450.00 | 0.277667 | ||||||||
\(428\) | 5316.00 | 0.600370 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1704.00 | 0.191103 | ||||||||
\(431\) | −5019.00 | −0.560920 | −0.280460 | − | 0.959866i | \(-0.590487\pi\) | ||||
−0.280460 | + | 0.959866i | \(0.590487\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14768.0 | 1.63904 | 0.819521 | − | 0.573050i | \(-0.194240\pi\) | ||||
0.819521 | + | 0.573050i | \(0.194240\pi\) | |||||||
\(434\) | −3724.00 | −0.411884 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −376.000 | −0.0413008 | ||||||||
\(437\) | 5160.00 | 0.564843 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2311.00 | −0.251248 | −0.125624 | − | 0.992078i | \(-0.540093\pi\) | ||||
−0.125624 | + | 0.992078i | \(0.540093\pi\) | |||||||
\(440\) | 264.000 | 0.0286039 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 492.000 | 0.0529458 | ||||||||
\(443\) | 252.000 | 0.0270268 | 0.0135134 | − | 0.999909i | \(-0.495698\pi\) | ||||
0.0135134 | + | 0.999909i | \(0.495698\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 990.000 | 0.105462 | ||||||||
\(446\) | −1204.00 | −0.127827 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | −1980.00 | −0.208111 | −0.104056 | − | 0.994571i | \(-0.533182\pi\) | ||||
−0.104056 | + | 0.994571i | \(0.533182\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2376.00 | −0.248074 | ||||||||
\(452\) | −792.000 | −0.0824171 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −852.000 | −0.0880756 | ||||||||
\(455\) | −861.000 | −0.0887128 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12164.0 | 1.24509 | 0.622547 | − | 0.782582i | \(-0.286098\pi\) | ||||
0.622547 | + | 0.782582i | \(0.286098\pi\) | |||||||
\(458\) | 8792.00 | 0.896994 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1440.00 | 0.145957 | ||||||||
\(461\) | 18732.0 | 1.89249 | 0.946243 | − | 0.323456i | \(-0.104845\pi\) | ||||
0.946243 | + | 0.323456i | \(0.104845\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13051.0 | −1.31000 | −0.655002 | − | 0.755628i | \(-0.727332\pi\) | ||||
−0.655002 | + | 0.755628i | \(0.727332\pi\) | |||||||
\(464\) | −1776.00 | −0.177691 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6396.00 | 0.635813 | ||||||||
\(467\) | −6717.00 | −0.665580 | −0.332790 | − | 0.943001i | \(-0.607990\pi\) | ||||
−0.332790 | + | 0.943001i | \(0.607990\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5747.00 | 0.565825 | ||||||||
\(470\) | −1278.00 | −0.125425 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3144.00 | 0.306598 | ||||||||
\(473\) | 3124.00 | 0.303682 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4988.00 | 0.481821 | ||||||||
\(476\) | −168.000 | −0.0161770 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5994.00 | 0.573555 | ||||||||
\(479\) | 18438.0 | 1.75878 | 0.879388 | − | 0.476106i | \(-0.157952\pi\) | ||||
0.879388 | + | 0.476106i | \(0.157952\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3239.00 | −0.307039 | ||||||||
\(482\) | 12470.0 | 1.17841 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 484.000 | 0.0454545 | ||||||||
\(485\) | −2940.00 | −0.275255 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10648.0 | −0.990774 | −0.495387 | − | 0.868672i | \(-0.664974\pi\) | ||||
−0.495387 | + | 0.868672i | \(0.664974\pi\) | |||||||
\(488\) | −2800.00 | −0.259734 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 294.000 | 0.0271052 | ||||||||
\(491\) | −16863.0 | −1.54993 | −0.774966 | − | 0.632003i | \(-0.782233\pi\) | ||||
−0.774966 | + | 0.632003i | \(0.782233\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 666.000 | 0.0608421 | ||||||||
\(494\) | 3526.00 | 0.321138 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4256.00 | 0.385282 | ||||||||
\(497\) | 1848.00 | 0.166789 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12683.0 | 1.13781 | 0.568907 | − | 0.822402i | \(-0.307366\pi\) | ||||
0.568907 | + | 0.822402i | \(0.307366\pi\) | |||||||
\(500\) | 2892.00 | 0.258668 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7470.00 | 0.664148 | ||||||||
\(503\) | −14472.0 | −1.28285 | −0.641426 | − | 0.767185i | \(-0.721657\pi\) | ||||
−0.641426 | + | 0.767185i | \(0.721657\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 630.000 | 0.0555141 | ||||||||
\(506\) | 2640.00 | 0.231941 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4264.00 | −0.372410 | ||||||||
\(509\) | 10722.0 | 0.933682 | 0.466841 | − | 0.884341i | \(-0.345392\pi\) | ||||
0.466841 | + | 0.884341i | \(0.345392\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6055.00 | −0.524183 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3030.00 | 0.260015 | ||||||||
\(515\) | 3990.00 | 0.341399 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2343.00 | −0.199313 | ||||||||
\(518\) | 1106.00 | 0.0938125 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 984.000 | 0.0829832 | ||||||||
\(521\) | 10341.0 | 0.869573 | 0.434786 | − | 0.900534i | \(-0.356824\pi\) | ||||
0.434786 | + | 0.900534i | \(0.356824\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5819.00 | 0.486515 | 0.243257 | − | 0.969962i | \(-0.421784\pi\) | ||||
0.243257 | + | 0.969962i | \(0.421784\pi\) | |||||||
\(524\) | 480.000 | 0.0400170 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8634.00 | −0.715704 | ||||||||
\(527\) | −1596.00 | −0.131922 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2233.00 | 0.183529 | ||||||||
\(530\) | 1296.00 | 0.106216 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1204.00 | −0.0981203 | ||||||||
\(533\) | −8856.00 | −0.719692 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3987.00 | −0.322193 | ||||||||
\(536\) | −6568.00 | −0.529281 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2868.00 | −0.229829 | ||||||||
\(539\) | 539.000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9668.00 | 0.768318 | 0.384159 | − | 0.923267i | \(-0.374492\pi\) | ||||
0.384159 | + | 0.923267i | \(0.374492\pi\) | |||||||
\(542\) | 1886.00 | 0.149466 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 192.000 | 0.0151322 | ||||||||
\(545\) | 282.000 | 0.0221643 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13160.0 | 1.02867 | 0.514334 | − | 0.857590i | \(-0.328039\pi\) | ||||
0.514334 | + | 0.857590i | \(0.328039\pi\) | |||||||
\(548\) | 7752.00 | 0.604287 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2552.00 | 0.197850 | ||||||||
\(551\) | 4773.00 | 0.369032 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3388.00 | −0.260529 | ||||||||
\(554\) | 11552.0 | 0.885916 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6848.00 | 0.522338 | ||||||||
\(557\) | 2253.00 | 0.171387 | 0.0856936 | − | 0.996322i | \(-0.472689\pi\) | ||||
0.0856936 | + | 0.996322i | \(0.472689\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11644.0 | 0.881017 | ||||||||
\(560\) | −336.000 | −0.0253546 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3306.00 | −0.248141 | ||||||||
\(563\) | 984.000 | 0.0736601 | 0.0368301 | − | 0.999322i | \(-0.488274\pi\) | ||||
0.0368301 | + | 0.999322i | \(0.488274\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 594.000 | 0.0442297 | ||||||||
\(566\) | −1354.00 | −0.100553 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2112.00 | −0.156017 | ||||||||
\(569\) | 16878.0 | 1.24352 | 0.621760 | − | 0.783208i | \(-0.286418\pi\) | ||||
0.621760 | + | 0.783208i | \(0.286418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4736.00 | 0.347102 | 0.173551 | − | 0.984825i | \(-0.444476\pi\) | ||||
0.173551 | + | 0.984825i | \(0.444476\pi\) | |||||||
\(572\) | 1804.00 | 0.131869 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3024.00 | 0.219894 | ||||||||
\(575\) | 13920.0 | 1.00957 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3694.00 | −0.266522 | −0.133261 | − | 0.991081i | \(-0.542545\pi\) | ||||
−0.133261 | + | 0.991081i | \(0.542545\pi\) | |||||||
\(578\) | 9754.00 | 0.701925 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1332.00 | 0.0953591 | ||||||||
\(581\) | −8106.00 | −0.578818 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2376.00 | 0.168789 | ||||||||
\(584\) | 6920.00 | 0.490328 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9504.00 | 0.669977 | ||||||||
\(587\) | 21237.0 | 1.49326 | 0.746631 | − | 0.665238i | \(-0.231670\pi\) | ||||
0.746631 | + | 0.665238i | \(0.231670\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11438.0 | −0.800161 | ||||||||
\(590\) | −2358.00 | −0.164538 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1264.00 | −0.0877535 | ||||||||
\(593\) | 7416.00 | 0.513556 | 0.256778 | − | 0.966470i | \(-0.417339\pi\) | ||||
0.256778 | + | 0.966470i | \(0.417339\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 126.000 | 0.00868151 | ||||||||
\(596\) | 7668.00 | 0.527003 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9840.00 | 0.672889 | ||||||||
\(599\) | 5484.00 | 0.374074 | 0.187037 | − | 0.982353i | \(-0.440112\pi\) | ||||
0.187037 | + | 0.982353i | \(0.440112\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11077.0 | −0.751814 | −0.375907 | − | 0.926657i | \(-0.622669\pi\) | ||||
−0.375907 | + | 0.926657i | \(0.622669\pi\) | |||||||
\(602\) | −3976.00 | −0.269185 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12088.0 | −0.814327 | ||||||||
\(605\) | −363.000 | −0.0243935 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5047.00 | −0.337482 | −0.168741 | − | 0.985660i | \(-0.553970\pi\) | ||||
−0.168741 | + | 0.985660i | \(0.553970\pi\) | |||||||
\(608\) | 1376.00 | 0.0917832 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2100.00 | 0.139388 | ||||||||
\(611\) | −8733.00 | −0.578231 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20066.0 | 1.32212 | 0.661059 | − | 0.750334i | \(-0.270107\pi\) | ||||
0.661059 | + | 0.750334i | \(0.270107\pi\) | |||||||
\(614\) | −3352.00 | −0.220319 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −616.000 | −0.0402911 | ||||||||
\(617\) | 16626.0 | 1.08483 | 0.542413 | − | 0.840112i | \(-0.317511\pi\) | ||||
0.542413 | + | 0.840112i | \(0.317511\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10162.0 | −0.659847 | −0.329923 | − | 0.944008i | \(-0.607023\pi\) | ||||
−0.329923 | + | 0.944008i | \(0.607023\pi\) | |||||||
\(620\) | −3192.00 | −0.206764 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12576.0 | −0.810694 | ||||||||
\(623\) | −2310.00 | −0.148552 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12331.0 | 0.789184 | ||||||||
\(626\) | 860.000 | 0.0549082 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8800.00 | −0.559169 | ||||||||
\(629\) | 474.000 | 0.0300471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16108.0 | −1.01624 | −0.508122 | − | 0.861285i | \(-0.669660\pi\) | ||||
−0.508122 | + | 0.861285i | \(0.669660\pi\) | |||||||
\(632\) | 3872.00 | 0.243702 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14352.0 | 0.899039 | ||||||||
\(635\) | 3198.00 | 0.199856 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2009.00 | 0.124960 | ||||||||
\(638\) | 2442.00 | 0.151536 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 384.000 | 0.0237171 | ||||||||
\(641\) | 19950.0 | 1.22929 | 0.614647 | − | 0.788802i | \(-0.289298\pi\) | ||||
0.614647 | + | 0.788802i | \(0.289298\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8260.00 | −0.506598 | −0.253299 | − | 0.967388i | \(-0.581516\pi\) | ||||
−0.253299 | + | 0.967388i | \(0.581516\pi\) | |||||||
\(644\) | −3360.00 | −0.205594 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −516.000 | −0.0314269 | ||||||||
\(647\) | 28833.0 | 1.75200 | 0.875999 | − | 0.482314i | \(-0.160203\pi\) | ||||
0.875999 | + | 0.482314i | \(0.160203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4323.00 | −0.261468 | ||||||||
\(650\) | 9512.00 | 0.573987 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14860.0 | −0.892581 | ||||||||
\(653\) | 13152.0 | 0.788174 | 0.394087 | − | 0.919073i | \(-0.371061\pi\) | ||||
0.394087 | + | 0.919073i | \(0.371061\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −360.000 | −0.0214754 | ||||||||
\(656\) | −3456.00 | −0.205692 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2982.00 | 0.176672 | ||||||||
\(659\) | 32229.0 | 1.90510 | 0.952552 | − | 0.304376i | \(-0.0984478\pi\) | ||||
0.952552 | + | 0.304376i | \(0.0984478\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −460.000 | −0.0270680 | −0.0135340 | − | 0.999908i | \(-0.504308\pi\) | ||||
−0.0135340 | + | 0.999908i | \(0.504308\pi\) | |||||||
\(662\) | −10720.0 | −0.629373 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9264.00 | 0.541435 | ||||||||
\(665\) | 903.000 | 0.0526569 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13320.0 | 0.773242 | ||||||||
\(668\) | −336.000 | −0.0194614 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4926.00 | 0.284042 | ||||||||
\(671\) | 3850.00 | 0.221502 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12784.0 | −0.732224 | −0.366112 | − | 0.930571i | \(-0.619311\pi\) | ||||
−0.366112 | + | 0.930571i | \(0.619311\pi\) | |||||||
\(674\) | 18752.0 | 1.07166 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2064.00 | −0.117433 | ||||||||
\(677\) | −2190.00 | −0.124326 | −0.0621629 | − | 0.998066i | \(-0.519800\pi\) | ||||
−0.0621629 | + | 0.998066i | \(0.519800\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6860.00 | 0.387721 | ||||||||
\(680\) | −144.000 | −0.00812081 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5852.00 | −0.328570 | ||||||||
\(683\) | −11514.0 | −0.645053 | −0.322526 | − | 0.946560i | \(-0.604532\pi\) | ||||
−0.322526 | + | 0.946560i | \(0.604532\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5814.00 | −0.324294 | ||||||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4544.00 | 0.251800 | ||||||||
\(689\) | 8856.00 | 0.489676 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11554.0 | −0.636085 | −0.318043 | − | 0.948076i | \(-0.603026\pi\) | ||||
−0.318043 | + | 0.948076i | \(0.603026\pi\) | |||||||
\(692\) | −7248.00 | −0.398161 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3216.00 | 0.175904 | ||||||||
\(695\) | −5136.00 | −0.280316 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1296.00 | 0.0704297 | ||||||||
\(698\) | −4954.00 | −0.268641 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3248.00 | −0.175376 | ||||||||
\(701\) | 18450.0 | 0.994075 | 0.497038 | − | 0.867729i | \(-0.334421\pi\) | ||||
0.497038 | + | 0.867729i | \(0.334421\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3397.00 | 0.182248 | ||||||||
\(704\) | 704.000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1950.00 | −0.103951 | ||||||||
\(707\) | −1470.00 | −0.0781967 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15203.0 | 0.805304 | 0.402652 | − | 0.915353i | \(-0.368088\pi\) | ||||
0.402652 | + | 0.915353i | \(0.368088\pi\) | |||||||
\(710\) | 1584.00 | 0.0837274 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2640.00 | 0.138958 | ||||||||
\(713\) | −31920.0 | −1.67660 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1353.00 | −0.0707683 | ||||||||
\(716\) | −768.000 | −0.0400859 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8232.00 | 0.427877 | ||||||||
\(719\) | −28515.0 | −1.47904 | −0.739520 | − | 0.673134i | \(-0.764948\pi\) | ||||
−0.739520 | + | 0.673134i | \(0.764948\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9310.00 | −0.480891 | ||||||||
\(722\) | 10020.0 | 0.516490 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12592.0 | −0.646378 | ||||||||
\(725\) | 12876.0 | 0.659590 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15932.0 | 0.812772 | 0.406386 | − | 0.913702i | \(-0.366789\pi\) | ||||
0.406386 | + | 0.913702i | \(0.366789\pi\) | |||||||
\(728\) | −2296.00 | −0.116889 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5190.00 | −0.263138 | ||||||||
\(731\) | −1704.00 | −0.0862171 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26630.0 | 1.34188 | 0.670942 | − | 0.741510i | \(-0.265890\pi\) | ||||
0.670942 | + | 0.741510i | \(0.265890\pi\) | |||||||
\(734\) | −4132.00 | −0.207786 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3840.00 | 0.192316 | ||||||||
\(737\) | 9031.00 | 0.451372 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3940.00 | −0.196123 | −0.0980617 | − | 0.995180i | \(-0.531264\pi\) | ||||
−0.0980617 | + | 0.995180i | \(0.531264\pi\) | |||||||
\(740\) | 948.000 | 0.0470935 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3024.00 | −0.149615 | ||||||||
\(743\) | −25203.0 | −1.24443 | −0.622213 | − | 0.782848i | \(-0.713766\pi\) | ||||
−0.622213 | + | 0.782848i | \(0.713766\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5751.00 | −0.282819 | ||||||||
\(746\) | −3556.00 | −0.174523 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −264.000 | −0.0129048 | ||||||||
\(749\) | 9303.00 | 0.453837 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17611.0 | −0.855705 | −0.427853 | − | 0.903849i | \(-0.640730\pi\) | ||||
−0.427853 | + | 0.903849i | \(0.640730\pi\) | |||||||
\(752\) | −3408.00 | −0.165262 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9102.00 | 0.439622 | ||||||||
\(755\) | 9066.00 | 0.437014 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28543.0 | −1.37043 | −0.685213 | − | 0.728342i | \(-0.740291\pi\) | ||||
−0.685213 | + | 0.728342i | \(0.740291\pi\) | |||||||
\(758\) | 21434.0 | 1.02707 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1032.00 | −0.0492560 | ||||||||
\(761\) | 16884.0 | 0.804263 | 0.402132 | − | 0.915582i | \(-0.368269\pi\) | ||||
0.402132 | + | 0.915582i | \(0.368269\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −658.000 | −0.0312204 | ||||||||
\(764\) | −18216.0 | −0.862607 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18720.0 | 0.883004 | ||||||||
\(767\) | −16113.0 | −0.758549 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22963.0 | −1.07681 | −0.538405 | − | 0.842686i | \(-0.680973\pi\) | ||||
−0.538405 | + | 0.842686i | \(0.680973\pi\) | |||||||
\(770\) | 462.000 | 0.0216225 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3760.00 | −0.175292 | ||||||||
\(773\) | 32601.0 | 1.51692 | 0.758458 | − | 0.651722i | \(-0.225953\pi\) | ||||
0.758458 | + | 0.651722i | \(0.225953\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30856.0 | −1.43017 | ||||||||
\(776\) | −7840.00 | −0.362680 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16728.0 | 0.770858 | ||||||||
\(779\) | 9288.00 | 0.427185 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2904.00 | 0.133052 | ||||||||
\(782\) | −1440.00 | −0.0658495 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 6600.00 | 0.300082 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17867.0 | 0.809263 | 0.404631 | − | 0.914480i | \(-0.367400\pi\) | ||||
0.404631 | + | 0.914480i | \(0.367400\pi\) | |||||||
\(788\) | 4488.00 | 0.202891 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2904.00 | −0.130784 | ||||||||
\(791\) | −1386.00 | −0.0623015 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14350.0 | 0.642602 | ||||||||
\(794\) | 1292.00 | 0.0577473 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15824.0 | 0.704607 | ||||||||
\(797\) | −17505.0 | −0.777991 | −0.388996 | − | 0.921240i | \(-0.627178\pi\) | ||||
−0.388996 | + | 0.921240i | \(0.627178\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1278.00 | 0.0565862 | ||||||||
\(800\) | 3712.00 | 0.164049 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5616.00 | 0.247267 | ||||||||
\(803\) | −9515.00 | −0.418153 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2520.00 | 0.110333 | ||||||||
\(806\) | −21812.0 | −0.953220 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1680.00 | 0.0731463 | ||||||||
\(809\) | −11079.0 | −0.481479 | −0.240740 | − | 0.970590i | \(-0.577390\pi\) | ||||
−0.240740 | + | 0.970590i | \(0.577390\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28021.0 | −1.21326 | −0.606628 | − | 0.794986i | \(-0.707478\pi\) | ||||
−0.606628 | + | 0.794986i | \(0.707478\pi\) | |||||||
\(812\) | −3108.00 | −0.134322 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1738.00 | 0.0748364 | ||||||||
\(815\) | 11145.0 | 0.479009 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12212.0 | −0.522942 | ||||||||
\(818\) | −17500.0 | −0.748011 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2592.00 | 0.110386 | ||||||||
\(821\) | −12309.0 | −0.523249 | −0.261624 | − | 0.965170i | \(-0.584258\pi\) | ||||
−0.261624 | + | 0.965170i | \(0.584258\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3893.00 | 0.164886 | 0.0824432 | − | 0.996596i | \(-0.473728\pi\) | ||||
0.0824432 | + | 0.996596i | \(0.473728\pi\) | |||||||
\(824\) | 10640.0 | 0.449832 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5502.00 | 0.231766 | ||||||||
\(827\) | −45063.0 | −1.89479 | −0.947397 | − | 0.320062i | \(-0.896296\pi\) | ||||
−0.947397 | + | 0.320062i | \(0.896296\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15136.0 | −0.634131 | −0.317066 | − | 0.948404i | \(-0.602698\pi\) | ||||
−0.317066 | + | 0.948404i | \(0.602698\pi\) | |||||||
\(830\) | −6948.00 | −0.290565 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2624.00 | 0.109340 | ||||||||
\(833\) | −294.000 | −0.0122287 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 252.000 | 0.0104441 | ||||||||
\(836\) | −1892.00 | −0.0782730 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26526.0 | 1.09347 | ||||||||
\(839\) | 20739.0 | 0.853385 | 0.426692 | − | 0.904397i | \(-0.359679\pi\) | ||||
0.426692 | + | 0.904397i | \(0.359679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12068.0 | −0.494813 | ||||||||
\(842\) | 11570.0 | 0.473549 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 488.000 | 0.0199024 | ||||||||
\(845\) | 1548.00 | 0.0630211 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 847.000 | 0.0343604 | ||||||||
\(848\) | 3456.00 | 0.139952 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1392.00 | −0.0561708 | ||||||||
\(851\) | 9480.00 | 0.381869 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37610.0 | 1.50966 | 0.754831 | − | 0.655919i | \(-0.227719\pi\) | ||||
0.754831 | + | 0.655919i | \(0.227719\pi\) | |||||||
\(854\) | −4900.00 | −0.196340 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10632.0 | −0.424526 | ||||||||
\(857\) | 37470.0 | 1.49352 | 0.746762 | − | 0.665091i | \(-0.231607\pi\) | ||||
0.746762 | + | 0.665091i | \(0.231607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15604.0 | −0.619792 | −0.309896 | − | 0.950770i | \(-0.600294\pi\) | ||||
−0.309896 | + | 0.950770i | \(0.600294\pi\) | |||||||
\(860\) | −3408.00 | −0.135130 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10038.0 | 0.396631 | ||||||||
\(863\) | −20004.0 | −0.789043 | −0.394521 | − | 0.918887i | \(-0.629090\pi\) | ||||
−0.394521 | + | 0.918887i | \(0.629090\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5436.00 | 0.213676 | ||||||||
\(866\) | −29536.0 | −1.15898 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7448.00 | 0.291246 | ||||||||
\(869\) | −5324.00 | −0.207830 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33661.0 | 1.30948 | ||||||||
\(872\) | 752.000 | 0.0292041 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10320.0 | −0.399404 | ||||||||
\(875\) | 5061.00 | 0.195535 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1064.00 | 0.0409678 | 0.0204839 | − | 0.999790i | \(-0.493479\pi\) | ||||
0.0204839 | + | 0.999790i | \(0.493479\pi\) | |||||||
\(878\) | 4622.00 | 0.177659 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −528.000 | −0.0202260 | ||||||||
\(881\) | −4179.00 | −0.159812 | −0.0799058 | − | 0.996802i | \(-0.525462\pi\) | ||||
−0.0799058 | + | 0.996802i | \(0.525462\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44509.0 | −1.69632 | −0.848158 | − | 0.529743i | \(-0.822288\pi\) | ||||
−0.848158 | + | 0.529743i | \(0.822288\pi\) | |||||||
\(884\) | −984.000 | −0.0374384 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −504.000 | −0.0191108 | ||||||||
\(887\) | −12642.0 | −0.478553 | −0.239277 | − | 0.970951i | \(-0.576910\pi\) | ||||
−0.239277 | + | 0.970951i | \(0.576910\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7462.00 | −0.281516 | ||||||||
\(890\) | −1980.00 | −0.0745728 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2408.00 | 0.0903877 | ||||||||
\(893\) | 9159.00 | 0.343219 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 576.000 | 0.0215124 | ||||||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3960.00 | 0.147157 | ||||||||
\(899\) | −29526.0 | −1.09538 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1296.00 | −0.0479201 | ||||||||
\(902\) | 4752.00 | 0.175415 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1584.00 | 0.0582777 | ||||||||
\(905\) | 9444.00 | 0.346883 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.0000 | −0.00102505 | −0.000512527 | − | 1.00000i | \(-0.500163\pi\) | ||||
−0.000512527 | 1.00000i | \(0.500163\pi\) | ||||||||
\(908\) | 1704.00 | 0.0622789 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1722.00 | 0.0627294 | ||||||||
\(911\) | 9774.00 | 0.355463 | 0.177732 | − | 0.984079i | \(-0.443124\pi\) | ||||
0.177732 | + | 0.984079i | \(0.443124\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12738.0 | −0.461737 | ||||||||
\(914\) | −24328.0 | −0.880414 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17584.0 | −0.634270 | ||||||||
\(917\) | 840.000 | 0.0302500 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23204.0 | 0.832894 | 0.416447 | − | 0.909160i | \(-0.363275\pi\) | ||||
0.416447 | + | 0.909160i | \(0.363275\pi\) | |||||||
\(920\) | −2880.00 | −0.103207 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −37464.0 | −1.33819 | ||||||||
\(923\) | 10824.0 | 0.385998 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9164.00 | 0.325741 | ||||||||
\(926\) | 26102.0 | 0.926312 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3552.00 | 0.125647 | ||||||||
\(929\) | −3633.00 | −0.128304 | −0.0641522 | − | 0.997940i | \(-0.520434\pi\) | ||||
−0.0641522 | + | 0.997940i | \(0.520434\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2107.00 | −0.0741720 | ||||||||
\(932\) | −12792.0 | −0.449588 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13434.0 | 0.470636 | ||||||||
\(935\) | 198.000 | 0.00692545 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18938.0 | 0.660275 | 0.330137 | − | 0.943933i | \(-0.392905\pi\) | ||||
0.330137 | + | 0.943933i | \(0.392905\pi\) | |||||||
\(938\) | −11494.0 | −0.400099 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2556.00 | 0.0886889 | ||||||||
\(941\) | −14784.0 | −0.512162 | −0.256081 | − | 0.966655i | \(-0.582431\pi\) | ||||
−0.256081 | + | 0.966655i | \(0.582431\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25920.0 | 0.895092 | ||||||||
\(944\) | −6288.00 | −0.216798 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6248.00 | −0.214736 | ||||||||
\(947\) | 31266.0 | 1.07287 | 0.536435 | − | 0.843941i | \(-0.319771\pi\) | ||||
0.536435 | + | 0.843941i | \(0.319771\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35465.0 | −1.21311 | ||||||||
\(950\) | −9976.00 | −0.340699 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 336.000 | 0.0114389 | ||||||||
\(953\) | −33951.0 | −1.15402 | −0.577010 | − | 0.816737i | \(-0.695781\pi\) | ||||
−0.577010 | + | 0.816737i | \(0.695781\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13662.0 | 0.462923 | ||||||||
\(956\) | −11988.0 | −0.405564 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −36876.0 | −1.24364 | ||||||||
\(959\) | 13566.0 | 0.456798 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40965.0 | 1.37508 | ||||||||
\(962\) | 6478.00 | 0.217109 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −24940.0 | −0.833261 | ||||||||
\(965\) | 2820.00 | 0.0940715 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16322.0 | 0.542792 | 0.271396 | − | 0.962468i | \(-0.412515\pi\) | ||||
0.271396 | + | 0.962468i | \(0.412515\pi\) | |||||||
\(968\) | −968.000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5880.00 | 0.194634 | ||||||||
\(971\) | −40779.0 | −1.34774 | −0.673872 | − | 0.738848i | \(-0.735370\pi\) | ||||
−0.673872 | + | 0.738848i | \(0.735370\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11984.0 | 0.394850 | ||||||||
\(974\) | 21296.0 | 0.700583 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5600.00 | 0.183659 | ||||||||
\(977\) | −21804.0 | −0.713994 | −0.356997 | − | 0.934106i | \(-0.616199\pi\) | ||||
−0.356997 | + | 0.934106i | \(0.616199\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3630.00 | −0.118504 | ||||||||
\(980\) | −588.000 | −0.0191663 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 33726.0 | 1.09597 | ||||||||
\(983\) | 35424.0 | 1.14939 | 0.574695 | − | 0.818368i | \(-0.305121\pi\) | ||||
0.574695 | + | 0.818368i | \(0.305121\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3366.00 | −0.108883 | ||||||||
\(986\) | −1332.00 | −0.0430218 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7052.00 | −0.227079 | ||||||||
\(989\) | −34080.0 | −1.09573 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37315.0 | −1.19612 | −0.598058 | − | 0.801453i | \(-0.704061\pi\) | ||||
−0.598058 | + | 0.801453i | \(0.704061\pi\) | |||||||
\(992\) | −8512.00 | −0.272436 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3696.00 | −0.117938 | ||||||||
\(995\) | −11868.0 | −0.378132 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30674.0 | 0.974378 | 0.487189 | − | 0.873296i | \(-0.338022\pi\) | ||||
0.487189 | + | 0.873296i | \(0.338022\pi\) | |||||||
\(998\) | −25366.0 | −0.804556 | ||||||||
\(999\) | 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 | 1386.4.a.c.1.1 | 1 | ||
3.2 | odd | 2 | 462.4.a.g.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.4.a.g.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
1386.4.a.c.1.1 | 1 | 1.1 | even | 1 | trivial |