Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2156,4,Mod(1,2156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2156, 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("2156.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2156.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: | \(127.208117972\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 308) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2156.1 |
$q$-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 | ||||||||
\(3\) | −4.00000 | −0.769800 | −0.384900 | − | 0.922958i | \(-0.625764\pi\) | ||||
−0.384900 | + | 0.922958i | \(0.625764\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 12.0000 | 1.07331 | 0.536656 | − | 0.843801i | \(-0.319687\pi\) | ||||
0.536656 | + | 0.843801i | \(0.319687\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −11.0000 | −0.407407 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.0000 | 0.213346 | 0.106673 | − | 0.994294i | \(-0.465980\pi\) | ||||
0.106673 | + | 0.994294i | \(0.465980\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −48.0000 | −0.826236 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −24.0000 | −0.342403 | −0.171202 | − | 0.985236i | \(-0.554765\pi\) | ||||
−0.171202 | + | 0.985236i | \(0.554765\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 94.0000 | 1.13500 | 0.567502 | − | 0.823372i | \(-0.307910\pi\) | ||||
0.567502 | + | 0.823372i | \(0.307910\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −180.000 | −1.63185 | −0.815926 | − | 0.578156i | \(-0.803772\pi\) | ||||
−0.815926 | + | 0.578156i | \(0.803772\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.0000 | 0.152000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 152.000 | 1.08342 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 30.0000 | 0.192099 | 0.0960493 | − | 0.995377i | \(-0.469379\pi\) | ||||
0.0960493 | + | 0.995377i | \(0.469379\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 94.0000 | 0.544610 | 0.272305 | − | 0.962211i | \(-0.412214\pi\) | ||||
0.272305 | + | 0.962211i | \(0.412214\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −44.0000 | −0.232104 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −214.000 | −0.950848 | −0.475424 | − | 0.879757i | \(-0.657705\pi\) | ||||
−0.475424 | + | 0.879757i | \(0.657705\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −40.0000 | −0.164234 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 48.0000 | 0.182838 | 0.0914188 | − | 0.995813i | \(-0.470860\pi\) | ||||
0.0914188 | + | 0.995813i | \(0.470860\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 0.0283718 | 0.0141859 | − | 0.999899i | \(-0.495484\pi\) | ||||
0.0141859 | + | 0.999899i | \(0.495484\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −132.000 | −0.437276 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −30.0000 | −0.0931053 | −0.0465527 | − | 0.998916i | \(-0.514824\pi\) | ||||
−0.0465527 | + | 0.998916i | \(0.514824\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 96.0000 | 0.263582 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 54.0000 | 0.139952 | 0.0699761 | − | 0.997549i | \(-0.477708\pi\) | ||||
0.0699761 | + | 0.997549i | \(0.477708\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 132.000 | 0.323616 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −376.000 | −0.873727 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −360.000 | −0.794373 | −0.397187 | − | 0.917738i | \(-0.630013\pi\) | ||||
−0.397187 | + | 0.917738i | \(0.630013\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 178.000 | 0.373616 | 0.186808 | − | 0.982396i | \(-0.440186\pi\) | ||||
0.186808 | + | 0.982396i | \(0.440186\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 120.000 | 0.228987 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −292.000 | −0.532440 | −0.266220 | − | 0.963912i | \(-0.585775\pi\) | ||||
−0.266220 | + | 0.963912i | \(0.585775\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 720.000 | 1.25620 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 312.000 | 0.521515 | 0.260758 | − | 0.965404i | \(-0.416028\pi\) | ||||
0.260758 | + | 0.965404i | \(0.416028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −728.000 | −1.16720 | −0.583602 | − | 0.812040i | \(-0.698357\pi\) | ||||
−0.583602 | + | 0.812040i | \(0.698357\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −76.0000 | −0.117010 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1288.00 | −1.83432 | −0.917160 | − | 0.398519i | \(-0.869524\pi\) | ||||
−0.917160 | + | 0.398519i | \(0.869524\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −311.000 | −0.426612 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −66.0000 | −0.0872824 | −0.0436412 | − | 0.999047i | \(-0.513896\pi\) | ||||
−0.0436412 | + | 0.999047i | \(0.513896\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −288.000 | −0.367506 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −120.000 | −0.147878 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 390.000 | 0.464493 | 0.232247 | − | 0.972657i | \(-0.425392\pi\) | ||||
0.232247 | + | 0.972657i | \(0.425392\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −376.000 | −0.419241 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1128.00 | 1.21821 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1510.00 | 1.58059 | 0.790295 | − | 0.612726i | \(-0.209927\pi\) | ||||
0.790295 | + | 0.612726i | \(0.209927\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −121.000 | −0.122838 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −90.0000 | −0.0886667 | −0.0443333 | − | 0.999017i | \(-0.514116\pi\) | ||||
−0.0443333 | + | 0.999017i | \(0.514116\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −302.000 | −0.288902 | −0.144451 | − | 0.989512i | \(-0.546142\pi\) | ||||
−0.144451 | + | 0.989512i | \(0.546142\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 240.000 | 0.216838 | 0.108419 | − | 0.994105i | \(-0.465421\pi\) | ||||
0.108419 | + | 0.994105i | \(0.465421\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −166.000 | −0.145871 | −0.0729354 | − | 0.997337i | \(-0.523237\pi\) | ||||
−0.0729354 | + | 0.997337i | \(0.523237\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 856.000 | 0.731963 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1662.00 | 1.38361 | 0.691804 | − | 0.722085i | \(-0.256816\pi\) | ||||
0.691804 | + | 0.722085i | \(0.256816\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2160.00 | −1.75149 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −110.000 | −0.0869188 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −192.000 | −0.140748 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1272.00 | −0.910169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1544.00 | 1.07880 | 0.539401 | − | 0.842049i | \(-0.318651\pi\) | ||||
0.539401 | + | 0.842049i | \(0.318651\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −32.0000 | −0.0218406 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2358.00 | −1.57267 | −0.786334 | − | 0.617802i | \(-0.788023\pi\) | ||||
−0.786334 | + | 0.617802i | \(0.788023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1824.00 | 1.16285 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1206.00 | 0.752084 | 0.376042 | − | 0.926603i | \(-0.377285\pi\) | ||||
0.376042 | + | 0.926603i | \(0.377285\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2630.00 | −1.60485 | −0.802423 | − | 0.596755i | \(-0.796456\pi\) | ||||
−0.802423 | + | 0.596755i | \(0.796456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 120.000 | 0.0716725 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 110.000 | 0.0643263 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 360.000 | 0.206182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −126.000 | −0.0692773 | −0.0346387 | − | 0.999400i | \(-0.511028\pi\) | ||||
−0.0346387 | + | 0.999400i | \(0.511028\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1456.00 | −0.784686 | −0.392343 | − | 0.919819i | \(-0.628335\pi\) | ||||
−0.392343 | + | 0.919819i | \(0.628335\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 264.000 | 0.139498 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1128.00 | 0.584536 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −992.000 | −0.504269 | −0.252134 | − | 0.967692i | \(-0.581133\pi\) | ||||
−0.252134 | + | 0.967692i | \(0.581133\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −216.000 | −0.107735 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3188.00 | 1.53192 | 0.765961 | − | 0.642887i | \(-0.222263\pi\) | ||||
0.765961 | + | 0.642887i | \(0.222263\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −528.000 | −0.249120 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 252.000 | 0.116769 | 0.0583843 | − | 0.998294i | \(-0.481405\pi\) | ||||
0.0583843 | + | 0.998294i | \(0.481405\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2097.00 | −0.954483 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1034.00 | −0.462409 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3882.00 | 1.70603 | 0.853014 | − | 0.521887i | \(-0.174772\pi\) | ||||
0.853014 | + | 0.521887i | \(0.174772\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1440.00 | 0.611509 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3300.00 | −1.37795 | −0.688976 | − | 0.724784i | \(-0.741940\pi\) | ||||
−0.688976 | + | 0.724784i | \(0.741940\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 124.000 | 0.0509218 | 0.0254609 | − | 0.999676i | \(-0.491895\pi\) | ||||
0.0254609 | + | 0.999676i | \(0.491895\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −712.000 | −0.287610 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2568.00 | −1.02056 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −264.000 | −0.103238 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1860.00 | 0.704633 | 0.352316 | − | 0.935881i | \(-0.385394\pi\) | ||||
0.352316 | + | 0.935881i | \(0.385394\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1318.00 | −0.491563 | −0.245782 | − | 0.969325i | \(-0.579045\pi\) | ||||
−0.245782 | + | 0.969325i | \(0.579045\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −480.000 | −0.176274 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1266.00 | −0.457862 | −0.228931 | − | 0.973443i | \(-0.573523\pi\) | ||||
−0.228931 | + | 0.973443i | \(0.573523\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −830.000 | −0.295664 | −0.147832 | − | 0.989012i | \(-0.547229\pi\) | ||||
−0.147832 | + | 0.989012i | \(0.547229\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1168.00 | 0.409872 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 576.000 | 0.196242 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1980.00 | 0.664829 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1034.00 | 0.342217 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4408.00 | −1.43820 | −0.719098 | − | 0.694909i | \(-0.755445\pi\) | ||||
−0.719098 | + | 0.694909i | \(0.755445\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1248.00 | −0.401463 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 96.0000 | 0.0304518 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2912.00 | 0.898515 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −240.000 | −0.0730504 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4246.00 | 1.27504 | 0.637518 | − | 0.770435i | \(-0.279961\pi\) | ||||
0.637518 | + | 0.770435i | \(0.279961\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −209.000 | −0.0619259 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1710.00 | −0.499985 | −0.249993 | − | 0.968248i | \(-0.580428\pi\) | ||||
−0.249993 | + | 0.968248i | \(0.580428\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2044.00 | 0.589831 | 0.294916 | − | 0.955523i | \(-0.404708\pi\) | ||||
0.294916 | + | 0.955523i | \(0.404708\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 54.0000 | 0.0151831 | 0.00759154 | − | 0.999971i | \(-0.497584\pi\) | ||||
0.00759154 | + | 0.999971i | \(0.497584\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −360.000 | −0.0999311 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5152.00 | 1.41206 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4416.00 | −1.19518 | −0.597588 | − | 0.801803i | \(-0.703874\pi\) | ||||
−0.597588 | + | 0.801803i | \(0.703874\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 808.000 | 0.215966 | 0.107983 | − | 0.994153i | \(-0.465561\pi\) | ||||
0.107983 | + | 0.994153i | \(0.465561\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2860.00 | −0.755017 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 940.000 | 0.242149 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 264.000 | 0.0671900 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5400.00 | −1.35795 | −0.678974 | − | 0.734162i | \(-0.737575\pi\) | ||||
−0.678974 | + | 0.734162i | \(0.737575\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1980.00 | −0.492022 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1152.00 | 0.282906 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3882.00 | −0.942228 | −0.471114 | − | 0.882072i | \(-0.656148\pi\) | ||||
−0.471114 | + | 0.882072i | \(0.656148\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −330.000 | −0.0782624 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7536.00 | −1.76688 | −0.883440 | − | 0.468543i | \(-0.844779\pi\) | ||||
−0.883440 | + | 0.468543i | \(0.844779\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 648.000 | 0.150213 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1560.00 | −0.357567 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1596.00 | −0.361747 | −0.180873 | − | 0.983506i | \(-0.557892\pi\) | ||||
−0.180873 | + | 0.983506i | \(0.557892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.0000 | −0.00448308 | −0.00224154 | − | 0.999997i | \(-0.500714\pi\) | ||||
−0.00224154 | + | 0.999997i | \(0.500714\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 209.000 | 0.0458297 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5374.00 | −1.16568 | −0.582838 | − | 0.812588i | \(-0.698058\pi\) | ||||
−0.582838 | + | 0.812588i | \(0.698058\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1034.00 | −0.221878 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −786.000 | −0.166864 | −0.0834321 | − | 0.996513i | \(-0.526588\pi\) | ||||
−0.0834321 | + | 0.996513i | \(0.526588\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3878.00 | −0.814570 | −0.407285 | − | 0.913301i | \(-0.633524\pi\) | ||||
−0.407285 | + | 0.913301i | \(0.633524\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4512.00 | −0.937782 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4337.00 | −0.882760 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6040.00 | −1.21674 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8226.00 | 1.64016 | 0.820082 | − | 0.572246i | \(-0.193928\pi\) | ||||
0.820082 | + | 0.572246i | \(0.193928\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4320.00 | −0.852611 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1672.00 | 0.326664 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1800.00 | −0.348149 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 360.000 | 0.0682556 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2136.00 | 0.401007 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3926.00 | −0.729865 | −0.364933 | − | 0.931034i | \(-0.618908\pi\) | ||||
−0.364933 | + | 0.931034i | \(0.618908\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1208.00 | 0.222397 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −618.000 | −0.112680 | −0.0563401 | − | 0.998412i | \(-0.517943\pi\) | ||||
−0.0563401 | + | 0.998412i | \(0.517943\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −686.000 | −0.123882 | −0.0619409 | − | 0.998080i | \(-0.519729\pi\) | ||||
−0.0619409 | + | 0.998080i | \(0.519729\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2094.00 | 0.371012 | 0.185506 | − | 0.982643i | \(-0.440608\pi\) | ||||
0.185506 | + | 0.982643i | \(0.440608\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 330.000 | 0.0579199 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −960.000 | −0.166922 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2256.00 | −0.388629 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 190.000 | 0.0324286 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 664.000 | 0.112291 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2444.00 | 0.405844 | 0.202922 | − | 0.979195i | \(-0.434956\pi\) | ||||
0.202922 | + | 0.979195i | \(0.434956\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2354.00 | 0.387383 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3504.00 | −0.571475 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7378.00 | −1.19260 | −0.596299 | − | 0.802763i | \(-0.703363\pi\) | ||||
−0.596299 | + | 0.802763i | \(0.703363\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6648.00 | −1.06510 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1034.00 | 0.164206 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8640.00 | 1.34830 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6840.00 | −1.05819 | −0.529093 | − | 0.848564i | \(-0.677468\pi\) | ||||
−0.529093 | + | 0.848564i | \(0.677468\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5614.00 | 0.861062 | 0.430531 | − | 0.902576i | \(-0.358326\pi\) | ||||
0.430531 | + | 0.902576i | \(0.358326\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1520.00 | 0.231144 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9066.00 | −1.36695 | −0.683477 | − | 0.729972i | \(-0.739533\pi\) | ||||
−0.683477 | + | 0.729972i | \(0.739533\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3744.00 | 0.559749 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5256.00 | −0.772705 | −0.386352 | − | 0.922351i | \(-0.626265\pi\) | ||||
−0.386352 | + | 0.922351i | \(0.626265\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1977.00 | 0.288234 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −484.000 | −0.0699819 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8736.00 | −1.25278 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2350.00 | 0.334248 | 0.167124 | − | 0.985936i | \(-0.446552\pi\) | ||||
0.167124 | + | 0.985936i | \(0.446552\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −528.000 | −0.0744894 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4306.00 | −0.597738 | −0.298869 | − | 0.954294i | \(-0.596609\pi\) | ||||
−0.298869 | + | 0.954294i | \(0.596609\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5088.00 | 0.700649 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 300.000 | 0.0409835 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14380.0 | −1.94895 | −0.974474 | − | 0.224502i | \(-0.927924\pi\) | ||||
−0.974474 | + | 0.224502i | \(0.927924\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6176.00 | −0.830462 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10746.0 | −1.43367 | −0.716834 | − | 0.697244i | \(-0.754410\pi\) | ||||
−0.716834 | + | 0.697244i | \(0.754410\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −88.0000 | −0.0115589 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6870.00 | −0.895431 | −0.447716 | − | 0.894176i | \(-0.647762\pi\) | ||||
−0.447716 | + | 0.894176i | \(0.647762\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4320.00 | 0.558751 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9432.00 | 1.21064 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15456.0 | −1.96880 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15728.0 | −1.98833 | −0.994163 | − | 0.107885i | \(-0.965592\pi\) | ||||
−0.994163 | + | 0.107885i | \(0.965592\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12846.0 | 1.59975 | 0.799874 | − | 0.600168i | \(-0.204900\pi\) | ||||
0.799874 | + | 0.600168i | \(0.204900\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 940.000 | 0.116190 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3732.00 | −0.457888 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2354.00 | −0.286692 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5740.00 | 0.693948 | 0.346974 | − | 0.937875i | \(-0.387209\pi\) | ||||
0.346974 | + | 0.937875i | \(0.387209\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4824.00 | −0.578955 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −792.000 | −0.0936813 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10520.0 | 1.23541 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2292.00 | −0.267235 | −0.133618 | − | 0.991033i | \(-0.542659\pi\) | ||||
−0.133618 | + | 0.991033i | \(0.542659\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10834.0 | −1.25420 | −0.627098 | − | 0.778940i | \(-0.715758\pi\) | ||||
−0.627098 | + | 0.778940i | \(0.715758\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 330.000 | 0.0379318 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −456.000 | −0.0520453 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −440.000 | −0.0495184 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11400.0 | −1.27406 | −0.637029 | − | 0.770840i | \(-0.719837\pi\) | ||||
−0.637029 | + | 0.770840i | \(0.719837\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15958.0 | 1.77111 | 0.885557 | − | 0.464530i | \(-0.153777\pi\) | ||||
0.885557 | + | 0.464530i | \(0.153777\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1440.00 | −0.158719 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16920.0 | −1.85216 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 268.000 | 0.0291365 | 0.0145683 | − | 0.999894i | \(-0.495363\pi\) | ||||
0.0145683 | + | 0.999894i | \(0.495363\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15324.0 | −1.64349 | −0.821744 | − | 0.569857i | \(-0.806999\pi\) | ||||
−0.821744 | + | 0.569857i | \(0.806999\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4680.00 | 0.498547 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 504.000 | 0.0533297 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2238.00 | 0.235229 | 0.117614 | − | 0.993059i | \(-0.462475\pi\) | ||||
0.117614 | + | 0.993059i | \(0.462475\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 528.000 | 0.0551276 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5824.00 | 0.604052 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9046.00 | −0.925939 | −0.462969 | − | 0.886374i | \(-0.653216\pi\) | ||||
−0.462969 | + | 0.886374i | \(0.653216\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3648.00 | −0.370967 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11898.0 | −1.20205 | −0.601025 | − | 0.799230i | \(-0.705241\pi\) | ||||
−0.601025 | + | 0.799230i | \(0.705241\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6512.00 | 0.653646 | 0.326823 | − | 0.945085i | \(-0.394022\pi\) | ||||
0.326823 | + | 0.945085i | \(0.394022\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4512.00 | −0.449976 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11676.0 | −1.15696 | −0.578481 | − | 0.815696i | \(-0.696354\pi\) | ||||
−0.578481 | + | 0.815696i | \(0.696354\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3968.00 | 0.388186 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 88.0000 | 0.00855443 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1786.00 | 0.172521 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −594.000 | −0.0570176 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16920.0 | −1.61398 | −0.806988 | − | 0.590568i | \(-0.798904\pi\) | ||||
−0.806988 | + | 0.590568i | \(0.798904\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2140.00 | −0.202860 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18120.0 | 1.69647 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5188.00 | −0.482732 | −0.241366 | − | 0.970434i | \(-0.577596\pi\) | ||||
−0.241366 | + | 0.970434i | \(0.577596\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12752.0 | −1.17927 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21036.0 | 1.93349 | 0.966743 | − | 0.255751i | \(-0.0823226\pi\) | ||||
0.966743 | + | 0.255751i | \(0.0823226\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −720.000 | −0.0657752 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1452.00 | −0.131844 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2284.00 | −0.204902 | −0.102451 | − | 0.994738i | \(-0.532668\pi\) | ||||
−0.102451 | + | 0.994738i | \(0.532668\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1008.00 | −0.0898885 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11004.0 | 0.975436 | 0.487718 | − | 0.873001i | \(-0.337830\pi\) | ||||
0.487718 | + | 0.873001i | \(0.337830\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1080.00 | −0.0951671 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8388.00 | 0.734762 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5244.00 | 0.456653 | 0.228326 | − | 0.973585i | \(-0.426675\pi\) | ||||
0.228326 | + | 0.973585i | \(0.426675\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14288.0 | 1.22969 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3624.00 | −0.310083 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −330.000 | −0.0280723 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15528.0 | −1.31330 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1902.00 | 0.159939 | 0.0799694 | − | 0.996797i | \(-0.474518\pi\) | ||||
0.0799694 | + | 0.996797i | \(0.474518\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8194.00 | 0.685083 | 0.342542 | − | 0.939503i | \(-0.388712\pi\) | ||||
0.342542 | + | 0.939503i | \(0.388712\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2256.00 | −0.186476 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20233.0 | 1.66294 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3960.00 | 0.323633 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 480.000 | 0.0390077 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2880.00 | 0.232735 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13200.0 | 1.06075 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10406.0 | 0.826967 | 0.413483 | − | 0.910512i | \(-0.364312\pi\) | ||||
0.413483 | + | 0.910512i | \(0.364312\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −496.000 | −0.0391996 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1992.00 | −0.156565 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20900.0 | 1.63367 | 0.816837 | − | 0.576869i | \(-0.195726\pi\) | ||||
0.816837 | + | 0.576869i | \(0.195726\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1958.00 | −0.152214 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2820.00 | 0.218033 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10272.0 | 0.785625 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10038.0 | 0.763597 | 0.381799 | − | 0.924246i | \(-0.375305\pi\) | ||||
0.381799 | + | 0.924246i | \(0.375305\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 80.0000 | 0.00605302 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1056.00 | 0.0794730 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8154.00 | 0.610391 | 0.305195 | − | 0.952290i | \(-0.401278\pi\) | ||||
0.305195 | + | 0.952290i | \(0.401278\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19944.0 | 1.48504 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2730.00 | −0.201138 | −0.100569 | − | 0.994930i | \(-0.532066\pi\) | ||||
−0.100569 | + | 0.994930i | \(0.532066\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3692.00 | 0.270587 | 0.135294 | − | 0.990806i | \(-0.456802\pi\) | ||||
0.135294 | + | 0.990806i | \(0.456802\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7440.00 | −0.542427 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3420.00 | −0.248041 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3946.00 | 0.284704 | 0.142352 | − | 0.989816i | \(-0.454534\pi\) | ||||
0.142352 | + | 0.989816i | \(0.454534\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5272.00 | 0.378406 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 594.000 | 0.0421972 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1320.00 | −0.0932911 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3312.00 | 0.232881 | 0.116440 | − | 0.993198i | \(-0.462852\pi\) | ||||
0.116440 | + | 0.993198i | \(0.462852\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8836.00 | 0.618134 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5064.00 | 0.352462 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10920.0 | 0.756207 | 0.378103 | − | 0.925763i | \(-0.376576\pi\) | ||||
0.378103 | + | 0.925763i | \(0.376576\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3320.00 | 0.227602 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25800.0 | −1.75987 | −0.879933 | − | 0.475098i | \(-0.842413\pi\) | ||||
−0.879933 | + | 0.475098i | \(0.842413\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24700.0 | 1.67643 | 0.838215 | − | 0.545340i | \(-0.183600\pi\) | ||||
0.838215 | + | 0.545340i | \(0.183600\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3212.00 | 0.216920 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1452.00 | 0.0975739 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9016.00 | 0.602880 | 0.301440 | − | 0.953485i | \(-0.402533\pi\) | ||||
0.301440 | + | 0.953485i | \(0.402533\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −300.000 | −0.0198637 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1618.00 | −0.106608 | −0.0533038 | − | 0.998578i | \(-0.516975\pi\) | ||||
−0.0533038 | + | 0.998578i | \(0.516975\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2304.00 | −0.151067 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11310.0 | −0.737963 | −0.368982 | − | 0.929437i | \(-0.620294\pi\) | ||||
−0.368982 | + | 0.929437i | \(0.620294\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24700.0 | 1.60384 | 0.801920 | − | 0.597432i | \(-0.203812\pi\) | ||||
0.801920 | + | 0.597432i | \(0.203812\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27360.0 | −1.76799 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17639.0 | −1.12890 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4136.00 | −0.263438 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5136.00 | 0.325573 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2500.00 | −0.157723 | −0.0788617 | − | 0.996886i | \(-0.525129\pi\) | ||||
−0.0788617 | + | 0.996886i | \(0.525129\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17632.0 | 1.10712 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18528.0 | 1.15789 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3432.00 | −0.212469 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3450.00 | 0.212585 | 0.106292 | − | 0.994335i | \(-0.466102\pi\) | ||||
0.106292 | + | 0.994335i | \(0.466102\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18416.0 | −1.12948 | −0.564740 | − | 0.825269i | \(-0.691024\pi\) | ||||
−0.564740 | + | 0.825269i | \(0.691024\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −384.000 | −0.0234418 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7014.00 | 0.426196 | 0.213098 | − | 0.977031i | \(-0.431645\pi\) | ||||
0.213098 | + | 0.977031i | \(0.431645\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3960.00 | −0.239512 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5070.00 | −0.303835 | −0.151918 | − | 0.988393i | \(-0.548545\pi\) | ||||
−0.151918 | + | 0.988393i | \(0.548545\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28296.0 | −1.68796 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8008.00 | 0.475528 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30600.0 | 1.80881 | 0.904406 | − | 0.426673i | \(-0.140315\pi\) | ||||
0.904406 | + | 0.426673i | \(0.140315\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22364.0 | −1.31597 | −0.657987 | − | 0.753029i | \(-0.728592\pi\) | ||||
−0.657987 | + | 0.753029i | \(0.728592\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 960.000 | 0.0562343 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5400.00 | −0.313477 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16984.0 | −0.981524 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1958.00 | 0.112649 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31522.0 | −1.80547 | −0.902737 | − | 0.430193i | \(-0.858445\pi\) | ||||
−0.902737 | + | 0.430193i | \(0.858445\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2888.00 | 0.164680 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30210.0 | 1.71501 | 0.857507 | − | 0.514472i | \(-0.172012\pi\) | ||||
0.857507 | + | 0.514472i | \(0.172012\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6840.00 | 0.384889 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12492.0 | 0.699843 | 0.349922 | − | 0.936779i | \(-0.386208\pi\) | ||||
0.349922 | + | 0.936779i | \(0.386208\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14472.0 | 0.807221 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8176.00 | −0.454052 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 540.000 | 0.0298583 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21608.0 | −1.18959 | −0.594795 | − | 0.803877i | \(-0.702767\pi\) | ||||
−0.594795 | + | 0.803877i | \(0.702767\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31560.0 | −1.72250 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1152.00 | −0.0626042 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −216.000 | −0.0116879 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28266.0 | 1.52296 | 0.761478 | − | 0.648191i | \(-0.224474\pi\) | ||||
0.761478 | + | 0.648191i | \(0.224474\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20116.0 | −1.07922 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1440.00 | 0.0769270 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5978.00 | 0.316655 | 0.158328 | − | 0.987387i | \(-0.449390\pi\) | ||||
0.158328 | + | 0.987387i | \(0.449390\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14168.0 | 0.747316 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16920.0 | −0.888722 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1320.00 | 0.0690422 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17664.0 | 0.920048 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6330.00 | −0.328330 | −0.164165 | − | 0.986433i | \(-0.552493\pi\) | ||||
−0.164165 | + | 0.986433i | \(0.552493\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3232.00 | −0.166251 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 570.000 | 0.0291990 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8710.00 | 0.444341 | 0.222171 | − | 0.975008i | \(-0.428686\pi\) | ||||
0.222171 | + | 0.975008i | \(0.428686\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19837.0 | 1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −192.000 | −0.00971461 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2506.00 | 0.126277 | 0.0631386 | − | 0.998005i | \(-0.479889\pi\) | ||||
0.0631386 | + | 0.998005i | \(0.479889\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3212.00 | −0.160537 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17060.0 | 0.849205 | 0.424602 | − | 0.905380i | \(-0.360414\pi\) | ||||
0.424602 | + | 0.905380i | \(0.360414\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3760.00 | −0.186406 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22392.0 | 1.10563 | 0.552815 | − | 0.833304i | \(-0.313554\pi\) | ||||
0.552815 | + | 0.833304i | \(0.313554\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1512.00 | −0.0743562 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 726.000 | 0.0355595 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16828.0 | −0.817660 | −0.408830 | − | 0.912611i | \(-0.634063\pi\) | ||||
−0.408830 | + | 0.912611i | \(0.634063\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21600.0 | 1.04535 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17472.0 | −0.842213 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10514.0 | 0.504806 | 0.252403 | − | 0.967622i | \(-0.418779\pi\) | ||||
0.252403 | + | 0.967622i | \(0.418779\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7920.00 | 0.378759 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12084.0 | −0.575617 | −0.287809 | − | 0.957688i | \(-0.592927\pi\) | ||||
−0.287809 | + | 0.957688i | \(0.592927\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3168.00 | 0.149725 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3600.00 | −0.169476 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1940.00 | −0.0909729 | −0.0454865 | − | 0.998965i | \(-0.514484\pi\) | ||||
−0.0454865 | + | 0.998965i | \(0.514484\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15528.0 | 0.725327 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10800.0 | 0.502521 | 0.251261 | − | 0.967919i | \(-0.419155\pi\) | ||||
0.251261 | + | 0.967919i | \(0.419155\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1786.00 | 0.0827807 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4512.00 | 0.207521 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3432.00 | 0.157243 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4560.00 | 0.208124 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11904.0 | −0.541238 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11378.0 | −0.515352 | −0.257676 | − | 0.966231i | \(-0.582957\pi\) | ||||
−0.257676 | + | 0.966231i | \(0.582957\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 30144.0 | 1.36015 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1780.00 | 0.0797095 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2592.00 | −0.115634 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15528.0 | −0.690125 | −0.345063 | − | 0.938580i | \(-0.612142\pi\) | ||||
−0.345063 | + | 0.938580i | \(0.612142\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 720.000 | 0.0318796 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4290.00 | −0.189238 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8008.00 | −0.351926 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6384.00 | 0.278473 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5082.00 | 0.220857 | 0.110429 | − | 0.993884i | \(-0.464778\pi\) | ||||
0.110429 | + | 0.993884i | \(0.464778\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24086.0 | −1.04288 | −0.521439 | − | 0.853289i | \(-0.674605\pi\) | ||||
−0.521439 | + | 0.853289i | \(0.674605\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 80.0000 | 0.00345107 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38256.0 | 1.64423 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 752.000 | 0.0322021 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6210.00 | 0.263984 | 0.131992 | − | 0.991251i | \(-0.457863\pi\) | ||||
0.131992 | + | 0.991251i | \(0.457863\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20612.0 | 0.873012 | 0.436506 | − | 0.899701i | \(-0.356216\pi\) | ||||
0.436506 | + | 0.899701i | \(0.356216\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −836.000 | −0.0352797 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3948.00 | −0.166004 | −0.0830021 | − | 0.996549i | \(-0.526451\pi\) | ||||
−0.0830021 | + | 0.996549i | \(0.526451\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5692.00 | 0.238470 | 0.119235 | − | 0.992866i | \(-0.461956\pi\) | ||||
0.119235 | + | 0.992866i | \(0.461956\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21496.0 | 0.897338 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3024.00 | 0.125329 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14288.0 | 0.590042 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29070.0 | 1.19620 | 0.598098 | − | 0.801423i | \(-0.295923\pi\) | ||||
0.598098 | + | 0.801423i | \(0.295923\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23489.0 | −0.963098 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3144.00 | 0.128452 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25164.0 | −1.02446 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15512.0 | 0.627056 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38520.0 | 1.55164 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20582.0 | −0.826160 | −0.413080 | − | 0.910695i | \(-0.635547\pi\) | ||||
−0.413080 | + | 0.910695i | \(0.635547\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12408.0 | −0.496310 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36156.0 | 1.44115 | 0.720575 | − | 0.693377i | \(-0.243878\pi\) | ||||
0.720575 | + | 0.693377i | \(0.243878\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19784.0 | −0.785822 | −0.392911 | − | 0.919576i | \(-0.628532\pi\) | ||||
−0.392911 | + | 0.919576i | \(0.628532\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34068.0 | −1.34379 | −0.671894 | − | 0.740648i | \(-0.734519\pi\) | ||||
−0.671894 | + | 0.740648i | \(0.734519\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 46584.0 | 1.83110 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17348.0 | 0.679549 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14168.0 | −0.553068 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2920.00 | −0.113594 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16610.0 | −0.643944 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19510.0 | −0.751204 | −0.375602 | − | 0.926781i | \(-0.622564\pi\) | ||||
−0.375602 | + | 0.926781i | \(0.622564\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32904.0 | −1.26260 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24474.0 | 0.935925 | 0.467963 | − | 0.883748i | \(-0.344988\pi\) | ||||
0.467963 | + | 0.883748i | \(0.344988\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49388.0 | 1.88226 | 0.941132 | − | 0.338040i | \(-0.109764\pi\) | ||||
0.941132 | + | 0.338040i | \(0.109764\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17280.0 | 0.656340 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30216.0 | 1.14380 | 0.571902 | − | 0.820322i | \(-0.306206\pi\) | ||||
0.571902 | + | 0.820322i | \(0.306206\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3421.00 | −0.128628 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2820.00 | −0.105675 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39600.0 | −1.47897 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7200.00 | 0.268006 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2820.00 | 0.104619 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1296.00 | −0.0479201 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1488.00 | 0.0546550 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4492.00 | −0.164448 | −0.0822240 | − | 0.996614i | \(-0.526202\pi\) | ||||
−0.0822240 | + | 0.996614i | \(0.526202\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 990.000 | 0.0361235 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28932.0 | 1.05221 | 0.526103 | − | 0.850421i | \(-0.323653\pi\) | ||||
0.526103 | + | 0.850421i | \(0.323653\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −726.000 | −0.0263166 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8544.00 | −0.308695 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32056.0 | −1.15063 | −0.575315 | − | 0.817932i | \(-0.695121\pi\) | ||||
−0.575315 | + | 0.817932i | \(0.695121\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15704.0 | 0.561851 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3120.00 | 0.111263 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4066.00 | −0.144529 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3322.00 | 0.117701 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22182.0 | 0.783388 | 0.391694 | − | 0.920095i | \(-0.371889\pi\) | ||||
0.391694 | + | 0.920095i | \(0.371889\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2472.00 | 0.0867413 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3168.00 | −0.110807 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29792.0 | −1.03870 | −0.519350 | − | 0.854562i | \(-0.673826\pi\) | ||||
−0.519350 | + | 0.854562i | \(0.673826\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2744.00 | 0.0953643 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30702.0 | −1.06361 | −0.531805 | − | 0.846867i | \(-0.678486\pi\) | ||||
−0.531805 | + | 0.846867i | \(0.678486\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8640.00 | −0.298364 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5244.00 | 0.179944 | 0.0899721 | − | 0.995944i | \(-0.471322\pi\) | ||||
0.0899721 | + | 0.995944i | \(0.471322\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7280.00 | −0.249019 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8376.00 | −0.285605 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24150.0 | −0.820876 | −0.410438 | − | 0.911888i | \(-0.634624\pi\) | ||||
−0.410438 | + | 0.911888i | \(0.634624\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22320.0 | 0.756291 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1320.00 | −0.0445868 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20955.0 | −0.703400 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2640.00 | −0.0883414 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15816.0 | −0.527601 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15512.0 | 0.515856 | 0.257928 | − | 0.966164i | \(-0.416960\pi\) | ||||
0.257928 | + | 0.966164i | \(0.416960\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9024.00 | 0.299167 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52404.0 | −1.73195 | −0.865975 | − | 0.500086i | \(-0.833302\pi\) | ||||
−0.865975 | + | 0.500086i | \(0.833302\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −760.000 | −0.0249636 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5070.00 | −0.166022 | −0.0830111 | − | 0.996549i | \(-0.526454\pi\) | ||||
−0.0830111 | + | 0.996549i | \(0.526454\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4290.00 | 0.140050 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1826.00 | 0.0594288 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18702.0 | −0.606817 | −0.303409 | − | 0.952861i | \(-0.598125\pi\) | ||||
−0.303409 | + | 0.952861i | \(0.598125\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15192.0 | −0.491429 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1440.00 | −0.0462986 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40496.0 | 1.29808 | 0.649040 | − | 0.760754i | \(-0.275171\pi\) | ||||
0.649040 | + | 0.760754i | \(0.275171\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9776.00 | −0.312419 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9960.00 | −0.317340 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23686.0 | 0.752400 | 0.376200 | − | 0.926538i | \(-0.377230\pi\) | ||||
0.376200 | + | 0.926538i | \(0.377230\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −32528.0 | −1.03017 |
(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 | 2156.4.a.a.1.1 | 1 | ||
7.6 | odd | 2 | 308.4.a.b.1.1 | ✓ | 1 | ||
28.27 | even | 2 | 1232.4.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
308.4.a.b.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
1232.4.a.c.1.1 | 1 | 28.27 | even | 2 | |||
2156.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial |