Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,4,Mod(1,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.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: | \(5.78218718056\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 14) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 98.1 |
$q$-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 | ||||||||
\(3\) | −8.00000 | −1.53960 | −0.769800 | − | 0.638285i | \(-0.779644\pi\) | ||||
−0.769800 | + | 0.638285i | \(0.779644\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 14.0000 | 1.25220 | 0.626099 | − | 0.779744i | \(-0.284651\pi\) | ||||
0.626099 | + | 0.779744i | \(0.284651\pi\) | |||||||
\(6\) | 16.0000 | 1.08866 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 37.0000 | 1.37037 | ||||||||
\(10\) | −28.0000 | −0.885438 | ||||||||
\(11\) | −28.0000 | −0.767483 | −0.383742 | − | 0.923440i | \(-0.625365\pi\) | ||||
−0.383742 | + | 0.923440i | \(0.625365\pi\) | |||||||
\(12\) | −32.0000 | −0.769800 | ||||||||
\(13\) | −18.0000 | −0.384023 | −0.192012 | − | 0.981393i | \(-0.561501\pi\) | ||||
−0.192012 | + | 0.981393i | \(0.561501\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −112.000 | −1.92789 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −74.0000 | −1.05574 | −0.527872 | − | 0.849324i | \(-0.677010\pi\) | ||||
−0.527872 | + | 0.849324i | \(0.677010\pi\) | |||||||
\(18\) | −74.0000 | −0.968998 | ||||||||
\(19\) | −80.0000 | −0.965961 | −0.482980 | − | 0.875631i | \(-0.660446\pi\) | ||||
−0.482980 | + | 0.875631i | \(0.660446\pi\) | |||||||
\(20\) | 56.0000 | 0.626099 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 56.0000 | 0.542693 | ||||||||
\(23\) | −112.000 | −1.01537 | −0.507687 | − | 0.861541i | \(-0.669499\pi\) | ||||
−0.507687 | + | 0.861541i | \(0.669499\pi\) | |||||||
\(24\) | 64.0000 | 0.544331 | ||||||||
\(25\) | 71.0000 | 0.568000 | ||||||||
\(26\) | 36.0000 | 0.271545 | ||||||||
\(27\) | −80.0000 | −0.570222 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 190.000 | 1.21662 | 0.608312 | − | 0.793698i | \(-0.291847\pi\) | ||||
0.608312 | + | 0.793698i | \(0.291847\pi\) | |||||||
\(30\) | 224.000 | 1.36322 | ||||||||
\(31\) | −72.0000 | −0.417148 | −0.208574 | − | 0.978007i | \(-0.566882\pi\) | ||||
−0.208574 | + | 0.978007i | \(0.566882\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 224.000 | 1.18162 | ||||||||
\(34\) | 148.000 | 0.746523 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 148.000 | 0.685185 | ||||||||
\(37\) | −346.000 | −1.53735 | −0.768676 | − | 0.639638i | \(-0.779084\pi\) | ||||
−0.768676 | + | 0.639638i | \(0.779084\pi\) | |||||||
\(38\) | 160.000 | 0.683038 | ||||||||
\(39\) | 144.000 | 0.591242 | ||||||||
\(40\) | −112.000 | −0.442719 | ||||||||
\(41\) | −162.000 | −0.617077 | −0.308538 | − | 0.951212i | \(-0.599840\pi\) | ||||
−0.308538 | + | 0.951212i | \(0.599840\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −412.000 | −1.46115 | −0.730575 | − | 0.682833i | \(-0.760748\pi\) | ||||
−0.730575 | + | 0.682833i | \(0.760748\pi\) | |||||||
\(44\) | −112.000 | −0.383742 | ||||||||
\(45\) | 518.000 | 1.71598 | ||||||||
\(46\) | 224.000 | 0.717978 | ||||||||
\(47\) | −24.0000 | −0.0744843 | −0.0372421 | − | 0.999306i | \(-0.511857\pi\) | ||||
−0.0372421 | + | 0.999306i | \(0.511857\pi\) | |||||||
\(48\) | −128.000 | −0.384900 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −142.000 | −0.401637 | ||||||||
\(51\) | 592.000 | 1.62542 | ||||||||
\(52\) | −72.0000 | −0.192012 | ||||||||
\(53\) | 318.000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 160.000 | 0.403208 | ||||||||
\(55\) | −392.000 | −0.961041 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 640.000 | 1.48719 | ||||||||
\(58\) | −380.000 | −0.860284 | ||||||||
\(59\) | 200.000 | 0.441318 | 0.220659 | − | 0.975351i | \(-0.429179\pi\) | ||||
0.220659 | + | 0.975351i | \(0.429179\pi\) | |||||||
\(60\) | −448.000 | −0.963943 | ||||||||
\(61\) | 198.000 | 0.415595 | 0.207798 | − | 0.978172i | \(-0.433370\pi\) | ||||
0.207798 | + | 0.978172i | \(0.433370\pi\) | |||||||
\(62\) | 144.000 | 0.294968 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −252.000 | −0.480873 | ||||||||
\(66\) | −448.000 | −0.835530 | ||||||||
\(67\) | −716.000 | −1.30557 | −0.652786 | − | 0.757542i | \(-0.726400\pi\) | ||||
−0.652786 | + | 0.757542i | \(0.726400\pi\) | |||||||
\(68\) | −296.000 | −0.527872 | ||||||||
\(69\) | 896.000 | 1.56327 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 392.000 | 0.655237 | 0.327619 | − | 0.944810i | \(-0.393754\pi\) | ||||
0.327619 | + | 0.944810i | \(0.393754\pi\) | |||||||
\(72\) | −296.000 | −0.484499 | ||||||||
\(73\) | −538.000 | −0.862577 | −0.431289 | − | 0.902214i | \(-0.641941\pi\) | ||||
−0.431289 | + | 0.902214i | \(0.641941\pi\) | |||||||
\(74\) | 692.000 | 1.08707 | ||||||||
\(75\) | −568.000 | −0.874493 | ||||||||
\(76\) | −320.000 | −0.482980 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −288.000 | −0.418072 | ||||||||
\(79\) | 240.000 | 0.341799 | 0.170899 | − | 0.985288i | \(-0.445333\pi\) | ||||
0.170899 | + | 0.985288i | \(0.445333\pi\) | |||||||
\(80\) | 224.000 | 0.313050 | ||||||||
\(81\) | −359.000 | −0.492455 | ||||||||
\(82\) | 324.000 | 0.436339 | ||||||||
\(83\) | 1072.00 | 1.41768 | 0.708839 | − | 0.705370i | \(-0.249219\pi\) | ||||
0.708839 | + | 0.705370i | \(0.249219\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1036.00 | −1.32200 | ||||||||
\(86\) | 824.000 | 1.03319 | ||||||||
\(87\) | −1520.00 | −1.87312 | ||||||||
\(88\) | 224.000 | 0.271346 | ||||||||
\(89\) | −810.000 | −0.964717 | −0.482359 | − | 0.875974i | \(-0.660220\pi\) | ||||
−0.482359 | + | 0.875974i | \(0.660220\pi\) | |||||||
\(90\) | −1036.00 | −1.21338 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −448.000 | −0.507687 | ||||||||
\(93\) | 576.000 | 0.642241 | ||||||||
\(94\) | 48.0000 | 0.0526683 | ||||||||
\(95\) | −1120.00 | −1.20957 | ||||||||
\(96\) | 256.000 | 0.272166 | ||||||||
\(97\) | −1354.00 | −1.41730 | −0.708649 | − | 0.705561i | \(-0.750695\pi\) | ||||
−0.708649 | + | 0.705561i | \(0.750695\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1036.00 | −1.05174 | ||||||||
\(100\) | 284.000 | 0.284000 | ||||||||
\(101\) | 1358.00 | 1.33788 | 0.668941 | − | 0.743316i | \(-0.266748\pi\) | ||||
0.668941 | + | 0.743316i | \(0.266748\pi\) | |||||||
\(102\) | −1184.00 | −1.14935 | ||||||||
\(103\) | 832.000 | 0.795916 | 0.397958 | − | 0.917404i | \(-0.369719\pi\) | ||||
0.397958 | + | 0.917404i | \(0.369719\pi\) | |||||||
\(104\) | 144.000 | 0.135773 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −636.000 | −0.582772 | ||||||||
\(107\) | 444.000 | 0.401150 | 0.200575 | − | 0.979678i | \(-0.435719\pi\) | ||||
0.200575 | + | 0.979678i | \(0.435719\pi\) | |||||||
\(108\) | −320.000 | −0.285111 | ||||||||
\(109\) | 1870.00 | 1.64324 | 0.821622 | − | 0.570033i | \(-0.193070\pi\) | ||||
0.821622 | + | 0.570033i | \(0.193070\pi\) | |||||||
\(110\) | 784.000 | 0.679559 | ||||||||
\(111\) | 2768.00 | 2.36691 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1378.00 | 1.14718 | 0.573590 | − | 0.819143i | \(-0.305550\pi\) | ||||
0.573590 | + | 0.819143i | \(0.305550\pi\) | |||||||
\(114\) | −1280.00 | −1.05161 | ||||||||
\(115\) | −1568.00 | −1.27145 | ||||||||
\(116\) | 760.000 | 0.608312 | ||||||||
\(117\) | −666.000 | −0.526254 | ||||||||
\(118\) | −400.000 | −0.312059 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 896.000 | 0.681610 | ||||||||
\(121\) | −547.000 | −0.410969 | ||||||||
\(122\) | −396.000 | −0.293870 | ||||||||
\(123\) | 1296.00 | 0.950052 | ||||||||
\(124\) | −288.000 | −0.208574 | ||||||||
\(125\) | −756.000 | −0.540950 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1944.00 | 1.35828 | 0.679142 | − | 0.734007i | \(-0.262352\pi\) | ||||
0.679142 | + | 0.734007i | \(0.262352\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 3296.00 | 2.24959 | ||||||||
\(130\) | 504.000 | 0.340029 | ||||||||
\(131\) | 848.000 | 0.565573 | 0.282787 | − | 0.959183i | \(-0.408741\pi\) | ||||
0.282787 | + | 0.959183i | \(0.408741\pi\) | |||||||
\(132\) | 896.000 | 0.590809 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1432.00 | 0.923179 | ||||||||
\(135\) | −1120.00 | −0.714031 | ||||||||
\(136\) | 592.000 | 0.373262 | ||||||||
\(137\) | −2966.00 | −1.84965 | −0.924827 | − | 0.380389i | \(-0.875790\pi\) | ||||
−0.924827 | + | 0.380389i | \(0.875790\pi\) | |||||||
\(138\) | −1792.00 | −1.10540 | ||||||||
\(139\) | −2800.00 | −1.70858 | −0.854291 | − | 0.519795i | \(-0.826008\pi\) | ||||
−0.854291 | + | 0.519795i | \(0.826008\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 192.000 | 0.114676 | ||||||||
\(142\) | −784.000 | −0.463323 | ||||||||
\(143\) | 504.000 | 0.294731 | ||||||||
\(144\) | 592.000 | 0.342593 | ||||||||
\(145\) | 2660.00 | 1.52346 | ||||||||
\(146\) | 1076.00 | 0.609934 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1384.00 | −0.768676 | ||||||||
\(149\) | 510.000 | 0.280408 | 0.140204 | − | 0.990123i | \(-0.455224\pi\) | ||||
0.140204 | + | 0.990123i | \(0.455224\pi\) | |||||||
\(150\) | 1136.00 | 0.618360 | ||||||||
\(151\) | 592.000 | 0.319048 | 0.159524 | − | 0.987194i | \(-0.449004\pi\) | ||||
0.159524 | + | 0.987194i | \(0.449004\pi\) | |||||||
\(152\) | 640.000 | 0.341519 | ||||||||
\(153\) | −2738.00 | −1.44676 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1008.00 | −0.522352 | ||||||||
\(156\) | 576.000 | 0.295621 | ||||||||
\(157\) | 2686.00 | 1.36539 | 0.682695 | − | 0.730704i | \(-0.260808\pi\) | ||||
0.682695 | + | 0.730704i | \(0.260808\pi\) | |||||||
\(158\) | −480.000 | −0.241688 | ||||||||
\(159\) | −2544.00 | −1.26888 | ||||||||
\(160\) | −448.000 | −0.221359 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 718.000 | 0.348219 | ||||||||
\(163\) | −1012.00 | −0.486294 | −0.243147 | − | 0.969989i | \(-0.578180\pi\) | ||||
−0.243147 | + | 0.969989i | \(0.578180\pi\) | |||||||
\(164\) | −648.000 | −0.308538 | ||||||||
\(165\) | 3136.00 | 1.47962 | ||||||||
\(166\) | −2144.00 | −1.00245 | ||||||||
\(167\) | −544.000 | −0.252072 | −0.126036 | − | 0.992026i | \(-0.540225\pi\) | ||||
−0.126036 | + | 0.992026i | \(0.540225\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1873.00 | −0.852526 | ||||||||
\(170\) | 2072.00 | 0.934795 | ||||||||
\(171\) | −2960.00 | −1.32372 | ||||||||
\(172\) | −1648.00 | −0.730575 | ||||||||
\(173\) | −1858.00 | −0.816538 | −0.408269 | − | 0.912862i | \(-0.633868\pi\) | ||||
−0.408269 | + | 0.912862i | \(0.633868\pi\) | |||||||
\(174\) | 3040.00 | 1.32449 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −448.000 | −0.191871 | ||||||||
\(177\) | −1600.00 | −0.679454 | ||||||||
\(178\) | 1620.00 | 0.682158 | ||||||||
\(179\) | −300.000 | −0.125268 | −0.0626342 | − | 0.998037i | \(-0.519950\pi\) | ||||
−0.0626342 | + | 0.998037i | \(0.519950\pi\) | |||||||
\(180\) | 2072.00 | 0.857988 | ||||||||
\(181\) | 2358.00 | 0.968336 | 0.484168 | − | 0.874975i | \(-0.339122\pi\) | ||||
0.484168 | + | 0.874975i | \(0.339122\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1584.00 | −0.639851 | ||||||||
\(184\) | 896.000 | 0.358989 | ||||||||
\(185\) | −4844.00 | −1.92507 | ||||||||
\(186\) | −1152.00 | −0.454133 | ||||||||
\(187\) | 2072.00 | 0.810265 | ||||||||
\(188\) | −96.0000 | −0.0372421 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2240.00 | 0.855298 | ||||||||
\(191\) | 1392.00 | 0.527338 | 0.263669 | − | 0.964613i | \(-0.415067\pi\) | ||||
0.263669 | + | 0.964613i | \(0.415067\pi\) | |||||||
\(192\) | −512.000 | −0.192450 | ||||||||
\(193\) | 1778.00 | 0.663126 | 0.331563 | − | 0.943433i | \(-0.392424\pi\) | ||||
0.331563 | + | 0.943433i | \(0.392424\pi\) | |||||||
\(194\) | 2708.00 | 1.00218 | ||||||||
\(195\) | 2016.00 | 0.740353 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1214.00 | 0.439055 | 0.219528 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219528 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(198\) | 2072.00 | 0.743690 | ||||||||
\(199\) | −1040.00 | −0.370471 | −0.185235 | − | 0.982694i | \(-0.559305\pi\) | ||||
−0.185235 | + | 0.982694i | \(0.559305\pi\) | |||||||
\(200\) | −568.000 | −0.200818 | ||||||||
\(201\) | 5728.00 | 2.01006 | ||||||||
\(202\) | −2716.00 | −0.946025 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2368.00 | 0.812712 | ||||||||
\(205\) | −2268.00 | −0.772702 | ||||||||
\(206\) | −1664.00 | −0.562798 | ||||||||
\(207\) | −4144.00 | −1.39144 | ||||||||
\(208\) | −288.000 | −0.0960058 | ||||||||
\(209\) | 2240.00 | 0.741359 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3868.00 | −1.26201 | −0.631005 | − | 0.775779i | \(-0.717357\pi\) | ||||
−0.631005 | + | 0.775779i | \(0.717357\pi\) | |||||||
\(212\) | 1272.00 | 0.412082 | ||||||||
\(213\) | −3136.00 | −1.00880 | ||||||||
\(214\) | −888.000 | −0.283656 | ||||||||
\(215\) | −5768.00 | −1.82965 | ||||||||
\(216\) | 640.000 | 0.201604 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3740.00 | −1.16195 | ||||||||
\(219\) | 4304.00 | 1.32802 | ||||||||
\(220\) | −1568.00 | −0.480521 | ||||||||
\(221\) | 1332.00 | 0.405430 | ||||||||
\(222\) | −5536.00 | −1.67366 | ||||||||
\(223\) | −3968.00 | −1.19156 | −0.595778 | − | 0.803149i | \(-0.703156\pi\) | ||||
−0.595778 | + | 0.803149i | \(0.703156\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2627.00 | 0.778370 | ||||||||
\(226\) | −2756.00 | −0.811179 | ||||||||
\(227\) | 3936.00 | 1.15084 | 0.575422 | − | 0.817857i | \(-0.304838\pi\) | ||||
0.575422 | + | 0.817857i | \(0.304838\pi\) | |||||||
\(228\) | 2560.00 | 0.743597 | ||||||||
\(229\) | −4810.00 | −1.38801 | −0.694004 | − | 0.719971i | \(-0.744155\pi\) | ||||
−0.694004 | + | 0.719971i | \(0.744155\pi\) | |||||||
\(230\) | 3136.00 | 0.899051 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1520.00 | −0.430142 | ||||||||
\(233\) | −2182.00 | −0.613509 | −0.306754 | − | 0.951789i | \(-0.599243\pi\) | ||||
−0.306754 | + | 0.951789i | \(0.599243\pi\) | |||||||
\(234\) | 1332.00 | 0.372118 | ||||||||
\(235\) | −336.000 | −0.0932690 | ||||||||
\(236\) | 800.000 | 0.220659 | ||||||||
\(237\) | −1920.00 | −0.526234 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3000.00 | −0.811941 | −0.405970 | − | 0.913886i | \(-0.633066\pi\) | ||||
−0.405970 | + | 0.913886i | \(0.633066\pi\) | |||||||
\(240\) | −1792.00 | −0.481971 | ||||||||
\(241\) | −2042.00 | −0.545796 | −0.272898 | − | 0.962043i | \(-0.587982\pi\) | ||||
−0.272898 | + | 0.962043i | \(0.587982\pi\) | |||||||
\(242\) | 1094.00 | 0.290599 | ||||||||
\(243\) | 5032.00 | 1.32841 | ||||||||
\(244\) | 792.000 | 0.207798 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2592.00 | −0.671788 | ||||||||
\(247\) | 1440.00 | 0.370951 | ||||||||
\(248\) | 576.000 | 0.147484 | ||||||||
\(249\) | −8576.00 | −2.18266 | ||||||||
\(250\) | 1512.00 | 0.382509 | ||||||||
\(251\) | 528.000 | 0.132777 | 0.0663886 | − | 0.997794i | \(-0.478852\pi\) | ||||
0.0663886 | + | 0.997794i | \(0.478852\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3136.00 | 0.779283 | ||||||||
\(254\) | −3888.00 | −0.960452 | ||||||||
\(255\) | 8288.00 | 2.03535 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −5634.00 | −1.36747 | −0.683734 | − | 0.729731i | \(-0.739645\pi\) | ||||
−0.683734 | + | 0.729731i | \(0.739645\pi\) | |||||||
\(258\) | −6592.00 | −1.59070 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1008.00 | −0.240437 | ||||||||
\(261\) | 7030.00 | 1.66723 | ||||||||
\(262\) | −1696.00 | −0.399921 | ||||||||
\(263\) | 168.000 | 0.0393891 | 0.0196945 | − | 0.999806i | \(-0.493731\pi\) | ||||
0.0196945 | + | 0.999806i | \(0.493731\pi\) | |||||||
\(264\) | −1792.00 | −0.417765 | ||||||||
\(265\) | 4452.00 | 1.03202 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6480.00 | 1.48528 | ||||||||
\(268\) | −2864.00 | −0.652786 | ||||||||
\(269\) | 1310.00 | 0.296922 | 0.148461 | − | 0.988918i | \(-0.452568\pi\) | ||||
0.148461 | + | 0.988918i | \(0.452568\pi\) | |||||||
\(270\) | 2240.00 | 0.504897 | ||||||||
\(271\) | 2208.00 | 0.494932 | 0.247466 | − | 0.968897i | \(-0.420402\pi\) | ||||
0.247466 | + | 0.968897i | \(0.420402\pi\) | |||||||
\(272\) | −1184.00 | −0.263936 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5932.00 | 1.30790 | ||||||||
\(275\) | −1988.00 | −0.435931 | ||||||||
\(276\) | 3584.00 | 0.781636 | ||||||||
\(277\) | 5294.00 | 1.14832 | 0.574162 | − | 0.818742i | \(-0.305328\pi\) | ||||
0.574162 | + | 0.818742i | \(0.305328\pi\) | |||||||
\(278\) | 5600.00 | 1.20815 | ||||||||
\(279\) | −2664.00 | −0.571647 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3242.00 | 0.688262 | 0.344131 | − | 0.938922i | \(-0.388174\pi\) | ||||
0.344131 | + | 0.938922i | \(0.388174\pi\) | |||||||
\(282\) | −384.000 | −0.0810882 | ||||||||
\(283\) | 1592.00 | 0.334398 | 0.167199 | − | 0.985923i | \(-0.446528\pi\) | ||||
0.167199 | + | 0.985923i | \(0.446528\pi\) | |||||||
\(284\) | 1568.00 | 0.327619 | ||||||||
\(285\) | 8960.00 | 1.86226 | ||||||||
\(286\) | −1008.00 | −0.208407 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1184.00 | −0.242250 | ||||||||
\(289\) | 563.000 | 0.114594 | ||||||||
\(290\) | −5320.00 | −1.07725 | ||||||||
\(291\) | 10832.0 | 2.18207 | ||||||||
\(292\) | −2152.00 | −0.431289 | ||||||||
\(293\) | 5022.00 | 1.00133 | 0.500663 | − | 0.865642i | \(-0.333090\pi\) | ||||
0.500663 | + | 0.865642i | \(0.333090\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2800.00 | 0.552618 | ||||||||
\(296\) | 2768.00 | 0.543536 | ||||||||
\(297\) | 2240.00 | 0.437636 | ||||||||
\(298\) | −1020.00 | −0.198279 | ||||||||
\(299\) | 2016.00 | 0.389927 | ||||||||
\(300\) | −2272.00 | −0.437247 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1184.00 | −0.225601 | ||||||||
\(303\) | −10864.0 | −2.05980 | ||||||||
\(304\) | −1280.00 | −0.241490 | ||||||||
\(305\) | 2772.00 | 0.520407 | ||||||||
\(306\) | 5476.00 | 1.02301 | ||||||||
\(307\) | 9536.00 | 1.77280 | 0.886398 | − | 0.462924i | \(-0.153200\pi\) | ||||
0.886398 | + | 0.462924i | \(0.153200\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6656.00 | −1.22539 | ||||||||
\(310\) | 2016.00 | 0.369358 | ||||||||
\(311\) | 968.000 | 0.176496 | 0.0882480 | − | 0.996099i | \(-0.471873\pi\) | ||||
0.0882480 | + | 0.996099i | \(0.471873\pi\) | |||||||
\(312\) | −1152.00 | −0.209036 | ||||||||
\(313\) | −3058.00 | −0.552231 | −0.276116 | − | 0.961124i | \(-0.589047\pi\) | ||||
−0.276116 | + | 0.961124i | \(0.589047\pi\) | |||||||
\(314\) | −5372.00 | −0.965476 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 960.000 | 0.170899 | ||||||||
\(317\) | −4986.00 | −0.883412 | −0.441706 | − | 0.897160i | \(-0.645627\pi\) | ||||
−0.441706 | + | 0.897160i | \(0.645627\pi\) | |||||||
\(318\) | 5088.00 | 0.897235 | ||||||||
\(319\) | −5320.00 | −0.933739 | ||||||||
\(320\) | 896.000 | 0.156525 | ||||||||
\(321\) | −3552.00 | −0.617612 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5920.00 | 1.01981 | ||||||||
\(324\) | −1436.00 | −0.246228 | ||||||||
\(325\) | −1278.00 | −0.218125 | ||||||||
\(326\) | 2024.00 | 0.343862 | ||||||||
\(327\) | −14960.0 | −2.52994 | ||||||||
\(328\) | 1296.00 | 0.218170 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6272.00 | −1.04625 | ||||||||
\(331\) | 8612.00 | 1.43009 | 0.715043 | − | 0.699081i | \(-0.246407\pi\) | ||||
0.715043 | + | 0.699081i | \(0.246407\pi\) | |||||||
\(332\) | 4288.00 | 0.708839 | ||||||||
\(333\) | −12802.0 | −2.10674 | ||||||||
\(334\) | 1088.00 | 0.178242 | ||||||||
\(335\) | −10024.0 | −1.63483 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10206.0 | −1.64972 | −0.824861 | − | 0.565336i | \(-0.808747\pi\) | ||||
−0.824861 | + | 0.565336i | \(0.808747\pi\) | |||||||
\(338\) | 3746.00 | 0.602827 | ||||||||
\(339\) | −11024.0 | −1.76620 | ||||||||
\(340\) | −4144.00 | −0.661000 | ||||||||
\(341\) | 2016.00 | 0.320154 | ||||||||
\(342\) | 5920.00 | 0.936014 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3296.00 | 0.516594 | ||||||||
\(345\) | 12544.0 | 1.95753 | ||||||||
\(346\) | 3716.00 | 0.577380 | ||||||||
\(347\) | 2004.00 | 0.310030 | 0.155015 | − | 0.987912i | \(-0.450457\pi\) | ||||
0.155015 | + | 0.987912i | \(0.450457\pi\) | |||||||
\(348\) | −6080.00 | −0.936558 | ||||||||
\(349\) | −1330.00 | −0.203992 | −0.101996 | − | 0.994785i | \(-0.532523\pi\) | ||||
−0.101996 | + | 0.994785i | \(0.532523\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1440.00 | 0.218979 | ||||||||
\(352\) | 896.000 | 0.135673 | ||||||||
\(353\) | −978.000 | −0.147461 | −0.0737304 | − | 0.997278i | \(-0.523490\pi\) | ||||
−0.0737304 | + | 0.997278i | \(0.523490\pi\) | |||||||
\(354\) | 3200.00 | 0.480447 | ||||||||
\(355\) | 5488.00 | 0.820487 | ||||||||
\(356\) | −3240.00 | −0.482359 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 600.000 | 0.0885782 | ||||||||
\(359\) | −9680.00 | −1.42309 | −0.711547 | − | 0.702638i | \(-0.752005\pi\) | ||||
−0.711547 | + | 0.702638i | \(0.752005\pi\) | |||||||
\(360\) | −4144.00 | −0.606689 | ||||||||
\(361\) | −459.000 | −0.0669194 | ||||||||
\(362\) | −4716.00 | −0.684717 | ||||||||
\(363\) | 4376.00 | 0.632728 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7532.00 | −1.08012 | ||||||||
\(366\) | 3168.00 | 0.452443 | ||||||||
\(367\) | 8656.00 | 1.23117 | 0.615585 | − | 0.788070i | \(-0.288920\pi\) | ||||
0.615585 | + | 0.788070i | \(0.288920\pi\) | |||||||
\(368\) | −1792.00 | −0.253844 | ||||||||
\(369\) | −5994.00 | −0.845624 | ||||||||
\(370\) | 9688.00 | 1.36123 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2304.00 | 0.321121 | ||||||||
\(373\) | 5278.00 | 0.732666 | 0.366333 | − | 0.930484i | \(-0.380613\pi\) | ||||
0.366333 | + | 0.930484i | \(0.380613\pi\) | |||||||
\(374\) | −4144.00 | −0.572944 | ||||||||
\(375\) | 6048.00 | 0.832846 | ||||||||
\(376\) | 192.000 | 0.0263342 | ||||||||
\(377\) | −3420.00 | −0.467212 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6340.00 | 0.859272 | 0.429636 | − | 0.903002i | \(-0.358642\pi\) | ||||
0.429636 | + | 0.903002i | \(0.358642\pi\) | |||||||
\(380\) | −4480.00 | −0.604787 | ||||||||
\(381\) | −15552.0 | −2.09122 | ||||||||
\(382\) | −2784.00 | −0.372884 | ||||||||
\(383\) | 6232.00 | 0.831437 | 0.415718 | − | 0.909493i | \(-0.363530\pi\) | ||||
0.415718 | + | 0.909493i | \(0.363530\pi\) | |||||||
\(384\) | 1024.00 | 0.136083 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3556.00 | −0.468901 | ||||||||
\(387\) | −15244.0 | −2.00232 | ||||||||
\(388\) | −5416.00 | −0.708649 | ||||||||
\(389\) | −14810.0 | −1.93033 | −0.965163 | − | 0.261649i | \(-0.915734\pi\) | ||||
−0.965163 | + | 0.261649i | \(0.915734\pi\) | |||||||
\(390\) | −4032.00 | −0.523508 | ||||||||
\(391\) | 8288.00 | 1.07197 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6784.00 | −0.870757 | ||||||||
\(394\) | −2428.00 | −0.310459 | ||||||||
\(395\) | 3360.00 | 0.428000 | ||||||||
\(396\) | −4144.00 | −0.525868 | ||||||||
\(397\) | −5154.00 | −0.651566 | −0.325783 | − | 0.945445i | \(-0.605628\pi\) | ||||
−0.325783 | + | 0.945445i | \(0.605628\pi\) | |||||||
\(398\) | 2080.00 | 0.261962 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1136.00 | 0.142000 | ||||||||
\(401\) | 3282.00 | 0.408716 | 0.204358 | − | 0.978896i | \(-0.434489\pi\) | ||||
0.204358 | + | 0.978896i | \(0.434489\pi\) | |||||||
\(402\) | −11456.0 | −1.42133 | ||||||||
\(403\) | 1296.00 | 0.160194 | ||||||||
\(404\) | 5432.00 | 0.668941 | ||||||||
\(405\) | −5026.00 | −0.616652 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9688.00 | 1.17989 | ||||||||
\(408\) | −4736.00 | −0.574674 | ||||||||
\(409\) | −5810.00 | −0.702411 | −0.351205 | − | 0.936298i | \(-0.614228\pi\) | ||||
−0.351205 | + | 0.936298i | \(0.614228\pi\) | |||||||
\(410\) | 4536.00 | 0.546383 | ||||||||
\(411\) | 23728.0 | 2.84773 | ||||||||
\(412\) | 3328.00 | 0.397958 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8288.00 | 0.983896 | ||||||||
\(415\) | 15008.0 | 1.77521 | ||||||||
\(416\) | 576.000 | 0.0678864 | ||||||||
\(417\) | 22400.0 | 2.63053 | ||||||||
\(418\) | −4480.00 | −0.524220 | ||||||||
\(419\) | −13560.0 | −1.58102 | −0.790512 | − | 0.612446i | \(-0.790186\pi\) | ||||
−0.790512 | + | 0.612446i | \(0.790186\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −738.000 | −0.0854345 | −0.0427172 | − | 0.999087i | \(-0.513601\pi\) | ||||
−0.0427172 | + | 0.999087i | \(0.513601\pi\) | |||||||
\(422\) | 7736.00 | 0.892376 | ||||||||
\(423\) | −888.000 | −0.102071 | ||||||||
\(424\) | −2544.00 | −0.291386 | ||||||||
\(425\) | −5254.00 | −0.599662 | ||||||||
\(426\) | 6272.00 | 0.713332 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1776.00 | 0.200575 | ||||||||
\(429\) | −4032.00 | −0.453769 | ||||||||
\(430\) | 11536.0 | 1.29376 | ||||||||
\(431\) | 1272.00 | 0.142158 | 0.0710790 | − | 0.997471i | \(-0.477356\pi\) | ||||
0.0710790 | + | 0.997471i | \(0.477356\pi\) | |||||||
\(432\) | −1280.00 | −0.142556 | ||||||||
\(433\) | 5062.00 | 0.561811 | 0.280906 | − | 0.959735i | \(-0.409365\pi\) | ||||
0.280906 | + | 0.959735i | \(0.409365\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21280.0 | −2.34551 | ||||||||
\(436\) | 7480.00 | 0.821622 | ||||||||
\(437\) | 8960.00 | 0.980812 | ||||||||
\(438\) | −8608.00 | −0.939055 | ||||||||
\(439\) | −5640.00 | −0.613172 | −0.306586 | − | 0.951843i | \(-0.599187\pi\) | ||||
−0.306586 | + | 0.951843i | \(0.599187\pi\) | |||||||
\(440\) | 3136.00 | 0.339779 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2664.00 | −0.286682 | ||||||||
\(443\) | 13388.0 | 1.43585 | 0.717927 | − | 0.696119i | \(-0.245091\pi\) | ||||
0.717927 | + | 0.696119i | \(0.245091\pi\) | |||||||
\(444\) | 11072.0 | 1.18345 | ||||||||
\(445\) | −11340.0 | −1.20802 | ||||||||
\(446\) | 7936.00 | 0.842557 | ||||||||
\(447\) | −4080.00 | −0.431717 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3230.00 | −0.339495 | −0.169747 | − | 0.985488i | \(-0.554295\pi\) | ||||
−0.169747 | + | 0.985488i | \(0.554295\pi\) | |||||||
\(450\) | −5254.00 | −0.550391 | ||||||||
\(451\) | 4536.00 | 0.473596 | ||||||||
\(452\) | 5512.00 | 0.573590 | ||||||||
\(453\) | −4736.00 | −0.491207 | ||||||||
\(454\) | −7872.00 | −0.813769 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5120.00 | −0.525803 | ||||||||
\(457\) | −10646.0 | −1.08971 | −0.544857 | − | 0.838529i | \(-0.683416\pi\) | ||||
−0.544857 | + | 0.838529i | \(0.683416\pi\) | |||||||
\(458\) | 9620.00 | 0.981470 | ||||||||
\(459\) | 5920.00 | 0.602009 | ||||||||
\(460\) | −6272.00 | −0.635725 | ||||||||
\(461\) | −7282.00 | −0.735698 | −0.367849 | − | 0.929886i | \(-0.619906\pi\) | ||||
−0.367849 | + | 0.929886i | \(0.619906\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12688.0 | 1.27357 | 0.636783 | − | 0.771043i | \(-0.280265\pi\) | ||||
0.636783 | + | 0.771043i | \(0.280265\pi\) | |||||||
\(464\) | 3040.00 | 0.304156 | ||||||||
\(465\) | 8064.00 | 0.804213 | ||||||||
\(466\) | 4364.00 | 0.433816 | ||||||||
\(467\) | 2816.00 | 0.279034 | 0.139517 | − | 0.990220i | \(-0.455445\pi\) | ||||
0.139517 | + | 0.990220i | \(0.455445\pi\) | |||||||
\(468\) | −2664.00 | −0.263127 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 672.000 | 0.0659512 | ||||||||
\(471\) | −21488.0 | −2.10215 | ||||||||
\(472\) | −1600.00 | −0.156030 | ||||||||
\(473\) | 11536.0 | 1.12141 | ||||||||
\(474\) | 3840.00 | 0.372103 | ||||||||
\(475\) | −5680.00 | −0.548666 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11766.0 | 1.12941 | ||||||||
\(478\) | 6000.00 | 0.574129 | ||||||||
\(479\) | 3160.00 | 0.301428 | 0.150714 | − | 0.988577i | \(-0.451843\pi\) | ||||
0.150714 | + | 0.988577i | \(0.451843\pi\) | |||||||
\(480\) | 3584.00 | 0.340805 | ||||||||
\(481\) | 6228.00 | 0.590379 | ||||||||
\(482\) | 4084.00 | 0.385936 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2188.00 | −0.205485 | ||||||||
\(485\) | −18956.0 | −1.77474 | ||||||||
\(486\) | −10064.0 | −0.939326 | ||||||||
\(487\) | −14176.0 | −1.31905 | −0.659523 | − | 0.751684i | \(-0.729242\pi\) | ||||
−0.659523 | + | 0.751684i | \(0.729242\pi\) | |||||||
\(488\) | −1584.00 | −0.146935 | ||||||||
\(489\) | 8096.00 | 0.748699 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11268.0 | −1.03568 | −0.517839 | − | 0.855478i | \(-0.673263\pi\) | ||||
−0.517839 | + | 0.855478i | \(0.673263\pi\) | |||||||
\(492\) | 5184.00 | 0.475026 | ||||||||
\(493\) | −14060.0 | −1.28444 | ||||||||
\(494\) | −2880.00 | −0.262302 | ||||||||
\(495\) | −14504.0 | −1.31698 | ||||||||
\(496\) | −1152.00 | −0.104287 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 17152.0 | 1.54337 | ||||||||
\(499\) | −4460.00 | −0.400114 | −0.200057 | − | 0.979784i | \(-0.564113\pi\) | ||||
−0.200057 | + | 0.979784i | \(0.564113\pi\) | |||||||
\(500\) | −3024.00 | −0.270475 | ||||||||
\(501\) | 4352.00 | 0.388090 | ||||||||
\(502\) | −1056.00 | −0.0938876 | ||||||||
\(503\) | 1512.00 | 0.134029 | 0.0670147 | − | 0.997752i | \(-0.478653\pi\) | ||||
0.0670147 | + | 0.997752i | \(0.478653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19012.0 | 1.67529 | ||||||||
\(506\) | −6272.00 | −0.551036 | ||||||||
\(507\) | 14984.0 | 1.31255 | ||||||||
\(508\) | 7776.00 | 0.679142 | ||||||||
\(509\) | 11790.0 | 1.02668 | 0.513342 | − | 0.858184i | \(-0.328407\pi\) | ||||
0.513342 | + | 0.858184i | \(0.328407\pi\) | |||||||
\(510\) | −16576.0 | −1.43921 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 6400.00 | 0.550813 | ||||||||
\(514\) | 11268.0 | 0.966946 | ||||||||
\(515\) | 11648.0 | 0.996645 | ||||||||
\(516\) | 13184.0 | 1.12479 | ||||||||
\(517\) | 672.000 | 0.0571654 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14864.0 | 1.25714 | ||||||||
\(520\) | 2016.00 | 0.170014 | ||||||||
\(521\) | −1362.00 | −0.114530 | −0.0572652 | − | 0.998359i | \(-0.518238\pi\) | ||||
−0.0572652 | + | 0.998359i | \(0.518238\pi\) | |||||||
\(522\) | −14060.0 | −1.17891 | ||||||||
\(523\) | −6968.00 | −0.582580 | −0.291290 | − | 0.956635i | \(-0.594084\pi\) | ||||
−0.291290 | + | 0.956635i | \(0.594084\pi\) | |||||||
\(524\) | 3392.00 | 0.282787 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −336.000 | −0.0278523 | ||||||||
\(527\) | 5328.00 | 0.440401 | ||||||||
\(528\) | 3584.00 | 0.295405 | ||||||||
\(529\) | 377.000 | 0.0309855 | ||||||||
\(530\) | −8904.00 | −0.729745 | ||||||||
\(531\) | 7400.00 | 0.604770 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2916.00 | 0.236972 | ||||||||
\(534\) | −12960.0 | −1.05025 | ||||||||
\(535\) | 6216.00 | 0.502320 | ||||||||
\(536\) | 5728.00 | 0.461589 | ||||||||
\(537\) | 2400.00 | 0.192863 | ||||||||
\(538\) | −2620.00 | −0.209956 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4480.00 | −0.357016 | ||||||||
\(541\) | 7062.00 | 0.561218 | 0.280609 | − | 0.959822i | \(-0.409464\pi\) | ||||
0.280609 | + | 0.959822i | \(0.409464\pi\) | |||||||
\(542\) | −4416.00 | −0.349969 | ||||||||
\(543\) | −18864.0 | −1.49085 | ||||||||
\(544\) | 2368.00 | 0.186631 | ||||||||
\(545\) | 26180.0 | 2.05767 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8196.00 | −0.640650 | −0.320325 | − | 0.947308i | \(-0.603792\pi\) | ||||
−0.320325 | + | 0.947308i | \(0.603792\pi\) | |||||||
\(548\) | −11864.0 | −0.924827 | ||||||||
\(549\) | 7326.00 | 0.569519 | ||||||||
\(550\) | 3976.00 | 0.308249 | ||||||||
\(551\) | −15200.0 | −1.17521 | ||||||||
\(552\) | −7168.00 | −0.552700 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10588.0 | −0.811987 | ||||||||
\(555\) | 38752.0 | 2.96384 | ||||||||
\(556\) | −11200.0 | −0.854291 | ||||||||
\(557\) | −7466.00 | −0.567944 | −0.283972 | − | 0.958833i | \(-0.591652\pi\) | ||||
−0.283972 | + | 0.958833i | \(0.591652\pi\) | |||||||
\(558\) | 5328.00 | 0.404215 | ||||||||
\(559\) | 7416.00 | 0.561115 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16576.0 | −1.24749 | ||||||||
\(562\) | −6484.00 | −0.486674 | ||||||||
\(563\) | −24968.0 | −1.86905 | −0.934526 | − | 0.355896i | \(-0.884176\pi\) | ||||
−0.934526 | + | 0.355896i | \(0.884176\pi\) | |||||||
\(564\) | 768.000 | 0.0573380 | ||||||||
\(565\) | 19292.0 | 1.43650 | ||||||||
\(566\) | −3184.00 | −0.236455 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3136.00 | −0.231661 | ||||||||
\(569\) | 14250.0 | 1.04990 | 0.524948 | − | 0.851134i | \(-0.324085\pi\) | ||||
0.524948 | + | 0.851134i | \(0.324085\pi\) | |||||||
\(570\) | −17920.0 | −1.31682 | ||||||||
\(571\) | 6372.00 | 0.467005 | 0.233503 | − | 0.972356i | \(-0.424981\pi\) | ||||
0.233503 | + | 0.972356i | \(0.424981\pi\) | |||||||
\(572\) | 2016.00 | 0.147366 | ||||||||
\(573\) | −11136.0 | −0.811890 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7952.00 | −0.576733 | ||||||||
\(576\) | 2368.00 | 0.171296 | ||||||||
\(577\) | 8366.00 | 0.603607 | 0.301803 | − | 0.953370i | \(-0.402411\pi\) | ||||
0.301803 | + | 0.953370i | \(0.402411\pi\) | |||||||
\(578\) | −1126.00 | −0.0810301 | ||||||||
\(579\) | −14224.0 | −1.02095 | ||||||||
\(580\) | 10640.0 | 0.761728 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −21664.0 | −1.54296 | ||||||||
\(583\) | −8904.00 | −0.632532 | ||||||||
\(584\) | 4304.00 | 0.304967 | ||||||||
\(585\) | −9324.00 | −0.658974 | ||||||||
\(586\) | −10044.0 | −0.708044 | ||||||||
\(587\) | −20384.0 | −1.43328 | −0.716642 | − | 0.697441i | \(-0.754322\pi\) | ||||
−0.716642 | + | 0.697441i | \(0.754322\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5760.00 | 0.402948 | ||||||||
\(590\) | −5600.00 | −0.390760 | ||||||||
\(591\) | −9712.00 | −0.675970 | ||||||||
\(592\) | −5536.00 | −0.384338 | ||||||||
\(593\) | −9378.00 | −0.649424 | −0.324712 | − | 0.945813i | \(-0.605267\pi\) | ||||
−0.324712 | + | 0.945813i | \(0.605267\pi\) | |||||||
\(594\) | −4480.00 | −0.309456 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2040.00 | 0.140204 | ||||||||
\(597\) | 8320.00 | 0.570377 | ||||||||
\(598\) | −4032.00 | −0.275720 | ||||||||
\(599\) | −9000.00 | −0.613907 | −0.306953 | − | 0.951725i | \(-0.599310\pi\) | ||||
−0.306953 | + | 0.951725i | \(0.599310\pi\) | |||||||
\(600\) | 4544.00 | 0.309180 | ||||||||
\(601\) | −7562.00 | −0.513245 | −0.256623 | − | 0.966512i | \(-0.582610\pi\) | ||||
−0.256623 | + | 0.966512i | \(0.582610\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26492.0 | −1.78912 | ||||||||
\(604\) | 2368.00 | 0.159524 | ||||||||
\(605\) | −7658.00 | −0.514615 | ||||||||
\(606\) | 21728.0 | 1.45650 | ||||||||
\(607\) | 2976.00 | 0.198999 | 0.0994993 | − | 0.995038i | \(-0.468276\pi\) | ||||
0.0994993 | + | 0.995038i | \(0.468276\pi\) | |||||||
\(608\) | 2560.00 | 0.170759 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5544.00 | −0.367984 | ||||||||
\(611\) | 432.000 | 0.0286037 | ||||||||
\(612\) | −10952.0 | −0.723380 | ||||||||
\(613\) | 4278.00 | 0.281871 | 0.140935 | − | 0.990019i | \(-0.454989\pi\) | ||||
0.140935 | + | 0.990019i | \(0.454989\pi\) | |||||||
\(614\) | −19072.0 | −1.25356 | ||||||||
\(615\) | 18144.0 | 1.18965 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18794.0 | 1.22629 | 0.613143 | − | 0.789972i | \(-0.289905\pi\) | ||||
0.613143 | + | 0.789972i | \(0.289905\pi\) | |||||||
\(618\) | 13312.0 | 0.866484 | ||||||||
\(619\) | −18040.0 | −1.17139 | −0.585694 | − | 0.810532i | \(-0.699178\pi\) | ||||
−0.585694 | + | 0.810532i | \(0.699178\pi\) | |||||||
\(620\) | −4032.00 | −0.261176 | ||||||||
\(621\) | 8960.00 | 0.578989 | ||||||||
\(622\) | −1936.00 | −0.124801 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2304.00 | 0.147811 | ||||||||
\(625\) | −19459.0 | −1.24538 | ||||||||
\(626\) | 6116.00 | 0.390486 | ||||||||
\(627\) | −17920.0 | −1.14140 | ||||||||
\(628\) | 10744.0 | 0.682695 | ||||||||
\(629\) | 25604.0 | 1.62305 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21688.0 | −1.36828 | −0.684141 | − | 0.729350i | \(-0.739823\pi\) | ||||
−0.684141 | + | 0.729350i | \(0.739823\pi\) | |||||||
\(632\) | −1920.00 | −0.120844 | ||||||||
\(633\) | 30944.0 | 1.94299 | ||||||||
\(634\) | 9972.00 | 0.624667 | ||||||||
\(635\) | 27216.0 | 1.70084 | ||||||||
\(636\) | −10176.0 | −0.634441 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10640.0 | 0.660253 | ||||||||
\(639\) | 14504.0 | 0.897918 | ||||||||
\(640\) | −1792.00 | −0.110680 | ||||||||
\(641\) | −10558.0 | −0.650571 | −0.325285 | − | 0.945616i | \(-0.605460\pi\) | ||||
−0.325285 | + | 0.945616i | \(0.605460\pi\) | |||||||
\(642\) | 7104.00 | 0.436717 | ||||||||
\(643\) | 26152.0 | 1.60394 | 0.801971 | − | 0.597363i | \(-0.203785\pi\) | ||||
0.801971 | + | 0.597363i | \(0.203785\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 46144.0 | 2.81693 | ||||||||
\(646\) | −11840.0 | −0.721112 | ||||||||
\(647\) | −25584.0 | −1.55458 | −0.777288 | − | 0.629145i | \(-0.783405\pi\) | ||||
−0.777288 | + | 0.629145i | \(0.783405\pi\) | |||||||
\(648\) | 2872.00 | 0.174109 | ||||||||
\(649\) | −5600.00 | −0.338705 | ||||||||
\(650\) | 2556.00 | 0.154238 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4048.00 | −0.243147 | ||||||||
\(653\) | 15198.0 | 0.910787 | 0.455393 | − | 0.890290i | \(-0.349499\pi\) | ||||
0.455393 | + | 0.890290i | \(0.349499\pi\) | |||||||
\(654\) | 29920.0 | 1.78894 | ||||||||
\(655\) | 11872.0 | 0.708210 | ||||||||
\(656\) | −2592.00 | −0.154269 | ||||||||
\(657\) | −19906.0 | −1.18205 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6100.00 | −0.360580 | −0.180290 | − | 0.983613i | \(-0.557704\pi\) | ||||
−0.180290 | + | 0.983613i | \(0.557704\pi\) | |||||||
\(660\) | 12544.0 | 0.739810 | ||||||||
\(661\) | 2318.00 | 0.136399 | 0.0681995 | − | 0.997672i | \(-0.478275\pi\) | ||||
0.0681995 | + | 0.997672i | \(0.478275\pi\) | |||||||
\(662\) | −17224.0 | −1.01122 | ||||||||
\(663\) | −10656.0 | −0.624200 | ||||||||
\(664\) | −8576.00 | −0.501225 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 25604.0 | 1.48969 | ||||||||
\(667\) | −21280.0 | −1.23533 | ||||||||
\(668\) | −2176.00 | −0.126036 | ||||||||
\(669\) | 31744.0 | 1.83452 | ||||||||
\(670\) | 20048.0 | 1.15600 | ||||||||
\(671\) | −5544.00 | −0.318962 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10222.0 | −0.585482 | −0.292741 | − | 0.956192i | \(-0.594567\pi\) | ||||
−0.292741 | + | 0.956192i | \(0.594567\pi\) | |||||||
\(674\) | 20412.0 | 1.16653 | ||||||||
\(675\) | −5680.00 | −0.323886 | ||||||||
\(676\) | −7492.00 | −0.426263 | ||||||||
\(677\) | −25434.0 | −1.44388 | −0.721941 | − | 0.691955i | \(-0.756750\pi\) | ||||
−0.721941 | + | 0.691955i | \(0.756750\pi\) | |||||||
\(678\) | 22048.0 | 1.24889 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8288.00 | 0.467397 | ||||||||
\(681\) | −31488.0 | −1.77184 | ||||||||
\(682\) | −4032.00 | −0.226383 | ||||||||
\(683\) | −8532.00 | −0.477991 | −0.238996 | − | 0.971021i | \(-0.576818\pi\) | ||||
−0.238996 | + | 0.971021i | \(0.576818\pi\) | |||||||
\(684\) | −11840.0 | −0.661862 | ||||||||
\(685\) | −41524.0 | −2.31613 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 38480.0 | 2.13698 | ||||||||
\(688\) | −6592.00 | −0.365287 | ||||||||
\(689\) | −5724.00 | −0.316498 | ||||||||
\(690\) | −25088.0 | −1.38418 | ||||||||
\(691\) | −20672.0 | −1.13806 | −0.569030 | − | 0.822317i | \(-0.692681\pi\) | ||||
−0.569030 | + | 0.822317i | \(0.692681\pi\) | |||||||
\(692\) | −7432.00 | −0.408269 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4008.00 | −0.219224 | ||||||||
\(695\) | −39200.0 | −2.13948 | ||||||||
\(696\) | 12160.0 | 0.662247 | ||||||||
\(697\) | 11988.0 | 0.651475 | ||||||||
\(698\) | 2660.00 | 0.144244 | ||||||||
\(699\) | 17456.0 | 0.944559 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21458.0 | −1.15614 | −0.578072 | − | 0.815985i | \(-0.696195\pi\) | ||||
−0.578072 | + | 0.815985i | \(0.696195\pi\) | |||||||
\(702\) | −2880.00 | −0.154841 | ||||||||
\(703\) | 27680.0 | 1.48502 | ||||||||
\(704\) | −1792.00 | −0.0959354 | ||||||||
\(705\) | 2688.00 | 0.143597 | ||||||||
\(706\) | 1956.00 | 0.104271 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6400.00 | −0.339727 | ||||||||
\(709\) | −9850.00 | −0.521755 | −0.260878 | − | 0.965372i | \(-0.584012\pi\) | ||||
−0.260878 | + | 0.965372i | \(0.584012\pi\) | |||||||
\(710\) | −10976.0 | −0.580172 | ||||||||
\(711\) | 8880.00 | 0.468391 | ||||||||
\(712\) | 6480.00 | 0.341079 | ||||||||
\(713\) | 8064.00 | 0.423561 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7056.00 | 0.369062 | ||||||||
\(716\) | −1200.00 | −0.0626342 | ||||||||
\(717\) | 24000.0 | 1.25006 | ||||||||
\(718\) | 19360.0 | 1.00628 | ||||||||
\(719\) | 18840.0 | 0.977209 | 0.488605 | − | 0.872505i | \(-0.337506\pi\) | ||||
0.488605 | + | 0.872505i | \(0.337506\pi\) | |||||||
\(720\) | 8288.00 | 0.428994 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 918.000 | 0.0473191 | ||||||||
\(723\) | 16336.0 | 0.840308 | ||||||||
\(724\) | 9432.00 | 0.484168 | ||||||||
\(725\) | 13490.0 | 0.691043 | ||||||||
\(726\) | −8752.00 | −0.447407 | ||||||||
\(727\) | −37504.0 | −1.91327 | −0.956634 | − | 0.291291i | \(-0.905915\pi\) | ||||
−0.956634 | + | 0.291291i | \(0.905915\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −30563.0 | −1.55276 | ||||||||
\(730\) | 15064.0 | 0.763758 | ||||||||
\(731\) | 30488.0 | 1.54260 | ||||||||
\(732\) | −6336.00 | −0.319925 | ||||||||
\(733\) | −13338.0 | −0.672101 | −0.336051 | − | 0.941844i | \(-0.609091\pi\) | ||||
−0.336051 | + | 0.941844i | \(0.609091\pi\) | |||||||
\(734\) | −17312.0 | −0.870569 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3584.00 | 0.179495 | ||||||||
\(737\) | 20048.0 | 1.00200 | ||||||||
\(738\) | 11988.0 | 0.597946 | ||||||||
\(739\) | 17100.0 | 0.851196 | 0.425598 | − | 0.904912i | \(-0.360064\pi\) | ||||
0.425598 | + | 0.904912i | \(0.360064\pi\) | |||||||
\(740\) | −19376.0 | −0.962535 | ||||||||
\(741\) | −11520.0 | −0.571117 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19632.0 | −0.969352 | −0.484676 | − | 0.874694i | \(-0.661062\pi\) | ||||
−0.484676 | + | 0.874694i | \(0.661062\pi\) | |||||||
\(744\) | −4608.00 | −0.227067 | ||||||||
\(745\) | 7140.00 | 0.351127 | ||||||||
\(746\) | −10556.0 | −0.518073 | ||||||||
\(747\) | 39664.0 | 1.94274 | ||||||||
\(748\) | 8288.00 | 0.405133 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −12096.0 | −0.588911 | ||||||||
\(751\) | 33912.0 | 1.64776 | 0.823879 | − | 0.566766i | \(-0.191805\pi\) | ||||
0.823879 | + | 0.566766i | \(0.191805\pi\) | |||||||
\(752\) | −384.000 | −0.0186211 | ||||||||
\(753\) | −4224.00 | −0.204424 | ||||||||
\(754\) | 6840.00 | 0.330369 | ||||||||
\(755\) | 8288.00 | 0.399512 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31386.0 | −1.50693 | −0.753463 | − | 0.657490i | \(-0.771618\pi\) | ||||
−0.753463 | + | 0.657490i | \(0.771618\pi\) | |||||||
\(758\) | −12680.0 | −0.607597 | ||||||||
\(759\) | −25088.0 | −1.19978 | ||||||||
\(760\) | 8960.00 | 0.427649 | ||||||||
\(761\) | 34558.0 | 1.64616 | 0.823079 | − | 0.567927i | \(-0.192254\pi\) | ||||
0.823079 | + | 0.567927i | \(0.192254\pi\) | |||||||
\(762\) | 31104.0 | 1.47871 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5568.00 | 0.263669 | ||||||||
\(765\) | −38332.0 | −1.81163 | ||||||||
\(766\) | −12464.0 | −0.587915 | ||||||||
\(767\) | −3600.00 | −0.169476 | ||||||||
\(768\) | −2048.00 | −0.0962250 | ||||||||
\(769\) | −39130.0 | −1.83493 | −0.917467 | − | 0.397812i | \(-0.869769\pi\) | ||||
−0.917467 | + | 0.397812i | \(0.869769\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 45072.0 | 2.10535 | ||||||||
\(772\) | 7112.00 | 0.331563 | ||||||||
\(773\) | 25982.0 | 1.20894 | 0.604468 | − | 0.796629i | \(-0.293386\pi\) | ||||
0.604468 | + | 0.796629i | \(0.293386\pi\) | |||||||
\(774\) | 30488.0 | 1.41585 | ||||||||
\(775\) | −5112.00 | −0.236940 | ||||||||
\(776\) | 10832.0 | 0.501090 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 29620.0 | 1.36495 | ||||||||
\(779\) | 12960.0 | 0.596072 | ||||||||
\(780\) | 8064.00 | 0.370176 | ||||||||
\(781\) | −10976.0 | −0.502884 | ||||||||
\(782\) | −16576.0 | −0.758001 | ||||||||
\(783\) | −15200.0 | −0.693747 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 37604.0 | 1.70974 | ||||||||
\(786\) | 13568.0 | 0.615718 | ||||||||
\(787\) | −35424.0 | −1.60448 | −0.802242 | − | 0.596999i | \(-0.796360\pi\) | ||||
−0.802242 | + | 0.596999i | \(0.796360\pi\) | |||||||
\(788\) | 4856.00 | 0.219528 | ||||||||
\(789\) | −1344.00 | −0.0606434 | ||||||||
\(790\) | −6720.00 | −0.302642 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8288.00 | 0.371845 | ||||||||
\(793\) | −3564.00 | −0.159598 | ||||||||
\(794\) | 10308.0 | 0.460727 | ||||||||
\(795\) | −35616.0 | −1.58889 | ||||||||
\(796\) | −4160.00 | −0.185235 | ||||||||
\(797\) | 30606.0 | 1.36025 | 0.680126 | − | 0.733096i | \(-0.261925\pi\) | ||||
0.680126 | + | 0.733096i | \(0.261925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1776.00 | 0.0786362 | ||||||||
\(800\) | −2272.00 | −0.100409 | ||||||||
\(801\) | −29970.0 | −1.32202 | ||||||||
\(802\) | −6564.00 | −0.289006 | ||||||||
\(803\) | 15064.0 | 0.662014 | ||||||||
\(804\) | 22912.0 | 1.00503 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2592.00 | −0.113275 | ||||||||
\(807\) | −10480.0 | −0.457142 | ||||||||
\(808\) | −10864.0 | −0.473013 | ||||||||
\(809\) | 16810.0 | 0.730542 | 0.365271 | − | 0.930901i | \(-0.380976\pi\) | ||||
0.365271 | + | 0.930901i | \(0.380976\pi\) | |||||||
\(810\) | 10052.0 | 0.436039 | ||||||||
\(811\) | 9368.00 | 0.405616 | 0.202808 | − | 0.979218i | \(-0.434993\pi\) | ||||
0.202808 | + | 0.979218i | \(0.434993\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17664.0 | −0.761997 | ||||||||
\(814\) | −19376.0 | −0.834310 | ||||||||
\(815\) | −14168.0 | −0.608937 | ||||||||
\(816\) | 9472.00 | 0.406356 | ||||||||
\(817\) | 32960.0 | 1.41141 | ||||||||
\(818\) | 11620.0 | 0.496679 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9072.00 | −0.386351 | ||||||||
\(821\) | 34382.0 | 1.46156 | 0.730780 | − | 0.682614i | \(-0.239157\pi\) | ||||
0.730780 | + | 0.682614i | \(0.239157\pi\) | |||||||
\(822\) | −47456.0 | −2.01365 | ||||||||
\(823\) | −4472.00 | −0.189410 | −0.0947048 | − | 0.995505i | \(-0.530191\pi\) | ||||
−0.0947048 | + | 0.995505i | \(0.530191\pi\) | |||||||
\(824\) | −6656.00 | −0.281399 | ||||||||
\(825\) | 15904.0 | 0.671159 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1716.00 | −0.0721538 | −0.0360769 | − | 0.999349i | \(-0.511486\pi\) | ||||
−0.0360769 | + | 0.999349i | \(0.511486\pi\) | |||||||
\(828\) | −16576.0 | −0.695720 | ||||||||
\(829\) | 7910.00 | 0.331394 | 0.165697 | − | 0.986177i | \(-0.447013\pi\) | ||||
0.165697 | + | 0.986177i | \(0.447013\pi\) | |||||||
\(830\) | −30016.0 | −1.25527 | ||||||||
\(831\) | −42352.0 | −1.76796 | ||||||||
\(832\) | −1152.00 | −0.0480029 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −44800.0 | −1.86007 | ||||||||
\(835\) | −7616.00 | −0.315644 | ||||||||
\(836\) | 8960.00 | 0.370680 | ||||||||
\(837\) | 5760.00 | 0.237867 | ||||||||
\(838\) | 27120.0 | 1.11795 | ||||||||
\(839\) | 19360.0 | 0.796641 | 0.398320 | − | 0.917246i | \(-0.369593\pi\) | ||||
0.398320 | + | 0.917246i | \(0.369593\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11711.0 | 0.480175 | ||||||||
\(842\) | 1476.00 | 0.0604113 | ||||||||
\(843\) | −25936.0 | −1.05965 | ||||||||
\(844\) | −15472.0 | −0.631005 | ||||||||
\(845\) | −26222.0 | −1.06753 | ||||||||
\(846\) | 1776.00 | 0.0721751 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5088.00 | 0.206041 | ||||||||
\(849\) | −12736.0 | −0.514839 | ||||||||
\(850\) | 10508.0 | 0.424025 | ||||||||
\(851\) | 38752.0 | 1.56099 | ||||||||
\(852\) | −12544.0 | −0.504402 | ||||||||
\(853\) | −698.000 | −0.0280177 | −0.0140088 | − | 0.999902i | \(-0.504459\pi\) | ||||
−0.0140088 | + | 0.999902i | \(0.504459\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −41440.0 | −1.65757 | ||||||||
\(856\) | −3552.00 | −0.141828 | ||||||||
\(857\) | 23406.0 | 0.932945 | 0.466472 | − | 0.884536i | \(-0.345525\pi\) | ||||
0.466472 | + | 0.884536i | \(0.345525\pi\) | |||||||
\(858\) | 8064.00 | 0.320863 | ||||||||
\(859\) | −7280.00 | −0.289162 | −0.144581 | − | 0.989493i | \(-0.546183\pi\) | ||||
−0.144581 | + | 0.989493i | \(0.546183\pi\) | |||||||
\(860\) | −23072.0 | −0.914824 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2544.00 | −0.100521 | ||||||||
\(863\) | 9808.00 | 0.386869 | 0.193435 | − | 0.981113i | \(-0.438037\pi\) | ||||
0.193435 | + | 0.981113i | \(0.438037\pi\) | |||||||
\(864\) | 2560.00 | 0.100802 | ||||||||
\(865\) | −26012.0 | −1.02247 | ||||||||
\(866\) | −10124.0 | −0.397260 | ||||||||
\(867\) | −4504.00 | −0.176429 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6720.00 | −0.262325 | ||||||||
\(870\) | 42560.0 | 1.65853 | ||||||||
\(871\) | 12888.0 | 0.501370 | ||||||||
\(872\) | −14960.0 | −0.580974 | ||||||||
\(873\) | −50098.0 | −1.94222 | ||||||||
\(874\) | −17920.0 | −0.693539 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 17216.0 | 0.664012 | ||||||||
\(877\) | −8066.00 | −0.310570 | −0.155285 | − | 0.987870i | \(-0.549630\pi\) | ||||
−0.155285 | + | 0.987870i | \(0.549630\pi\) | |||||||
\(878\) | 11280.0 | 0.433578 | ||||||||
\(879\) | −40176.0 | −1.54164 | ||||||||
\(880\) | −6272.00 | −0.240260 | ||||||||
\(881\) | −25842.0 | −0.988240 | −0.494120 | − | 0.869394i | \(-0.664510\pi\) | ||||
−0.494120 | + | 0.869394i | \(0.664510\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5692.00 | −0.216932 | −0.108466 | − | 0.994100i | \(-0.534594\pi\) | ||||
−0.108466 | + | 0.994100i | \(0.534594\pi\) | |||||||
\(884\) | 5328.00 | 0.202715 | ||||||||
\(885\) | −22400.0 | −0.850811 | ||||||||
\(886\) | −26776.0 | −1.01530 | ||||||||
\(887\) | 13536.0 | 0.512395 | 0.256198 | − | 0.966624i | \(-0.417530\pi\) | ||||
0.256198 | + | 0.966624i | \(0.417530\pi\) | |||||||
\(888\) | −22144.0 | −0.836829 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 22680.0 | 0.854197 | ||||||||
\(891\) | 10052.0 | 0.377951 | ||||||||
\(892\) | −15872.0 | −0.595778 | ||||||||
\(893\) | 1920.00 | 0.0719489 | ||||||||
\(894\) | 8160.00 | 0.305270 | ||||||||
\(895\) | −4200.00 | −0.156861 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16128.0 | −0.600332 | ||||||||
\(898\) | 6460.00 | 0.240059 | ||||||||
\(899\) | −13680.0 | −0.507512 | ||||||||
\(900\) | 10508.0 | 0.389185 | ||||||||
\(901\) | −23532.0 | −0.870105 | ||||||||
\(902\) | −9072.00 | −0.334883 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11024.0 | −0.405589 | ||||||||
\(905\) | 33012.0 | 1.21255 | ||||||||
\(906\) | 9472.00 | 0.347336 | ||||||||
\(907\) | 17004.0 | 0.622501 | 0.311251 | − | 0.950328i | \(-0.399252\pi\) | ||||
0.311251 | + | 0.950328i | \(0.399252\pi\) | |||||||
\(908\) | 15744.0 | 0.575422 | ||||||||
\(909\) | 50246.0 | 1.83339 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14568.0 | −0.529813 | −0.264906 | − | 0.964274i | \(-0.585341\pi\) | ||||
−0.264906 | + | 0.964274i | \(0.585341\pi\) | |||||||
\(912\) | 10240.0 | 0.371799 | ||||||||
\(913\) | −30016.0 | −1.08804 | ||||||||
\(914\) | 21292.0 | 0.770544 | ||||||||
\(915\) | −22176.0 | −0.801220 | ||||||||
\(916\) | −19240.0 | −0.694004 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −11840.0 | −0.425684 | ||||||||
\(919\) | −1400.00 | −0.0502522 | −0.0251261 | − | 0.999684i | \(-0.507999\pi\) | ||||
−0.0251261 | + | 0.999684i | \(0.507999\pi\) | |||||||
\(920\) | 12544.0 | 0.449525 | ||||||||
\(921\) | −76288.0 | −2.72940 | ||||||||
\(922\) | 14564.0 | 0.520217 | ||||||||
\(923\) | −7056.00 | −0.251626 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24566.0 | −0.873216 | ||||||||
\(926\) | −25376.0 | −0.900548 | ||||||||
\(927\) | 30784.0 | 1.09070 | ||||||||
\(928\) | −6080.00 | −0.215071 | ||||||||
\(929\) | 13830.0 | 0.488426 | 0.244213 | − | 0.969722i | \(-0.421470\pi\) | ||||
0.244213 | + | 0.969722i | \(0.421470\pi\) | |||||||
\(930\) | −16128.0 | −0.568664 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8728.00 | −0.306754 | ||||||||
\(933\) | −7744.00 | −0.271733 | ||||||||
\(934\) | −5632.00 | −0.197307 | ||||||||
\(935\) | 29008.0 | 1.01461 | ||||||||
\(936\) | 5328.00 | 0.186059 | ||||||||
\(937\) | 24166.0 | 0.842549 | 0.421275 | − | 0.906933i | \(-0.361583\pi\) | ||||
0.421275 | + | 0.906933i | \(0.361583\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24464.0 | 0.850216 | ||||||||
\(940\) | −1344.00 | −0.0466345 | ||||||||
\(941\) | 10838.0 | 0.375461 | 0.187730 | − | 0.982221i | \(-0.439887\pi\) | ||||
0.187730 | + | 0.982221i | \(0.439887\pi\) | |||||||
\(942\) | 42976.0 | 1.48645 | ||||||||
\(943\) | 18144.0 | 0.626564 | ||||||||
\(944\) | 3200.00 | 0.110330 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23072.0 | −0.792955 | ||||||||
\(947\) | −40916.0 | −1.40400 | −0.702002 | − | 0.712175i | \(-0.747710\pi\) | ||||
−0.702002 | + | 0.712175i | \(0.747710\pi\) | |||||||
\(948\) | −7680.00 | −0.263117 | ||||||||
\(949\) | 9684.00 | 0.331250 | ||||||||
\(950\) | 11360.0 | 0.387965 | ||||||||
\(951\) | 39888.0 | 1.36010 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56618.0 | 1.92449 | 0.962244 | − | 0.272189i | \(-0.0877475\pi\) | ||||
0.962244 | + | 0.272189i | \(0.0877475\pi\) | |||||||
\(954\) | −23532.0 | −0.798613 | ||||||||
\(955\) | 19488.0 | 0.660332 | ||||||||
\(956\) | −12000.0 | −0.405970 | ||||||||
\(957\) | 42560.0 | 1.43759 | ||||||||
\(958\) | −6320.00 | −0.213142 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −7168.00 | −0.240986 | ||||||||
\(961\) | −24607.0 | −0.825988 | ||||||||
\(962\) | −12456.0 | −0.417461 | ||||||||
\(963\) | 16428.0 | 0.549725 | ||||||||
\(964\) | −8168.00 | −0.272898 | ||||||||
\(965\) | 24892.0 | 0.830365 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17504.0 | 0.582100 | 0.291050 | − | 0.956708i | \(-0.405995\pi\) | ||||
0.291050 | + | 0.956708i | \(0.405995\pi\) | |||||||
\(968\) | 4376.00 | 0.145300 | ||||||||
\(969\) | −47360.0 | −1.57010 | ||||||||
\(970\) | 37912.0 | 1.25493 | ||||||||
\(971\) | −23112.0 | −0.763851 | −0.381926 | − | 0.924193i | \(-0.624739\pi\) | ||||
−0.381926 | + | 0.924193i | \(0.624739\pi\) | |||||||
\(972\) | 20128.0 | 0.664204 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 28352.0 | 0.932707 | ||||||||
\(975\) | 10224.0 | 0.335826 | ||||||||
\(976\) | 3168.00 | 0.103899 | ||||||||
\(977\) | 23874.0 | 0.781778 | 0.390889 | − | 0.920438i | \(-0.372168\pi\) | ||||
0.390889 | + | 0.920438i | \(0.372168\pi\) | |||||||
\(978\) | −16192.0 | −0.529410 | ||||||||
\(979\) | 22680.0 | 0.740404 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 69190.0 | 2.25185 | ||||||||
\(982\) | 22536.0 | 0.732335 | ||||||||
\(983\) | 15312.0 | 0.496823 | 0.248411 | − | 0.968655i | \(-0.420091\pi\) | ||||
0.248411 | + | 0.968655i | \(0.420091\pi\) | |||||||
\(984\) | −10368.0 | −0.335894 | ||||||||
\(985\) | 16996.0 | 0.549784 | ||||||||
\(986\) | 28120.0 | 0.908239 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5760.00 | 0.185476 | ||||||||
\(989\) | 46144.0 | 1.48361 | ||||||||
\(990\) | 29008.0 | 0.931247 | ||||||||
\(991\) | −16528.0 | −0.529797 | −0.264899 | − | 0.964276i | \(-0.585339\pi\) | ||||
−0.264899 | + | 0.964276i | \(0.585339\pi\) | |||||||
\(992\) | 2304.00 | 0.0737420 | ||||||||
\(993\) | −68896.0 | −2.20176 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14560.0 | −0.463903 | ||||||||
\(996\) | −34304.0 | −1.09133 | ||||||||
\(997\) | 28606.0 | 0.908687 | 0.454344 | − | 0.890827i | \(-0.349874\pi\) | ||||
0.454344 | + | 0.890827i | \(0.349874\pi\) | |||||||
\(998\) | 8920.00 | 0.282924 | ||||||||
\(999\) | 27680.0 | 0.876633 |
(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 | 98.4.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 882.4.a.i.1.1 | 1 | |||
4.3 | odd | 2 | 784.4.a.s.1.1 | 1 | |||
5.4 | even | 2 | 2450.4.a.bo.1.1 | 1 | |||
7.2 | even | 3 | 98.4.c.f.67.1 | 2 | |||
7.3 | odd | 6 | 98.4.c.d.79.1 | 2 | |||
7.4 | even | 3 | 98.4.c.f.79.1 | 2 | |||
7.5 | odd | 6 | 98.4.c.d.67.1 | 2 | |||
7.6 | odd | 2 | 14.4.a.a.1.1 | ✓ | 1 | ||
21.2 | odd | 6 | 882.4.g.k.361.1 | 2 | |||
21.5 | even | 6 | 882.4.g.b.361.1 | 2 | |||
21.11 | odd | 6 | 882.4.g.k.667.1 | 2 | |||
21.17 | even | 6 | 882.4.g.b.667.1 | 2 | |||
21.20 | even | 2 | 126.4.a.h.1.1 | 1 | |||
28.27 | even | 2 | 112.4.a.a.1.1 | 1 | |||
35.13 | even | 4 | 350.4.c.b.99.2 | 2 | |||
35.27 | even | 4 | 350.4.c.b.99.1 | 2 | |||
35.34 | odd | 2 | 350.4.a.l.1.1 | 1 | |||
56.13 | odd | 2 | 448.4.a.b.1.1 | 1 | |||
56.27 | even | 2 | 448.4.a.o.1.1 | 1 | |||
77.76 | even | 2 | 1694.4.a.g.1.1 | 1 | |||
84.83 | odd | 2 | 1008.4.a.s.1.1 | 1 | |||
91.90 | odd | 2 | 2366.4.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.4.a.a.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
98.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
98.4.c.d.67.1 | 2 | 7.5 | odd | 6 | |||
98.4.c.d.79.1 | 2 | 7.3 | odd | 6 | |||
98.4.c.f.67.1 | 2 | 7.2 | even | 3 | |||
98.4.c.f.79.1 | 2 | 7.4 | even | 3 | |||
112.4.a.a.1.1 | 1 | 28.27 | even | 2 | |||
126.4.a.h.1.1 | 1 | 21.20 | even | 2 | |||
350.4.a.l.1.1 | 1 | 35.34 | odd | 2 | |||
350.4.c.b.99.1 | 2 | 35.27 | even | 4 | |||
350.4.c.b.99.2 | 2 | 35.13 | even | 4 | |||
448.4.a.b.1.1 | 1 | 56.13 | odd | 2 | |||
448.4.a.o.1.1 | 1 | 56.27 | even | 2 | |||
784.4.a.s.1.1 | 1 | 4.3 | odd | 2 | |||
882.4.a.i.1.1 | 1 | 3.2 | odd | 2 | |||
882.4.g.b.361.1 | 2 | 21.5 | even | 6 | |||
882.4.g.b.667.1 | 2 | 21.17 | even | 6 | |||
882.4.g.k.361.1 | 2 | 21.2 | odd | 6 | |||
882.4.g.k.667.1 | 2 | 21.11 | odd | 6 | |||
1008.4.a.s.1.1 | 1 | 84.83 | odd | 2 | |||
1694.4.a.g.1.1 | 1 | 77.76 | even | 2 | |||
2366.4.a.h.1.1 | 1 | 91.90 | odd | 2 | |||
2450.4.a.bo.1.1 | 1 | 5.4 | even | 2 |