Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,4,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, 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("448.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(26.4328556826\) |
Analytic rank: | \(0\) |
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 | \(\chi\) | \(=\) | 448.1 |
$q$-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 | ||||||||
\(3\) | −8.00000 | −1.53960 | −0.769800 | − | 0.638285i | \(-0.779644\pi\) | ||||
−0.769800 | + | 0.638285i | \(0.779644\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.0000 | 1.25220 | 0.626099 | − | 0.779744i | \(-0.284651\pi\) | ||||
0.626099 | + | 0.779744i | \(0.284651\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 37.0000 | 1.37037 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 28.0000 | 0.767483 | 0.383742 | − | 0.923440i | \(-0.374635\pi\) | ||||
0.383742 | + | 0.923440i | \(0.374635\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −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 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 74.0000 | 1.05574 | 0.527872 | − | 0.849324i | \(-0.322990\pi\) | ||||
0.527872 | + | 0.849324i | \(0.322990\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −80.0000 | −0.965961 | −0.482980 | − | 0.875631i | \(-0.660446\pi\) | ||||
−0.482980 | + | 0.875631i | \(0.660446\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 56.0000 | 0.581914 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −112.000 | −1.01537 | −0.507687 | − | 0.861541i | \(-0.669499\pi\) | ||||
−0.507687 | + | 0.861541i | \(0.669499\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 71.0000 | 0.568000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −80.0000 | −0.570222 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −190.000 | −1.21662 | −0.608312 | − | 0.793698i | \(-0.708153\pi\) | ||||
−0.608312 | + | 0.793698i | \(0.708153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 72.0000 | 0.417148 | 0.208574 | − | 0.978007i | \(-0.433118\pi\) | ||||
0.208574 | + | 0.978007i | \(0.433118\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −224.000 | −1.18162 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −98.0000 | −0.473286 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 346.000 | 1.53735 | 0.768676 | − | 0.639638i | \(-0.220916\pi\) | ||||
0.768676 | + | 0.639638i | \(0.220916\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 144.000 | 0.591242 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 162.000 | 0.617077 | 0.308538 | − | 0.951212i | \(-0.400160\pi\) | ||||
0.308538 | + | 0.951212i | \(0.400160\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 412.000 | 1.46115 | 0.730575 | − | 0.682833i | \(-0.239252\pi\) | ||||
0.730575 | + | 0.682833i | \(0.239252\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 518.000 | 1.71598 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 24.0000 | 0.0744843 | 0.0372421 | − | 0.999306i | \(-0.488143\pi\) | ||||
0.0372421 | + | 0.999306i | \(0.488143\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −592.000 | −1.62542 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −318.000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 392.000 | 0.961041 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 640.000 | 1.48719 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 200.000 | 0.441318 | 0.220659 | − | 0.975351i | \(-0.429179\pi\) | ||||
0.220659 | + | 0.975351i | \(0.429179\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 198.000 | 0.415595 | 0.207798 | − | 0.978172i | \(-0.433370\pi\) | ||||
0.207798 | + | 0.978172i | \(0.433370\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −259.000 | −0.517951 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −252.000 | −0.480873 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 716.000 | 1.30557 | 0.652786 | − | 0.757542i | \(-0.273600\pi\) | ||||
0.652786 | + | 0.757542i | \(0.273600\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 896.000 | 1.56327 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 392.000 | 0.655237 | 0.327619 | − | 0.944810i | \(-0.393754\pi\) | ||||
0.327619 | + | 0.944810i | \(0.393754\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 538.000 | 0.862577 | 0.431289 | − | 0.902214i | \(-0.358059\pi\) | ||||
0.431289 | + | 0.902214i | \(0.358059\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −568.000 | −0.874493 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −196.000 | −0.290081 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 240.000 | 0.341799 | 0.170899 | − | 0.985288i | \(-0.445333\pi\) | ||||
0.170899 | + | 0.985288i | \(0.445333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −359.000 | −0.492455 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 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 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1520.00 | 1.87312 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 810.000 | 0.964717 | 0.482359 | − | 0.875974i | \(-0.339780\pi\) | ||||
0.482359 | + | 0.875974i | \(0.339780\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 126.000 | 0.145147 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −576.000 | −0.642241 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1120.00 | −1.20957 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1354.00 | 1.41730 | 0.708649 | − | 0.705561i | \(-0.249305\pi\) | ||||
0.708649 | + | 0.705561i | \(0.249305\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1036.00 | 1.05174 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1358.00 | 1.33788 | 0.668941 | − | 0.743316i | \(-0.266748\pi\) | ||||
0.668941 | + | 0.743316i | \(0.266748\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −832.000 | −0.795916 | −0.397958 | − | 0.917404i | \(-0.630281\pi\) | ||||
−0.397958 | + | 0.917404i | \(0.630281\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 784.000 | 0.728672 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −444.000 | −0.401150 | −0.200575 | − | 0.979678i | \(-0.564281\pi\) | ||||
−0.200575 | + | 0.979678i | \(0.564281\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1870.00 | −1.64324 | −0.821622 | − | 0.570033i | \(-0.806930\pi\) | ||||
−0.821622 | + | 0.570033i | \(0.806930\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2768.00 | −2.36691 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1378.00 | 1.14718 | 0.573590 | − | 0.819143i | \(-0.305550\pi\) | ||||
0.573590 | + | 0.819143i | \(0.305550\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1568.00 | −1.27145 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −666.000 | −0.526254 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −518.000 | −0.399033 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −547.000 | −0.410969 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1296.00 | −0.950052 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −756.000 | −0.540950 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1944.00 | 1.35828 | 0.679142 | − | 0.734007i | \(-0.262352\pi\) | ||||
0.679142 | + | 0.734007i | \(0.262352\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3296.00 | −2.24959 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 848.000 | 0.565573 | 0.282787 | − | 0.959183i | \(-0.408741\pi\) | ||||
0.282787 | + | 0.959183i | \(0.408741\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 560.000 | 0.365099 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1120.00 | −0.714031 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2966.00 | −1.84965 | −0.924827 | − | 0.380389i | \(-0.875790\pi\) | ||||
−0.924827 | + | 0.380389i | \(0.875790\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −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 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −504.000 | −0.294731 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2660.00 | −1.52346 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −392.000 | −0.219943 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −510.000 | −0.280408 | −0.140204 | − | 0.990123i | \(-0.544776\pi\) | ||||
−0.140204 | + | 0.990123i | \(0.544776\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 592.000 | 0.319048 | 0.159524 | − | 0.987194i | \(-0.449004\pi\) | ||||
0.159524 | + | 0.987194i | \(0.449004\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2738.00 | 1.44676 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1008.00 | 0.522352 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2686.00 | 1.36539 | 0.682695 | − | 0.730704i | \(-0.260808\pi\) | ||||
0.682695 | + | 0.730704i | \(0.260808\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2544.00 | 1.26888 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 784.000 | 0.383776 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1012.00 | 0.486294 | 0.243147 | − | 0.969989i | \(-0.421820\pi\) | ||||
0.243147 | + | 0.969989i | \(0.421820\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3136.00 | −1.47962 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 544.000 | 0.252072 | 0.126036 | − | 0.992026i | \(-0.459775\pi\) | ||||
0.126036 | + | 0.992026i | \(0.459775\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1873.00 | −0.852526 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2960.00 | −1.32372 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1858.00 | −0.816538 | −0.408269 | − | 0.912862i | \(-0.633868\pi\) | ||||
−0.408269 | + | 0.912862i | \(0.633868\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −497.000 | −0.214684 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1600.00 | −0.679454 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 300.000 | 0.125268 | 0.0626342 | − | 0.998037i | \(-0.480050\pi\) | ||||
0.0626342 | + | 0.998037i | \(0.480050\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 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 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4844.00 | 1.92507 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2072.00 | 0.810265 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 560.000 | 0.215524 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1392.00 | 0.527338 | 0.263669 | − | 0.964613i | \(-0.415067\pi\) | ||||
0.263669 | + | 0.964613i | \(0.415067\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1778.00 | 0.663126 | 0.331563 | − | 0.943433i | \(-0.392424\pi\) | ||||
0.331563 | + | 0.943433i | \(0.392424\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2016.00 | 0.740353 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1214.00 | −0.439055 | −0.219528 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219528 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1040.00 | 0.370471 | 0.185235 | − | 0.982694i | \(-0.440695\pi\) | ||||
0.185235 | + | 0.982694i | \(0.440695\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5728.00 | −2.01006 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1330.00 | 0.459841 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2268.00 | 0.772702 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4144.00 | −1.39144 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2240.00 | −0.741359 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3868.00 | 1.26201 | 0.631005 | − | 0.775779i | \(-0.282643\pi\) | ||||
0.631005 | + | 0.775779i | \(0.282643\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3136.00 | −1.00880 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5768.00 | 1.82965 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −504.000 | −0.157667 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4304.00 | −1.32802 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1332.00 | −0.405430 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3968.00 | 1.19156 | 0.595778 | − | 0.803149i | \(-0.296844\pi\) | ||||
0.595778 | + | 0.803149i | \(0.296844\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2627.00 | 0.778370 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3936.00 | 1.15084 | 0.575422 | − | 0.817857i | \(-0.304838\pi\) | ||||
0.575422 | + | 0.817857i | \(0.304838\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4810.00 | −1.38801 | −0.694004 | − | 0.719971i | \(-0.744155\pi\) | ||||
−0.694004 | + | 0.719971i | \(0.744155\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1568.00 | 0.446610 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2182.00 | −0.613509 | −0.306754 | − | 0.951789i | \(-0.599243\pi\) | ||||
−0.306754 | + | 0.951789i | \(0.599243\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 336.000 | 0.0932690 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1920.00 | −0.526234 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3000.00 | −0.811941 | −0.405970 | − | 0.913886i | \(-0.633066\pi\) | ||||
−0.405970 | + | 0.913886i | \(0.633066\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2042.00 | 0.545796 | 0.272898 | − | 0.962043i | \(-0.412018\pi\) | ||||
0.272898 | + | 0.962043i | \(0.412018\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5032.00 | 1.32841 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 686.000 | 0.178885 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1440.00 | 0.370951 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8576.00 | −2.18266 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 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 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8288.00 | −2.03535 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5634.00 | 1.36747 | 0.683734 | − | 0.729731i | \(-0.260355\pi\) | ||||
0.683734 | + | 0.729731i | \(0.260355\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2422.00 | −0.581065 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7030.00 | −1.66723 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 168.000 | 0.0393891 | 0.0196945 | − | 0.999806i | \(-0.493731\pi\) | ||||
0.0196945 | + | 0.999806i | \(0.493731\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4452.00 | −1.03202 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6480.00 | −1.48528 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1310.00 | 0.296922 | 0.148461 | − | 0.988918i | \(-0.452568\pi\) | ||||
0.148461 | + | 0.988918i | \(0.452568\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2208.00 | −0.494932 | −0.247466 | − | 0.968897i | \(-0.579598\pi\) | ||||
−0.247466 | + | 0.968897i | \(0.579598\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1008.00 | −0.223469 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1988.00 | 0.435931 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5294.00 | −1.14832 | −0.574162 | − | 0.818742i | \(-0.694672\pi\) | ||||
−0.574162 | + | 0.818742i | \(0.694672\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2664.00 | 0.571647 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3242.00 | 0.688262 | 0.344131 | − | 0.938922i | \(-0.388174\pi\) | ||||
0.344131 | + | 0.938922i | \(0.388174\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1592.00 | 0.334398 | 0.167199 | − | 0.985923i | \(-0.446528\pi\) | ||||
0.167199 | + | 0.985923i | \(0.446528\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8960.00 | 1.86226 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1134.00 | −0.233233 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 563.000 | 0.114594 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10832.0 | −2.18207 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 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 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2240.00 | −0.437636 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2016.00 | 0.389927 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2884.00 | −0.552262 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10864.0 | −2.05980 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2772.00 | 0.520407 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 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 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −968.000 | −0.176496 | −0.0882480 | − | 0.996099i | \(-0.528127\pi\) | ||||
−0.0882480 | + | 0.996099i | \(0.528127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3058.00 | 0.552231 | 0.276116 | − | 0.961124i | \(-0.410953\pi\) | ||||
0.276116 | + | 0.961124i | \(0.410953\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3626.00 | −0.648578 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4986.00 | 0.883412 | 0.441706 | − | 0.897160i | \(-0.354373\pi\) | ||||
0.441706 | + | 0.897160i | \(0.354373\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5320.00 | −0.933739 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3552.00 | 0.617612 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5920.00 | −1.01981 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1278.00 | −0.218125 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14960.0 | 2.52994 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −168.000 | −0.0281524 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8612.00 | −1.43009 | −0.715043 | − | 0.699081i | \(-0.753593\pi\) | ||||
−0.715043 | + | 0.699081i | \(0.753593\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12802.0 | 2.10674 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10024.0 | 1.63483 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10206.0 | −1.64972 | −0.824861 | − | 0.565336i | \(-0.808747\pi\) | ||||
−0.824861 | + | 0.565336i | \(0.808747\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11024.0 | −1.76620 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2016.00 | 0.320154 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12544.0 | 1.95753 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2004.00 | −0.310030 | −0.155015 | − | 0.987912i | \(-0.549543\pi\) | ||||
−0.155015 | + | 0.987912i | \(0.549543\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −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 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 978.000 | 0.147461 | 0.0737304 | − | 0.997278i | \(-0.476510\pi\) | ||||
0.0737304 | + | 0.997278i | \(0.476510\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5488.00 | 0.820487 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4144.00 | 0.614352 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9680.00 | −1.42309 | −0.711547 | − | 0.702638i | \(-0.752005\pi\) | ||||
−0.711547 | + | 0.702638i | \(0.752005\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −459.000 | −0.0669194 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4376.00 | 0.632728 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7532.00 | 1.08012 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8656.00 | −1.23117 | −0.615585 | − | 0.788070i | \(-0.711080\pi\) | ||||
−0.615585 | + | 0.788070i | \(0.711080\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5994.00 | 0.845624 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2226.00 | 0.311504 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5278.00 | −0.732666 | −0.366333 | − | 0.930484i | \(-0.619387\pi\) | ||||
−0.366333 | + | 0.930484i | \(0.619387\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6048.00 | 0.832846 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3420.00 | 0.467212 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6340.00 | −0.859272 | −0.429636 | − | 0.903002i | \(-0.641358\pi\) | ||||
−0.429636 | + | 0.903002i | \(0.641358\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15552.0 | −2.09122 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6232.00 | −0.831437 | −0.415718 | − | 0.909493i | \(-0.636470\pi\) | ||||
−0.415718 | + | 0.909493i | \(0.636470\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2744.00 | −0.363239 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15244.0 | 2.00232 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14810.0 | 1.93033 | 0.965163 | − | 0.261649i | \(-0.0842664\pi\) | ||||
0.965163 | + | 0.261649i | \(0.0842664\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8288.00 | −1.07197 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6784.00 | −0.870757 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3360.00 | 0.428000 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5154.00 | −0.651566 | −0.325783 | − | 0.945445i | \(-0.605628\pi\) | ||||
−0.325783 | + | 0.945445i | \(0.605628\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4480.00 | −0.562107 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3282.00 | 0.408716 | 0.204358 | − | 0.978896i | \(-0.434489\pi\) | ||||
0.204358 | + | 0.978896i | \(0.434489\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1296.00 | −0.160194 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5026.00 | −0.616652 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9688.00 | 1.17989 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5810.00 | 0.702411 | 0.351205 | − | 0.936298i | \(-0.385772\pi\) | ||||
0.351205 | + | 0.936298i | \(0.385772\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23728.0 | 2.84773 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1400.00 | −0.166803 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15008.0 | 1.77521 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22400.0 | 2.63053 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −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 | \(-0.486399\pi\) | ||||
0.0427172 | + | 0.999087i | \(0.486399\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 888.000 | 0.102071 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5254.00 | 0.599662 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1386.00 | −0.157080 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4032.00 | 0.453769 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1272.00 | 0.142158 | 0.0710790 | − | 0.997471i | \(-0.477356\pi\) | ||||
0.0710790 | + | 0.997471i | \(0.477356\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5062.00 | −0.561811 | −0.280906 | − | 0.959735i | \(-0.590635\pi\) | ||||
−0.280906 | + | 0.959735i | \(0.590635\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21280.0 | 2.34551 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8960.00 | 0.980812 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5640.00 | 0.613172 | 0.306586 | − | 0.951843i | \(-0.400813\pi\) | ||||
0.306586 | + | 0.951843i | \(0.400813\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1813.00 | 0.195767 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13388.0 | −1.43585 | −0.717927 | − | 0.696119i | \(-0.754909\pi\) | ||||
−0.717927 | + | 0.696119i | \(0.754909\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11340.0 | 1.20802 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4080.00 | 0.431717 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3230.00 | −0.339495 | −0.169747 | − | 0.985488i | \(-0.554295\pi\) | ||||
−0.169747 | + | 0.985488i | \(0.554295\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4536.00 | 0.473596 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4736.00 | −0.491207 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1764.00 | 0.181753 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10646.0 | −1.08971 | −0.544857 | − | 0.838529i | \(-0.683416\pi\) | ||||
−0.544857 | + | 0.838529i | \(0.683416\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5920.00 | −0.602009 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −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 | \(0.280265\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8064.00 | −0.804213 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2816.00 | 0.279034 | 0.139517 | − | 0.990220i | \(-0.455445\pi\) | ||||
0.139517 | + | 0.990220i | \(0.455445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5012.00 | −0.493460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21488.0 | −2.10215 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11536.0 | 1.12141 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5680.00 | −0.548666 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11766.0 | −1.12941 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3160.00 | −0.301428 | −0.150714 | − | 0.988577i | \(-0.548157\pi\) | ||||
−0.150714 | + | 0.988577i | \(0.548157\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6228.00 | −0.590379 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6272.00 | −0.590861 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18956.0 | 1.77474 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14176.0 | −1.31905 | −0.659523 | − | 0.751684i | \(-0.729242\pi\) | ||||
−0.659523 | + | 0.751684i | \(0.729242\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8096.00 | −0.748699 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11268.0 | 1.03568 | 0.517839 | − | 0.855478i | \(-0.326737\pi\) | ||||
0.517839 | + | 0.855478i | \(0.326737\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14060.0 | −1.28444 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14504.0 | 1.31698 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2744.00 | −0.247656 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4460.00 | 0.400114 | 0.200057 | − | 0.979784i | \(-0.435887\pi\) | ||||
0.200057 | + | 0.979784i | \(0.435887\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4352.00 | −0.388090 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1512.00 | −0.134029 | −0.0670147 | − | 0.997752i | \(-0.521347\pi\) | ||||
−0.0670147 | + | 0.997752i | \(0.521347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19012.0 | 1.67529 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14984.0 | 1.31255 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11790.0 | 1.02668 | 0.513342 | − | 0.858184i | \(-0.328407\pi\) | ||||
0.513342 | + | 0.858184i | \(0.328407\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3766.00 | −0.326024 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6400.00 | 0.550813 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11648.0 | −0.996645 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 672.000 | 0.0571654 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14864.0 | 1.25714 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1362.00 | 0.114530 | 0.0572652 | − | 0.998359i | \(-0.481762\pi\) | ||||
0.0572652 | + | 0.998359i | \(0.481762\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6968.00 | −0.582580 | −0.291290 | − | 0.956635i | \(-0.594084\pi\) | ||||
−0.291290 | + | 0.956635i | \(0.594084\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3976.00 | 0.330527 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5328.00 | 0.440401 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 377.000 | 0.0309855 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7400.00 | 0.604770 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2916.00 | −0.236972 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6216.00 | −0.502320 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2400.00 | −0.192863 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1372.00 | 0.109640 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7062.00 | −0.561218 | −0.280609 | − | 0.959822i | \(-0.590536\pi\) | ||||
−0.280609 | + | 0.959822i | \(0.590536\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18864.0 | −1.49085 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26180.0 | −2.05767 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8196.00 | 0.640650 | 0.320325 | − | 0.947308i | \(-0.396208\pi\) | ||||
0.320325 | + | 0.947308i | \(0.396208\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7326.00 | 0.569519 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15200.0 | 1.17521 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1680.00 | −0.129188 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −38752.0 | −2.96384 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7466.00 | 0.567944 | 0.283972 | − | 0.958833i | \(-0.408348\pi\) | ||||
0.283972 | + | 0.958833i | \(0.408348\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7416.00 | −0.561115 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16576.0 | −1.24749 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24968.0 | −1.86905 | −0.934526 | − | 0.355896i | \(-0.884176\pi\) | ||||
−0.934526 | + | 0.355896i | \(0.884176\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19292.0 | 1.43650 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2513.00 | 0.186131 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14250.0 | 1.04990 | 0.524948 | − | 0.851134i | \(-0.324085\pi\) | ||||
0.524948 | + | 0.851134i | \(0.324085\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6372.00 | −0.467005 | −0.233503 | − | 0.972356i | \(-0.575019\pi\) | ||||
−0.233503 | + | 0.972356i | \(0.575019\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11136.0 | −0.811890 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7952.00 | −0.576733 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8366.00 | −0.603607 | −0.301803 | − | 0.953370i | \(-0.597589\pi\) | ||||
−0.301803 | + | 0.953370i | \(0.597589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14224.0 | −1.02095 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7504.00 | −0.535832 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8904.00 | −0.632532 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9324.00 | −0.658974 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −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 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9712.00 | 0.675970 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9378.00 | 0.649424 | 0.324712 | − | 0.945813i | \(-0.394733\pi\) | ||||
0.324712 | + | 0.945813i | \(0.394733\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7252.00 | −0.499669 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8320.00 | −0.570377 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9000.00 | −0.613907 | −0.306953 | − | 0.951725i | \(-0.599310\pi\) | ||||
−0.306953 | + | 0.951725i | \(0.599310\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7562.00 | 0.513245 | 0.256623 | − | 0.966512i | \(-0.417390\pi\) | ||||
0.256623 | + | 0.966512i | \(0.417390\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26492.0 | 1.78912 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7658.00 | −0.514615 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2976.00 | −0.198999 | −0.0994993 | − | 0.995038i | \(-0.531724\pi\) | ||||
−0.0994993 | + | 0.995038i | \(0.531724\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10640.0 | −0.707971 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −432.000 | −0.0286037 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4278.00 | −0.281871 | −0.140935 | − | 0.990019i | \(-0.545011\pi\) | ||||
−0.140935 | + | 0.990019i | \(0.545011\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18144.0 | −1.18965 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18794.0 | 1.22629 | 0.613143 | − | 0.789972i | \(-0.289905\pi\) | ||||
0.613143 | + | 0.789972i | \(0.289905\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18040.0 | −1.17139 | −0.585694 | − | 0.810532i | \(-0.699178\pi\) | ||||
−0.585694 | + | 0.810532i | \(0.699178\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8960.00 | 0.578989 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5670.00 | −0.364629 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19459.0 | −1.24538 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17920.0 | 1.14140 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25604.0 | 1.62305 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21688.0 | −1.36828 | −0.684141 | − | 0.729350i | \(-0.739823\pi\) | ||||
−0.684141 | + | 0.729350i | \(0.739823\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −30944.0 | −1.94299 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 27216.0 | 1.70084 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −882.000 | −0.0548605 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14504.0 | 0.897918 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10558.0 | −0.650571 | −0.325285 | − | 0.945616i | \(-0.605460\pi\) | ||||
−0.325285 | + | 0.945616i | \(0.605460\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 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 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25584.0 | 1.55458 | 0.777288 | − | 0.629145i | \(-0.216595\pi\) | ||||
0.777288 | + | 0.629145i | \(0.216595\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5600.00 | 0.338705 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4032.00 | 0.242744 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15198.0 | −0.910787 | −0.455393 | − | 0.890290i | \(-0.650501\pi\) | ||||
−0.455393 | + | 0.890290i | \(0.650501\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11872.0 | 0.708210 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19906.0 | 1.18205 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6100.00 | 0.360580 | 0.180290 | − | 0.983613i | \(-0.442296\pi\) | ||||
0.180290 | + | 0.983613i | \(0.442296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2318.00 | 0.136399 | 0.0681995 | − | 0.997672i | \(-0.478275\pi\) | ||||
0.0681995 | + | 0.997672i | \(0.478275\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10656.0 | 0.624200 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7840.00 | 0.457176 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21280.0 | 1.23533 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −31744.0 | −1.83452 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5544.00 | 0.318962 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10222.0 | −0.585482 | −0.292741 | − | 0.956192i | \(-0.594567\pi\) | ||||
−0.292741 | + | 0.956192i | \(0.594567\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5680.00 | −0.323886 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25434.0 | −1.44388 | −0.721941 | − | 0.691955i | \(-0.756750\pi\) | ||||
−0.721941 | + | 0.691955i | \(0.756750\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9478.00 | −0.535688 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −31488.0 | −1.77184 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8532.00 | 0.477991 | 0.238996 | − | 0.971021i | \(-0.423182\pi\) | ||||
0.238996 | + | 0.971021i | \(0.423182\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −41524.0 | −2.31613 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 38480.0 | 2.13698 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5724.00 | 0.316498 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20672.0 | −1.13806 | −0.569030 | − | 0.822317i | \(-0.692681\pi\) | ||||
−0.569030 | + | 0.822317i | \(0.692681\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7252.00 | −0.397519 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −39200.0 | −2.13948 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11988.0 | 0.651475 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17456.0 | 0.944559 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21458.0 | 1.15614 | 0.578072 | − | 0.815985i | \(-0.303805\pi\) | ||||
0.578072 | + | 0.815985i | \(0.303805\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27680.0 | −1.48502 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2688.00 | −0.143597 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9506.00 | −0.505672 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9850.00 | 0.521755 | 0.260878 | − | 0.965372i | \(-0.415988\pi\) | ||||
0.260878 | + | 0.965372i | \(0.415988\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8880.00 | 0.468391 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8064.00 | −0.423561 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7056.00 | −0.369062 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24000.0 | 1.25006 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18840.0 | −0.977209 | −0.488605 | − | 0.872505i | \(-0.662494\pi\) | ||||
−0.488605 | + | 0.872505i | \(0.662494\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5824.00 | 0.300828 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16336.0 | −0.840308 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13490.0 | −0.691043 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37504.0 | 1.91327 | 0.956634 | − | 0.291291i | \(-0.0940849\pi\) | ||||
0.956634 | + | 0.291291i | \(0.0940849\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −30563.0 | −1.55276 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30488.0 | 1.54260 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13338.0 | −0.672101 | −0.336051 | − | 0.941844i | \(-0.609091\pi\) | ||||
−0.336051 | + | 0.941844i | \(0.609091\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5488.00 | −0.275412 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20048.0 | 1.00200 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17100.0 | −0.851196 | −0.425598 | − | 0.904912i | \(-0.639936\pi\) | ||||
−0.425598 | + | 0.904912i | \(0.639936\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11520.0 | −0.571117 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19632.0 | −0.969352 | −0.484676 | − | 0.874694i | \(-0.661062\pi\) | ||||
−0.484676 | + | 0.874694i | \(0.661062\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7140.00 | −0.351127 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 39664.0 | 1.94274 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3108.00 | 0.151621 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33912.0 | 1.64776 | 0.823879 | − | 0.566766i | \(-0.191805\pi\) | ||||
0.823879 | + | 0.566766i | \(0.191805\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4224.00 | −0.204424 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8288.00 | 0.399512 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31386.0 | 1.50693 | 0.753463 | − | 0.657490i | \(-0.228382\pi\) | ||||
0.753463 | + | 0.657490i | \(0.228382\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25088.0 | 1.19978 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34558.0 | −1.64616 | −0.823079 | − | 0.567927i | \(-0.807746\pi\) | ||||
−0.823079 | + | 0.567927i | \(0.807746\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13090.0 | 0.621088 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 38332.0 | 1.81163 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3600.00 | −0.169476 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39130.0 | 1.83493 | 0.917467 | − | 0.397812i | \(-0.130231\pi\) | ||||
0.917467 | + | 0.397812i | \(0.130231\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45072.0 | −2.10535 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25982.0 | 1.20894 | 0.604468 | − | 0.796629i | \(-0.293386\pi\) | ||||
0.604468 | + | 0.796629i | \(0.293386\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5112.00 | 0.236940 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19376.0 | 0.894608 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12960.0 | −0.596072 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10976.0 | 0.502884 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15200.0 | 0.693747 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 37604.0 | 1.70974 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35424.0 | −1.60448 | −0.802242 | − | 0.596999i | \(-0.796360\pi\) | ||||
−0.802242 | + | 0.596999i | \(0.796360\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1344.00 | −0.0606434 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9646.00 | −0.433593 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3564.00 | −0.159598 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 35616.0 | 1.58889 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 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 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29970.0 | 1.32202 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15064.0 | 0.662014 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10976.0 | 0.480563 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10480.0 | −0.457142 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16810.0 | 0.730542 | 0.365271 | − | 0.930901i | \(-0.380976\pi\) | ||||
0.365271 | + | 0.930901i | \(0.380976\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 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 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14168.0 | 0.608937 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32960.0 | −1.41141 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4662.00 | 0.198905 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34382.0 | −1.46156 | −0.730780 | − | 0.682614i | \(-0.760843\pi\) | ||||
−0.730780 | + | 0.682614i | \(0.760843\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4472.00 | −0.189410 | −0.0947048 | − | 0.995505i | \(-0.530191\pi\) | ||||
−0.0947048 | + | 0.995505i | \(0.530191\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15904.0 | −0.671159 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1716.00 | 0.0721538 | 0.0360769 | − | 0.999349i | \(-0.488514\pi\) | ||||
0.0360769 | + | 0.999349i | \(0.488514\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7910.00 | 0.331394 | 0.165697 | − | 0.986177i | \(-0.447013\pi\) | ||||
0.165697 | + | 0.986177i | \(0.447013\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42352.0 | 1.76796 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3626.00 | 0.150820 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7616.00 | 0.315644 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5760.00 | −0.237867 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19360.0 | −0.796641 | −0.398320 | − | 0.917246i | \(-0.630407\pi\) | ||||
−0.398320 | + | 0.917246i | \(0.630407\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11711.0 | 0.480175 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25936.0 | −1.05965 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26222.0 | −1.06753 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3829.00 | 0.155332 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12736.0 | −0.514839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38752.0 | −1.56099 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −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 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23406.0 | −0.932945 | −0.466472 | − | 0.884536i | \(-0.654475\pi\) | ||||
−0.466472 | + | 0.884536i | \(0.654475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7280.00 | −0.289162 | −0.144581 | − | 0.989493i | \(-0.546183\pi\) | ||||
−0.144581 | + | 0.989493i | \(0.546183\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9072.00 | 0.359086 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9808.00 | 0.386869 | 0.193435 | − | 0.981113i | \(-0.438037\pi\) | ||||
0.193435 | + | 0.981113i | \(0.438037\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26012.0 | −1.02247 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4504.00 | −0.176429 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6720.00 | 0.262325 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12888.0 | −0.501370 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 50098.0 | 1.94222 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5292.00 | 0.204460 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8066.00 | 0.310570 | 0.155285 | − | 0.987870i | \(-0.450370\pi\) | ||||
0.155285 | + | 0.987870i | \(0.450370\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −40176.0 | −1.54164 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25842.0 | 0.988240 | 0.494120 | − | 0.869394i | \(-0.335490\pi\) | ||||
0.494120 | + | 0.869394i | \(0.335490\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5692.00 | 0.216932 | 0.108466 | − | 0.994100i | \(-0.465406\pi\) | ||||
0.108466 | + | 0.994100i | \(0.465406\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22400.0 | −0.850811 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13536.0 | −0.512395 | −0.256198 | − | 0.966624i | \(-0.582470\pi\) | ||||
−0.256198 | + | 0.966624i | \(0.582470\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13608.0 | −0.513383 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10052.0 | −0.377951 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1920.00 | −0.0719489 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4200.00 | 0.156861 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16128.0 | −0.600332 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13680.0 | −0.507512 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23532.0 | −0.870105 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23072.0 | 0.850264 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33012.0 | 1.21255 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17004.0 | −0.622501 | −0.311251 | − | 0.950328i | \(-0.600748\pi\) | ||||
−0.311251 | + | 0.950328i | \(0.600748\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 50246.0 | 1.83339 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14568.0 | −0.529813 | −0.264906 | − | 0.964274i | \(-0.585341\pi\) | ||||
−0.264906 | + | 0.964274i | \(0.585341\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30016.0 | 1.08804 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −22176.0 | −0.801220 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5936.00 | −0.213767 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1400.00 | −0.0502522 | −0.0251261 | − | 0.999684i | \(-0.507999\pi\) | ||||
−0.0251261 | + | 0.999684i | \(0.507999\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −76288.0 | −2.72940 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7056.00 | −0.251626 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24566.0 | 0.873216 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30784.0 | −1.09070 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13830.0 | −0.488426 | −0.244213 | − | 0.969722i | \(-0.578530\pi\) | ||||
−0.244213 | + | 0.969722i | \(0.578530\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3920.00 | −0.137994 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7744.00 | 0.271733 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29008.0 | 1.01461 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24166.0 | −0.842549 | −0.421275 | − | 0.906933i | \(-0.638417\pi\) | ||||
−0.421275 | + | 0.906933i | \(0.638417\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24464.0 | −0.850216 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10838.0 | 0.375461 | 0.187730 | − | 0.982221i | \(-0.439887\pi\) | ||||
0.187730 | + | 0.982221i | \(0.439887\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18144.0 | −0.626564 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7840.00 | 0.269879 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40916.0 | 1.40400 | 0.702002 | − | 0.712175i | \(-0.252290\pi\) | ||||
0.702002 | + | 0.712175i | \(0.252290\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9684.00 | −0.331250 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39888.0 | −1.36010 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56618.0 | 1.92449 | 0.962244 | − | 0.272189i | \(-0.0877475\pi\) | ||||
0.962244 | + | 0.272189i | \(0.0877475\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19488.0 | 0.660332 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 42560.0 | 1.43759 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20762.0 | 0.699103 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24607.0 | −0.825988 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16428.0 | −0.549725 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24892.0 | 0.830365 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17504.0 | 0.582100 | 0.291050 | − | 0.956708i | \(-0.405995\pi\) | ||||
0.291050 | + | 0.956708i | \(0.405995\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 47360.0 | 1.57010 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23112.0 | −0.763851 | −0.381926 | − | 0.924193i | \(-0.624739\pi\) | ||||
−0.381926 | + | 0.924193i | \(0.624739\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19600.0 | 0.645783 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10224.0 | 0.335826 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23874.0 | 0.781778 | 0.390889 | − | 0.920438i | \(-0.372168\pi\) | ||||
0.390889 | + | 0.920438i | \(0.372168\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22680.0 | 0.740404 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −69190.0 | −2.25185 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15312.0 | −0.496823 | −0.248411 | − | 0.968655i | \(-0.579909\pi\) | ||||
−0.248411 | + | 0.968655i | \(0.579909\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16996.0 | −0.549784 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1344.00 | 0.0433435 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −46144.0 | −1.48361 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16528.0 | −0.529797 | −0.264899 | − | 0.964276i | \(-0.585339\pi\) | ||||
−0.264899 | + | 0.964276i | \(0.585339\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 68896.0 | 2.20176 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14560.0 | 0.463903 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28606.0 | 0.908687 | 0.454344 | − | 0.890827i | \(-0.349874\pi\) | ||||
0.454344 | + | 0.890827i | \(0.349874\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −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 | 448.4.a.b.1.1 | 1 | ||
4.3 | odd | 2 | 448.4.a.o.1.1 | 1 | |||
8.3 | odd | 2 | 112.4.a.a.1.1 | 1 | |||
8.5 | even | 2 | 14.4.a.a.1.1 | ✓ | 1 | ||
24.5 | odd | 2 | 126.4.a.h.1.1 | 1 | |||
24.11 | even | 2 | 1008.4.a.s.1.1 | 1 | |||
40.13 | odd | 4 | 350.4.c.b.99.2 | 2 | |||
40.29 | even | 2 | 350.4.a.l.1.1 | 1 | |||
40.37 | odd | 4 | 350.4.c.b.99.1 | 2 | |||
56.5 | odd | 6 | 98.4.c.f.67.1 | 2 | |||
56.13 | odd | 2 | 98.4.a.a.1.1 | 1 | |||
56.27 | even | 2 | 784.4.a.s.1.1 | 1 | |||
56.37 | even | 6 | 98.4.c.d.67.1 | 2 | |||
56.45 | odd | 6 | 98.4.c.f.79.1 | 2 | |||
56.53 | even | 6 | 98.4.c.d.79.1 | 2 | |||
88.21 | odd | 2 | 1694.4.a.g.1.1 | 1 | |||
104.77 | even | 2 | 2366.4.a.h.1.1 | 1 | |||
168.5 | even | 6 | 882.4.g.k.361.1 | 2 | |||
168.53 | odd | 6 | 882.4.g.b.667.1 | 2 | |||
168.101 | even | 6 | 882.4.g.k.667.1 | 2 | |||
168.125 | even | 2 | 882.4.a.i.1.1 | 1 | |||
168.149 | odd | 6 | 882.4.g.b.361.1 | 2 | |||
280.69 | odd | 2 | 2450.4.a.bo.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.4.a.a.1.1 | ✓ | 1 | 8.5 | even | 2 | ||
98.4.a.a.1.1 | 1 | 56.13 | odd | 2 | |||
98.4.c.d.67.1 | 2 | 56.37 | even | 6 | |||
98.4.c.d.79.1 | 2 | 56.53 | even | 6 | |||
98.4.c.f.67.1 | 2 | 56.5 | odd | 6 | |||
98.4.c.f.79.1 | 2 | 56.45 | odd | 6 | |||
112.4.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
126.4.a.h.1.1 | 1 | 24.5 | odd | 2 | |||
350.4.a.l.1.1 | 1 | 40.29 | even | 2 | |||
350.4.c.b.99.1 | 2 | 40.37 | odd | 4 | |||
350.4.c.b.99.2 | 2 | 40.13 | odd | 4 | |||
448.4.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
448.4.a.o.1.1 | 1 | 4.3 | odd | 2 | |||
784.4.a.s.1.1 | 1 | 56.27 | even | 2 | |||
882.4.a.i.1.1 | 1 | 168.125 | even | 2 | |||
882.4.g.b.361.1 | 2 | 168.149 | odd | 6 | |||
882.4.g.b.667.1 | 2 | 168.53 | odd | 6 | |||
882.4.g.k.361.1 | 2 | 168.5 | even | 6 | |||
882.4.g.k.667.1 | 2 | 168.101 | even | 6 | |||
1008.4.a.s.1.1 | 1 | 24.11 | even | 2 | |||
1694.4.a.g.1.1 | 1 | 88.21 | odd | 2 | |||
2366.4.a.h.1.1 | 1 | 104.77 | even | 2 | |||
2450.4.a.bo.1.1 | 1 | 280.69 | odd | 2 |