Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1694,4,Mod(1,1694)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1694, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1694.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1694 = 2 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1694.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: | \(99.9492355497\) |
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 | \(\chi\) | \(=\) | 1694.1 |
$q$-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 | \(-0.220356\pi\) | ||||
0.769800 | + | 0.638285i | \(0.220356\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −14.0000 | −1.25220 | −0.626099 | − | 0.779744i | \(-0.715349\pi\) | ||||
−0.626099 | + | 0.779744i | \(0.715349\pi\) | |||||||
\(6\) | 16.0000 | 1.08866 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 37.0000 | 1.37037 | ||||||||
\(10\) | −28.0000 | −0.885438 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 32.0000 | 0.769800 | ||||||||
\(13\) | −18.0000 | −0.384023 | −0.192012 | − | 0.981393i | \(-0.561501\pi\) | ||||
−0.192012 | + | 0.981393i | \(0.561501\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | −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 | ||||||||
\(21\) | 56.0000 | 0.581914 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −112.000 | −1.01537 | −0.507687 | − | 0.861541i | \(-0.669499\pi\) | ||||
−0.507687 | + | 0.861541i | \(0.669499\pi\) | |||||||
\(24\) | 64.0000 | 0.544331 | ||||||||
\(25\) | 71.0000 | 0.568000 | ||||||||
\(26\) | −36.0000 | −0.271545 | ||||||||
\(27\) | 80.0000 | 0.570222 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | −190.000 | −1.21662 | −0.608312 | − | 0.793698i | \(-0.708153\pi\) | ||||
−0.608312 | + | 0.793698i | \(0.708153\pi\) | |||||||
\(30\) | −224.000 | −1.36322 | ||||||||
\(31\) | 72.0000 | 0.417148 | 0.208574 | − | 0.978007i | \(-0.433118\pi\) | ||||
0.208574 | + | 0.978007i | \(0.433118\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −148.000 | −0.746523 | ||||||||
\(35\) | −98.0000 | −0.473286 | ||||||||
\(36\) | 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 | \(0.599840\pi\) | |||||||
\(42\) | 112.000 | 0.411476 | ||||||||
\(43\) | 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 | ||||||||
\(46\) | −224.000 | −0.717978 | ||||||||
\(47\) | 24.0000 | 0.0744843 | 0.0372421 | − | 0.999306i | \(-0.488143\pi\) | ||||
0.0372421 | + | 0.999306i | \(0.488143\pi\) | |||||||
\(48\) | 128.000 | 0.384900 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 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 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | −640.000 | −1.48719 | ||||||||
\(58\) | −380.000 | −0.860284 | ||||||||
\(59\) | −200.000 | −0.441318 | −0.220659 | − | 0.975351i | \(-0.570821\pi\) | ||||
−0.220659 | + | 0.975351i | \(0.570821\pi\) | |||||||
\(60\) | −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 | ||||||||
\(63\) | 259.000 | 0.517951 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 252.000 | 0.480873 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −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 | ||||||||
\(70\) | −196.000 | −0.334664 | ||||||||
\(71\) | 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 | \(-0.554667\pi\) | ||||
−0.170899 | + | 0.985288i | \(0.554667\pi\) | |||||||
\(80\) | −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 | \(0.249219\pi\) | |||||||
\(84\) | 224.000 | 0.290957 | ||||||||
\(85\) | 1036.00 | 1.32200 | ||||||||
\(86\) | 824.000 | 1.03319 | ||||||||
\(87\) | −1520.00 | −1.87312 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 810.000 | 0.964717 | 0.482359 | − | 0.875974i | \(-0.339780\pi\) | ||||
0.482359 | + | 0.875974i | \(0.339780\pi\) | |||||||
\(90\) | −1036.00 | −1.21338 | ||||||||
\(91\) | −126.000 | −0.145147 | ||||||||
\(92\) | −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 | \(-0.249305\pi\) | ||||
0.708649 | + | 0.705561i | \(0.249305\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 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 | \(-0.630281\pi\) | ||||
−0.397958 | + | 0.917404i | \(0.630281\pi\) | |||||||
\(104\) | −144.000 | −0.135773 | ||||||||
\(105\) | −784.000 | −0.728672 | ||||||||
\(106\) | 636.000 | 0.582772 | ||||||||
\(107\) | −444.000 | −0.401150 | −0.200575 | − | 0.979678i | \(-0.564281\pi\) | ||||
−0.200575 | + | 0.979678i | \(0.564281\pi\) | |||||||
\(108\) | 320.000 | 0.285111 | ||||||||
\(109\) | −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 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | 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 | ||||||||
\(119\) | −518.000 | −0.399033 | ||||||||
\(120\) | −896.000 | −0.681610 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 396.000 | 0.293870 | ||||||||
\(123\) | −1296.00 | −0.950052 | ||||||||
\(124\) | 288.000 | 0.208574 | ||||||||
\(125\) | 756.000 | 0.540950 | ||||||||
\(126\) | 518.000 | 0.366247 | ||||||||
\(127\) | −1944.00 | −1.35828 | −0.679142 | − | 0.734007i | \(-0.737648\pi\) | ||||
−0.679142 | + | 0.734007i | \(0.737648\pi\) | |||||||
\(128\) | 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 | \(0.408741\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −560.000 | −0.365099 | ||||||||
\(134\) | −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 | \(0.826008\pi\) | |||||||
\(140\) | −392.000 | −0.236643 | ||||||||
\(141\) | 192.000 | 0.114676 | ||||||||
\(142\) | 784.000 | 0.463323 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 592.000 | 0.342593 | ||||||||
\(145\) | 2660.00 | 1.52346 | ||||||||
\(146\) | −1076.00 | −0.609934 | ||||||||
\(147\) | 392.000 | 0.219943 | ||||||||
\(148\) | −1384.00 | −0.768676 | ||||||||
\(149\) | −510.000 | −0.280408 | −0.140204 | − | 0.990123i | \(-0.544776\pi\) | ||||
−0.140204 | + | 0.990123i | \(0.544776\pi\) | |||||||
\(150\) | 1136.00 | 0.618360 | ||||||||
\(151\) | −592.000 | −0.319048 | −0.159524 | − | 0.987194i | \(-0.550996\pi\) | ||||
−0.159524 | + | 0.987194i | \(0.550996\pi\) | |||||||
\(152\) | −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 | \(-0.739192\pi\) | ||||
−0.682695 | + | 0.730704i | \(0.739192\pi\) | |||||||
\(158\) | −480.000 | −0.241688 | ||||||||
\(159\) | 2544.00 | 1.26888 | ||||||||
\(160\) | −448.000 | −0.221359 | ||||||||
\(161\) | −784.000 | −0.383776 | ||||||||
\(162\) | −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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2144.00 | 1.00245 | ||||||||
\(167\) | −544.000 | −0.252072 | −0.126036 | − | 0.992026i | \(-0.540225\pi\) | ||||
−0.126036 | + | 0.992026i | \(0.540225\pi\) | |||||||
\(168\) | 448.000 | 0.205738 | ||||||||
\(169\) | −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 | ||||||||
\(175\) | 497.000 | 0.214684 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −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 | \(-0.660878\pi\) | ||||
−0.484168 | + | 0.874975i | \(0.660878\pi\) | |||||||
\(182\) | −252.000 | −0.102635 | ||||||||
\(183\) | 1584.00 | 0.639851 | ||||||||
\(184\) | −896.000 | −0.358989 | ||||||||
\(185\) | 4844.00 | 1.92507 | ||||||||
\(186\) | 1152.00 | 0.454133 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 96.0000 | 0.0372421 | ||||||||
\(189\) | 560.000 | 0.215524 | ||||||||
\(190\) | 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 | \(-0.607576\pi\) | ||||
−0.331563 | + | 0.943433i | \(0.607576\pi\) | |||||||
\(194\) | 2708.00 | 1.00218 | ||||||||
\(195\) | 2016.00 | 0.740353 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | −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 | \(0.440695\pi\) | |||||||
\(200\) | 568.000 | 0.200818 | ||||||||
\(201\) | −5728.00 | −2.01006 | ||||||||
\(202\) | 2716.00 | 0.946025 | ||||||||
\(203\) | −1330.00 | −0.459841 | ||||||||
\(204\) | −2368.00 | −0.812712 | ||||||||
\(205\) | 2268.00 | 0.772702 | ||||||||
\(206\) | −1664.00 | −0.562798 | ||||||||
\(207\) | −4144.00 | −1.39144 | ||||||||
\(208\) | −288.000 | −0.0960058 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1568.00 | −0.515249 | ||||||||
\(211\) | 3868.00 | 1.26201 | 0.631005 | − | 0.775779i | \(-0.282643\pi\) | ||||
0.631005 | + | 0.775779i | \(0.282643\pi\) | |||||||
\(212\) | 1272.00 | 0.412082 | ||||||||
\(213\) | 3136.00 | 1.00880 | ||||||||
\(214\) | −888.000 | −0.283656 | ||||||||
\(215\) | −5768.00 | −1.82965 | ||||||||
\(216\) | 640.000 | 0.201604 | ||||||||
\(217\) | 504.000 | 0.157667 | ||||||||
\(218\) | −3740.00 | −1.16195 | ||||||||
\(219\) | −4304.00 | −1.32802 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1332.00 | 0.405430 | ||||||||
\(222\) | −5536.00 | −1.67366 | ||||||||
\(223\) | 3968.00 | 1.19156 | 0.595778 | − | 0.803149i | \(-0.296844\pi\) | ||||
0.595778 | + | 0.803149i | \(0.296844\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | 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 | \(-0.255845\pi\) | ||||
0.694004 | + | 0.719971i | \(0.255845\pi\) | |||||||
\(230\) | 3136.00 | 0.899051 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1520.00 | −0.430142 | ||||||||
\(233\) | 2182.00 | 0.613509 | 0.306754 | − | 0.951789i | \(-0.400757\pi\) | ||||
0.306754 | + | 0.951789i | \(0.400757\pi\) | |||||||
\(234\) | −1332.00 | −0.372118 | ||||||||
\(235\) | −336.000 | −0.0932690 | ||||||||
\(236\) | −800.000 | −0.220659 | ||||||||
\(237\) | −1920.00 | −0.526234 | ||||||||
\(238\) | −1036.00 | −0.282159 | ||||||||
\(239\) | 3000.00 | 0.811941 | 0.405970 | − | 0.913886i | \(-0.366934\pi\) | ||||
0.405970 | + | 0.913886i | \(0.366934\pi\) | |||||||
\(240\) | −1792.00 | −0.481971 | ||||||||
\(241\) | −2042.00 | −0.545796 | −0.272898 | − | 0.962043i | \(-0.587982\pi\) | ||||
−0.272898 | + | 0.962043i | \(0.587982\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5032.00 | −1.32841 | ||||||||
\(244\) | 792.000 | 0.207798 | ||||||||
\(245\) | −686.000 | −0.178885 | ||||||||
\(246\) | −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 | \(-0.521148\pi\) | ||||
−0.0663886 | + | 0.997794i | \(0.521148\pi\) | |||||||
\(252\) | 1036.00 | 0.258976 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −3888.00 | −0.960452 | ||||||||
\(255\) | 8288.00 | 2.03535 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5634.00 | 1.36747 | 0.683734 | − | 0.729731i | \(-0.260355\pi\) | ||||
0.683734 | + | 0.729731i | \(0.260355\pi\) | |||||||
\(258\) | 6592.00 | 1.59070 | ||||||||
\(259\) | −2422.00 | −0.581065 | ||||||||
\(260\) | 1008.00 | 0.240437 | ||||||||
\(261\) | −7030.00 | −1.66723 | ||||||||
\(262\) | 1696.00 | 0.399921 | ||||||||
\(263\) | −168.000 | −0.0393891 | −0.0196945 | − | 0.999806i | \(-0.506269\pi\) | ||||
−0.0196945 | + | 0.999806i | \(0.506269\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4452.00 | −1.03202 | ||||||||
\(266\) | −1120.00 | −0.258164 | ||||||||
\(267\) | 6480.00 | 1.48528 | ||||||||
\(268\) | −2864.00 | −0.652786 | ||||||||
\(269\) | −1310.00 | −0.296922 | −0.148461 | − | 0.988918i | \(-0.547432\pi\) | ||||
−0.148461 | + | 0.988918i | \(0.547432\pi\) | |||||||
\(270\) | −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 | ||||||||
\(273\) | −1008.00 | −0.223469 | ||||||||
\(274\) | −5932.00 | −1.30790 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3584.00 | −0.781636 | ||||||||
\(277\) | −5294.00 | −1.14832 | −0.574162 | − | 0.818742i | \(-0.694672\pi\) | ||||
−0.574162 | + | 0.818742i | \(0.694672\pi\) | |||||||
\(278\) | −5600.00 | −1.20815 | ||||||||
\(279\) | 2664.00 | 0.571647 | ||||||||
\(280\) | −784.000 | −0.167332 | ||||||||
\(281\) | −3242.00 | −0.688262 | −0.344131 | − | 0.938922i | \(-0.611826\pi\) | ||||
−0.344131 | + | 0.938922i | \(0.611826\pi\) | |||||||
\(282\) | 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 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1134.00 | −0.233233 | ||||||||
\(288\) | 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 | \(0.333090\pi\) | |||||||
\(294\) | 784.000 | 0.155523 | ||||||||
\(295\) | 2800.00 | 0.552618 | ||||||||
\(296\) | −2768.00 | −0.543536 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1020.00 | −0.198279 | ||||||||
\(299\) | 2016.00 | 0.389927 | ||||||||
\(300\) | 2272.00 | 0.437247 | ||||||||
\(301\) | 2884.00 | 0.552262 | ||||||||
\(302\) | −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 | \(-0.528127\pi\) | ||||
−0.0882480 | + | 0.996099i | \(0.528127\pi\) | |||||||
\(312\) | −1152.00 | −0.209036 | ||||||||
\(313\) | 3058.00 | 0.552231 | 0.276116 | − | 0.961124i | \(-0.410953\pi\) | ||||
0.276116 | + | 0.961124i | \(0.410953\pi\) | |||||||
\(314\) | −5372.00 | −0.965476 | ||||||||
\(315\) | −3626.00 | −0.648578 | ||||||||
\(316\) | −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 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −896.000 | −0.156525 | ||||||||
\(321\) | −3552.00 | −0.617612 | ||||||||
\(322\) | −1568.00 | −0.271370 | ||||||||
\(323\) | 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 | ||||||||
\(329\) | 168.000 | 0.0281524 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 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 | ||||||||
\(336\) | 896.000 | 0.145479 | ||||||||
\(337\) | 10206.0 | 1.64972 | 0.824861 | − | 0.565336i | \(-0.191253\pi\) | ||||
0.824861 | + | 0.565336i | \(0.191253\pi\) | |||||||
\(338\) | −3746.00 | −0.602827 | ||||||||
\(339\) | 11024.0 | 1.76620 | ||||||||
\(340\) | 4144.00 | 0.661000 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −5920.00 | −0.936014 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 3296.00 | 0.516594 | ||||||||
\(345\) | 12544.0 | 1.95753 | ||||||||
\(346\) | −3716.00 | −0.577380 | ||||||||
\(347\) | −2004.00 | −0.310030 | −0.155015 | − | 0.987912i | \(-0.549543\pi\) | ||||
−0.155015 | + | 0.987912i | \(0.549543\pi\) | |||||||
\(348\) | −6080.00 | −0.936558 | ||||||||
\(349\) | −1330.00 | −0.203992 | −0.101996 | − | 0.994785i | \(-0.532523\pi\) | ||||
−0.101996 | + | 0.994785i | \(0.532523\pi\) | |||||||
\(350\) | 994.000 | 0.151804 | ||||||||
\(351\) | −1440.00 | −0.218979 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 978.000 | 0.147461 | 0.0737304 | − | 0.997278i | \(-0.476510\pi\) | ||||
0.0737304 | + | 0.997278i | \(0.476510\pi\) | |||||||
\(354\) | −3200.00 | −0.480447 | ||||||||
\(355\) | −5488.00 | −0.820487 | ||||||||
\(356\) | 3240.00 | 0.482359 | ||||||||
\(357\) | −4144.00 | −0.614352 | ||||||||
\(358\) | −600.000 | −0.0885782 | ||||||||
\(359\) | 9680.00 | 1.42309 | 0.711547 | − | 0.702638i | \(-0.247995\pi\) | ||||
0.711547 | + | 0.702638i | \(0.247995\pi\) | |||||||
\(360\) | −4144.00 | −0.606689 | ||||||||
\(361\) | −459.000 | −0.0669194 | ||||||||
\(362\) | −4716.00 | −0.684717 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −504.000 | −0.0725736 | ||||||||
\(365\) | 7532.00 | 1.08012 | ||||||||
\(366\) | 3168.00 | 0.452443 | ||||||||
\(367\) | −8656.00 | −1.23117 | −0.615585 | − | 0.788070i | \(-0.711080\pi\) | ||||
−0.615585 | + | 0.788070i | \(0.711080\pi\) | |||||||
\(368\) | −1792.00 | −0.253844 | ||||||||
\(369\) | −5994.00 | −0.845624 | ||||||||
\(370\) | 9688.00 | 1.36123 | ||||||||
\(371\) | 2226.00 | 0.311504 | ||||||||
\(372\) | 2304.00 | 0.321121 | ||||||||
\(373\) | −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 | ||||||||
\(376\) | 192.000 | 0.0263342 | ||||||||
\(377\) | 3420.00 | 0.467212 | ||||||||
\(378\) | 1120.00 | 0.152398 | ||||||||
\(379\) | 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 | \(-0.636470\pi\) | ||||
−0.415718 | + | 0.909493i | \(0.636470\pi\) | |||||||
\(384\) | 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 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | 6784.00 | 0.870757 | ||||||||
\(394\) | −2428.00 | −0.310459 | ||||||||
\(395\) | 3360.00 | 0.428000 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5154.00 | 0.651566 | 0.325783 | − | 0.945445i | \(-0.394372\pi\) | ||||
0.325783 | + | 0.945445i | \(0.394372\pi\) | |||||||
\(398\) | 2080.00 | 0.261962 | ||||||||
\(399\) | −4480.00 | −0.562107 | ||||||||
\(400\) | 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 | ||||||||
\(406\) | −2660.00 | −0.325157 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −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 | ||||||||
\(413\) | −1400.00 | −0.166803 | ||||||||
\(414\) | −8288.00 | −0.983896 | ||||||||
\(415\) | −15008.0 | −1.77521 | ||||||||
\(416\) | −576.000 | −0.0678864 | ||||||||
\(417\) | −22400.0 | −2.63053 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13560.0 | 1.58102 | 0.790512 | − | 0.612446i | \(-0.209814\pi\) | ||||
0.790512 | + | 0.612446i | \(0.209814\pi\) | |||||||
\(420\) | −3136.00 | −0.364336 | ||||||||
\(421\) | −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 | ||||||||
\(427\) | 1386.00 | 0.157080 | ||||||||
\(428\) | −1776.00 | −0.200575 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11536.0 | −1.29376 | ||||||||
\(431\) | −1272.00 | −0.142158 | −0.0710790 | − | 0.997471i | \(-0.522644\pi\) | ||||
−0.0710790 | + | 0.997471i | \(0.522644\pi\) | |||||||
\(432\) | 1280.00 | 0.142556 | ||||||||
\(433\) | −5062.00 | −0.561811 | −0.280906 | − | 0.959735i | \(-0.590635\pi\) | ||||
−0.280906 | + | 0.959735i | \(0.590635\pi\) | |||||||
\(434\) | 1008.00 | 0.111487 | ||||||||
\(435\) | 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 | \(0.599187\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1813.00 | 0.195767 | ||||||||
\(442\) | 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 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | −3230.00 | −0.339495 | −0.169747 | − | 0.985488i | \(-0.554295\pi\) | ||||
−0.169747 | + | 0.985488i | \(0.554295\pi\) | |||||||
\(450\) | 5254.00 | 0.550391 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 5512.00 | 0.573590 | ||||||||
\(453\) | −4736.00 | −0.491207 | ||||||||
\(454\) | 7872.00 | 0.813769 | ||||||||
\(455\) | 1764.00 | 0.181753 | ||||||||
\(456\) | −5120.00 | −0.525803 | ||||||||
\(457\) | 10646.0 | 1.08971 | 0.544857 | − | 0.838529i | \(-0.316584\pi\) | ||||
0.544857 | + | 0.838529i | \(0.316584\pi\) | |||||||
\(458\) | 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 | \(-0.544555\pi\) | ||||
−0.139517 | + | 0.990220i | \(0.544555\pi\) | |||||||
\(468\) | −2664.00 | −0.263127 | ||||||||
\(469\) | −5012.00 | −0.493460 | ||||||||
\(470\) | −672.000 | −0.0659512 | ||||||||
\(471\) | −21488.0 | −2.10215 | ||||||||
\(472\) | −1600.00 | −0.156030 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −3840.00 | −0.372103 | ||||||||
\(475\) | −5680.00 | −0.548666 | ||||||||
\(476\) | −2072.00 | −0.199517 | ||||||||
\(477\) | 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 | ||||||||
\(483\) | −6272.00 | −0.590861 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −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 | ||||||||
\(490\) | −1372.00 | −0.126491 | ||||||||
\(491\) | 11268.0 | 1.03568 | 0.517839 | − | 0.855478i | \(-0.326737\pi\) | ||||
0.517839 | + | 0.855478i | \(0.326737\pi\) | |||||||
\(492\) | −5184.00 | −0.475026 | ||||||||
\(493\) | 14060.0 | 1.28444 | ||||||||
\(494\) | 2880.00 | 0.262302 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1152.00 | 0.104287 | ||||||||
\(497\) | 2744.00 | 0.247656 | ||||||||
\(498\) | 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 | \(0.478653\pi\) | |||||||
\(504\) | 2072.00 | 0.183123 | ||||||||
\(505\) | −19012.0 | −1.67529 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14984.0 | −1.31255 | ||||||||
\(508\) | −7776.00 | −0.679142 | ||||||||
\(509\) | −11790.0 | −1.02668 | −0.513342 | − | 0.858184i | \(-0.671593\pi\) | ||||
−0.513342 | + | 0.858184i | \(0.671593\pi\) | |||||||
\(510\) | 16576.0 | 1.43921 | ||||||||
\(511\) | −3766.00 | −0.326024 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −6400.00 | −0.550813 | ||||||||
\(514\) | 11268.0 | 0.966946 | ||||||||
\(515\) | 11648.0 | 0.996645 | ||||||||
\(516\) | 13184.0 | 1.12479 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4844.00 | −0.410875 | ||||||||
\(519\) | −14864.0 | −1.25714 | ||||||||
\(520\) | 2016.00 | 0.170014 | ||||||||
\(521\) | 1362.00 | 0.114530 | 0.0572652 | − | 0.998359i | \(-0.481762\pi\) | ||||
0.0572652 | + | 0.998359i | \(0.481762\pi\) | |||||||
\(522\) | −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 | ||||||||
\(525\) | 3976.00 | 0.330527 | ||||||||
\(526\) | −336.000 | −0.0278523 | ||||||||
\(527\) | −5328.00 | −0.440401 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 377.000 | 0.0309855 | ||||||||
\(530\) | −8904.00 | −0.729745 | ||||||||
\(531\) | −7400.00 | −0.604770 | ||||||||
\(532\) | −2240.00 | −0.182549 | ||||||||
\(533\) | 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 | \(-0.590536\pi\) | ||||
−0.280609 | + | 0.959822i | \(0.590536\pi\) | |||||||
\(542\) | 4416.00 | 0.349969 | ||||||||
\(543\) | −18864.0 | −1.49085 | ||||||||
\(544\) | −2368.00 | −0.186631 | ||||||||
\(545\) | 26180.0 | 2.05767 | ||||||||
\(546\) | −2016.00 | −0.158016 | ||||||||
\(547\) | 8196.00 | 0.640650 | 0.320325 | − | 0.947308i | \(-0.396208\pi\) | ||||
0.320325 | + | 0.947308i | \(0.396208\pi\) | |||||||
\(548\) | −11864.0 | −0.924827 | ||||||||
\(549\) | 7326.00 | 0.569519 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15200.0 | 1.17521 | ||||||||
\(552\) | −7168.00 | −0.552700 | ||||||||
\(553\) | −1680.00 | −0.129188 | ||||||||
\(554\) | −10588.0 | −0.811987 | ||||||||
\(555\) | 38752.0 | 2.96384 | ||||||||
\(556\) | −11200.0 | −0.854291 | ||||||||
\(557\) | 7466.00 | 0.567944 | 0.283972 | − | 0.958833i | \(-0.408348\pi\) | ||||
0.283972 | + | 0.958833i | \(0.408348\pi\) | |||||||
\(558\) | 5328.00 | 0.404215 | ||||||||
\(559\) | −7416.00 | −0.561115 | ||||||||
\(560\) | −1568.00 | −0.118322 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −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 | ||||||||
\(567\) | −2513.00 | −0.186131 | ||||||||
\(568\) | 3136.00 | 0.231661 | ||||||||
\(569\) | −14250.0 | −1.04990 | −0.524948 | − | 0.851134i | \(-0.675915\pi\) | ||||
−0.524948 | + | 0.851134i | \(0.675915\pi\) | |||||||
\(570\) | 17920.0 | 1.31682 | ||||||||
\(571\) | −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 | ||||||||
\(574\) | −2268.00 | −0.164921 | ||||||||
\(575\) | −7952.00 | −0.576733 | ||||||||
\(576\) | 2368.00 | 0.171296 | ||||||||
\(577\) | −8366.00 | −0.603607 | −0.301803 | − | 0.953370i | \(-0.597589\pi\) | ||||
−0.301803 | + | 0.953370i | \(0.597589\pi\) | |||||||
\(578\) | 1126.00 | 0.0810301 | ||||||||
\(579\) | −14224.0 | −1.02095 | ||||||||
\(580\) | 10640.0 | 0.761728 | ||||||||
\(581\) | 7504.00 | 0.535832 | ||||||||
\(582\) | 21664.0 | 1.54296 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −4304.00 | −0.304967 | ||||||||
\(585\) | 9324.00 | 0.658974 | ||||||||
\(586\) | 10044.0 | 0.708044 | ||||||||
\(587\) | 20384.0 | 1.43328 | 0.716642 | − | 0.697441i | \(-0.245678\pi\) | ||||
0.716642 | + | 0.697441i | \(0.245678\pi\) | |||||||
\(588\) | 1568.00 | 0.109971 | ||||||||
\(589\) | −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 | \(0.605267\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7252.00 | 0.499669 | ||||||||
\(596\) | −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 | \(0.582610\pi\) | |||||||
\(602\) | 5768.00 | 0.390509 | ||||||||
\(603\) | −26492.0 | −1.78912 | ||||||||
\(604\) | −2368.00 | −0.159524 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 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 | ||||||||
\(609\) | −10640.0 | −0.707971 | ||||||||
\(610\) | −5544.00 | −0.367984 | ||||||||
\(611\) | −432.000 | −0.0286037 | ||||||||
\(612\) | −10952.0 | −0.723380 | ||||||||
\(613\) | −4278.00 | −0.281871 | −0.140935 | − | 0.990019i | \(-0.545011\pi\) | ||||
−0.140935 | + | 0.990019i | \(0.545011\pi\) | |||||||
\(614\) | 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 | \(-0.300822\pi\) | ||||
0.585694 | + | 0.810532i | \(0.300822\pi\) | |||||||
\(620\) | −4032.00 | −0.261176 | ||||||||
\(621\) | −8960.00 | −0.578989 | ||||||||
\(622\) | −1936.00 | −0.124801 | ||||||||
\(623\) | 5670.00 | 0.364629 | ||||||||
\(624\) | −2304.00 | −0.147811 | ||||||||
\(625\) | −19459.0 | −1.24538 | ||||||||
\(626\) | 6116.00 | 0.390486 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10744.0 | −0.682695 | ||||||||
\(629\) | 25604.0 | 1.62305 | ||||||||
\(630\) | −7252.00 | −0.458614 | ||||||||
\(631\) | −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 | ||||||||
\(637\) | −882.000 | −0.0548605 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 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 | \(-0.796215\pi\) | ||||
−0.801971 | + | 0.597363i | \(0.796215\pi\) | |||||||
\(644\) | −3136.00 | −0.191888 | ||||||||
\(645\) | −46144.0 | −2.81693 | ||||||||
\(646\) | 11840.0 | 0.721112 | ||||||||
\(647\) | 25584.0 | 1.55458 | 0.777288 | − | 0.629145i | \(-0.216595\pi\) | ||||
0.777288 | + | 0.629145i | \(0.216595\pi\) | |||||||
\(648\) | −2872.00 | −0.174109 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2556.00 | −0.154238 | ||||||||
\(651\) | 4032.00 | 0.242744 | ||||||||
\(652\) | −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 | ||||||||
\(658\) | 336.000 | 0.0199068 | ||||||||
\(659\) | 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 | \(-0.521725\pi\) | ||||
−0.0681995 | + | 0.997672i | \(0.521725\pi\) | |||||||
\(662\) | 17224.0 | 1.01122 | ||||||||
\(663\) | 10656.0 | 0.624200 | ||||||||
\(664\) | 8576.00 | 0.501225 | ||||||||
\(665\) | 7840.00 | 0.457176 | ||||||||
\(666\) | −25604.0 | −1.48969 | ||||||||
\(667\) | 21280.0 | 1.23533 | ||||||||
\(668\) | −2176.00 | −0.126036 | ||||||||
\(669\) | 31744.0 | 1.83452 | ||||||||
\(670\) | 20048.0 | 1.15600 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1792.00 | 0.102869 | ||||||||
\(673\) | 10222.0 | 0.585482 | 0.292741 | − | 0.956192i | \(-0.405433\pi\) | ||||
0.292741 | + | 0.956192i | \(0.405433\pi\) | |||||||
\(674\) | 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 | ||||||||
\(679\) | 9478.00 | 0.535688 | ||||||||
\(680\) | 8288.00 | 0.467397 | ||||||||
\(681\) | 31488.0 | 1.77184 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −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 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 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 | \(-0.307319\pi\) | ||||
0.569030 | + | 0.822317i | \(0.307319\pi\) | |||||||
\(692\) | −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 | ||||||||
\(700\) | 1988.00 | 0.107342 | ||||||||
\(701\) | 21458.0 | 1.15614 | 0.578072 | − | 0.815985i | \(-0.303805\pi\) | ||||
0.578072 | + | 0.815985i | \(0.303805\pi\) | |||||||
\(702\) | −2880.00 | −0.154841 | ||||||||
\(703\) | 27680.0 | 1.48502 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2688.00 | −0.143597 | ||||||||
\(706\) | 1956.00 | 0.104271 | ||||||||
\(707\) | 9506.00 | 0.505672 | ||||||||
\(708\) | −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 | ||||||||
\(714\) | −8288.00 | −0.434413 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1200.00 | −0.0626342 | ||||||||
\(717\) | 24000.0 | 1.25006 | ||||||||
\(718\) | 19360.0 | 1.00628 | ||||||||
\(719\) | −18840.0 | −0.977209 | −0.488605 | − | 0.872505i | \(-0.662494\pi\) | ||||
−0.488605 | + | 0.872505i | \(0.662494\pi\) | |||||||
\(720\) | −8288.00 | −0.428994 | ||||||||
\(721\) | −5824.00 | −0.300828 | ||||||||
\(722\) | −918.000 | −0.0473191 | ||||||||
\(723\) | −16336.0 | −0.840308 | ||||||||
\(724\) | −9432.00 | −0.484168 | ||||||||
\(725\) | −13490.0 | −0.691043 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37504.0 | 1.91327 | 0.956634 | − | 0.291291i | \(-0.0940849\pi\) | ||||
0.956634 | + | 0.291291i | \(0.0940849\pi\) | |||||||
\(728\) | −1008.00 | −0.0513173 | ||||||||
\(729\) | −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 | ||||||||
\(735\) | −5488.00 | −0.275412 | ||||||||
\(736\) | −3584.00 | −0.179495 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −11988.0 | −0.597946 | ||||||||
\(739\) | −17100.0 | −0.851196 | −0.425598 | − | 0.904912i | \(-0.639936\pi\) | ||||
−0.425598 | + | 0.904912i | \(0.639936\pi\) | |||||||
\(740\) | 19376.0 | 0.962535 | ||||||||
\(741\) | 11520.0 | 0.571117 | ||||||||
\(742\) | 4452.00 | 0.220267 | ||||||||
\(743\) | 19632.0 | 0.969352 | 0.484676 | − | 0.874694i | \(-0.338938\pi\) | ||||
0.484676 | + | 0.874694i | \(0.338938\pi\) | |||||||
\(744\) | 4608.00 | 0.227067 | ||||||||
\(745\) | 7140.00 | 0.351127 | ||||||||
\(746\) | −10556.0 | −0.518073 | ||||||||
\(747\) | 39664.0 | 1.94274 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3108.00 | −0.151621 | ||||||||
\(750\) | 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 | ||||||||
\(756\) | 2240.00 | 0.107762 | ||||||||
\(757\) | −31386.0 | −1.50693 | −0.753463 | − | 0.657490i | \(-0.771618\pi\) | ||||
−0.753463 | + | 0.657490i | \(0.771618\pi\) | |||||||
\(758\) | 12680.0 | 0.607597 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 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 | ||||||||
\(763\) | −13090.0 | −0.621088 | ||||||||
\(764\) | 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 | \(-0.706614\pi\) | ||||
−0.604468 | + | 0.796629i | \(0.706614\pi\) | |||||||
\(774\) | 30488.0 | 1.41585 | ||||||||
\(775\) | 5112.00 | 0.236940 | ||||||||
\(776\) | 10832.0 | 0.501090 | ||||||||
\(777\) | −19376.0 | −0.894608 | ||||||||
\(778\) | −29620.0 | −1.36495 | ||||||||
\(779\) | 12960.0 | 0.596072 | ||||||||
\(780\) | 8064.00 | 0.370176 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 16576.0 | 0.758001 | ||||||||
\(783\) | −15200.0 | −0.693747 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 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 | ||||||||
\(791\) | 9646.00 | 0.433593 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −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 | \(-0.738075\pi\) | ||||
−0.680126 | + | 0.733096i | \(0.738075\pi\) | |||||||
\(798\) | −8960.00 | −0.397469 | ||||||||
\(799\) | −1776.00 | −0.0786362 | ||||||||
\(800\) | 2272.00 | 0.100409 | ||||||||
\(801\) | 29970.0 | 1.32202 | ||||||||
\(802\) | 6564.00 | 0.289006 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −22912.0 | −1.00503 | ||||||||
\(805\) | 10976.0 | 0.480563 | ||||||||
\(806\) | −2592.00 | −0.113275 | ||||||||
\(807\) | −10480.0 | −0.457142 | ||||||||
\(808\) | 10864.0 | 0.473013 | ||||||||
\(809\) | −16810.0 | −0.730542 | −0.365271 | − | 0.930901i | \(-0.619024\pi\) | ||||
−0.365271 | + | 0.930901i | \(0.619024\pi\) | |||||||
\(810\) | 10052.0 | 0.436039 | ||||||||
\(811\) | 9368.00 | 0.405616 | 0.202808 | − | 0.979218i | \(-0.434993\pi\) | ||||
0.202808 | + | 0.979218i | \(0.434993\pi\) | |||||||
\(812\) | −5320.00 | −0.229920 | ||||||||
\(813\) | 17664.0 | 0.761997 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14168.0 | 0.608937 | ||||||||
\(816\) | −9472.00 | −0.406356 | ||||||||
\(817\) | −32960.0 | −1.41141 | ||||||||
\(818\) | −11620.0 | −0.496679 | ||||||||
\(819\) | −4662.00 | −0.198905 | ||||||||
\(820\) | 9072.00 | 0.386351 | ||||||||
\(821\) | −34382.0 | −1.46156 | −0.730780 | − | 0.682614i | \(-0.760843\pi\) | ||||
−0.730780 | + | 0.682614i | \(0.760843\pi\) | |||||||
\(822\) | −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 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2800.00 | −0.117947 | ||||||||
\(827\) | 1716.00 | 0.0721538 | 0.0360769 | − | 0.999349i | \(-0.488514\pi\) | ||||
0.0360769 | + | 0.999349i | \(0.488514\pi\) | |||||||
\(828\) | −16576.0 | −0.695720 | ||||||||
\(829\) | −7910.00 | −0.331394 | −0.165697 | − | 0.986177i | \(-0.552987\pi\) | ||||
−0.165697 | + | 0.986177i | \(0.552987\pi\) | |||||||
\(830\) | −30016.0 | −1.25527 | ||||||||
\(831\) | −42352.0 | −1.76796 | ||||||||
\(832\) | −1152.00 | −0.0480029 | ||||||||
\(833\) | −3626.00 | −0.150820 | ||||||||
\(834\) | −44800.0 | −1.86007 | ||||||||
\(835\) | 7616.00 | 0.315644 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5760.00 | 0.237867 | ||||||||
\(838\) | 27120.0 | 1.11795 | ||||||||
\(839\) | −19360.0 | −0.796641 | −0.398320 | − | 0.917246i | \(-0.630407\pi\) | ||||
−0.398320 | + | 0.917246i | \(0.630407\pi\) | |||||||
\(840\) | −6272.00 | −0.257624 | ||||||||
\(841\) | 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 | \(0.504459\pi\) | |||||||
\(854\) | 2772.00 | 0.111072 | ||||||||
\(855\) | 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 | \(0.345525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7280.00 | 0.289162 | 0.144581 | − | 0.989493i | \(-0.453817\pi\) | ||||
0.144581 | + | 0.989493i | \(0.453817\pi\) | |||||||
\(860\) | −23072.0 | −0.914824 | ||||||||
\(861\) | −9072.00 | −0.359086 | ||||||||
\(862\) | −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 | ||||||||
\(868\) | 2016.00 | 0.0788335 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 42560.0 | 1.65853 | ||||||||
\(871\) | 12888.0 | 0.501370 | ||||||||
\(872\) | −14960.0 | −0.580974 | ||||||||
\(873\) | 50098.0 | 1.94222 | ||||||||
\(874\) | 17920.0 | 0.693539 | ||||||||
\(875\) | 5292.00 | 0.204460 | ||||||||
\(876\) | −17216.0 | −0.664012 | ||||||||
\(877\) | 8066.00 | 0.310570 | 0.155285 | − | 0.987870i | \(-0.450370\pi\) | ||||
0.155285 | + | 0.987870i | \(0.450370\pi\) | |||||||
\(878\) | −11280.0 | −0.433578 | ||||||||
\(879\) | 40176.0 | 1.54164 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25842.0 | 0.988240 | 0.494120 | − | 0.869394i | \(-0.335490\pi\) | ||||
0.494120 | + | 0.869394i | \(0.335490\pi\) | |||||||
\(882\) | 3626.00 | 0.138428 | ||||||||
\(883\) | −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 | ||||||||
\(889\) | −13608.0 | −0.513383 | ||||||||
\(890\) | −22680.0 | −0.854197 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15872.0 | 0.595778 | ||||||||
\(893\) | −1920.00 | −0.0719489 | ||||||||
\(894\) | −8160.00 | −0.305270 | ||||||||
\(895\) | 4200.00 | 0.156861 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | 16128.0 | 0.600332 | ||||||||
\(898\) | −6460.00 | −0.240059 | ||||||||
\(899\) | −13680.0 | −0.507512 | ||||||||
\(900\) | 10508.0 | 0.389185 | ||||||||
\(901\) | −23532.0 | −0.870105 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23072.0 | 0.850264 | ||||||||
\(904\) | 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 | ||||||||
\(910\) | 3528.00 | 0.128519 | ||||||||
\(911\) | −14568.0 | −0.529813 | −0.264906 | − | 0.964274i | \(-0.585341\pi\) | ||||
−0.264906 | + | 0.964274i | \(0.585341\pi\) | |||||||
\(912\) | −10240.0 | −0.371799 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 21292.0 | 0.770544 | ||||||||
\(915\) | −22176.0 | −0.801220 | ||||||||
\(916\) | 19240.0 | 0.694004 | ||||||||
\(917\) | 5936.00 | 0.213767 | ||||||||
\(918\) | −11840.0 | −0.425684 | ||||||||
\(919\) | 1400.00 | 0.0502522 | 0.0251261 | − | 0.999684i | \(-0.492001\pi\) | ||||
0.0251261 | + | 0.999684i | \(0.492001\pi\) | |||||||
\(920\) | 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 | \(-0.578530\pi\) | ||||
−0.244213 | + | 0.969722i | \(0.578530\pi\) | |||||||
\(930\) | −16128.0 | −0.568664 | ||||||||
\(931\) | −3920.00 | −0.137994 | ||||||||
\(932\) | 8728.00 | 0.306754 | ||||||||
\(933\) | −7744.00 | −0.271733 | ||||||||
\(934\) | −5632.00 | −0.197307 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5328.00 | −0.186059 | ||||||||
\(937\) | 24166.0 | 0.842549 | 0.421275 | − | 0.906933i | \(-0.361583\pi\) | ||||
0.421275 | + | 0.906933i | \(0.361583\pi\) | |||||||
\(938\) | −10024.0 | −0.348929 | ||||||||
\(939\) | 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 | ||||||||
\(945\) | −7840.00 | −0.269879 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −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 | ||||||||
\(952\) | −4144.00 | −0.141080 | ||||||||
\(953\) | −56618.0 | −1.92449 | −0.962244 | − | 0.272189i | \(-0.912253\pi\) | ||||
−0.962244 | + | 0.272189i | \(0.912253\pi\) | |||||||
\(954\) | 23532.0 | 0.798613 | ||||||||
\(955\) | −19488.0 | −0.660332 | ||||||||
\(956\) | 12000.0 | 0.405970 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6320.00 | 0.213142 | ||||||||
\(959\) | −20762.0 | −0.699103 | ||||||||
\(960\) | −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 | ||||||||
\(966\) | −12544.0 | −0.417802 | ||||||||
\(967\) | −17504.0 | −0.582100 | −0.291050 | − | 0.956708i | \(-0.594005\pi\) | ||||
−0.291050 | + | 0.956708i | \(0.594005\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 47360.0 | 1.57010 | ||||||||
\(970\) | −37912.0 | −1.25493 | ||||||||
\(971\) | 23112.0 | 0.763851 | 0.381926 | − | 0.924193i | \(-0.375261\pi\) | ||||
0.381926 | + | 0.924193i | \(0.375261\pi\) | |||||||
\(972\) | −20128.0 | −0.664204 | ||||||||
\(973\) | −19600.0 | −0.645783 | ||||||||
\(974\) | −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 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2744.00 | −0.0894427 | ||||||||
\(981\) | −69190.0 | −2.25185 | ||||||||
\(982\) | 22536.0 | 0.732335 | ||||||||
\(983\) | −15312.0 | −0.496823 | −0.248411 | − | 0.968655i | \(-0.579909\pi\) | ||||
−0.248411 | + | 0.968655i | \(0.579909\pi\) | |||||||
\(984\) | −10368.0 | −0.335894 | ||||||||
\(985\) | 16996.0 | 0.549784 | ||||||||
\(986\) | 28120.0 | 0.908239 | ||||||||
\(987\) | 1344.00 | 0.0433435 | ||||||||
\(988\) | 5760.00 | 0.185476 | ||||||||
\(989\) | −46144.0 | −1.48361 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16528.0 | −0.529797 | −0.264899 | − | 0.964276i | \(-0.585339\pi\) | ||||
−0.264899 | + | 0.964276i | \(0.585339\pi\) | |||||||
\(992\) | 2304.00 | 0.0737420 | ||||||||
\(993\) | 68896.0 | 2.20176 | ||||||||
\(994\) | 5488.00 | 0.175120 | ||||||||
\(995\) | −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 | 1694.4.a.g.1.1 | 1 | ||
11.10 | odd | 2 | 14.4.a.a.1.1 | ✓ | 1 | ||
33.32 | even | 2 | 126.4.a.h.1.1 | 1 | |||
44.43 | even | 2 | 112.4.a.a.1.1 | 1 | |||
55.32 | even | 4 | 350.4.c.b.99.1 | 2 | |||
55.43 | even | 4 | 350.4.c.b.99.2 | 2 | |||
55.54 | odd | 2 | 350.4.a.l.1.1 | 1 | |||
77.10 | even | 6 | 98.4.c.f.79.1 | 2 | |||
77.32 | odd | 6 | 98.4.c.d.79.1 | 2 | |||
77.54 | even | 6 | 98.4.c.f.67.1 | 2 | |||
77.65 | odd | 6 | 98.4.c.d.67.1 | 2 | |||
77.76 | even | 2 | 98.4.a.a.1.1 | 1 | |||
88.21 | odd | 2 | 448.4.a.b.1.1 | 1 | |||
88.43 | even | 2 | 448.4.a.o.1.1 | 1 | |||
132.131 | odd | 2 | 1008.4.a.s.1.1 | 1 | |||
143.142 | odd | 2 | 2366.4.a.h.1.1 | 1 | |||
231.32 | even | 6 | 882.4.g.b.667.1 | 2 | |||
231.65 | even | 6 | 882.4.g.b.361.1 | 2 | |||
231.131 | odd | 6 | 882.4.g.k.361.1 | 2 | |||
231.164 | odd | 6 | 882.4.g.k.667.1 | 2 | |||
231.230 | odd | 2 | 882.4.a.i.1.1 | 1 | |||
308.307 | odd | 2 | 784.4.a.s.1.1 | 1 | |||
385.384 | even | 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 | 11.10 | odd | 2 | ||
98.4.a.a.1.1 | 1 | 77.76 | even | 2 | |||
98.4.c.d.67.1 | 2 | 77.65 | odd | 6 | |||
98.4.c.d.79.1 | 2 | 77.32 | odd | 6 | |||
98.4.c.f.67.1 | 2 | 77.54 | even | 6 | |||
98.4.c.f.79.1 | 2 | 77.10 | even | 6 | |||
112.4.a.a.1.1 | 1 | 44.43 | even | 2 | |||
126.4.a.h.1.1 | 1 | 33.32 | even | 2 | |||
350.4.a.l.1.1 | 1 | 55.54 | odd | 2 | |||
350.4.c.b.99.1 | 2 | 55.32 | even | 4 | |||
350.4.c.b.99.2 | 2 | 55.43 | even | 4 | |||
448.4.a.b.1.1 | 1 | 88.21 | odd | 2 | |||
448.4.a.o.1.1 | 1 | 88.43 | even | 2 | |||
784.4.a.s.1.1 | 1 | 308.307 | odd | 2 | |||
882.4.a.i.1.1 | 1 | 231.230 | odd | 2 | |||
882.4.g.b.361.1 | 2 | 231.65 | even | 6 | |||
882.4.g.b.667.1 | 2 | 231.32 | even | 6 | |||
882.4.g.k.361.1 | 2 | 231.131 | odd | 6 | |||
882.4.g.k.667.1 | 2 | 231.164 | odd | 6 | |||
1008.4.a.s.1.1 | 1 | 132.131 | odd | 2 | |||
1694.4.a.g.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2366.4.a.h.1.1 | 1 | 143.142 | odd | 2 | |||
2450.4.a.bo.1.1 | 1 | 385.384 | even | 2 |