Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7280,2,Mod(1,7280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7280.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: | \(58.1310926715\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3640) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.820249\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7280.1 |
$q$-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 | ||||||||
\(3\) | −0.820249 | −0.473571 | −0.236786 | − | 0.971562i | \(-0.576094\pi\) | ||||
−0.236786 | + | 0.971562i | \(0.576094\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.32719 | −0.775730 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.23607 | −0.372689 | −0.186344 | − | 0.982485i | \(-0.559664\pi\) | ||||
−0.186344 | + | 0.982485i | \(0.559664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.820249 | −0.211787 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.313307 | −0.0759882 | −0.0379941 | − | 0.999278i | \(-0.512097\pi\) | ||||
−0.0379941 | + | 0.999278i | \(0.512097\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.90888 | 0.437926 | 0.218963 | − | 0.975733i | \(-0.429733\pi\) | ||||
0.218963 | + | 0.975733i | \(0.429733\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.820249 | −0.178993 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.89045 | 1.64527 | 0.822636 | − | 0.568568i | \(-0.192502\pi\) | ||||
0.822636 | + | 0.568568i | \(0.192502\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.36962 | 0.840935 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.42970 | 0.636880 | 0.318440 | − | 0.947943i | \(-0.396841\pi\) | ||||
0.318440 | + | 0.947943i | \(0.396841\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.27850 | 1.12765 | 0.563826 | − | 0.825894i | \(-0.309329\pi\) | ||||
0.563826 | + | 0.825894i | \(0.309329\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.01388 | 0.176495 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.05632 | −0.666854 | −0.333427 | − | 0.942776i | \(-0.608205\pi\) | ||||
−0.333427 | + | 0.942776i | \(0.608205\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.820249 | −0.131345 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.79933 | −1.21805 | −0.609025 | − | 0.793151i | \(-0.708439\pi\) | ||||
−0.609025 | + | 0.793151i | \(0.708439\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.87657 | −0.438672 | −0.219336 | − | 0.975649i | \(-0.570389\pi\) | ||||
−0.219336 | + | 0.975649i | \(0.570389\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.32719 | −0.346917 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.5987 | −1.69184 | −0.845919 | − | 0.533312i | \(-0.820947\pi\) | ||||
−0.845919 | + | 0.533312i | \(0.820947\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.256990 | 0.0359858 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.65438 | −0.639329 | −0.319664 | − | 0.947531i | \(-0.603570\pi\) | ||||
−0.319664 | + | 0.947531i | \(0.603570\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.23607 | −0.166671 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.56575 | −0.207389 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.50240 | 1.23711 | 0.618554 | − | 0.785743i | \(-0.287719\pi\) | ||||
0.618554 | + | 0.785743i | \(0.287719\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.01388 | −0.385888 | −0.192944 | − | 0.981210i | \(-0.561804\pi\) | ||||
−0.192944 | + | 0.981210i | \(0.561804\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.32719 | −0.293199 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.4398 | 1.39760 | 0.698799 | − | 0.715319i | \(-0.253718\pi\) | ||||
0.698799 | + | 0.715319i | \(0.253718\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.47214 | −0.779154 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.77782 | 0.448344 | 0.224172 | − | 0.974550i | \(-0.428032\pi\) | ||||
0.224172 | + | 0.974550i | \(0.428032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.66827 | −0.663420 | −0.331710 | − | 0.943381i | \(-0.607626\pi\) | ||||
−0.331710 | + | 0.943381i | \(0.607626\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.820249 | −0.0947142 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.23607 | −0.140863 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.5525 | −1.29975 | −0.649877 | − | 0.760040i | \(-0.725179\pi\) | ||||
−0.649877 | + | 0.760040i | \(0.725179\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.39739 | 0.377488 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.1404 | −1.11305 | −0.556527 | − | 0.830830i | \(-0.687866\pi\) | ||||
−0.556527 | + | 0.830830i | \(0.687866\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.313307 | −0.0339830 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.81321 | −0.301608 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.2106 | 1.61232 | 0.806160 | − | 0.591697i | \(-0.201542\pi\) | ||||
0.806160 | + | 0.591697i | \(0.201542\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.14994 | −0.534023 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.90888 | 0.195847 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.7670 | 1.29629 | 0.648147 | − | 0.761515i | \(-0.275544\pi\) | ||||
0.648147 | + | 0.761515i | \(0.275544\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.87657 | 0.289106 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.2253 | −1.81348 | −0.906741 | − | 0.421688i | \(-0.861438\pi\) | ||||
−0.906741 | + | 0.421688i | \(0.861438\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.83926 | 0.969492 | 0.484746 | − | 0.874655i | \(-0.338912\pi\) | ||||
0.484746 | + | 0.874655i | \(0.338912\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.820249 | −0.0800481 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.7132 | 1.32570 | 0.662852 | − | 0.748750i | \(-0.269346\pi\) | ||||
0.662852 | + | 0.748750i | \(0.269346\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.48602 | −0.525465 | −0.262733 | − | 0.964869i | \(-0.584624\pi\) | ||||
−0.262733 | + | 0.964869i | \(0.584624\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.32719 | 0.315803 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.37339 | −0.129197 | −0.0645986 | − | 0.997911i | \(-0.520577\pi\) | ||||
−0.0645986 | + | 0.997911i | \(0.520577\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.89045 | 0.735788 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.32719 | −0.215149 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.313307 | −0.0287208 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.47214 | −0.861103 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.39739 | 0.576833 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.23607 | −0.109683 | −0.0548416 | − | 0.998495i | \(-0.517465\pi\) | ||||
−0.0548416 | + | 0.998495i | \(0.517465\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.35950 | 0.207743 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.9720 | 1.65759 | 0.828797 | − | 0.559549i | \(-0.189026\pi\) | ||||
0.828797 | + | 0.559549i | \(0.189026\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.90888 | 0.165521 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.36962 | 0.376077 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.0056 | −0.940270 | −0.470135 | − | 0.882594i | \(-0.655795\pi\) | ||||
−0.470135 | + | 0.882594i | \(0.655795\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.9304 | 1.01192 | 0.505961 | − | 0.862556i | \(-0.331138\pi\) | ||||
0.505961 | + | 0.862556i | \(0.331138\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.51379 | 0.801205 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.23607 | −0.103365 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.42970 | 0.284821 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.820249 | −0.0676530 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.9923 | 1.71976 | 0.859878 | − | 0.510500i | \(-0.170540\pi\) | ||||
0.859878 | + | 0.510500i | \(0.170540\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.2131 | 1.48216 | 0.741080 | − | 0.671416i | \(-0.234314\pi\) | ||||
0.741080 | + | 0.671416i | \(0.234314\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.729126 | 0.0589463 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.27850 | 0.504301 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.3879 | 1.38770 | 0.693851 | − | 0.720119i | \(-0.255913\pi\) | ||||
0.693851 | + | 0.720119i | \(0.255913\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.81775 | 0.302768 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.89045 | 0.621855 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.54234 | −0.120805 | −0.0604026 | − | 0.998174i | \(-0.519238\pi\) | ||||
−0.0604026 | + | 0.998174i | \(0.519238\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.01388 | 0.0789307 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.51379 | 0.736199 | 0.368099 | − | 0.929786i | \(-0.380009\pi\) | ||||
0.368099 | + | 0.929786i | \(0.380009\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.44232 | −0.339713 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.80945 | 0.745799 | 0.372899 | − | 0.927872i | \(-0.378364\pi\) | ||||
0.372899 | + | 0.927872i | \(0.378364\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.79434 | −0.585858 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.7625 | −1.62660 | −0.813302 | − | 0.581842i | \(-0.802332\pi\) | ||||
−0.813302 | + | 0.581842i | \(0.802332\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.1190 | 1.56976 | 0.784881 | − | 0.619646i | \(-0.212724\pi\) | ||||
0.784881 | + | 0.619646i | \(0.212724\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.47214 | 0.182746 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.05632 | −0.298226 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.387269 | 0.0283199 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.36962 | 0.317843 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.5842 | 0.838202 | 0.419101 | − | 0.907940i | \(-0.362345\pi\) | ||||
0.419101 | + | 0.907940i | \(0.362345\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.5752 | −1.26509 | −0.632547 | − | 0.774522i | \(-0.717990\pi\) | ||||
−0.632547 | + | 0.774522i | \(0.717990\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.820249 | −0.0587393 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.9221 | −1.27690 | −0.638448 | − | 0.769665i | \(-0.720423\pi\) | ||||
−0.638448 | + | 0.769665i | \(0.720423\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.7873 | −1.04824 | −0.524121 | − | 0.851644i | \(-0.675606\pi\) | ||||
−0.524121 | + | 0.851644i | \(0.675606\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.38351 | −0.661862 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.42970 | 0.240718 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.79933 | −0.544729 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.3626 | −1.27629 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.35950 | −0.163210 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.7069 | 1.21900 | 0.609498 | − | 0.792788i | \(-0.291371\pi\) | ||||
0.609498 | + | 0.792788i | \(0.291371\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.09875 | −0.212323 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.87657 | −0.196180 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.27850 | 0.426212 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.64939 | 0.314177 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.313307 | −0.0210753 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.8885 | 1.19791 | 0.598953 | − | 0.800784i | \(-0.295584\pi\) | ||||
0.598953 | + | 0.800784i | \(0.295584\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.32719 | −0.155146 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.8658 | 1.45128 | 0.725641 | − | 0.688074i | \(-0.241543\pi\) | ||||
0.725641 | + | 0.688074i | \(0.241543\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.82709 | −0.649393 | −0.324696 | − | 0.945818i | \(-0.605262\pi\) | ||||
−0.324696 | + | 0.945818i | \(0.605262\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.01388 | 0.0667087 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.7302 | 1.62013 | 0.810063 | − | 0.586342i | \(-0.199433\pi\) | ||||
0.810063 | + | 0.586342i | \(0.199433\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.5987 | −0.756613 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.47590 | 0.615526 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.51207 | 0.162493 | 0.0812463 | − | 0.996694i | \(-0.474110\pi\) | ||||
0.0812463 | + | 0.996694i | \(0.474110\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.0524 | 1.42052 | 0.710259 | − | 0.703941i | \(-0.248578\pi\) | ||||
0.710259 | + | 0.703941i | \(0.248578\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.8956 | −1.01970 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.90888 | 0.121459 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.31766 | 0.527110 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.2594 | −1.34188 | −0.670941 | − | 0.741511i | \(-0.734109\pi\) | ||||
−0.670941 | + | 0.741511i | \(0.734109\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.75313 | −0.613174 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.256990 | 0.0160933 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.2530 | −0.764323 | −0.382162 | − | 0.924095i | \(-0.624820\pi\) | ||||
−0.382162 | + | 0.924095i | \(0.624820\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.05632 | −0.252047 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.98157 | −0.494047 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.1435 | −1.61208 | −0.806038 | − | 0.591863i | \(-0.798392\pi\) | ||||
−0.806038 | + | 0.591863i | \(0.798392\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.65438 | −0.285916 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.4765 | −0.763549 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.9734 | −1.82751 | −0.913756 | − | 0.406264i | \(-0.866831\pi\) | ||||
−0.913756 | + | 0.406264i | \(0.866831\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.3967 | −0.935284 | −0.467642 | − | 0.883918i | \(-0.654896\pi\) | ||||
−0.467642 | + | 0.883918i | \(0.654896\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.820249 | −0.0496437 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.23607 | −0.0745377 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.56952 | 0.394724 | 0.197362 | − | 0.980331i | \(-0.436763\pi\) | ||||
0.197362 | + | 0.980331i | \(0.436763\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.6113 | −0.874754 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.9923 | 1.25229 | 0.626147 | − | 0.779705i | \(-0.284631\pi\) | ||||
0.626147 | + | 0.779705i | \(0.284631\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.0582 | −0.657340 | −0.328670 | − | 0.944445i | \(-0.606600\pi\) | ||||
−0.328670 | + | 0.944445i | \(0.606600\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.56575 | −0.0927473 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.79933 | −0.460380 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9018 | −0.994226 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.4721 | −0.613887 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.267113 | 0.0156049 | 0.00780246 | − | 0.999970i | \(-0.497516\pi\) | ||||
0.00780246 | + | 0.999970i | \(0.497516\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.50240 | 0.553251 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.40115 | −0.313407 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.89045 | 0.456317 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.87657 | −0.165803 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.9493 | 0.858813 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.01388 | −0.172574 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.57089 | 0.317947 | 0.158974 | − | 0.987283i | \(-0.449182\pi\) | ||||
0.158974 | + | 0.987283i | \(0.449182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.07065 | −0.459123 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.4353 | 1.72583 | 0.862913 | − | 0.505352i | \(-0.168637\pi\) | ||||
0.862913 | + | 0.505352i | \(0.168637\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.0333 | 0.736688 | 0.368344 | − | 0.929689i | \(-0.379925\pi\) | ||||
0.368344 | + | 0.929689i | \(0.379925\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.32719 | −0.131122 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.3151 | 1.70267 | 0.851334 | − | 0.524625i | \(-0.175794\pi\) | ||||
0.851334 | + | 0.524625i | \(0.175794\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.23935 | −0.237358 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.2482 | −0.627815 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.598065 | −0.0332772 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.49990 | 0.248845 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.5987 | −0.639455 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.5462 | 1.95380 | 0.976898 | − | 0.213706i | \(-0.0685534\pi\) | ||||
0.976898 | + | 0.213706i | \(0.0685534\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.43983 | 0.517299 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.4398 | 0.625024 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.3088 | 1.26971 | 0.634855 | − | 0.772632i | \(-0.281060\pi\) | ||||
0.634855 | + | 0.772632i | \(0.281060\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.12652 | 0.0611841 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.76065 | −0.420263 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.47214 | −0.348448 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.7423 | 1.11351 | 0.556753 | − | 0.830678i | \(-0.312047\pi\) | ||||
0.556753 | + | 0.830678i | \(0.312047\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.18146 | −0.223829 | −0.111914 | − | 0.993718i | \(-0.535698\pi\) | ||||
−0.111914 | + | 0.993718i | \(0.535698\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.36962 | 0.233233 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.6417 | 1.15187 | 0.575935 | − | 0.817495i | \(-0.304638\pi\) | ||||
0.575935 | + | 0.817495i | \(0.304638\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.77782 | 0.200506 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.256990 | 0.0136014 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.83335 | 0.413428 | 0.206714 | − | 0.978401i | \(-0.433723\pi\) | ||||
0.206714 | + | 0.978401i | \(0.433723\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3562 | −0.808220 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.76951 | 0.407794 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.66827 | −0.296691 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.4802 | 1.48665 | 0.743327 | − | 0.668928i | \(-0.233246\pi\) | ||||
0.743327 | + | 0.668928i | \(0.233246\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.1505 | 0.944879 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.65438 | −0.241643 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.0683 | 1.03910 | 0.519548 | − | 0.854442i | \(-0.326101\pi\) | ||||
0.519548 | + | 0.854442i | \(0.326101\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.820249 | −0.0423575 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.42970 | 0.176639 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.81448 | −0.452769 | −0.226385 | − | 0.974038i | \(-0.572691\pi\) | ||||
−0.226385 | + | 0.974038i | \(0.572691\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.01388 | 0.0519428 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.21638 | −0.266544 | −0.133272 | − | 0.991079i | \(-0.542548\pi\) | ||||
−0.133272 | + | 0.991079i | \(0.542548\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.23607 | −0.0629959 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.69432 | 0.340291 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.85506 | 0.347565 | 0.173783 | − | 0.984784i | \(-0.444401\pi\) | ||||
0.173783 | + | 0.984784i | \(0.444401\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.47214 | −0.125021 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.5618 | −0.784989 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.5525 | −0.581267 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.4150 | 1.02460 | 0.512301 | − | 0.858806i | \(-0.328793\pi\) | ||||
0.512301 | + | 0.858806i | \(0.328793\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.56575 | −0.0783858 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.4858 | −1.52239 | −0.761195 | − | 0.648523i | \(-0.775387\pi\) | ||||
−0.761195 | + | 0.648523i | \(0.775387\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.27850 | 0.312754 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.39739 | 0.168818 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.01388 | 0.248529 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.5063 | −1.45899 | −0.729495 | − | 0.683986i | \(-0.760245\pi\) | ||||
−0.729495 | + | 0.683986i | \(0.760245\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.02732 | 0.445285 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.50240 | 0.467582 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.1404 | −0.497773 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.78589 | −0.479217 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.1176 | 0.494278 | 0.247139 | − | 0.968980i | \(-0.420510\pi\) | ||||
0.247139 | + | 0.968980i | \(0.420510\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0000 | 0.877266 | 0.438633 | − | 0.898666i | \(-0.355463\pi\) | ||||
0.438633 | + | 0.898666i | \(0.355463\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26.9923 | 1.31241 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.313307 | −0.0151976 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.01388 | −0.145852 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.01388 | 0.0489508 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.97785 | −0.287943 | −0.143971 | − | 0.989582i | \(-0.545987\pi\) | ||||
−0.143971 | + | 0.989582i | \(0.545987\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.52585 | −0.121385 | −0.0606923 | − | 0.998157i | \(-0.519331\pi\) | ||||
−0.0606923 | + | 0.998157i | \(0.519331\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.81321 | −0.134883 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.0619 | 0.720508 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.6835 | 0.653079 | 0.326539 | − | 0.945184i | \(-0.394117\pi\) | ||||
0.326539 | + | 0.945184i | \(0.394117\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.32719 | −0.110819 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.0372 | 1.75969 | 0.879846 | − | 0.475260i | \(-0.157646\pi\) | ||||
0.879846 | + | 0.475260i | \(0.157646\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.2106 | 0.721052 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.2189 | −0.814426 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.6544 | 0.785969 | 0.392984 | − | 0.919545i | \(-0.371443\pi\) | ||||
0.392984 | + | 0.919545i | \(0.371443\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.64050 | 0.453953 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.9393 | −0.701909 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00000 | 0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.30318 | 0.107738 | 0.0538692 | − | 0.998548i | \(-0.482845\pi\) | ||||
0.0538692 | + | 0.998548i | \(0.482845\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.36904 | −0.0639011 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.8183 | −1.15591 | −0.577953 | − | 0.816070i | \(-0.696148\pi\) | ||||
−0.577953 | + | 0.816070i | \(0.696148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.8410 | −0.968562 | −0.484281 | − | 0.874912i | \(-0.660919\pi\) | ||||
−0.484281 | + | 0.874912i | \(0.660919\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.14994 | −0.238823 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.8668 | −1.33580 | −0.667899 | − | 0.744252i | \(-0.732806\pi\) | ||||
−0.667899 | + | 0.744252i | \(0.732806\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.4398 | 0.528242 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.2624 | −0.657176 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.55563 | 0.163488 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.90888 | 0.0875853 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.8316 | 0.495947 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.4810 | −0.661653 | −0.330827 | − | 0.943692i | \(-0.607328\pi\) | ||||
−0.330827 | + | 0.943692i | \(0.607328\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.05632 | −0.184952 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.47214 | −0.294492 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.7670 | 0.579720 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.1043 | −0.911014 | −0.455507 | − | 0.890232i | \(-0.650542\pi\) | ||||
−0.455507 | + | 0.890232i | \(0.650542\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.26510 | 0.0572098 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.9049 | 1.84601 | 0.923006 | − | 0.384786i | \(-0.125725\pi\) | ||||
0.923006 | + | 0.384786i | \(0.125725\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.07455 | −0.0483953 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.87657 | 0.129292 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.77782 | 0.169458 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.5184 | −0.784233 | −0.392116 | − | 0.919916i | \(-0.628257\pi\) | ||||
−0.392116 | + | 0.919916i | \(0.628257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.80368 | −0.348643 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.1155 | −1.65490 | −0.827450 | − | 0.561540i | \(-0.810209\pi\) | ||||
−0.827450 | + | 0.561540i | \(0.810209\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.2253 | −0.811014 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.820249 | −0.0364285 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.6701 | −0.871861 | −0.435931 | − | 0.899980i | \(-0.643581\pi\) | ||||
−0.435931 | + | 0.899980i | \(0.643581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.66827 | −0.250749 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.34107 | 0.368267 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.83926 | 0.433570 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.3367 | 0.630528 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.04619 | −0.353189 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.640306 | 0.0280523 | 0.0140262 | − | 0.999902i | \(-0.495535\pi\) | ||||
0.0140262 | + | 0.999902i | \(0.495535\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.7269 | 1.38732 | 0.693660 | − | 0.720303i | \(-0.255997\pi\) | ||||
0.693660 | + | 0.720303i | \(0.255997\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.820249 | −0.0357986 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.96710 | −0.0856882 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39.2592 | 1.70692 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.1139 | −0.959662 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.79933 | −0.337826 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.7132 | 0.592873 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.8507 | 0.770313 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.23607 | −0.0532412 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.2733 | 1.38754 | 0.693768 | − | 0.720198i | \(-0.255949\pi\) | ||||
0.693768 | + | 0.720198i | \(0.255949\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.3228 | −0.743394 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.48602 | −0.234995 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.1082 | 1.11631 | 0.558153 | − | 0.829738i | \(-0.311510\pi\) | ||||
0.558153 | + | 0.829738i | \(0.311510\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.01388 | 0.299345 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.54688 | 0.278906 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.5525 | −0.491261 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.32719 | 0.141231 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 40.8437 | 1.73060 | 0.865302 | − | 0.501251i | \(-0.167127\pi\) | ||||
0.865302 | + | 0.501251i | \(0.167127\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.87657 | −0.121666 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.317657 | −0.0134115 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.0366 | 1.72949 | 0.864743 | − | 0.502215i | \(-0.167481\pi\) | ||||
0.864743 | + | 0.502215i | \(0.167481\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.37339 | −0.0577788 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.39739 | 0.142677 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.9917 | −0.754251 | −0.377126 | − | 0.926162i | \(-0.623087\pi\) | ||||
−0.377126 | + | 0.926162i | \(0.623087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.56121 | 0.358276 | 0.179138 | − | 0.983824i | \(-0.442669\pi\) | ||||
0.179138 | + | 0.983824i | \(0.442669\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.50192 | −0.396948 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.89045 | 0.329055 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.7821 | −1.32311 | −0.661553 | − | 0.749899i | \(-0.730102\pi\) | ||||
−0.661553 | + | 0.749899i | \(0.730102\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.4161 | 0.599112 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.1404 | −0.420695 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.75313 | 0.238270 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.32719 | −0.0962175 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.2025 | −0.833846 | −0.416923 | − | 0.908942i | \(-0.636892\pi\) | ||||
−0.416923 | + | 0.908942i | \(0.636892\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.9849 | 0.493829 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.7006 | 0.604701 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.17569 | −0.171475 | −0.0857375 | − | 0.996318i | \(-0.527325\pi\) | ||||
−0.0857375 | + | 0.996318i | \(0.527325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.313307 | −0.0128443 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.1292 | 0.496417 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.8924 | −0.567626 | −0.283813 | − | 0.958880i | \(-0.591600\pi\) | ||||
−0.283813 | + | 0.958880i | \(0.591600\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.2176 | 1.19181 | 0.595904 | − | 0.803055i | \(-0.296794\pi\) | ||||
0.595904 | + | 0.803055i | \(0.296794\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26.6227 | −1.08416 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.47214 | −0.385097 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.67965 | 0.149353 | 0.0746763 | − | 0.997208i | \(-0.476208\pi\) | ||||
0.0746763 | + | 0.997208i | \(0.476208\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.81321 | −0.113997 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.5987 | −0.469231 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.49354 | 0.141103 | 0.0705514 | − | 0.997508i | \(-0.477524\pi\) | ||||
0.0705514 | + | 0.997508i | \(0.477524\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.39739 | 0.257968 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.1928 | 1.61810 | 0.809050 | − | 0.587740i | \(-0.199982\pi\) | ||||
0.809050 | + | 0.587740i | \(0.199982\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.0314 | −1.16687 | −0.583436 | − | 0.812159i | \(-0.698292\pi\) | ||||
−0.583436 | + | 0.812159i | \(0.698292\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.4783 | 1.38357 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.2106 | 0.609400 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.93538 | 0.0772916 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.27087 | 0.0506731 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.6943 | −0.584972 | −0.292486 | − | 0.956270i | \(-0.594482\pi\) | ||||
−0.292486 | + | 0.956270i | \(0.594482\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.5241 | −0.577281 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.23607 | −0.0490519 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.79170 | −0.347794 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.8183 | −1.13826 | −0.569128 | − | 0.822249i | \(-0.692719\pi\) | ||||
−0.569128 | + | 0.822249i | \(0.692719\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.06599 | −0.278656 | −0.139328 | − | 0.990246i | \(-0.544494\pi\) | ||||
−0.139328 | + | 0.990246i | \(0.544494\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.35950 | 0.0929053 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.81545 | 0.228629 | 0.114314 | − | 0.993445i | \(-0.463533\pi\) | ||||
0.114314 | + | 0.993445i | \(0.463533\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.7456 | −0.461056 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.14994 | −0.201842 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.1315 | 0.826940 | 0.413470 | − | 0.910518i | \(-0.364317\pi\) | ||||
0.413470 | + | 0.910518i | \(0.364317\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.9720 | 0.741299 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.1911 | 0.514635 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.7095 | −0.845681 | −0.422840 | − | 0.906204i | \(-0.638967\pi\) | ||||
−0.422840 | + | 0.906204i | \(0.638967\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.1079 | 1.32664 | 0.663322 | − | 0.748334i | \(-0.269146\pi\) | ||||
0.663322 | + | 0.748334i | \(0.269146\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.256990 | 0.00998067 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.90888 | 0.0740231 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.0619 | 1.04784 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.6731 | −0.567293 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.72537 | 0.143816 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.7024 | 0.875113 | 0.437557 | − | 0.899191i | \(-0.355844\pi\) | ||||
0.437557 | + | 0.899191i | \(0.355844\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.36962 | 0.168187 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.6733 | 0.448640 | 0.224320 | − | 0.974516i | \(-0.427984\pi\) | ||||
0.224320 | + | 0.974516i | \(0.427984\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.7670 | 0.489953 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.9354 | −0.687285 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.5600 | −0.518858 | −0.259429 | − | 0.965762i | \(-0.583534\pi\) | ||||
−0.259429 | + | 0.965762i | \(0.583534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.0056 | −0.420502 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.06067 | 0.307534 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.65438 | −0.177318 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.05803 | −0.344584 | −0.172292 | − | 0.985046i | \(-0.555117\pi\) | ||||
−0.172292 | + | 0.985046i | \(0.555117\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.87657 | 0.109272 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.9304 | 0.452545 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.44359 | 0.0925574 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.2849 | −0.767245 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.05236 | −0.0775167 | −0.0387584 | − | 0.999249i | \(-0.512340\pi\) | ||||
−0.0387584 | + | 0.999249i | \(0.512340\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.74301 | −0.292033 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.51379 | 0.358310 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.2253 | −0.685432 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.1593 | 0.569319 | 0.284659 | − | 0.958629i | \(-0.408120\pi\) | ||||
0.284659 | + | 0.958629i | \(0.408120\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.8848 | 1.00826 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 49.5402 | 1.85530 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.23607 | −0.0462263 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.06053 | −0.0769518 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.2808 | −0.457997 | −0.228998 | − | 0.973427i | \(-0.573545\pi\) | ||||
−0.228998 | + | 0.973427i | \(0.573545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.83926 | 0.366433 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.0884 | −0.672716 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.42970 | 0.127376 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.4949 | −1.31643 | −0.658216 | − | 0.752829i | \(-0.728689\pi\) | ||||
−0.658216 | + | 0.752829i | \(0.728689\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.84616 | 0.105413 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.901249 | 0.0333339 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0202 | 0.961080 | 0.480540 | − | 0.876973i | \(-0.340441\pi\) | ||||
0.480540 | + | 0.876973i | \(0.340441\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.820249 | −0.0302553 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.1404 | −0.520868 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −50.2889 | −1.84991 | −0.924953 | − | 0.380081i | \(-0.875896\pi\) | ||||
−0.924953 | + | 0.380081i | \(0.875896\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.56575 | −0.0575194 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.6121 | −0.572752 | −0.286376 | − | 0.958117i | \(-0.592451\pi\) | ||||
−0.286376 | + | 0.958117i | \(0.592451\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.9923 | 0.769098 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.5987 | 0.863430 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.7132 | 0.501069 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.2929 | 0.849971 | 0.424986 | − | 0.905200i | \(-0.360279\pi\) | ||||
0.424986 | + | 0.905200i | \(0.360279\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.4380 | 0.635476 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.2131 | 0.662843 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.1961 | 0.697695 | 0.348848 | − | 0.937179i | \(-0.386573\pi\) | ||||
0.348848 | + | 0.937179i | \(0.386573\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.00000 | 0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.6598 | −1.40142 | −0.700708 | − | 0.713448i | \(-0.747132\pi\) | ||||
−0.700708 | + | 0.713448i | \(0.747132\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.48602 | −0.198607 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.729126 | 0.0263616 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.50240 | 0.343112 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.94427 | −0.250417 | −0.125208 | − | 0.992130i | \(-0.539960\pi\) | ||||
−0.125208 | + | 0.992130i | \(0.539960\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.0505 | 0.361962 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −51.3618 | −1.84735 | −0.923677 | − | 0.383171i | \(-0.874832\pi\) | ||||
−0.923677 | + | 0.383171i | \(0.874832\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.27850 | 0.225530 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.32719 | 0.119362 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.8880 | −0.533416 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.66964 | −0.167093 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.9865 | 0.535574 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.3879 | 0.620599 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.3365 | −0.689273 | −0.344636 | − | 0.938736i | \(-0.611998\pi\) | ||||
−0.344636 | + | 0.938736i | \(0.611998\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.4442 | 0.763433 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.37339 | −0.0488320 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.01388 | −0.107026 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.81775 | 0.135402 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.19173 | −0.148479 | −0.0742393 | − | 0.997240i | \(-0.523653\pi\) | ||||
−0.0742393 | + | 0.997240i | \(0.523653\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.63394 | 0.128560 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −35.3980 | −1.25073 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.00636 | 0.247249 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.89045 | 0.278102 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.5857 | 0.865456 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −48.5800 | −1.70798 | −0.853992 | − | 0.520287i | \(-0.825825\pi\) | ||||
−0.853992 | + | 0.520287i | \(0.825825\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.6220 | 0.829480 | 0.414740 | − | 0.909940i | \(-0.363873\pi\) | ||||
0.414740 | + | 0.909940i | \(0.363873\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.6291 | 0.442923 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.54234 | −0.0540257 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.49101 | −0.192106 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.32719 | −0.0813186 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.8328 | 0.866671 | 0.433336 | − | 0.901233i | \(-0.357336\pi\) | ||||
0.433336 | + | 0.901233i | \(0.357336\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −45.5230 | −1.58683 | −0.793417 | − | 0.608679i | \(-0.791700\pi\) | ||||
−0.793417 | + | 0.608679i | \(0.791700\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.01388 | 0.0352989 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.2806 | 1.71365 | 0.856827 | − | 0.515603i | \(-0.172432\pi\) | ||||
0.856827 | + | 0.515603i | \(0.172432\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.3225 | 1.01841 | 0.509205 | − | 0.860645i | \(-0.329939\pi\) | ||||
0.509205 | + | 0.860645i | \(0.329939\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.38864 | −0.186930 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.313307 | −0.0108555 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.51379 | 0.329238 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27.4347 | 0.948282 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.1649 | −1.42117 | −0.710585 | − | 0.703611i | \(-0.751570\pi\) | ||||
−0.710585 | + | 0.703611i | \(0.751570\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.2371 | −0.594384 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.2189 | −0.593051 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.47214 | −0.325466 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.07046 | 0.311297 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.0062 | −1.09716 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.1365 | 0.792179 | 0.396089 | − | 0.918212i | \(-0.370367\pi\) | ||||
0.396089 | + | 0.918212i | \(0.370367\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.44232 | −0.151924 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.07909 | 0.139339 | 0.0696696 | − | 0.997570i | \(-0.477806\pi\) | ||||
0.0696696 | + | 0.997570i | \(0.477806\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.24667 | −0.247253 | −0.123627 | − | 0.992329i | \(-0.539453\pi\) | ||||
−0.123627 | + | 0.992329i | \(0.539453\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.39739 | 0.218023 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.6776 | 0.805995 | 0.402998 | − | 0.915201i | \(-0.367968\pi\) | ||||
0.402998 | + | 0.915201i | \(0.367968\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.80945 | 0.333531 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.8637 | 0.470837 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.2796 | 0.484403 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.4398 | 0.387624 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −29.7113 | −1.00557 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.8107 | 1.51315 | 0.756575 | − | 0.653907i | \(-0.226871\pi\) | ||||
0.756575 | + | 0.653907i | \(0.226871\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.219099 | −0.00739004 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −53.8935 | −1.81572 | −0.907860 | − | 0.419274i | \(-0.862285\pi\) | ||||
−0.907860 | + | 0.419274i | \(0.862285\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.8256 | 0.633533 | 0.316767 | − | 0.948504i | \(-0.397403\pi\) | ||||
0.316767 | + | 0.948504i | \(0.397403\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.79434 | −0.262004 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.9331 | 0.400673 | 0.200337 | − | 0.979727i | \(-0.435796\pi\) | ||||
0.200337 | + | 0.979727i | \(0.435796\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.23607 | −0.0414564 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.19941 | −0.140685 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.1404 | −0.740900 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.7625 | −0.727439 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.47214 | −0.216098 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.5334 | 0.718179 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.45825 | 0.0485814 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.35950 | 0.0785193 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.1190 | 0.702019 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.8916 | −1.52381 | −0.761903 | − | 0.647691i | \(-0.775735\pi\) | ||||
−0.761903 | + | 0.647691i | \(0.775735\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 42.4137 | 1.40677 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.7625 | −0.588497 | −0.294249 | − | 0.955729i | \(-0.595069\pi\) | ||||
−0.294249 | + | 0.955729i | \(0.595069\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.5342 | 0.414822 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.47214 | 0.0817263 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.9720 | 0.626512 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.6181 | 0.977012 | 0.488506 | − | 0.872561i | \(-0.337542\pi\) | ||||
0.488506 | + | 0.872561i | \(0.337542\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.56952 | −0.150571 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.77782 | 0.124348 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.05632 | −0.133371 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.8979 | −0.752064 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43.1940 | −1.41715 | −0.708575 | − | 0.705636i | \(-0.750661\pi\) | ||||
−0.708575 | + | 0.705636i | \(0.750661\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.90888 | 0.0625609 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.9645 | −0.817302 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.387269 | 0.0126651 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.04210 | −0.0667125 | −0.0333563 | − | 0.999444i | \(-0.510620\pi\) | ||||
−0.0333563 | + | 0.999444i | \(0.510620\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.6906 | −0.348874 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.4170 | −0.567780 | −0.283890 | − | 0.958857i | \(-0.591625\pi\) | ||||
−0.283890 | + | 0.958857i | \(0.591625\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −61.5402 | −2.00402 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.36962 | 0.142144 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.5852 | −1.15636 | −0.578182 | − | 0.815908i | \(-0.696238\pi\) | ||||
−0.578182 | + | 0.815908i | \(0.696238\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.66827 | −0.184000 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.8660 | −0.806334 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.2621 | −0.332423 | −0.166211 | − | 0.986090i | \(-0.553153\pi\) | ||||
−0.166211 | + | 0.986090i | \(0.553153\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.5842 | 0.374855 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.47732 | 0.112406 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.0056 | −0.355389 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.41958 | 0.271599 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −31.9132 | −1.02839 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.5752 | −0.565767 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.2727 | −0.362505 | −0.181253 | − | 0.983437i | \(-0.558015\pi\) | ||||
−0.181253 | + | 0.983437i | \(0.558015\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.490562 | 0.0157591 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.1579 | 0.390166 | 0.195083 | − | 0.980787i | \(-0.437502\pi\) | ||||
0.195083 | + | 0.980787i | \(0.437502\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.9304 | 0.382471 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.820249 | −0.0262690 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.62843 | 0.276048 | 0.138024 | − | 0.990429i | \(-0.455925\pi\) | ||||
0.138024 | + | 0.990429i | \(0.455925\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.8013 | −0.600893 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.7670 | 0.407619 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.1566 | 1.59975 | 0.799873 | − | 0.600170i | \(-0.204900\pi\) | ||||
0.799873 | + | 0.600170i | \(0.204900\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.9221 | −0.571045 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.51379 | 0.302827 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.6974 | −0.721735 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.9042 | 1.17230 | 0.586151 | − | 0.810202i | \(-0.300643\pi\) | ||||
0.586151 | + | 0.810202i | \(0.300643\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29.1567 | −0.925261 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.7873 | −0.468788 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.0141 | −1.04557 | −0.522784 | − | 0.852465i | \(-0.675107\pi\) | ||||
−0.522784 | + | 0.852465i | \(0.675107\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17.7246 | −0.560781 |
(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 | 7280.2.a.ca.1.2 | 4 | ||
4.3 | odd | 2 | 3640.2.a.s.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3640.2.a.s.1.3 | ✓ | 4 | 4.3 | odd | 2 | ||
7280.2.a.ca.1.2 | 4 | 1.1 | even | 1 | trivial |