Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4000,2,Mod(1,4000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4000, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4000.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4000 = 2^{5} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4000.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: | \(31.9401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.578340050000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 21x^{6} + 129x^{4} - 220x^{2} + 80 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.33481\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4000.1 |
$q$-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 | ||||||||
\(3\) | −3.33481 | −1.92535 | −0.962677 | − | 0.270652i | \(-0.912761\pi\) | ||||
−0.962677 | + | 0.270652i | \(0.912761\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.78602 | −0.675052 | −0.337526 | − | 0.941316i | \(-0.609590\pi\) | ||||
−0.337526 | + | 0.941316i | \(0.609590\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.12097 | 2.70699 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.05479 | −1.22257 | −0.611283 | − | 0.791412i | \(-0.709346\pi\) | ||||
−0.611283 | + | 0.791412i | \(0.709346\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.78297 | −1.32656 | −0.663278 | − | 0.748373i | \(-0.730835\pi\) | ||||
−0.663278 | + | 0.748373i | \(0.730835\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.40100 | −1.06740 | −0.533700 | − | 0.845674i | \(-0.679199\pi\) | ||||
−0.533700 | + | 0.845674i | \(0.679199\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.94463 | −1.59321 | −0.796604 | − | 0.604502i | \(-0.793372\pi\) | ||||
−0.796604 | + | 0.604502i | \(0.793372\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.95604 | 1.29971 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.78101 | 0.579880 | 0.289940 | − | 0.957045i | \(-0.406365\pi\) | ||||
0.289940 | + | 0.957045i | \(0.406365\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −17.0775 | −3.28656 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.16493 | 0.959104 | 0.479552 | − | 0.877514i | \(-0.340799\pi\) | ||||
0.479552 | + | 0.877514i | \(0.340799\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.06103 | −0.370171 | −0.185086 | − | 0.982722i | \(-0.559256\pi\) | ||||
−0.185086 | + | 0.982722i | \(0.559256\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.5220 | 2.35387 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.33800 | −0.877562 | −0.438781 | − | 0.898594i | \(-0.644590\pi\) | ||||
−0.438781 | + | 0.898594i | \(0.644590\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.9503 | 2.55409 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.50293 | −0.390892 | −0.195446 | − | 0.980714i | \(-0.562616\pi\) | ||||
−0.195446 | + | 0.980714i | \(0.562616\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.73821 | 0.570072 | 0.285036 | − | 0.958517i | \(-0.407994\pi\) | ||||
0.285036 | + | 0.958517i | \(0.407994\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.0717 | −1.46911 | −0.734554 | − | 0.678550i | \(-0.762609\pi\) | ||||
−0.734554 | + | 0.678550i | \(0.762609\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.81014 | −0.544305 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.6765 | 2.05512 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.4590 | −1.71137 | −0.855685 | − | 0.517496i | \(-0.826864\pi\) | ||||
−0.855685 | + | 0.517496i | \(0.826864\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 23.1590 | 3.06749 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.658848 | −0.0857747 | −0.0428873 | − | 0.999080i | \(-0.513656\pi\) | ||||
−0.0428873 | + | 0.999080i | \(0.513656\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.75217 | 0.736490 | 0.368245 | − | 0.929729i | \(-0.379959\pi\) | ||||
0.368245 | + | 0.929729i | \(0.379959\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −14.5042 | −1.82736 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.73065 | −1.06662 | −0.533309 | − | 0.845920i | \(-0.679052\pi\) | ||||
−0.533309 | + | 0.845920i | \(0.679052\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.27414 | −1.11647 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.2000 | −1.44787 | −0.723936 | − | 0.689867i | \(-0.757669\pi\) | ||||
−0.723936 | + | 0.689867i | \(0.757669\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.41276 | 0.633516 | 0.316758 | − | 0.948506i | \(-0.397406\pi\) | ||||
0.316758 | + | 0.948506i | \(0.397406\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.24193 | 0.825295 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.04146 | 0.229683 | 0.114841 | − | 0.993384i | \(-0.463364\pi\) | ||||
0.114841 | + | 0.993384i | \(0.463364\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 32.5872 | 3.62080 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.77989 | −0.195368 | −0.0976842 | − | 0.995217i | \(-0.531143\pi\) | ||||
−0.0976842 | + | 0.995217i | \(0.531143\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −17.2241 | −1.84661 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.7771 | −1.77837 | −0.889183 | − | 0.457552i | \(-0.848726\pi\) | ||||
−0.889183 | + | 0.457552i | \(0.848726\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.54247 | 0.895494 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.87314 | 0.712711 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.68690 | −0.678952 | −0.339476 | − | 0.940615i | \(-0.610250\pi\) | ||||
−0.339476 | + | 0.940615i | \(0.610250\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −32.9288 | −3.30947 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.63120 | 0.261814 | 0.130907 | − | 0.991395i | \(-0.458211\pi\) | ||||
0.130907 | + | 0.991395i | \(0.458211\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.7489 | 1.15765 | 0.578826 | − | 0.815451i | \(-0.303511\pi\) | ||||
0.578826 | + | 0.815451i | \(0.303511\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.55492 | −0.150320 | −0.0751600 | − | 0.997171i | \(-0.523947\pi\) | ||||
−0.0751600 | + | 0.997171i | \(0.523947\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.4662 | −1.57718 | −0.788590 | − | 0.614920i | \(-0.789188\pi\) | ||||
−0.788590 | + | 0.614920i | \(0.789188\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.8012 | 1.68962 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.4069 | −1.26121 | −0.630606 | − | 0.776103i | \(-0.717194\pi\) | ||||
−0.630606 | + | 0.776103i | \(0.717194\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −38.8423 | −3.59097 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.86027 | 0.720550 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.44134 | 0.494667 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.34681 | 0.752607 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.14407 | 0.633934 | 0.316967 | − | 0.948437i | \(-0.397336\pi\) | ||||
0.316967 | + | 0.948437i | \(0.397336\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.4662 | −1.09759 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.45575 | −0.564041 | −0.282021 | − | 0.959408i | \(-0.591005\pi\) | ||||
−0.282021 | + | 0.959408i | \(0.591005\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.4032 | 1.07550 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.1364 | 1.20775 | 0.603876 | − | 0.797078i | \(-0.293622\pi\) | ||||
0.603876 | + | 0.797078i | \(0.293622\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.83468 | −0.494891 | −0.247446 | − | 0.968902i | \(-0.579591\pi\) | ||||
−0.247446 | + | 0.968902i | \(0.579591\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.5872 | 2.82855 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.3939 | 1.62180 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.7061 | 1.04798 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.16493 | 0.750820 | 0.375410 | − | 0.926859i | \(-0.377502\pi\) | ||||
0.375410 | + | 0.926859i | \(0.377502\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.743331 | −0.0604914 | −0.0302457 | − | 0.999542i | \(-0.509629\pi\) | ||||
−0.0302457 | + | 0.999542i | \(0.509629\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −35.7404 | −2.88944 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.04983 | 0.562638 | 0.281319 | − | 0.959614i | \(-0.409228\pi\) | ||||
0.281319 | + | 0.959614i | \(0.409228\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 41.5483 | 3.29500 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.96693 | −0.391449 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.8503 | 1.16316 | 0.581581 | − | 0.813489i | \(-0.302434\pi\) | ||||
0.581581 | + | 0.813489i | \(0.302434\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.7439 | −0.986150 | −0.493075 | − | 0.869987i | \(-0.664127\pi\) | ||||
−0.493075 | + | 0.869987i | \(0.664127\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.87676 | 0.759751 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −56.3971 | −4.31280 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.94287 | 0.451828 | 0.225914 | − | 0.974147i | \(-0.427463\pi\) | ||||
0.225914 | + | 0.974147i | \(0.427463\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.19713 | 0.165147 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.74908 | 0.354963 | 0.177481 | − | 0.984124i | \(-0.443205\pi\) | ||||
0.177481 | + | 0.984124i | \(0.443205\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.8079 | −1.32365 | −0.661824 | − | 0.749659i | \(-0.730217\pi\) | ||||
−0.661824 | + | 0.749659i | \(0.730217\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.1824 | −1.41800 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.8451 | 1.30497 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 30.5007 | 2.21860 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.0458 | 1.23339 | 0.616696 | − | 0.787202i | \(-0.288471\pi\) | ||||
0.616696 | + | 0.787202i | \(0.288471\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.9171 | 1.07376 | 0.536878 | − | 0.843660i | \(-0.319603\pi\) | ||||
0.536878 | + | 0.843660i | \(0.319603\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.87314 | −0.347197 | −0.173598 | − | 0.984817i | \(-0.555539\pi\) | ||||
−0.173598 | + | 0.984817i | \(0.555539\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.2165 | −1.57489 | −0.787443 | − | 0.616387i | \(-0.788596\pi\) | ||||
−0.787443 | + | 0.616387i | \(0.788596\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 29.1151 | 2.05362 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.22466 | −0.647445 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.5845 | 1.56973 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28.1590 | 1.94780 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.5211 | 1.41273 | 0.706365 | − | 0.707847i | \(-0.250334\pi\) | ||||
0.706365 | + | 0.707847i | \(0.250334\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 40.6846 | 2.78767 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.68103 | 0.249885 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.0505 | −1.21974 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.0498 | 1.41596 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.2927 | −0.957108 | −0.478554 | − | 0.878058i | \(-0.658839\pi\) | ||||
−0.478554 | + | 0.878058i | \(0.658839\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.14614 | 0.607051 | 0.303525 | − | 0.952823i | \(-0.401836\pi\) | ||||
0.303525 | + | 0.952823i | \(0.401836\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.1268 | 1.06569 | 0.532846 | − | 0.846212i | \(-0.321123\pi\) | ||||
0.532846 | + | 0.846212i | \(0.321123\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.1505 | −1.58899 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.54327 | −0.166615 | −0.0833077 | − | 0.996524i | \(-0.526548\pi\) | ||||
−0.0833077 | + | 0.996524i | \(0.526548\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.80790 | −0.442220 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.3020 | 1.63665 | 0.818325 | − | 0.574755i | \(-0.194903\pi\) | ||||
0.818325 | + | 0.574755i | \(0.194903\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.66786 | −0.171852 | −0.0859261 | − | 0.996302i | \(-0.527385\pi\) | ||||
−0.0859261 | + | 0.996302i | \(0.527385\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −57.4398 | −3.68477 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.2159 | 2.11348 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.93560 | 0.376153 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.7005 | 1.55908 | 0.779541 | − | 0.626351i | \(-0.215452\pi\) | ||||
0.779541 | + | 0.626351i | \(0.215452\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.2764 | −0.708942 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.87900 | −0.241965 | −0.120983 | − | 0.992655i | \(-0.538605\pi\) | ||||
−0.120983 | + | 0.992655i | \(0.538605\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.53377 | 0.592400 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 41.9442 | 2.59628 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.9876 | 1.54080 | 0.770401 | − | 0.637560i | \(-0.220056\pi\) | ||||
0.770401 | + | 0.637560i | \(0.220056\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 55.9484 | 3.42398 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.5161 | 0.763120 | 0.381560 | − | 0.924344i | \(-0.375387\pi\) | ||||
0.381560 | + | 0.924344i | \(0.375387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.6890 | −0.649309 | −0.324654 | − | 0.945833i | \(-0.605248\pi\) | ||||
−0.324654 | + | 0.945833i | \(0.605248\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −28.4875 | −1.72414 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.8423 | −1.55272 | −0.776358 | − | 0.630292i | \(-0.782935\pi\) | ||||
−0.776358 | + | 0.630292i | \(0.782935\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16.7375 | −1.00205 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.30493 | −0.137501 | −0.0687504 | − | 0.997634i | \(-0.521901\pi\) | ||||
−0.0687504 | + | 0.997634i | \(0.521901\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.3632 | 1.38880 | 0.694400 | − | 0.719589i | \(-0.255670\pi\) | ||||
0.694400 | + | 0.719589i | \(0.255670\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.47029 | 0.263873 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.36880 | 0.139341 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.2995 | 1.30722 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.51247 | 0.438883 | 0.219442 | − | 0.975626i | \(-0.429576\pi\) | ||||
0.219442 | + | 0.975626i | \(0.429576\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 69.2455 | 4.01803 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.3015 | −0.769243 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.67652 | −0.384828 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.77456 | −0.504085 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.4708 | −1.11126 | −0.555630 | − | 0.831430i | \(-0.687523\pi\) | ||||
−0.555630 | + | 0.831430i | \(0.687523\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −39.1803 | −2.22889 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.5223 | −1.10701 | −0.553505 | − | 0.832846i | \(-0.686710\pi\) | ||||
−0.553505 | + | 0.832846i | \(0.686710\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.9443 | 0.731654 | 0.365827 | − | 0.930683i | \(-0.380786\pi\) | ||||
0.365827 | + | 0.930683i | \(0.380786\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.69052 | 0.0949493 | 0.0474746 | − | 0.998872i | \(-0.484883\pi\) | ||||
0.0474746 | + | 0.998872i | \(0.484883\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.9427 | −1.17257 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.18537 | 0.289419 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.5633 | 1.70059 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 54.9118 | 3.03663 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.9882 | 0.991724 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.6197 | −1.46315 | −0.731575 | − | 0.681760i | \(-0.761215\pi\) | ||||
−0.731575 | + | 0.681760i | \(0.761215\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −43.3497 | −2.37555 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.3453 | 1.27170 | 0.635849 | − | 0.771813i | \(-0.280650\pi\) | ||||
0.635849 | + | 0.771813i | \(0.280650\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 44.7094 | 2.42828 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.35704 | 0.452559 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.3071 | 1.04249 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.8473 | −1.11914 | −0.559572 | − | 0.828782i | \(-0.689034\pi\) | ||||
−0.559572 | + | 0.828782i | \(0.689034\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.9728 | −1.87205 | −0.936025 | − | 0.351932i | \(-0.885525\pi\) | ||||
−0.936025 | + | 0.351932i | \(0.885525\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 81.6809 | 4.35980 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.8695 | 1.69624 | 0.848120 | − | 0.529804i | \(-0.177735\pi\) | ||||
0.848120 | + | 0.529804i | \(0.177735\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −26.2125 | −1.38731 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.2488 | −0.752020 | −0.376010 | − | 0.926616i | \(-0.622704\pi\) | ||||
−0.376010 | + | 0.926616i | \(0.622704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.2279 | 1.53831 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.1458 | −0.952410 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.45931 | −0.284974 | −0.142487 | − | 0.989797i | \(-0.545510\pi\) | ||||
−0.142487 | + | 0.989797i | \(0.545510\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.3262 | −1.05814 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.2520 | 1.15526 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.6071 | −1.11877 | −0.559387 | − | 0.828907i | \(-0.688963\pi\) | ||||
−0.559387 | + | 0.828907i | \(0.688963\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.7037 | −1.27230 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.937644 | 0.0481635 | 0.0240818 | − | 0.999710i | \(-0.492334\pi\) | ||||
0.0240818 | + | 0.999710i | \(0.492334\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −23.8241 | −1.22055 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.03060 | −0.0526610 | −0.0263305 | − | 0.999653i | \(-0.508382\pi\) | ||||
−0.0263305 | + | 0.999653i | \(0.508382\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 30.3579 | 1.54318 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.15907 | 0.312277 | 0.156139 | − | 0.987735i | \(-0.450095\pi\) | ||||
0.156139 | + | 0.987735i | \(0.450095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.2392 | −0.618964 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.5287 | 1.08598 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.4794 | 0.525946 | 0.262973 | − | 0.964803i | \(-0.415297\pi\) | ||||
0.262973 | + | 0.964803i | \(0.415297\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −41.3625 | −2.07071 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.42455 | −0.420702 | −0.210351 | − | 0.977626i | \(-0.567461\pi\) | ||||
−0.210351 | + | 0.977626i | \(0.567461\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.85782 | 0.491053 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.6445 | 1.07288 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.0199 | −1.13826 | −0.569130 | − | 0.822248i | \(-0.692720\pi\) | ||||
−0.569130 | + | 0.822248i | \(0.692720\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −47.1421 | −2.32535 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.17671 | 0.0579023 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.4576 | 0.952841 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.1995 | −1.03566 | −0.517832 | − | 0.855482i | \(-0.673261\pi\) | ||||
−0.517832 | + | 0.855482i | \(0.673261\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.7412 | −1.20581 | −0.602907 | − | 0.797811i | \(-0.705991\pi\) | ||||
−0.602907 | + | 0.797811i | \(0.705991\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −81.7919 | −3.97686 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.2735 | −0.497169 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −64.6751 | −3.12254 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.12915 | 0.391567 | 0.195784 | − | 0.980647i | \(-0.437275\pi\) | ||||
0.195784 | + | 0.980647i | \(0.437275\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.6656 | −0.945068 | −0.472534 | − | 0.881312i | \(-0.656661\pi\) | ||||
−0.472534 | + | 0.881312i | \(0.656661\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.3131 | −0.923869 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.3362 | 1.16150 | 0.580752 | − | 0.814080i | \(-0.302758\pi\) | ||||
0.580752 | + | 0.814080i | \(0.302758\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −30.9420 | −1.47343 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.57922 | −0.122543 | −0.0612713 | − | 0.998121i | \(-0.519515\pi\) | ||||
−0.0612713 | + | 0.998121i | \(0.519515\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −30.5633 | −1.44560 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.48530 | 0.306060 | 0.153030 | − | 0.988222i | \(-0.451097\pi\) | ||||
0.153030 | + | 0.988222i | \(0.451097\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.1489 | 0.477892 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.47887 | 0.116467 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0820 | −0.518394 | −0.259197 | − | 0.965824i | \(-0.583458\pi\) | ||||
−0.259197 | + | 0.965824i | \(0.583458\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 75.1579 | 3.50807 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.0380 | −1.72503 | −0.862517 | − | 0.506029i | \(-0.831113\pi\) | ||||
−0.862517 | + | 0.506029i | \(0.831113\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.0285 | −0.698435 | −0.349217 | − | 0.937042i | \(-0.613553\pi\) | ||||
−0.349217 | + | 0.937042i | \(0.613553\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.633156 | −0.0292990 | −0.0146495 | − | 0.999893i | \(-0.504663\pi\) | ||||
−0.0146495 | + | 0.999893i | \(0.504663\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.5931 | 0.720023 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.5099 | −1.08328 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.1577 | −0.696951 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −101.179 | −4.63266 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.21499 | −0.0555144 | −0.0277572 | − | 0.999615i | \(-0.508837\pi\) | ||||
−0.0277572 | + | 0.999615i | \(0.508837\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.5315 | 1.16414 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.5638 | 0.753678 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.87838 | −0.447632 | −0.223816 | − | 0.974631i | \(-0.571851\pi\) | ||||
−0.223816 | + | 0.974631i | \(0.571851\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −49.5228 | −2.23950 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.26035 | 0.0568788 | 0.0284394 | − | 0.999596i | \(-0.490946\pi\) | ||||
0.0284394 | + | 0.999596i | \(0.490946\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.7309 | −1.02375 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.7894 | 0.977388 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.0660 | 1.43547 | 0.717736 | − | 0.696315i | \(-0.245178\pi\) | ||||
0.717736 | + | 0.696315i | \(0.245178\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.4984 | 1.89869 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.6134 | 1.49875 | 0.749373 | − | 0.662148i | \(-0.230355\pi\) | ||||
0.749373 | + | 0.662148i | \(0.230355\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.9371 | −1.46279 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.3021 | 1.47609 | 0.738046 | − | 0.674751i | \(-0.235749\pi\) | ||||
0.738046 | + | 0.674751i | \(0.235749\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.66730 | −0.427656 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 118.597 | 5.23617 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.8386 | 1.79608 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.8183 | −0.869929 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.09690 | 0.179489 | 0.0897443 | − | 0.995965i | \(-0.471395\pi\) | ||||
0.0897443 | + | 0.995965i | \(0.471395\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.2414 | 0.622735 | 0.311368 | − | 0.950290i | \(-0.399213\pi\) | ||||
0.311368 | + | 0.950290i | \(0.399213\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.07058 | 0.395121 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.2660 | −0.663739 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.35048 | −0.232191 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.9714 | 0.518541 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.8373 | −0.683430 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.4493 | 0.665449 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.80200 | 0.120467 | 0.0602337 | − | 0.998184i | \(-0.480815\pi\) | ||||
0.0602337 | + | 0.998184i | \(0.480815\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 59.3859 | 2.54849 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.85292 | 0.378523 | 0.189262 | − | 0.981927i | \(-0.439391\pi\) | ||||
0.189262 | + | 0.981927i | \(0.439391\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 46.7132 | 1.99367 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.8685 | −1.52805 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.64609 | −0.155048 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.44721 | −0.188434 | −0.0942171 | − | 0.995552i | \(-0.530035\pi\) | ||||
−0.0942171 | + | 0.995552i | \(0.530035\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.8797 | −0.756233 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −59.5102 | −2.51252 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.3846 | 1.65986 | 0.829931 | − | 0.557866i | \(-0.188380\pi\) | ||||
0.829931 | + | 0.557866i | \(0.188380\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −58.2014 | −2.44423 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.48079 | −0.104000 | −0.0520001 | − | 0.998647i | \(-0.516560\pi\) | ||||
−0.0520001 | + | 0.998647i | \(0.516560\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.32601 | −0.181038 | −0.0905190 | − | 0.995895i | \(-0.528853\pi\) | ||||
−0.0905190 | + | 0.995895i | \(0.528853\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −56.8445 | −2.37472 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.38643 | 0.224240 | 0.112120 | − | 0.993695i | \(-0.464236\pi\) | ||||
0.112120 | + | 0.993695i | \(0.464236\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −49.7457 | −2.06736 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.17892 | 0.131884 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.5185 | 2.09226 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.63539 | −0.108774 | −0.0543871 | − | 0.998520i | \(-0.517321\pi\) | ||||
−0.0543871 | + | 0.998520i | \(0.517321\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.3131 | 0.589760 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.2510 | 0.668476 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.8849 | −0.446988 | −0.223494 | − | 0.974705i | \(-0.571746\pi\) | ||||
−0.223494 | + | 0.974705i | \(0.571746\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 74.0879 | 3.03221 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.9152 | −1.46746 | −0.733729 | − | 0.679443i | \(-0.762222\pi\) | ||||
−0.733729 | + | 0.679443i | \(0.762222\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.5505 | −1.04223 | −0.521114 | − | 0.853487i | \(-0.674483\pi\) | ||||
−0.521114 | + | 0.853487i | \(0.674483\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −70.9013 | −2.88732 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.3993 | −0.503270 | −0.251635 | − | 0.967822i | \(-0.580968\pi\) | ||||
−0.251635 | + | 0.967822i | \(0.580968\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30.7625 | 1.24656 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 48.1726 | 1.94885 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.45088 | 0.0586005 | 0.0293003 | − | 0.999571i | \(-0.490672\pi\) | ||||
0.0293003 | + | 0.999571i | \(0.490672\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.74714 | −0.352147 | −0.176073 | − | 0.984377i | \(-0.556340\pi\) | ||||
−0.176073 | + | 0.984377i | \(0.556340\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 48.2337 | 1.93868 | 0.969338 | − | 0.245730i | \(-0.0790278\pi\) | ||||
0.969338 | + | 0.245730i | \(0.0790278\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −47.4925 | −1.90581 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.9642 | 1.20049 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −93.9051 | −3.75021 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.4925 | 0.936709 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.4575 | −1.80963 | −0.904817 | − | 0.425801i | \(-0.859992\pi\) | ||||
−0.904817 | + | 0.425801i | \(0.859992\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −68.4340 | −2.72001 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.2238 | 0.722052 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −99.0757 | −3.91937 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.9442 | 1.49871 | 0.749353 | − | 0.662170i | \(-0.230364\pi\) | ||||
0.749353 | + | 0.662170i | \(0.230364\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.4638 | −0.807012 | −0.403506 | − | 0.914977i | \(-0.632209\pi\) | ||||
−0.403506 | + | 0.914977i | \(0.632209\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.7257 | −1.32589 | −0.662947 | − | 0.748666i | \(-0.730695\pi\) | ||||
−0.662947 | + | 0.748666i | \(0.730695\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.67149 | 0.104865 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.2755 | −0.481117 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.2243 | 0.400106 | 0.200053 | − | 0.979785i | \(-0.435889\pi\) | ||||
0.200053 | + | 0.979785i | \(0.435889\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 43.9569 | 1.71492 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.2742 | 0.789772 | 0.394886 | − | 0.918730i | \(-0.370784\pi\) | ||||
0.394886 | + | 0.918730i | \(0.370784\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.329864 | 0.0128302 | 0.00641510 | − | 0.999979i | \(-0.497958\pi\) | ||||
0.00641510 | + | 0.999979i | \(0.497958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −70.1972 | −2.72623 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.3637 | 0.556165 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 47.6633 | 1.84277 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.3238 | −0.900407 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.3960 | 1.13313 | 0.566566 | − | 0.824017i | \(-0.308272\pi\) | ||||
0.566566 | + | 0.824017i | \(0.308272\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.05346 | 0.0404876 | 0.0202438 | − | 0.999795i | \(-0.493556\pi\) | ||||
0.0202438 | + | 0.999795i | \(0.493556\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.9429 | 0.458327 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.5007 | −1.16879 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.5661 | −0.748675 | −0.374337 | − | 0.927293i | \(-0.622130\pi\) | ||||
−0.374337 | + | 0.927293i | \(0.622130\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −53.7799 | −2.05183 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 59.5908 | 2.27023 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.2129 | 1.75802 | 0.879011 | − | 0.476802i | \(-0.158204\pi\) | ||||
0.879011 | + | 0.476802i | \(0.158204\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 58.8115 | 2.23406 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.0154 | 0.417238 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.48133 | 0.320793 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.2134 | −0.725679 | −0.362840 | − | 0.931852i | \(-0.618193\pi\) | ||||
−0.362840 | + | 0.931852i | \(0.618193\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.0704 | 1.39814 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.69937 | −0.176738 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.96644 | −0.186519 | −0.0932594 | − | 0.995642i | \(-0.529729\pi\) | ||||
−0.0932594 | + | 0.995642i | \(0.529729\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.5787 | 0.621748 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.73173 | −0.214655 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −84.3774 | −3.15113 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.76975 | 0.103294 | 0.0516471 | − | 0.998665i | \(-0.483553\pi\) | ||||
0.0516471 | + | 0.998665i | \(0.483553\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.9837 | −0.781475 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.89683 | 0.330877 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.9826 | −1.26035 | −0.630173 | − | 0.776455i | \(-0.717016\pi\) | ||||
−0.630173 | + | 0.776455i | \(0.717016\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 93.7893 | 3.47368 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.4519 | −0.608495 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.75576 | 0.360337 | 0.180169 | − | 0.983636i | \(-0.442336\pi\) | ||||
0.180169 | + | 0.983636i | \(0.442336\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.4010 | 1.30401 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.98140 | 0.146458 | 0.0732291 | − | 0.997315i | \(-0.476670\pi\) | ||||
0.0732291 | + | 0.997315i | \(0.476670\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −110.769 | −4.06920 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −39.5319 | −1.45029 | −0.725143 | − | 0.688599i | \(-0.758226\pi\) | ||||
−0.725143 | + | 0.688599i | \(0.758226\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.4544 | −0.528860 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.77712 | 0.101474 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.99037 | −0.109120 | −0.0545600 | − | 0.998510i | \(-0.517376\pi\) | ||||
−0.0545600 | + | 0.998510i | \(0.517376\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −82.3715 | −3.00178 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.4685 | −0.525866 | −0.262933 | − | 0.964814i | \(-0.584690\pi\) | ||||
−0.262933 | + | 0.964814i | \(0.584690\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 37.6047 | 1.36496 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.76482 | −0.281474 | −0.140737 | − | 0.990047i | \(-0.544947\pi\) | ||||
−0.140737 | + | 0.990047i | \(0.544947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.4090 | 1.06468 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.15125 | 0.113785 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.2823 | −1.48868 | −0.744338 | − | 0.667803i | \(-0.767235\pi\) | ||||
−0.744338 | + | 0.667803i | \(0.767235\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.9357 | 0.465869 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.3856 | 0.553381 | 0.276691 | − | 0.960959i | \(-0.410762\pi\) | ||||
0.276691 | + | 0.960959i | \(0.410762\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −31.7933 | −1.14058 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.3819 | 0.622773 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.4684 | 1.77012 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −88.2039 | −3.15215 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.3700 | 1.08257 | 0.541287 | − | 0.840838i | \(-0.317937\pi\) | ||||
0.541287 | + | 0.840838i | \(0.317937\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −83.3289 | −2.96659 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.9449 | 0.851383 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.5124 | −0.976995 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.9375 | −0.422848 | −0.211424 | − | 0.977394i | \(-0.567810\pi\) | ||||
−0.211424 | + | 0.977394i | \(0.567810\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.3255 | 1.56812 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −136.246 | −4.81402 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.9476 | −0.774515 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −41.7388 | −1.46928 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.92975 | 0.349111 | 0.174556 | − | 0.984647i | \(-0.444151\pi\) | ||||
0.174556 | + | 0.984647i | \(0.444151\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.0971 | 1.23243 | 0.616213 | − | 0.787580i | \(-0.288666\pi\) | ||||
0.616213 | + | 0.787580i | \(0.288666\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 35.6457 | 1.25015 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.9605 | −0.908244 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 69.3731 | 2.42409 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.2442 | 0.462224 | 0.231112 | − | 0.972927i | \(-0.425764\pi\) | ||||
0.231112 | + | 0.972927i | \(0.425764\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.3502 | 0.360786 | 0.180393 | − | 0.983595i | \(-0.442263\pi\) | ||||
0.180393 | + | 0.983595i | \(0.442263\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.7372 | −0.929743 | −0.464871 | − | 0.885378i | \(-0.653899\pi\) | ||||
−0.464871 | + | 0.885378i | \(0.653899\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.2632 | −1.08582 | −0.542909 | − | 0.839792i | \(-0.682677\pi\) | ||||
−0.542909 | + | 0.839792i | \(0.682677\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 86.1793 | 2.98953 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.7684 | 0.580991 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 35.1971 | 1.21659 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.7498 | −0.440173 | −0.220087 | − | 0.975480i | \(-0.570634\pi\) | ||||
−0.220087 | + | 0.975480i | \(0.570634\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.32348 | −0.0801200 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.68652 | 0.264738 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.71833 | −0.333926 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −77.9120 | −2.67393 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.8450 | −0.508881 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.5497 | −1.14872 | −0.574359 | − | 0.818603i | \(-0.694749\pi\) | ||||
−0.574359 | + | 0.818603i | \(0.694749\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.07787 | −0.275935 | −0.137967 | − | 0.990437i | \(-0.544057\pi\) | ||||
−0.137967 | + | 0.990437i | \(0.544057\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.1730 | −1.67776 | −0.838880 | − | 0.544316i | \(-0.816789\pi\) | ||||
−0.838880 | + | 0.544316i | \(0.816789\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.9076 | −0.508048 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.7683 | 0.468680 | 0.234340 | − | 0.972155i | \(-0.424707\pi\) | ||||
0.234340 | + | 0.972155i | \(0.424707\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.89950 | −0.268281 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.27771 | −0.280802 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41.7584 | 1.41493 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −54.3041 | −1.83791 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.4377 | −0.656364 | −0.328182 | − | 0.944614i | \(-0.606436\pi\) | ||||
−0.328182 | + | 0.944614i | \(0.606436\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.0527 | −0.845006 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.89720 | 0.232373 | 0.116186 | − | 0.993227i | \(-0.462933\pi\) | ||||
0.116186 | + | 0.993227i | \(0.462933\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.1775 | 0.611721 | 0.305861 | − | 0.952076i | \(-0.401056\pi\) | ||||
0.305861 | + | 0.952076i | \(0.401056\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.0469 | −0.538801 | −0.269400 | − | 0.963028i | \(-0.586826\pi\) | ||||
−0.269400 | + | 0.963028i | \(0.586826\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.7595 | −0.427938 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −132.134 | −4.42667 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 69.9442 | 2.34059 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 44.3579 | 1.48107 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.6451 | −0.355033 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 54.8319 | 1.82672 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.2649 | 0.740931 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.16580 | 0.138323 | 0.0691615 | − | 0.997605i | \(-0.477968\pi\) | ||||
0.0691615 | + | 0.997605i | \(0.477968\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.3679 | 0.708729 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.3846 | −1.30487 | −0.652435 | − | 0.757845i | \(-0.726252\pi\) | ||||
−0.652435 | + | 0.757845i | \(0.726252\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.21708 | 0.238851 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.5301 | 0.380757 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.6597 | −1.67111 | −0.835555 | − | 0.549406i | \(-0.814854\pi\) | ||||
−0.835555 | + | 0.549406i | \(0.814854\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 64.9316 | 2.13957 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 58.3521 | 1.92068 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 95.4123 | 3.13375 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.1283 | 0.365107 | 0.182553 | − | 0.983196i | \(-0.441564\pi\) | ||||
0.182553 | + | 0.983196i | \(0.441564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.4600 | 0.867191 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 65.1033 | 2.13139 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.4472 | −1.06000 | −0.530001 | − | 0.847997i | \(-0.677809\pi\) | ||||
−0.530001 | + | 0.847997i | \(0.677809\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −43.1667 | −1.40869 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.7793 | −1.13377 | −0.566887 | − | 0.823796i | \(-0.691852\pi\) | ||||
−0.566887 | + | 0.823796i | \(0.691852\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.96068 | −0.226671 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.9403 | 0.745459 | 0.372729 | − | 0.927940i | \(-0.378422\pi\) | ||||
0.372729 | + | 0.927940i | \(0.378422\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.8891 | −0.840394 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.63758 | −0.182811 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.1854 | −1.33412 | −0.667062 | − | 0.745002i | \(-0.732449\pi\) | ||||
−0.667062 | + | 0.745002i | \(0.732449\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 69.8400 | 2.25761 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.2478 | −0.815295 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.7522 | −0.862973 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.6275 | −0.406914 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.4819 | −0.915916 | −0.457958 | − | 0.888974i | \(-0.651419\pi\) | ||||
−0.457958 | + | 0.888974i | \(0.651419\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −101.923 | −3.27424 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.1014 | 1.60783 | 0.803916 | − | 0.594743i | \(-0.202746\pi\) | ||||
0.803916 | + | 0.594743i | \(0.202746\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.4209 | 0.334077 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.6370 | 0.468280 | 0.234140 | − | 0.972203i | \(-0.424773\pi\) | ||||
0.234140 | + | 0.972203i | \(0.424773\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 68.0275 | 2.17417 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −133.722 | −4.26941 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.1817 | 0.611800 | 0.305900 | − | 0.952064i | \(-0.401043\pi\) | ||||
0.305900 | + | 0.952064i | \(0.401043\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −59.9874 | −1.90942 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.3960 | 0.330574 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.30268 | −0.231977 | −0.115989 | − | 0.993251i | \(-0.537004\pi\) | ||||
−0.115989 | + | 0.993251i | \(0.537004\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 88.7717 | 2.81708 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −57.4816 | −1.82046 | −0.910230 | − | 0.414104i | \(-0.864095\pi\) | ||||
−0.910230 | + | 0.414104i | \(0.864095\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 91.1595 | 2.88416 |
(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 | 4000.2.a.q.1.1 | ✓ | 8 | |
4.3 | odd | 2 | inner | 4000.2.a.q.1.8 | yes | 8 | |
5.2 | odd | 4 | 4000.2.c.h.1249.15 | 16 | |||
5.3 | odd | 4 | 4000.2.c.h.1249.1 | 16 | |||
5.4 | even | 2 | 4000.2.a.r.1.8 | yes | 8 | ||
8.3 | odd | 2 | 8000.2.a.cb.1.1 | 8 | |||
8.5 | even | 2 | 8000.2.a.cb.1.8 | 8 | |||
20.3 | even | 4 | 4000.2.c.h.1249.16 | 16 | |||
20.7 | even | 4 | 4000.2.c.h.1249.2 | 16 | |||
20.19 | odd | 2 | 4000.2.a.r.1.1 | yes | 8 | ||
40.19 | odd | 2 | 8000.2.a.ca.1.8 | 8 | |||
40.29 | even | 2 | 8000.2.a.ca.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4000.2.a.q.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
4000.2.a.q.1.8 | yes | 8 | 4.3 | odd | 2 | inner | |
4000.2.a.r.1.1 | yes | 8 | 20.19 | odd | 2 | ||
4000.2.a.r.1.8 | yes | 8 | 5.4 | even | 2 | ||
4000.2.c.h.1249.1 | 16 | 5.3 | odd | 4 | |||
4000.2.c.h.1249.2 | 16 | 20.7 | even | 4 | |||
4000.2.c.h.1249.15 | 16 | 5.2 | odd | 4 | |||
4000.2.c.h.1249.16 | 16 | 20.3 | even | 4 | |||
8000.2.a.ca.1.1 | 8 | 40.29 | even | 2 | |||
8000.2.a.ca.1.8 | 8 | 40.19 | odd | 2 | |||
8000.2.a.cb.1.1 | 8 | 8.3 | odd | 2 | |||
8000.2.a.cb.1.8 | 8 | 8.5 | even | 2 |