Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6160,2,Mod(1,6160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6160, 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("6160.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6160.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: | \(49.1878476451\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3080) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6160.1 |
$q$-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 | ||||||||
\(3\) | −2.82843 | −1.63299 | −0.816497 | − | 0.577350i | \(-0.804087\pi\) | ||||
−0.816497 | + | 0.577350i | \(0.804087\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.00000 | 1.66667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.82843 | 1.33916 | 0.669582 | − | 0.742738i | \(-0.266473\pi\) | ||||
0.669582 | + | 0.742738i | \(0.266473\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.82843 | 0.730297 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.828427 | −0.200923 | −0.100462 | − | 0.994941i | \(-0.532032\pi\) | ||||
−0.100462 | + | 0.994941i | \(0.532032\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82843 | 0.617213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.82843 | −1.22642 | −0.613211 | − | 0.789919i | \(-0.710122\pi\) | ||||
−0.613211 | + | 0.789919i | \(0.710122\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.82843 | −0.492366 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.6569 | 1.91638 | 0.958188 | − | 0.286141i | \(-0.0923726\pi\) | ||||
0.958188 | + | 0.286141i | \(0.0923726\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13.6569 | −2.18685 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.82843 | 1.37877 | 0.689384 | − | 0.724396i | \(-0.257881\pi\) | ||||
0.689384 | + | 0.724396i | \(0.257881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.65685 | −0.252668 | −0.126334 | − | 0.991988i | \(-0.540321\pi\) | ||||
−0.126334 | + | 0.991988i | \(0.540321\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.00000 | −0.745356 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.34315 | 0.328106 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.65685 | 0.502308 | 0.251154 | − | 0.967947i | \(-0.419190\pi\) | ||||
0.251154 | + | 0.967947i | \(0.419190\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.82843 | 0.888985 | 0.444493 | − | 0.895782i | \(-0.353384\pi\) | ||||
0.444493 | + | 0.895782i | \(0.353384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.17157 | 0.406078 | 0.203039 | − | 0.979171i | \(-0.434918\pi\) | ||||
0.203039 | + | 0.979171i | \(0.434918\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.00000 | −0.629941 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.82843 | −0.598893 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.65685 | −0.691095 | −0.345547 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345547 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.3137 | −1.36201 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.17157 | −0.371205 | −0.185602 | − | 0.982625i | \(-0.559424\pi\) | ||||
−0.185602 | + | 0.982625i | \(0.559424\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.82843 | −0.326599 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.65685 | −0.620920 | −0.310460 | − | 0.950586i | \(-0.600483\pi\) | ||||
−0.310460 | + | 0.950586i | \(0.600483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.828427 | 0.0898555 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.65685 | 0.606478 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.3137 | −1.83525 | −0.917625 | − | 0.397448i | \(-0.869896\pi\) | ||||
−0.917625 | + | 0.397448i | \(0.869896\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.82843 | −0.506157 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.3137 | 2.00274 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.31371 | −0.945664 | −0.472832 | − | 0.881153i | \(-0.656768\pi\) | ||||
−0.472832 | + | 0.881153i | \(0.656768\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.00000 | 0.502519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.4853 | −1.04332 | −0.521662 | − | 0.853152i | \(-0.674688\pi\) | ||||
−0.521662 | + | 0.853152i | \(0.674688\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.17157 | −0.509570 | −0.254785 | − | 0.966998i | \(-0.582005\pi\) | ||||
−0.254785 | + | 0.966998i | \(0.582005\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.82843 | −0.276026 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.31371 | −0.508961 | −0.254480 | − | 0.967078i | \(-0.581904\pi\) | ||||
−0.254480 | + | 0.967078i | \(0.581904\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −32.9706 | −3.12943 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 24.1421 | 2.23194 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.828427 | 0.0759418 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −24.9706 | −2.25152 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.68629 | 0.412605 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3431 | −0.903685 | −0.451842 | − | 0.892098i | \(-0.649233\pi\) | ||||
−0.451842 | + | 0.892098i | \(0.649233\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.65685 | 0.486864 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0000 | 0.854358 | 0.427179 | − | 0.904167i | \(-0.359507\pi\) | ||||
0.427179 | + | 0.904167i | \(0.359507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.82843 | 0.403773 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.82843 | −0.233285 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.34315 | 0.683497 | 0.341749 | − | 0.939791i | \(-0.388981\pi\) | ||||
0.341749 | + | 0.939791i | \(0.388981\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.14214 | −0.334872 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.82843 | 0.548472 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.31371 | −0.104845 | −0.0524227 | − | 0.998625i | \(-0.516694\pi\) | ||||
−0.0524227 | + | 0.998625i | \(0.516694\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.3431 | −0.820265 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.9706 | 1.95585 | 0.977923 | − | 0.208967i | \(-0.0670101\pi\) | ||||
0.977923 | + | 0.208967i | \(0.0670101\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.82843 | 0.220193 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.31371 | −0.256422 | −0.128211 | − | 0.991747i | \(-0.540924\pi\) | ||||
−0.128211 | + | 0.991747i | \(0.540924\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3137 | 0.793362 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.14214 | 0.619035 | 0.309518 | − | 0.950894i | \(-0.399832\pi\) | ||||
0.309518 | + | 0.950894i | \(0.399832\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.3137 | −1.45171 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.3137 | 1.14460 | 0.572300 | − | 0.820044i | \(-0.306051\pi\) | ||||
0.572300 | + | 0.820044i | \(0.306051\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.6569 | 1.16376 | 0.581882 | − | 0.813273i | \(-0.302316\pi\) | ||||
0.581882 | + | 0.813273i | \(0.302316\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.97056 | −0.663123 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.6569 | −0.857029 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.828427 | −0.0605806 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.65685 | 0.411476 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3137 | 1.39749 | 0.698745 | − | 0.715370i | \(-0.253742\pi\) | ||||
0.698745 | + | 0.715370i | \(0.253742\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.6569 | 0.977988 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.3137 | 1.51854 | 0.759269 | − | 0.650776i | \(-0.225556\pi\) | ||||
0.759269 | + | 0.650776i | \(0.225556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.1716 | −1.21726 | −0.608630 | − | 0.793454i | \(-0.708281\pi\) | ||||
−0.608630 | + | 0.793454i | \(0.708281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.0000 | 1.12855 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.00000 | 0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.82843 | −0.616604 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.0000 | 1.39010 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.0000 | 1.09630 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.65685 | 0.112997 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.82843 | 0.463544 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.97056 | 0.606174 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.82843 | 0.189405 | 0.0947027 | − | 0.995506i | \(-0.469810\pi\) | ||||
0.0947027 | + | 0.995506i | \(0.469810\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00000 | 0.333333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.3137 | 1.28190 | 0.640948 | − | 0.767584i | \(-0.278541\pi\) | ||||
0.640948 | + | 0.767584i | \(0.278541\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.9706 | −1.51794 | −0.758969 | − | 0.651127i | \(-0.774296\pi\) | ||||
−0.758969 | + | 0.651127i | \(0.774296\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.82843 | 0.186097 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.6569 | 1.81186 | 0.905930 | − | 0.423427i | \(-0.139173\pi\) | ||||
0.905930 | + | 0.423427i | \(0.139173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.82843 | −0.184506 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.34315 | −0.151565 | −0.0757827 | − | 0.997124i | \(-0.524146\pi\) | ||||
−0.0757827 | + | 0.997124i | \(0.524146\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.7990 | −1.40420 | −0.702098 | − | 0.712080i | \(-0.747753\pi\) | ||||
−0.702098 | + | 0.712080i | \(0.747753\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.1421 | 0.907218 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.0000 | 1.01396 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.1421 | −1.14512 | −0.572561 | − | 0.819862i | \(-0.694050\pi\) | ||||
−0.572561 | + | 0.819862i | \(0.694050\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.34315 | −0.146733 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.343146 | −0.0214048 | −0.0107024 | − | 0.999943i | \(-0.503407\pi\) | ||||
−0.0107024 | + | 0.999943i | \(0.503407\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.6569 | −0.724322 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.0000 | −0.618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.3137 | 0.697633 | 0.348817 | − | 0.937191i | \(-0.386584\pi\) | ||||
0.348817 | + | 0.937191i | \(0.386584\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.65685 | −0.224639 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 48.9706 | 2.99695 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.65685 | −0.222962 | −0.111481 | − | 0.993767i | \(-0.535559\pi\) | ||||
−0.111481 | + | 0.993767i | \(0.535559\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6569 | −0.829595 | −0.414797 | − | 0.909914i | \(-0.636148\pi\) | ||||
−0.414797 | + | 0.909914i | \(0.636148\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.6569 | 0.826550 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −34.1421 | −2.04404 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.97056 | −0.415829 | −0.207914 | − | 0.978147i | \(-0.566668\pi\) | ||||
−0.207914 | + | 0.978147i | \(0.566668\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3137 | 0.672530 | 0.336265 | − | 0.941767i | \(-0.390836\pi\) | ||||
0.336265 | + | 0.941767i | \(0.390836\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.82843 | −0.521126 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3137 | −0.959630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 26.3431 | 1.54426 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.48528 | 0.145192 | 0.0725958 | − | 0.997361i | \(-0.476872\pi\) | ||||
0.0725958 | + | 0.997361i | \(0.476872\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.82843 | −0.397566 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.65685 | −0.328244 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.3137 | 1.11694 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.65685 | 0.0954995 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 29.6569 | 1.70374 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.17157 | −0.181604 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0000 | 0.913168 | 0.456584 | − | 0.889680i | \(-0.349073\pi\) | ||||
0.456584 | + | 0.889680i | \(0.349073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.6274 | 0.832125 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.1421 | 1.48238 | 0.741192 | − | 0.671293i | \(-0.234261\pi\) | ||||
0.741192 | + | 0.671293i | \(0.234261\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.34315 | 0.245489 | 0.122745 | − | 0.992438i | \(-0.460830\pi\) | ||||
0.122745 | + | 0.992438i | \(0.460830\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.00000 | 0.281718 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.9706 | −1.51482 | −0.757409 | − | 0.652941i | \(-0.773535\pi\) | ||||
−0.757409 | + | 0.652941i | \(0.773535\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.00000 | −0.111979 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.3137 | −0.631470 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.82843 | 0.267833 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.0294 | 0.831130 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.82843 | −0.155936 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.6274 | 1.90329 | 0.951647 | − | 0.307192i | \(-0.0993895\pi\) | ||||
0.951647 | + | 0.307192i | \(0.0993895\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 58.2843 | 3.19396 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.65685 | 0.309067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.6569 | −0.852883 | −0.426442 | − | 0.904515i | \(-0.640233\pi\) | ||||
−0.426442 | + | 0.904515i | \(0.640233\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.9706 | 0.921714 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.82843 | −0.369780 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.3137 | 0.609110 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.2843 | −1.73311 | −0.866555 | − | 0.499081i | \(-0.833671\pi\) | ||||
−0.866555 | + | 0.499081i | \(0.833671\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.48528 | 0.347149 | 0.173575 | − | 0.984821i | \(-0.444468\pi\) | ||||
0.173575 | + | 0.984821i | \(0.444468\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.3137 | −1.45790 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.9706 | 1.43550 | 0.717749 | − | 0.696302i | \(-0.245172\pi\) | ||||
0.717749 | + | 0.696302i | \(0.245172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.65685 | 0.300235 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.34315 | −0.124012 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.3137 | 1.44156 | 0.720781 | − | 0.693163i | \(-0.243783\pi\) | ||||
0.720781 | + | 0.693163i | \(0.243783\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.82843 | −0.148454 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.17157 | 0.166008 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.14214 | 0.320617 | 0.160308 | − | 0.987067i | \(-0.448751\pi\) | ||||
0.160308 | + | 0.987067i | \(0.448751\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 44.1421 | 2.29795 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.65685 | −0.189854 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.82843 | 0.146059 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.65685 | −0.497353 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.65685 | 0.496039 | 0.248020 | − | 0.968755i | \(-0.420220\pi\) | ||||
0.248020 | + | 0.968755i | \(0.420220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.4853 | 0.842359 | 0.421179 | − | 0.906977i | \(-0.361616\pi\) | ||||
0.421179 | + | 0.906977i | \(0.361616\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.00000 | 0.0509647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.28427 | −0.421113 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.31371 | 0.472224 | 0.236112 | − | 0.971726i | \(-0.424127\pi\) | ||||
0.236112 | + | 0.971726i | \(0.424127\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.31371 | −0.167581 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.2548 | 1.47571 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.68629 | −0.134147 | −0.0670735 | − | 0.997748i | \(-0.521366\pi\) | ||||
−0.0670735 | + | 0.997748i | \(0.521366\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.9706 | −1.64238 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.6569 | 0.577809 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.17157 | 0.156824 | 0.0784121 | − | 0.996921i | \(-0.475015\pi\) | ||||
0.0784121 | + | 0.996921i | \(0.475015\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −28.2843 | −1.39516 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.82843 | −0.336005 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.65685 | 0.277684 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.6274 | −1.10807 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.17157 | −0.0572351 | −0.0286175 | − | 0.999590i | \(-0.509110\pi\) | ||||
−0.0286175 | + | 0.999590i | \(0.509110\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.0000 | 1.46211 | 0.731055 | − | 0.682318i | \(-0.239028\pi\) | ||||
0.731055 | + | 0.682318i | \(0.239028\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.1421 | 0.687614 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.828427 | −0.0401846 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.17157 | −0.153483 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.6569 | −0.659359 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.6863 | 0.611077 | 0.305539 | − | 0.952180i | \(-0.401164\pi\) | ||||
0.305539 | + | 0.952180i | \(0.401164\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.3137 | 1.40873 | 0.704363 | − | 0.709839i | \(-0.251233\pi\) | ||||
0.704363 | + | 0.709839i | \(0.251233\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.65685 | −0.271225 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.970563 | 0.0463224 | 0.0231612 | − | 0.999732i | \(-0.492627\pi\) | ||||
0.0231612 | + | 0.999732i | \(0.492627\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00000 | 0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.6274 | 1.83524 | 0.917622 | − | 0.397454i | \(-0.130106\pi\) | ||||
0.917622 | + | 0.397454i | \(0.130106\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.3137 | 0.820748 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.5980 | −1.11615 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.82843 | 0.415714 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.6274 | 1.06313 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.82843 | 0.226360 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −40.6274 | −1.90047 | −0.950235 | − | 0.311533i | \(-0.899157\pi\) | ||||
−0.950235 | + | 0.311533i | \(0.899157\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.68629 | 0.218737 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.51472 | −0.0705475 | −0.0352737 | − | 0.999378i | \(-0.511230\pi\) | ||||
−0.0352737 | + | 0.999378i | \(0.511230\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.3137 | −1.82706 | −0.913531 | − | 0.406768i | \(-0.866656\pi\) | ||||
−0.913531 | + | 0.406768i | \(0.866656\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.3137 | −0.895652 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.7696 | 1.70149 | 0.850746 | − | 0.525577i | \(-0.176151\pi\) | ||||
0.850746 | + | 0.525577i | \(0.176151\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.65685 | 0.261209 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.71573 | 0.171212 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.65685 | −0.0761822 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.2843 | 0.837179 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.9706 | −1.14093 | −0.570467 | − | 0.821320i | \(-0.693238\pi\) | ||||
−0.570467 | + | 0.821320i | \(0.693238\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 56.2843 | 2.56634 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.3137 | 0.514792 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.31371 | 0.422914 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.6274 | 0.844089 | 0.422044 | − | 0.906575i | \(-0.361313\pi\) | ||||
0.422044 | + | 0.906575i | \(0.361313\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −70.6274 | −3.19388 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.9706 | −1.30742 | −0.653712 | − | 0.756744i | \(-0.726789\pi\) | ||||
−0.653712 | + | 0.756744i | \(0.726789\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.65685 | 0.0746210 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.00000 | −0.224733 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.65685 | 0.253745 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.9706 | 0.938771 | 0.469386 | − | 0.882993i | \(-0.344475\pi\) | ||||
0.469386 | + | 0.882993i | \(0.344475\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.37258 | 0.418736 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.9706 | 1.47008 | 0.735042 | − | 0.678021i | \(-0.237162\pi\) | ||||
0.735042 | + | 0.678021i | \(0.237162\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.4853 | 0.466589 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −29.1716 | −1.29556 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.65685 | −0.162087 | −0.0810436 | − | 0.996711i | \(-0.525825\pi\) | ||||
−0.0810436 | + | 0.996711i | \(0.525825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.17157 | 0.140302 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.17157 | 0.227887 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.82843 | 0.124394 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.0294 | −1.01088 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.343146 | −0.0150335 | −0.00751674 | − | 0.999972i | \(-0.502393\pi\) | ||||
−0.00751674 | + | 0.999972i | \(0.502393\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.6274 | 1.33924 | 0.669622 | − | 0.742702i | \(-0.266456\pi\) | ||||
0.669622 | + | 0.742702i | \(0.266456\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.82843 | 0.123443 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.65685 | 0.246416 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 34.1421 | 1.48164 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.6274 | 1.84640 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00000 | −0.172935 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −43.3137 | −1.86912 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.2843 | 0.786102 | 0.393051 | − | 0.919517i | \(-0.371420\pi\) | ||||
0.393051 | + | 0.919517i | \(0.371420\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −44.2843 | −1.90042 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.31371 | 0.227614 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.8579 | 0.676797 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 32.9706 | 1.39952 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 45.3137 | 1.92000 | 0.960002 | − | 0.279994i | \(-0.0903325\pi\) | ||||
0.960002 | + | 0.279994i | \(0.0903325\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.34315 | 0.0989277 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.3431 | −0.435912 | −0.217956 | − | 0.975959i | \(-0.569939\pi\) | ||||
−0.217956 | + | 0.975959i | \(0.569939\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.00000 | 0.252422 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.9706 | 0.795287 | 0.397644 | − | 0.917540i | \(-0.369828\pi\) | ||||
0.397644 | + | 0.917540i | \(0.369828\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.3137 | −1.31044 | −0.655219 | − | 0.755439i | \(-0.727424\pi\) | ||||
−0.655219 | + | 0.755439i | \(0.727424\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −54.6274 | −2.28209 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.0000 | −1.58196 | −0.790980 | − | 0.611842i | \(-0.790429\pi\) | ||||
−0.790980 | + | 0.611842i | \(0.790429\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −39.5980 | −1.64564 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.65685 | 0.234686 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.65685 | 0.151451 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −24.1421 | −0.998154 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.79899 | −0.156801 | −0.0784005 | − | 0.996922i | \(-0.524981\pi\) | ||||
−0.0784005 | + | 0.996922i | \(0.524981\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −60.2843 | −2.47976 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.4558 | 1.12748 | 0.563738 | − | 0.825954i | \(-0.309363\pi\) | ||||
0.563738 | + | 0.825954i | \(0.309363\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.828427 | −0.0339622 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 48.5685 | 1.98778 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.6569 | −0.884875 | −0.442438 | − | 0.896799i | \(-0.645886\pi\) | ||||
−0.442438 | + | 0.896799i | \(0.645886\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.85786 | −0.157366 | −0.0786828 | − | 0.996900i | \(-0.525071\pi\) | ||||
−0.0786828 | + | 0.996900i | \(0.525071\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −28.2843 | −1.15182 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.0000 | 0.974130 | 0.487065 | − | 0.873366i | \(-0.338067\pi\) | ||||
0.487065 | + | 0.873366i | \(0.338067\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.65685 | −0.229227 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.6569 | 0.552497 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.02944 | −0.203137 | −0.101569 | − | 0.994829i | \(-0.532386\pi\) | ||||
−0.101569 | + | 0.994829i | \(0.532386\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.9706 | 1.00691 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.9411 | −0.963833 | −0.481917 | − | 0.876217i | \(-0.660059\pi\) | ||||
−0.481917 | + | 0.876217i | \(0.660059\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.79899 | 0.313468 | 0.156734 | − | 0.987641i | \(-0.449903\pi\) | ||||
0.156734 | + | 0.987641i | \(0.449903\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.6274 | −0.908007 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.3137 | 0.693659 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.65685 | −0.385044 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.9411 | 1.03270 | 0.516350 | − | 0.856378i | \(-0.327290\pi\) | ||||
0.516350 | + | 0.856378i | \(0.327290\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.3137 | −0.449680 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.82843 | 0.191309 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28.2843 | −1.11891 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.6274 | −0.498753 | −0.249376 | − | 0.968407i | \(-0.580226\pi\) | ||||
−0.249376 | + | 0.968407i | \(0.580226\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.85786 | −0.388756 | −0.194378 | − | 0.980927i | \(-0.562269\pi\) | ||||
−0.194378 | + | 0.980927i | \(0.562269\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.68629 | −0.184523 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.4558 | −1.31528 | −0.657642 | − | 0.753330i | \(-0.728446\pi\) | ||||
−0.657642 | + | 0.753330i | \(0.728446\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.82843 | 0.268039 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.3137 | −0.756964 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.9706 | −1.05544 | −0.527720 | − | 0.849418i | \(-0.676953\pi\) | ||||
−0.527720 | + | 0.849418i | \(0.676953\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.3431 | 0.404140 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.8579 | −0.618674 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.9706 | 1.12853 | 0.564266 | − | 0.825593i | \(-0.309159\pi\) | ||||
0.564266 | + | 0.825593i | \(0.309159\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.6863 | 0.571231 | 0.285615 | − | 0.958344i | \(-0.407802\pi\) | ||||
0.285615 | + | 0.958344i | \(0.407802\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.3137 | 0.439388 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.00000 | −0.309761 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.00000 | −0.309298 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.17157 | 0.122437 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.2843 | 1.32156 | 0.660781 | − | 0.750579i | \(-0.270225\pi\) | ||||
0.660781 | + | 0.750579i | \(0.270225\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.65685 | −0.217732 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −46.4853 | −1.78657 | −0.893287 | − | 0.449486i | \(-0.851607\pi\) | ||||
−0.893287 | + | 0.449486i | \(0.851607\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.31371 | 0.357427 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −54.6274 | −2.09333 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.3137 | 0.739019 | 0.369509 | − | 0.929227i | \(-0.379526\pi\) | ||||
0.369509 | + | 0.929227i | \(0.379526\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.0000 | −0.382080 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 64.9706 | 2.47878 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.6569 | 0.672673 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.1421 | 0.690159 | 0.345080 | − | 0.938573i | \(-0.387852\pi\) | ||||
0.345080 | + | 0.938573i | \(0.387852\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.00000 | −0.189934 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.00000 | −0.303457 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.31371 | −0.277026 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −78.2254 | −2.95876 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.3137 | −1.10716 | −0.553582 | − | 0.832795i | \(-0.686739\pi\) | ||||
−0.553582 | + | 0.832795i | \(0.686739\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.00000 | 0.301297 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.4853 | 0.394340 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.6274 | 0.774679 | 0.387339 | − | 0.921937i | \(-0.373394\pi\) | ||||
0.387339 | + | 0.921937i | \(0.373394\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.3137 | −1.02291 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.82843 | −0.180573 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.62742 | 0.247505 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.4558 | −0.800168 | −0.400084 | − | 0.916478i | \(-0.631019\pi\) | ||||
−0.400084 | + | 0.916478i | \(0.631019\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.17157 | 0.192599 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 61.6569 | 2.29304 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.8284 | −0.995011 | −0.497506 | − | 0.867461i | \(-0.665751\pi\) | ||||
−0.497506 | + | 0.867461i | \(0.665751\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.0000 | −1.59259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.37258 | 0.0507668 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.8579 | 0.437980 | 0.218990 | − | 0.975727i | \(-0.429724\pi\) | ||||
0.218990 | + | 0.975727i | \(0.429724\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.82843 | 0.104328 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.65685 | −0.208373 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.0000 | 0.441427 | 0.220714 | − | 0.975339i | \(-0.429161\pi\) | ||||
0.220714 | + | 0.975339i | \(0.429161\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.6274 | 1.12361 | 0.561805 | − | 0.827269i | \(-0.310107\pi\) | ||||
0.561805 | + | 0.827269i | \(0.310107\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.34315 | −0.305669 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −28.2843 | −1.03487 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.2843 | 1.03211 | 0.516054 | − | 0.856556i | \(-0.327400\pi\) | ||||
0.516054 | + | 0.856556i | \(0.327400\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 51.3137 | 1.86998 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.6569 | −0.569058 | −0.284529 | − | 0.958667i | \(-0.591837\pi\) | ||||
−0.284529 | + | 0.958667i | \(0.591837\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.3137 | −0.410662 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.4853 | 1.68509 | 0.842545 | − | 0.538626i | \(-0.181056\pi\) | ||||
0.842545 | + | 0.538626i | \(0.181056\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.31371 | 0.192369 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.14214 | 0.149759 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 32.9706 | 1.19050 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.51472 | −0.0546222 | −0.0273111 | − | 0.999627i | \(-0.508694\pi\) | ||||
−0.0273111 | + | 0.999627i | \(0.508694\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.970563 | 0.0349540 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.9706 | −0.826194 | −0.413097 | − | 0.910687i | \(-0.635553\pi\) | ||||
−0.413097 | + | 0.910687i | \(0.635553\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.82843 | −0.245284 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32.9706 | 1.18281 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.65685 | −0.202418 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.3137 | 0.404319 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.31371 | 0.0468883 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.97056 | 0.319766 | 0.159883 | − | 0.987136i | \(-0.448888\pi\) | ||||
0.159883 | + | 0.987136i | \(0.448888\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −32.0000 | −1.13923 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.00000 | 0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.3137 | 0.543806 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.3431 | 0.366834 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.6863 | −0.945277 | −0.472638 | − | 0.881256i | \(-0.656698\pi\) | ||||
−0.472638 | + | 0.881256i | \(0.656698\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.34315 | −0.0828945 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −86.5685 | −3.05875 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.17157 | −0.111922 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00000 | 0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.3431 | 0.364096 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.68629 | −0.0944450 | −0.0472225 | − | 0.998884i | \(-0.515037\pi\) | ||||
−0.0472225 | + | 0.998884i | \(0.515037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.2843 | −0.993195 | −0.496598 | − | 0.867981i | \(-0.665417\pi\) | ||||
−0.496598 | + | 0.867981i | \(0.665417\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 38.6274 | 1.35472 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.9706 | −0.874681 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −24.1421 | −0.843594 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 54.9706 | 1.91849 | 0.959243 | − | 0.282583i | \(-0.0911912\pi\) | ||||
0.959243 | + | 0.282583i | \(0.0911912\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.9706 | 1.00985 | 0.504925 | − | 0.863163i | \(-0.331520\pi\) | ||||
0.504925 | + | 0.863163i | \(0.331520\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.82843 | −0.0984732 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.65685 | −0.0576145 | −0.0288072 | − | 0.999585i | \(-0.509171\pi\) | ||||
−0.0288072 | + | 0.999585i | \(0.509171\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.3137 | 1.57381 | 0.786905 | − | 0.617074i | \(-0.211682\pi\) | ||||
0.786905 | + | 0.617074i | \(0.211682\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.65685 | −0.196234 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.828427 | −0.0287033 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.31371 | 0.114676 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.6274 | 1.33516 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.1127 | 0.659844 | 0.329922 | − | 0.944008i | \(-0.392978\pi\) | ||||
0.329922 | + | 0.944008i | \(0.392978\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.7157 | 0.679046 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.3137 | −0.354802 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −32.0000 | −1.09824 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46.6274 | 1.59837 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.4264 | −1.38417 | −0.692087 | − | 0.721814i | \(-0.743309\pi\) | ||||
−0.692087 | + | 0.721814i | \(0.743309\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.8284 | 0.711486 | 0.355743 | − | 0.934584i | \(-0.384228\pi\) | ||||
0.355743 | + | 0.934584i | \(0.384228\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.7990 | 1.08497 | 0.542484 | − | 0.840066i | \(-0.317484\pi\) | ||||
0.542484 | + | 0.840066i | \(0.317484\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.9706 | 0.850995 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.2843 | −0.826646 | −0.413323 | − | 0.910584i | \(-0.635632\pi\) | ||||
−0.413323 | + | 0.910584i | \(0.635632\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.14214 | −0.276841 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 46.1421 | 1.56707 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.3137 | −0.925490 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −46.5685 | −1.57611 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −58.2843 | −1.96812 | −0.984060 | − | 0.177837i | \(-0.943090\pi\) | ||||
−0.984060 | + | 0.177837i | \(0.943090\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.02944 | −0.237097 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.3431 | 1.22443 | 0.612216 | − | 0.790691i | \(-0.290278\pi\) | ||||
0.612216 | + | 0.790691i | \(0.290278\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.3137 | 0.649223 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.9706 | 0.569816 | 0.284908 | − | 0.958555i | \(-0.408037\pi\) | ||||
0.284908 | + | 0.958555i | \(0.408037\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.3137 | −0.511881 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −54.6274 | −1.82396 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.6569 | 0.455482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.02944 | −0.100925 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.68629 | −0.155950 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.6569 | −0.520451 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.97056 | −0.297863 | −0.148931 | − | 0.988848i | \(-0.547583\pi\) | ||||
−0.148931 | + | 0.988848i | \(0.547583\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −52.4264 | −1.73887 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.2843 | 1.20215 | 0.601076 | − | 0.799192i | \(-0.294739\pi\) | ||||
0.601076 | + | 0.799192i | \(0.294739\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.65685 | −0.187215 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.97056 | 0.296558 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.3431 | 0.341561 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.9706 | −1.61539 | −0.807695 | − | 0.589601i | \(-0.799285\pi\) | ||||
−0.807695 | + | 0.589601i | \(0.799285\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −45.2548 | −1.49120 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27.3137 | −0.899042 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.6569 | 0.383275 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.8579 | −0.849284 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.6569 | 1.30110 | 0.650550 | − | 0.759464i | \(-0.274539\pi\) | ||||
0.650550 | + | 0.759464i | \(0.274539\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −73.9411 | −2.42072 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.828427 | 0.0270925 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.2010 | 0.463927 | 0.231963 | − | 0.972725i | \(-0.425485\pi\) | ||||
0.231963 | + | 0.972725i | \(0.425485\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.2843 | −0.400882 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.7696 | −1.26385 | −0.631926 | − | 0.775029i | \(-0.717735\pi\) | ||||
−0.631926 | + | 0.775029i | \(0.717735\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.3137 | 1.14997 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.65685 | −0.184017 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.9411 | 0.583008 | 0.291504 | − | 0.956570i | \(-0.405844\pi\) | ||||
0.291504 | + | 0.956570i | \(0.405844\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.3137 | −0.497104 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 76.2843 | 2.47369 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.6863 | −0.734881 | −0.367441 | − | 0.930047i | \(-0.619766\pi\) | ||||
−0.367441 | + | 0.930047i | \(0.619766\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.3137 | −0.624977 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.65685 | 0.182860 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.0000 | −0.322917 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.6274 | 0.504110 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.0000 | 0.644491 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.0000 | −0.450676 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.9706 | 1.31752 | 0.658762 | − | 0.752351i | \(-0.271080\pi\) | ||||
0.658762 | + | 0.752351i | \(0.271080\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.8284 | −0.732599 | −0.366300 | − | 0.930497i | \(-0.619375\pi\) | ||||
−0.366300 | + | 0.930497i | \(0.619375\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.00000 | −0.256468 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.6569 | −0.437369 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.3137 | −0.553915 | −0.276957 | − | 0.960882i | \(-0.589326\pi\) | ||||
−0.276957 | + | 0.960882i | \(0.589326\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.3137 | −0.553349 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.5685 | −0.848268 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.8284 | 0.855694 | 0.427847 | − | 0.903851i | \(-0.359272\pi\) | ||||
0.427847 | + | 0.903851i | \(0.359272\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.3137 | −0.679111 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.00000 | 0.254643 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.62742 | −0.210740 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.2843 | −0.390223 | −0.195111 | − | 0.980781i | \(-0.562507\pi\) | ||||
−0.195111 | + | 0.980781i | \(0.562507\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −97.9411 | −3.10807 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.1716 | 0.544375 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.4853 | −1.47220 | −0.736102 | − | 0.676871i | \(-0.763336\pi\) | ||||
−0.736102 | + | 0.676871i | \(0.763336\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −65.9411 | −2.08628 |
(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 | 6160.2.a.x.1.1 | 2 | ||
4.3 | odd | 2 | 3080.2.a.g.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3080.2.a.g.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
6160.2.a.x.1.1 | 2 | 1.1 | even | 1 | trivial |