Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6840,2,Mod(1,6840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6840, 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("6840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6840 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6840.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: | \(54.6176749826\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 760) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.86081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6840.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.39821 | −0.528473 | −0.264236 | − | 0.964458i | \(-0.585120\pi\) | ||||
−0.264236 | + | 0.964458i | \(0.585120\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.32340 | 1.19910 | 0.599548 | − | 0.800339i | \(-0.295347\pi\) | ||||
0.599548 | + | 0.800339i | \(0.295347\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.601793 | −0.145956 | −0.0729781 | − | 0.997334i | \(-0.523250\pi\) | ||||
−0.0729781 | + | 0.997334i | \(0.523250\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.04502 | −1.26047 | −0.630236 | − | 0.776403i | \(-0.717042\pi\) | ||||
−0.630236 | + | 0.776403i | \(0.717042\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.60179 | −0.854531 | −0.427266 | − | 0.904126i | \(-0.640523\pi\) | ||||
−0.427266 | + | 0.904126i | \(0.640523\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.79641 | 0.502251 | 0.251125 | − | 0.967955i | \(-0.419199\pi\) | ||||
0.251125 | + | 0.967955i | \(0.419199\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.39821 | 0.236340 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.07480 | 0.176697 | 0.0883483 | − | 0.996090i | \(-0.471841\pi\) | ||||
0.0883483 | + | 0.996090i | \(0.471841\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.44322 | 0.850089 | 0.425044 | − | 0.905173i | \(-0.360259\pi\) | ||||
0.425044 | + | 0.905173i | \(0.360259\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.64681 | −1.31863 | −0.659313 | − | 0.751869i | \(-0.729153\pi\) | ||||
−0.659313 | + | 0.751869i | \(0.729153\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.85039 | 0.269908 | 0.134954 | − | 0.990852i | \(-0.456911\pi\) | ||||
0.134954 | + | 0.990852i | \(0.456911\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.04502 | −0.720717 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.11982 | 0.428540 | 0.214270 | − | 0.976774i | \(-0.431263\pi\) | ||||
0.214270 | + | 0.976774i | \(0.431263\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.69182 | 0.871201 | 0.435601 | − | 0.900140i | \(-0.356536\pi\) | ||||
0.435601 | + | 0.900140i | \(0.356536\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.64681 | −0.338889 | −0.169445 | − | 0.985540i | \(-0.554197\pi\) | ||||
−0.169445 | + | 0.985540i | \(0.554197\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.32340 | −0.536252 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.4134 | −1.76088 | −0.880441 | − | 0.474156i | \(-0.842753\pi\) | ||||
−0.880441 | + | 0.474156i | \(0.842753\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.59283 | 0.663747 | 0.331873 | − | 0.943324i | \(-0.392319\pi\) | ||||
0.331873 | + | 0.943324i | \(0.392319\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.6918 | 1.48547 | 0.742733 | − | 0.669588i | \(-0.233529\pi\) | ||||
0.742733 | + | 0.669588i | \(0.233529\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.64681 | −0.522807 | −0.261403 | − | 0.965230i | \(-0.584185\pi\) | ||||
−0.261403 | + | 0.965230i | \(0.584185\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.20359 | 0.132111 | 0.0660553 | − | 0.997816i | \(-0.478959\pi\) | ||||
0.0660553 | + | 0.997816i | \(0.478959\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.601793 | 0.0652736 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.44322 | −1.00098 | −0.500490 | − | 0.865742i | \(-0.666847\pi\) | ||||
−0.500490 | + | 0.865742i | \(0.666847\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.04502 | −0.633690 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.51803 | 0.458736 | 0.229368 | − | 0.973340i | \(-0.426334\pi\) | ||||
0.229368 | + | 0.973340i | \(0.426334\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.05398 | 0.502890 | 0.251445 | − | 0.967872i | \(-0.419094\pi\) | ||||
0.251445 | + | 0.967872i | \(0.419094\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.0748 | −1.09123 | −0.545616 | − | 0.838035i | \(-0.683704\pi\) | ||||
−0.545616 | + | 0.838035i | \(0.683704\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.17380 | 0.403496 | 0.201748 | − | 0.979437i | \(-0.435338\pi\) | ||||
0.201748 | + | 0.979437i | \(0.435338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.8414 | 1.42155 | 0.710776 | − | 0.703419i | \(-0.248344\pi\) | ||||
0.710776 | + | 0.703419i | \(0.248344\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.72161 | −0.161956 | −0.0809778 | − | 0.996716i | \(-0.525804\pi\) | ||||
−0.0809778 | + | 0.996716i | \(0.525804\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.04502 | 0.563701 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.841431 | 0.0771338 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.12878 | −0.188899 | −0.0944494 | − | 0.995530i | \(-0.530109\pi\) | ||||
−0.0944494 | + | 0.995530i | \(0.530109\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.59283 | −0.139166 | −0.0695831 | − | 0.997576i | \(-0.522167\pi\) | ||||
−0.0695831 | + | 0.997576i | \(0.522167\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.39821 | −0.121240 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.89541 | −0.845422 | −0.422711 | − | 0.906265i | \(-0.638921\pi\) | ||||
−0.422711 | + | 0.906265i | \(0.638921\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.70079 | 0.313897 | 0.156948 | − | 0.987607i | \(-0.449834\pi\) | ||||
0.156948 | + | 0.987607i | \(0.449834\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.60179 | 0.382158 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.3476 | −1.50309 | −0.751547 | − | 0.659680i | \(-0.770692\pi\) | ||||
−0.751547 | + | 0.659680i | \(0.770692\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.9404 | 1.13446 | 0.567228 | − | 0.823561i | \(-0.308016\pi\) | ||||
0.567228 | + | 0.823561i | \(0.308016\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.79641 | −0.224613 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.149606 | −0.0119399 | −0.00596994 | − | 0.999982i | \(-0.501900\pi\) | ||||
−0.00596994 | + | 0.999982i | \(0.501900\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.45219 | 0.666126 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.6468 | −1.93049 | −0.965244 | − | 0.261352i | \(-0.915832\pi\) | ||||
−0.965244 | + | 0.261352i | \(0.915832\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.8656 | 1.45987 | 0.729933 | − | 0.683519i | \(-0.239551\pi\) | ||||
0.729933 | + | 0.683519i | \(0.239551\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.69182 | 0.437833 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.36842 | 0.484182 | 0.242091 | − | 0.970254i | \(-0.422167\pi\) | ||||
0.242091 | + | 0.970254i | \(0.422167\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.39821 | −0.105695 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.4432 | −0.855307 | −0.427653 | − | 0.903943i | \(-0.640660\pi\) | ||||
−0.427653 | + | 0.903943i | \(0.640660\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.29362 | −0.244813 | −0.122406 | − | 0.992480i | \(-0.539061\pi\) | ||||
−0.122406 | + | 0.992480i | \(0.539061\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.07480 | −0.0790211 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.5422 | −1.48638 | −0.743191 | − | 0.669079i | \(-0.766689\pi\) | ||||
−0.743191 | + | 0.669079i | \(0.766689\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.6620 | −1.41530 | −0.707652 | − | 0.706561i | \(-0.750246\pi\) | ||||
−0.707652 | + | 0.706561i | \(0.750246\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.74580 | −0.690862 | −0.345431 | − | 0.938444i | \(-0.612267\pi\) | ||||
−0.345431 | + | 0.938444i | \(0.612267\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.43426 | 0.451597 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.44322 | −0.380171 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.09899 | −0.626401 | −0.313200 | − | 0.949687i | \(-0.601401\pi\) | ||||
−0.313200 | + | 0.949687i | \(0.601401\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.64681 | 0.589707 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.90997 | −0.265426 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.60179 | −0.175016 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.8712 | −0.928885 | −0.464443 | − | 0.885603i | \(-0.653745\pi\) | ||||
−0.464443 | + | 0.885603i | \(0.653745\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.3234 | −0.685188 | −0.342594 | − | 0.939483i | \(-0.611306\pi\) | ||||
−0.342594 | + | 0.939483i | \(0.611306\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.7368 | −0.973838 | −0.486919 | − | 0.873447i | \(-0.661879\pi\) | ||||
−0.486919 | + | 0.873447i | \(0.661879\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.1857 | −0.863821 | −0.431911 | − | 0.901916i | \(-0.642160\pi\) | ||||
−0.431911 | + | 0.901916i | \(0.642160\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.85039 | −0.120706 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.452186 | 0.0292495 | 0.0146247 | − | 0.999893i | \(-0.495345\pi\) | ||||
0.0146247 | + | 0.999893i | \(0.495345\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.5333 | 0.871754 | 0.435877 | − | 0.900006i | \(-0.356438\pi\) | ||||
0.435877 | + | 0.900006i | \(0.356438\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.04502 | 0.322314 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.32340 | 0.275092 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.2936 | −1.34404 | −0.672021 | − | 0.740532i | \(-0.734573\pi\) | ||||
−0.672021 | + | 0.740532i | \(0.734573\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.3989 | 1.77147 | 0.885737 | − | 0.464188i | \(-0.153654\pi\) | ||||
0.885737 | + | 0.464188i | \(0.153654\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.50280 | −0.0933793 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.1857 | −0.689737 | −0.344869 | − | 0.938651i | \(-0.612077\pi\) | ||||
−0.344869 | + | 0.938651i | \(0.612077\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.11982 | −0.191649 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.5928 | −1.19460 | −0.597298 | − | 0.802019i | \(-0.703759\pi\) | ||||
−0.597298 | + | 0.802019i | \(0.703759\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.95498 | 0.361740 | 0.180870 | − | 0.983507i | \(-0.442109\pi\) | ||||
0.180870 | + | 0.983507i | \(0.442109\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.9404 | −1.43844 | −0.719220 | − | 0.694782i | \(-0.755501\pi\) | ||||
−0.719220 | + | 0.694782i | \(0.755501\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.7368 | −0.640506 | −0.320253 | − | 0.947332i | \(-0.603768\pi\) | ||||
−0.320253 | + | 0.947332i | \(0.603768\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.0900 | −0.956453 | −0.478227 | − | 0.878237i | \(-0.658720\pi\) | ||||
−0.478227 | + | 0.878237i | \(0.658720\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.61076 | −0.449249 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6378 | −0.978697 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.5630 | −0.850782 | −0.425391 | − | 0.905010i | \(-0.639863\pi\) | ||||
−0.425391 | + | 0.905010i | \(0.639863\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.69182 | −0.389613 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −26.1350 | −1.51143 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0900 | 0.696858 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.64681 | 0.151556 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.77559 | 0.158411 | 0.0792057 | − | 0.996858i | \(-0.474762\pi\) | ||||
0.0792057 | + | 0.996858i | \(0.474762\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.63785 | 0.433102 | 0.216551 | − | 0.976271i | \(-0.430519\pi\) | ||||
0.216551 | + | 0.976271i | \(0.430519\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.5243 | −1.83838 | −0.919191 | − | 0.393812i | \(-0.871156\pi\) | ||||
−0.919191 | + | 0.393812i | \(0.871156\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.8206 | −0.607746 | −0.303873 | − | 0.952713i | \(-0.598280\pi\) | ||||
−0.303873 | + | 0.952713i | \(0.598280\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.601793 | −0.0334846 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.32340 | 0.239819 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.58723 | −0.142639 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.6918 | 0.807536 | 0.403768 | − | 0.914861i | \(-0.367700\pi\) | ||||
0.403768 | + | 0.914861i | \(0.367700\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.4134 | 0.787490 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.07480 | −0.0585483 | −0.0292741 | − | 0.999571i | \(-0.509320\pi\) | ||||
−0.0292741 | + | 0.999571i | \(0.509320\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.8414 | 0.909352 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.0900 | −1.72268 | −0.861342 | − | 0.508026i | \(-0.830375\pi\) | ||||
−0.861342 | + | 0.508026i | \(0.830375\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.4737 | 1.68475 | 0.842374 | − | 0.538894i | \(-0.181158\pi\) | ||||
0.842374 | + | 0.538894i | \(0.181158\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.4882 | 0.611457 | 0.305729 | − | 0.952119i | \(-0.401100\pi\) | ||||
0.305729 | + | 0.952119i | \(0.401100\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.59283 | −0.296837 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.0450 | −1.37460 | −0.687302 | − | 0.726372i | \(-0.741205\pi\) | ||||
−0.687302 | + | 0.726372i | \(0.741205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.6918 | −0.664320 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.5512 | −1.12496 | −0.562481 | − | 0.826810i | \(-0.690153\pi\) | ||||
−0.562481 | + | 0.826810i | \(0.690153\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.36215 | −0.226472 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.9702 | 1.29291 | 0.646454 | − | 0.762953i | \(-0.276251\pi\) | ||||
0.646454 | + | 0.762953i | \(0.276251\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.8954 | −1.02467 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.6323 | 1.47074 | 0.735370 | − | 0.677666i | \(-0.237008\pi\) | ||||
0.735370 | + | 0.677666i | \(0.237008\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.9612 | −0.917777 | −0.458889 | − | 0.888494i | \(-0.651752\pi\) | ||||
−0.458889 | + | 0.888494i | \(0.651752\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.09003 | 0.308777 | 0.154388 | − | 0.988010i | \(-0.450659\pi\) | ||||
0.154388 | + | 0.988010i | \(0.450659\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.63785 | 0.183974 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.64681 | 0.233806 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.8325 | 1.09574 | 0.547870 | − | 0.836563i | \(-0.315439\pi\) | ||||
0.547870 | + | 0.836563i | \(0.315439\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.7064 | 0.634526 | 0.317263 | − | 0.948338i | \(-0.397236\pi\) | ||||
0.317263 | + | 0.948338i | \(0.397236\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0900 | 0.602247 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.8864 | 0.834981 | 0.417491 | − | 0.908681i | \(-0.362910\pi\) | ||||
0.417491 | + | 0.908681i | \(0.362910\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.35656 | −0.460406 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.20359 | −0.0590817 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.7908 | −1.35767 | −0.678835 | − | 0.734291i | \(-0.737515\pi\) | ||||
−0.678835 | + | 0.734291i | \(0.737515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.0090 | 0.731492 | 0.365746 | − | 0.930715i | \(-0.380814\pi\) | ||||
0.365746 | + | 0.930715i | \(0.380814\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.601793 | −0.0291912 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.70079 | 0.179094 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.736841 | 0.0354924 | 0.0177462 | − | 0.999843i | \(-0.494351\pi\) | ||||
0.0177462 | + | 0.999843i | \(0.494351\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.4945 | 1.51353 | 0.756765 | − | 0.653687i | \(-0.226779\pi\) | ||||
0.756765 | + | 0.653687i | \(0.226779\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.04502 | −0.289172 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.2340 | −1.10890 | −0.554450 | − | 0.832217i | \(-0.687071\pi\) | ||||
−0.554450 | + | 0.832217i | \(0.687071\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.4793 | −0.782954 | −0.391477 | − | 0.920188i | \(-0.628036\pi\) | ||||
−0.391477 | + | 0.920188i | \(0.628036\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.44322 | 0.447652 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.29921 | 0.108507 | 0.0542533 | − | 0.998527i | \(-0.482722\pi\) | ||||
0.0542533 | + | 0.998527i | \(0.482722\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.04502 | 0.283395 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.0450 | −0.937666 | −0.468833 | − | 0.883287i | \(-0.655325\pi\) | ||||
−0.468833 | + | 0.883287i | \(0.655325\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.5872 | −1.51774 | −0.758869 | − | 0.651243i | \(-0.774248\pi\) | ||||
−0.758869 | + | 0.651243i | \(0.774248\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.58723 | 0.120239 | 0.0601195 | − | 0.998191i | \(-0.480852\pi\) | ||||
0.0601195 | + | 0.998191i | \(0.480852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.299213 | 0.0138459 | 0.00692295 | − | 0.999976i | \(-0.497796\pi\) | ||||
0.00692295 | + | 0.999976i | \(0.497796\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.1530 | 0.930578 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.0665 | 1.60223 | 0.801115 | − | 0.598511i | \(-0.204241\pi\) | ||||
0.801115 | + | 0.598511i | \(0.204241\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.64681 | 0.211876 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.51803 | −0.205153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.7521 | −1.89197 | −0.945983 | − | 0.324215i | \(-0.894900\pi\) | ||||
−0.945983 | + | 0.324215i | \(0.894900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.9765 | 1.39795 | 0.698974 | − | 0.715147i | \(-0.253640\pi\) | ||||
0.698974 | + | 0.715147i | \(0.253640\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.76932 | 0.124724 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.81994 | −0.350772 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.90997 | −0.175034 | −0.0875171 | − | 0.996163i | \(-0.527893\pi\) | ||||
−0.0875171 | + | 0.996163i | \(0.527893\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.4522 | −0.733567 | −0.366783 | − | 0.930306i | \(-0.619541\pi\) | ||||
−0.366783 | + | 0.930306i | \(0.619541\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.05398 | −0.224899 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.4432 | 1.12775 | 0.563876 | − | 0.825860i | \(-0.309310\pi\) | ||||
0.563876 | + | 0.825860i | \(0.309310\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.7458 | −0.785028 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.0748 | 0.488014 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.3836 | 1.19970 | 0.599850 | − | 0.800113i | \(-0.295227\pi\) | ||||
0.599850 | + | 0.800113i | \(0.295227\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.5574 | 1.81718 | 0.908590 | − | 0.417689i | \(-0.137160\pi\) | ||||
0.908590 | + | 0.417689i | \(0.137160\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.68286 | −0.0733066 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.5422 | 0.588792 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.5333 | 1.01934 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.17380 | −0.180449 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.6468 | 0.629715 | 0.314858 | − | 0.949139i | \(-0.398043\pi\) | ||||
0.314858 | + | 0.949139i | \(0.398043\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.8414 | −0.635737 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.9252 | −1.06572 | −0.532862 | − | 0.846202i | \(-0.678884\pi\) | ||||
−0.532862 | + | 0.846202i | \(0.678884\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.60179 | −0.196043 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.49720 | 0.276289 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 44.9348 | 1.90395 | 0.951975 | − | 0.306176i | \(-0.0990496\pi\) | ||||
0.951975 | + | 0.306176i | \(0.0990496\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.3836 | −1.58116 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.2605 | 0.432427 | 0.216213 | − | 0.976346i | \(-0.430629\pi\) | ||||
0.216213 | + | 0.976346i | \(0.430629\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.72161 | 0.0724287 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.6773 | −1.03452 | −0.517262 | − | 0.855827i | \(-0.673049\pi\) | ||||
−0.517262 | + | 0.855827i | \(0.673049\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.9765 | −0.459351 | −0.229676 | − | 0.973267i | \(-0.573767\pi\) | ||||
−0.229676 | + | 0.973267i | \(0.573767\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.04502 | −0.252095 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.1295 | −1.87876 | −0.939382 | − | 0.342873i | \(-0.888600\pi\) | ||||
−0.939382 | + | 0.342873i | \(0.888600\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.68286 | −0.0698169 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.90997 | −0.326479 | −0.163240 | − | 0.986586i | \(-0.552194\pi\) | ||||
−0.163240 | + | 0.986586i | \(0.552194\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.79641 | 0.115224 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.29362 | 0.299513 | 0.149756 | − | 0.988723i | \(-0.452151\pi\) | ||||
0.149756 | + | 0.988723i | \(0.452151\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.841431 | −0.0344953 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.6468 | −0.843606 | −0.421803 | − | 0.906688i | \(-0.638603\pi\) | ||||
−0.421803 | + | 0.906688i | \(0.638603\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.1440 | 1.84146 | 0.920731 | − | 0.390197i | \(-0.127593\pi\) | ||||
0.920731 | + | 0.390197i | \(0.127593\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.0000 | 0.447214 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.7577 | −0.842528 | −0.421264 | − | 0.906938i | \(-0.638413\pi\) | ||||
−0.421264 | + | 0.906938i | \(0.638413\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.3476 | 1.22573 | 0.612864 | − | 0.790188i | \(-0.290017\pi\) | ||||
0.612864 | + | 0.790188i | \(0.290017\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −47.2161 | −1.90085 | −0.950425 | − | 0.310955i | \(-0.899351\pi\) | ||||
−0.950425 | + | 0.310955i | \(0.899351\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.7064 | −0.912647 | −0.456323 | − | 0.889814i | \(-0.650834\pi\) | ||||
−0.456323 | + | 0.889814i | \(0.650834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.2036 | 0.528990 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.646809 | −0.0257899 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.4793 | 1.29298 | 0.646490 | − | 0.762923i | \(-0.276236\pi\) | ||||
0.646490 | + | 0.762923i | \(0.276236\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.12878 | 0.0844781 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.8116 | −0.864209 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.9460 | −0.432342 | −0.216171 | − | 0.976356i | \(-0.569357\pi\) | ||||
−0.216171 | + | 0.976356i | \(0.569357\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.38924 | 0.173095 | 0.0865475 | − | 0.996248i | \(-0.472417\pi\) | ||||
0.0865475 | + | 0.996248i | \(0.472417\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.4522 | −0.646802 | −0.323401 | − | 0.946262i | \(-0.604826\pi\) | ||||
−0.323401 | + | 0.946262i | \(0.604826\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.53326 | −0.0600009 | −0.0300005 | − | 0.999550i | \(-0.509551\pi\) | ||||
−0.0300005 | + | 0.999550i | \(0.509551\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.59283 | 0.0622370 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.1767 | −0.863881 | −0.431941 | − | 0.901902i | \(-0.642171\pi\) | ||||
−0.431941 | + | 0.901902i | \(0.642171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.0755 | −1.01422 | −0.507109 | − | 0.861882i | \(-0.669286\pi\) | ||||
−0.507109 | + | 0.861882i | \(0.669286\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.39821 | 0.0542202 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.8179 | 1.07711 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.4168 | −1.17248 | −0.586241 | − | 0.810137i | \(-0.699393\pi\) | ||||
−0.586241 | + | 0.810137i | \(0.699393\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.2043 | 1.69891 | 0.849454 | − | 0.527663i | \(-0.176932\pi\) | ||||
0.849454 | + | 0.527663i | \(0.176932\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.31714 | −0.242430 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.3989 | −1.62235 | −0.811174 | − | 0.584805i | \(-0.801171\pi\) | ||||
−0.811174 | + | 0.584805i | \(0.801171\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.89541 | 0.378084 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.4882 | 0.513861 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.79082 | 0.296377 | 0.148188 | − | 0.988959i | \(-0.452656\pi\) | ||||
0.148188 | + | 0.988959i | \(0.452656\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.70079 | −0.140379 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.27569 | −0.124076 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.05957 | 0.304406 | 0.152203 | − | 0.988349i | \(-0.451363\pi\) | ||||
0.152203 | + | 0.988349i | \(0.451363\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.07480 | 0.0405370 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.06651 | −0.265763 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.2936 | −1.32548 | −0.662740 | − | 0.748850i | \(-0.730606\pi\) | ||||
−0.662740 | + | 0.748850i | \(0.730606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.9044 | −0.633074 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 48.9315 | 1.82484 | 0.912418 | − | 0.409260i | \(-0.134213\pi\) | ||||
0.912418 | + | 0.409260i | \(0.134213\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.4849 | 0.576687 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.60179 | −0.170906 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.29025 | −0.122029 | −0.0610143 | − | 0.998137i | \(-0.519434\pi\) | ||||
−0.0610143 | + | 0.998137i | \(0.519434\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.20359 | 0.192462 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.3892 | 0.826966 | 0.413483 | − | 0.910512i | \(-0.364312\pi\) | ||||
0.413483 | + | 0.910512i | \(0.364312\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.90437 | 0.180410 | 0.0902051 | − | 0.995923i | \(-0.471248\pi\) | ||||
0.0902051 | + | 0.995923i | \(0.471248\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.1592 | −1.03306 | −0.516531 | − | 0.856268i | \(-0.672777\pi\) | ||||
−0.516531 | + | 0.856268i | \(0.672777\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.3476 | 0.672204 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.83584 | −0.213237 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.9348 | 1.56671 | 0.783357 | − | 0.621572i | \(-0.213506\pi\) | ||||
0.783357 | + | 0.621572i | \(0.213506\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.9404 | −0.507344 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.0665 | −0.911058 | −0.455529 | − | 0.890221i | \(-0.650550\pi\) | ||||
−0.455529 | + | 0.890221i | \(0.650550\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.8898 | 1.11975 | 0.559877 | − | 0.828575i | \(-0.310848\pi\) | ||||
0.559877 | + | 0.828575i | \(0.310848\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.7514 | −0.751251 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.9315 | 1.04465 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.78745 | 0.280823 | 0.140411 | − | 0.990093i | \(-0.455157\pi\) | ||||
0.140411 | + | 0.990093i | \(0.455157\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.7126 | −0.744982 | −0.372491 | − | 0.928036i | \(-0.621496\pi\) | ||||
−0.372491 | + | 0.928036i | \(0.621496\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.79641 | 0.100450 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.44322 | 0.195024 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.149606 | 0.00533968 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.5035 | 0.374408 | 0.187204 | − | 0.982321i | \(-0.440057\pi\) | ||||
0.187204 | + | 0.982321i | \(0.440057\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.40717 | 0.0855891 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.4432 | −0.406361 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.8871 | 1.34203 | 0.671015 | − | 0.741444i | \(-0.265858\pi\) | ||||
0.671015 | + | 0.741444i | \(0.265858\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.11355 | −0.0393947 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.45219 | −0.297900 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.9438 | 1.19340 | 0.596700 | − | 0.802464i | \(-0.296478\pi\) | ||||
0.596700 | + | 0.802464i | \(0.296478\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.66137 | 0.163683 | 0.0818414 | − | 0.996645i | \(-0.473920\pi\) | ||||
0.0818414 | + | 0.996645i | \(0.473920\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.6468 | 0.863340 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.64681 | −0.302514 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.5693 | 0.927275 | 0.463638 | − | 0.886025i | \(-0.346544\pi\) | ||||
0.463638 | + | 0.886025i | \(0.346544\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.7998 | 0.864466 | 0.432233 | − | 0.901762i | \(-0.357726\pi\) | ||||
0.432233 | + | 0.901762i | \(0.357726\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.11422 | 0.0735188 | 0.0367594 | − | 0.999324i | \(-0.488296\pi\) | ||||
0.0367594 | + | 0.999324i | \(0.488296\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.7279 | 1.58819 | 0.794097 | − | 0.607790i | \(-0.207944\pi\) | ||||
0.794097 | + | 0.607790i | \(0.207944\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.03605 | 0.105193 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.8656 | −0.652872 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.4432 | −0.533159 | −0.266580 | − | 0.963813i | \(-0.585894\pi\) | ||||
−0.266580 | + | 0.963813i | \(0.585894\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.82351 | −0.269776 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.69182 | −0.195805 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.3803 | 0.528473 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.49720 | −0.222721 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.1801 | 1.30726 | 0.653630 | − | 0.756814i | \(-0.273245\pi\) | ||||
0.653630 | + | 0.756814i | \(0.273245\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −52.2672 | −1.78541 | −0.892707 | − | 0.450638i | \(-0.851196\pi\) | ||||
−0.892707 | + | 0.450638i | \(0.851196\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.8809 | −1.36072 | −0.680359 | − | 0.732879i | \(-0.738176\pi\) | ||||
−0.680359 | + | 0.732879i | \(0.738176\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.9557 | −0.781420 | −0.390710 | − | 0.920514i | \(-0.627770\pi\) | ||||
−0.390710 | + | 0.920514i | \(0.627770\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.36842 | −0.216533 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −62.3151 | −2.11147 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.39821 | 0.0472680 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.73057 | −0.0922050 | −0.0461025 | − | 0.998937i | \(-0.514680\pi\) | ||||
−0.0461025 | + | 0.998937i | \(0.514680\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.14401 | −0.308070 | −0.154035 | − | 0.988065i | \(-0.549227\pi\) | ||||
−0.154035 | + | 0.988065i | \(0.549227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.0540 | −0.371996 | −0.185998 | − | 0.982550i | \(-0.559552\pi\) | ||||
−0.185998 | + | 0.982550i | \(0.559552\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37.1469 | −1.24727 | −0.623636 | − | 0.781715i | \(-0.714345\pi\) | ||||
−0.623636 | + | 0.781715i | \(0.714345\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.97648 | 0.0998279 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.85039 | 0.0619211 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.4432 | 0.382505 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.8685 | −0.429189 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.87748 | −0.0625481 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.29362 | 0.109484 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.00627 | 0.133026 | 0.0665129 | − | 0.997786i | \(-0.478813\pi\) | ||||
0.0665129 | + | 0.997786i | \(0.478813\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.2161 | −0.702921 | −0.351461 | − | 0.936203i | \(-0.614315\pi\) | ||||
−0.351461 | + | 0.936203i | \(0.614315\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.22711 | 0.0735455 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.5478 | −0.776771 | −0.388385 | − | 0.921497i | \(-0.626967\pi\) | ||||
−0.388385 | + | 0.921497i | \(0.626967\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.1801 | 0.795896 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.07480 | 0.0353393 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.7223 | 1.40167 | 0.700836 | − | 0.713322i | \(-0.252810\pi\) | ||||
0.700836 | + | 0.713322i | \(0.252810\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.04502 | −0.165344 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.1890 | −1.01890 | −0.509451 | − | 0.860500i | \(-0.670151\pi\) | ||||
−0.509451 | + | 0.860500i | \(0.670151\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.2251 | −0.659319 | −0.329659 | − | 0.944100i | \(-0.606934\pi\) | ||||
−0.329659 | + | 0.944100i | \(0.606934\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.9044 | −1.07151 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.1801 | 0.655764 | 0.327882 | − | 0.944719i | \(-0.393665\pi\) | ||||
0.327882 | + | 0.944719i | \(0.393665\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 54.8719 | 1.78122 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.6856 | −0.670071 | −0.335035 | − | 0.942206i | \(-0.608748\pi\) | ||||
−0.335035 | + | 0.942206i | \(0.608748\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.5422 | 0.664731 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.8358 | 0.446782 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.1801 | −0.747744 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.6620 | 0.632943 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.9530 | −1.73501 | −0.867505 | − | 0.497428i | \(-0.834278\pi\) | ||||
−0.867505 | + | 0.497428i | \(0.834278\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.41277 | 0.302070 | 0.151035 | − | 0.988528i | \(-0.451739\pi\) | ||||
0.151035 | + | 0.988528i | \(0.451739\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.17447 | −0.165886 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.21881 | 0.134972 | 0.0674859 | − | 0.997720i | \(-0.478502\pi\) | ||||
0.0674859 | + | 0.997720i | \(0.478502\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.3088 | 0.328801 | 0.164401 | − | 0.986394i | \(-0.447431\pi\) | ||||
0.164401 | + | 0.986394i | \(0.447431\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.00000 | −0.0637253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 52.2701 | 1.66209 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.6356 | 1.73556 | 0.867779 | − | 0.496951i | \(-0.165547\pi\) | ||||
0.867779 | + | 0.496951i | \(0.165547\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.74580 | 0.308963 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.9169 | 0.725786 | 0.362893 | − | 0.931831i | \(-0.381789\pi\) | ||||
0.362893 | + | 0.931831i | \(0.381789\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 6840.2.a.bg.1.2 | 3 | ||
3.2 | odd | 2 | 760.2.a.j.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 1520.2.a.s.1.1 | 3 | |||
15.2 | even | 4 | 3800.2.d.l.3649.2 | 6 | |||
15.8 | even | 4 | 3800.2.d.l.3649.5 | 6 | |||
15.14 | odd | 2 | 3800.2.a.x.1.1 | 3 | |||
24.5 | odd | 2 | 6080.2.a.bv.1.1 | 3 | |||
24.11 | even | 2 | 6080.2.a.bq.1.3 | 3 | |||
60.59 | even | 2 | 7600.2.a.bq.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.a.j.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
1520.2.a.s.1.1 | 3 | 12.11 | even | 2 | |||
3800.2.a.x.1.1 | 3 | 15.14 | odd | 2 | |||
3800.2.d.l.3649.2 | 6 | 15.2 | even | 4 | |||
3800.2.d.l.3649.5 | 6 | 15.8 | even | 4 | |||
6080.2.a.bq.1.3 | 3 | 24.11 | even | 2 | |||
6080.2.a.bv.1.1 | 3 | 24.5 | odd | 2 | |||
6840.2.a.bg.1.2 | 3 | 1.1 | even | 1 | trivial | ||
7600.2.a.bq.1.3 | 3 | 60.59 | even | 2 |