Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(1,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, 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("1560.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.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: | \(12.4566627153\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.56155 | 0.590211 | 0.295106 | − | 0.955465i | \(-0.404645\pi\) | ||||
0.295106 | + | 0.955465i | \(0.404645\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.56155 | −1.67687 | −0.838436 | − | 0.545001i | \(-0.816529\pi\) | ||||
−0.838436 | + | 0.545001i | \(0.816529\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.68466 | −1.62127 | −0.810634 | − | 0.585553i | \(-0.800877\pi\) | ||||
−0.810634 | + | 0.585553i | \(0.800877\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.12311 | 0.716490 | 0.358245 | − | 0.933628i | \(-0.383375\pi\) | ||||
0.358245 | + | 0.933628i | \(0.383375\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.56155 | −0.340759 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.56155 | −1.15966 | −0.579832 | − | 0.814736i | \(-0.696882\pi\) | ||||
−0.579832 | + | 0.814736i | \(0.696882\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.12311 | −1.27935 | −0.639674 | − | 0.768647i | \(-0.720931\pi\) | ||||
−0.639674 | + | 0.768647i | \(0.720931\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.56155 | 0.968142 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.56155 | 0.263951 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.80776 | 1.61239 | 0.806193 | − | 0.591652i | \(-0.201524\pi\) | ||||
0.806193 | + | 0.591652i | \(0.201524\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.68466 | 0.419273 | 0.209637 | − | 0.977779i | \(-0.432772\pi\) | ||||
0.209637 | + | 0.977779i | \(0.432772\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.2462 | −1.56253 | −0.781266 | − | 0.624198i | \(-0.785426\pi\) | ||||
−0.781266 | + | 0.624198i | \(0.785426\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.12311 | 1.03901 | 0.519506 | − | 0.854467i | \(-0.326116\pi\) | ||||
0.519506 | + | 0.854467i | \(0.326116\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.56155 | −0.651650 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.68466 | 0.936039 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.56155 | 0.489217 | 0.244608 | − | 0.969622i | \(-0.421341\pi\) | ||||
0.244608 | + | 0.969622i | \(0.421341\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.56155 | −0.749920 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.12311 | −0.413665 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.6847 | −1.36803 | −0.684015 | − | 0.729468i | \(-0.739768\pi\) | ||||
−0.684015 | + | 0.729468i | \(0.739768\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.56155 | 0.196737 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.2462 | −1.74045 | −0.870226 | − | 0.492653i | \(-0.836027\pi\) | ||||
−0.870226 | + | 0.492653i | \(0.836027\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.56155 | 0.669532 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.68466 | 0.555967 | 0.277983 | − | 0.960586i | \(-0.410334\pi\) | ||||
0.277983 | + | 0.960586i | \(0.410334\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.2462 | 1.90148 | 0.950738 | − | 0.309997i | \(-0.100328\pi\) | ||||
0.950738 | + | 0.309997i | \(0.100328\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.68466 | −0.989709 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.8078 | 1.32848 | 0.664239 | − | 0.747521i | \(-0.268756\pi\) | ||||
0.664239 | + | 0.747521i | \(0.268756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.68466 | −0.725053 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00000 | 0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.6847 | −1.55657 | −0.778285 | − | 0.627911i | \(-0.783910\pi\) | ||||
−0.778285 | + | 0.627911i | \(0.783910\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.56155 | 0.163695 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.12311 | 0.738632 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.12311 | 0.320424 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.8078 | −1.80810 | −0.904052 | − | 0.427422i | \(-0.859422\pi\) | ||||
−0.904052 | + | 0.427422i | \(0.859422\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.56155 | −0.558957 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.12311 | 0.111753 | 0.0558766 | − | 0.998438i | \(-0.482205\pi\) | ||||
0.0558766 | + | 0.998438i | \(0.482205\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2462 | 1.40372 | 0.701860 | − | 0.712314i | \(-0.252353\pi\) | ||||
0.701860 | + | 0.712314i | \(0.252353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.56155 | −0.152392 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.8078 | −1.52819 | −0.764097 | − | 0.645101i | \(-0.776815\pi\) | ||||
−0.764097 | + | 0.645101i | \(0.776815\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.1231 | −1.25697 | −0.628483 | − | 0.777824i | \(-0.716324\pi\) | ||||
−0.628483 | + | 0.777824i | \(0.716324\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.80776 | −0.930912 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.56155 | −0.518617 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.4384 | −0.956891 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.9309 | 1.81190 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.68466 | −0.242067 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.3693 | −1.54128 | −0.770639 | − | 0.637272i | \(-0.780063\pi\) | ||||
−0.770639 | + | 0.637272i | \(0.780063\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.2462 | 0.902129 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.1231 | −1.32131 | −0.660656 | − | 0.750689i | \(-0.729722\pi\) | ||||
−0.660656 | + | 0.750689i | \(0.729722\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.87689 | 0.422880 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.2462 | 1.38801 | 0.694004 | − | 0.719971i | \(-0.255845\pi\) | ||||
0.694004 | + | 0.719971i | \(0.255845\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.56155 | −0.811000 | −0.405500 | − | 0.914095i | \(-0.632903\pi\) | ||||
−0.405500 | + | 0.914095i | \(0.632903\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.12311 | −0.599874 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.56155 | −0.465080 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.56155 | 0.376231 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.4384 | −1.01900 | −0.509499 | − | 0.860471i | \(-0.670169\pi\) | ||||
−0.509499 | + | 0.860471i | \(0.670169\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.68466 | −0.540423 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.12311 | −0.572142 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4924 | 0.837386 | 0.418693 | − | 0.908128i | \(-0.362488\pi\) | ||||
0.418693 | + | 0.908128i | \(0.362488\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.56155 | −0.282450 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.68466 | −0.684447 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.5616 | 1.06222 | 0.531111 | − | 0.847302i | \(-0.321775\pi\) | ||||
0.531111 | + | 0.847302i | \(0.321775\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.56155 | 0.432966 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.75379 | −0.445242 | −0.222621 | − | 0.974905i | \(-0.571461\pi\) | ||||
−0.222621 | + | 0.974905i | \(0.571461\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.12311 | 0.238830 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.0000 | 1.06440 | 0.532200 | − | 0.846619i | \(-0.321365\pi\) | ||||
0.532200 | + | 0.846619i | \(0.321365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.56155 | 0.118042 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.00000 | 0.601317 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.1231 | −1.72830 | −0.864151 | − | 0.503233i | \(-0.832144\pi\) | ||||
−0.864151 | + | 0.503233i | \(0.832144\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.93087 | −0.663826 | −0.331913 | − | 0.943310i | \(-0.607694\pi\) | ||||
−0.331913 | + | 0.943310i | \(0.607694\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.6847 | 0.789833 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.80776 | 0.721081 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 37.1771 | 2.71866 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.56155 | −0.113586 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.31534 | 0.670533 | 0.335266 | − | 0.942123i | \(-0.391174\pi\) | ||||
0.335266 | + | 0.942123i | \(0.391174\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.36932 | 0.525042 | 0.262521 | − | 0.964926i | \(-0.415446\pi\) | ||||
0.262521 | + | 0.964926i | \(0.415446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.75379 | 0.124323 | 0.0621614 | − | 0.998066i | \(-0.480201\pi\) | ||||
0.0621614 | + | 0.998066i | \(0.480201\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.2462 | 1.00485 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.12311 | −0.219199 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.68466 | 0.187505 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.56155 | −0.386555 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.3693 | −1.20146 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.68466 | −0.320988 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.2462 | −0.698786 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.1231 | −0.755086 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.2462 | −1.09782 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.68466 | −0.449659 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.24621 | −0.150417 | −0.0752087 | − | 0.997168i | \(-0.523962\pi\) | ||||
−0.0752087 | + | 0.997168i | \(0.523962\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.3693 | 1.68382 | 0.841910 | − | 0.539617i | \(-0.181431\pi\) | ||||
0.841910 | + | 0.539617i | \(0.181431\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.68466 | 0.571409 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.6847 | 1.22407 | 0.612036 | − | 0.790830i | \(-0.290351\pi\) | ||||
0.612036 | + | 0.790830i | \(0.290351\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.12311 | 0.464660 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.8078 | −0.766997 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.31534 | −0.214452 | −0.107226 | − | 0.994235i | \(-0.534197\pi\) | ||||
−0.107226 | + | 0.994235i | \(0.534197\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.7538 | 0.757128 | 0.378564 | − | 0.925575i | \(-0.376418\pi\) | ||||
0.378564 | + | 0.925575i | \(0.376418\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.56155 | −0.291427 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.12311 | 0.198718 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.00000 | 0.506979 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.49242 | 0.536037 | 0.268018 | − | 0.963414i | \(-0.413631\pi\) | ||||
0.268018 | + | 0.963414i | \(0.413631\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.9309 | 1.94461 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.68466 | 0.418610 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.4924 | 0.904012 | 0.452006 | − | 0.892015i | \(-0.350708\pi\) | ||||
0.452006 | + | 0.892015i | \(0.350708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.3153 | 0.951649 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.4924 | 1.75692 | 0.878459 | − | 0.477818i | \(-0.158572\pi\) | ||||
0.878459 | + | 0.477818i | \(0.158572\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.56155 | 0.218784 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.6847 | 0.898687 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.1231 | −0.800130 | −0.400065 | − | 0.916487i | \(-0.631012\pi\) | ||||
−0.400065 | + | 0.916487i | \(0.631012\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.36932 | −0.326163 | −0.163081 | − | 0.986613i | \(-0.552143\pi\) | ||||
−0.163081 | + | 0.986613i | \(0.552143\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.56155 | −0.0945095 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.56155 | −0.335374 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.4924 | −1.35144 | −0.675719 | − | 0.737159i | \(-0.736167\pi\) | ||||
−0.675719 | + | 0.737159i | \(0.736167\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.12311 | −0.426449 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.75379 | 0.223932 | 0.111966 | − | 0.993712i | \(-0.464285\pi\) | ||||
0.111966 | + | 0.993712i | \(0.464285\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.7386 | 1.82722 | 0.913611 | − | 0.406589i | \(-0.133282\pi\) | ||||
0.913611 | + | 0.406589i | \(0.133282\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.12311 | −0.184997 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.19224 | 0.247460 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.6847 | 1.62851 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.8078 | 1.04391 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.6155 | −1.02911 | −0.514555 | − | 0.857457i | \(-0.672043\pi\) | ||||
−0.514555 | + | 0.857457i | \(0.672043\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.56155 | 0.322714 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.56155 | −0.321633 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | −0.922225 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.12311 | −0.0645207 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.6847 | −0.611802 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.5616 | 0.773999 | 0.386999 | − | 0.922080i | \(-0.373512\pi\) | ||||
0.386999 | + | 0.922080i | \(0.373512\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.2462 | −0.810439 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.7386 | −1.51621 | −0.758104 | − | 0.652133i | \(-0.773874\pi\) | ||||
−0.758104 | + | 0.652133i | \(0.773874\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.7386 | −1.39831 | −0.699155 | − | 0.714970i | \(-0.746440\pi\) | ||||
−0.699155 | + | 0.714970i | \(0.746440\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.56155 | 0.0879835 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.87689 | 0.161582 | 0.0807912 | − | 0.996731i | \(-0.474255\pi\) | ||||
0.0807912 | + | 0.996731i | \(0.474255\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.1231 | 0.622774 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.8078 | 0.882303 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.8769 | −1.16162 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.1231 | 0.725709 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.1231 | 0.613237 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.75379 | 0.536117 | 0.268058 | − | 0.963403i | \(-0.413618\pi\) | ||||
0.268058 | + | 0.963403i | \(0.413618\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.80776 | 0.537462 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.2462 | −0.778354 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.87689 | −0.156714 | −0.0783572 | − | 0.996925i | \(-0.524967\pi\) | ||||
−0.0783572 | + | 0.996925i | \(0.524967\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.00000 | −0.108625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 39.6155 | 2.14530 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0540 | −0.974823 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.56155 | 0.299424 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.05398 | −0.324994 | −0.162497 | − | 0.986709i | \(-0.551955\pi\) | ||||
−0.162497 | + | 0.986709i | \(0.551955\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.630683 | −0.0337597 | −0.0168798 | − | 0.999858i | \(-0.505373\pi\) | ||||
−0.0168798 | + | 0.999858i | \(0.505373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.24621 | −0.226003 | −0.113002 | − | 0.993595i | \(-0.536046\pi\) | ||||
−0.113002 | + | 0.993595i | \(0.536046\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.68466 | 0.248636 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.4384 | 0.552461 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.24621 | −0.118550 | −0.0592752 | − | 0.998242i | \(-0.518879\pi\) | ||||
−0.0592752 | + | 0.998242i | \(0.518879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.24621 | −0.486643 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.9309 | −1.04610 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.2462 | 0.850366 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.2462 | 0.743646 | 0.371823 | − | 0.928304i | \(-0.378733\pi\) | ||||
0.371823 | + | 0.928304i | \(0.378733\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.68466 | 0.139758 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.56155 | 0.288741 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.8769 | −0.770296 | −0.385148 | − | 0.922855i | \(-0.625850\pi\) | ||||
−0.385148 | + | 0.922855i | \(0.625850\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.00000 | −0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.1231 | 0.571356 | 0.285678 | − | 0.958326i | \(-0.407781\pi\) | ||||
0.285678 | + | 0.958326i | \(0.407781\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.3693 | 0.889857 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.63068 | 0.134422 | 0.0672108 | − | 0.997739i | \(-0.478590\pi\) | ||||
0.0672108 | + | 0.997739i | \(0.478590\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.68466 | −0.442611 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.2462 | −0.520844 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.8617 | 1.81826 | 0.909131 | − | 0.416510i | \(-0.136747\pi\) | ||||
0.909131 | + | 0.416510i | \(0.136747\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.1771 | 1.88013 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.1231 | 0.762860 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.8078 | 0.594113 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.8078 | 1.69676 | 0.848382 | − | 0.529385i | \(-0.177577\pi\) | ||||
0.848382 | + | 0.529385i | \(0.177577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.87689 | −0.244150 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.24621 | −0.212046 | −0.106023 | − | 0.994364i | \(-0.533812\pi\) | ||||
−0.106023 | + | 0.994364i | \(0.533812\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.12311 | −0.354827 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −54.5464 | −2.70376 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.4924 | −0.914391 | −0.457196 | − | 0.889366i | \(-0.651146\pi\) | ||||
−0.457196 | + | 0.889366i | \(0.651146\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.2462 | −0.801367 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.4924 | −0.614712 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.56155 | 0.468231 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.876894 | 0.0428391 | 0.0214195 | − | 0.999771i | \(-0.493181\pi\) | ||||
0.0214195 | + | 0.999771i | \(0.493181\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.8617 | 0.968002 | 0.484001 | − | 0.875067i | \(-0.339183\pi\) | ||||
0.484001 | + | 0.875067i | \(0.339183\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.12311 | 0.346337 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.68466 | −0.324254 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.6847 | −0.807427 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.56155 | 0.268514 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.7538 | 0.662497 | 0.331248 | − | 0.943544i | \(-0.392530\pi\) | ||||
0.331248 | + | 0.943544i | \(0.392530\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.3693 | 1.69974 | 0.849870 | − | 0.526992i | \(-0.176680\pi\) | ||||
0.849870 | + | 0.526992i | \(0.176680\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.00000 | 0.0958927 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17.3693 | −0.830887 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.93087 | 0.330792 | 0.165396 | − | 0.986227i | \(-0.447110\pi\) | ||||
0.165396 | + | 0.986227i | \(0.447110\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.56155 | −0.217217 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.31534 | −0.157517 | −0.0787583 | − | 0.996894i | \(-0.525096\pi\) | ||||
−0.0787583 | + | 0.996894i | \(0.525096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.6847 | −0.696120 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.4384 | 0.588318 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.6847 | 0.504240 | 0.252120 | − | 0.967696i | \(-0.418872\pi\) | ||||
0.252120 | + | 0.967696i | \(0.418872\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.9309 | −0.703067 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.00000 | −0.187936 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.56155 | 0.0732067 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.5616 | −1.66350 | −0.831750 | − | 0.555151i | \(-0.812660\pi\) | ||||
−0.831750 | + | 0.555151i | \(0.812660\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.68466 | 0.312013 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.5616 | −0.724774 | −0.362387 | − | 0.932028i | \(-0.618038\pi\) | ||||
−0.362387 | + | 0.932028i | \(0.618038\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.43845 | −0.299220 | −0.149610 | − | 0.988745i | \(-0.547802\pi\) | ||||
−0.149610 | + | 0.988745i | \(0.547802\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.12311 | 0.330326 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.1771 | 1.16506 | 0.582528 | − | 0.812811i | \(-0.302064\pi\) | ||||
0.582528 | + | 0.812811i | \(0.302064\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.2462 | −1.02723 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.4924 | −0.483465 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 56.9848 | 2.62017 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.12311 | 0.143298 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.56155 | 0.163072 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.5464 | 1.57847 | 0.789233 | − | 0.614094i | \(-0.210479\pi\) | ||||
0.789233 | + | 0.614094i | \(0.210479\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.80776 | 0.447196 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.68466 | 0.395166 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.8078 | −0.808609 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.68466 | 0.212282 | 0.106141 | − | 0.994351i | \(-0.466150\pi\) | ||||
0.106141 | + | 0.994351i | \(0.466150\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.5616 | −0.613275 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.50758 | −0.338812 | −0.169406 | − | 0.985546i | \(-0.554185\pi\) | ||||
−0.169406 | + | 0.985546i | \(0.554185\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.3693 | 0.602124 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.56155 | −0.249973 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.31534 | 0.328138 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.8617 | −1.69492 | −0.847462 | − | 0.530856i | \(-0.821871\pi\) | ||||
−0.847462 | + | 0.530856i | \(0.821871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.75379 | 0.257060 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.7386 | 0.835514 | 0.417757 | − | 0.908559i | \(-0.362816\pi\) | ||||
0.417757 | + | 0.908559i | \(0.362816\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.12311 | 0.0499775 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −42.6847 | −1.89196 | −0.945982 | − | 0.324219i | \(-0.894899\pi\) | ||||
−0.945982 | + | 0.324219i | \(0.894899\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.3693 | 1.12227 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.12311 | −0.137888 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.2462 | 0.627763 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −39.6155 | −1.74229 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.0000 | −0.614532 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.7538 | 0.601411 | 0.300706 | − | 0.953717i | \(-0.402778\pi\) | ||||
0.300706 | + | 0.953717i | \(0.402778\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.56155 | −0.0681518 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 47.6155 | 2.07416 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.93087 | 0.344820 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.68466 | 0.116285 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.8078 | −0.683429 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.1231 | 0.997836 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.3693 | 1.09273 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.0000 | −1.46177 | −0.730887 | − | 0.682498i | \(-0.760893\pi\) | ||||
−0.730887 | + | 0.682498i | \(0.760893\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.93087 | 0.383260 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.1231 | −0.562132 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.73863 | −0.288123 | −0.144062 | − | 0.989569i | \(-0.546016\pi\) | ||||
−0.144062 | + | 0.989569i | \(0.546016\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.6847 | −0.456010 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.24621 | −0.266098 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.4384 | 0.784083 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.80776 | −0.416316 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.0000 | −1.44063 | −0.720313 | − | 0.693649i | \(-0.756002\pi\) | ||||
−0.720313 | + | 0.693649i | \(0.756002\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.2462 | −0.433369 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.1771 | −1.56962 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.5616 | −1.07729 | −0.538646 | − | 0.842533i | \(-0.681064\pi\) | ||||
−0.538646 | + | 0.842533i | \(0.681064\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00000 | 0.0841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.56155 | 0.0655791 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.12311 | −0.0470830 | −0.0235415 | − | 0.999723i | \(-0.507494\pi\) | ||||
−0.0235415 | + | 0.999723i | \(0.507494\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.5616 | 1.06972 | 0.534859 | − | 0.844941i | \(-0.320365\pi\) | ||||
0.534859 | + | 0.844941i | \(0.320365\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.00000 | −0.334205 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.56155 | −0.231933 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.5464 | −1.52145 | −0.760723 | − | 0.649076i | \(-0.775156\pi\) | ||||
−0.760723 | + | 0.649076i | \(0.775156\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.31534 | −0.387132 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.4924 | −0.518273 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.8078 | −0.820354 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.00000 | 0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.3693 | −0.716908 | −0.358454 | − | 0.933547i | \(-0.616696\pi\) | ||||
−0.358454 | + | 0.933547i | \(0.616696\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.2462 | −0.916639 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.36932 | −0.303133 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.61553 | −0.230602 | −0.115301 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115301 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.4384 | −0.427935 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.75379 | −0.0717778 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.7386 | −0.765640 | −0.382820 | − | 0.923823i | \(-0.625047\pi\) | ||||
−0.382820 | + | 0.923823i | \(0.625047\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.56155 | −0.145279 | −0.0726394 | − | 0.997358i | \(-0.523142\pi\) | ||||
−0.0726394 | + | 0.997358i | \(0.523142\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.2462 | −0.580151 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.9309 | 0.810305 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.7386 | 1.08529 | 0.542644 | − | 0.839963i | \(-0.317423\pi\) | ||||
0.542644 | + | 0.839963i | \(0.317423\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.12311 | 0.126555 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.12311 | 0.288170 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.93087 | 0.199156 | 0.0995780 | − | 0.995030i | \(-0.468251\pi\) | ||||
0.0995780 | + | 0.995030i | \(0.468251\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.68466 | −0.108256 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.246211 | 0.00991209 | 0.00495605 | − | 0.999988i | \(-0.498422\pi\) | ||||
0.00495605 | + | 0.999988i | \(0.498422\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.63068 | 0.266510 | 0.133255 | − | 0.991082i | \(-0.457457\pi\) | ||||
0.133255 | + | 0.991082i | \(0.457457\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.56155 | 0.223177 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.9309 | −0.918706 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.3693 | 0.693664 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −65.5616 | −2.61411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.2462 | 1.04485 | 0.522423 | − | 0.852687i | \(-0.325028\pi\) | ||||
0.522423 | + | 0.852687i | \(0.325028\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | −0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.3693 | −0.689280 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.56155 | −0.180735 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.68466 | 0.185322 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.630683 | 0.0249105 | 0.0124552 | − | 0.999922i | \(-0.496035\pi\) | ||||
0.0124552 | + | 0.999922i | \(0.496035\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.8078 | 0.465653 | 0.232826 | − | 0.972518i | \(-0.425203\pi\) | ||||
0.232826 | + | 0.972518i | \(0.425203\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.2462 | 0.403444 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.684658 | −0.0269167 | −0.0134584 | − | 0.999909i | \(-0.504284\pi\) | ||||
−0.0134584 | + | 0.999909i | \(0.504284\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 44.4924 | 1.74648 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.1231 | 0.435949 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.7538 | 0.929558 | 0.464779 | − | 0.885427i | \(-0.346134\pi\) | ||||
0.464779 | + | 0.885427i | \(0.346134\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.1231 | −0.590909 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.2462 | 0.633825 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.49242 | 0.330818 | 0.165409 | − | 0.986225i | \(-0.447106\pi\) | ||||
0.165409 | + | 0.986225i | \(0.447106\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.8769 | −1.20097 | −0.600486 | − | 0.799635i | \(-0.705026\pi\) | ||||
−0.600486 | + | 0.799635i | \(0.705026\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.68466 | 0.259611 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.87689 | 0.189118 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.1231 | 0.430688 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.24621 | 0.0868435 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 59.4233 | 2.29401 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.0000 | −0.539660 | −0.269830 | − | 0.962908i | \(-0.586968\pi\) | ||||
−0.269830 | + | 0.962908i | \(0.586968\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.06913 | 0.271689 | 0.135844 | − | 0.990730i | \(-0.456625\pi\) | ||||
0.135844 | + | 0.990730i | \(0.456625\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.8078 | −1.06716 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.3693 | −0.972154 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.49242 | 0.171898 | 0.0859489 | − | 0.996300i | \(-0.472608\pi\) | ||||
0.0859489 | + | 0.996300i | \(0.472608\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.2462 | 0.620736 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.0000 | 0.381524 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.56155 | 0.135684 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.8769 | 1.09853 | 0.549264 | − | 0.835649i | \(-0.314908\pi\) | ||||
0.549264 | + | 0.835649i | \(0.314908\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.68466 | −0.329903 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.56155 | −0.362690 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.9460 | −0.679754 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.6847 | −0.706719 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.3693 | −0.731569 | −0.365785 | − | 0.930700i | \(-0.619199\pi\) | ||||
−0.365785 | + | 0.930700i | \(0.619199\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.6307 | 1.15526 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.12311 | −0.268272 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.75379 | 0.0659580 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.1231 | 0.643072 | 0.321536 | − | 0.946897i | \(-0.395801\pi\) | ||||
0.321536 | + | 0.946897i | \(0.395801\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.8078 | 0.442826 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39.6155 | 1.48361 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.56155 | −0.207990 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.31534 | 0.123814 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.75379 | 0.363755 | 0.181877 | − | 0.983321i | \(-0.441783\pi\) | ||||
0.181877 | + | 0.983321i | \(0.441783\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.2462 | 0.828492 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.7538 | −0.437128 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.6307 | −0.839326 | −0.419663 | − | 0.907680i | \(-0.637852\pi\) | ||||
−0.419663 | + | 0.907680i | \(0.637852\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 68.4924 | 2.53328 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.4233 | −1.08677 | −0.543387 | − | 0.839482i | \(-0.682858\pi\) | ||||
−0.543387 | + | 0.839482i | \(0.682858\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.56155 | 0.168255 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 79.2311 | 2.91851 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.8617 | 1.09848 | 0.549241 | − | 0.835664i | \(-0.314917\pi\) | ||||
0.549241 | + | 0.835664i | \(0.314917\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.12311 | −0.114730 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.87689 | −0.325662 | −0.162831 | − | 0.986654i | \(-0.552062\pi\) | ||||
−0.162831 | + | 0.986654i | \(0.552062\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.4384 | −0.455709 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.00000 | −0.292705 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.6847 | −0.901958 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.31534 | −0.266941 | −0.133470 | − | 0.991053i | \(-0.542612\pi\) | ||||
−0.133470 | + | 0.991053i | \(0.542612\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.49242 | −0.309481 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.00000 | 0.145575 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.8769 | −0.540710 | −0.270355 | − | 0.962761i | \(-0.587141\pi\) | ||||
−0.270355 | + | 0.962761i | \(0.587141\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −30.9309 | −1.12272 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.4924 | 0.815350 | 0.407675 | − | 0.913127i | \(-0.366340\pi\) | ||||
0.407675 | + | 0.913127i | \(0.366340\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.4924 | −0.741876 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.68466 | −0.241684 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.00000 | −0.288863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.6155 | 0.923720 | 0.461860 | − | 0.886953i | \(-0.347182\pi\) | ||||
0.461860 | + | 0.886953i | \(0.347182\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.4924 | −0.521932 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.1231 | −0.759745 | −0.379873 | − | 0.925039i | \(-0.624032\pi\) | ||||
−0.379873 | + | 0.925039i | \(0.624032\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.12311 | −0.255870 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.3153 | −0.549435 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.38447 | 0.300405 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.0540 | −0.932285 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00000 | 0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.4924 | 0.374491 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.7386 | −0.667960 | −0.333980 | − | 0.942580i | \(-0.608392\pi\) | ||||
−0.333980 | + | 0.942580i | \(0.608392\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.4924 | −1.01436 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.12311 | 0.111045 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.6847 | −0.379423 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.56155 | −0.126315 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.4233 | 1.46729 | 0.733644 | − | 0.679534i | \(-0.237818\pi\) | ||||
0.733644 | + | 0.679534i | \(0.237818\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.6155 | −1.68452 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.6847 | −0.518857 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −90.3542 | −3.18853 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.68466 | −0.306094 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.1231 | 0.461955 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.4924 | −0.650159 | −0.325079 | − | 0.945687i | \(-0.605391\pi\) | ||||
−0.325079 | + | 0.945687i | \(0.605391\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.9848 | 1.43917 | 0.719586 | − | 0.694403i | \(-0.244331\pi\) | ||||
0.719586 | + | 0.694403i | \(0.244331\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.36932 | 0.188310 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.5616 | 0.475040 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.0000 | −1.11954 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.56155 | 0.0545651 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.3153 | −1.16271 | −0.581357 | − | 0.813649i | \(-0.697478\pi\) | ||||
−0.581357 | + | 0.813649i | \(0.697478\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.5076 | −0.401129 | −0.200564 | − | 0.979681i | \(-0.564278\pi\) | ||||
−0.200564 | + | 0.979681i | \(0.564278\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.56155 | 0.193628 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.6307 | 0.786946 | 0.393473 | − | 0.919336i | \(-0.371273\pi\) | ||||
0.393473 | + | 0.919336i | \(0.371273\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.0000 | 1.04194 | 0.520972 | − | 0.853574i | \(-0.325570\pi\) | ||||
0.520972 | + | 0.853574i | \(0.325570\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.4924 | 0.780253 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.4924 | 1.05650 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.75379 | −0.199118 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.12311 | 0.246211 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.8078 | −1.09813 | −0.549063 | − | 0.835781i | \(-0.685015\pi\) | ||||
−0.549063 | + | 0.835781i | \(0.685015\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.75379 | −0.129287 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.1231 | 1.06940 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.7386 | −1.05495 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −54.5464 | −1.86983 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.5616 | −1.35456 | −0.677281 | − | 0.735725i | \(-0.736842\pi\) | ||||
−0.677281 | + | 0.735725i | \(0.736842\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.12311 | 0.106808 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.7926 | −1.18849 | −0.594246 | − | 0.804283i | \(-0.702550\pi\) | ||||
−0.594246 | + | 0.804283i | \(0.702550\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.1922 | 1.09838 | 0.549192 | − | 0.835696i | \(-0.314935\pi\) | ||||
0.549192 | + | 0.835696i | \(0.314935\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.19224 | −0.142871 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.86174 | 0.0633743 | 0.0316872 | − | 0.999498i | \(-0.489912\pi\) | ||||
0.0316872 | + | 0.999498i | \(0.489912\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.0000 | 0.476014 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −27.6847 | −0.940220 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −65.6695 | −2.22769 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.2462 | −0.482714 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.8078 | −0.602701 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.56155 | 0.0527901 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.0000 | −1.14810 | −0.574049 | − | 0.818821i | \(-0.694628\pi\) | ||||
−0.574049 | + | 0.818821i | \(0.694628\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.6155 | 0.594157 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.24621 | 0.277822 | 0.138911 | − | 0.990305i | \(-0.455640\pi\) | ||||
0.138911 | + | 0.990305i | \(0.455640\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.4924 | 1.09346 | 0.546729 | − | 0.837310i | \(-0.315873\pi\) | ||||
0.546729 | + | 0.837310i | \(0.315873\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.00000 | 0.268917 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.0540 | 0.874807 | 0.437403 | − | 0.899265i | \(-0.355898\pi\) | ||||
0.437403 | + | 0.899265i | \(0.355898\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.1231 | −0.909680 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.56155 | −0.186319 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.2462 | 0.744441 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.1231 | −0.772920 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.56155 | 0.185695 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.2462 | 0.475138 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.8078 | −0.793152 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.0000 | 0.532447 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.93087 | −0.296872 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.1231 | −1.56470 | −0.782349 | − | 0.622841i | \(-0.785978\pi\) | ||||
−0.782349 | + | 0.622841i | \(0.785978\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.12311 | 0.0372511 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.7538 | 0.588209 | 0.294105 | − | 0.955773i | \(-0.404979\pi\) | ||||
0.294105 | + | 0.955773i | \(0.404979\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.4924 | 1.47248 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.6847 | 0.353224 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.6155 | −0.779853 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.1922 | −0.402185 | −0.201092 | − | 0.979572i | \(-0.564449\pi\) | ||||
−0.201092 | + | 0.979572i | \(0.564449\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.5616 | −0.446868 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.68466 | 0.154197 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.80776 | 0.322477 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.2462 | 0.467907 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.3002 | 0.600410 | 0.300205 | − | 0.953875i | \(-0.402945\pi\) | ||||
0.300205 | + | 0.953875i | \(0.402945\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.2462 | −0.466901 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.7386 | 0.875384 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 37.1771 | 1.21582 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.7538 | −1.03735 | −0.518676 | − | 0.854971i | \(-0.673575\pi\) | ||||
−0.518676 | + | 0.854971i | \(0.673575\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.7386 | 0.807315 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.5464 | 0.669793 | 0.334897 | − | 0.942255i | \(-0.391299\pi\) | ||||
0.334897 | + | 0.942255i | \(0.391299\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.9309 | −0.486216 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.56155 | −0.0507973 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50.7386 | −1.64878 | −0.824392 | − | 0.566019i | \(-0.808483\pi\) | ||||
−0.824392 | + | 0.566019i | \(0.808483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.2462 | 0.527374 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.87689 | −0.0932897 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.8078 | 0.965568 | 0.482784 | − | 0.875739i | \(-0.339626\pi\) | ||||
0.482784 | + | 0.875739i | \(0.339626\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000 | 0.258874 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.1231 | −0.359559 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.3693 | 0.819218 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.7386 | 0.636730 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.8078 | −0.509398 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.31534 | 0.299871 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.2462 | −1.35855 | −0.679273 | − | 0.733885i | \(-0.737705\pi\) | ||||
−0.679273 | + | 0.733885i | \(0.737705\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.8769 | 0.670662 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.49242 | −0.272535 | −0.136267 | − | 0.990672i | \(-0.543511\pi\) | ||||
−0.136267 | + | 0.990672i | \(0.543511\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.9309 | −0.478662 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.8617 | −1.40326 | −0.701631 | − | 0.712541i | \(-0.747544\pi\) | ||||
−0.701631 | + | 0.712541i | \(0.747544\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 81.6695 | 2.61017 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.1231 | −0.418989 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52.9848 | −1.68995 | −0.844977 | − | 0.534803i | \(-0.820386\pi\) | ||||
−0.844977 | + | 0.534803i | \(0.820386\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.36932 | 0.234806 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.1231 | −0.354052 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 56.9848 | 1.81201 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.0540 | −1.08176 | −0.540880 | − | 0.841100i | \(-0.681909\pi\) | ||||
−0.540880 | + | 0.841100i | \(0.681909\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.75379 | −0.309527 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.75379 | 0.0555988 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.8769 | 0.344475 | 0.172237 | − | 0.985055i | \(-0.444900\pi\) | ||||
0.172237 | + | 0.985055i | \(0.444900\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.80776 | −0.310304 |
(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 | 1560.2.a.o.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 4680.2.a.y.1.2 | 2 | |||
4.3 | odd | 2 | 3120.2.a.bg.1.1 | 2 | |||
5.4 | even | 2 | 7800.2.a.bd.1.1 | 2 | |||
12.11 | even | 2 | 9360.2.a.ci.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.a.o.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3120.2.a.bg.1.1 | 2 | 4.3 | odd | 2 | |||
4680.2.a.y.1.2 | 2 | 3.2 | odd | 2 | |||
7800.2.a.bd.1.1 | 2 | 5.4 | even | 2 | |||
9360.2.a.ci.1.1 | 2 | 12.11 | even | 2 |