Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2760,2,Mod(1,2760)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2760, 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("2760.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2760.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: | \(22.0387109579\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.254102\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2760.1 |
$q$-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 | ||||||||
\(7\) | 3.18953 | 1.20553 | 0.602765 | − | 0.797919i | \(-0.294066\pi\) | ||||
0.602765 | + | 0.797919i | \(0.294066\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.36266 | −0.932634 | −0.466317 | − | 0.884618i | \(-0.654419\pi\) | ||||
−0.466317 | + | 0.884618i | \(0.654419\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.18953 | 1.25865 | 0.629323 | − | 0.777143i | \(-0.283332\pi\) | ||||
0.629323 | + | 0.777143i | \(0.283332\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.18953 | 0.696013 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.18953 | −0.220891 | −0.110445 | − | 0.993882i | \(-0.535228\pi\) | ||||
−0.110445 | + | 0.993882i | \(0.535228\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.17313 | 0.390305 | 0.195153 | − | 0.980773i | \(-0.437480\pi\) | ||||
0.195153 | + | 0.980773i | \(0.437480\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.18953 | 0.539130 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.53579 | 1.56767 | 0.783837 | − | 0.620967i | \(-0.213260\pi\) | ||||
0.783837 | + | 0.620967i | \(0.213260\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.36266 | −0.538457 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.55220 | −1.02328 | −0.511640 | − | 0.859200i | \(-0.670962\pi\) | ||||
−0.511640 | + | 0.859200i | \(0.670962\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.01641 | −0.155001 | −0.0775003 | − | 0.996992i | \(-0.524694\pi\) | ||||
−0.0775003 | + | 0.996992i | \(0.524694\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.37907 | 0.930483 | 0.465241 | − | 0.885184i | \(-0.345968\pi\) | ||||
0.465241 | + | 0.885184i | \(0.345968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.17313 | 0.453304 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.18953 | 0.726680 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.55220 | −0.350571 | −0.175285 | − | 0.984518i | \(-0.556085\pi\) | ||||
−0.175285 | + | 0.984518i | \(0.556085\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.55220 | 1.11340 | 0.556700 | − | 0.830713i | \(-0.312067\pi\) | ||||
0.556700 | + | 0.830713i | \(0.312067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.01641 | −0.386211 | −0.193106 | − | 0.981178i | \(-0.561856\pi\) | ||||
−0.193106 | + | 0.981178i | \(0.561856\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.18953 | 0.401844 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.36266 | −0.417087 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.53579 | −0.920643 | −0.460322 | − | 0.887752i | \(-0.652266\pi\) | ||||
−0.460322 | + | 0.887752i | \(0.652266\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9149 | 1.65139 | 0.825695 | − | 0.564117i | \(-0.190783\pi\) | ||||
0.825695 | + | 0.564117i | \(0.190783\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.37907 | 0.980696 | 0.490348 | − | 0.871527i | \(-0.336870\pi\) | ||||
0.490348 | + | 0.871527i | \(0.336870\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.74173 | −0.871013 | −0.435506 | − | 0.900186i | \(-0.643431\pi\) | ||||
−0.435506 | + | 0.900186i | \(0.643431\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.91486 | −1.08830 | −0.544148 | − | 0.838989i | \(-0.683147\pi\) | ||||
−0.544148 | + | 0.838989i | \(0.683147\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.18953 | 0.562884 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.18953 | −0.127531 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.3463 | 1.09670 | 0.548350 | − | 0.836249i | \(-0.315256\pi\) | ||||
0.548350 | + | 0.836249i | \(0.315256\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.7253 | −1.12432 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.17313 | 0.225343 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.01641 | 0.306270 | 0.153135 | − | 0.988205i | \(-0.451063\pi\) | ||||
0.153135 | + | 0.988205i | \(0.451063\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.18953 | −0.118363 | −0.0591815 | − | 0.998247i | \(-0.518849\pi\) | ||||
−0.0591815 | + | 0.998247i | \(0.518849\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.7417 | −1.15695 | −0.578473 | − | 0.815701i | \(-0.696351\pi\) | ||||
−0.578473 | + | 0.815701i | \(0.696351\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.18953 | 0.311267 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.18953 | −0.695038 | −0.347519 | − | 0.937673i | \(-0.612976\pi\) | ||||
−0.347519 | + | 0.937673i | \(0.612976\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0880 | −0.966254 | −0.483127 | − | 0.875550i | \(-0.660499\pi\) | ||||
−0.483127 | + | 0.875550i | \(0.660499\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.53579 | 0.905097 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.9149 | 1.49714 | 0.748572 | − | 0.663054i | \(-0.230740\pi\) | ||||
0.748572 | + | 0.663054i | \(0.230740\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.36266 | −0.310878 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.5522 | 1.51734 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.55220 | −0.590792 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.36266 | 0.120917 | 0.0604583 | − | 0.998171i | \(-0.480744\pi\) | ||||
0.0604583 | + | 0.998171i | \(0.480744\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.01641 | −0.0894896 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.7253 | −0.937076 | −0.468538 | − | 0.883443i | \(-0.655219\pi\) | ||||
−0.468538 | + | 0.883443i | \(0.655219\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.01641 | 0.257709 | 0.128855 | − | 0.991664i | \(-0.458870\pi\) | ||||
0.128855 | + | 0.991664i | \(0.458870\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.20594 | −0.696019 | −0.348009 | − | 0.937491i | \(-0.613142\pi\) | ||||
−0.348009 | + | 0.937491i | \(0.613142\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.37907 | 0.537214 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.18953 | −0.0987854 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.17313 | 0.261715 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.18953 | 0.419549 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.17313 | 0.174550 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.56860 | −0.604040 | −0.302020 | − | 0.953302i | \(-0.597661\pi\) | ||||
−0.302020 | + | 0.953302i | \(0.597661\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.55220 | −0.202402 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.18953 | 0.251370 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.10439 | 0.399807 | 0.199903 | − | 0.979816i | \(-0.435937\pi\) | ||||
0.199903 | + | 0.979816i | \(0.435937\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.62093 | −0.125431 | −0.0627157 | − | 0.998031i | \(-0.519976\pi\) | ||||
−0.0627157 | + | 0.998031i | \(0.519976\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.69251 | −0.130193 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.62093 | 0.275294 | 0.137647 | − | 0.990481i | \(-0.456046\pi\) | ||||
0.137647 | + | 0.990481i | \(0.456046\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.18953 | 0.241106 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.55220 | 0.642822 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.1208 | 1.19825 | 0.599125 | − | 0.800656i | \(-0.295515\pi\) | ||||
0.599125 | + | 0.800656i | \(0.295515\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.01641 | −0.222979 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.53579 | 0.701085 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.18953 | 0.232004 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.1044 | −1.23763 | −0.618815 | − | 0.785537i | \(-0.712387\pi\) | ||||
−0.618815 | + | 0.785537i | \(0.712387\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.1044 | 0.799312 | 0.399656 | − | 0.916665i | \(-0.369130\pi\) | ||||
0.399656 | + | 0.916665i | \(0.369130\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.36266 | −0.240805 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.4835 | 1.81562 | 0.907811 | − | 0.419380i | \(-0.137753\pi\) | ||||
0.907811 | + | 0.419380i | \(0.137753\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.36266 | −0.0965965 | −0.0482982 | − | 0.998833i | \(-0.515380\pi\) | ||||
−0.0482982 | + | 0.998833i | \(0.515380\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.53579 | −0.531534 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.79406 | −0.266291 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.55220 | −0.457625 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.9313 | 0.752539 | 0.376270 | − | 0.926510i | \(-0.377207\pi\) | ||||
0.376270 | + | 0.926510i | \(0.377207\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.9149 | 0.953430 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.01641 | −0.0693184 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.93126 | 0.470525 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.37907 | 0.566205 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.4506 | −1.17386 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.08798 | 0.273752 | 0.136876 | − | 0.990588i | \(-0.456294\pi\) | ||||
0.136876 | + | 0.990588i | \(0.456294\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.7745 | −1.17974 | −0.589869 | − | 0.807499i | \(-0.700821\pi\) | ||||
−0.589869 | + | 0.807499i | \(0.700821\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.0552 | 1.32528 | 0.662641 | − | 0.748937i | \(-0.269435\pi\) | ||||
0.662641 | + | 0.748937i | \(0.269435\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.65375 | 0.108340 | 0.0541702 | − | 0.998532i | \(-0.482749\pi\) | ||||
0.0541702 | + | 0.998532i | \(0.482749\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.37907 | 0.416125 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.74173 | −0.502879 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.6014 | 1.26791 | 0.633955 | − | 0.773370i | \(-0.281430\pi\) | ||||
0.633955 | + | 0.773370i | \(0.281430\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.3463 | −0.666461 | −0.333230 | − | 0.942845i | \(-0.608139\pi\) | ||||
−0.333230 | + | 0.942845i | \(0.608139\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.17313 | 0.202724 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.91486 | −0.628329 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.31344 | 0.146023 | 0.0730116 | − | 0.997331i | \(-0.476739\pi\) | ||||
0.0730116 | + | 0.997331i | \(0.476739\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.18953 | 0.324981 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.7581 | 1.17010 | 0.585050 | − | 0.810997i | \(-0.301075\pi\) | ||||
0.585050 | + | 0.810997i | \(0.301075\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 30.4147 | 1.88988 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.18953 | −0.0736303 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.82687 | −0.359300 | −0.179650 | − | 0.983731i | \(-0.557497\pi\) | ||||
−0.179650 | + | 0.983731i | \(0.557497\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.55220 | −0.156780 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.3463 | 0.633180 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.43140 | 0.514071 | 0.257036 | − | 0.966402i | \(-0.417254\pi\) | ||||
0.257036 | + | 0.966402i | \(0.417254\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.8984 | −1.26949 | −0.634745 | − | 0.772722i | \(-0.718895\pi\) | ||||
−0.634745 | + | 0.772722i | \(0.718895\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.7253 | −0.649126 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.4999 | −1.35189 | −0.675943 | − | 0.736954i | \(-0.736263\pi\) | ||||
−0.675943 | + | 0.736954i | \(0.736263\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.17313 | 0.130102 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.41188 | −0.143881 | −0.0719404 | − | 0.997409i | \(-0.522919\pi\) | ||||
−0.0719404 | + | 0.997409i | \(0.522919\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.8820 | −1.18186 | −0.590932 | − | 0.806721i | \(-0.701240\pi\) | ||||
−0.590932 | + | 0.806721i | \(0.701240\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.8984 | −1.23360 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.93126 | 0.584192 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.01641 | 0.176825 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.3103 | 1.59549 | 0.797743 | − | 0.602997i | \(-0.206027\pi\) | ||||
0.797743 | + | 0.602997i | \(0.206027\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.55220 | 0.497928 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.36266 | −0.194468 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.24186 | −0.186858 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.18953 | −0.0683369 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.01641 | −0.172719 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.7253 | −0.840419 | −0.420209 | − | 0.907427i | \(-0.638043\pi\) | ||||
−0.420209 | + | 0.907427i | \(0.638043\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.7417 | −0.667964 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.7745 | −0.781083 | −0.390541 | − | 0.920585i | \(-0.627712\pi\) | ||||
−0.390541 | + | 0.920585i | \(0.627712\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.56860 | −0.427803 | −0.213901 | − | 0.976855i | \(-0.568617\pi\) | ||||
−0.213901 | + | 0.976855i | \(0.568617\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.18953 | 0.179710 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.2088 | −1.35970 | −0.679850 | − | 0.733351i | \(-0.737955\pi\) | ||||
−0.679850 | + | 0.733351i | \(0.737955\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.18953 | −0.401281 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.36266 | −0.186527 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.0880 | −0.557867 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.3463 | 1.12173 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.5850 | −0.801665 | −0.400832 | − | 0.916151i | \(-0.631279\pi\) | ||||
−0.400832 | + | 0.916151i | \(0.631279\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.53579 | 0.522558 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.53579 | −0.411724 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.4999 | −1.66143 | −0.830717 | − | 0.556695i | \(-0.812069\pi\) | ||||
−0.830717 | + | 0.556695i | \(0.812069\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.9149 | 0.864376 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.2059 | −0.659059 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.0000 | −0.644194 | −0.322097 | − | 0.946707i | \(-0.604388\pi\) | ||||
−0.322097 | + | 0.946707i | \(0.604388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.9313 | 0.692195 | 0.346097 | − | 0.938199i | \(-0.387507\pi\) | ||||
0.346097 | + | 0.938199i | \(0.387507\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.36266 | −0.179486 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.4835 | −0.930551 | −0.465275 | − | 0.885166i | \(-0.654045\pi\) | ||||
−0.465275 | + | 0.885166i | \(0.654045\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.9149 | 0.738524 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.5522 | 0.876035 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.10439 | −0.0582875 | −0.0291438 | − | 0.999575i | \(-0.509278\pi\) | ||||
−0.0291438 | + | 0.999575i | \(0.509278\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.0000 | −0.577350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.37907 | 0.438580 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.56860 | 0.499477 | 0.249738 | − | 0.968313i | \(-0.419655\pi\) | ||||
0.249738 | + | 0.968313i | \(0.419655\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.55220 | −0.341094 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.14031 | −0.422624 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.4342 | −0.954489 | −0.477244 | − | 0.878771i | \(-0.658364\pi\) | ||||
−0.477244 | + | 0.878771i | \(0.658364\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000 | 0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.0328 | −0.926283 | −0.463142 | − | 0.886284i | \(-0.653278\pi\) | ||||
−0.463142 | + | 0.886284i | \(0.653278\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.36266 | 0.0698113 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.82687 | −0.297739 | −0.148870 | − | 0.988857i | \(-0.547563\pi\) | ||||
−0.148870 | + | 0.988857i | \(0.547563\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.01641 | −0.0516669 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.27468 | 0.166033 | 0.0830164 | − | 0.996548i | \(-0.473545\pi\) | ||||
0.0830164 | + | 0.996548i | \(0.473545\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.18953 | 0.262446 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.7253 | −0.541021 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.74173 | −0.389529 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0880 | 0.506301 | 0.253151 | − | 0.967427i | \(-0.418533\pi\) | ||||
0.253151 | + | 0.967427i | \(0.418533\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.9341 | 1.74453 | 0.872263 | − | 0.489037i | \(-0.162652\pi\) | ||||
0.872263 | + | 0.489037i | \(0.162652\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.30749 | −0.364012 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.2775 | 1.05211 | 0.526053 | − | 0.850452i | \(-0.323671\pi\) | ||||
0.526053 | + | 0.850452i | \(0.323671\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.01641 | 0.148788 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.2775 | 1.34224 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.91486 | −0.486701 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.20594 | −0.401847 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.4835 | 1.14724 | 0.573621 | − | 0.819121i | \(-0.305538\pi\) | ||||
0.573621 | + | 0.819121i | \(0.305538\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.8461 | 0.918504 | 0.459252 | − | 0.888306i | \(-0.348118\pi\) | ||||
0.459252 | + | 0.888306i | \(0.348118\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.37907 | 0.310161 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.18953 | 0.251729 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.62093 | −0.465590 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.03281 | 0.0979172 | 0.0489586 | − | 0.998801i | \(-0.484410\pi\) | ||||
0.0489586 | + | 0.998801i | \(0.484410\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.497025 | −0.0238855 | −0.0119427 | − | 0.999929i | \(-0.503802\pi\) | ||||
−0.0119427 | + | 0.999929i | \(0.503802\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.18953 | −0.0570338 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.4178 | −0.926763 | −0.463381 | − | 0.886159i | \(-0.653364\pi\) | ||||
−0.463381 | + | 0.886159i | \(0.653364\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.17313 | 0.151101 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.3791 | −1.25331 | −0.626654 | − | 0.779298i | \(-0.715576\pi\) | ||||
−0.626654 | + | 0.779298i | \(0.715576\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.3463 | 0.490460 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.10155 | 0.240757 | 0.120379 | − | 0.992728i | \(-0.461589\pi\) | ||||
0.120379 | + | 0.992728i | \(0.461589\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.7253 | −0.502811 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.2611 | −0.760663 | −0.380331 | − | 0.924850i | \(-0.624190\pi\) | ||||
−0.380331 | + | 0.924850i | \(0.624190\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.18953 | 0.242227 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.7745 | −1.29359 | −0.646795 | − | 0.762664i | \(-0.723891\pi\) | ||||
−0.646795 | + | 0.762664i | \(0.723891\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.7417 | −1.47516 | −0.737582 | − | 0.675258i | \(-0.764032\pi\) | ||||
−0.737582 | + | 0.675258i | \(0.764032\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.17313 | 0.100776 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.73889 | −0.0804662 | −0.0402331 | − | 0.999190i | \(-0.512810\pi\) | ||||
−0.0402331 | + | 0.999190i | \(0.512810\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.0357 | −1.10986 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.56860 | −0.348743 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.55220 | −0.116857 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.8625 | 1.72998 | 0.864992 | − | 0.501787i | \(-0.167324\pi\) | ||||
0.864992 | + | 0.501787i | \(0.167324\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.0656 | −1.46207 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.18953 | 0.145129 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.01641 | 0.136968 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.0552 | 0.818158 | 0.409079 | − | 0.912499i | \(-0.365850\pi\) | ||||
0.409079 | + | 0.912499i | \(0.365850\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.10439 | 0.230829 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.89845 | 0.221064 | 0.110532 | − | 0.993873i | \(-0.464745\pi\) | ||||
0.110532 | + | 0.993873i | \(0.464745\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.17313 | −0.278024 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 44.3819 | 1.99080 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −43.1072 | −1.92974 | −0.964872 | − | 0.262719i | \(-0.915381\pi\) | ||||
−0.964872 | + | 0.262719i | \(0.915381\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.62093 | −0.0724179 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.5522 | −0.738026 | −0.369013 | − | 0.929424i | \(-0.620304\pi\) | ||||
−0.369013 | + | 0.929424i | \(0.620304\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.18953 | −0.0529336 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.69251 | −0.0751670 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.95078 | −0.130791 | −0.0653955 | − | 0.997859i | \(-0.520831\pi\) | ||||
−0.0653955 | + | 0.997859i | \(0.520831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.7253 | 1.18226 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.7417 | −0.517402 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.62093 | 0.158941 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.379068 | −0.0166073 | −0.00830364 | − | 0.999966i | \(-0.502643\pi\) | ||||
−0.00830364 | + | 0.999966i | \(0.502643\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.9836 | −0.655187 | −0.327593 | − | 0.944819i | \(-0.606238\pi\) | ||||
−0.327593 | + | 0.944819i | \(0.606238\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.18953 | 0.139203 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.2775 | 0.491256 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.55220 | 0.371134 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.0328 | 0.954347 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.18953 | −0.310831 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0656 | 0.432755 | 0.216378 | − | 0.976310i | \(-0.430576\pi\) | ||||
0.216378 | + | 0.976310i | \(0.430576\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.1208 | 0.691810 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0880 | −0.432122 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.4506 | 0.746136 | 0.373068 | − | 0.927804i | \(-0.378306\pi\) | ||||
0.373068 | + | 0.927804i | \(0.378306\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.01641 | −0.128737 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.6925 | −1.05003 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.53579 | 0.404772 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.9313 | 0.547915 | 0.273958 | − | 0.961742i | \(-0.411667\pi\) | ||||
0.273958 | + | 0.961742i | \(0.411667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.41783 | 0.144559 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.8105 | −1.04564 | −0.522818 | − | 0.852444i | \(-0.675119\pi\) | ||||
−0.522818 | + | 0.852444i | \(0.675119\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.9149 | 0.669543 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.18953 | 0.133948 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.0328 | 1.34289 | 0.671443 | − | 0.741056i | \(-0.265675\pi\) | ||||
0.671443 | + | 0.741056i | \(0.265675\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.280628 | −0.0117439 | −0.00587195 | − | 0.999983i | \(-0.501869\pi\) | ||||
−0.00587195 | + | 0.999983i | \(0.501869\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.1044 | −0.714546 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.1372 | −1.37952 | −0.689760 | − | 0.724038i | \(-0.742284\pi\) | ||||
−0.689760 | + | 0.724038i | \(0.742284\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.1044 | 0.461483 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.6238 | −1.31198 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.36266 | −0.139029 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −41.8625 | −1.72785 | −0.863926 | − | 0.503619i | \(-0.832001\pi\) | ||||
−0.863926 | + | 0.503619i | \(0.832001\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.4835 | 1.04825 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.00000 | 0.246390 | 0.123195 | − | 0.992382i | \(-0.460686\pi\) | ||||
0.123195 | + | 0.992382i | \(0.460686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.5522 | 0.678574 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.36266 | −0.0557700 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.4342 | 1.48866 | 0.744331 | − | 0.667811i | \(-0.232768\pi\) | ||||
0.744331 | + | 0.667811i | \(0.232768\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.5850 | −1.65550 | −0.827749 | − | 0.561099i | \(-0.810379\pi\) | ||||
−0.827749 | + | 0.561099i | \(0.810379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.53579 | −0.306881 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.0000 | −0.447214 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.36266 | −0.380019 | −0.190009 | − | 0.981782i | \(-0.560852\pi\) | ||||
−0.190009 | + | 0.981782i | \(0.560852\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.79406 | −0.153743 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.4506 | −0.867800 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.6761 | −0.552373 | −0.276186 | − | 0.961104i | \(-0.589071\pi\) | ||||
−0.276186 | + | 0.961104i | \(0.589071\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.55220 | −0.264210 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.6730 | −1.63743 | −0.818717 | − | 0.574198i | \(-0.805314\pi\) | ||||
−0.818717 | + | 0.574198i | \(0.805314\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.7581 | −0.834340 | −0.417170 | − | 0.908828i | \(-0.636978\pi\) | ||||
−0.417170 | + | 0.908828i | \(0.636978\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 32.9997 | 1.32211 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 49.4863 | 1.97315 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.8133 | −0.589708 | −0.294854 | − | 0.955542i | \(-0.595271\pi\) | ||||
−0.294854 | + | 0.955542i | \(0.595271\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.9313 | 0.434479 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.36266 | 0.0540756 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.6702 | −0.422767 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.9149 | 0.550463 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.41188 | 0.253254 | 0.126627 | − | 0.991950i | \(-0.459585\pi\) | ||||
0.126627 | + | 0.991950i | \(0.459585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.5030 | −0.532505 | −0.266253 | − | 0.963903i | \(-0.585786\pi\) | ||||
−0.266253 | + | 0.963903i | \(0.585786\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.01641 | −0.0400210 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.4506 | 0.528799 | 0.264400 | − | 0.964413i | \(-0.414826\pi\) | ||||
0.264400 | + | 0.964413i | \(0.414826\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.93126 | 0.271658 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.961236 | −0.0376161 | −0.0188080 | − | 0.999823i | \(-0.505987\pi\) | ||||
−0.0188080 | + | 0.999823i | \(0.505987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.7253 | −0.419073 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.37907 | 0.326899 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.5163 | −1.30561 | −0.652804 | − | 0.757527i | \(-0.726408\pi\) | ||||
−0.652804 | + | 0.757527i | \(0.726408\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6761 | 0.531939 | 0.265969 | − | 0.963981i | \(-0.414308\pi\) | ||||
0.265969 | + | 0.963981i | \(0.414308\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.4506 | −0.677727 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.18953 | −0.0460589 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.08798 | 0.158051 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.4178 | −1.59654 | −0.798270 | − | 0.602300i | \(-0.794251\pi\) | ||||
−0.798270 | + | 0.602300i | \(0.794251\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.6238 | −1.59973 | −0.799866 | − | 0.600179i | \(-0.795096\pi\) | ||||
−0.799866 | + | 0.600179i | \(0.795096\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.62093 | 0.369217 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.7745 | −0.681122 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.4119 | −1.39326 | −0.696631 | − | 0.717430i | \(-0.745318\pi\) | ||||
−0.696631 | + | 0.717430i | \(0.745318\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.01641 | 0.115251 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.0552 | 0.765152 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.58217 | 0.326955 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.6597 | 0.709848 | 0.354924 | − | 0.934895i | \(-0.384507\pi\) | ||||
0.354924 | + | 0.934895i | \(0.384507\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.20594 | −0.311269 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34.0028 | −1.28795 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.65375 | 0.0625504 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.2088 | 0.914353 | 0.457177 | − | 0.889376i | \(-0.348861\pi\) | ||||
0.457177 | + | 0.889376i | \(0.348861\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.37907 | 0.240250 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.79406 | −0.142690 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.98359 | 0.187163 | 0.0935814 | − | 0.995612i | \(-0.470168\pi\) | ||||
0.0935814 | + | 0.995612i | \(0.470168\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.74173 | −0.290338 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.17313 | 0.0813843 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.6014 | 0.732028 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.1236 | −0.899660 | −0.449830 | − | 0.893114i | \(-0.648515\pi\) | ||||
−0.449830 | + | 0.893114i | \(0.648515\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −37.4506 | −1.39473 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.3463 | −0.384781 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.18953 | −0.0441782 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.640179 | −0.0237429 | −0.0118715 | − | 0.999930i | \(-0.503779\pi\) | ||||
−0.0118715 | + | 0.999930i | \(0.503779\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.27468 | −0.195091 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.26111 | 0.157388 | 0.0786939 | − | 0.996899i | \(-0.474925\pi\) | ||||
0.0786939 | + | 0.996899i | \(0.474925\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.17313 | 0.117043 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.3103 | −1.51963 | −0.759813 | − | 0.650142i | \(-0.774709\pi\) | ||||
−0.759813 | + | 0.650142i | \(0.774709\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.4506 | −1.08044 | −0.540220 | − | 0.841524i | \(-0.681659\pi\) | ||||
−0.540220 | + | 0.841524i | \(0.681659\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | 0.219823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.91486 | −0.362766 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.9313 | −0.837890 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.1924 | 1.64909 | 0.824547 | − | 0.565794i | \(-0.191430\pi\) | ||||
0.824547 | + | 0.565794i | \(0.191430\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.31344 | 0.0843065 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.9864 | −1.27160 | −0.635802 | − | 0.771852i | \(-0.719330\pi\) | ||||
−0.635802 | + | 0.771852i | \(0.719330\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.5522 | −0.817516 | −0.408758 | − | 0.912643i | \(-0.634038\pi\) | ||||
−0.408758 | + | 0.912643i | \(0.634038\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −32.1760 | −1.16485 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.18953 | 0.187628 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −28.7581 | −1.03840 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.9669 | 1.18882 | 0.594409 | − | 0.804163i | \(-0.297386\pi\) | ||||
0.594409 | + | 0.804163i | \(0.297386\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.7581 | 0.675558 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.48346 | −0.0533563 | −0.0266781 | − | 0.999644i | \(-0.508493\pi\) | ||||
−0.0266781 | + | 0.999644i | \(0.508493\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.17313 | 0.0780610 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.4147 | 1.09112 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.18953 | −0.0425105 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.56860 | −0.270135 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.4639 | 1.76320 | 0.881600 | − | 0.471998i | \(-0.156467\pi\) | ||||
0.881600 | + | 0.471998i | \(0.156467\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.82687 | −0.207442 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 50.7610 | 1.80485 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.1432 | 0.360194 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.55220 | −0.0905170 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.7225 | −0.521497 | −0.260749 | − | 0.965407i | \(-0.583969\pi\) | ||||
−0.260749 | + | 0.965407i | \(0.583969\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.1044 | 1.17115 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.3463 | 0.365567 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.18953 | 0.112416 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.43140 | 0.296799 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.7941 | 0.766238 | 0.383119 | − | 0.923699i | \(-0.374850\pi\) | ||||
0.383119 | + | 0.923699i | \(0.374850\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.6178 | −0.864449 | −0.432224 | − | 0.901766i | \(-0.642271\pi\) | ||||
−0.432224 | + | 0.901766i | \(0.642271\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.8984 | −0.732941 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.10439 | 0.178799 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.7253 | −0.374773 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.9177 | 1.32334 | 0.661668 | − | 0.749797i | \(-0.269849\pi\) | ||||
0.661668 | + | 0.749797i | \(0.269849\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.4342 | 0.572862 | 0.286431 | − | 0.958101i | \(-0.407531\pi\) | ||||
0.286431 | + | 0.958101i | \(0.407531\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.7058 | 0.859105 | 0.429553 | − | 0.903042i | \(-0.358671\pi\) | ||||
0.429553 | + | 0.903042i | \(0.358671\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.1013 | 1.18439 | 0.592193 | − | 0.805796i | \(-0.298262\pi\) | ||||
0.592193 | + | 0.805796i | \(0.298262\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.4999 | −0.780512 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.4671 | 0.570550 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.62093 | −0.0560947 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.17313 | 0.0751143 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.6207 | −0.919047 | −0.459524 | − | 0.888166i | \(-0.651980\pi\) | ||||
−0.459524 | + | 0.888166i | \(0.651980\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.5850 | −0.951207 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.41188 | −0.0830696 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.69251 | −0.0582241 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.0849 | −1.20553 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.8820 | −0.682350 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.53579 | 0.326883 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.0820 | −0.653356 | −0.326678 | − | 0.945136i | \(-0.605929\pi\) | ||||
−0.326678 | + | 0.945136i | \(0.605929\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.54935 | −0.155403 | −0.0777015 | − | 0.996977i | \(-0.524758\pi\) | ||||
−0.0777015 | + | 0.996977i | \(0.524758\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.1072 | 1.47080 | 0.735400 | − | 0.677633i | \(-0.236994\pi\) | ||||
0.735400 | + | 0.677633i | \(0.236994\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.8984 | −0.712217 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.10439 | 0.309917 | 0.154959 | − | 0.987921i | \(-0.450476\pi\) | ||||
0.154959 | + | 0.987921i | \(0.450476\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.62093 | 0.123115 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.93126 | 0.337283 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.3403 | 0.858623 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.01641 | 0.102090 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.18953 | 0.107826 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.1596 | 0.579437 | 0.289719 | − | 0.957112i | \(-0.406438\pi\) | ||||
0.289719 | + | 0.957112i | \(0.406438\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.3103 | 0.921155 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.4176 | −1.83337 | −0.916687 | − | 0.399606i | \(-0.869147\pi\) | ||||
−0.916687 | + | 0.399606i | \(0.869147\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.3791 | −0.618505 | −0.309252 | − | 0.950980i | \(-0.600079\pi\) | ||||
−0.309252 | + | 0.950980i | \(0.600079\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.55220 | 0.287479 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.7641 | −1.33515 | −0.667574 | − | 0.744544i | \(-0.732667\pi\) | ||||
−0.667574 | + | 0.744544i | \(0.732667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.34625 | 0.145769 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.36266 | −0.112276 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.58501 | −0.0862149 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.2447 | −0.441245 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.24186 | −0.107882 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.1208 | 0.535873 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.0192 | −0.498706 | −0.249353 | − | 0.968413i | \(-0.580218\pi\) | ||||
−0.249353 | + | 0.968413i | \(0.580218\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.18953 | −0.0394544 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.2419 | 0.637511 | 0.318756 | − | 0.947837i | \(-0.396735\pi\) | ||||
0.318756 | + | 0.947837i | \(0.396735\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.01641 | −0.0997193 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −34.2088 | −1.12967 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.2255 | 0.469255 | 0.234627 | − | 0.972085i | \(-0.424613\pi\) | ||||
0.234627 | + | 0.972085i | \(0.424613\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.7253 | −0.485216 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −46.7909 | −1.54014 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.53579 | 0.313535 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.7417 | −0.385649 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.6566 | −0.776147 | −0.388074 | − | 0.921628i | \(-0.626859\pi\) | ||||
−0.388074 | + | 0.921628i | \(0.626859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.7745 | −0.450958 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.9177 | 1.50007 | 0.750033 | − | 0.661401i | \(-0.230038\pi\) | ||||
0.750033 | + | 0.661401i | \(0.230038\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.56860 | −0.246992 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.6925 | −0.870151 | −0.435075 | − | 0.900394i | \(-0.643278\pi\) | ||||
−0.435075 | + | 0.900394i | \(0.643278\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.55220 | −0.213369 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.18953 | 0.103756 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.9341 | −0.550284 | −0.275142 | − | 0.961404i | \(-0.588725\pi\) | ||||
−0.275142 | + | 0.961404i | \(0.588725\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.1760 | −0.914631 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.2088 | −0.785024 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.4671 | −0.403847 | −0.201924 | − | 0.979401i | \(-0.564719\pi\) | ||||
−0.201924 | + | 0.979401i | \(0.564719\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.1044 | −0.553485 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.62093 | 0.310676 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.2775 | −0.847662 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.18953 | −0.231679 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.1044 | 0.357463 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.1208 | 1.74041 | 0.870204 | − | 0.492692i | \(-0.163987\pi\) | ||||
0.870204 | + | 0.492692i | \(0.163987\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.9669 | −0.993776 | −0.496888 | − | 0.867815i | \(-0.665524\pi\) | ||||
−0.496888 | + | 0.867815i | \(0.665524\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.1731 | −0.839072 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.36266 | −0.107691 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.326738 | 0.0104533 | 0.00522664 | − | 0.999986i | \(-0.498336\pi\) | ||||
0.00522664 | + | 0.999986i | \(0.498336\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0880 | −0.322085 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.2444 | 1.34739 | 0.673694 | − | 0.739010i | \(-0.264707\pi\) | ||||
0.673694 | + | 0.739010i | \(0.264707\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.4835 | 0.811971 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.3463 | 0.647628 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.01641 | −0.0323199 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.9641 | 0.793010 | 0.396505 | − | 0.918033i | \(-0.370223\pi\) | ||||
0.396505 | + | 0.918033i | \(0.370223\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.5850 | −0.462841 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.36266 | −0.0431993 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.8789 | 1.29465 | 0.647324 | − | 0.762215i | \(-0.275888\pi\) | ||||
0.647324 | + | 0.762215i | \(0.275888\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.53579 | 0.301699 |
(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 | 2760.2.a.t.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 8280.2.a.bh.1.3 | 3 | |||
4.3 | odd | 2 | 5520.2.a.ca.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.t.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
5520.2.a.ca.1.1 | 3 | 4.3 | odd | 2 | |||
8280.2.a.bh.1.3 | 3 | 3.2 | odd | 2 |