Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(191,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.2593100598870016.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} + x^{8} + 4x^{6} + 4x^{4} - 32x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.12 | ||
Root | \(1.37027 - 0.349801i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.191 |
Dual form | 912.2.d.a.191.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.72007 | + | 0.203364i | 0.993083 | + | 0.117412i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.74054i | 1.22561i | 0.790235 | + | 0.612803i | \(0.209958\pi\) | ||||
−0.790235 | + | 0.612803i | \(0.790042\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.91729i | 0.724666i | 0.932049 | + | 0.362333i | \(0.118020\pi\) | ||||
−0.932049 | + | 0.362333i | \(0.881980\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.91729 | + | 0.699602i | 0.972429 | + | 0.233201i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.463141 | −0.139642 | −0.0698212 | − | 0.997560i | \(-0.522243\pi\) | ||||
−0.0698212 | + | 0.997560i | \(0.522243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.406728 | 0.112806 | 0.0564031 | − | 0.998408i | \(-0.482037\pi\) | ||||
0.0564031 | + | 0.998408i | \(0.482037\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.557328 | + | 4.71392i | −0.143901 | + | 1.21713i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.415054i | − | 0.100665i | −0.998733 | − | 0.0503327i | \(-0.983972\pi\) | ||
0.998733 | − | 0.0503327i | \(-0.0160282\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.389907 | + | 3.29787i | −0.0850848 | + | 0.719654i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.91913 | −0.608681 | −0.304341 | − | 0.952563i | \(-0.598436\pi\) | ||||
−0.304341 | + | 0.952563i | \(0.598436\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.51056 | −0.502112 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.87566 | + | 1.79664i | 0.938322 | + | 0.345763i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.11674i | 1.32155i | 0.750586 | + | 0.660773i | \(0.229771\pi\) | ||||
−0.750586 | + | 0.660773i | \(0.770229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.40673i | − | 0.432261i | −0.976364 | − | 0.216131i | \(-0.930656\pi\) | ||
0.976364 | − | 0.216131i | \(-0.0693437\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.796636 | − | 0.0941864i | −0.138676 | − | 0.0163957i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.25440 | −0.888155 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.61439 | −1.08740 | −0.543699 | − | 0.839280i | \(-0.682977\pi\) | ||||
−0.543699 | + | 0.839280i | \(0.682977\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.699602 | + | 0.0827140i | 0.112026 | + | 0.0132448i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.43299i | 0.848491i | 0.905547 | + | 0.424245i | \(0.139461\pi\) | ||||
−0.905547 | + | 0.424245i | \(0.860539\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.91729i | − | 0.902378i | −0.892429 | − | 0.451189i | \(-0.851000\pi\) | ||
0.892429 | − | 0.451189i | \(-0.149000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.91729 | + | 7.99494i | −0.285812 | + | 1.19181i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.61873 | 0.527847 | 0.263923 | − | 0.964544i | \(-0.414983\pi\) | ||||
0.263923 | + | 0.964544i | \(0.414983\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.32401 | 0.474859 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0844071 | − | 0.713922i | 0.0118194 | − | 0.0999690i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.15768i | 1.25790i | 0.777444 | + | 0.628952i | \(0.216516\pi\) | ||||
−0.777444 | + | 0.628952i | \(0.783484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.26926i | − | 0.171147i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.203364 | − | 1.72007i | 0.0269362 | − | 0.227829i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.99494 | −1.04085 | −0.520426 | − | 0.853907i | \(-0.674227\pi\) | ||||
−0.520426 | + | 0.853907i | \(0.674227\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.15859 | 1.04460 | 0.522300 | − | 0.852762i | \(-0.325074\pi\) | ||||
0.522300 | + | 0.852762i | \(0.325074\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.34134 | + | 5.59327i | −0.168993 | + | 0.704686i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.11466i | 0.138256i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 14.8557i | − | 1.81491i | −0.420148 | − | 0.907456i | \(-0.638022\pi\) | ||
0.420148 | − | 0.907456i | \(-0.361978\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.02112 | − | 0.593647i | −0.604471 | − | 0.0714667i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.75133 | 1.15727 | 0.578635 | − | 0.815587i | \(-0.303586\pi\) | ||||
0.578635 | + | 0.815587i | \(0.303586\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.13747 | −0.133131 | −0.0665655 | − | 0.997782i | \(-0.521204\pi\) | ||||
−0.0665655 | + | 0.997782i | \(0.521204\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.31834 | − | 0.510558i | −0.498639 | − | 0.0589541i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.887974i | − | 0.101194i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.8346i | − | 1.55651i | −0.627948 | − | 0.778255i | \(-0.716105\pi\) | ||
0.627948 | − | 0.778255i | \(-0.283895\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.02112 | + | 4.08188i | 0.891235 | + | 0.453542i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.54765 | 0.718698 | 0.359349 | − | 0.933203i | \(-0.382999\pi\) | ||||
0.359349 | + | 0.933203i | \(0.382999\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.13747 | 0.123376 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.44729 | + | 12.2413i | −0.155166 | + | 1.31241i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.83219i | − | 0.724211i | −0.932137 | − | 0.362106i | \(-0.882058\pi\) | ||
0.932137 | − | 0.362106i | \(-0.117942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.779815i | 0.0817468i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.489442 | − | 4.13974i | 0.0507528 | − | 0.429271i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.74054 | 0.281173 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.2624 | 1.14353 | 0.571763 | − | 0.820419i | \(-0.306260\pi\) | ||||
0.571763 | + | 0.820419i | \(0.306260\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.35112 | − | 0.324014i | −0.135792 | − | 0.0325647i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.75639i | − | 0.174767i | −0.996175 | − | 0.0873837i | \(-0.972149\pi\) | ||
0.996175 | − | 0.0873837i | \(-0.0278506\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.85569i | 0.872577i | 0.899807 | + | 0.436288i | \(0.143707\pi\) | ||||
−0.899807 | + | 0.436288i | \(0.856293\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.03794 | − | 1.06856i | −0.882012 | − | 0.104280i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.05018 | 0.584892 | 0.292446 | − | 0.956282i | \(-0.405531\pi\) | ||||
0.292446 | + | 0.956282i | \(0.405531\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.83457 | 0.941981 | 0.470991 | − | 0.882138i | \(-0.343897\pi\) | ||||
0.470991 | + | 0.882138i | \(0.343897\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.3772 | − | 1.34513i | −1.07988 | − | 0.127674i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.4821i | − | 1.17422i | −0.809509 | − | 0.587108i | \(-0.800266\pi\) | ||
0.809509 | − | 0.587108i | \(-0.199734\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 8.00000i | − | 0.746004i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.18654 | + | 0.284548i | 0.109696 | + | 0.0263065i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.795777 | 0.0729487 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7855 | −0.980500 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.10488 | + | 9.34513i | −0.0996233 | + | 0.842622i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.82242i | 0.610215i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.0211i | − | 1.33291i | −0.745546 | − | 0.666454i | \(-0.767811\pi\) | ||
0.745546 | − | 0.666454i | \(-0.232189\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.20336 | − | 10.1781i | 0.105950 | − | 0.896136i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.2237 | −1.24273 | −0.621365 | − | 0.783521i | \(-0.713422\pi\) | ||||
−0.621365 | + | 0.783521i | \(0.713422\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.91729 | 0.166250 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.92375 | + | 13.3620i | −0.423769 | + | 1.15001i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 9.26364i | − | 0.791446i | −0.918370 | − | 0.395723i | \(-0.870494\pi\) | ||
0.918370 | − | 0.395723i | \(-0.129506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.1461i | 1.62395i | 0.583694 | + | 0.811974i | \(0.301607\pi\) | ||||
−0.583694 | + | 0.811974i | \(0.698393\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.22448 | + | 0.735921i | 0.524196 | + | 0.0619757i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.188373 | −0.0157525 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.5037 | −1.61970 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.71754 | + | 0.675986i | 0.471575 | + | 0.0557544i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.6065i | 1.11469i | 0.830281 | + | 0.557345i | \(0.188180\pi\) | ||||
−0.830281 | + | 0.557345i | \(0.811820\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.7798i | − | 0.877249i | −0.898670 | − | 0.438624i | \(-0.855466\pi\) | ||
0.898670 | − | 0.438624i | \(-0.144534\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.290372 | − | 1.21083i | 0.0234752 | − | 0.0978898i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.59573 | 0.529782 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0422 | 0.801457 | 0.400729 | − | 0.916197i | \(-0.368757\pi\) | ||||
0.400729 | + | 0.916197i | \(0.368757\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.86234 | + | 15.7519i | −0.147694 | + | 1.24920i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 5.59681i | − | 0.441091i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.4826i | 1.29102i | 0.763753 | + | 0.645508i | \(0.223354\pi\) | ||||
−0.763753 | + | 0.645508i | \(0.776646\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.258121 | − | 2.18321i | 0.0200947 | − | 0.169963i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.42692 | 0.497330 | 0.248665 | − | 0.968590i | \(-0.420008\pi\) | ||||
0.248665 | + | 0.968590i | \(0.420008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8346 | −0.987275 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.699602 | − | 2.91729i | 0.0534999 | − | 0.223090i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 22.6337i | − | 1.72081i | −0.509612 | − | 0.860404i | \(-0.670211\pi\) | ||
0.509612 | − | 0.860404i | \(-0.329789\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.81346i | − | 0.363863i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.7519 | − | 1.62588i | −1.03365 | − | 0.122209i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.3891 | 1.29972 | 0.649860 | − | 0.760054i | \(-0.274827\pi\) | ||||
0.649860 | + | 0.760054i | \(0.274827\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.3383 | −1.28874 | −0.644372 | − | 0.764712i | \(-0.722881\pi\) | ||||
−0.644372 | + | 0.764712i | \(0.722881\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.0333 | + | 1.65916i | 1.03737 | + | 0.122649i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 18.1270i | − | 1.33272i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.192229i | 0.0140571i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.44466 | + | 9.34804i | −0.250562 | + | 0.679970i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.94422 | 0.430109 | 0.215054 | − | 0.976602i | \(-0.431007\pi\) | ||||
0.215054 | + | 0.976602i | \(0.431007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.20766 | 0.302874 | 0.151437 | − | 0.988467i | \(-0.451610\pi\) | ||||
0.151437 | + | 0.988467i | \(0.451610\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.226681 | + | 1.91729i | −0.0162330 | + | 0.137300i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.28347i | − | 0.0914434i | −0.998954 | − | 0.0457217i | \(-0.985441\pi\) | ||
0.998954 | − | 0.0457217i | \(-0.0145587\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.75186i | − | 0.691291i | −0.938365 | − | 0.345645i | \(-0.887660\pi\) | ||
0.938365 | − | 0.345645i | \(-0.112340\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.02112 | − | 25.5528i | 0.213093 | − | 1.80236i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.6448 | −0.957679 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.8893 | −1.03992 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.51595 | − | 2.04223i | −0.591899 | − | 0.141945i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.463141i | 0.0320362i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 11.4701i | − | 0.789632i | −0.918760 | − | 0.394816i | \(-0.870808\pi\) | ||
0.918760 | − | 0.394816i | \(-0.129192\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.7730 | + | 1.98307i | 1.14927 | + | 0.135878i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.2166 | 1.10596 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.61439 | 0.313245 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.95653 | − | 0.231321i | −0.132210 | − | 0.0156312i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 0.168814i | − | 0.0113557i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.44896i | 0.163994i | 0.996633 | + | 0.0819972i | \(0.0261299\pi\) | ||||
−0.996633 | + | 0.0819972i | \(0.973870\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.32401 | − | 1.75639i | −0.488268 | − | 0.117093i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.8292 | −1.38248 | −0.691242 | − | 0.722623i | \(-0.742936\pi\) | ||||
−0.691242 | + | 0.722623i | \(0.742936\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.9720 | 0.725053 | 0.362527 | − | 0.931973i | \(-0.381914\pi\) | ||||
0.362527 | + | 0.931973i | \(0.381914\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.180582 | − | 1.52738i | 0.0118814 | − | 0.100494i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 24.7806i | − | 1.62343i | −0.584053 | − | 0.811715i | \(-0.698534\pi\) | ||
0.584053 | − | 0.811715i | \(-0.301466\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.91729i | 0.646932i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.81346 | − | 23.7964i | 0.182754 | − | 1.54574i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.3016 | −1.63662 | −0.818312 | − | 0.574774i | \(-0.805090\pi\) | ||||
−0.818312 | + | 0.574774i | \(0.805090\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.8009 | 0.888996 | 0.444498 | − | 0.895780i | \(-0.353382\pi\) | ||||
0.444498 | + | 0.895780i | \(0.353382\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.9668 | + | 8.65232i | 0.831819 | + | 0.555047i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.10959i | 0.581991i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.406728i | − | 0.0258795i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.2624 | + | 1.33156i | 0.713727 | + | 0.0843840i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.09981 | 0.574375 | 0.287188 | − | 0.957874i | \(-0.407280\pi\) | ||||
0.287188 | + | 0.957874i | \(0.407280\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.35197 | 0.0849977 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.95653 | + | 0.231321i | 0.122523 | + | 0.0144859i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 9.70324i | − | 0.605272i | −0.953106 | − | 0.302636i | \(-0.902133\pi\) | ||
0.953106 | − | 0.302636i | \(-0.0978666\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 12.6817i | − | 0.788001i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.97888 | + | 20.7616i | −0.308185 | + | 1.28511i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.7785 | −1.15793 | −0.578966 | − | 0.815352i | \(-0.696544\pi\) | ||||
−0.578966 | + | 0.815352i | \(0.696544\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.0970 | −1.54170 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.38942 | − | 11.7519i | 0.0850314 | − | 0.719202i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 5.07580i | − | 0.309477i | −0.987955 | − | 0.154739i | \(-0.950546\pi\) | ||
0.987955 | − | 0.154739i | \(-0.0494535\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 28.1517i | − | 1.71010i | −0.518548 | − | 0.855048i | \(-0.673527\pi\) | ||
0.518548 | − | 0.855048i | \(-0.326473\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.158586 | + | 1.34134i | −0.00959809 | + | 0.0811814i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.16274 | 0.0701160 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.1586 | 0.610370 | 0.305185 | − | 0.952293i | \(-0.401282\pi\) | ||||
0.305185 | + | 0.952293i | \(0.401282\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.68375 | − | 7.02112i | 0.100804 | − | 0.420343i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.34605i | − | 0.557539i | −0.960358 | − | 0.278769i | \(-0.910073\pi\) | ||
0.960358 | − | 0.278769i | \(-0.0899265\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.1711i | 0.782941i | 0.920191 | + | 0.391471i | \(0.128034\pi\) | ||||
−0.920191 | + | 0.391471i | \(0.871966\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.71392 | + | 0.557328i | 0.279229 | + | 0.0330132i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.4166 | −0.614872 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8277 | 0.989866 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.3722 | + | 2.29037i | 1.13562 | + | 0.134264i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 3.86497i | − | 0.225794i | −0.993607 | − | 0.112897i | \(-0.963987\pi\) | ||
0.993607 | − | 0.112897i | \(-0.0360130\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 21.9104i | − | 1.27568i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.25812 | − | 0.832096i | −0.131029 | − | 0.0482831i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.18729 | −0.0686630 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.3451 | 0.653922 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.357187 | − | 3.02112i | 0.0205199 | − | 0.173559i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.3589i | 1.28027i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.16543i | 0.123588i | 0.998089 | + | 0.0617938i | \(0.0196821\pi\) | ||||
−0.998089 | + | 0.0617938i | \(0.980318\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.80093 | + | 15.2324i | −0.102451 | + | 0.866541i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.5708 | −1.73351 | −0.866755 | − | 0.498735i | \(-0.833798\pi\) | ||||
−0.866755 | + | 0.498735i | \(0.833798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.0845 | 1.36133 | 0.680667 | − | 0.732593i | \(-0.261690\pi\) | ||||
0.680667 | + | 0.732593i | \(0.261690\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.3286 | − | 3.67599i | −0.863668 | − | 0.207118i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.98779i | 0.560970i | 0.959858 | + | 0.280485i | \(0.0904953\pi\) | ||||
−0.959858 | + | 0.280485i | \(0.909505\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.29606i | − | 0.184544i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.4067 | + | 1.23039i | 0.580847 | + | 0.0686736i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.415054 | −0.0230942 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.02112 | −0.0566413 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.9162 | + | 2.00000i | 0.935466 | + | 0.110600i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.93815i | 0.382513i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.58074i | 0.361710i | 0.983510 | + | 0.180855i | \(0.0578865\pi\) | ||||
−0.983510 | + | 0.180855i | \(0.942113\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −19.2961 | − | 4.62744i | −1.05742 | − | 0.253582i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 40.7126 | 2.22437 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.22019 | 0.284362 | 0.142181 | − | 0.989841i | \(-0.454589\pi\) | ||||
0.142181 | + | 0.989841i | \(0.454589\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.53841 | − | 21.4701i | 0.137868 | − | 1.16609i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.11466i | 0.0603620i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7941i | 1.06878i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.62691 | − | 13.7606i | 0.0875901 | − | 0.740844i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.4929 | 1.04643 | 0.523216 | − | 0.852200i | \(-0.324732\pi\) | ||||
0.523216 | + | 0.852200i | \(0.324732\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.7604 | −1.59304 | −0.796520 | − | 0.604612i | \(-0.793328\pi\) | ||||
−0.796520 | + | 0.604612i | \(0.793328\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.98307 | + | 0.730743i | 0.105849 | + | 0.0390042i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.0297i | 1.01285i | 0.862284 | + | 0.506425i | \(0.169033\pi\) | ||||
−0.862284 | + | 0.506425i | \(0.830967\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.7239i | 1.41836i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.36879 | + | 0.161833i | 0.0724442 | + | 0.00856508i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.4654 | −1.76623 | −0.883117 | − | 0.469153i | \(-0.844559\pi\) | ||||
−0.883117 | + | 0.469153i | \(0.844559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.5518 | − | 2.19338i | −0.973718 | − | 0.115123i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3.11729i | − | 0.163166i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 20.0000i | − | 1.04399i | −0.852948 | − | 0.521996i | \(-0.825188\pi\) | ||
0.852948 | − | 0.521996i | \(-0.174812\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.80093 | + | 15.8496i | −0.197869 | + | 0.825097i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.5579 | −0.911560 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.6903 | −1.27841 | −0.639207 | − | 0.769035i | \(-0.720737\pi\) | ||||
−0.639207 | + | 0.769035i | \(0.720737\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.38744 | + | 11.7350i | −0.0716468 | + | 0.605995i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.89458i | 0.149079i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.4404i | 1.04995i | 0.851117 | + | 0.524976i | \(0.175926\pi\) | ||||
−0.851117 | + | 0.524976i | \(0.824074\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.05476 | − | 25.8374i | 0.156500 | − | 1.32369i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.75531 | −0.140790 | −0.0703949 | − | 0.997519i | \(-0.522426\pi\) | ||||
−0.0703949 | + | 0.997519i | \(0.522426\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.43353 | 0.124024 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.13974 | − | 17.2624i | 0.210435 | − | 0.877498i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.4316i | 1.49224i | 0.665812 | + | 0.746120i | \(0.268085\pi\) | ||||
−0.665812 | + | 0.746120i | \(0.731915\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.21160i | 0.0612731i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.4658 | − | 2.89259i | −1.23414 | − | 0.145912i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 37.9142 | 1.90767 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.3029 | −0.567276 | −0.283638 | − | 0.958931i | \(-0.591541\pi\) | ||||
−0.283638 | + | 0.958931i | \(0.591541\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.29787 | + | 0.389907i | 0.165100 | + | 0.0195198i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.35004i | 0.117355i | 0.998277 | + | 0.0586776i | \(0.0186884\pi\) | ||||
−0.998277 | + | 0.0586776i | \(0.981312\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.978885i | − | 0.0487617i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.1865 | + | 21.9822i | −0.555864 | + | 1.09230i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.06340 | 0.151847 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.2202 | 0.653696 | 0.326848 | − | 0.945077i | \(-0.394013\pi\) | ||||
0.326848 | + | 0.945077i | \(0.394013\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.88389 | − | 15.9341i | 0.0929255 | − | 0.785972i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 15.3286i | − | 0.754270i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.9441i | 0.880841i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.89362 | + | 32.9326i | −0.190672 | + | 1.61272i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.43407 | 0.216618 | 0.108309 | − | 0.994117i | \(-0.465456\pi\) | ||||
0.108309 | + | 0.994117i | \(0.465456\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0086 | −0.585263 | −0.292631 | − | 0.956225i | \(-0.594531\pi\) | ||||
−0.292631 | + | 0.956225i | \(0.594531\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.5569 | + | 2.53167i | 0.513293 | + | 0.123094i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.04202i | 0.0505452i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.6423i | 0.756986i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.324014 | − | 0.0383083i | −0.0156436 | − | 0.00184954i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.60788 | 0.221954 | 0.110977 | − | 0.993823i | \(-0.464602\pi\) | ||||
0.110977 | + | 0.993823i | \(0.464602\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.10951 | 0.389718 | 0.194859 | − | 0.980831i | \(-0.437575\pi\) | ||||
0.194859 | + | 0.980831i | \(0.437575\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −33.5478 | − | 3.96636i | −1.60849 | − | 0.190172i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.91913i | 0.139641i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.9230i | 0.616780i | 0.951260 | + | 0.308390i | \(0.0997901\pi\) | ||||
−0.951260 | + | 0.308390i | \(0.900210\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.69710 | + | 2.32549i | 0.461767 | + | 0.110737i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 40.3652 | 1.91781 | 0.958904 | − | 0.283730i | \(-0.0915721\pi\) | ||||
0.958904 | + | 0.283730i | \(0.0915721\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.7239 | 0.887598 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.76708 | + | 23.4042i | −0.130878 | + | 1.10698i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.3626i | 1.81044i | 0.424942 | + | 0.905221i | \(0.360295\pi\) | ||||
−0.424942 | + | 0.905221i | \(0.639705\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.51624i | − | 0.118485i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.19223 | − | 18.5420i | 0.103000 | − | 0.871181i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.13711 | −0.100189 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.34513 | −0.343591 | −0.171795 | − | 0.985133i | \(-0.554957\pi\) | ||||
−0.171795 | + | 0.985133i | \(0.554957\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.745700 | − | 2.02366i | 0.0348063 | − | 0.0944565i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13.2298i | − | 0.616172i | −0.951358 | − | 0.308086i | \(-0.900312\pi\) | ||
0.951358 | − | 0.308086i | \(-0.0996885\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 0.124944i | − | 0.00580665i | −0.999996 | − | 0.00290333i | \(-0.999076\pi\) | ||
0.999996 | − | 0.00290333i | \(-0.000924159\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.3451 | + | 1.34134i | 0.526118 | + | 0.0622030i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.5626 | −1.18290 | −0.591448 | − | 0.806343i | \(-0.701444\pi\) | ||||
−0.591448 | + | 0.806343i | \(0.701444\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.4826 | 1.31520 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.2733 | + | 2.04223i | 0.795914 | + | 0.0941010i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.74054i | 0.126010i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.51056i | 0.115192i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.40673 | + | 26.7156i | −0.293344 | + | 1.22322i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.5734 | 1.48832 | 0.744158 | − | 0.668003i | \(-0.232851\pi\) | ||||
0.744158 | + | 0.668003i | \(0.232851\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.69026 | −0.122665 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.13819 | − | 9.62691i | 0.0517895 | − | 0.438040i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30.8651i | 1.40151i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.2162i | 0.916086i | 0.888930 | + | 0.458043i | \(0.151449\pi\) | ||||
−0.888930 | + | 0.458043i | \(0.848551\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.35197 | + | 28.3512i | −0.151581 | + | 1.28209i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.2908 | −0.825453 | −0.412726 | − | 0.910855i | \(-0.635423\pi\) | ||||
−0.412726 | + | 0.910855i | \(0.635423\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.95383 | 0.133034 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.887974 | − | 3.70279i | 0.0399115 | − | 0.166428i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.6961i | 0.838634i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 44.6075i | 1.99691i | 0.0555845 | + | 0.998454i | \(0.482298\pi\) | ||||
−0.0555845 | + | 0.998454i | \(0.517702\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.0548 | + | 1.30701i | 0.493890 | + | 0.0583927i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.43191 | −0.286785 | −0.143392 | − | 0.989666i | \(-0.545801\pi\) | ||||
−0.143392 | + | 0.989666i | \(0.545801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.81346 | 0.214196 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.0764 | − | 2.61009i | −0.980446 | − | 0.115918i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.9858i | 1.37342i | 0.726930 | + | 0.686711i | \(0.240946\pi\) | ||||
−0.726930 | + | 0.686711i | \(0.759054\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2.18086i | − | 0.0964755i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.79664 | − | 4.87566i | 0.0793234 | − | 0.215266i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.2694 | −1.06944 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.67599 | −0.0737098 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.60288 | − | 38.9316i | 0.202044 | − | 1.70891i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 29.8712i | − | 1.30868i | −0.756201 | − | 0.654340i | \(-0.772947\pi\) | ||
0.756201 | − | 0.654340i | \(-0.227053\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.4615i | 1.46317i | 0.681751 | + | 0.731584i | \(0.261219\pi\) | ||||
−0.681751 | + | 0.731584i | \(0.738781\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.978885 | − | 8.27949i | 0.0427220 | − | 0.361346i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.998922 | −0.0435137 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.4787 | −0.629507 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.3235 | − | 5.59327i | −1.01215 | − | 0.242727i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.20975i | 0.0957150i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.5807i | 0.716848i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 29.9104 | + | 3.53632i | 1.29073 | + | 0.152603i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.53949 | −0.0663105 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.1797 | −0.996573 | −0.498287 | − | 0.867012i | \(-0.666037\pi\) | ||||
−0.498287 | + | 0.867012i | \(0.666037\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −29.8231 | − | 3.52599i | −1.27983 | − | 0.151315i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.9520i | 1.15450i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 30.3508i | − | 1.29771i | −0.760913 | − | 0.648854i | \(-0.775249\pi\) | ||
0.760913 | − | 0.648854i | \(-0.224751\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.8009 | + | 5.70776i | 1.01580 | + | 0.243601i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.11674 | 0.303183 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.5248 | 1.12795 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.68638 | − | 31.1797i | 0.156478 | − | 1.32350i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 16.7130i | − | 0.708153i | −0.935216 | − | 0.354077i | \(-0.884795\pi\) | ||
0.935216 | − | 0.354077i | \(-0.115205\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.40673i | − | 0.101794i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0390924 | + | 0.330647i | −0.00165048 | + | 0.0139599i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 47.2888 | 1.99298 | 0.996492 | − | 0.0836864i | \(-0.0266694\pi\) | ||||
0.996492 | + | 0.0836864i | \(0.0266694\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 34.2077 | 1.43913 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.82612 | + | 15.3788i | −0.328666 | + | 0.645848i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 7.64274i | − | 0.320400i | −0.987085 | − | 0.160200i | \(-0.948786\pi\) | ||
0.987085 | − | 0.160200i | \(-0.0512140\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.14431i | 0.215283i | 0.994190 | + | 0.107641i | \(0.0343298\pi\) | ||||
−0.994190 | + | 0.107641i | \(0.965670\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.2245 | + | 1.20884i | 0.427134 | + | 0.0505001i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.32865 | 0.305626 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.84141 | −0.159920 | −0.0799601 | − | 0.996798i | \(-0.525479\pi\) | ||||
−0.0799601 | + | 0.996798i | \(0.525479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.23747 | + | 0.855687i | 0.300779 | + | 0.0355611i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.5537i | 0.520816i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.24130i | − | 0.175657i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.779815 | + | 3.25177i | −0.0322414 | + | 0.134444i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.5811 | −1.38604 | −0.693020 | − | 0.720919i | \(-0.743720\pi\) | ||||
−0.693020 | + | 0.720919i | \(0.743720\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.40673 | −0.0991675 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.261012 | − | 2.20766i | 0.0107366 | − | 0.0908109i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.85782i | 0.240552i | 0.992740 | + | 0.120276i | \(0.0383780\pi\) | ||||
−0.992740 | + | 0.120276i | \(0.961622\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.18086i | 0.0894065i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.98318 | − | 16.7739i | 0.0811661 | − | 0.686509i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.5027 | 0.796857 | 0.398428 | − | 0.917199i | \(-0.369556\pi\) | ||||
0.398428 | + | 0.917199i | \(0.369556\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.98747 | 0.366607 | 0.183303 | − | 0.983056i | \(-0.441321\pi\) | ||||
0.183303 | + | 0.983056i | \(0.441321\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.3931 | − | 43.3383i | 0.423238 | − | 1.76487i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 29.5581i | − | 1.20171i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.8893i | 0.604339i | 0.953254 | + | 0.302170i | \(0.0977109\pi\) | ||||
−0.953254 | + | 0.302170i | \(0.902289\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23.4701 | − | 2.77487i | −0.951055 | − | 0.112443i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.47184 | 0.0595444 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.3662 | −0.903364 | −0.451682 | − | 0.892179i | \(-0.649176\pi\) | ||||
−0.451682 | + | 0.892179i | \(0.649176\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −25.6107 | − | 3.02796i | −1.03272 | − | 0.122099i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.1911i | 1.49726i | 0.662991 | + | 0.748628i | \(0.269287\pi\) | ||||
−0.662991 | + | 0.748628i | \(0.730713\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 31.9190i | − | 1.28293i | −0.767151 | − | 0.641467i | \(-0.778326\pi\) | ||
0.767151 | − | 0.641467i | \(-0.221674\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.2327 | − | 5.24462i | −0.571139 | − | 0.210459i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.0993 | 0.524811 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2499 | −1.25000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0941864 | + | 0.796636i | −0.00376144 | + | 0.0318146i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.74533i | 0.109463i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.45580i | 0.336620i | 0.985734 | + | 0.168310i | \(0.0538310\pi\) | ||||
−0.985734 | + | 0.168310i | \(0.946169\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.33260 | − | 19.7293i | 0.0927126 | − | 0.784171i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 41.1660 | 1.63362 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.35197 | 0.0535670 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.4474 | + | 6.82204i | 1.12536 | + | 0.269876i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 19.4546i | − | 0.768409i | −0.923248 | − | 0.384205i | \(-0.874476\pi\) | ||
0.923248 | − | 0.384205i | \(-0.125524\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.9846i | 0.866987i | 0.901157 | + | 0.433493i | \(0.142719\pi\) | ||||
−0.901157 | + | 0.433493i | \(0.857281\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27.8936 | + | 3.29787i | 1.09831 | + | 0.129853i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.3711 | 0.486360 | 0.243180 | − | 0.969981i | \(-0.421809\pi\) | ||||
0.243180 | + | 0.969981i | \(0.421809\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.70279 | 0.145347 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.93707 | + | 0.938401i | 0.311078 | + | 0.0367788i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 47.6312i | − | 1.86395i | −0.362519 | − | 0.931976i | \(-0.618083\pi\) | ||
0.362519 | − | 0.931976i | \(-0.381917\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 38.9806i | − | 1.52310i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.31833 | − | 0.795777i | −0.129460 | − | 0.0310462i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.1362 | −0.862305 | −0.431152 | − | 0.902279i | \(-0.641893\pi\) | ||||
−0.431152 | + | 0.902279i | \(0.641893\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.2749 | −0.633022 | −0.316511 | − | 0.948589i | \(-0.602511\pi\) | ||||
−0.316511 | + | 0.948589i | \(0.602511\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.0343308 | − | 0.290372i | 0.00133330 | − | 0.0112771i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.25440i | 0.203757i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 20.7747i | − | 0.804400i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.498031 | + | 4.21238i | −0.0192550 | + | 0.162860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.77858 | −0.145870 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.3258 | −1.40026 | −0.700128 | − | 0.714018i | \(-0.746874\pi\) | ||||
−0.700128 | + | 0.714018i | \(0.746874\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.2406 | − | 4.51056i | −0.471142 | − | 0.173611i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 6.40237i | − | 0.246063i | −0.992403 | − | 0.123032i | \(-0.960738\pi\) | ||
0.992403 | − | 0.123032i | \(-0.0392616\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.5933i | 0.828674i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −35.8277 | − | 4.23592i | −1.37292 | − | 0.162321i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.0891 | −1.11307 | −0.556533 | − | 0.830826i | \(-0.687869\pi\) | ||||
−0.556533 | + | 0.830826i | \(0.687869\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.3874 | 0.970001 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.8727 | + | 2.23132i | 0.720038 | + | 0.0851302i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.72469i | 0.141899i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 28.2904i | − | 1.07622i | −0.842876 | − | 0.538108i | \(-0.819139\pi\) | ||
0.842876 | − | 0.538108i | \(-0.180861\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.621228 | − | 2.59048i | 0.0235985 | − | 0.0984040i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −52.4705 | −1.99032 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.25498 | 0.0854136 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.03949 | − | 42.6244i | 0.190611 | − | 1.61220i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 10.1516i | − | 0.383421i | −0.981452 | − | 0.191711i | \(-0.938597\pi\) | ||
0.981452 | − | 0.191711i | \(-0.0614035\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.61439i | 0.249466i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.01682 | + | 17.0584i | −0.0759579 | + | 0.642458i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.36750 | 0.126648 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.8557 | 0.858363 | 0.429182 | − | 0.903218i | \(-0.358802\pi\) | ||||
0.429182 | + | 0.903218i | \(0.358802\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.67869 | − | 40.3594i | 0.362979 | − | 1.51360i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.02556i | 0.263109i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 0.516243i | − | 0.0193064i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −43.5205 | − | 5.14544i | −1.62530 | − | 0.192160i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.5932 | −1.17823 | −0.589114 | − | 0.808050i | \(-0.700523\pi\) | ||||
−0.589114 | + | 0.808050i | \(0.700523\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.9789 | −0.632327 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.7386 | + | 2.80662i | 0.882847 | + | 0.104379i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 17.8670i | − | 0.663563i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.51915i | 0.0563420i | 0.999603 | + | 0.0281710i | \(0.00896829\pi\) | ||||
−0.999603 | + | 0.0281710i | \(0.991032\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.5442 | + | 17.5196i | 0.760896 | + | 0.648874i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.45599 | −0.0908381 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.5499 | −0.759027 | −0.379514 | − | 0.925186i | \(-0.623909\pi\) | ||||
−0.379514 | + | 0.925186i | \(0.623909\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.85257 | + | 15.6691i | −0.0683329 | + | 0.577965i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.88028i | 0.253438i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.8191i | 1.09691i | 0.836178 | + | 0.548457i | \(0.184785\pi\) | ||||
−0.836178 | + | 0.548457i | \(0.815215\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0827140 | − | 0.699602i | 0.00303857 | − | 0.0257005i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.6727 | −1.38208 | −0.691039 | − | 0.722817i | \(-0.742847\pi\) | ||||
−0.691039 | + | 0.722817i | \(0.742847\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.2892 | −1.36617 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.1014 | + | 4.58074i | 0.698882 | + | 0.167601i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.5999i | 0.423852i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.4364i | 1.51204i | 0.654550 | + | 0.756018i | \(0.272858\pi\) | ||||
−0.654550 | + | 0.756018i | \(0.727142\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.6523 | + | 1.85058i | 0.570402 | + | 0.0674388i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29.5425 | 1.07516 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.8911 | 1.55890 | 0.779451 | − | 0.626463i | \(-0.215498\pi\) | ||||
0.779451 | + | 0.626463i | \(0.215498\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.32549 | + | 0.274943i | 0.0844098 | + | 0.00997978i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 15.5748i | − | 0.564587i | −0.959328 | − | 0.282293i | \(-0.908905\pi\) | ||
0.959328 | − | 0.282293i | \(-0.0910952\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.8557i | 0.682622i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.31833 | + | 0.795777i | 0.119974 | + | 0.0287714i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.25177 | −0.117415 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.07019 | −0.182836 | −0.0914178 | − | 0.995813i | \(-0.529140\pi\) | ||||
−0.0914178 | + | 0.995813i | \(0.529140\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.97329 | − | 16.6903i | 0.0710664 | − | 0.601085i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 40.2111i | − | 1.44629i | −0.690694 | − | 0.723147i | \(-0.742695\pi\) | ||
0.690694 | − | 0.723147i | \(-0.257305\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.04223i | 0.217043i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.57900 | − | 21.8134i | 0.0925210 | − | 0.782550i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.43299 | 0.194657 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.51624 | −0.161604 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.7862 | + | 34.6988i | −0.456941 | + | 1.24004i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.5211i | 0.982271i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 30.5921i | − | 1.09049i | −0.838276 | − | 0.545246i | \(-0.816436\pi\) | ||
0.838276 | − | 0.545246i | \(-0.183564\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −32.3004 | − | 3.81888i | −1.14992 | − | 0.135956i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.9317 | 0.850914 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.31833 | 0.117837 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −43.1686 | − | 5.10383i | −1.53103 | − | 0.181014i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 20.0472i | − | 0.710108i | −0.934846 | − | 0.355054i | \(-0.884462\pi\) | ||
0.934846 | − | 0.355054i | \(-0.115538\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.50197i | − | 0.0531359i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.77981 | − | 19.9315i | 0.168886 | − | 0.704244i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.526810 | 0.0185907 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.3383 | 0.540604 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.03224 | − | 8.73074i | 0.0363365 | − | 0.307337i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.5891i | 0.407452i | 0.979028 | + | 0.203726i | \(0.0653051\pi\) | ||||
−0.979028 | + | 0.203726i | \(0.934695\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.7239i | 1.57047i | 0.619199 | + | 0.785234i | \(0.287458\pi\) | ||||
−0.619199 | + | 0.785234i | \(0.712542\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.72506 | − | 48.4230i | 0.200787 | − | 1.69827i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −45.1712 | −1.58228 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.91729 | −0.207020 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.545560 | + | 2.27494i | −0.0190634 | + | 0.0794929i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 30.2421i | − | 1.05546i | −0.849413 | − | 0.527728i | \(-0.823044\pi\) | ||
0.849413 | − | 0.527728i | \(-0.176956\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 33.0901i | − | 1.15345i | −0.816938 | − | 0.576725i | \(-0.804330\pi\) | ||
0.816938 | − | 0.576725i | \(-0.195670\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.00000 | + | 0.236460i | 0.0696311 | + | 0.00823249i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.8332 | −0.724441 | −0.362221 | − | 0.932092i | \(-0.617981\pi\) | ||||
−0.362221 | + | 0.932092i | \(0.617981\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.3594 | 0.568186 | 0.284093 | − | 0.958797i | \(-0.408308\pi\) | ||||
0.284093 | + | 0.958797i | \(0.408308\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.4735 | + | 2.06589i | 0.606149 | + | 0.0716650i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.37964i | − | 0.0478019i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.6132i | 0.609531i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.32401 | − | 11.7344i | 0.149460 | − | 0.405600i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.9224 | 1.48184 | 0.740922 | − | 0.671591i | \(-0.234389\pi\) | ||||
0.740922 | + | 0.671591i | \(0.234389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.6480 | −0.746484 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.90065 | − | 16.0759i | 0.0654620 | − | 0.553682i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 35.1737i | − | 1.21001i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 20.6789i | − | 0.710535i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.67853 | + | 22.6552i | −0.0919270 | + | 0.777526i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.3083 | 0.661879 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.93665 | −0.305985 | −0.152993 | − | 0.988227i | \(-0.548891\pi\) | ||||
−0.152993 | + | 0.988227i | \(0.548891\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.99494 | + | 1.91729i | 0.273421 | + | 0.0655698i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 33.9961i | − | 1.16129i | −0.814158 | − | 0.580643i | \(-0.802801\pi\) | ||
0.814158 | − | 0.580643i | \(-0.197199\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.9595i | 1.09044i | 0.838291 | + | 0.545222i | \(0.183555\pi\) | ||||
−0.838291 | + | 0.545222i | \(0.816445\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.9173 | − | 2.11836i | −0.610619 | − | 0.0721936i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.77777 | −0.128597 | −0.0642984 | − | 0.997931i | \(-0.520481\pi\) | ||||
−0.0642984 | + | 0.997931i | \(0.520481\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 62.0285 | 2.10903 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.9449 | + | 3.42216i | 0.983020 | + | 0.116223i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.40736i | 0.217355i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 6.04223i | − | 0.204733i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 32.8557 | + | 7.87920i | 1.11200 | + | 0.266671i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.0805 | −0.442202 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.8807 | −0.637557 | −0.318779 | − | 0.947829i | \(-0.603273\pi\) | ||||
−0.318779 | + | 0.947829i | \(0.603273\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.785997 | − | 6.64803i | 0.0265110 | − | 0.224232i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.9442i | 0.469790i | 0.972021 | + | 0.234895i | \(0.0754747\pi\) | ||||
−0.972021 | + | 0.234895i | \(0.924525\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.4210i | 0.855485i | 0.903901 | + | 0.427742i | \(0.140691\pi\) | ||||
−0.903901 | + | 0.427742i | \(0.859309\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.45580 | − | 37.6875i | 0.149780 | − | 1.26685i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.0790 | 0.338419 | 0.169209 | − | 0.985580i | \(-0.445879\pi\) | ||||
0.169209 | + | 0.985580i | \(0.445879\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.7998 | 0.965913 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.71491 | − | 1.89049i | −0.124454 | − | 0.0633336i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 3.61873i | − | 0.121096i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 47.6555i | 1.59295i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.04223 | − | 0.241453i | −0.0681881 | − | 0.00806189i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.1281 | 0.571253 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.80093 | 0.126627 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.5144 | + | 2.30719i | 0.649399 | + | 0.0767786i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 47.5163i | − | 1.57949i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 25.9241i | − | 0.860797i | −0.902639 | − | 0.430398i | \(-0.858373\pi\) | ||
0.902639 | − | 0.430398i | \(-0.141627\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.22877 | − | 5.12389i | 0.0407558 | − | 0.169949i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.2694 | −0.804080 | −0.402040 | − | 0.915622i | \(-0.631699\pi\) | ||||
−0.402040 | + | 0.915622i | \(0.631699\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.03249 | −0.100361 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.54701 | + | 38.4589i | −0.150319 | + | 1.27141i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 27.2709i | − | 0.900565i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18.9401i | − | 0.624778i | −0.949954 | − | 0.312389i | \(-0.898871\pi\) | ||
0.949954 | − | 0.312389i | \(-0.101129\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.440371 | + | 3.72469i | −0.0145107 | + | 0.122733i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.96614 | 0.130547 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.6058 | 0.545995 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.19545 | + | 25.8346i | −0.203485 | + | 0.848519i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.4115i | 0.604063i | 0.953298 | + | 0.302031i | \(0.0976648\pi\) | ||||
−0.953298 | + | 0.302031i | \(0.902335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 3.32401i | − | 0.108940i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −52.5839 | − | 6.21700i | −1.72152 | − | 0.203535i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.526810 | −0.0172285 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.8066 | 1.00641 | 0.503204 | − | 0.864168i | \(-0.332154\pi\) | ||||
0.503204 | + | 0.864168i | \(0.332154\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 41.4270 | + | 4.89792i | 1.35192 | + | 0.159837i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 48.7361i | − | 1.58875i | −0.607427 | − | 0.794375i | \(-0.707798\pi\) | ||
0.607427 | − | 0.794375i | \(-0.292202\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 15.8596i | − | 0.516460i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −25.6187 | − | 9.44024i | −0.833376 | − | 0.307091i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −51.7955 | −1.68313 | −0.841564 | − | 0.540158i | \(-0.818364\pi\) | ||||
−0.841564 | + | 0.540158i | \(0.818364\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.462642 | −0.0150180 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.03116 | + | 17.1797i | −0.0658648 | + | 0.557090i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 11.8834i | − | 0.384943i | −0.981303 | − | 0.192471i | \(-0.938350\pi\) | ||
0.981303 | − | 0.192471i | \(-0.0616502\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.2904i | 0.527144i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.670300 | − | 5.66945i | 0.0216677 | − | 0.183267i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.7610 | 0.573534 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.2077 | 0.813150 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.6501 | + | 4.23271i | 0.568766 | + | 0.136397i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.5313i | 0.371204i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.8807i | 0.671479i | 0.941955 | + | 0.335740i | \(0.108986\pi\) | ||||
−0.941955 | + | 0.335740i | \(0.891014\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.713922 | − | 0.0844071i | −0.0229345 | − | 0.00271155i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.6869 | −1.59453 | −0.797264 | − | 0.603630i | \(-0.793720\pi\) | ||||
−0.797264 | + | 0.603630i | \(0.793720\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.7085 | −1.17682 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.75639 | − | 0.207658i | −0.0562495 | − | 0.00665039i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.2694i | 0.520505i | 0.965541 | + | 0.260253i | \(0.0838058\pi\) | ||||
−0.965541 | + | 0.260253i | \(0.916194\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.16427i | 0.101131i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.6903 | + | 6.88028i | 0.916009 | + | 0.219671i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.3543 | 1.09573 | 0.547867 | − | 0.836566i | \(-0.315440\pi\) | ||||
0.547867 | + | 0.836566i | \(0.315440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.51740 | 0.112074 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.41097 | + | 11.9341i | −0.0449117 | + | 0.379867i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.2733i | 0.549260i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.13922i | 0.226785i | 0.993550 | + | 0.113392i | \(0.0361717\pi\) | ||||
−0.993550 | + | 0.113392i | \(0.963828\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.33829 | + | 11.3193i | −0.0424693 | + | 0.359209i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.7254 | 0.847251 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.4758 | −1.15520 | −0.577599 | − | 0.816320i | \(-0.696010\pi\) | ||||
−0.577599 | + | 0.816320i | \(0.696010\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −32.2495 | − | 11.8836i | −1.02033 | − | 0.375982i |
(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 | 912.2.d.a.191.12 | yes | 12 | |
3.2 | odd | 2 | inner | 912.2.d.a.191.2 | yes | 12 | |
4.3 | odd | 2 | inner | 912.2.d.a.191.1 | ✓ | 12 | |
12.11 | even | 2 | inner | 912.2.d.a.191.11 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.d.a.191.1 | ✓ | 12 | 4.3 | odd | 2 | inner | |
912.2.d.a.191.2 | yes | 12 | 3.2 | odd | 2 | inner | |
912.2.d.a.191.11 | yes | 12 | 12.11 | even | 2 | inner | |
912.2.d.a.191.12 | yes | 12 | 1.1 | even | 1 | trivial |