Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(1567,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.1567");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.b (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.7 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1567 |
Dual form | 1728.3.b.g.1567.2 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.48528i | 1.69706i | 0.529150 | + | 0.848528i | \(0.322511\pi\) | ||||
−0.529150 | + | 0.848528i | \(0.677489\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.48528 | −0.771389 | −0.385695 | − | 0.922627i | \(-0.626038\pi\) | ||||
−0.385695 | + | 0.922627i | \(0.626038\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 19.0526i | − 1.46558i | −0.680454 | − | 0.732791i | \(-0.738217\pi\) | ||||
0.680454 | − | 0.732791i | \(-0.261783\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.6969 | −0.864526 | −0.432263 | − | 0.901748i | \(-0.642285\pi\) | ||||
−0.432263 | + | 0.901748i | \(0.642285\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.66025 | 0.455803 | 0.227901 | − | 0.973684i | \(-0.426814\pi\) | ||||
0.227901 | + | 0.973684i | \(0.426814\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 14.6969i | − 0.638997i | −0.947587 | − | 0.319499i | \(-0.896486\pi\) | ||||
0.947587 | − | 0.319499i | \(-0.103514\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −47.0000 | −1.88000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 50.9117i | 1.75558i | 0.479050 | + | 0.877788i | \(0.340981\pi\) | ||||
−0.479050 | + | 0.877788i | \(0.659019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 10.0000i | − 0.322581i | −0.986907 | − | 0.161290i | \(-0.948434\pi\) | ||||
0.986907 | − | 0.161290i | \(-0.0515656\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −59.3970 | −1.69706 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 19.0526i | 0.514934i | 0.966287 | + | 0.257467i | \(0.0828879\pi\) | ||||
−0.966287 | + | 0.257467i | \(0.917112\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −58.7878 | −1.43385 | −0.716924 | − | 0.697152i | \(-0.754450\pi\) | ||||
−0.716924 | + | 0.697152i | \(0.754450\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −41.5692 | −0.966726 | −0.483363 | − | 0.875420i | \(-0.660585\pi\) | ||||
−0.483363 | + | 0.875420i | \(0.660585\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 73.4847i | − 1.56350i | −0.623589 | − | 0.781752i | \(-0.714326\pi\) | ||||
0.623589 | − | 0.781752i | \(-0.285674\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 16.9706i | − 0.320199i | −0.987101 | − | 0.160100i | \(-0.948818\pi\) | ||||
0.987101 | − | 0.160100i | \(-0.0511816\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 72.0000i | − 1.30909i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −25.4558 | −0.431455 | −0.215727 | − | 0.976454i | \(-0.569212\pi\) | ||||
−0.215727 | + | 0.976454i | \(0.569212\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 19.0526i | − 0.312337i | −0.987730 | − | 0.156169i | \(-0.950086\pi\) | ||||
0.987730 | − | 0.156169i | \(-0.0499143\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 161.666 | 2.48717 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 116.047 | 1.73205 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 117.576i | 1.65599i | 0.560733 | + | 0.827997i | \(0.310519\pi\) | ||||
−0.560733 | + | 0.827997i | \(0.689481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −71.0000 | −0.972603 | −0.486301 | − | 0.873791i | \(-0.661654\pi\) | ||||
−0.486301 | + | 0.873791i | \(0.661654\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 59.3970i | − 0.771389i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 151.000i | − 1.91139i | −0.294355 | − | 0.955696i | \(-0.595105\pi\) | ||||
0.294355 | − | 0.955696i | \(-0.404895\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 135.765 | 1.63572 | 0.817858 | − | 0.575419i | \(-0.195161\pi\) | ||||
0.817858 | + | 0.575419i | \(0.195161\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 124.708i | − 1.46715i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −161.666 | −1.81648 | −0.908238 | − | 0.418454i | \(-0.862572\pi\) | ||||
−0.908238 | + | 0.418454i | \(0.862572\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 133.368 | 1.46558 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 73.4847i | 0.773523i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −25.0000 | −0.257732 | −0.128866 | − | 0.991662i | \(-0.541134\pi\) | ||||
−0.128866 | + | 0.991662i | \(0.541134\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 16.9706i | − 0.168025i | −0.996465 | − | 0.0840127i | \(-0.973226\pi\) | ||||
0.996465 | − | 0.0840127i | \(-0.0267736\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 103.000i | − 1.00000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 110.309 | 1.03092 | 0.515461 | − | 0.856913i | \(-0.327621\pi\) | ||||
0.515461 | + | 0.856913i | \(0.327621\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 41.5692i | − 0.381369i | −0.981651 | − | 0.190684i | \(-0.938929\pi\) | ||||
0.981651 | − | 0.190684i | \(-0.0610707\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 161.666 | 1.43068 | 0.715338 | − | 0.698779i | \(-0.246273\pi\) | ||||
0.715338 | + | 0.698779i | \(0.246273\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 124.708 | 1.08441 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 102.879i | − 0.864526i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −49.0000 | −0.404959 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 186.676i | − 1.49341i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 34.0000i | 0.267717i | 0.991000 | + | 0.133858i | \(0.0427367\pi\) | ||||
−0.991000 | + | 0.133858i | \(0.957263\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 118.794 | 0.906824 | 0.453412 | − | 0.891301i | \(-0.350207\pi\) | ||||
0.453412 | + | 0.891301i | \(0.350207\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 60.6218i | 0.455803i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.6969 | 0.107277 | 0.0536385 | − | 0.998560i | \(-0.482918\pi\) | ||||
0.0536385 | + | 0.998560i | \(0.482918\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −216.506 | −1.55760 | −0.778800 | − | 0.627273i | \(-0.784171\pi\) | ||||
−0.778800 | + | 0.627273i | \(0.784171\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 161.666i | 1.13053i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −432.000 | −2.97931 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 33.9411i | − 0.227793i | −0.993493 | − | 0.113896i | \(-0.963667\pi\) | ||||
0.993493 | − | 0.113896i | \(-0.0363332\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 209.000i | − 1.38411i | −0.721847 | − | 0.692053i | \(-0.756706\pi\) | ||||
0.721847 | − | 0.692053i | \(-0.243294\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 84.8528 | 0.547438 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 290.985i | − 1.85340i | −0.375796 | − | 0.926702i | \(-0.622631\pi\) | ||||
0.375796 | − | 0.926702i | \(-0.377369\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 102.879 | 0.638997 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 74.4782 | 0.456921 | 0.228461 | − | 0.973553i | \(-0.426631\pi\) | ||||
0.228461 | + | 0.973553i | \(0.426631\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 44.0908i | 0.264017i | 0.991249 | + | 0.132008i | \(0.0421426\pi\) | ||||
−0.991249 | + | 0.132008i | \(0.957857\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −194.000 | −1.14793 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 67.8823i | 0.392383i | 0.980566 | + | 0.196191i | \(0.0628574\pi\) | ||||
−0.980566 | + | 0.196191i | \(0.937143\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 329.000i | − 1.88000i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −271.529 | −1.51692 | −0.758461 | − | 0.651719i | \(-0.774048\pi\) | ||||
−0.758461 | + | 0.651719i | \(0.774048\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 143.760i | 0.794255i | 0.917763 | + | 0.397128i | \(0.129993\pi\) | ||||
−0.917763 | + | 0.397128i | \(0.870007\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −161.666 | −0.873872 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 124.708 | 0.666886 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 132.272i | − 0.692526i | −0.938138 | − | 0.346263i | \(-0.887451\pi\) | ||||
0.938138 | − | 0.346263i | \(-0.112549\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −265.000 | −1.37306 | −0.686528 | − | 0.727103i | \(-0.740866\pi\) | ||||
−0.686528 | + | 0.727103i | \(0.740866\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 144.250i | 0.732232i | 0.930569 | + | 0.366116i | \(0.119313\pi\) | ||||
−0.930569 | + | 0.366116i | \(0.880687\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 89.0000i | 0.447236i | 0.974677 | + | 0.223618i | \(0.0717868\pi\) | ||||
−0.974677 | + | 0.223618i | \(0.928213\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −356.382 | −1.75558 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 498.831i | − 2.43332i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −73.4847 | −0.351601 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −74.4782 | −0.352977 | −0.176489 | − | 0.984303i | \(-0.556474\pi\) | ||||
−0.176489 | + | 0.984303i | \(0.556474\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 352.727i | − 1.64059i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 70.0000 | 0.322581 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 280.014i | 1.26703i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 202.000i | 0.905830i | 0.891554 | + | 0.452915i | \(0.149616\pi\) | ||||
−0.891554 | + | 0.452915i | \(0.850384\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −305.470 | −1.34568 | −0.672842 | − | 0.739786i | \(-0.734926\pi\) | ||||
−0.672842 | + | 0.739786i | \(0.734926\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 166.277i | 0.726100i | 0.931770 | + | 0.363050i | \(0.118265\pi\) | ||||
−0.931770 | + | 0.363050i | \(0.881735\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −29.3939 | −0.126154 | −0.0630770 | − | 0.998009i | \(-0.520091\pi\) | ||||
−0.0630770 | + | 0.998009i | \(0.520091\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 623.538 | 2.65335 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 29.3939i | − 0.122987i | −0.998107 | − | 0.0614935i | \(-0.980414\pi\) | ||||
0.998107 | − | 0.0614935i | \(-0.0195863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 169.000 | 0.701245 | 0.350622 | − | 0.936517i | \(-0.385970\pi\) | ||||
0.350622 | + | 0.936517i | \(0.385970\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 165.000i | − 0.668016i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 203.647 | 0.811342 | 0.405671 | − | 0.914019i | \(-0.367038\pi\) | ||||
0.405671 | + | 0.914019i | \(0.367038\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 124.708i | 0.492916i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −146.969 | −0.571865 | −0.285933 | − | 0.958250i | \(-0.592303\pi\) | ||||
−0.285933 | + | 0.958250i | \(0.592303\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −133.368 | −0.514934 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 323.333i | 1.22940i | 0.788760 | + | 0.614701i | \(0.210723\pi\) | ||||
−0.788760 | + | 0.614701i | \(0.789277\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 144.000 | 0.543396 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 330.926i | 1.23021i | 0.788446 | + | 0.615104i | \(0.210886\pi\) | ||||
−0.788446 | + | 0.615104i | \(0.789114\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 305.000i | − 1.12546i | −0.826640 | − | 0.562731i | \(-0.809751\pi\) | ||||
0.826640 | − | 0.562731i | \(-0.190249\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 398.808 | 1.45021 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 207.846i | − 0.750347i | −0.926955 | − | 0.375173i | \(-0.877583\pi\) | ||||
0.926955 | − | 0.375173i | \(-0.122417\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −440.908 | −1.56907 | −0.784534 | − | 0.620086i | \(-0.787098\pi\) | ||||
−0.784534 | + | 0.620086i | \(0.787098\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −207.846 | −0.734439 | −0.367219 | − | 0.930134i | \(-0.619690\pi\) | ||||
−0.367219 | + | 0.930134i | \(0.619690\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 411.514i | − 1.43385i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −73.0000 | −0.252595 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 76.3675i | 0.260640i | 0.991472 | + | 0.130320i | \(0.0416005\pi\) | ||||
−0.991472 | + | 0.130320i | \(0.958400\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 216.000i | − 0.732203i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −280.014 | −0.936503 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 290.985i | − 0.966726i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 161.666 | 0.530054 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 374.123 | 1.21864 | 0.609321 | − | 0.792924i | \(-0.291442\pi\) | ||||
0.609321 | + | 0.792924i | \(0.291442\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 367.423i | − 1.18143i | −0.806882 | − | 0.590713i | \(-0.798847\pi\) | ||||
0.806882 | − | 0.590713i | \(-0.201153\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −335.000 | −1.07029 | −0.535144 | − | 0.844761i | \(-0.679743\pi\) | ||||
−0.535144 | + | 0.844761i | \(0.679743\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 135.765i | − 0.428279i | −0.976803 | − | 0.214140i | \(-0.931305\pi\) | ||||
0.976803 | − | 0.214140i | \(-0.0686947\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 432.000i | − 1.35423i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −127.279 | −0.394053 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 895.470i | 2.75529i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 514.393 | 1.56350 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.9090 | 0.0994229 | 0.0497114 | − | 0.998764i | \(-0.484170\pi\) | ||||
0.0497114 | + | 0.998764i | \(0.484170\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 984.695i | 2.93939i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 599.000 | 1.77745 | 0.888724 | − | 0.458443i | \(-0.151593\pi\) | ||||
0.888724 | + | 0.458443i | \(0.151593\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 84.8528i | 0.248835i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 1.00000i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −220.617 | −0.635785 | −0.317892 | − | 0.948127i | \(-0.602975\pi\) | ||||
−0.317892 | + | 0.948127i | \(0.602975\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 226.899i | 0.650139i | 0.945690 | + | 0.325070i | \(0.105388\pi\) | ||||
−0.945690 | + | 0.325070i | \(0.894612\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −382.120 | −1.08249 | −0.541247 | − | 0.840864i | \(-0.682048\pi\) | ||||
−0.541247 | + | 0.840864i | \(0.682048\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −997.661 | −2.81031 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 367.423i | 1.02346i | 0.859145 | + | 0.511732i | \(0.170996\pi\) | ||||
−0.859145 | + | 0.511732i | \(0.829004\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −286.000 | −0.792244 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 602.455i | − 1.65056i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 425.000i | 1.15804i | 0.815314 | + | 0.579019i | \(0.196564\pi\) | ||||
−0.815314 | + | 0.579019i | \(0.803436\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 118.794 | 0.320199 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 230.363i | − 0.617595i | −0.951128 | − | 0.308797i | \(-0.900074\pi\) | ||||
0.951128 | − | 0.308797i | \(-0.0999265\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 969.998 | 2.57294 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 74.4782 | 0.196512 | 0.0982562 | − | 0.995161i | \(-0.468674\pi\) | ||||
0.0982562 | + | 0.995161i | \(0.468674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 382.120i | − 0.997703i | −0.866687 | − | 0.498852i | \(-0.833755\pi\) | ||||
0.866687 | − | 0.498852i | \(-0.166245\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 504.000 | 1.30909 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 721.249i | − 1.85411i | −0.374925 | − | 0.927055i | \(-0.622332\pi\) | ||||
0.374925 | − | 0.927055i | \(-0.377668\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 216.000i | 0.552430i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1281.28 | 3.24374 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 41.5692i | − 0.104708i | −0.998629 | − | 0.0523542i | \(-0.983328\pi\) | ||||
0.998629 | − | 0.0523542i | \(-0.0166725\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −440.908 | −1.09952 | −0.549761 | − | 0.835322i | \(-0.685281\pi\) | ||||
−0.549761 | + | 0.835322i | \(0.685281\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −190.526 | −0.472768 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 161.666i | − 0.397215i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 193.000 | 0.471883 | 0.235941 | − | 0.971767i | \(-0.424183\pi\) | ||||
0.235941 | + | 0.971767i | \(0.424183\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 178.191i | − 0.431455i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1152.00i | 2.77590i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 636.396 | 1.51885 | 0.759423 | − | 0.650598i | \(-0.225482\pi\) | ||||
0.759423 | + | 0.650598i | \(0.225482\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 646.055i | 1.53457i | 0.641305 | + | 0.767286i | \(0.278393\pi\) | ||||
−0.641305 | + | 0.767286i | \(0.721607\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 690.756 | 1.62531 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 133.368 | 0.312337 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 220.454i | − 0.511494i | −0.966744 | − | 0.255747i | \(-0.917679\pi\) | ||||
0.966744 | − | 0.255747i | \(-0.0823215\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −362.000 | −0.836028 | −0.418014 | − | 0.908441i | \(-0.637274\pi\) | ||||
−0.418014 | + | 0.908441i | \(0.637274\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 127.279i | − 0.291257i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 58.0000i | − 0.132118i | −0.997816 | − | 0.0660592i | \(-0.978957\pi\) | ||||
0.997816 | − | 0.0660592i | \(-0.0210426\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −356.382 | −0.804474 | −0.402237 | − | 0.915536i | \(-0.631767\pi\) | ||||
−0.402237 | + | 0.915536i | \(0.631767\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1371.78i | − 3.08266i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −338.030 | −0.752850 | −0.376425 | − | 0.926447i | \(-0.622847\pi\) | ||||
−0.376425 | + | 0.926447i | \(0.622847\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 498.831 | 1.10605 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1131.66i | 2.48717i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 454.000 | 0.993435 | 0.496718 | − | 0.867912i | \(-0.334538\pi\) | ||||
0.496718 | + | 0.867912i | \(0.334538\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 93.3381i | − 0.202469i | −0.994863 | − | 0.101234i | \(-0.967721\pi\) | ||||
0.994863 | − | 0.101234i | \(-0.0322792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 391.000i | 0.844492i | 0.906481 | + | 0.422246i | \(0.138758\pi\) | ||||
−0.906481 | + | 0.422246i | \(0.861242\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −704.278 | −1.50809 | −0.754045 | − | 0.656822i | \(-0.771900\pi\) | ||||
−0.754045 | + | 0.656822i | \(0.771900\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 812.332i | 1.73205i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 352.727 | 0.745722 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −407.032 | −0.856909 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 499.696i | − 1.04321i | −0.853188 | − | 0.521603i | \(-0.825334\pi\) | ||||
0.853188 | − | 0.521603i | \(-0.174666\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 363.000 | 0.754678 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 212.132i | − 0.437386i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 559.000i | 1.14784i | 0.818910 | + | 0.573922i | \(0.194579\pi\) | ||||
−0.818910 | + | 0.573922i | \(0.805421\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −364.867 | −0.743110 | −0.371555 | − | 0.928411i | \(-0.621175\pi\) | ||||
−0.371555 | + | 0.928411i | \(0.621175\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 748.246i | − 1.51774i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −823.029 | −1.65599 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −249.415 | −0.499830 | −0.249915 | − | 0.968268i | \(-0.580403\pi\) | ||||
−0.249915 | + | 0.968268i | \(0.580403\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 514.393i | − 1.02265i | −0.859387 | − | 0.511325i | \(-0.829155\pi\) | ||||
0.859387 | − | 0.511325i | \(-0.170845\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 144.000 | 0.285149 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 313.955i | 0.616808i | 0.951255 | + | 0.308404i | \(0.0997949\pi\) | ||||
−0.951255 | + | 0.308404i | \(0.900205\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 497.000i | − 0.972603i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 873.984 | 1.69706 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 623.538i | 1.20607i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −367.423 | −0.705227 | −0.352614 | − | 0.935769i | \(-0.614707\pi\) | ||||
−0.352614 | + | 0.935769i | \(0.614707\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −715.337 | −1.36776 | −0.683879 | − | 0.729596i | \(-0.739708\pi\) | ||||
−0.683879 | + | 0.729596i | \(0.739708\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 146.969i | 0.278879i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 313.000 | 0.591682 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1120.06i | 2.10142i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 936.000i | 1.74953i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 604.486i | 1.11735i | 0.829387 | + | 0.558674i | \(0.188690\pi\) | ||||
−0.829387 | + | 0.558674i | \(0.811310\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 352.727 | 0.647205 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −798.475 | −1.45974 | −0.729868 | − | 0.683588i | \(-0.760418\pi\) | ||||
−0.729868 | + | 0.683588i | \(0.760418\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 440.908i | 0.800196i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1057.00 | 1.91139 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 161.220i | 0.289444i | 0.989472 | + | 0.144722i | \(0.0462288\pi\) | ||||
−0.989472 | + | 0.144722i | \(0.953771\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 792.000i | 1.41682i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −339.411 | −0.602862 | −0.301431 | − | 0.953488i | \(-0.597464\pi\) | ||||
−0.301431 | + | 0.953488i | \(0.597464\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1371.78i | 2.42794i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 308.636 | 0.542418 | 0.271209 | − | 0.962521i | \(-0.412577\pi\) | ||||
0.271209 | + | 0.962521i | \(0.412577\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −282.324 | −0.494438 | −0.247219 | − | 0.968960i | \(-0.579517\pi\) | ||||
−0.247219 | + | 0.968960i | \(0.579517\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 690.756i | 1.20131i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 145.000 | 0.251300 | 0.125650 | − | 0.992075i | \(-0.459898\pi\) | ||||
0.125650 | + | 0.992075i | \(0.459898\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 950.352i | 1.63572i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 144.000i | 0.246998i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.48528 | 0.0144553 | 0.00722767 | − | 0.999974i | \(-0.497699\pi\) | ||||
0.00722767 | + | 0.999974i | \(0.497699\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 86.6025i | − 0.147033i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −411.514 | −0.693953 | −0.346977 | − | 0.937874i | \(-0.612792\pi\) | ||||
−0.346977 | + | 0.937874i | \(0.612792\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 872.954 | 1.46715 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 1028.79i | − 1.71751i | −0.512390 | − | 0.858753i | \(-0.671240\pi\) | ||||
0.512390 | − | 0.858753i | \(-0.328760\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 698.000 | 1.16140 | 0.580699 | − | 0.814118i | \(-0.302779\pi\) | ||||
0.580699 | + | 0.814118i | \(0.302779\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 415.779i | − 0.687238i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 977.000i | − 1.60956i | −0.593576 | − | 0.804778i | \(-0.702285\pi\) | ||||
0.593576 | − | 0.804778i | \(-0.297715\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1400.07 | −2.29144 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1061.75i | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −749.544 | −1.21482 | −0.607410 | − | 0.794389i | \(-0.707791\pi\) | ||||
−0.607410 | + | 0.794389i | \(0.707791\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −573.309 | −0.926185 | −0.463093 | − | 0.886310i | \(-0.653260\pi\) | ||||
−0.463093 | + | 0.886310i | \(0.653260\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1131.66i | − 1.81648i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 409.000 | 0.654400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 280.014i | − 0.445174i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 449.000i | − 0.711569i | −0.934568 | − | 0.355784i | \(-0.884214\pi\) | ||||
0.934568 | − | 0.355784i | \(-0.115786\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −288.500 | −0.454330 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 705.453 | 1.10055 | 0.550275 | − | 0.834983i | \(-0.314523\pi\) | ||||
0.550275 | + | 0.834983i | \(0.314523\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −374.123 | −0.581840 | −0.290920 | − | 0.956747i | \(-0.593961\pi\) | ||||
−0.290920 | + | 0.956747i | \(0.593961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 117.576i | 0.181724i | 0.995863 | + | 0.0908621i | \(0.0289622\pi\) | ||||
−0.995863 | + | 0.0908621i | \(0.971038\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 216.000 | 0.332820 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 780.646i | 1.19548i | 0.801691 | + | 0.597738i | \(0.203934\pi\) | ||||
−0.801691 | + | 0.597738i | \(0.796066\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1008.00i | 1.53893i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −729.734 | −1.10734 | −0.553668 | − | 0.832738i | \(-0.686772\pi\) | ||||
−0.553668 | + | 0.832738i | \(0.686772\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 601.022i | − 0.909261i | −0.890680 | − | 0.454631i | \(-0.849771\pi\) | ||||
0.890680 | − | 0.454631i | \(-0.150229\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −514.393 | −0.773523 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 748.246 | 1.12181 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 161.666i | 0.240933i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −695.000 | −1.03269 | −0.516345 | − | 0.856381i | \(-0.672708\pi\) | ||||
−0.516345 | + | 0.856381i | \(0.672708\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 534.573i | 0.789620i | 0.918763 | + | 0.394810i | \(0.129190\pi\) | ||||
−0.918763 | + | 0.394810i | \(0.870810\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 175.000i | − 0.257732i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −661.852 | −0.969037 | −0.484518 | − | 0.874781i | \(-0.661005\pi\) | ||||
−0.484518 | + | 0.874781i | \(0.661005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 124.708i | 0.182055i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −323.333 | −0.469278 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 706.677 | 1.02269 | 0.511344 | − | 0.859376i | \(-0.329148\pi\) | ||||
0.511344 | + | 0.859376i | \(0.329148\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1837.12i | − 2.64333i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 864.000 | 1.23960 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 670.337i | 0.956259i | 0.878289 | + | 0.478129i | \(0.158685\pi\) | ||||
−0.878289 | + | 0.478129i | \(0.841315\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 165.000i | 0.234708i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 118.794 | 0.168025 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 559.452i | − 0.789073i | −0.918880 | − | 0.394536i | \(-0.870905\pi\) | ||||
0.918880 | − | 0.394536i | \(-0.129095\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −146.969 | −0.206128 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1371.78 | −1.91858 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 881.816i | 1.22645i | 0.789909 | + | 0.613224i | \(0.210128\pi\) | ||||
−0.789909 | + | 0.613224i | \(0.789872\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 721.000 | 1.00000 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 2392.85i | − 3.30048i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 778.000i | 1.07015i | 0.844804 | + | 0.535076i | \(0.179717\pi\) | ||||
−0.844804 | + | 0.535076i | \(0.820283\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 610.940 | 0.835760 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 540.400i | − 0.737244i | −0.929579 | − | 0.368622i | \(-0.879830\pi\) | ||||
0.929579 | − | 0.368622i | \(-0.120170\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −984.695 | −1.33609 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 540.400 | 0.731258 | 0.365629 | − | 0.930761i | \(-0.380854\pi\) | ||||
0.365629 | + | 0.930761i | \(0.380854\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 426.211i | 0.573636i | 0.957985 | + | 0.286818i | \(0.0925974\pi\) | ||||
−0.957985 | + | 0.286818i | \(0.907403\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 288.000 | 0.386577 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 772.161i | 1.03092i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 113.000i | 0.150466i | 0.997166 | + | 0.0752330i | \(0.0239701\pi\) | ||||
−0.997166 | + | 0.0752330i | \(0.976030\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1773.42 | 2.34891 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 937.039i | 1.23783i | 0.785457 | + | 0.618916i | \(0.212428\pi\) | ||||
−0.785457 | + | 0.618916i | \(0.787572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 396.817 | 0.521442 | 0.260721 | − | 0.965414i | \(-0.416040\pi\) | ||||
0.260721 | + | 0.965414i | \(0.416040\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 290.985 | 0.381369 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 484.999i | 0.632332i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 383.000 | 0.498049 | 0.249025 | − | 0.968497i | \(-0.419890\pi\) | ||||
0.249025 | + | 0.968497i | \(0.419890\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 814.587i | − 1.05380i | −0.849927 | − | 0.526900i | \(-0.823354\pi\) | ||||
0.849927 | − | 0.526900i | \(-0.176646\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 470.000i | 0.606452i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −509.117 | −0.653552 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 997.661i | − 1.27742i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2469.09 | 3.14533 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −240.755 | −0.305915 | −0.152957 | − | 0.988233i | \(-0.548880\pi\) | ||||
−0.152957 | + | 0.988233i | \(0.548880\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1131.66i | 1.43068i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −363.000 | −0.457755 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 492.146i | − 0.617499i | −0.951143 | − | 0.308749i | \(-0.900090\pi\) | ||||
0.951143 | − | 0.308749i | \(-0.0999104\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1080.00i | 1.35169i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 602.455 | 0.750255 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 872.954i | 1.08441i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −540.400 | −0.666338 | −0.333169 | − | 0.942867i | \(-0.608118\pi\) | ||||
−0.333169 | + | 0.942867i | \(0.608118\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 631.968i | 0.775421i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −360.000 | −0.440636 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 636.396i | 0.775148i | 0.921839 | + | 0.387574i | \(0.126687\pi\) | ||||
−0.921839 | + | 0.387574i | \(0.873313\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 967.000i | 1.17497i | 0.809235 | + | 0.587485i | \(0.199882\pi\) | ||||
−0.809235 | + | 0.587485i | \(0.800118\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −381.838 | −0.461714 | −0.230857 | − | 0.972988i | \(-0.574153\pi\) | ||||
−0.230857 | + | 0.972988i | \(0.574153\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1020.18i | − 1.23061i | −0.788288 | − | 0.615306i | \(-0.789032\pi\) | ||||
0.788288 | − | 0.615306i | \(-0.210968\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −374.123 | −0.448051 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 440.908i | 0.525516i | 0.964862 | + | 0.262758i | \(0.0846321\pi\) | ||||
−0.964862 | + | 0.262758i | \(0.915368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1751.00 | −2.08205 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1646.14i | − 1.94810i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 343.000i | − 0.404959i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 280.014 | 0.329041 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 143.760i | 0.168535i | 0.996443 | + | 0.0842674i | \(0.0268550\pi\) | ||||
−0.996443 | + | 0.0842674i | \(0.973145\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 293.939 | 0.342986 | 0.171493 | − | 0.985185i | \(-0.445141\pi\) | ||||
0.171493 | + | 0.985185i | \(0.445141\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 91.7987 | 0.106867 | 0.0534335 | − | 0.998571i | \(-0.482983\pi\) | ||||
0.0534335 | + | 0.998571i | \(0.482983\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 955.301i | − 1.10695i | −0.832865 | − | 0.553477i | \(-0.813301\pi\) | ||||
0.832865 | − | 0.553477i | \(-0.186699\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −576.000 | −0.665896 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1281.28i | 1.47443i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 2211.00i | − 2.53846i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1306.73 | 1.49341 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 434.745i | 0.495718i | 0.968796 | + | 0.247859i | \(0.0797270\pi\) | ||||
−0.968796 | + | 0.247859i | \(0.920273\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1043.48 | 1.18443 | 0.592215 | − | 0.805780i | \(-0.298254\pi\) | ||||
0.592215 | + | 0.805780i | \(0.298254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −133.368 | −0.151040 | −0.0755198 | − | 0.997144i | \(-0.524062\pi\) | ||||
−0.0755198 | + | 0.997144i | \(0.524062\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 411.514i | − 0.463939i | −0.972723 | − | 0.231970i | \(-0.925483\pi\) | ||||
0.972723 | − | 0.231970i | \(-0.0745170\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −238.000 | −0.267717 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 636.396i | − 0.712650i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 2304.00i | − 2.57430i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 509.117 | 0.566315 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 249.415i | 0.276821i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1219.85 | −1.34790 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −465.922 | −0.513695 | −0.256848 | − | 0.966452i | \(-0.582684\pi\) | ||||
−0.256848 | + | 0.966452i | \(0.582684\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 117.576i | 0.129062i | 0.997916 | + | 0.0645310i | \(0.0205551\pi\) | ||||
−0.997916 | + | 0.0645310i | \(0.979445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1152.00 | −1.26177 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 831.558i | 0.906824i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 394.000i | 0.428727i | 0.976754 | + | 0.214363i | \(0.0687677\pi\) | ||||
−0.976754 | + | 0.214363i | \(0.931232\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2240.11 | 2.42699 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 895.470i | − 0.968076i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −617.271 | −0.664447 | −0.332224 | − | 0.943201i | \(-0.607799\pi\) | ||||
−0.332224 | + | 0.943201i | \(0.607799\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1058.18i | 1.13174i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1439.00 | −1.53575 | −0.767876 | − | 0.640598i | \(-0.778686\pi\) | ||||
−0.767876 | + | 0.640598i | \(0.778686\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1009.75i | − 1.07306i | −0.843882 | − | 0.536529i | \(-0.819735\pi\) | ||||
0.843882 | − | 0.536529i | \(-0.180265\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 864.000i | 0.916225i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −551.543 | −0.582411 | −0.291206 | − | 0.956661i | \(-0.594056\pi\) | ||||
−0.291206 | + | 0.956661i | \(0.594056\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1352.73i | 1.42543i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1249.24 | −1.31085 | −0.655425 | − | 0.755260i | \(-0.727510\pi\) | ||||
−0.655425 | + | 0.755260i | \(0.727510\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1122.37 | 1.17526 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 102.879i | 0.107277i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 861.000 | 0.895942 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 2248.60i | − 2.33015i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 689.000i | 0.712513i | 0.934388 | + | 0.356256i | \(0.115947\pi\) | ||||
−0.934388 | + | 0.356256i | \(0.884053\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −568.514 | −0.585493 | −0.292747 | − | 0.956190i | \(-0.594569\pi\) | ||||
−0.292747 | + | 0.956190i | \(0.594569\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1515.54i | − 1.55760i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1881.21 | 1.92549 | 0.962747 | − | 0.270403i | \(-0.0871569\pi\) | ||||
0.962747 | + | 0.270403i | \(0.0871569\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1371.78 | 1.40121 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1807.72i | 1.83899i | 0.393106 | + | 0.919493i | \(0.371400\pi\) | ||||
−0.393106 | + | 0.919493i | \(0.628600\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1224.00 | −1.24264 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 610.940i | 0.617735i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 233.000i | 0.235116i | 0.993066 | + | 0.117558i | \(0.0375066\pi\) | ||||
−0.993066 | + | 0.117558i | \(0.962493\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −755.190 | −0.758985 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 374.123i | 0.375249i | 0.982241 | + | 0.187624i | \(0.0600788\pi\) | ||||
−0.982241 | + | 0.187624i | \(0.939921\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.3.b.g.1567.7 | yes | 8 | |
3.2 | odd | 2 | inner | 1728.3.b.g.1567.3 | yes | 8 | |
4.3 | odd | 2 | inner | 1728.3.b.g.1567.5 | yes | 8 | |
8.3 | odd | 2 | inner | 1728.3.b.g.1567.2 | yes | 8 | |
8.5 | even | 2 | inner | 1728.3.b.g.1567.4 | yes | 8 | |
12.11 | even | 2 | inner | 1728.3.b.g.1567.1 | ✓ | 8 | |
24.5 | odd | 2 | inner | 1728.3.b.g.1567.8 | yes | 8 | |
24.11 | even | 2 | inner | 1728.3.b.g.1567.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.3.b.g.1567.1 | ✓ | 8 | 12.11 | even | 2 | inner | |
1728.3.b.g.1567.2 | yes | 8 | 8.3 | odd | 2 | inner | |
1728.3.b.g.1567.3 | yes | 8 | 3.2 | odd | 2 | inner | |
1728.3.b.g.1567.4 | yes | 8 | 8.5 | even | 2 | inner | |
1728.3.b.g.1567.5 | yes | 8 | 4.3 | odd | 2 | inner | |
1728.3.b.g.1567.6 | yes | 8 | 24.11 | even | 2 | inner | |
1728.3.b.g.1567.7 | yes | 8 | 1.1 | even | 1 | trivial | |
1728.3.b.g.1567.8 | yes | 8 | 24.5 | odd | 2 | inner |