Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,3,Mod(161,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.h (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: | \(15.6948632272\) |
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: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.1 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.161 |
Dual form | 576.3.h.b.161.2 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −7.34847 | −1.46969 | −0.734847 | − | 0.678233i | \(-0.762746\pi\) | ||||
−0.734847 | + | 0.678233i | \(0.762746\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.3923 | −1.48461 | −0.742307 | − | 0.670059i | \(-0.766269\pi\) | ||||
−0.742307 | + | 0.670059i | \(0.766269\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.48528 | 0.771389 | 0.385695 | − | 0.922627i | \(-0.373962\pi\) | ||||
0.385695 | + | 0.922627i | \(0.373962\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 10.3923i | − 0.799408i | −0.916644 | − | 0.399704i | \(-0.869113\pi\) | ||||
0.916644 | − | 0.399704i | \(-0.130887\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 21.2132i | 1.24784i | 0.781490 | + | 0.623918i | \(0.214460\pi\) | ||||
−0.781490 | + | 0.623918i | \(0.785540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 20.0000i | − 1.05263i | −0.850289 | − | 0.526316i | \(-0.823573\pi\) | ||||
0.850289 | − | 0.526316i | \(-0.176427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 14.6969i | 0.638997i | 0.947587 | + | 0.319499i | \(0.103514\pi\) | ||||
−0.947587 | + | 0.319499i | \(0.896486\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 29.0000 | 1.16000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 36.7423 | 1.26698 | 0.633489 | − | 0.773752i | \(-0.281622\pi\) | ||||
0.633489 | + | 0.773752i | \(0.281622\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 51.9615 | 1.67618 | 0.838089 | − | 0.545533i | \(-0.183673\pi\) | ||||
0.838089 | + | 0.545533i | \(0.183673\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 76.3675 | 2.18193 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 41.5692i | 1.12349i | 0.827310 | + | 0.561746i | \(0.189870\pi\) | ||||
−0.827310 | + | 0.561746i | \(0.810130\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 72.1249i | 1.75914i | 0.475766 | + | 0.879572i | \(0.342171\pi\) | ||||
−0.475766 | + | 0.879572i | \(0.657829\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 40.0000i | − 0.930233i | −0.885250 | − | 0.465116i | \(-0.846013\pi\) | ||||
0.885250 | − | 0.465116i | \(-0.153987\pi\) | |||||||
\(44\) | 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 | ||||||||
\(49\) | 59.0000 | 1.20408 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −36.7423 | −0.693252 | −0.346626 | − | 0.938003i | \(-0.612673\pi\) | ||||
−0.346626 | + | 0.938003i | \(0.612673\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −62.3538 | −1.13371 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 33.9411 | 0.575273 | 0.287637 | − | 0.957740i | \(-0.407130\pi\) | ||||
0.287637 | + | 0.957740i | \(0.407130\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 76.3675i | 1.17489i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 100.000i | − 1.49254i | −0.665645 | − | 0.746269i | \(-0.731843\pi\) | ||||
0.665645 | − | 0.746269i | \(-0.268157\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 73.4847i | 1.03500i | 0.855685 | + | 0.517498i | \(0.173136\pi\) | ||||
−0.855685 | + | 0.517498i | \(0.826864\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 20.0000 | 0.273973 | 0.136986 | − | 0.990573i | \(-0.456258\pi\) | ||||
0.136986 | + | 0.990573i | \(0.456258\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −88.1816 | −1.14522 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −51.9615 | −0.657741 | −0.328870 | − | 0.944375i | \(-0.606668\pi\) | ||||
−0.328870 | + | 0.944375i | \(0.606668\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 127.279 | 1.53348 | 0.766742 | − | 0.641955i | \(-0.221876\pi\) | ||||
0.766742 | + | 0.641955i | \(0.221876\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 155.885i | − 1.83394i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.7279i | 0.143010i | 0.997440 | + | 0.0715052i | \(0.0227802\pi\) | ||||
−0.997440 | + | 0.0715052i | \(0.977220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 108.000i | 1.18681i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 146.969i | 1.54705i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 40.0000 | 0.412371 | 0.206186 | − | 0.978513i | \(-0.433895\pi\) | ||||
0.206186 | + | 0.978513i | \(0.433895\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 183.712 | 1.81893 | 0.909464 | − | 0.415783i | \(-0.136492\pi\) | ||||
0.909464 | + | 0.415783i | \(0.136492\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 93.5307 | 0.908065 | 0.454033 | − | 0.890985i | \(-0.349985\pi\) | ||||
0.454033 | + | 0.890985i | \(0.349985\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −169.706 | −1.58603 | −0.793017 | − | 0.609200i | \(-0.791491\pi\) | ||||
−0.793017 | + | 0.609200i | \(0.791491\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 51.9615i | 0.476711i | 0.971178 | + | 0.238356i | \(0.0766084\pi\) | ||||
−0.971178 | + | 0.238356i | \(0.923392\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 63.6396i | − 0.563182i | −0.959534 | − | 0.281591i | \(-0.909138\pi\) | ||||
0.959534 | − | 0.281591i | \(-0.0908622\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 108.000i | − 0.939130i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 220.454i | − 1.85256i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −49.0000 | −0.404959 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −29.3939 | −0.235151 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3923 | 0.0818292 | 0.0409146 | − | 0.999163i | \(-0.486973\pi\) | ||||
0.0409146 | + | 0.999163i | \(0.486973\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 50.9117 | 0.388639 | 0.194319 | − | 0.980938i | \(-0.437750\pi\) | ||||
0.194319 | + | 0.980938i | \(0.437750\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 207.846i | 1.56275i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 106.066i | − 0.774205i | −0.922037 | − | 0.387102i | \(-0.873476\pi\) | ||||
0.922037 | − | 0.387102i | \(-0.126524\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 172.000i | 1.23741i | 0.785623 | + | 0.618705i | \(0.212342\pi\) | ||||
−0.785623 | + | 0.618705i | \(0.787658\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 88.1816i | − 0.616655i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −270.000 | −1.86207 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −110.227 | −0.739779 | −0.369889 | − | 0.929076i | \(-0.620604\pi\) | ||||
−0.369889 | + | 0.929076i | \(0.620604\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 155.885 | 1.03235 | 0.516174 | − | 0.856484i | \(-0.327356\pi\) | ||||
0.516174 | + | 0.856484i | \(0.327356\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −381.838 | −2.46347 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 166.277i | 1.05909i | 0.848282 | + | 0.529544i | \(0.177637\pi\) | ||||
−0.848282 | + | 0.529544i | \(0.822363\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 152.735i | − 0.948665i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 160.000i | 0.981595i | 0.871274 | + | 0.490798i | \(0.163295\pi\) | ||||
−0.871274 | + | 0.490798i | \(0.836705\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 58.7878i | − 0.352022i | −0.984388 | − | 0.176011i | \(-0.943680\pi\) | ||||
0.984388 | − | 0.176011i | \(-0.0563195\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 61.0000 | 0.360947 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 36.7423 | 0.212384 | 0.106192 | − | 0.994346i | \(-0.466134\pi\) | ||||
0.106192 | + | 0.994346i | \(0.466134\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −301.377 | −1.72215 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 50.9117 | 0.284423 | 0.142211 | − | 0.989836i | \(-0.454579\pi\) | ||||
0.142211 | + | 0.989836i | \(0.454579\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 259.808i | − 1.43540i | −0.696352 | − | 0.717701i | \(-0.745195\pi\) | ||||
0.696352 | − | 0.717701i | \(-0.254805\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 305.470i | − 1.65119i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 180.000i | 0.962567i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 293.939i | 1.53895i | 0.638679 | + | 0.769473i | \(0.279481\pi\) | ||||
−0.638679 | + | 0.769473i | \(0.720519\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0000 | −0.0518135 | −0.0259067 | − | 0.999664i | \(-0.508247\pi\) | ||||
−0.0259067 | + | 0.999664i | \(0.508247\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.0454 | −0.111906 | −0.0559528 | − | 0.998433i | \(-0.517820\pi\) | ||||
−0.0559528 | + | 0.998433i | \(0.517820\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 51.9615 | 0.261113 | 0.130557 | − | 0.991441i | \(-0.458324\pi\) | ||||
0.130557 | + | 0.991441i | \(0.458324\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −381.838 | −1.88097 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 530.008i | − 2.58540i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 169.706i | − 0.811989i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 172.000i | − 0.815166i | −0.913168 | − | 0.407583i | \(-0.866372\pi\) | ||||
0.913168 | − | 0.407583i | \(-0.133628\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 293.939i | 1.36716i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −540.000 | −2.48848 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 220.454 | 0.997530 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3923 | 0.0466023 | 0.0233011 | − | 0.999728i | \(-0.492582\pi\) | ||||
0.0233011 | + | 0.999728i | \(0.492582\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 42.4264 | 0.186900 | 0.0934502 | − | 0.995624i | \(-0.470210\pi\) | ||||
0.0934502 | + | 0.995624i | \(0.470210\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 259.808i | 1.13453i | 0.823535 | + | 0.567266i | \(0.191999\pi\) | ||||
−0.823535 | + | 0.567266i | \(0.808001\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 106.066i | 0.455219i | 0.973752 | + | 0.227609i | \(0.0730910\pi\) | ||||
−0.973752 | + | 0.227609i | \(0.926909\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 540.000i | 2.29787i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 146.969i | − 0.614935i | −0.951559 | − | 0.307467i | \(-0.900519\pi\) | ||||
0.951559 | − | 0.307467i | \(-0.0994815\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 140.000 | 0.580913 | 0.290456 | − | 0.956888i | \(-0.406193\pi\) | ||||
0.290456 | + | 0.956888i | \(0.406193\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −433.560 | −1.76963 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −207.846 | −0.841482 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −246.073 | −0.980371 | −0.490186 | − | 0.871618i | \(-0.663071\pi\) | ||||
−0.490186 | + | 0.871618i | \(0.663071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 124.708i | 0.492916i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 21.2132i | − 0.0825416i | −0.999148 | − | 0.0412708i | \(-0.986859\pi\) | ||||
0.999148 | − | 0.0412708i | \(-0.0131406\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 432.000i | − 1.66795i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 88.1816i | − 0.335291i | −0.985847 | − | 0.167646i | \(-0.946384\pi\) | ||||
0.985847 | − | 0.167646i | \(-0.0536165\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 270.000 | 1.01887 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 110.227 | 0.409766 | 0.204883 | − | 0.978786i | \(-0.434319\pi\) | ||||
0.204883 | + | 0.978786i | \(0.434319\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 467.654 | 1.72566 | 0.862830 | − | 0.505495i | \(-0.168690\pi\) | ||||
0.862830 | + | 0.505495i | \(0.168690\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 246.073 | 0.894811 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 322.161i | 1.16304i | 0.813533 | + | 0.581519i | \(0.197541\pi\) | ||||
−0.813533 | + | 0.581519i | \(0.802459\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 140.007i | − 0.498246i | −0.968472 | − | 0.249123i | \(-0.919858\pi\) | ||||
0.968472 | − | 0.249123i | \(-0.0801424\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 80.0000i | − 0.282686i | −0.989961 | − | 0.141343i | \(-0.954858\pi\) | ||||
0.989961 | − | 0.141343i | \(-0.0451420\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 749.544i | − 2.61165i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −161.000 | −0.557093 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 315.984 | 1.07844 | 0.539222 | − | 0.842164i | \(-0.318718\pi\) | ||||
0.539222 | + | 0.842164i | \(0.318718\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −249.415 | −0.845476 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 152.735 | 0.510820 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 415.692i | 1.38104i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 380.000i | 1.23779i | 0.785476 | + | 0.618893i | \(0.212418\pi\) | ||||
−0.785476 | + | 0.618893i | \(0.787582\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 146.969i | − 0.472570i | −0.971684 | − | 0.236285i | \(-0.924070\pi\) | ||||
0.971684 | − | 0.236285i | \(-0.0759300\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 310.000 | 0.990415 | 0.495208 | − | 0.868775i | \(-0.335092\pi\) | ||||
0.495208 | + | 0.868775i | \(0.335092\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −242.499 | −0.764983 | −0.382491 | − | 0.923959i | \(-0.624934\pi\) | ||||
−0.382491 | + | 0.923959i | \(0.624934\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 311.769 | 0.977333 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 424.264 | 1.31351 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 301.377i | − 0.927313i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 763.675i | 2.32120i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 500.000i | − 1.51057i | −0.655394 | − | 0.755287i | \(-0.727497\pi\) | ||||
0.655394 | − | 0.755287i | \(-0.272503\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 734.847i | 2.19357i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 100.000 | 0.296736 | 0.148368 | − | 0.988932i | \(-0.452598\pi\) | ||||
0.148368 | + | 0.988932i | \(0.452598\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 440.908 | 1.29299 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −103.923 | −0.302983 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −42.4264 | −0.122266 | −0.0611332 | − | 0.998130i | \(-0.519471\pi\) | ||||
−0.0611332 | + | 0.998130i | \(0.519471\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 207.846i | − 0.595548i | −0.954636 | − | 0.297774i | \(-0.903756\pi\) | ||||
0.954636 | − | 0.297774i | \(-0.0962441\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 615.183i | 1.74273i | 0.490637 | + | 0.871364i | \(0.336764\pi\) | ||||
−0.490637 | + | 0.871364i | \(0.663236\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 540.000i | − 1.52113i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 514.393i | 1.43285i | 0.697665 | + | 0.716425i | \(0.254223\pi\) | ||||
−0.697665 | + | 0.716425i | \(0.745777\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −39.0000 | −0.108033 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −146.969 | −0.402656 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 218.238 | 0.594655 | 0.297328 | − | 0.954776i | \(-0.403905\pi\) | ||||
0.297328 | + | 0.954776i | \(0.403905\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 381.838 | 1.02921 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 665.108i | − 1.78313i | −0.452893 | − | 0.891565i | \(-0.649608\pi\) | ||||
0.452893 | − | 0.891565i | \(-0.350392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 381.838i | − 1.01283i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 92.0000i | 0.242744i | 0.992607 | + | 0.121372i | \(0.0387294\pi\) | ||||
−0.992607 | + | 0.121372i | \(0.961271\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 146.969i | − 0.383732i | −0.981421 | − | 0.191866i | \(-0.938546\pi\) | ||||
0.981421 | − | 0.191866i | \(-0.0614539\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 648.000 | 1.68312 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −257.196 | −0.661173 | −0.330587 | − | 0.943776i | \(-0.607247\pi\) | ||||
−0.330587 | + | 0.943776i | \(0.607247\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −311.769 | −0.797364 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 381.838 | 0.966678 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 41.5692i | 0.104708i | 0.998629 | + | 0.0523542i | \(0.0166725\pi\) | ||||
−0.998629 | + | 0.0523542i | \(0.983328\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 224.860i | 0.560748i | 0.959891 | + | 0.280374i | \(0.0904585\pi\) | ||||
−0.959891 | + | 0.280374i | \(0.909542\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 540.000i | − 1.33995i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 352.727i | 0.866650i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 368.000 | 0.899756 | 0.449878 | − | 0.893090i | \(-0.351468\pi\) | ||||
0.449878 | + | 0.893090i | \(0.351468\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −352.727 | −0.854059 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −935.307 | −2.25375 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 432.749 | 1.03281 | 0.516407 | − | 0.856343i | \(-0.327269\pi\) | ||||
0.516407 | + | 0.856343i | \(0.327269\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 51.9615i | − 0.123424i | −0.998094 | − | 0.0617120i | \(-0.980344\pi\) | ||||
0.998094 | − | 0.0617120i | \(-0.0196560\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 615.183i | 1.44749i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 367.423i | − 0.852491i | −0.904608 | − | 0.426245i | \(-0.859836\pi\) | ||||
0.904608 | − | 0.426245i | \(-0.140164\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −470.000 | −1.08545 | −0.542725 | − | 0.839910i | \(-0.682607\pi\) | ||||
−0.542725 | + | 0.839910i | \(0.682607\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 293.939 | 0.672629 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 155.885 | 0.355090 | 0.177545 | − | 0.984113i | \(-0.443184\pi\) | ||||
0.177545 | + | 0.984113i | \(0.443184\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 551.543 | 1.24502 | 0.622509 | − | 0.782612i | \(-0.286113\pi\) | ||||
0.622509 | + | 0.782612i | \(0.286113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 93.5307i | − 0.210181i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 691.550i | 1.54020i | 0.637922 | + | 0.770101i | \(0.279794\pi\) | ||||
−0.637922 | + | 0.770101i | \(0.720206\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 612.000i | 1.35698i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 793.635i | − 1.74425i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 680.000 | 1.48796 | 0.743982 | − | 0.668199i | \(-0.232935\pi\) | ||||
0.743982 | + | 0.668199i | \(0.232935\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −330.681 | −0.717313 | −0.358656 | − | 0.933470i | \(-0.616765\pi\) | ||||
−0.358656 | + | 0.933470i | \(0.616765\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 322.161 | 0.695813 | 0.347907 | − | 0.937529i | \(-0.386893\pi\) | ||||
0.347907 | + | 0.937529i | \(0.386893\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −466.690 | −0.999337 | −0.499669 | − | 0.866217i | \(-0.666545\pi\) | ||||
−0.499669 | + | 0.866217i | \(0.666545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1039.23i | 2.21584i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 339.411i | − 0.717571i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 580.000i | − 1.22105i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 220.454i | − 0.460238i | −0.973162 | − | 0.230119i | \(-0.926088\pi\) | ||||
0.973162 | − | 0.230119i | \(-0.0739116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 432.000 | 0.898129 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −293.939 | −0.606059 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 633.931 | 1.30171 | 0.650853 | − | 0.759204i | \(-0.274412\pi\) | ||||
0.650853 | + | 0.759204i | \(0.274412\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 220.617 | 0.449322 | 0.224661 | − | 0.974437i | \(-0.427872\pi\) | ||||
0.224661 | + | 0.974437i | \(0.427872\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 779.423i | 1.58098i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 763.675i | − 1.53657i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 640.000i | − 1.28257i | −0.767305 | − | 0.641283i | \(-0.778403\pi\) | ||||
0.767305 | − | 0.641283i | \(-0.221597\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 73.4847i | − 0.146093i | −0.997329 | − | 0.0730464i | \(-0.976728\pi\) | ||||
0.997329 | − | 0.0730464i | \(-0.0232721\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1350.00 | −2.67327 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 624.620 | 1.22715 | 0.613576 | − | 0.789636i | \(-0.289731\pi\) | ||||
0.613576 | + | 0.789636i | \(0.289731\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −207.846 | −0.406744 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −687.308 | −1.33458 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 623.538i | − 1.20607i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 861.256i | 1.65308i | 0.562876 | + | 0.826541i | \(0.309695\pi\) | ||||
−0.562876 | + | 0.826541i | \(0.690305\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0000i | 0.0382409i | 0.999817 | + | 0.0191205i | \(0.00608660\pi\) | ||||
−0.999817 | + | 0.0191205i | \(0.993913\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1102.27i | 2.09159i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 313.000 | 0.591682 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 749.544 | 1.40627 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1247.08 | 2.33098 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 500.632 | 0.928816 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 363.731i | − 0.672330i | −0.941803 | − | 0.336165i | \(-0.890870\pi\) | ||||
0.941803 | − | 0.336165i | \(-0.109130\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 381.838i | − 0.700620i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 760.000i | 1.38940i | 0.719301 | + | 0.694698i | \(0.244462\pi\) | ||||
−0.719301 | + | 0.694698i | \(0.755538\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 734.847i | − 1.33366i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 540.000 | 0.976492 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 992.043 | 1.78105 | 0.890524 | − | 0.454937i | \(-0.150338\pi\) | ||||
0.890524 | + | 0.454937i | \(0.150338\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −415.692 | −0.743635 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −212.132 | −0.376789 | −0.188394 | − | 0.982093i | \(-0.560328\pi\) | ||||
−0.188394 | + | 0.982093i | \(0.560328\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 467.654i | 0.827706i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 479.418i | − 0.842563i | −0.906930 | − | 0.421282i | \(-0.861580\pi\) | ||||
0.906930 | − | 0.421282i | \(-0.138420\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 280.000i | 0.490368i | 0.969477 | + | 0.245184i | \(0.0788483\pi\) | ||||
−0.969477 | + | 0.245184i | \(0.921152\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 426.211i | 0.741237i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −650.000 | −1.12652 | −0.563258 | − | 0.826281i | \(-0.690452\pi\) | ||||
−0.563258 | + | 0.826281i | \(0.690452\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1322.72 | −2.27663 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −311.769 | −0.534767 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −678.823 | −1.15643 | −0.578213 | − | 0.815886i | \(-0.696250\pi\) | ||||
−0.578213 | + | 0.815886i | \(0.696250\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1039.23i | − 1.76440i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 445.477i | − 0.751226i | −0.926777 | − | 0.375613i | \(-0.877432\pi\) | ||||
0.926777 | − | 0.375613i | \(-0.122568\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1620.00i | 2.72269i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 367.423i | 0.613395i | 0.951807 | + | 0.306697i | \(0.0992240\pi\) | ||||
−0.951807 | + | 0.306697i | \(0.900776\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −490.000 | −0.815308 | −0.407654 | − | 0.913137i | \(-0.633653\pi\) | ||||
−0.407654 | + | 0.913137i | \(0.633653\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 360.075 | 0.595165 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −322.161 | −0.530744 | −0.265372 | − | 0.964146i | \(-0.585495\pi\) | ||||
−0.265372 | + | 0.964146i | \(0.585495\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −763.675 | −1.24988 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 374.123i | − 0.610315i | −0.952302 | − | 0.305157i | \(-0.901291\pi\) | ||||
0.952302 | − | 0.305157i | \(-0.0987091\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 784.889i | − 1.27210i | −0.771646 | − | 0.636052i | \(-0.780566\pi\) | ||||
0.771646 | − | 0.636052i | \(-0.219434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 1112.00i | − 1.79645i | −0.439540 | − | 0.898223i | \(-0.644859\pi\) | ||||
0.439540 | − | 0.898223i | \(-0.355141\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 132.272i | − 0.212315i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −509.000 | −0.814400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −881.816 | −1.40193 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −987.269 | −1.56461 | −0.782305 | − | 0.622896i | \(-0.785956\pi\) | ||||
−0.782305 | + | 0.622896i | \(0.785956\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −76.3675 | −0.120264 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 613.146i | − 0.962553i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 97.5807i | − 0.152232i | −0.997099 | − | 0.0761160i | \(-0.975748\pi\) | ||||
0.997099 | − | 0.0761160i | \(-0.0242519\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 80.0000i | − 0.124417i | −0.998063 | − | 0.0622084i | \(-0.980186\pi\) | ||||
0.998063 | − | 0.0622084i | \(-0.0198143\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 514.393i | 0.795043i | 0.917593 | + | 0.397522i | \(0.130130\pi\) | ||||
−0.917593 | + | 0.397522i | \(0.869870\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 288.000 | 0.443760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1080.22 | −1.65425 | −0.827125 | − | 0.562018i | \(-0.810025\pi\) | ||||
−0.827125 | + | 0.562018i | \(0.810025\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −374.123 | −0.571180 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −712.764 | −1.08158 | −0.540792 | − | 0.841156i | \(-0.681875\pi\) | ||||
−0.540792 | + | 0.841156i | \(0.681875\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1247.08i | 1.88665i | 0.331868 | + | 0.943326i | \(0.392321\pi\) | ||||
−0.331868 | + | 0.943326i | \(0.607679\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 1527.35i | − 2.29677i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 540.000i | 0.809595i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.0000 | −0.0742942 | −0.0371471 | − | 0.999310i | \(-0.511827\pi\) | ||||
−0.0371471 | + | 0.999310i | \(0.511827\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 169.015 | 0.249653 | 0.124826 | − | 0.992179i | \(-0.460163\pi\) | ||||
0.124826 | + | 0.992179i | \(0.460163\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −415.692 | −0.612212 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.4264 | 0.0621177 | 0.0310589 | − | 0.999518i | \(-0.490112\pi\) | ||||
0.0310589 | + | 0.999518i | \(0.490112\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 779.423i | 1.13784i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 381.838i | 0.554191i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 400.000i | 0.578871i | 0.957197 | + | 0.289436i | \(0.0934676\pi\) | ||||
−0.957197 | + | 0.289436i | \(0.906532\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1263.94i | − 1.81861i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1530.00 | −2.19512 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −992.043 | −1.41518 | −0.707592 | − | 0.706622i | \(-0.750218\pi\) | ||||
−0.707592 | + | 0.706622i | \(0.750218\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 831.384 | 1.18262 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1909.19 | −2.70041 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1195.12i | − 1.68563i | −0.538200 | − | 0.842817i | \(-0.680895\pi\) | ||||
0.538200 | − | 0.842817i | \(-0.319105\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 763.675i | 1.07107i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 648.000i | 0.906294i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 661.362i | − 0.919836i | −0.887961 | − | 0.459918i | \(-0.847879\pi\) | ||||
0.887961 | − | 0.459918i | \(-0.152121\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −972.000 | −1.34813 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1065.53 | 1.46969 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 93.5307 | 0.128653 | 0.0643265 | − | 0.997929i | \(-0.479510\pi\) | ||||
0.0643265 | + | 0.997929i | \(0.479510\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 848.528 | 1.16078 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 613.146i | 0.836488i | 0.908335 | + | 0.418244i | \(0.137354\pi\) | ||||
−0.908335 | + | 0.418244i | \(0.862646\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 848.528i | − 1.15133i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 920.000i | 1.24493i | 0.782649 | + | 0.622463i | \(0.213868\pi\) | ||||
−0.782649 | + | 0.622463i | \(0.786132\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1175.76i | 1.58244i | 0.611530 | + | 0.791221i | \(0.290554\pi\) | ||||
−0.611530 | + | 0.791221i | \(0.709446\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 810.000 | 1.08725 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1763.63 | 2.35465 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.9615 | 0.0691898 | 0.0345949 | − | 0.999401i | \(-0.488986\pi\) | ||||
0.0345949 | + | 0.999401i | \(0.488986\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1145.51 | −1.51724 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 405.300i | − 0.535403i | −0.963502 | − | 0.267701i | \(-0.913736\pi\) | ||||
0.963502 | − | 0.267701i | \(-0.0862641\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 1030.96i | − 1.35475i | −0.735640 | − | 0.677373i | \(-0.763118\pi\) | ||||
0.735640 | − | 0.677373i | \(-0.236882\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 540.000i | − 0.707733i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 352.727i | − 0.459878i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 890.000 | 1.15735 | 0.578674 | − | 0.815559i | \(-0.303571\pi\) | ||||
0.578674 | + | 0.815559i | \(0.303571\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 933.256 | 1.20732 | 0.603658 | − | 0.797243i | \(-0.293709\pi\) | ||||
0.603658 | + | 0.797243i | \(0.293709\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1506.88 | 1.94437 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1442.50 | 1.85173 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 623.538i | 0.798384i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 1221.88i | − 1.55654i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 100.000i | 0.127065i | 0.997980 | + | 0.0635324i | \(0.0202366\pi\) | ||||
−0.997980 | + | 0.0635324i | \(0.979763\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 661.362i | 0.836109i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −404.166 | −0.507109 | −0.253554 | − | 0.967321i | \(-0.581600\pi\) | ||||
−0.253554 | + | 0.967321i | \(0.581600\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1558.85 | 1.95100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 169.706 | 0.211340 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1122.37i | 1.39425i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1090.36i | 1.34779i | 0.738829 | + | 0.673893i | \(0.235379\pi\) | ||||
−0.738829 | + | 0.673893i | \(0.764621\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 772.000i | − 0.951911i | −0.879469 | − | 0.475956i | \(-0.842102\pi\) | ||||
0.879469 | − | 0.475956i | \(-0.157898\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1175.76i | − 1.44264i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −800.000 | −0.979192 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 477.650 | 0.581791 | 0.290896 | − | 0.956755i | \(-0.406047\pi\) | ||||
0.290896 | + | 0.956755i | \(0.406047\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1132.76 | −1.37638 | −0.688190 | − | 0.725530i | \(-0.741595\pi\) | ||||
−0.688190 | + | 0.725530i | \(0.741595\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −763.675 | −0.923428 | −0.461714 | − | 0.887029i | \(-0.652765\pi\) | ||||
−0.461714 | + | 0.887029i | \(0.652765\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 363.731i | − 0.438758i | −0.975640 | − | 0.219379i | \(-0.929597\pi\) | ||||
0.975640 | − | 0.219379i | \(-0.0704032\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1251.58i | 1.50250i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 432.000i | 0.517365i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 808.332i | 0.963447i | 0.876323 | + | 0.481723i | \(0.159989\pi\) | ||||
−0.876323 | + | 0.481723i | \(0.840011\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 509.000 | 0.605232 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −448.257 | −0.530481 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 509.223 | 0.601208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −610.940 | −0.717909 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 997.661i | − 1.16959i | −0.811181 | − | 0.584796i | \(-0.801175\pi\) | ||||
0.811181 | − | 0.584796i | \(-0.198825\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 572.756i | − 0.668327i | −0.942515 | − | 0.334164i | \(-0.891546\pi\) | ||||
0.942515 | − | 0.334164i | \(-0.108454\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 568.000i | − 0.661234i | −0.943765 | − | 0.330617i | \(-0.892743\pi\) | ||||
0.943765 | − | 0.330617i | \(-0.107257\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 823.029i | 0.953683i | 0.878989 | + | 0.476842i | \(0.158218\pi\) | ||||
−0.878989 | + | 0.476842i | \(0.841782\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −270.000 | −0.312139 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −440.908 | −0.507374 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1039.23 | −1.19315 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 305.470 | 0.349109 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.5692i | 0.0473993i | 0.999719 | + | 0.0236997i | \(0.00754455\pi\) | ||||
−0.999719 | + | 0.0236997i | \(0.992455\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.7279i | 0.0144471i | 0.999974 | + | 0.00722357i | \(0.00229935\pi\) | ||||
−0.999974 | + | 0.00722357i | \(0.997701\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 520.000i | 0.588901i | 0.955667 | + | 0.294451i | \(0.0951367\pi\) | ||||
−0.955667 | + | 0.294451i | \(0.904863\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 88.1816i | 0.0994156i | 0.998764 | + | 0.0497078i | \(0.0158290\pi\) | ||||
−0.998764 | + | 0.0497078i | \(0.984171\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −108.000 | −0.121485 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1469.69 | −1.64579 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −374.123 | −0.418014 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1909.19 | 2.12368 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 779.423i | − 0.865064i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1909.19i | 2.10960i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 40.0000i | − 0.0441014i | −0.999757 | − | 0.0220507i | \(-0.992980\pi\) | ||||
0.999757 | − | 0.0220507i | \(-0.00701953\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1175.76i | − 1.29062i | −0.763921 | − | 0.645310i | \(-0.776728\pi\) | ||||
0.763921 | − | 0.645310i | \(-0.223272\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1080.00 | 1.18291 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −529.090 | −0.576979 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1714.73 | −1.86587 | −0.932933 | − | 0.360051i | \(-0.882759\pi\) | ||||
−0.932933 | + | 0.360051i | \(0.882759\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 763.675 | 0.827384 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1205.51i | 1.30325i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1412.80i | 1.52077i | 0.649470 | + | 0.760387i | \(0.274991\pi\) | ||||
−0.649470 | + | 0.760387i | \(0.725009\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1180.00i | − 1.26745i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 1322.72i | − 1.41468i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −470.000 | −0.501601 | −0.250800 | − | 0.968039i | \(-0.580694\pi\) | ||||
−0.250800 | + | 0.968039i | \(0.580694\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −624.620 | −0.663783 | −0.331892 | − | 0.943318i | \(-0.607687\pi\) | ||||
−0.331892 | + | 0.943318i | \(0.607687\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1060.02 | −1.12409 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −339.411 | −0.358407 | −0.179203 | − | 0.983812i | \(-0.557352\pi\) | ||||
−0.179203 | + | 0.983812i | \(0.557352\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 207.846i | − 0.219016i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 530.330i | − 0.556485i | −0.960511 | − | 0.278242i | \(-0.910248\pi\) | ||||
0.960511 | − | 0.278242i | \(-0.0897519\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 2160.00i | − 2.26178i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1102.27i | 1.14940i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1739.00 | 1.80957 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 73.4847 | 0.0761499 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1028.84 | −1.06395 | −0.531974 | − | 0.846761i | \(-0.678550\pi\) | ||||
−0.531974 | + | 0.846761i | \(0.678550\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1603.72 | 1.65162 | 0.825808 | − | 0.563952i | \(-0.190720\pi\) | ||||
0.825808 | + | 0.563952i | \(0.190720\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1787.48i | − 1.83708i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 1378.86i | − 1.41132i | −0.708551 | − | 0.705659i | \(-0.750651\pi\) | ||||
0.708551 | − | 0.705659i | \(-0.249349\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 108.000i | 0.110317i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 440.908i | 0.448533i | 0.974528 | + | 0.224267i | \(0.0719986\pi\) | ||||
−0.974528 | + | 0.224267i | \(0.928001\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 162.000 | 0.164467 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 587.878 | 0.594416 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 467.654 | 0.471901 | 0.235950 | − | 0.971765i | \(-0.424180\pi\) | ||||
0.235950 | + | 0.971765i | \(0.424180\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −381.838 | −0.383756 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 249.415i | 0.250166i | 0.992146 | + | 0.125083i | \(0.0399197\pi\) | ||||
−0.992146 | + | 0.125083i | \(0.960080\pi\) | |||||||
\(998\) | 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 | 576.3.h.b.161.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 576.3.h.b.161.5 | yes | 8 | |
4.3 | odd | 2 | inner | 576.3.h.b.161.3 | yes | 8 | |
8.3 | odd | 2 | inner | 576.3.h.b.161.8 | yes | 8 | |
8.5 | even | 2 | inner | 576.3.h.b.161.6 | yes | 8 | |
12.11 | even | 2 | inner | 576.3.h.b.161.7 | yes | 8 | |
16.3 | odd | 4 | 2304.3.e.g.1025.3 | 4 | |||
16.5 | even | 4 | 2304.3.e.g.1025.2 | 4 | |||
16.11 | odd | 4 | 2304.3.e.j.1025.1 | 4 | |||
16.13 | even | 4 | 2304.3.e.j.1025.4 | 4 | |||
24.5 | odd | 2 | inner | 576.3.h.b.161.2 | yes | 8 | |
24.11 | even | 2 | inner | 576.3.h.b.161.4 | yes | 8 | |
48.5 | odd | 4 | 2304.3.e.g.1025.4 | 4 | |||
48.11 | even | 4 | 2304.3.e.j.1025.3 | 4 | |||
48.29 | odd | 4 | 2304.3.e.j.1025.2 | 4 | |||
48.35 | even | 4 | 2304.3.e.g.1025.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.3.h.b.161.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
576.3.h.b.161.2 | yes | 8 | 24.5 | odd | 2 | inner | |
576.3.h.b.161.3 | yes | 8 | 4.3 | odd | 2 | inner | |
576.3.h.b.161.4 | yes | 8 | 24.11 | even | 2 | inner | |
576.3.h.b.161.5 | yes | 8 | 3.2 | odd | 2 | inner | |
576.3.h.b.161.6 | yes | 8 | 8.5 | even | 2 | inner | |
576.3.h.b.161.7 | yes | 8 | 12.11 | even | 2 | inner | |
576.3.h.b.161.8 | yes | 8 | 8.3 | odd | 2 | inner | |
2304.3.e.g.1025.1 | 4 | 48.35 | even | 4 | |||
2304.3.e.g.1025.2 | 4 | 16.5 | even | 4 | |||
2304.3.e.g.1025.3 | 4 | 16.3 | odd | 4 | |||
2304.3.e.g.1025.4 | 4 | 48.5 | odd | 4 | |||
2304.3.e.j.1025.1 | 4 | 16.11 | odd | 4 | |||
2304.3.e.j.1025.2 | 4 | 48.29 | odd | 4 | |||
2304.3.e.j.1025.3 | 4 | 48.11 | even | 4 | |||
2304.3.e.j.1025.4 | 4 | 16.13 | even | 4 |