Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(2015,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.2015");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2015.17 | ||
Character | \(\chi\) | \(=\) | 2736.2015 |
Dual form | 2736.2.d.b.2015.8 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.03314i | 0.909250i | 0.890683 | + | 0.454625i | \(0.150227\pi\) | ||||
−0.890683 | + | 0.454625i | \(0.849773\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 3.00897i | − 1.13729i | −0.822585 | − | 0.568643i | \(-0.807469\pi\) | ||||
0.822585 | − | 0.568643i | \(-0.192531\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.39868 | −1.32625 | −0.663126 | − | 0.748508i | \(-0.730771\pi\) | ||||
−0.663126 | + | 0.748508i | \(0.730771\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.79346 | 1.32947 | 0.664733 | − | 0.747081i | \(-0.268545\pi\) | ||||
0.664733 | + | 0.747081i | \(0.268545\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.70773i | 0.656721i | 0.944553 | + | 0.328360i | \(0.106496\pi\) | ||||
−0.944553 | + | 0.328360i | \(0.893504\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.00000i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.06706 | −0.222498 | −0.111249 | − | 0.993793i | \(-0.535485\pi\) | ||||
−0.111249 | + | 0.993793i | \(0.535485\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.866325 | 0.173265 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.56438i | 0.476194i | 0.971241 | + | 0.238097i | \(0.0765236\pi\) | ||||
−0.971241 | + | 0.238097i | \(0.923476\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.28336i | 0.410104i | 0.978751 | + | 0.205052i | \(0.0657364\pi\) | ||||
−0.978751 | + | 0.205052i | \(0.934264\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.11768 | 1.03408 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.52611 | 0.744088 | 0.372044 | − | 0.928215i | \(-0.378657\pi\) | ||||
0.372044 | + | 0.928215i | \(0.378657\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 2.51222i | − 0.392342i | −0.980570 | − | 0.196171i | \(-0.937149\pi\) | ||||
0.980570 | − | 0.196171i | \(-0.0628508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.98914i | 0.608338i | 0.952618 | + | 0.304169i | \(0.0983788\pi\) | ||||
−0.952618 | + | 0.304169i | \(0.901621\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.12272 | 0.163765 | 0.0818826 | − | 0.996642i | \(-0.473907\pi\) | ||||
0.0818826 | + | 0.996642i | \(0.473907\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.05393 | −0.293418 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 6.72681i | − 0.923998i | −0.886881 | − | 0.461999i | \(-0.847132\pi\) | ||||
0.886881 | − | 0.461999i | \(-0.152868\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 8.94315i | − 1.20589i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.15876 | 0.931991 | 0.465996 | − | 0.884787i | \(-0.345696\pi\) | ||||
0.465996 | + | 0.884787i | \(0.345696\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.9611 | 1.65950 | 0.829749 | − | 0.558136i | \(-0.188483\pi\) | ||||
0.829749 | + | 0.558136i | \(0.188483\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.74579i | 1.20882i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.75060i | 0.213870i | 0.994266 | + | 0.106935i | \(0.0341036\pi\) | ||||
−0.994266 | + | 0.106935i | \(0.965896\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.70842 | 0.558787 | 0.279393 | − | 0.960177i | \(-0.409867\pi\) | ||||
0.279393 | + | 0.960177i | \(0.409867\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.322316 | −0.0377243 | −0.0188621 | − | 0.999822i | \(-0.506004\pi\) | ||||
−0.0188621 | + | 0.999822i | \(0.506004\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.2355i | 1.50833i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.71440i | 0.305394i | 0.988273 | + | 0.152697i | \(0.0487958\pi\) | ||||
−0.988273 | + | 0.152697i | \(0.951204\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.57724 | 0.721946 | 0.360973 | − | 0.932576i | \(-0.382445\pi\) | ||||
0.360973 | + | 0.932576i | \(0.382445\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.50520 | −0.597123 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 3.49594i | − 0.370569i | −0.982685 | − | 0.185285i | \(-0.940679\pi\) | ||||
0.982685 | − | 0.185285i | \(-0.0593207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 14.4234i | − 1.51198i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.03314 | 0.208596 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.69074 | −0.882411 | −0.441206 | − | 0.897406i | \(-0.645449\pi\) | ||||
−0.441206 | + | 0.897406i | \(0.645449\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.4577i | 1.53810i | 0.639189 | + | 0.769049i | \(0.279270\pi\) | ||||
−0.639189 | + | 0.769049i | \(0.720730\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 2.44705i | − 0.241115i | −0.992706 | − | 0.120557i | \(-0.961532\pi\) | ||||
0.992706 | − | 0.120557i | \(-0.0384682\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.7807 | 1.52558 | 0.762791 | − | 0.646646i | \(-0.223829\pi\) | ||||
0.762791 | + | 0.646646i | \(0.223829\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.0071 | 1.43742 | 0.718711 | − | 0.695309i | \(-0.244733\pi\) | ||||
0.718711 | + | 0.695309i | \(0.244733\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.11357i | 0.857333i | 0.903463 | + | 0.428666i | \(0.141016\pi\) | ||||
−0.903463 | + | 0.428666i | \(0.858984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.16949i | − 0.202306i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.14749 | 0.746879 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.34838 | 0.758943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.9271i | 1.06679i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 17.7108i | − 1.57158i | −0.618495 | − | 0.785789i | \(-0.712257\pi\) | ||||
0.618495 | − | 0.785789i | \(-0.287743\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.6503 | 1.01790 | 0.508948 | − | 0.860797i | \(-0.330035\pi\) | ||||
0.508948 | + | 0.860797i | \(0.330035\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00897 | −0.260911 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.35138i | 0.286327i | 0.989699 | + | 0.143164i | \(0.0457275\pi\) | ||||
−0.989699 | + | 0.143164i | \(0.954272\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.81965i | 0.154340i | 0.997018 | + | 0.0771702i | \(0.0245885\pi\) | ||||
−0.997018 | + | 0.0771702i | \(0.975412\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.0849 | −1.76321 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.21376 | −0.432979 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.8578i | 1.95451i | 0.212073 | + | 0.977254i | \(0.431979\pi\) | ||||
−0.212073 | + | 0.977254i | \(0.568021\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.7987i | 1.20430i | 0.798381 | + | 0.602152i | \(0.205690\pi\) | ||||
−0.798381 | + | 0.602152i | \(0.794310\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.64241 | −0.372887 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.5569 | −1.08196 | −0.540979 | − | 0.841036i | \(-0.681946\pi\) | ||||
−0.540979 | + | 0.841036i | \(0.681946\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.21077i | 0.253044i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.64350i | 0.363707i | 0.983326 | + | 0.181853i | \(0.0582096\pi\) | ||||
−0.983326 | + | 0.181853i | \(0.941790\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.54323 | −0.661095 | −0.330547 | − | 0.943789i | \(-0.607233\pi\) | ||||
−0.330547 | + | 0.943789i | \(0.607233\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.97724 | 0.767480 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 13.9082i | − 1.05742i | −0.848802 | − | 0.528711i | \(-0.822676\pi\) | ||||
0.848802 | − | 0.528711i | \(-0.177324\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 2.60675i | − 0.197052i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.9649 | 1.71648 | 0.858238 | − | 0.513252i | \(-0.171559\pi\) | ||||
0.858238 | + | 0.513252i | \(0.171559\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.5023 | −1.07795 | −0.538974 | − | 0.842322i | \(-0.681188\pi\) | ||||
−0.538974 | + | 0.842322i | \(0.681188\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.20223i | 0.676561i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 11.9104i | − 0.870977i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.6862 | −1.93095 | −0.965474 | − | 0.260499i | \(-0.916113\pi\) | ||||
−0.965474 | + | 0.260499i | \(0.916113\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.0859 | 1.73374 | 0.866870 | − | 0.498535i | \(-0.166128\pi\) | ||||
0.866870 | + | 0.498535i | \(0.166128\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 14.5502i | − 1.03666i | −0.855181 | − | 0.518329i | \(-0.826554\pi\) | ||||
0.855181 | − | 0.518329i | \(-0.173446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.04572i | 0.215905i | 0.994156 | + | 0.107953i | \(0.0344295\pi\) | ||||
−0.994156 | + | 0.107953i | \(0.965571\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.71616 | 0.541569 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.10769 | 0.356737 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.39868i | 0.304263i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.5472i | 0.794945i | 0.917614 | + | 0.397473i | \(0.130113\pi\) | ||||
−0.917614 | + | 0.397473i | \(0.869887\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.11050 | −0.553131 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.87059 | 0.466406 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.9794i | 0.873088i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.5633i | 1.97970i | 0.142107 | + | 0.989851i | \(0.454612\pi\) | ||||
−0.142107 | + | 0.989851i | \(0.545388\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.6363 | 0.838701 | 0.419350 | − | 0.907825i | \(-0.362258\pi\) | ||||
0.419350 | + | 0.907825i | \(0.362258\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.6361 | 1.09935 | 0.549673 | − | 0.835380i | \(-0.314752\pi\) | ||||
0.549673 | + | 0.835380i | \(0.314752\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 6.92402i | − 0.453607i | −0.973940 | − | 0.226804i | \(-0.927172\pi\) | ||||
0.973940 | − | 0.226804i | \(-0.0728276\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.28265i | 0.148903i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.36426 | −0.476354 | −0.238177 | − | 0.971222i | \(-0.576550\pi\) | ||||
−0.238177 | + | 0.971222i | \(0.576550\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.9442 | 0.769392 | 0.384696 | − | 0.923043i | \(-0.374306\pi\) | ||||
0.384696 | + | 0.923043i | \(0.374306\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 4.17593i | − 0.266790i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4.79346i | − 0.305000i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.53492 | −0.601839 | −0.300919 | − | 0.953650i | \(-0.597293\pi\) | ||||
−0.300919 | + | 0.953650i | \(0.597293\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.69367 | 0.295088 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 1.58370i | − 0.0987882i | −0.998779 | − | 0.0493941i | \(-0.984271\pi\) | ||||
0.998779 | − | 0.0493941i | \(-0.0157290\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 13.6189i | − 0.846240i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.4030 | 1.19644 | 0.598221 | − | 0.801331i | \(-0.295874\pi\) | ||||
0.598221 | + | 0.801331i | \(0.295874\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.6766 | 0.840145 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 9.26187i | − 0.564706i | −0.959311 | − | 0.282353i | \(-0.908885\pi\) | ||||
0.959311 | − | 0.282353i | \(-0.0911150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.3507i | 0.810995i | 0.914096 | + | 0.405497i | \(0.132902\pi\) | ||||
−0.914096 | + | 0.405497i | \(0.867098\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.81069 | −0.229793 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.9813 | −0.840054 | −0.420027 | − | 0.907512i | \(-0.637979\pi\) | ||||
−0.420027 | + | 0.907512i | \(0.637979\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 27.4391i | − 1.63688i | −0.574593 | − | 0.818439i | \(-0.694840\pi\) | ||||
0.574593 | − | 0.818439i | \(-0.305160\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 29.1181i | − 1.73089i | −0.501001 | − | 0.865446i | \(-0.667035\pi\) | ||||
0.501001 | − | 0.865446i | \(-0.332965\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.55919 | −0.446205 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.66820 | 0.568718 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 5.85015i | − 0.341769i | −0.985291 | − | 0.170885i | \(-0.945337\pi\) | ||||
0.985291 | − | 0.170885i | \(-0.0546625\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.5548i | 0.847413i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.11492 | −0.295804 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0032 | 0.691854 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.3518i | 1.50890i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 32.8827i | − 1.87671i | −0.345668 | − | 0.938357i | \(-0.612348\pi\) | ||||
0.345668 | − | 0.938357i | \(-0.387652\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.4253 | 0.704575 | 0.352288 | − | 0.935892i | \(-0.385404\pi\) | ||||
0.352288 | + | 0.935892i | \(0.385404\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.1767 | −1.81874 | −0.909368 | − | 0.415993i | \(-0.863434\pi\) | ||||
−0.909368 | + | 0.415993i | \(0.863434\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.93547i | 0.277204i | 0.990348 | + | 0.138602i | \(0.0442608\pi\) | ||||
−0.990348 | + | 0.138602i | \(0.955739\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 11.2799i | − 0.631553i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.70773 | 0.150662 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.15269 | 0.230350 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 3.37823i | − 0.186248i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 5.18147i | − 0.284799i | −0.989809 | − | 0.142400i | \(-0.954518\pi\) | ||||
0.989809 | − | 0.142400i | \(-0.0454818\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.55922 | −0.194461 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.6071 | 1.12254 | 0.561270 | − | 0.827633i | \(-0.310313\pi\) | ||||
0.561270 | + | 0.827633i | \(0.310313\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 10.0438i | − 0.543902i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 14.8826i | − 0.803585i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.6179 | 1.37524 | 0.687621 | − | 0.726070i | \(-0.258655\pi\) | ||||
0.687621 | + | 0.726070i | \(0.258655\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.9243 | −1.17358 | −0.586789 | − | 0.809740i | \(-0.699608\pi\) | ||||
−0.586789 | + | 0.809740i | \(0.699608\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.5098i | 0.931950i | 0.884798 | + | 0.465975i | \(0.154296\pi\) | ||||
−0.884798 | + | 0.465975i | \(0.845704\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.57290i | 0.508077i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.33437 | 0.387094 | 0.193547 | − | 0.981091i | \(-0.438001\pi\) | ||||
0.193547 | + | 0.981091i | \(0.438001\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 0.655315i | − 0.0343008i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.78728i | 0.510892i | 0.966823 | + | 0.255446i | \(0.0822223\pi\) | ||||
−0.966823 | + | 0.255446i | \(0.917778\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.2408 | −1.05085 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.1684 | −0.785390 | −0.392695 | − | 0.919669i | \(-0.628457\pi\) | ||||
−0.392695 | + | 0.919669i | \(0.628457\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.2923i | 0.633084i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 3.14950i | − 0.161779i | −0.996723 | − | 0.0808896i | \(-0.974224\pi\) | ||||
0.996723 | − | 0.0808896i | \(-0.0257761\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.9070 | −0.659517 | −0.329759 | − | 0.944065i | \(-0.606967\pi\) | ||||
−0.329759 | + | 0.944065i | \(0.606967\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.9097 | −1.37145 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 29.7262i | − 1.50718i | −0.657347 | − | 0.753588i | \(-0.728321\pi\) | ||||
0.657347 | − | 0.753588i | \(-0.271679\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 2.88932i | − 0.146119i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.51876 | −0.277679 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.0678479 | 0.00340519 | 0.00170259 | − | 0.999999i | \(-0.499458\pi\) | ||||
0.00170259 | + | 0.999999i | \(0.499458\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 28.2624i | − 1.41135i | −0.708533 | − | 0.705677i | \(-0.750643\pi\) | ||||
0.708533 | − | 0.705677i | \(-0.249357\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.9452i | 0.545220i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.9089 | −0.986847 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.96033 | −0.195826 | −0.0979129 | − | 0.995195i | \(-0.531217\pi\) | ||||
−0.0979129 | + | 0.995195i | \(0.531217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 21.5405i | − 1.05994i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.3725i | 0.656429i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.1752 | 0.741355 | 0.370678 | − | 0.928762i | \(-0.379125\pi\) | ||||
0.370678 | + | 0.928762i | \(0.379125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.5641 | −1.19718 | −0.598592 | − | 0.801054i | \(-0.704273\pi\) | ||||
−0.598592 | + | 0.801054i | \(0.704273\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.34577i | 0.113787i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 38.9996i | − 1.88732i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.6482 | −1.33177 | −0.665884 | − | 0.746056i | \(-0.731945\pi\) | ||||
−0.665884 | + | 0.746056i | \(0.731945\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.6176 | −1.61556 | −0.807779 | − | 0.589486i | \(-0.799330\pi\) | ||||
−0.807779 | + | 0.589486i | \(0.799330\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.06706i | 0.0510445i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.4454i | 1.64399i | 0.569497 | + | 0.821994i | \(0.307138\pi\) | ||||
−0.569497 | + | 0.821994i | \(0.692862\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.8632 | 0.658662 | 0.329331 | − | 0.944214i | \(-0.393177\pi\) | ||||
0.329331 | + | 0.944214i | \(0.393177\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.10776 | 0.336940 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 15.7089i | − 0.741351i | −0.928762 | − | 0.370675i | \(-0.879126\pi\) | ||||
0.928762 | − | 0.370675i | \(-0.120874\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.0504i | 0.520344i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 29.3248 | 1.37477 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.23978 | −0.338663 | −0.169331 | − | 0.985559i | \(-0.554161\pi\) | ||||
−0.169331 | + | 0.985559i | \(0.554161\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 19.4060i | − 0.903826i | −0.892062 | − | 0.451913i | \(-0.850742\pi\) | ||||
0.892062 | − | 0.451913i | \(-0.149258\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 8.30741i | − 0.386078i | −0.981191 | − | 0.193039i | \(-0.938166\pi\) | ||||
0.981191 | − | 0.193039i | \(-0.0618344\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.2788 | −1.53996 | −0.769980 | − | 0.638068i | \(-0.779734\pi\) | ||||
−0.769980 | + | 0.638068i | \(0.779734\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.26751 | 0.243231 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 17.5469i | − 0.806809i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 0.866325i | − 0.0397497i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.7480 | 0.765237 | 0.382618 | − | 0.923906i | \(-0.375022\pi\) | ||||
0.382618 | + | 0.923906i | \(0.375022\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.6957 | 0.989239 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 17.6695i | − 0.802332i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.0304i | 0.681090i | 0.940228 | + | 0.340545i | \(0.110612\pi\) | ||||
−0.940228 | + | 0.340545i | \(0.889388\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.7982 | −1.38990 | −0.694951 | − | 0.719057i | \(-0.744574\pi\) | ||||
−0.694951 | + | 0.719057i | \(0.744574\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.94366 | −0.312727 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 14.1675i | − 0.635500i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.5272i | 1.05322i | 0.850106 | + | 0.526612i | \(0.176538\pi\) | ||||
−0.850106 | + | 0.526612i | \(0.823462\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.2951 | −1.03868 | −0.519338 | − | 0.854569i | \(-0.673822\pi\) | ||||
−0.519338 | + | 0.854569i | \(0.673822\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.4277 | −1.39852 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.08852i | − 0.0482478i | −0.999709 | − | 0.0241239i | \(-0.992320\pi\) | ||||
0.999709 | − | 0.0241239i | \(-0.00767962\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.969841i | 0.0429032i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.97520 | 0.219234 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.93848 | −0.217194 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.0616i | 1.40464i | 0.711860 | + | 0.702322i | \(0.247853\pi\) | ||||
−0.711860 | + | 0.702322i | \(0.752147\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.5989i | 1.60036i | 0.599761 | + | 0.800179i | \(0.295262\pi\) | ||||
−0.599761 | + | 0.800179i | \(0.704738\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.18273 | −0.269324 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.8614 | −0.950495 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 12.0422i | − 0.521605i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.0845i | 1.38713i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.03457 | 0.389146 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.53331 | −0.194902 | −0.0974511 | − | 0.995240i | \(-0.531069\pi\) | ||||
−0.0974511 | + | 0.995240i | \(0.531069\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.5116i | 1.30697i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.16144i | 0.0496598i | 0.999692 | + | 0.0248299i | \(0.00790441\pi\) | ||||
−0.999692 | + | 0.0248299i | \(0.992096\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.56438 | 0.109246 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.16755 | 0.347320 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.2062i | 1.19514i | 0.801818 | + | 0.597568i | \(0.203866\pi\) | ||||
−0.801818 | + | 0.597568i | \(0.796134\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.1218i | 0.808765i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.8312 | −0.962221 | −0.481111 | − | 0.876660i | \(-0.659766\pi\) | ||||
−0.481111 | + | 0.876660i | \(0.659766\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.5292 | −0.779529 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 27.5857i | − 1.15645i | −0.815877 | − | 0.578226i | \(-0.803745\pi\) | ||||
0.815877 | − | 0.578226i | \(-0.196255\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 0.702859i | − 0.0294137i | −0.999892 | − | 0.0147069i | \(-0.995318\pi\) | ||||
0.999892 | − | 0.0147069i | \(-0.00468151\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.924424 | −0.0385511 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.7000 | 0.778490 | 0.389245 | − | 0.921134i | \(-0.372736\pi\) | ||||
0.389245 | + | 0.921134i | \(0.372736\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 19.7907i | − 0.821058i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.5891i | 1.22545i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.8797 | 1.48091 | 0.740457 | − | 0.672104i | \(-0.234609\pi\) | ||||
0.740457 | + | 0.672104i | \(0.234609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.28336 | 0.0940844 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 37.3570i | − 1.53407i | −0.641607 | − | 0.767034i | \(-0.721732\pi\) | ||||
0.641607 | − | 0.767034i | \(-0.278268\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.5650i | 0.679100i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.4528 | −1.24427 | −0.622134 | − | 0.782911i | \(-0.713734\pi\) | ||||
−0.622134 | + | 0.782911i | \(0.713734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.96592 | −0.161773 | −0.0808866 | − | 0.996723i | \(-0.525775\pi\) | ||||
−0.0808866 | + | 0.996723i | \(0.525775\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.9735i | 0.690069i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.01627i | 0.0818380i | 0.999162 | + | 0.0409190i | \(0.0130286\pi\) | ||||
−0.999162 | + | 0.0409190i | \(0.986971\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.38170 | 0.217720 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.3109 | 1.58775 | 0.793876 | − | 0.608080i | \(-0.208060\pi\) | ||||
0.793876 | + | 0.608080i | \(0.208060\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 5.59842i | − 0.225384i | −0.993630 | − | 0.112692i | \(-0.964053\pi\) | ||||
0.993630 | − | 0.112692i | \(-0.0359473\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 43.5734i | − 1.75136i | −0.482888 | − | 0.875682i | \(-0.660412\pi\) | ||||
0.482888 | − | 0.875682i | \(-0.339588\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.5192 | −0.421443 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.9179 | −0.796714 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.2555i | 0.488658i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 12.3862i | − 0.493085i | −0.969132 | − | 0.246543i | \(-0.920705\pi\) | ||||
0.969132 | − | 0.246543i | \(-0.0792945\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36.0086 | 1.42896 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.84542 | −0.390090 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.1951i | 1.42962i | 0.699319 | + | 0.714810i | \(0.253487\pi\) | ||||
−0.699319 | + | 0.714810i | \(0.746513\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 20.8723i | − 0.823121i | −0.911382 | − | 0.411561i | \(-0.864984\pi\) | ||||
0.911382 | − | 0.411561i | \(-0.135016\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.59359 | −0.180593 | −0.0902964 | − | 0.995915i | \(-0.528781\pi\) | ||||
−0.0902964 | + | 0.995915i | \(0.528781\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.4891 | −1.23605 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 24.4420i | − 0.956490i | −0.878226 | − | 0.478245i | \(-0.841273\pi\) | ||||
0.878226 | − | 0.478245i | \(-0.158727\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.6868i | 0.925521i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −50.0946 | −1.95141 | −0.975704 | − | 0.219091i | \(-0.929691\pi\) | ||||
−0.975704 | + | 0.219091i | \(0.929691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.80962 | 0.187072 | 0.0935362 | − | 0.995616i | \(-0.470183\pi\) | ||||
0.0935362 | + | 0.995616i | \(0.470183\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 6.11768i | − 0.237233i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.73636i | − 0.105952i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −57.0117 | −2.20091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.5173 | −0.559599 | −0.279800 | − | 0.960058i | \(-0.590268\pi\) | ||||
−0.279800 | + | 0.960058i | \(0.590268\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.87263i | 0.148837i | 0.997227 | + | 0.0744186i | \(0.0237101\pi\) | ||||
−0.997227 | + | 0.0744186i | \(0.976290\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.1502i | 1.00355i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.1199 | 1.07598 | 0.537989 | − | 0.842952i | \(-0.319184\pi\) | ||||
0.537989 | + | 0.842952i | \(0.319184\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.81383 | −0.260343 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 32.2447i | − 1.22842i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.9629i | 1.13984i | 0.821699 | + | 0.569922i | \(0.193027\pi\) | ||||
−0.821699 | + | 0.569922i | \(0.806973\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.69961 | −0.140334 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.80240 | 0.257659 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.5634i | 0.512281i | 0.966640 | + | 0.256141i | \(0.0824510\pi\) | ||||
−0.966640 | + | 0.256141i | \(0.917549\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 4.52611i | − 0.170705i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 46.5118 | 1.74926 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.5749 | −0.397148 | −0.198574 | − | 0.980086i | \(-0.563631\pi\) | ||||
−0.198574 | + | 0.980086i | \(0.563631\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 2.43649i | − 0.0912474i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 42.8686i | − 1.60319i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −50.6671 | −1.88956 | −0.944781 | − | 0.327701i | \(-0.893726\pi\) | ||||
−0.944781 | + | 0.327701i | \(0.893726\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.36310 | −0.274216 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.22159i | 0.0825078i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 17.7169i | − 0.657083i | −0.944490 | − | 0.328541i | \(-0.893443\pi\) | ||||
0.944490 | − | 0.328541i | \(-0.106557\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.8015 | −0.399508 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.76075 | 0.286650 | 0.143325 | − | 0.989676i | \(-0.454221\pi\) | ||||
0.143325 | + | 0.989676i | \(0.454221\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 7.70033i | − 0.283645i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.60803i | 0.0591525i | 0.999563 | + | 0.0295762i | \(0.00941578\pi\) | ||||
−0.999563 | + | 0.0295762i | \(0.990584\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.1992 | −1.62151 | −0.810756 | − | 0.585385i | \(-0.800943\pi\) | ||||
−0.810756 | + | 0.585385i | \(0.800943\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −48.5064 | −1.77714 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 47.4838i | − 1.73502i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 38.2523i | − 1.39585i | −0.716172 | − | 0.697924i | \(-0.754107\pi\) | ||||
0.716172 | − | 0.697924i | \(-0.245893\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −30.0880 | −1.09501 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.1231 | 1.49464 | 0.747322 | − | 0.664462i | \(-0.231339\pi\) | ||||
0.747322 | + | 0.664462i | \(0.231339\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 22.5026i | − 0.815718i | −0.913045 | − | 0.407859i | \(-0.866275\pi\) | ||||
0.913045 | − | 0.407859i | \(-0.133725\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 45.1560i | − 1.63476i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.3152 | 1.23905 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.33370 | −0.120216 | −0.0601082 | − | 0.998192i | \(-0.519145\pi\) | ||||
−0.0601082 | + | 0.998192i | \(0.519145\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.88156i | 0.139610i | 0.997561 | + | 0.0698050i | \(0.0222377\pi\) | ||||
−0.997561 | + | 0.0698050i | \(0.977762\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.97814i | 0.0710568i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.51222 | −0.0900094 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.7108 | −0.741092 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 27.5631i | − 0.983770i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 6.07170i | − 0.216433i | −0.994127 | − | 0.108216i | \(-0.965486\pi\) | ||||
0.994127 | − | 0.108216i | \(-0.0345139\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.4225 | 0.975032 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 62.1285 | 2.20625 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 19.4601i | − 0.689313i | −0.938729 | − | 0.344657i | \(-0.887995\pi\) | ||||
0.938729 | − | 0.344657i | \(-0.112005\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.04002i | 0.107548i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.41777 | 0.0500318 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.52795 | −0.230080 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 46.5669i | − 1.63721i | −0.574360 | − | 0.818603i | \(-0.694749\pi\) | ||||
0.574360 | − | 0.818603i | \(-0.305251\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.6852i | 1.95537i | 0.210068 | + | 0.977687i | \(0.432631\pi\) | ||||
−0.210068 | + | 0.977687i | \(0.567369\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.44090 | −0.330700 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.98914 | 0.139562 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.5583i | 0.822190i | 0.911593 | + | 0.411095i | \(0.134854\pi\) | ||||
−0.911593 | + | 0.411095i | \(0.865146\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.8311i | 0.621554i | 0.950483 | + | 0.310777i | \(0.100589\pi\) | ||||
−0.950483 | + | 0.310777i | \(0.899411\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.1324 | 0.560979 | 0.280489 | − | 0.959857i | \(-0.409503\pi\) | ||||
0.280489 | + | 0.959857i | \(0.409503\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.73814 | −0.0603681 | −0.0301841 | − | 0.999544i | \(-0.509609\pi\) | ||||
−0.0301841 | + | 0.999544i | \(0.509609\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 5.56148i | − 0.192694i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 17.3696i | − 0.601100i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.53654 | 0.225666 | 0.112833 | − | 0.993614i | \(-0.464007\pi\) | ||||
0.112833 | + | 0.993614i | \(0.464007\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.4239 | 0.773239 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.2852i | 0.697831i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 25.1201i | − 0.863135i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.82964 | −0.165558 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.0685 | −1.61160 | −0.805798 | − | 0.592190i | \(-0.798263\pi\) | ||||
−0.805798 | + | 0.592190i | \(0.798263\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.67316i | 0.0913134i | 0.998957 | + | 0.0456567i | \(0.0145380\pi\) | ||||
−0.998957 | + | 0.0456567i | \(0.985462\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 48.6192i | − 1.65887i | −0.558607 | − | 0.829433i | \(-0.688664\pi\) | ||||
0.558607 | − | 0.829433i | \(-0.311336\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.2319 | −0.382339 | −0.191169 | − | 0.981557i | \(-0.561228\pi\) | ||||
−0.191169 | + | 0.981557i | \(0.561228\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.2774 | 0.961460 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 11.9398i | − 0.405029i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.39143i | 0.284333i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 35.8883 | 1.21325 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.0409 | −0.507894 | −0.253947 | − | 0.967218i | \(-0.581729\pi\) | ||||
−0.253947 | + | 0.967218i | \(0.581729\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 47.9839i | − 1.61662i | −0.588757 | − | 0.808310i | \(-0.700383\pi\) | ||||
0.588757 | − | 0.808310i | \(-0.299617\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.5172i | 0.353930i | 0.984217 | + | 0.176965i | \(0.0566280\pi\) | ||||
−0.984217 | + | 0.176965i | \(0.943372\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.0309 | −0.941184 | −0.470592 | − | 0.882351i | \(-0.655960\pi\) | ||||
−0.470592 | + | 0.882351i | \(0.655960\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −53.2913 | −1.78733 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.12272i | − 0.0375703i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46.6909i | 1.56070i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.85542 | −0.195289 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.2144 | 0.606809 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 29.4853i | − 0.980124i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.3296i | 0.741442i | 0.928744 | + | 0.370721i | \(0.120889\pi\) | ||||
−0.928744 | + | 0.370721i | \(0.879111\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.0293 | 1.06118 | 0.530589 | − | 0.847629i | \(-0.321971\pi\) | ||||
0.530589 | + | 0.847629i | \(0.321971\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.9312 | −0.957481 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 35.0556i | − 1.15764i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 28.1786i | − 0.929526i | −0.885435 | − | 0.464763i | \(-0.846140\pi\) | ||||
0.885435 | − | 0.464763i | \(-0.153860\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.5696 | 0.742888 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.92108 | 0.128924 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 17.4154i | − 0.571380i | −0.958322 | − | 0.285690i | \(-0.907777\pi\) | ||||
0.958322 | − | 0.285690i | \(-0.0922228\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.05393i | 0.0673148i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.2156 | 0.791936 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.9692 | 0.619695 | 0.309848 | − | 0.950786i | \(-0.399722\pi\) | ||||
0.309848 | + | 0.950786i | \(0.399722\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.2246i | 0.887497i | 0.896151 | + | 0.443749i | \(0.146352\pi\) | ||||
−0.896151 | + | 0.443749i | \(0.853648\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.68069i | 0.0872953i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.6756 | −1.38677 | −0.693385 | − | 0.720568i | \(-0.743881\pi\) | ||||
−0.693385 | + | 0.720568i | \(0.743881\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.54501 | −0.0501531 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.4103i | 1.73013i | 0.501660 | + | 0.865065i | \(0.332723\pi\) | ||||
−0.501660 | + | 0.865065i | \(0.667277\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 54.2570i | − 1.75571i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.0842 | 0.325636 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.7862 | 0.831814 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 48.9701i | 1.57640i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 37.1872i | − 1.19586i | −0.801549 | − | 0.597929i | \(-0.795990\pi\) | ||||
0.801549 | − | 0.597929i | \(-0.204010\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.3408 | 1.51924 | 0.759619 | − | 0.650368i | \(-0.225385\pi\) | ||||
0.759619 | + | 0.650368i | \(0.225385\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.47527 | 0.175529 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 7.49046i | − 0.239641i | −0.992796 | − | 0.119820i | \(-0.961768\pi\) | ||||
0.992796 | − | 0.119820i | \(-0.0382319\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.3775i | 0.491468i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.68273 | −0.181251 | −0.0906255 | − | 0.995885i | \(-0.528887\pi\) | ||||
−0.0906255 | + | 0.995885i | \(0.528887\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.5826 | 0.942581 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 4.25666i | − 0.135354i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.7187i | 0.816981i | 0.912762 | + | 0.408491i | \(0.133945\pi\) | ||||
−0.912762 | + | 0.408491i | \(0.866055\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.19239 | −0.196312 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.0257 | 1.45765 | 0.728825 | − | 0.684700i | \(-0.240067\pi\) | ||||
0.728825 | + | 0.684700i | \(0.240067\pi\) | |||||||
\(998\) | 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 | 2736.2.d.b.2015.17 | yes | 24 | |
3.2 | odd | 2 | inner | 2736.2.d.b.2015.7 | ✓ | 24 | |
4.3 | odd | 2 | inner | 2736.2.d.b.2015.18 | yes | 24 | |
12.11 | even | 2 | inner | 2736.2.d.b.2015.8 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.d.b.2015.7 | ✓ | 24 | 3.2 | odd | 2 | inner | |
2736.2.d.b.2015.8 | yes | 24 | 12.11 | even | 2 | inner | |
2736.2.d.b.2015.17 | yes | 24 | 1.1 | even | 1 | trivial | |
2736.2.d.b.2015.18 | yes | 24 | 4.3 | odd | 2 | inner |