Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1537,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3072.1537");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.d (of order \(2\), degree \(1\), not 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: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 1536) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1537.3 | ||
Root | \(0.923880 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1537 |
Dual form | 3072.2.d.e.1537.6 |
$q$-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 \(\left(\mathbb{Z}/3072\mathbb{Z}\right)^\times\).
\(n\) | \(1025\) | \(2047\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.19891i | 0.536170i | 0.963395 | + | 0.268085i | \(0.0863908\pi\) | ||||
−0.963395 | + | 0.268085i | \(0.913609\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.613126 | 0.231740 | 0.115870 | − | 0.993264i | \(-0.463034\pi\) | ||||
0.115870 | + | 0.993264i | \(0.463034\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.53073i | 0.461534i | 0.973009 | + | 0.230767i | \(0.0741234\pi\) | ||||
−0.973009 | + | 0.230767i | \(0.925877\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.24943i | − 0.346529i | −0.984875 | − | 0.173265i | \(-0.944568\pi\) | ||||
0.984875 | − | 0.173265i | \(-0.0554316\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.19891 | 0.309558 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.35916 | −1.05725 | −0.528626 | − | 0.848855i | \(-0.677293\pi\) | ||||
−0.528626 | + | 0.848855i | \(0.677293\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.29769i | 0.297711i | 0.988859 | + | 0.148856i | \(0.0475590\pi\) | ||||
−0.988859 | + | 0.148856i | \(0.952441\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 0.613126i | − 0.133795i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.56261 | 0.712522 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 0.965872i | − 0.179358i | −0.995971 | − | 0.0896790i | \(-0.971416\pi\) | ||||
0.995971 | − | 0.0896790i | \(-0.0285841\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.77791 | 1.21735 | 0.608674 | − | 0.793420i | \(-0.291702\pi\) | ||||
0.608674 | + | 0.793420i | \(0.291702\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.53073 | 0.266467 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.735084i | 0.124252i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.8052i | 1.77637i | 0.459484 | + | 0.888186i | \(0.348034\pi\) | ||||
−0.459484 | + | 0.888186i | \(0.651966\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.24943 | −0.200069 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.68873 | −1.35695 | −0.678476 | − | 0.734623i | \(-0.737359\pi\) | ||||
−0.678476 | + | 0.734623i | \(0.737359\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.68873i | 1.32502i | 0.749054 | + | 0.662509i | \(0.230509\pi\) | ||||
−0.749054 | + | 0.662509i | \(0.769491\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 1.19891i | − 0.178723i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.65685 | 1.40860 | 0.704298 | − | 0.709904i | \(-0.251262\pi\) | ||||
0.704298 | + | 0.709904i | \(0.251262\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.62408 | −0.946297 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.35916i | 0.610405i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 11.4184i | − 1.56843i | −0.620486 | − | 0.784217i | \(-0.713065\pi\) | ||||
0.620486 | − | 0.784217i | \(-0.286935\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.83522 | −0.247460 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.29769 | 0.171884 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.04789i | 1.17794i | 0.808157 | + | 0.588968i | \(0.200465\pi\) | ||||
−0.808157 | + | 0.588968i | \(0.799535\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.52432i | − 0.195169i | −0.995227 | − | 0.0975845i | \(-0.968888\pi\) | ||||
0.995227 | − | 0.0975845i | \(-0.0311116\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.613126 | −0.0772466 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.49796 | 0.185799 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.1094i | 1.47939i | 0.672940 | + | 0.739697i | \(0.265031\pi\) | ||||
−0.672940 | + | 0.739697i | \(0.734969\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000i | 0.481543i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.56940 | −0.423610 | −0.211805 | − | 0.977312i | \(-0.567934\pi\) | ||||
−0.211805 | + | 0.977312i | \(0.567934\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.15800 | −0.603698 | −0.301849 | − | 0.953356i | \(-0.597604\pi\) | ||||
−0.301849 | + | 0.953356i | \(0.597604\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 3.56261i | − 0.411375i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.938533i | 0.106956i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.49623 | −0.843392 | −0.421696 | − | 0.906737i | \(-0.638565\pi\) | ||||
−0.421696 | + | 0.906737i | \(0.638565\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.18759i | 0.788940i | 0.918909 | + | 0.394470i | \(0.129072\pi\) | ||||
−0.918909 | + | 0.394470i | \(0.870928\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 5.22625i | − 0.566867i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.965872 | −0.103552 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.672715 | 0.0713076 | 0.0356538 | − | 0.999364i | \(-0.488649\pi\) | ||||
0.0356538 | + | 0.999364i | \(0.488649\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 0.766057i | − 0.0803046i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 6.77791i | − 0.702837i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.55582 | −0.159624 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.71832 | 0.479073 | 0.239536 | − | 0.970887i | \(-0.423005\pi\) | ||||
0.239536 | + | 0.970887i | \(0.423005\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 1.53073i | − 0.153845i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.68419i | 0.565598i | 0.959179 | + | 0.282799i | \(0.0912630\pi\) | ||||
−0.959179 | + | 0.282799i | \(0.908737\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.5381 | −1.53101 | −0.765506 | − | 0.643428i | \(-0.777511\pi\) | ||||
−0.765506 | + | 0.643428i | \(0.777511\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.735084 | 0.0717369 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 0.0773278i | − 0.00747556i | −0.999993 | − | 0.00373778i | \(-0.998810\pi\) | ||||
0.999993 | − | 0.00373778i | \(-0.00118977\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.23585i | 0.309938i | 0.987919 | + | 0.154969i | \(0.0495278\pi\) | ||||
−0.987919 | + | 0.154969i | \(0.950472\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.8052 | 1.02559 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.65685 | −0.720296 | −0.360148 | − | 0.932895i | \(-0.617274\pi\) | ||||
−0.360148 | + | 0.932895i | \(0.617274\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 4.79565i | − 0.447197i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.24943i | 0.115510i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.67271 | −0.245007 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.65685 | 0.786987 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.68873i | 0.783436i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.2658i | 0.918203i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.9008 | 1.85465 | 0.927325 | − | 0.374257i | \(-0.122102\pi\) | ||||
0.927325 | + | 0.374257i | \(0.122102\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.68873 | 0.765000 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.72061i | 0.674552i | 0.941406 | + | 0.337276i | \(0.109506\pi\) | ||||
−0.941406 | + | 0.337276i | \(0.890494\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.795649i | 0.0689916i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.19891 | −0.103186 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.42063 | −0.633987 | −0.316994 | − | 0.948428i | \(-0.602673\pi\) | ||||
−0.316994 | + | 0.948428i | \(0.602673\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2522i | 1.03922i | 0.854403 | + | 0.519611i | \(0.173923\pi\) | ||||
−0.854403 | + | 0.519611i | \(0.826077\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 9.65685i | − 0.813254i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.91254 | 0.159935 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.15800 | 0.0961663 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.62408i | 0.546345i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 3.54206i | − 0.290177i | −0.989419 | − | 0.145088i | \(-0.953653\pi\) | ||||
0.989419 | − | 0.145088i | \(-0.0463466\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.0019 | −1.05808 | −0.529039 | − | 0.848598i | \(-0.677447\pi\) | ||||
−0.529039 | + | 0.848598i | \(0.677447\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.35916 | 0.352417 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.12612i | 0.652706i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.14840i | 0.0916519i | 0.998949 | + | 0.0458260i | \(0.0145920\pi\) | ||||
−0.998949 | + | 0.0458260i | \(0.985408\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.4184 | −0.905536 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.45250 | −0.193284 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.4821i | 1.44763i | 0.689994 | + | 0.723815i | \(0.257613\pi\) | ||||
−0.689994 | + | 0.723815i | \(0.742387\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.83522i | 0.142871i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.2104 | −1.56393 | −0.781964 | − | 0.623324i | \(-0.785782\pi\) | ||||
−0.781964 | + | 0.623324i | \(0.785782\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.4389 | 0.879917 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 1.29769i | − 0.0992371i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.1374i | 0.770736i | 0.922763 | + | 0.385368i | \(0.125925\pi\) | ||||
−0.922763 | + | 0.385368i | \(0.874075\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.18433 | 0.165120 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.04789 | 0.680081 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.1094i | 1.50304i | 0.659708 | + | 0.751522i | \(0.270680\pi\) | ||||
−0.659708 | + | 0.751522i | \(0.729320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.57900i | 0.712001i | 0.934486 | + | 0.356001i | \(0.115860\pi\) | ||||
−0.934486 | + | 0.356001i | \(0.884140\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.52432 | −0.112681 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.9545 | −0.952437 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6.67271i | − 0.487957i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.613126i | 0.0445983i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.30767 | 0.166977 | 0.0834885 | − | 0.996509i | \(-0.473394\pi\) | ||||
0.0834885 | + | 0.996509i | \(0.473394\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.03278 | 0.146323 | 0.0731613 | − | 0.997320i | \(-0.476691\pi\) | ||||
0.0731613 | + | 0.997320i | \(0.476691\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1.49796i | − 0.107271i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 26.4025i | − 1.88110i | −0.339653 | − | 0.940551i | \(-0.610310\pi\) | ||||
0.339653 | − | 0.940551i | \(-0.389690\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.1927 | 0.722538 | 0.361269 | − | 0.932462i | \(-0.382344\pi\) | ||||
0.361269 | + | 0.932462i | \(0.382344\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.1094 | 0.854128 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 0.592201i | − 0.0415644i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 10.4170i | − 0.727557i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.98642 | −0.137404 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 7.06147i | − 0.486131i | −0.970010 | − | 0.243066i | \(-0.921847\pi\) | ||||
0.970010 | − | 0.243066i | \(-0.0781531\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.56940i | 0.244571i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.4170 | −0.710435 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.15571 | 0.282108 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.15800i | 0.348545i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.44646i | 0.366369i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.9646 | 1.26996 | 0.634982 | − | 0.772527i | \(-0.281008\pi\) | ||||
0.634982 | + | 0.772527i | \(0.281008\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.56261 | −0.237507 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 15.5945i | − 1.03504i | −0.855670 | − | 0.517521i | \(-0.826855\pi\) | ||||
0.855670 | − | 0.517521i | \(-0.173145\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 6.37465i | − 0.421249i | −0.977567 | − | 0.210624i | \(-0.932450\pi\) | ||||
0.977567 | − | 0.210624i | \(-0.0675497\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.938533 | 0.0617509 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.13880 | 0.0746050 | 0.0373025 | − | 0.999304i | \(-0.488123\pi\) | ||||
0.0373025 | + | 0.999304i | \(0.488123\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.5777i | 0.755247i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.49623i | 0.486933i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.6652 | 1.66014 | 0.830071 | − | 0.557657i | \(-0.188300\pi\) | ||||
0.830071 | + | 0.557657i | \(0.188300\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.2172 | 1.23789 | 0.618944 | − | 0.785435i | \(-0.287561\pi\) | ||||
0.618944 | + | 0.785435i | \(0.287561\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 7.94169i | − 0.507376i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.62138 | 0.103166 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.18759 | 0.455495 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.46927i | 0.408336i | 0.978936 | + | 0.204168i | \(0.0654490\pi\) | ||||
−0.978936 | + | 0.204168i | \(0.934551\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 6.12293i | − 0.384946i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.22625 | −0.327281 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.1094 | −1.37914 | −0.689572 | − | 0.724217i | \(-0.742201\pi\) | ||||
−0.689572 | + | 0.724217i | \(0.742201\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.62498i | 0.411656i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.965872i | 0.0597860i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.8914 | 1.41155 | 0.705773 | − | 0.708438i | \(-0.250600\pi\) | ||||
0.705773 | + | 0.708438i | \(0.250600\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.6896 | 0.840947 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 0.672715i | − 0.0411695i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.4776i | 1.43145i | 0.698381 | + | 0.715726i | \(0.253904\pi\) | ||||
−0.698381 | + | 0.715726i | \(0.746096\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.5837 | −1.55410 | −0.777049 | − | 0.629440i | \(-0.783284\pi\) | ||||
−0.777049 | + | 0.629440i | \(0.783284\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.766057 | −0.0463639 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.45341i | 0.328853i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.6692i | 0.821300i | 0.911793 | + | 0.410650i | \(0.134698\pi\) | ||||
−0.911793 | + | 0.410650i | \(0.865302\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.77791 | −0.405783 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.1116 | −1.25941 | −0.629707 | − | 0.776832i | \(-0.716825\pi\) | ||||
−0.629707 | + | 0.776832i | \(0.716825\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 17.0479i | − 1.01339i | −0.862125 | − | 0.506696i | \(-0.830867\pi\) | ||||
0.862125 | − | 0.506696i | \(-0.169133\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.55582i | 0.0921589i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.32729 | −0.314460 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.00228 | 0.117781 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 4.71832i | − 0.276593i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 16.1047i | − 0.940845i | −0.882441 | − | 0.470422i | \(-0.844102\pi\) | ||||
0.882441 | − | 0.470422i | \(-0.155898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.8476 | −0.631573 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.53073 | −0.0888222 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.99772i | 0.289025i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.32729i | 0.307060i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.68419 | 0.326548 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.82752 | 0.104644 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 6.91858i | − 0.394864i | −0.980317 | − | 0.197432i | \(-0.936740\pi\) | ||||
0.980317 | − | 0.197432i | \(-0.0632602\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.5381i | 0.883931i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.4389 | 1.15899 | 0.579493 | − | 0.814977i | \(-0.303251\pi\) | ||||
0.579493 | + | 0.814977i | \(0.303251\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.6241 | −0.657032 | −0.328516 | − | 0.944498i | \(-0.606548\pi\) | ||||
−0.328516 | + | 0.944498i | \(0.606548\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 0.735084i | − 0.0414173i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.5368i | 1.20963i | 0.796367 | + | 0.604814i | \(0.206752\pi\) | ||||
−0.796367 | + | 0.604814i | \(0.793248\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.47849 | 0.0827797 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.0773278 | −0.00431601 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 5.65685i | − 0.314756i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4.45123i | − 0.246910i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.23585 | 0.178943 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.92087 | 0.326428 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.8435i | 0.760910i | 0.924799 | + | 0.380455i | \(0.124233\pi\) | ||||
−0.924799 | + | 0.380455i | \(0.875767\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 10.8052i | − 0.592124i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.5181 | −0.793206 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.8428 | 1.84353 | 0.921767 | − | 0.387744i | \(-0.126745\pi\) | ||||
0.921767 | + | 0.387744i | \(0.126745\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.65685i | 0.415863i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3752i | 0.561847i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.35327 | −0.451034 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.79565 | −0.258189 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.6560i | 0.572041i | 0.958223 | + | 0.286021i | \(0.0923326\pi\) | ||||
−0.958223 | + | 0.286021i | \(0.907667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 15.6009i | − 0.835097i | −0.908655 | − | 0.417548i | \(-0.862889\pi\) | ||||
0.908655 | − | 0.417548i | \(-0.137111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.24943 | 0.0666896 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.2978 | −1.50614 | −0.753071 | − | 0.657939i | \(-0.771428\pi\) | ||||
−0.753071 | + | 0.657939i | \(0.771428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 4.27939i | − 0.227127i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.67271i | 0.141455i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.41474 | −0.180223 | −0.0901116 | − | 0.995932i | \(-0.528722\pi\) | ||||
−0.0901116 | + | 0.995932i | \(0.528722\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.3160 | 0.911368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 8.65685i | − 0.454367i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 6.18399i | − 0.323685i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.0916 | 0.526778 | 0.263389 | − | 0.964690i | \(-0.415160\pi\) | ||||
0.263389 | + | 0.964690i | \(0.415160\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.68873 | 0.452317 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 7.00090i | − 0.363469i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.9610i | 0.774649i | 0.921943 | + | 0.387325i | \(0.126601\pi\) | ||||
−0.921943 | + | 0.387325i | \(0.873399\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.2658 | 0.530125 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.20679 | −0.0621528 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.9681i | 0.666128i | 0.942904 | + | 0.333064i | \(0.108082\pi\) | ||||
−0.942904 | + | 0.333064i | \(0.891918\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 20.9008i | − 1.07078i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.81527 | 0.194951 | 0.0974755 | − | 0.995238i | \(-0.468923\pi\) | ||||
0.0974755 | + | 0.995238i | \(0.468923\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.12522 | −0.0573464 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 8.68873i | − 0.441673i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 28.1239i | − 1.42594i | −0.701196 | − | 0.712968i | \(-0.747350\pi\) | ||||
0.701196 | − | 0.712968i | \(-0.252650\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.4366 | 0.881809 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.72061 | 0.389453 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 8.98733i | − 0.452201i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 32.0862i | − 1.61036i | −0.593031 | − | 0.805180i | \(-0.702069\pi\) | ||||
0.593031 | − | 0.805180i | \(-0.297931\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.795649 | 0.0398323 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.9545 | −0.746794 | −0.373397 | − | 0.927672i | \(-0.621807\pi\) | ||||
−0.373397 | + | 0.927672i | \(0.621807\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 8.46852i | − 0.421847i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.19891i | 0.0595744i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.5400 | −0.819855 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.5298 | −0.520667 | −0.260333 | − | 0.965519i | \(-0.583832\pi\) | ||||
−0.260333 | + | 0.965519i | \(0.583832\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.42063i | 0.366033i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.54750i | 0.272974i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.61729 | −0.423006 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.2522 | 0.599995 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.7853i | 1.01543i | 0.861526 | + | 0.507713i | \(0.169509\pi\) | ||||
−0.861526 | + | 0.507713i | \(0.830491\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 14.0179i | − 0.683192i | −0.939847 | − | 0.341596i | \(-0.889033\pi\) | ||||
0.939847 | − | 0.341596i | \(-0.110967\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.65685 | −0.469532 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.5300 | −0.753315 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 0.934599i | − 0.0452284i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 1.91254i | − 0.0923385i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.8318 | 0.666253 | 0.333126 | − | 0.942882i | \(-0.391896\pi\) | ||||
0.333126 | + | 0.942882i | \(0.391896\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.8476 | −0.713531 | −0.356766 | − | 0.934194i | \(-0.616121\pi\) | ||||
−0.356766 | + | 0.934194i | \(0.616121\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 1.15800i | − 0.0555217i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 5.19077i | − 0.248308i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.7840 | 1.70787 | 0.853937 | − | 0.520376i | \(-0.174208\pi\) | ||||
0.853937 | + | 0.520376i | \(0.174208\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.62408 | 0.315432 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 33.0311i | − 1.56936i | −0.619903 | − | 0.784678i | \(-0.712828\pi\) | ||||
0.619903 | − | 0.784678i | \(-0.287172\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.806526i | 0.0382330i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.54206 | −0.167534 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.27775 | −0.343458 | −0.171729 | − | 0.985144i | \(-0.554935\pi\) | ||||
−0.171729 | + | 0.985144i | \(0.554935\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 13.3001i | − 0.626279i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.0019i | 0.610882i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.918436 | 0.0430569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.3096 | −0.669376 | −0.334688 | − | 0.942329i | \(-0.608631\pi\) | ||||
−0.334688 | + | 0.942329i | \(0.608631\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 4.35916i | − 0.203468i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.4923i | 1.09414i | 0.837086 | + | 0.547072i | \(0.184258\pi\) | ||||
−0.837086 | + | 0.547072i | \(0.815742\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.7704 | −1.38355 | −0.691773 | − | 0.722115i | \(-0.743170\pi\) | ||||
−0.691773 | + | 0.722115i | \(0.743170\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.12612 | 0.376840 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 23.4398i | − 1.08467i | −0.840164 | − | 0.542333i | \(-0.817541\pi\) | ||||
0.840164 | − | 0.542333i | \(-0.182459\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.42456i | 0.342834i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.14840 | 0.0529153 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.3001 | −0.611541 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.62317i | 0.212126i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.4184i | 0.522812i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.2104 | −1.10620 | −0.553101 | − | 0.833115i | \(-0.686555\pi\) | ||||
−0.553101 | + | 0.833115i | \(0.686555\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.5004 | 0.615565 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.45250i | 0.111593i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.65685i | 0.256865i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.0498 | −0.455399 | −0.227699 | − | 0.973732i | \(-0.573120\pi\) | ||||
−0.227699 | + | 0.973732i | \(0.573120\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.4821 | 0.835789 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 36.6848i | − 1.65556i | −0.561052 | − | 0.827781i | \(-0.689603\pi\) | ||||
0.561052 | − | 0.827781i | \(-0.310397\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.21039i | 0.189626i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.83522 | 0.0824868 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.18849 | −0.0981672 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.98005i | 0.0886393i | 0.999017 | + | 0.0443196i | \(0.0141120\pi\) | ||||
−0.999017 | + | 0.0443196i | \(0.985888\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.2104i | 0.902934i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0739 | 0.538348 | 0.269174 | − | 0.963092i | \(-0.413249\pi\) | ||||
0.269174 | + | 0.963092i | \(0.413249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.81485 | −0.303257 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 11.4389i | − 0.508021i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 4.48892i | − 0.198968i | −0.995039 | − | 0.0994838i | \(-0.968281\pi\) | ||||
0.995039 | − | 0.0994838i | \(-0.0317192\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.16250 | −0.139901 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.29769 | −0.0572946 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 18.6288i | − 0.820883i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.7821i | 0.650115i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.1374 | 0.444984 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.75428 | −0.208289 | −0.104145 | − | 0.994562i | \(-0.533210\pi\) | ||||
−0.104145 | + | 0.994562i | \(0.533210\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 34.7343i | − 1.51883i | −0.650609 | − | 0.759413i | \(-0.725486\pi\) | ||||
0.650609 | − | 0.759413i | \(-0.274514\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 2.18433i | − 0.0953319i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.5460 | −1.28704 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 9.04789i | − 0.392645i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.8560i | 0.470223i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0927092 | 0.00400817 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.1094 | 0.867783 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 10.1397i | − 0.436748i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 16.2981i | − 0.700709i | −0.936617 | − | 0.350354i | \(-0.886061\pi\) | ||||
0.936617 | − | 0.350354i | \(-0.113939\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.57900 | 0.411074 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.87950 | −0.166180 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.84339i | 0.378116i | 0.981966 | + | 0.189058i | \(0.0605434\pi\) | ||||
−0.981966 | + | 0.189058i | \(0.939457\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.52432i | 0.0650563i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.25341 | 0.0533969 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.59613 | −0.195448 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.9545i | 0.549890i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 34.3335i | − 1.45476i | −0.686236 | − | 0.727379i | \(-0.740738\pi\) | ||||
0.686236 | − | 0.727379i | \(-0.259262\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.8560 | 0.459158 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.67271 | −0.281722 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 27.8788i | − 1.17495i | −0.809243 | − | 0.587475i | \(-0.800122\pi\) | ||||
0.809243 | − | 0.587475i | \(-0.199878\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 9.17990i | − 0.386201i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.613126 | 0.0257489 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.1525 | −0.928682 | −0.464341 | − | 0.885656i | \(-0.653709\pi\) | ||||
−0.464341 | + | 0.885656i | \(0.653709\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 34.4845i | − 1.44313i | −0.692345 | − | 0.721566i | \(-0.743422\pi\) | ||||
0.692345 | − | 0.721566i | \(-0.256578\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 2.30767i | − 0.0964042i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.2504 | −0.594284 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.3488 | −0.930391 | −0.465196 | − | 0.885208i | \(-0.654016\pi\) | ||||
−0.465196 | + | 0.885208i | \(0.654016\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 2.03278i | − 0.0844794i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.40690i | 0.182829i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.4785 | 0.723885 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.49796 | −0.0619329 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.3096i | 0.590621i | 0.955401 | + | 0.295311i | \(0.0954231\pi\) | ||||
−0.955401 | + | 0.295311i | \(0.904577\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.79565i | 0.362418i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.4025 | −1.08605 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.3439 | −1.12288 | −0.561440 | − | 0.827517i | \(-0.689753\pi\) | ||||
−0.561440 | + | 0.827517i | \(0.689753\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 3.20435i | − 0.131366i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 10.1927i | − 0.417157i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.4684 | 0.958891 | 0.479446 | − | 0.877572i | \(-0.340838\pi\) | ||||
0.479446 | + | 0.877572i | \(0.340838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.4717 | 0.835058 | 0.417529 | − | 0.908664i | \(-0.362896\pi\) | ||||
0.417529 | + | 0.908664i | \(0.362896\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 12.1094i | − 0.493131i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.3788i | 0.421959i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.6633 | −1.32576 | −0.662881 | − | 0.748725i | \(-0.730667\pi\) | ||||
−0.662881 | + | 0.748725i | \(0.730667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.592201 | −0.0239972 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 12.0656i | − 0.488120i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.11562i | 0.287397i | 0.989622 | + | 0.143699i | \(0.0458996\pi\) | ||||
−0.989622 | + | 0.143699i | \(0.954100\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.4170 | −0.420055 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.5619 | −0.827789 | −0.413895 | − | 0.910325i | \(-0.635832\pi\) | ||||
−0.413895 | + | 0.910325i | \(0.635832\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 35.4412i | − 1.42450i | −0.701925 | − | 0.712251i | \(-0.747676\pi\) | ||||
0.701925 | − | 0.712251i | \(-0.252324\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 4.00000i | − 0.160514i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.412459 | 0.0165248 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50523 | 0.220209 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.98642i | 0.0793301i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 47.1018i | − 1.87807i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.05731 | 0.121709 | 0.0608547 | − | 0.998147i | \(-0.480617\pi\) | ||||
0.0608547 | + | 0.998147i | \(0.480617\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.06147 | −0.280668 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25.0583i | 0.994408i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.27631i | 0.327920i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.56940 | 0.141203 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.8890 | 0.430089 | 0.215045 | − | 0.976604i | \(-0.431010\pi\) | ||||
0.215045 | + | 0.976604i | \(0.431010\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 23.6729i | − 0.933567i | −0.884372 | − | 0.466783i | \(-0.845413\pi\) | ||||
0.884372 | − | 0.466783i | \(-0.154587\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.4170i | 0.410170i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 42.3417 | 1.66462 | 0.832311 | − | 0.554309i | \(-0.187017\pi\) | ||||
0.832311 | + | 0.554309i | \(0.187017\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.8499 | −0.543657 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 4.15571i | − 0.162875i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 48.3535i | 1.89222i | 0.323850 | + | 0.946109i | \(0.395023\pi\) | ||||
−0.323850 | + | 0.946109i | \(0.604977\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.25633 | −0.361675 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.15800 | 0.201233 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.0023i | 0.896042i | 0.894023 | + | 0.448021i | \(0.147871\pi\) | ||||
−0.894023 | + | 0.448021i | \(0.852129\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 21.4790i | − 0.835437i | −0.908576 | − | 0.417719i | \(-0.862830\pi\) | ||||
0.908576 | − | 0.417719i | \(-0.137170\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.44646 | 0.211523 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.953914 | −0.0369912 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.86349i | 0.149595i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 18.9646i | − 0.733214i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.33333 | 0.0900771 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.6569 | 0.680622 | 0.340311 | − | 0.940313i | \(-0.389468\pi\) | ||||
0.340311 | + | 0.940313i | \(0.389468\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.56261i | 0.137125i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.2287i | 1.23865i | 0.785135 | + | 0.619325i | \(0.212594\pi\) | ||||
−0.785135 | + | 0.619325i | \(0.787406\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.89293 | 0.111020 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.5945 | −0.597582 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.4037i | 0.704198i | 0.935963 | + | 0.352099i | \(0.114532\pi\) | ||||
−0.935963 | + | 0.352099i | \(0.885468\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 8.89668i | − 0.339925i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.37465 | −0.243208 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.2665 | −0.543509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.5138i | 0.476048i | 0.971259 | + | 0.238024i | \(0.0764997\pi\) | ||||
−0.971259 | + | 0.238024i | \(0.923500\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 0.938533i | − 0.0356519i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.6894 | −0.557199 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.8756 | 1.43464 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 1.13880i | − 0.0430732i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 4.41159i | − 0.166623i | −0.996524 | − | 0.0833117i | \(-0.973450\pi\) | ||||
0.996524 | − | 0.0833117i | \(-0.0265497\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0219 | −0.528846 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.5777 | 0.436042 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.48513i | 0.131072i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.7819i | 1.53159i | 0.643082 | + | 0.765797i | \(0.277655\pi\) | ||||
−0.643082 | + | 0.765797i | \(0.722345\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.49623 | 0.281131 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.1116 | −1.01534 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.29297i | 0.0857523i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 25.6652i | − 0.958484i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.4170 | −1.43271 | −0.716357 | − | 0.697734i | \(-0.754192\pi\) | ||||
−0.716357 | + | 0.697734i | \(0.754192\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.52680 | −0.354797 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 19.2172i | − 0.714695i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 3.44102i | − 0.127796i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.48610 | 0.0551165 | 0.0275583 | − | 0.999620i | \(-0.491227\pi\) | ||||
0.0275583 | + | 0.999620i | \(0.491227\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 37.8756i | − 1.40088i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.74829i | 0.286190i | 0.989709 | + | 0.143095i | \(0.0457054\pi\) | ||||
−0.989709 | + | 0.143095i | \(0.954295\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.94169 | −0.292934 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.5362 | −0.682790 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 42.6392i | − 1.56851i | −0.620440 | − | 0.784254i | \(-0.713046\pi\) | ||||
0.620440 | − | 0.784254i | \(-0.286954\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 1.62138i | − 0.0595627i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.6516 | −1.60142 | −0.800711 | − | 0.599051i | \(-0.795545\pi\) | ||||
−0.800711 | + | 0.599051i | \(0.795545\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.24662 | 0.155584 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 7.18759i | − 0.262980i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 0.0474117i | − 0.00173238i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.3854 | 1.58315 | 0.791577 | − | 0.611069i | \(-0.209260\pi\) | ||||
0.791577 | + | 0.611069i | \(0.209260\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.46927 | 0.235753 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 15.5881i | − 0.567310i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.6861i | 0.824539i | 0.911062 | + | 0.412270i | \(0.135264\pi\) | ||||
−0.911062 | + | 0.412270i | \(0.864736\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.12293 | −0.222248 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.0047 | 1.12392 | 0.561960 | − | 0.827164i | \(-0.310047\pi\) | ||||
0.561960 | + | 0.827164i | \(0.310047\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.98398i | 0.0718251i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.22625i | 0.188956i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.3047 | 0.408189 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.3767 | 1.56420 | 0.782102 | − | 0.623150i | \(-0.214148\pi\) | ||||
0.782102 | + | 0.623150i | \(0.214148\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.1094i | 0.796249i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 5.42745i | − 0.195212i | −0.995225 | − | 0.0976059i | \(-0.968882\pi\) | ||||
0.995225 | − | 0.0976059i | \(-0.0311185\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.1470 | 0.867387 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.62498 | 0.237670 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 11.2753i | − 0.403980i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 5.46380i | − 0.195510i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.965872 | 0.0345175 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.37683 | −0.0491410 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.6824i | 0.452077i | 0.974118 | + | 0.226039i | \(0.0725776\pi\) | ||||
−0.974118 | + | 0.226039i | \(0.927422\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 22.8914i | − 0.814957i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.69462 | −0.166921 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.90453 | −0.0676318 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 13.6896i | − 0.485521i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.7038i | 0.875054i | 0.899205 | + | 0.437527i | \(0.144146\pi\) | ||||
−0.899205 | + | 0.437527i | \(0.855854\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −42.0958 | −1.48924 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.672715 | −0.0237692 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 7.89552i | − 0.278627i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.94034i | − 0.103633i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.4776 | 0.826449 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.81166 | 0.239485 | 0.119743 | − | 0.992805i | \(-0.461793\pi\) | ||||
0.119743 | + | 0.992805i | \(0.461793\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 2.81804i | − 0.0989546i | −0.998775 | − | 0.0494773i | \(-0.984244\pi\) | ||||
0.998775 | − | 0.0494773i | \(-0.0157555\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.5837i | 0.897259i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.1584 | −0.776175 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.2753 | −0.394473 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.766057i | 0.0267682i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 36.5756i | − 1.27650i | −0.769830 | − | 0.638249i | \(-0.779659\pi\) | ||||
0.769830 | − | 0.638249i | \(-0.220341\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.15309 | 0.179625 | 0.0898126 | − | 0.995959i | \(-0.471373\pi\) | ||||
0.0898126 | + | 0.995959i | \(0.471373\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.45341 | 0.189863 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 35.6433i | − 1.23944i | −0.784824 | − | 0.619719i | \(-0.787247\pi\) | ||||
0.784824 | − | 0.619719i | \(-0.212753\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 42.3283i | − 1.47012i | −0.678001 | − | 0.735061i | \(-0.737153\pi\) | ||||
0.678001 | − | 0.735061i | \(-0.262847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.6692 | 0.474178 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.8754 | 1.00047 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 24.2305i | − 0.838531i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.77791i | 0.234279i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.7768 | 1.68396 | 0.841981 | − | 0.539507i | \(-0.181389\pi\) | ||||
0.841981 | + | 0.539507i | \(0.181389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.0671 | 0.967831 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.1116i | 0.727124i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.7143i | 0.471785i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.30774 | 0.182376 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.0479 | −0.585082 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 43.2210i | − 1.48160i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 40.3965i | − 1.38315i | −0.722304 | − | 0.691576i | \(-0.756917\pi\) | ||||
0.722304 | − | 0.691576i | \(-0.243083\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.55582 | 0.0532079 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.2977 | 0.864153 | 0.432076 | − | 0.901837i | \(-0.357781\pi\) | ||||
0.432076 | + | 0.901837i | \(0.357781\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.1412i | 1.19900i | 0.800373 | + | 0.599502i | \(0.204635\pi\) | ||||
−0.800373 | + | 0.599502i | \(0.795365\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.32729i | 0.181553i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.4193 | 1.00144 | 0.500722 | − | 0.865608i | \(-0.333068\pi\) | ||||
0.500722 | + | 0.865608i | \(0.333068\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.1539 | −0.413245 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 2.00228i | − 0.0680011i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 11.4747i | − 0.389254i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.1298 | 0.512653 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.71832 | −0.159691 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.29424i | 0.212784i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3.89312i | − 0.131461i | −0.997837 | − | 0.0657307i | \(-0.979062\pi\) | ||||
0.997837 | − | 0.0657307i | \(-0.0209378\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.1047 | −0.543197 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.6049 | −0.727887 | −0.363943 | − | 0.931421i | \(-0.618570\pi\) | ||||
−0.363943 | + | 0.931421i | \(0.618570\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 23.0974i | − 0.777290i | −0.921387 | − | 0.388645i | \(-0.872943\pi\) | ||||
0.921387 | − | 0.388645i | \(-0.127057\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.8476i | 0.364639i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 56.1260 | 1.88453 | 0.942263 | − | 0.334873i | \(-0.108693\pi\) | ||||
0.942263 | + | 0.334873i | \(0.108693\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.8149 | 0.429796 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.53073i | 0.0512815i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.5316i | 0.419355i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.1094 | −0.805887 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.99772 | 0.166869 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 6.54659i | − 0.218341i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 49.7745i | 1.65823i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.32729 | 0.177281 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.4844 | −0.381754 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 26.2683i | − 0.872223i | −0.899893 | − | 0.436112i | \(-0.856355\pi\) | ||||
0.899893 | − | 0.436112i | \(-0.143645\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 5.68419i | − 0.188533i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.8560 | −0.757251 | −0.378626 | − | 0.925550i | \(-0.623603\pi\) | ||||
−0.378626 | + | 0.925550i | \(0.623603\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.0023 | −0.364122 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 1.82752i | − 0.0604161i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.73370i | 0.156321i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.319035 | 0.0105240 | 0.00526200 | − | 0.999986i | \(-0.498325\pi\) | ||||
0.00526200 | + | 0.999986i | \(0.498325\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.91858 | −0.227975 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.45971i | 0.146793i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.4949i | 1.26570i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.5381 | 0.510338 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 57.3735 | 1.88236 | 0.941182 | − | 0.337900i | \(-0.109716\pi\) | ||||
0.941182 | + | 0.337900i | \(0.109716\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 8.59602i | − 0.281723i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 20.4389i | − 0.669140i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.00000 | 0.261628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.8100 | −1.30054 | −0.650268 | − | 0.759705i | \(-0.725343\pi\) | ||||
−0.650268 | + | 0.759705i | \(0.725343\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.6241i | 0.379337i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 45.2038i | − 1.47360i | −0.676110 | − | 0.736801i | \(-0.736336\pi\) | ||||
0.676110 | − | 0.736801i | \(-0.263664\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.7549 | 1.13178 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.735084 | −0.0239123 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.1772i | 1.40307i | 0.712635 | + | 0.701535i | \(0.247502\pi\) | ||||
−0.712635 | + | 0.701535i | \(0.752498\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.44455i | 0.209199i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.5368 | 0.698379 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.1594 | −0.491060 | −0.245530 | − | 0.969389i | \(-0.578962\pi\) | ||||
−0.245530 | + | 0.969389i | \(0.578962\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.76669i | 0.0895280i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.47849i | − 0.0477929i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.54978 | −0.146920 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.9401 | 0.481938 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0773278i | 0.00249185i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.43712i | 0.0784537i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.1170 | −0.518287 | −0.259143 | − | 0.965839i | \(-0.583440\pi\) | ||||
−0.259143 | + | 0.965839i | \(0.583440\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.65685 | −0.181724 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.15965i | 0.133489i | 0.997770 | + | 0.0667447i | \(0.0212613\pi\) | ||||
−0.997770 | + | 0.0667447i | \(0.978739\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.51217i | 0.240829i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.45123 | −0.142553 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.2552 | 1.31987 | 0.659935 | − | 0.751323i | \(-0.270584\pi\) | ||||
0.659935 | + | 0.751323i | \(0.270584\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.02975i | 0.0329109i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 3.23585i | − 0.103313i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.0257 | −1.02146 | −0.510730 | − | 0.859741i | \(-0.670625\pi\) | ||||
−0.510730 | + | 0.859741i | \(0.670625\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.6543 | 1.00859 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 5.92087i | − 0.188463i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 34.7549i | − 1.10514i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.94041 | −0.315768 | −0.157884 | − | 0.987458i | \(-0.550467\pi\) | ||||
−0.157884 | + | 0.987458i | \(0.550467\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.8435 | 0.439311 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.2201i | 0.387403i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 18.0161i | − 0.570574i | −0.958442 | − | 0.285287i | \(-0.907911\pi\) | ||||
0.958442 | − | 0.285287i | \(-0.0920890\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.8052 | −0.341863 |
(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 | 3072.2.d.e.1537.3 | 8 | ||
4.3 | odd | 2 | 3072.2.d.j.1537.7 | 8 | |||
8.3 | odd | 2 | 3072.2.d.j.1537.2 | 8 | |||
8.5 | even | 2 | inner | 3072.2.d.e.1537.6 | 8 | ||
16.3 | odd | 4 | 3072.2.a.j.1.3 | 4 | |||
16.5 | even | 4 | 3072.2.a.m.1.2 | 4 | |||
16.11 | odd | 4 | 3072.2.a.p.1.2 | 4 | |||
16.13 | even | 4 | 3072.2.a.s.1.3 | 4 | |||
32.3 | odd | 8 | 1536.2.j.i.385.1 | yes | 8 | ||
32.5 | even | 8 | 1536.2.j.j.1153.3 | yes | 8 | ||
32.11 | odd | 8 | 1536.2.j.f.1153.4 | yes | 8 | ||
32.13 | even | 8 | 1536.2.j.e.385.2 | ✓ | 8 | ||
32.19 | odd | 8 | 1536.2.j.f.385.4 | yes | 8 | ||
32.21 | even | 8 | 1536.2.j.e.1153.2 | yes | 8 | ||
32.27 | odd | 8 | 1536.2.j.i.1153.1 | yes | 8 | ||
32.29 | even | 8 | 1536.2.j.j.385.3 | yes | 8 | ||
48.5 | odd | 4 | 9216.2.a.bl.1.3 | 4 | |||
48.11 | even | 4 | 9216.2.a.z.1.3 | 4 | |||
48.29 | odd | 4 | 9216.2.a.bm.1.2 | 4 | |||
48.35 | even | 4 | 9216.2.a.ba.1.2 | 4 | |||
96.5 | odd | 8 | 4608.2.k.be.1153.4 | 8 | |||
96.11 | even | 8 | 4608.2.k.bj.1153.1 | 8 | |||
96.29 | odd | 8 | 4608.2.k.be.3457.4 | 8 | |||
96.35 | even | 8 | 4608.2.k.bc.3457.4 | 8 | |||
96.53 | odd | 8 | 4608.2.k.bh.1153.1 | 8 | |||
96.59 | even | 8 | 4608.2.k.bc.1153.4 | 8 | |||
96.77 | odd | 8 | 4608.2.k.bh.3457.1 | 8 | |||
96.83 | even | 8 | 4608.2.k.bj.3457.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.j.e.385.2 | ✓ | 8 | 32.13 | even | 8 | ||
1536.2.j.e.1153.2 | yes | 8 | 32.21 | even | 8 | ||
1536.2.j.f.385.4 | yes | 8 | 32.19 | odd | 8 | ||
1536.2.j.f.1153.4 | yes | 8 | 32.11 | odd | 8 | ||
1536.2.j.i.385.1 | yes | 8 | 32.3 | odd | 8 | ||
1536.2.j.i.1153.1 | yes | 8 | 32.27 | odd | 8 | ||
1536.2.j.j.385.3 | yes | 8 | 32.29 | even | 8 | ||
1536.2.j.j.1153.3 | yes | 8 | 32.5 | even | 8 | ||
3072.2.a.j.1.3 | 4 | 16.3 | odd | 4 | |||
3072.2.a.m.1.2 | 4 | 16.5 | even | 4 | |||
3072.2.a.p.1.2 | 4 | 16.11 | odd | 4 | |||
3072.2.a.s.1.3 | 4 | 16.13 | even | 4 | |||
3072.2.d.e.1537.3 | 8 | 1.1 | even | 1 | trivial | ||
3072.2.d.e.1537.6 | 8 | 8.5 | even | 2 | inner | ||
3072.2.d.j.1537.2 | 8 | 8.3 | odd | 2 | |||
3072.2.d.j.1537.7 | 8 | 4.3 | odd | 2 | |||
4608.2.k.bc.1153.4 | 8 | 96.59 | even | 8 | |||
4608.2.k.bc.3457.4 | 8 | 96.35 | even | 8 | |||
4608.2.k.be.1153.4 | 8 | 96.5 | odd | 8 | |||
4608.2.k.be.3457.4 | 8 | 96.29 | odd | 8 | |||
4608.2.k.bh.1153.1 | 8 | 96.53 | odd | 8 | |||
4608.2.k.bh.3457.1 | 8 | 96.77 | odd | 8 | |||
4608.2.k.bj.1153.1 | 8 | 96.11 | even | 8 | |||
4608.2.k.bj.3457.1 | 8 | 96.83 | even | 8 | |||
9216.2.a.z.1.3 | 4 | 48.11 | even | 4 | |||
9216.2.a.ba.1.2 | 4 | 48.35 | even | 4 | |||
9216.2.a.bl.1.3 | 4 | 48.5 | odd | 4 | |||
9216.2.a.bm.1.2 | 4 | 48.29 | odd | 4 |