Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(829,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4140.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.f (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: | \(33.0580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 829.2 | ||
Character | \(\chi\) | \(=\) | 4140.829 |
Dual form | 4140.2.f.d.829.1 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | −2.23083 | + | 0.152950i | −0.997658 | + | 0.0684015i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.09652i | 1.54834i | 0.632979 | + | 0.774169i | \(0.281832\pi\) | ||||
−0.632979 | + | 0.774169i | \(0.718168\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.777594 | 0.234453 | 0.117227 | − | 0.993105i | \(-0.462600\pi\) | ||||
0.117227 | + | 0.993105i | \(0.462600\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.67412i | 0.464318i | 0.972678 | + | 0.232159i | \(0.0745789\pi\) | ||||
−0.972678 | + | 0.232159i | \(0.925421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.55545i | − | 0.862324i | −0.902274 | − | 0.431162i | \(-0.858104\pi\) | ||
0.902274 | − | 0.431162i | \(-0.141896\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.61421 | 1.05857 | 0.529286 | − | 0.848444i | \(-0.322460\pi\) | ||||
0.529286 | + | 0.848444i | \(0.322460\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.95321 | − | 0.682413i | 0.990642 | − | 0.136483i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.24889 | 1.53178 | 0.765890 | − | 0.642972i | \(-0.222299\pi\) | ||||
0.765890 | + | 0.642972i | \(0.222299\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.43498 | 1.15576 | 0.577878 | − | 0.816123i | \(-0.303881\pi\) | ||||
0.577878 | + | 0.816123i | \(0.303881\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.626564 | − | 9.13864i | −0.105909 | − | 1.54471i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.05292i | − | 0.173099i | −0.996248 | − | 0.0865495i | \(-0.972416\pi\) | ||
0.996248 | − | 0.0865495i | \(-0.0275841\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.98753 | −0.935095 | −0.467548 | − | 0.883968i | \(-0.654862\pi\) | ||||
−0.467548 | + | 0.883968i | \(0.654862\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.37477i | − | 0.514648i | −0.966325 | − | 0.257324i | \(-0.917159\pi\) | ||
0.966325 | − | 0.257324i | \(-0.0828408\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.24747i | 0.181962i | 0.995853 | + | 0.0909809i | \(0.0290002\pi\) | ||||
−0.995853 | + | 0.0909809i | \(0.971000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.78146 | −1.39735 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.08565i | − | 0.835928i | −0.908463 | − | 0.417964i | \(-0.862744\pi\) | ||
0.908463 | − | 0.417964i | \(-0.137256\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.73468 | + | 0.118933i | −0.233904 | + | 0.0160370i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.37044 | −0.308605 | −0.154302 | − | 0.988024i | \(-0.549313\pi\) | ||||
−0.154302 | + | 0.988024i | \(0.549313\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.12459 | −0.272026 | −0.136013 | − | 0.990707i | \(-0.543429\pi\) | ||||
−0.136013 | + | 0.990707i | \(0.543429\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.256057 | − | 3.73468i | −0.0317600 | − | 0.463230i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.7691i | 1.80433i | 0.431391 | + | 0.902165i | \(0.358023\pi\) | ||||
−0.431391 | + | 0.902165i | \(0.641977\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4600 | 1.36005 | 0.680026 | − | 0.733188i | \(-0.261968\pi\) | ||||
0.680026 | + | 0.733188i | \(0.261968\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.7443i | 1.84273i | 0.388698 | + | 0.921365i | \(0.372925\pi\) | ||||
−0.388698 | + | 0.921365i | \(0.627075\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.18543i | 0.363013i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.63206 | 0.183621 | 0.0918104 | − | 0.995777i | \(-0.470735\pi\) | ||||
0.0918104 | + | 0.995777i | \(0.470735\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.0898i | 1.87585i | 0.346844 | + | 0.937923i | \(0.387253\pi\) | ||||
−0.346844 | + | 0.937923i | \(0.612747\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.543808 | + | 7.93162i | 0.0589843 | + | 0.860305i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.52443 | 0.585588 | 0.292794 | − | 0.956176i | \(-0.405415\pi\) | ||||
0.292794 | + | 0.956176i | \(0.405415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.85807 | −0.718921 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.2935 | + | 0.705745i | −1.05609 | + | 0.0724079i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.78620i | 0.892103i | 0.895007 | + | 0.446052i | \(0.147170\pi\) | ||||
−0.895007 | + | 0.446052i | \(0.852830\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.88643 | −0.983736 | −0.491868 | − | 0.870670i | \(-0.663686\pi\) | ||||
−0.491868 | + | 0.870670i | \(0.663686\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.75550i | 0.370040i | 0.982735 | + | 0.185020i | \(0.0592350\pi\) | ||||
−0.982735 | + | 0.185020i | \(0.940765\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.92219i | 0.282499i | 0.989974 | + | 0.141249i | \(0.0451120\pi\) | ||||
−0.989974 | + | 0.141249i | \(0.954888\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.9690 | −1.14642 | −0.573210 | − | 0.819409i | \(-0.694302\pi\) | ||||
−0.573210 | + | 0.819409i | \(0.694302\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 16.0939i | − | 1.51399i | −0.653424 | − | 0.756993i | \(-0.726668\pi\) | ||
0.653424 | − | 0.756993i | \(-0.273332\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.152950 | − | 2.23083i | −0.0142627 | − | 0.208026i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.5650 | 1.33517 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3953 | −0.945032 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.9454 | + | 2.27994i | −0.978987 | + | 0.203924i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.16468i | − | 0.813234i | −0.913599 | − | 0.406617i | \(-0.866708\pi\) | ||
0.913599 | − | 0.406617i | \(-0.133292\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.843290 | −0.0736786 | −0.0368393 | − | 0.999321i | \(-0.511729\pi\) | ||||
−0.0368393 | + | 0.999321i | \(0.511729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.9022i | 1.63903i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.39231i | − | 0.204389i | −0.994764 | − | 0.102195i | \(-0.967414\pi\) | ||
0.994764 | − | 0.102195i | \(-0.0325864\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.7194 | −0.909209 | −0.454605 | − | 0.890693i | \(-0.650219\pi\) | ||||
−0.454605 | + | 0.890693i | \(0.650219\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.30179i | 0.108861i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.4019 | + | 1.26167i | −1.52819 | + | 0.104776i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.3312 | 1.41983 | 0.709913 | − | 0.704289i | \(-0.248734\pi\) | ||||
0.709913 | + | 0.704289i | \(0.248734\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0120 | 1.62855 | 0.814275 | − | 0.580479i | \(-0.197135\pi\) | ||||
0.814275 | + | 0.580479i | \(0.197135\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.3554 | + | 0.984233i | −1.15305 | + | 0.0790555i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.92120i | − | 0.632181i | −0.948729 | − | 0.316090i | \(-0.897630\pi\) | ||
0.948729 | − | 0.316090i | \(-0.102370\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.09652 | −0.322851 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.8908i | 0.931363i | 0.884952 | + | 0.465681i | \(0.154191\pi\) | ||||
−0.884952 | + | 0.465681i | \(0.845809\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.5289i | 1.20166i | 0.799375 | + | 0.600832i | \(0.205164\pi\) | ||||
−0.799375 | + | 0.600832i | \(0.794836\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.1973 | 0.784409 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.9023i | 1.20903i | 0.796595 | + | 0.604513i | \(0.206632\pi\) | ||||
−0.796595 | + | 0.604513i | \(0.793368\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.79552 | + | 20.2909i | 0.211321 | + | 1.53385i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.1510 | −0.758723 | −0.379362 | − | 0.925248i | \(-0.623856\pi\) | ||||
−0.379362 | + | 0.925248i | \(0.623856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.4562 | −0.925861 | −0.462930 | − | 0.886395i | \(-0.653202\pi\) | ||||
−0.462930 | + | 0.886395i | \(0.653202\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.161045 | + | 2.34889i | 0.0118402 | + | 0.172694i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.76470i | − | 0.202175i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3633 | −0.749860 | −0.374930 | − | 0.927053i | \(-0.622333\pi\) | ||||
−0.374930 | + | 0.927053i | \(0.622333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.6888i | 1.05732i | 0.848833 | + | 0.528660i | \(0.177305\pi\) | ||||
−0.848833 | + | 0.528660i | \(0.822695\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 19.2517i | − | 1.37163i | −0.727777 | − | 0.685814i | \(-0.759447\pi\) | ||
0.727777 | − | 0.685814i | \(-0.240553\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.57495 | 0.607862 | 0.303931 | − | 0.952694i | \(-0.401701\pi\) | ||||
0.303931 | + | 0.952694i | \(0.401701\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 33.7917i | 2.37171i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.3572 | − | 0.915796i | 0.932905 | − | 0.0639619i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.58798 | 0.248186 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0719 | −1.10644 | −0.553218 | − | 0.833036i | \(-0.686600\pi\) | ||||
−0.553218 | + | 0.833036i | \(0.686600\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.516173 | + | 7.52855i | 0.0352027 | + | 0.513443i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.3610i | 1.78950i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.95226 | 0.400392 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 15.4350i | − | 1.03360i | −0.856105 | − | 0.516802i | \(-0.827122\pi\) | ||
0.856105 | − | 0.516802i | \(-0.172878\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 19.5993i | − | 1.30085i | −0.759571 | − | 0.650424i | \(-0.774591\pi\) | ||
0.759571 | − | 0.650424i | \(-0.225409\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.7275 | 1.17147 | 0.585734 | − | 0.810504i | \(-0.300806\pi\) | ||||
0.585734 | + | 0.810504i | \(0.300806\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.4197i | 1.53428i | 0.641482 | + | 0.767138i | \(0.278320\pi\) | ||||
−0.641482 | + | 0.767138i | \(0.721680\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.190801 | − | 2.78289i | −0.0124465 | − | 0.181536i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.79898 | 0.504474 | 0.252237 | − | 0.967666i | \(-0.418834\pi\) | ||||
0.252237 | + | 0.967666i | \(0.418834\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.1742 | −1.04187 | −0.520936 | − | 0.853595i | \(-0.674417\pi\) | ||||
−0.520936 | + | 0.853595i | \(0.674417\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.8208 | − | 1.49608i | 1.39408 | − | 0.0955810i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.72474i | 0.491513i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.46275 | 0.471045 | 0.235522 | − | 0.971869i | \(-0.424320\pi\) | ||||
0.235522 | + | 0.971869i | \(0.424320\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.777594i | 0.0488869i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.8277i | 0.737794i | 0.929470 | + | 0.368897i | \(0.120264\pi\) | ||||
−0.929470 | + | 0.368897i | \(0.879736\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.31330 | 0.268016 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.466006i | 0.0287352i | 0.999897 | + | 0.0143676i | \(0.00457350\pi\) | ||||
−0.999897 | + | 0.0143676i | \(0.995426\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.930803 | + | 13.5761i | 0.0571788 | + | 0.833971i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.5971 | 0.707089 | 0.353545 | − | 0.935418i | \(-0.384976\pi\) | ||||
0.353545 | + | 0.935418i | \(0.384976\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0761 | 0.976553 | 0.488276 | − | 0.872689i | \(-0.337626\pi\) | ||||
0.488276 | + | 0.872689i | \(0.337626\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.85159 | − | 0.530640i | 0.232259 | − | 0.0319988i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.6670i | 1.06151i | 0.847526 | + | 0.530754i | \(0.178091\pi\) | ||||
−0.847526 | + | 0.530754i | \(0.821909\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.9009 | −1.12753 | −0.563767 | − | 0.825934i | \(-0.690648\pi\) | ||||
−0.563767 | + | 0.825934i | \(0.690648\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 0.0766236i | − | 0.00455480i | −0.999997 | − | 0.00227740i | \(-0.999275\pi\) | ||
0.999997 | − | 0.00227740i | \(-0.000724919\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 24.5280i | − | 1.44784i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.35875 | 0.256397 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.75829i | − | 0.102720i | −0.998680 | − | 0.0513602i | \(-0.983644\pi\) | ||
0.998680 | − | 0.0513602i | \(-0.0163557\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.28805 | − | 0.362560i | 0.307882 | − | 0.0211090i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.67412 | −0.0968169 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.8248 | 0.796849 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.73960 | − | 0.324957i | 0.271389 | − | 0.0186070i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.55583i | − | 0.145869i | −0.997337 | − | 0.0729345i | \(-0.976764\pi\) | ||
0.997337 | − | 0.0729345i | \(-0.0232364\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.4792 | −1.16127 | −0.580636 | − | 0.814163i | \(-0.697196\pi\) | ||||
−0.580636 | + | 0.814163i | \(0.697196\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.11052i | − | 0.119294i | −0.998220 | − | 0.0596468i | \(-0.981003\pi\) | ||
0.998220 | − | 0.0596468i | \(-0.0189974\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 25.3095i | − | 1.42152i | −0.703433 | − | 0.710761i | \(-0.748351\pi\) | ||
0.703433 | − | 0.710761i | \(-0.251649\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.41428 | 0.359131 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 16.4056i | − | 0.912832i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.14244 | + | 8.29228i | 0.0633713 | + | 0.459973i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.11027 | −0.281739 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.2710 | 0.894336 | 0.447168 | − | 0.894450i | \(-0.352433\pi\) | ||||
0.447168 | + | 0.894450i | \(0.352433\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.25894 | − | 32.9473i | −0.123419 | − | 1.80010i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.1877i | 1.91680i | 0.285434 | + | 0.958398i | \(0.407862\pi\) | ||||
−0.285434 | + | 0.958398i | \(0.592138\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.00380 | 0.270971 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 11.3943i | − | 0.615235i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.66067i | 0.0891493i | 0.999006 | + | 0.0445747i | \(0.0141933\pi\) | ||||
−0.999006 | + | 0.0445747i | \(0.985807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.43378 | 0.290863 | 0.145432 | − | 0.989368i | \(-0.453543\pi\) | ||||
0.145432 | + | 0.989368i | \(0.453543\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.4056i | 1.72478i | 0.506248 | + | 0.862388i | \(0.331032\pi\) | ||||
−0.506248 | + | 0.862388i | \(0.668968\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.5653 | + | 1.75281i | −1.35687 | + | 0.0930296i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.9119 | −1.42036 | −0.710178 | − | 0.704023i | \(-0.751385\pi\) | ||||
−0.710178 | + | 0.704023i | \(0.751385\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.29090 | 0.120573 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.40810 | − | 35.1229i | −0.126046 | − | 1.83841i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.0525023i | 0.00274060i | 0.999999 | + | 0.00137030i | \(0.000436179\pi\) | ||||
−0.999999 | + | 0.00137030i | \(0.999564\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.9300 | 1.29430 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 0.561607i | − | 0.0290789i | −0.999894 | − | 0.0145395i | \(-0.995372\pi\) | ||
0.999894 | − | 0.0145395i | \(-0.00462822\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.8096i | 0.711232i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.3025 | −1.04287 | −0.521434 | − | 0.853292i | \(-0.674603\pi\) | ||||
−0.521434 | + | 0.853292i | \(0.674603\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.7628i | 1.16313i | 0.813501 | + | 0.581564i | \(0.197559\pi\) | ||||
−0.813501 | + | 0.581564i | \(0.802441\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.487212 | − | 7.10615i | −0.0248306 | − | 0.362163i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.0468 | −1.57414 | −0.787068 | − | 0.616866i | \(-0.788402\pi\) | ||||
−0.787068 | + | 0.616866i | \(0.788402\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.55545 | 0.179807 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.64085 | + | 0.249624i | −0.183191 | + | 0.0125599i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 0.111698i | − | 0.00560595i | −0.999996 | − | 0.00280297i | \(-0.999108\pi\) | ||
0.999996 | − | 0.00280297i | \(-0.000892215\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.8391 | −0.940778 | −0.470389 | − | 0.882459i | \(-0.655886\pi\) | ||||
−0.470389 | + | 0.882459i | \(0.655886\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.7729i | 0.536638i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.818744i | − | 0.0405836i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.8758 | 1.32892 | 0.664461 | − | 0.747323i | \(-0.268661\pi\) | ||||
0.664461 | + | 0.747323i | \(0.268661\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 9.71055i | − | 0.477825i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.61389 | − | 38.1244i | −0.128311 | − | 1.87145i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.8796 | 1.65513 | 0.827564 | − | 0.561372i | \(-0.189726\pi\) | ||||
0.827564 | + | 0.561372i | \(0.189726\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.0252 | 1.21965 | 0.609827 | − | 0.792535i | \(-0.291239\pi\) | ||||
0.609827 | + | 0.792535i | \(0.291239\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.42629 | − | 17.6109i | −0.117692 | − | 0.854255i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.70342i | − | 0.421188i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.3854 | 0.885595 | 0.442798 | − | 0.896622i | \(-0.353986\pi\) | ||||
0.442798 | + | 0.896622i | \(0.353986\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.6774i | 1.28203i | 0.767527 | + | 0.641016i | \(0.221487\pi\) | ||||
−0.767527 | + | 0.641016i | \(0.778513\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.61421i | 0.220727i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.3341 | 0.875037 | 0.437519 | − | 0.899209i | \(-0.355857\pi\) | ||||
0.437519 | + | 0.899209i | \(0.355857\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.7077i | 1.26892i | 0.772955 | + | 0.634461i | \(0.218778\pi\) | ||||
−0.772955 | + | 0.634461i | \(0.781222\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.3241 | + | 0.844964i | −0.584217 | + | 0.0400551i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.44716 | 0.209875 | 0.104937 | − | 0.994479i | \(-0.466536\pi\) | ||||
0.104937 | + | 0.994479i | \(0.466536\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.65587 | −0.219236 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.2992 | − | 1.04894i | 0.717237 | − | 0.0491753i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 16.6048i | − | 0.776739i | −0.921504 | − | 0.388370i | \(-0.873038\pi\) | ||
0.921504 | − | 0.388370i | \(-0.126962\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.58567 | 0.446449 | 0.223225 | − | 0.974767i | \(-0.428342\pi\) | ||||
0.223225 | + | 0.974767i | \(0.428342\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.87507i | 0.273038i | 0.990637 | + | 0.136519i | \(0.0435914\pi\) | ||||
−0.990637 | + | 0.136519i | \(0.956409\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 37.0199i | − | 1.71308i | −0.516082 | − | 0.856539i | \(-0.672610\pi\) | ||
0.516082 | − | 0.856539i | \(-0.327390\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −60.5018 | −2.79371 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.62420i | − | 0.120661i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.8551 | − | 3.14879i | 1.04867 | − | 0.144477i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.1392 | −1.05726 | −0.528628 | − | 0.848854i | \(-0.677293\pi\) | ||||
−0.528628 | + | 0.848854i | \(0.677293\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.76271 | 0.0803729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.34385 | − | 19.6005i | −0.0610212 | − | 0.890014i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.00217i | 0.136041i | 0.997684 | + | 0.0680206i | \(0.0216684\pi\) | ||||
−0.997684 | + | 0.0680206i | \(0.978332\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.4243 | 1.05713 | 0.528563 | − | 0.848894i | \(-0.322731\pi\) | ||||
0.528563 | + | 0.848894i | \(0.322731\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 29.3285i | − | 1.32089i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 46.9461i | 2.10582i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.5583 | −1.23368 | −0.616839 | − | 0.787089i | \(-0.711587\pi\) | ||||
−0.616839 | + | 0.787089i | \(0.711587\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 14.5757i | − | 0.649898i | −0.945732 | − | 0.324949i | \(-0.894653\pi\) | ||
0.945732 | − | 0.324949i | \(-0.105347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.0549 | − | 1.51213i | 0.981432 | − | 0.0672890i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.03925 | 0.223361 | 0.111680 | − | 0.993744i | \(-0.464377\pi\) | ||||
0.111680 | + | 0.993744i | \(0.464377\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −64.4968 | −2.85317 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.574405 | − | 8.37788i | −0.0253113 | − | 0.369173i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.970023i | 0.0426616i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.06479 | 0.178082 | 0.0890409 | − | 0.996028i | \(-0.471620\pi\) | ||||
0.0890409 | + | 0.996028i | \(0.471620\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 17.3203i | − | 0.757362i | −0.925527 | − | 0.378681i | \(-0.876378\pi\) | ||
0.925527 | − | 0.378681i | \(-0.123622\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 22.8793i | − | 0.996637i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 10.0239i | − | 0.434181i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.446950 | − | 6.51892i | −0.0193234 | − | 0.281837i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.60600 | −0.327614 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.2414 | 0.526298 | 0.263149 | − | 0.964755i | \(-0.415239\pi\) | ||||
0.263149 | + | 0.964755i | \(0.415239\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.7008 | − | 1.83066i | 1.14373 | − | 0.0784168i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 40.5381i | − | 1.73328i | −0.498931 | − | 0.866642i | \(-0.666274\pi\) | ||
0.498931 | − | 0.866642i | \(-0.333726\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 38.0621 | 1.62150 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.68576i | 0.284307i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 23.7396i | − | 1.00588i | −0.864322 | − | 0.502940i | \(-0.832252\pi\) | ||
0.864322 | − | 0.502940i | \(-0.167748\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.64978 | 0.238960 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.4297i | 0.439558i | 0.975550 | + | 0.219779i | \(0.0705336\pi\) | ||||
−0.975550 | + | 0.219779i | \(0.929466\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.46157 | + | 35.9027i | 0.103559 | + | 1.51044i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.80513 | −0.369130 | −0.184565 | − | 0.982820i | \(-0.559088\pi\) | ||||
−0.184565 | + | 0.982820i | \(0.559088\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.1688 | −1.55546 | −0.777732 | − | 0.628596i | \(-0.783630\pi\) | ||||
−0.777732 | + | 0.628596i | \(0.783630\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.682413 | + | 4.95321i | 0.0284586 | + | 0.206563i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.71439i | 0.0713710i | 0.999363 | + | 0.0356855i | \(0.0113615\pi\) | ||||
−0.999363 | + | 0.0356855i | \(0.988639\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −70.0085 | −2.90444 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.73216i | − | 0.195986i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 22.4610i | − | 0.927064i | −0.886080 | − | 0.463532i | \(-0.846582\pi\) | ||
0.886080 | − | 0.463532i | \(-0.153418\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.6923 | 1.22345 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.76392i | 0.359891i | 0.983677 | + | 0.179945i | \(0.0575921\pi\) | ||||
−0.983677 | + | 0.179945i | \(0.942408\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.4920 | + | 2.22772i | −1.33204 | + | 0.0913276i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.7472 | −1.70575 | −0.852873 | − | 0.522119i | \(-0.825142\pi\) | ||||
−0.852873 | + | 0.522119i | \(0.825142\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.55678 | −0.308247 | −0.154124 | − | 0.988052i | \(-0.549255\pi\) | ||||
−0.154124 | + | 0.988052i | \(0.549255\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.1903 | − | 1.58997i | 0.942818 | − | 0.0646416i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 33.5791i | − | 1.36293i | −0.731849 | − | 0.681466i | \(-0.761343\pi\) | ||
0.731849 | − | 0.681466i | \(-0.238657\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.08841 | −0.0844881 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8.48045i | − | 0.342522i | −0.985226 | − | 0.171261i | \(-0.945216\pi\) | ||
0.985226 | − | 0.171261i | \(-0.0547842\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.4302i | 0.822490i | 0.911525 | + | 0.411245i | \(0.134906\pi\) | ||||
−0.911525 | + | 0.411245i | \(0.865094\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.9158 | −0.840677 | −0.420338 | − | 0.907367i | \(-0.638089\pi\) | ||||
−0.420338 | + | 0.907367i | \(0.638089\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.6309i | 0.906689i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0686 | − | 6.76027i | 0.962745 | − | 0.270411i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.74361 | −0.149267 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.8205 | 0.510375 | 0.255187 | − | 0.966892i | \(-0.417863\pi\) | ||||
0.255187 | + | 0.966892i | \(0.417863\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.40174 | + | 20.4449i | 0.0556264 | + | 0.811329i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 16.3753i | − | 0.648815i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.35480 | 0.329995 | 0.164997 | − | 0.986294i | \(-0.447238\pi\) | ||||
0.164997 | + | 0.986294i | \(0.447238\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 28.6155i | − | 1.12849i | −0.825609 | − | 0.564243i | \(-0.809168\pi\) | ||
0.825609 | − | 0.564243i | \(-0.190832\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 47.9816i | 1.88635i | 0.332297 | + | 0.943175i | \(0.392176\pi\) | ||||
−0.332297 | + | 0.943175i | \(0.607824\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.84324 | −0.0723534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.3883i | 1.85445i | 0.374510 | + | 0.927223i | \(0.377811\pi\) | ||||
−0.374510 | + | 0.927223i | \(0.622189\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.88124 | − | 0.128982i | 0.0735060 | − | 0.00503973i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.2054 | −0.826046 | −0.413023 | − | 0.910721i | \(-0.635527\pi\) | ||||
−0.413023 | + | 0.910721i | \(0.635527\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.00823 | 0.311484 | 0.155742 | − | 0.987798i | \(-0.450223\pi\) | ||||
0.155742 | + | 0.987798i | \(0.450223\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.89110 | − | 42.1676i | −0.112112 | − | 1.63519i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.24889i | 0.319398i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.65207 | −0.0637773 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 21.5201i | − | 0.829540i | −0.909926 | − | 0.414770i | \(-0.863862\pi\) | ||
0.909926 | − | 0.414770i | \(-0.136138\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.53930i | 0.0975932i | 0.998809 | + | 0.0487966i | \(0.0155386\pi\) | ||||
−0.998809 | + | 0.0487966i | \(0.984461\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.9928 | −1.38128 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.5117i | 0.823123i | 0.911382 | + | 0.411561i | \(0.135016\pi\) | ||||
−0.911382 | + | 0.411561i | \(0.864984\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.365905 | + | 5.33685i | 0.0139805 | + | 0.203910i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.1881 | 0.388136 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.2563 | 0.618420 | 0.309210 | − | 0.950994i | \(-0.399935\pi\) | ||||
0.309210 | + | 0.950994i | \(0.399935\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.9132 | − | 1.63954i | 0.907080 | − | 0.0621913i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.2884i | 0.806355i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.7080 | 1.00875 | 0.504373 | − | 0.863486i | \(-0.331724\pi\) | ||||
0.504373 | + | 0.863486i | \(0.331724\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.85839i | − | 0.183238i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 40.4999i | − | 1.52316i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.7454 | −0.553774 | −0.276887 | − | 0.960902i | \(-0.589303\pi\) | ||||
−0.276887 | + | 0.960902i | \(0.589303\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.43498i | 0.240992i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.199109 | − | 2.90406i | −0.00744624 | − | 0.108606i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.8495 | −0.852143 | −0.426071 | − | 0.904689i | \(-0.640103\pi\) | ||||
−0.426071 | + | 0.904689i | \(0.640103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.3845 | −0.572947 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40.8585 | − | 5.62915i | 1.51745 | − | 0.209061i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 16.4360i | − | 0.609578i | −0.952420 | − | 0.304789i | \(-0.901414\pi\) | ||
0.952420 | − | 0.304789i | \(-0.0985860\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.9989 | −0.443794 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.6694i | 1.13280i | 0.824130 | + | 0.566400i | \(0.191664\pi\) | ||||
−0.824130 | + | 0.566400i | \(0.808336\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.4843i | 0.423031i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.64541 | 0.244455 | 0.122228 | − | 0.992502i | \(-0.460996\pi\) | ||||
0.122228 | + | 0.992502i | \(0.460996\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.54318i | 0.0566137i | 0.999599 | + | 0.0283068i | \(0.00901155\pi\) | ||||
−0.999599 | + | 0.0283068i | \(0.990988\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.6629 | + | 2.65081i | −1.41650 | + | 0.0971182i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.9708 | −0.437404 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.2481 | 1.83358 | 0.916790 | − | 0.399369i | \(-0.130771\pi\) | ||||
0.916790 | + | 0.399369i | \(0.130771\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −44.6433 | + | 3.06084i | −1.62474 | + | 0.111395i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 35.2879i | − | 1.28256i | −0.767307 | − | 0.641280i | \(-0.778404\pi\) | ||
0.767307 | − | 0.641280i | \(-0.221596\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.39667 | 0.340629 | 0.170315 | − | 0.985390i | \(-0.445522\pi\) | ||||
0.170315 | + | 0.985390i | \(0.445522\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 49.0311i | − | 1.77505i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.96840i | − | 0.143291i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.6412 | −0.491913 | −0.245957 | − | 0.969281i | \(-0.579102\pi\) | ||||
−0.245957 | + | 0.969281i | \(0.579102\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.3829i | 1.41650i | 0.705960 | + | 0.708252i | \(0.250516\pi\) | ||||
−0.705960 | + | 0.708252i | \(0.749484\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.8738 | − | 4.39131i | 1.14494 | − | 0.157741i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.6277 | −0.989865 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.91123 | 0.318869 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.21155 | + | 17.6709i | 0.0432421 | + | 0.630700i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 21.3591i | − | 0.761369i | −0.924705 | − | 0.380685i | \(-0.875688\pi\) | ||
0.924705 | − | 0.380685i | \(-0.124312\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 65.9289 | 2.34416 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.55682i | − | 0.126306i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.83989i | 0.136016i | 0.997685 | + | 0.0680080i | \(0.0216643\pi\) | ||||
−0.997685 | + | 0.0680080i | \(0.978336\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.43531 | 0.156910 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.2427i | 0.432034i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.13864 | − | 0.626564i | 0.322095 | − | 0.0220835i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.8509 | −0.873710 | −0.436855 | − | 0.899532i | \(-0.643908\pi\) | ||||
−0.436855 | + | 0.899532i | \(0.643908\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.9097 | 0.980043 | 0.490021 | − | 0.871710i | \(-0.336989\pi\) | ||||
0.490021 | + | 0.871710i | \(0.336989\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.81871 | − | 26.5265i | −0.0637066 | − | 0.929181i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 15.5719i | − | 0.544792i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.2831 | −1.40589 | −0.702945 | − | 0.711245i | \(-0.748132\pi\) | ||||
−0.702945 | + | 0.711245i | \(0.748132\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.67595i | 0.162993i | 0.996674 | + | 0.0814967i | \(0.0259700\pi\) | ||||
−0.996674 | + | 0.0814967i | \(0.974030\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 13.4452i | − | 0.467537i | −0.972292 | − | 0.233768i | \(-0.924894\pi\) | ||
0.972292 | − | 0.233768i | \(-0.0751057\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.5096 | 1.40695 | 0.703477 | − | 0.710718i | \(-0.251630\pi\) | ||||
0.703477 | + | 0.710718i | \(0.251630\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.7775i | 1.20497i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.37515 | − | 34.6424i | −0.0821956 | − | 1.19885i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.7585 | −1.23452 | −0.617260 | − | 0.786759i | \(-0.711757\pi\) | ||||
−0.617260 | + | 0.786759i | \(0.711757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.0441 | 1.34635 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.7485 | + | 1.55968i | −0.782572 | + | 0.0536548i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 42.5847i | − | 1.46323i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.05292 | 0.0360936 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.42183i | − | 0.185640i | −0.995683 | − | 0.0928200i | \(-0.970412\pi\) | ||
0.995683 | − | 0.0928200i | \(-0.0295881\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.5420i | 1.38489i | 0.721471 | + | 0.692444i | \(0.243466\pi\) | ||||
−0.721471 | + | 0.692444i | \(0.756534\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.0671 | 0.923517 | 0.461758 | − | 0.887006i | \(-0.347219\pi\) | ||||
0.461758 | + | 0.887006i | \(0.347219\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 21.6380i | − | 0.736566i | −0.929714 | − | 0.368283i | \(-0.879946\pi\) | ||
0.929714 | − | 0.368283i | \(-0.120054\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.43226 | − | 35.4752i | −0.0826992 | − | 1.20619i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.26908 | 0.0430505 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.7252 | −0.837782 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.33983 | − | 44.8380i | −0.315744 | − | 1.51580i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.5945i | 0.931799i | 0.884838 | + | 0.465899i | \(0.154269\pi\) | ||||
−0.884838 | + | 0.465899i | \(0.845731\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.8296 | 1.07237 | 0.536183 | − | 0.844102i | \(-0.319866\pi\) | ||||
0.536183 | + | 0.844102i | \(0.319866\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 29.9009i | − | 1.00625i | −0.864215 | − | 0.503123i | \(-0.832184\pi\) | ||
0.864215 | − | 0.503123i | \(-0.167816\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 33.1746i | − | 1.11389i | −0.830548 | − | 0.556947i | \(-0.811973\pi\) | ||
0.830548 | − | 0.556947i | \(-0.188027\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.5433 | 1.25916 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.75607i | 0.192620i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.6452 | − | 1.55260i | 0.756946 | − | 0.0518978i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 53.0814 | 1.77036 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.6373 | −0.720841 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.7876 | − | 1.90518i | 0.923692 | − | 0.0633303i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 45.3211i | − | 1.50486i | −0.658671 | − | 0.752431i | \(-0.728881\pi\) | ||
0.658671 | − | 0.752431i | \(-0.271119\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.8181 | 0.789128 | 0.394564 | − | 0.918869i | \(-0.370896\pi\) | ||||
0.394564 | + | 0.918869i | \(0.370896\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.2889i | 0.439798i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 3.45455i | − | 0.114079i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.6196 | 1.57083 | 0.785413 | − | 0.618972i | \(-0.212450\pi\) | ||||
0.785413 | + | 0.618972i | \(0.212450\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.1854i | 0.631496i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.718526 | − | 5.21534i | −0.0236250 | − | 0.171479i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.1069 | 0.331595 | 0.165798 | − | 0.986160i | \(-0.446980\pi\) | ||||
0.165798 | + | 0.986160i | \(0.446980\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.1337 | −1.47920 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.422862 | + | 6.16757i | 0.0138291 | + | 0.201701i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.1597i | 0.854601i | 0.904110 | + | 0.427300i | \(0.140535\pi\) | ||||
−0.904110 | + | 0.427300i | \(0.859465\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.5128 | −0.407905 | −0.203952 | − | 0.978981i | \(-0.565379\pi\) | ||||
−0.203952 | + | 0.978981i | \(0.565379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.98753i | − | 0.194981i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1.43126i | − | 0.0465097i | −0.999730 | − | 0.0232549i | \(-0.992597\pi\) | ||
0.999730 | − | 0.0232549i | \(-0.00740292\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.3579 | −0.855612 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49.3959i | 1.60009i | 0.599940 | + | 0.800045i | \(0.295191\pi\) | ||||
−0.599940 | + | 0.800045i | \(0.704809\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.1187 | − | 1.58507i | 0.748103 | − | 0.0512915i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.80016 | 0.316464 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.4090 | 0.335773 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.24665 | − | 32.7682i | −0.0723223 | − | 1.05484i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.4504i | 0.496852i | 0.968651 | + | 0.248426i | \(0.0799132\pi\) | ||||
−0.968651 | + | 0.248426i | \(0.920087\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.3962 | −0.847095 | −0.423548 | − | 0.905874i | \(-0.639215\pi\) | ||||
−0.423548 | + | 0.905874i | \(0.639215\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 43.9123i | − | 1.40776i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 52.0950i | − | 1.66667i | −0.552770 | − | 0.833334i | \(-0.686429\pi\) | ||
0.552770 | − | 0.833334i | \(-0.313571\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.29576 | 0.137293 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.7660i | 0.470962i | 0.971879 | + | 0.235481i | \(0.0756666\pi\) | ||||
−0.971879 | + | 0.235481i | \(0.924333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.94456 | + | 42.9473i | 0.0938214 | + | 1.36841i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.37477 | 0.107312 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.5090 | 1.47741 | 0.738703 | − | 0.674031i | \(-0.235439\pi\) | ||||
0.738703 | + | 0.674031i | \(0.235439\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.1293 | + | 1.31154i | −0.606438 | + | 0.0415787i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 53.1892i | − | 1.68452i | −0.539071 | − | 0.842260i | \(-0.681225\pi\) | ||
0.539071 | − | 0.842260i | \(-0.318775\pi\) | |||||||
\(998\) | 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 | 4140.2.f.d.829.2 | yes | 24 | |
3.2 | odd | 2 | inner | 4140.2.f.d.829.23 | yes | 24 | |
5.4 | even | 2 | inner | 4140.2.f.d.829.1 | ✓ | 24 | |
15.14 | odd | 2 | inner | 4140.2.f.d.829.24 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.f.d.829.1 | ✓ | 24 | 5.4 | even | 2 | inner | |
4140.2.f.d.829.2 | yes | 24 | 1.1 | even | 1 | trivial | |
4140.2.f.d.829.23 | yes | 24 | 3.2 | odd | 2 | inner | |
4140.2.f.d.829.24 | yes | 24 | 15.14 | odd | 2 | inner |