Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,3,Mod(449,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.c (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: | \(85.8312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.9671731157401600000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 7x^{12} + 753x^{8} + 112x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.5 | ||
Root | \(-0.941471 - 2.08559i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.449 |
Dual form | 3150.3.c.f.449.4 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 6.61683i | − 0.601530i | −0.953698 | − | 0.300765i | \(-0.902758\pi\) | ||||
0.953698 | − | 0.300765i | \(-0.0972420\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.21640i | 0.478185i | 0.970997 | + | 0.239092i | \(0.0768499\pi\) | ||||
−0.970997 | + | 0.239092i | \(0.923150\pi\) | |||||||
\(14\) | − 3.74166i | − 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −6.35806 | −0.374003 | −0.187002 | − | 0.982360i | \(-0.559877\pi\) | ||||
−0.187002 | + | 0.982360i | \(0.559877\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 23.5709 | 1.24057 | 0.620287 | − | 0.784375i | \(-0.287016\pi\) | ||||
0.620287 | + | 0.784375i | \(0.287016\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.35761i | 0.425346i | ||||||||
\(23\) | −12.8687 | −0.559508 | −0.279754 | − | 0.960072i | \(-0.590253\pi\) | ||||
−0.279754 | + | 0.960072i | \(0.590253\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − 8.79132i | − 0.338128i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.29150i | 0.188982i | ||||||||
\(29\) | − 21.7071i | − 0.748522i | −0.927323 | − | 0.374261i | \(-0.877896\pi\) | ||||
0.927323 | − | 0.374261i | \(-0.122104\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −39.5362 | −1.27536 | −0.637681 | − | 0.770300i | \(-0.720106\pi\) | ||||
−0.637681 | + | 0.770300i | \(0.720106\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.99165 | 0.264460 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 56.9502i | 1.53920i | 0.638529 | + | 0.769598i | \(0.279543\pi\) | ||||
−0.638529 | + | 0.769598i | \(0.720457\pi\) | |||||||
\(38\) | −33.3343 | −0.877219 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 44.4993i | 1.08535i | 0.839943 | + | 0.542674i | \(0.182588\pi\) | ||||
−0.839943 | + | 0.542674i | \(0.817412\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 60.1402i | − 1.39861i | −0.714824 | − | 0.699305i | \(-0.753493\pi\) | ||||
0.714824 | − | 0.699305i | \(-0.246507\pi\) | |||||||
\(44\) | − 13.2337i | − 0.300765i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.1991 | 0.395632 | ||||||||
\(47\) | 20.6191 | 0.438705 | 0.219352 | − | 0.975646i | \(-0.429606\pi\) | ||||
0.219352 | + | 0.975646i | \(0.429606\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 12.4328i | 0.239092i | ||||||||
\(53\) | 40.0788 | 0.756204 | 0.378102 | − | 0.925764i | \(-0.376577\pi\) | ||||
0.378102 | + | 0.925764i | \(0.376577\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 7.48331i | − 0.133631i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 30.6985i | 0.529285i | ||||||||
\(59\) | − 25.4866i | − 0.431976i | −0.976396 | − | 0.215988i | \(-0.930703\pi\) | ||||
0.976396 | − | 0.215988i | \(-0.0692971\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.743719 | −0.0121921 | −0.00609606 | − | 0.999981i | \(-0.501940\pi\) | ||||
−0.00609606 | + | 0.999981i | \(0.501940\pi\) | |||||||
\(62\) | 55.9127 | 0.901818 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 68.8315i | 1.02734i | 0.857989 | + | 0.513668i | \(0.171714\pi\) | ||||
−0.857989 | + | 0.513668i | \(0.828286\pi\) | |||||||
\(68\) | −12.7161 | −0.187002 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 56.6306i | − 0.797614i | −0.917035 | − | 0.398807i | \(-0.869424\pi\) | ||||
0.917035 | − | 0.398807i | \(-0.130576\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.1000i | 0.179452i | 0.995966 | + | 0.0897261i | \(0.0285992\pi\) | ||||
−0.995966 | + | 0.0897261i | \(0.971401\pi\) | |||||||
\(74\) | − 80.5398i | − 1.08838i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 47.1418 | 0.620287 | ||||||||
\(77\) | 17.5065 | 0.227357 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 22.2403 | 0.281522 | 0.140761 | − | 0.990044i | \(-0.455045\pi\) | ||||
0.140761 | + | 0.990044i | \(0.455045\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 62.9315i | − 0.767458i | ||||||||
\(83\) | −151.071 | −1.82013 | −0.910066 | − | 0.414463i | \(-0.863969\pi\) | ||||
−0.910066 | + | 0.414463i | \(0.863969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 85.0511i | 0.988966i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 18.7152i | 0.212673i | ||||||||
\(89\) | 6.08695i | 0.0683927i | 0.999415 | + | 0.0341963i | \(0.0108872\pi\) | ||||
−0.999415 | + | 0.0341963i | \(0.989113\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.4471 | −0.180737 | ||||||||
\(92\) | −25.7374 | −0.279754 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −29.1598 | −0.310211 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 135.146i | 1.39326i | 0.717431 | + | 0.696630i | \(0.245318\pi\) | ||||
−0.717431 | + | 0.696630i | \(0.754682\pi\) | |||||||
\(98\) | 9.89949 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 99.7356i | − 0.987481i | −0.869609 | − | 0.493741i | \(-0.835629\pi\) | ||||
0.869609 | − | 0.493741i | \(-0.164371\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 92.9283i | 0.902216i | 0.892469 | + | 0.451108i | \(0.148971\pi\) | ||||
−0.892469 | + | 0.451108i | \(0.851029\pi\) | |||||||
\(104\) | − 17.5826i | − 0.169064i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −56.6800 | −0.534717 | ||||||||
\(107\) | 41.9615 | 0.392164 | 0.196082 | − | 0.980588i | \(-0.437178\pi\) | ||||
0.196082 | + | 0.980588i | \(0.437178\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −145.762 | −1.33727 | −0.668635 | − | 0.743591i | \(-0.733121\pi\) | ||||
−0.668635 | + | 0.743591i | \(0.733121\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.5830i | 0.0944911i | ||||||||
\(113\) | −29.6161 | −0.262089 | −0.131045 | − | 0.991376i | \(-0.541833\pi\) | ||||
−0.131045 | + | 0.991376i | \(0.541833\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − 43.4143i | − 0.374261i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 36.0434i | 0.305453i | ||||||||
\(119\) | − 16.8218i | − 0.141360i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 77.2176 | 0.638162 | ||||||||
\(122\) | 1.05178 | 0.00862113 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −79.0725 | −0.637681 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 213.731i | 1.68292i | 0.540319 | + | 0.841460i | \(0.318304\pi\) | ||||
−0.540319 | + | 0.841460i | \(0.681696\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 136.249i | − 1.04007i | −0.854146 | − | 0.520033i | \(-0.825920\pi\) | ||||
0.854146 | − | 0.520033i | \(-0.174080\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 62.3628i | 0.468893i | ||||||||
\(134\) | − 97.3424i | − 0.726436i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.9833 | 0.132230 | ||||||||
\(137\) | −5.36713 | −0.0391761 | −0.0195881 | − | 0.999808i | \(-0.506235\pi\) | ||||
−0.0195881 | + | 0.999808i | \(0.506235\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −135.187 | −0.972571 | −0.486286 | − | 0.873800i | \(-0.661649\pi\) | ||||
−0.486286 | + | 0.873800i | \(0.661649\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 80.0878i | 0.563998i | ||||||||
\(143\) | 41.1329 | 0.287643 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − 18.5262i | − 0.126892i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 113.900i | 0.769598i | ||||||||
\(149\) | − 102.343i | − 0.686864i | −0.939178 | − | 0.343432i | \(-0.888411\pi\) | ||||
0.939178 | − | 0.343432i | \(-0.111589\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 38.7465 | 0.256599 | 0.128300 | − | 0.991735i | \(-0.459048\pi\) | ||||
0.128300 | + | 0.991735i | \(0.459048\pi\) | |||||||
\(152\) | −66.6686 | −0.438609 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −24.7579 | −0.160766 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.44059i | 0.0155451i | 0.999970 | + | 0.00777257i | \(0.00247411\pi\) | ||||
−0.999970 | + | 0.00777257i | \(0.997526\pi\) | |||||||
\(158\) | −31.4525 | −0.199066 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 34.0473i | − 0.211474i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 134.270i | − 0.823742i | −0.911242 | − | 0.411871i | \(-0.864875\pi\) | ||||
0.911242 | − | 0.411871i | \(-0.135125\pi\) | |||||||
\(164\) | 88.9986i | 0.542674i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 213.647 | 1.28703 | ||||||||
\(167\) | −130.041 | −0.778691 | −0.389346 | − | 0.921092i | \(-0.627299\pi\) | ||||
−0.389346 | + | 0.921092i | \(0.627299\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 130.356 | 0.771339 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 120.280i | − 0.699305i | ||||||||
\(173\) | −63.1882 | −0.365250 | −0.182625 | − | 0.983183i | \(-0.558459\pi\) | ||||
−0.182625 | + | 0.983183i | \(0.558459\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 26.4673i | − 0.150382i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 8.60825i | − 0.0483609i | ||||||||
\(179\) | 302.826i | 1.69177i | 0.533368 | + | 0.845883i | \(0.320926\pi\) | ||||
−0.533368 | + | 0.845883i | \(0.679074\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 49.3100 | 0.272431 | 0.136216 | − | 0.990679i | \(-0.456506\pi\) | ||||
0.136216 | + | 0.990679i | \(0.456506\pi\) | |||||||
\(182\) | 23.2597 | 0.127800 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 36.3981 | 0.197816 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 42.0702i | 0.224974i | ||||||||
\(188\) | 41.2382 | 0.219352 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 42.4520i | − 0.222262i | −0.993806 | − | 0.111131i | \(-0.964553\pi\) | ||||
0.993806 | − | 0.111131i | \(-0.0354473\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 84.2418i | − 0.436486i | −0.975894 | − | 0.218243i | \(-0.929967\pi\) | ||||
0.975894 | − | 0.218243i | \(-0.0700325\pi\) | |||||||
\(194\) | − 191.126i | − 0.985183i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −188.098 | −0.954814 | −0.477407 | − | 0.878682i | \(-0.658423\pi\) | ||||
−0.477407 | + | 0.878682i | \(0.658423\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −36.9792 | −0.185825 | −0.0929127 | − | 0.995674i | \(-0.529618\pi\) | ||||
−0.0929127 | + | 0.995674i | \(0.529618\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 141.047i | 0.698255i | ||||||||
\(203\) | 57.4317 | 0.282915 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − 131.420i | − 0.637963i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 24.8656i | 0.119546i | ||||||||
\(209\) | − 155.965i | − 0.746243i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −142.836 | −0.676948 | −0.338474 | − | 0.940976i | \(-0.609911\pi\) | ||||
−0.338474 | + | 0.940976i | \(0.609911\pi\) | |||||||
\(212\) | 80.1576 | 0.378102 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −59.3425 | −0.277302 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 104.603i | − 0.482042i | ||||||||
\(218\) | 206.139 | 0.945593 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 39.5243i | − 0.178843i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 69.1669i | − 0.310165i | −0.987901 | − | 0.155083i | \(-0.950436\pi\) | ||||
0.987901 | − | 0.155083i | \(-0.0495644\pi\) | |||||||
\(224\) | − 14.9666i | − 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 41.8835 | 0.185325 | ||||||||
\(227\) | −212.932 | −0.938025 | −0.469012 | − | 0.883192i | \(-0.655390\pi\) | ||||
−0.469012 | + | 0.883192i | \(0.655390\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −386.569 | −1.68807 | −0.844036 | − | 0.536286i | \(-0.819827\pi\) | ||||
−0.844036 | + | 0.536286i | \(0.819827\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 61.3970i | 0.264642i | ||||||||
\(233\) | −220.391 | −0.945886 | −0.472943 | − | 0.881093i | \(-0.656808\pi\) | ||||
−0.472943 | + | 0.881093i | \(0.656808\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − 50.9731i | − 0.215988i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 23.7897i | 0.0999566i | ||||||||
\(239\) | − 174.401i | − 0.729711i | −0.931064 | − | 0.364856i | \(-0.881118\pi\) | ||||
0.931064 | − | 0.364856i | \(-0.118882\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 383.572 | 1.59159 | 0.795793 | − | 0.605569i | \(-0.207054\pi\) | ||||
0.795793 | + | 0.605569i | \(0.207054\pi\) | |||||||
\(242\) | −109.202 | −0.451249 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.48744 | −0.00609606 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 146.526i | 0.593224i | ||||||||
\(248\) | 111.825 | 0.450909 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 289.914i | 1.15503i | 0.816378 | + | 0.577517i | \(0.195978\pi\) | ||||
−0.816378 | + | 0.577517i | \(0.804022\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 85.1498i | 0.336561i | ||||||||
\(254\) | − 302.261i | − 1.19000i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −335.260 | −1.30451 | −0.652257 | − | 0.757998i | \(-0.726178\pi\) | ||||
−0.652257 | + | 0.757998i | \(0.726178\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −150.676 | −0.581761 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 192.685i | 0.735437i | ||||||||
\(263\) | 365.898 | 1.39125 | 0.695623 | − | 0.718407i | \(-0.255128\pi\) | ||||
0.695623 | + | 0.718407i | \(0.255128\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − 88.1943i | − 0.331558i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 137.663i | 0.513668i | ||||||||
\(269\) | 319.390i | 1.18732i | 0.804715 | + | 0.593661i | \(0.202318\pi\) | ||||
−0.804715 | + | 0.593661i | \(0.797682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 69.4293 | 0.256197 | 0.128098 | − | 0.991761i | \(-0.459113\pi\) | ||||
0.128098 | + | 0.991761i | \(0.459113\pi\) | |||||||
\(272\) | −25.4322 | −0.0935008 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.59026 | 0.0277017 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 544.473i | 1.96561i | 0.184657 | + | 0.982803i | \(0.440882\pi\) | ||||
−0.184657 | + | 0.982803i | \(0.559118\pi\) | |||||||
\(278\) | 191.184 | 0.687712 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 54.2597i | 0.193095i | 0.995328 | + | 0.0965476i | \(0.0307800\pi\) | ||||
−0.995328 | + | 0.0965476i | \(0.969220\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 256.916i | 0.907829i | 0.891045 | + | 0.453914i | \(0.149973\pi\) | ||||
−0.891045 | + | 0.453914i | \(0.850027\pi\) | |||||||
\(284\) | − 113.261i | − 0.398807i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −58.1707 | −0.203394 | ||||||||
\(287\) | −117.734 | −0.410223 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −248.575 | −0.860121 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 26.2000i | 0.0897261i | ||||||||
\(293\) | −118.382 | −0.404035 | −0.202017 | − | 0.979382i | \(-0.564750\pi\) | ||||
−0.202017 | + | 0.979382i | \(0.564750\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − 161.080i | − 0.544188i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 144.734i | 0.485686i | ||||||||
\(299\) | − 79.9969i | − 0.267548i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 159.116 | 0.528625 | ||||||||
\(302\) | −54.7958 | −0.181443 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 94.2837 | 0.310144 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 144.092i | 0.469355i | 0.972073 | + | 0.234677i | \(0.0754034\pi\) | ||||
−0.972073 | + | 0.234677i | \(0.924597\pi\) | |||||||
\(308\) | 35.0130 | 0.113678 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 126.216i | − 0.405839i | −0.979195 | − | 0.202920i | \(-0.934957\pi\) | ||||
0.979195 | − | 0.202920i | \(-0.0650430\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 112.210i | 0.358498i | 0.983804 | + | 0.179249i | \(0.0573668\pi\) | ||||
−0.983804 | + | 0.179249i | \(0.942633\pi\) | |||||||
\(314\) | − 3.45151i | − 0.0109921i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 44.4805 | 0.140761 | ||||||||
\(317\) | 454.598 | 1.43406 | 0.717032 | − | 0.697040i | \(-0.245500\pi\) | ||||
0.717032 | + | 0.697040i | \(0.245500\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −143.632 | −0.450258 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 48.1502i | 0.149535i | ||||||||
\(323\) | −149.865 | −0.463979 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 189.886i | 0.582473i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 125.863i | − 0.383729i | ||||||||
\(329\) | 54.5530i | 0.165815i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −453.034 | −1.36868 | −0.684342 | − | 0.729161i | \(-0.739910\pi\) | ||||
−0.684342 | + | 0.729161i | \(0.739910\pi\) | |||||||
\(332\) | −302.142 | −0.910066 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 183.906 | 0.550618 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 201.485i | − 0.597878i | −0.954272 | − | 0.298939i | \(-0.903367\pi\) | ||||
0.954272 | − | 0.298939i | \(-0.0966328\pi\) | |||||||
\(338\) | −184.352 | −0.545419 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 261.604i | 0.767169i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 18.5203i | − 0.0539949i | ||||||||
\(344\) | 170.102i | 0.494483i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 89.3616 | 0.258271 | ||||||||
\(347\) | −138.431 | −0.398936 | −0.199468 | − | 0.979904i | \(-0.563921\pi\) | ||||
−0.199468 | + | 0.979904i | \(0.563921\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −221.471 | −0.634586 | −0.317293 | − | 0.948327i | \(-0.602774\pi\) | ||||
−0.317293 | + | 0.948327i | \(0.602774\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 37.4304i | 0.106336i | ||||||||
\(353\) | −644.762 | −1.82652 | −0.913260 | − | 0.407377i | \(-0.866444\pi\) | ||||
−0.913260 | + | 0.407377i | \(0.866444\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.1739i | 0.0341963i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 428.261i | − 1.19626i | ||||||||
\(359\) | − 429.577i | − 1.19659i | −0.801275 | − | 0.598296i | \(-0.795845\pi\) | ||||
0.801275 | − | 0.598296i | \(-0.204155\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 194.588 | 0.539026 | ||||||||
\(362\) | −69.7349 | −0.192638 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −32.8941 | −0.0903685 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 394.169i | 1.07403i | 0.843573 | + | 0.537015i | \(0.180448\pi\) | ||||
−0.843573 | + | 0.537015i | \(0.819552\pi\) | |||||||
\(368\) | −51.4747 | −0.139877 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 106.039i | 0.285818i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 23.1268i | − 0.0620021i | −0.999519 | − | 0.0310011i | \(-0.990130\pi\) | ||||
0.999519 | − | 0.0310011i | \(-0.00986952\pi\) | |||||||
\(374\) | − 59.4962i | − 0.159081i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −58.3197 | −0.155105 | ||||||||
\(377\) | 134.940 | 0.357932 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −593.049 | −1.56477 | −0.782387 | − | 0.622793i | \(-0.785998\pi\) | ||||
−0.782387 | + | 0.622793i | \(0.785998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 60.0362i | 0.157163i | ||||||||
\(383\) | −116.922 | −0.305280 | −0.152640 | − | 0.988282i | \(-0.548778\pi\) | ||||
−0.152640 | + | 0.988282i | \(0.548778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 119.136i | 0.308642i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 270.292i | 0.696630i | ||||||||
\(389\) | − 105.357i | − 0.270841i | −0.990788 | − | 0.135421i | \(-0.956761\pi\) | ||||
0.990788 | − | 0.135421i | \(-0.0432386\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 81.8198 | 0.209258 | ||||||||
\(392\) | 19.7990 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 266.011 | 0.675156 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 353.467i | − 0.890346i | −0.895445 | − | 0.445173i | \(-0.853142\pi\) | ||||
0.895445 | − | 0.445173i | \(-0.146858\pi\) | |||||||
\(398\) | 52.2965 | 0.131398 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 768.878i | 1.91740i | 0.284417 | + | 0.958701i | \(0.408200\pi\) | ||||
−0.284417 | + | 0.958701i | \(0.591800\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 245.773i | − 0.609859i | ||||||||
\(404\) | − 199.471i | − 0.493741i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −81.2206 | −0.200051 | ||||||||
\(407\) | 376.830 | 0.925872 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −585.131 | −1.43064 | −0.715319 | − | 0.698798i | \(-0.753718\pi\) | ||||
−0.715319 | + | 0.698798i | \(0.753718\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 185.857i | 0.451108i | ||||||||
\(413\) | 67.4311 | 0.163271 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − 35.1653i | − 0.0845320i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 220.567i | 0.527673i | ||||||||
\(419\) | − 287.325i | − 0.685740i | −0.939383 | − | 0.342870i | \(-0.888601\pi\) | ||||
0.939383 | − | 0.342870i | \(-0.111399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −437.539 | −1.03929 | −0.519643 | − | 0.854383i | \(-0.673935\pi\) | ||||
−0.519643 | + | 0.854383i | \(0.673935\pi\) | |||||||
\(422\) | 202.001 | 0.478674 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −113.360 | −0.267358 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.96770i | − 0.00460819i | ||||||||
\(428\) | 83.9230 | 0.196082 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 51.0877i | 0.118533i | 0.998242 | + | 0.0592665i | \(0.0188762\pi\) | ||||
−0.998242 | + | 0.0592665i | \(0.981124\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 124.021i | 0.286422i | 0.989692 | + | 0.143211i | \(0.0457428\pi\) | ||||
−0.989692 | + | 0.143211i | \(0.954257\pi\) | |||||||
\(434\) | 147.931i | 0.340855i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −291.525 | −0.668635 | ||||||||
\(437\) | −303.327 | −0.694111 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 497.601 | 1.13349 | 0.566743 | − | 0.823894i | \(-0.308203\pi\) | ||||
0.566743 | + | 0.823894i | \(0.308203\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 55.8957i | 0.126461i | ||||||||
\(443\) | −823.485 | −1.85888 | −0.929441 | − | 0.368971i | \(-0.879710\pi\) | ||||
−0.929441 | + | 0.368971i | \(0.879710\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 97.8167i | 0.219320i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 21.1660i | 0.0472456i | ||||||||
\(449\) | − 583.811i | − 1.30025i | −0.759828 | − | 0.650124i | \(-0.774717\pi\) | ||||
0.759828 | − | 0.650124i | \(-0.225283\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 294.444 | 0.652870 | ||||||||
\(452\) | −59.2322 | −0.131045 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 301.131 | 0.663284 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 317.492i | 0.694731i | 0.937730 | + | 0.347366i | \(0.112924\pi\) | ||||
−0.937730 | + | 0.347366i | \(0.887076\pi\) | |||||||
\(458\) | 546.691 | 1.19365 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 703.769i | 1.52661i | 0.646036 | + | 0.763307i | \(0.276425\pi\) | ||||
−0.646036 | + | 0.763307i | \(0.723575\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 296.981i | − 0.641428i | −0.947176 | − | 0.320714i | \(-0.896077\pi\) | ||||
0.947176 | − | 0.320714i | \(-0.103923\pi\) | |||||||
\(464\) | − 86.8285i | − 0.187130i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 311.680 | 0.668842 | ||||||||
\(467\) | −839.787 | −1.79826 | −0.899130 | − | 0.437682i | \(-0.855800\pi\) | ||||
−0.899130 | + | 0.437682i | \(0.855800\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −182.111 | −0.388296 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 72.0869i | 0.152726i | ||||||||
\(473\) | −397.937 | −0.841305 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − 33.6437i | − 0.0706800i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 246.640i | 0.515984i | ||||||||
\(479\) | 840.794i | 1.75531i | 0.479292 | + | 0.877655i | \(0.340893\pi\) | ||||
−0.479292 | + | 0.877655i | \(0.659107\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −354.026 | −0.736020 | ||||||||
\(482\) | −542.453 | −1.12542 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 154.435 | 0.319081 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 274.175i | 0.562987i | 0.959563 | + | 0.281494i | \(0.0908298\pi\) | ||||
−0.959563 | + | 0.281494i | \(0.909170\pi\) | |||||||
\(488\) | 2.10356 | 0.00431057 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 165.218i | − 0.336494i | −0.985745 | − | 0.168247i | \(-0.946189\pi\) | ||||
0.985745 | − | 0.168247i | \(-0.0538106\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 138.015i | 0.279950i | ||||||||
\(494\) | − 207.220i | − 0.419473i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −158.145 | −0.318841 | ||||||||
\(497\) | 149.830 | 0.301470 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −61.0172 | −0.122279 | −0.0611395 | − | 0.998129i | \(-0.519473\pi\) | ||||
−0.0611395 | + | 0.998129i | \(0.519473\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 410.000i | − 0.816733i | ||||||||
\(503\) | −129.075 | −0.256611 | −0.128305 | − | 0.991735i | \(-0.540954\pi\) | ||||
−0.128305 | + | 0.991735i | \(0.540954\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − 120.420i | − 0.237984i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 427.462i | 0.841460i | ||||||||
\(509\) | 490.684i | 0.964016i | 0.876167 | + | 0.482008i | \(0.160092\pi\) | ||||
−0.876167 | + | 0.482008i | \(0.839908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.6594 | −0.0678265 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 474.129 | 0.922430 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 136.433i | − 0.263894i | ||||||||
\(518\) | 213.088 | 0.411367 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 770.179i | 1.47827i | 0.673557 | + | 0.739135i | \(0.264766\pi\) | ||||
−0.673557 | + | 0.739135i | \(0.735234\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 74.8406i | − 0.143099i | −0.997437 | − | 0.0715494i | \(-0.977206\pi\) | ||||
0.997437 | − | 0.0715494i | \(-0.0227943\pi\) | |||||||
\(524\) | − 272.497i | − 0.520033i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −517.458 | −0.983760 | ||||||||
\(527\) | 251.374 | 0.476990 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −363.397 | −0.686951 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 124.726i | 0.234447i | ||||||||
\(533\) | −276.626 | −0.518998 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − 194.685i | − 0.363218i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 451.685i | − 0.839564i | ||||||||
\(539\) | 46.3178i | 0.0859328i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −899.685 | −1.66300 | −0.831502 | − | 0.555522i | \(-0.812519\pi\) | ||||
−0.831502 | + | 0.555522i | \(0.812519\pi\) | |||||||
\(542\) | −98.1878 | −0.181158 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 35.9666 | 0.0661151 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 92.3806i | 0.168886i | 0.996428 | + | 0.0844430i | \(0.0269111\pi\) | ||||
−0.996428 | + | 0.0844430i | \(0.973089\pi\) | |||||||
\(548\) | −10.7343 | −0.0195881 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 511.657i | − 0.928597i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 58.8422i | 0.106405i | ||||||||
\(554\) | − 770.001i | − 1.38989i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −270.375 | −0.486286 | ||||||||
\(557\) | −202.763 | −0.364026 | −0.182013 | − | 0.983296i | \(-0.558261\pi\) | ||||
−0.182013 | + | 0.983296i | \(0.558261\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 373.856 | 0.668794 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 76.7349i | − 0.136539i | ||||||||
\(563\) | 445.660 | 0.791581 | 0.395791 | − | 0.918341i | \(-0.370471\pi\) | ||||
0.395791 | + | 0.918341i | \(0.370471\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − 363.333i | − 0.641932i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 160.176i | 0.281999i | ||||||||
\(569\) | 1063.41i | 1.86891i | 0.356080 | + | 0.934456i | \(0.384113\pi\) | ||||
−0.356080 | + | 0.934456i | \(0.615887\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −825.254 | −1.44528 | −0.722639 | − | 0.691226i | \(-0.757071\pi\) | ||||
−0.722639 | + | 0.691226i | \(0.757071\pi\) | |||||||
\(572\) | 82.2658 | 0.143821 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 166.501 | 0.290072 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 1013.50i | − 1.75651i | −0.478196 | − | 0.878253i | \(-0.658709\pi\) | ||||
0.478196 | − | 0.878253i | \(-0.341291\pi\) | |||||||
\(578\) | 351.538 | 0.608198 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 399.696i | − 0.687945i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 265.195i | − 0.454879i | ||||||||
\(584\) | − 37.0524i | − 0.0634459i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 167.418 | 0.285696 | ||||||||
\(587\) | −57.3023 | −0.0976189 | −0.0488095 | − | 0.998808i | \(-0.515543\pi\) | ||||
−0.0488095 | + | 0.998808i | \(0.515543\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −931.906 | −1.58218 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 227.801i | 0.384799i | ||||||||
\(593\) | −684.040 | −1.15352 | −0.576762 | − | 0.816912i | \(-0.695684\pi\) | ||||
−0.576762 | + | 0.816912i | \(0.695684\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 204.685i | − 0.343432i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 113.133i | 0.189185i | ||||||||
\(599\) | 715.347i | 1.19423i | 0.802154 | + | 0.597117i | \(0.203687\pi\) | ||||
−0.802154 | + | 0.597117i | \(0.796313\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −333.692 | −0.555227 | −0.277614 | − | 0.960693i | \(-0.589543\pi\) | ||||
−0.277614 | + | 0.960693i | \(0.589543\pi\) | |||||||
\(602\) | −225.024 | −0.373794 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 77.4930 | 0.128300 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 109.174i | 0.179858i | 0.995948 | + | 0.0899290i | \(0.0286640\pi\) | ||||
−0.995948 | + | 0.0899290i | \(0.971336\pi\) | |||||||
\(608\) | −133.337 | −0.219305 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 128.177i | 0.209782i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 326.936i | 0.533338i | 0.963788 | + | 0.266669i | \(0.0859231\pi\) | ||||
−0.963788 | + | 0.266669i | \(0.914077\pi\) | |||||||
\(614\) | − 203.777i | − 0.331884i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −49.5158 | −0.0803828 | ||||||||
\(617\) | −525.085 | −0.851030 | −0.425515 | − | 0.904951i | \(-0.639907\pi\) | ||||
−0.425515 | + | 0.904951i | \(0.639907\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 314.513 | 0.508099 | 0.254050 | − | 0.967191i | \(-0.418237\pi\) | ||||
0.254050 | + | 0.967191i | \(0.418237\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 178.496i | 0.286972i | ||||||||
\(623\) | −16.1046 | −0.0258500 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − 158.689i | − 0.253497i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.88118i | 0.00777257i | ||||||||
\(629\) | − 362.093i | − 0.575664i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 361.534 | 0.572954 | 0.286477 | − | 0.958087i | \(-0.407516\pi\) | ||||
0.286477 | + | 0.958087i | \(0.407516\pi\) | |||||||
\(632\) | −62.9049 | −0.0995331 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −642.899 | −1.01404 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 43.5148i | − 0.0683121i | ||||||||
\(638\) | 203.127 | 0.318381 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 299.674i | − 0.467510i | −0.972296 | − | 0.233755i | \(-0.924899\pi\) | ||||
0.972296 | − | 0.233755i | \(-0.0751013\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 276.617i | − 0.430198i | −0.976592 | − | 0.215099i | \(-0.930993\pi\) | ||||
0.976592 | − | 0.215099i | \(-0.0690074\pi\) | |||||||
\(644\) | − 68.0947i | − 0.105737i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 211.941 | 0.328083 | ||||||||
\(647\) | 900.003 | 1.39104 | 0.695520 | − | 0.718507i | \(-0.255174\pi\) | ||||
0.695520 | + | 0.718507i | \(0.255174\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −168.640 | −0.259846 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 268.540i | − 0.411871i | ||||||||
\(653\) | 173.928 | 0.266352 | 0.133176 | − | 0.991092i | \(-0.457482\pi\) | ||||
0.133176 | + | 0.991092i | \(0.457482\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 177.997i | 0.271337i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 77.1497i | − 0.117249i | ||||||||
\(659\) | 238.864i | 0.362465i | 0.983440 | + | 0.181232i | \(0.0580086\pi\) | ||||
−0.983440 | + | 0.181232i | \(0.941991\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 852.168 | 1.28921 | 0.644605 | − | 0.764516i | \(-0.277022\pi\) | ||||
0.644605 | + | 0.764516i | \(0.277022\pi\) | |||||||
\(662\) | 640.687 | 0.967806 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 427.293 | 0.643514 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 279.342i | 0.418804i | ||||||||
\(668\) | −260.083 | −0.389346 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.92106i | 0.00733392i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 159.472i | − 0.236957i | −0.992957 | − | 0.118479i | \(-0.962198\pi\) | ||||
0.992957 | − | 0.118479i | \(-0.0378017\pi\) | |||||||
\(674\) | 284.943i | 0.422764i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 260.713 | 0.385670 | ||||||||
\(677\) | −1100.80 | −1.62600 | −0.812999 | − | 0.582265i | \(-0.802167\pi\) | ||||
−0.812999 | + | 0.582265i | \(0.802167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −357.563 | −0.526603 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 369.965i | − 0.542470i | ||||||||
\(683\) | 1305.66 | 1.91166 | 0.955830 | − | 0.293919i | \(-0.0949596\pi\) | ||||
0.955830 | + | 0.293919i | \(0.0949596\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 240.561i | − 0.349652i | ||||||||
\(689\) | 249.146i | 0.361605i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −322.487 | −0.466696 | −0.233348 | − | 0.972393i | \(-0.574968\pi\) | ||||
−0.233348 | + | 0.972393i | \(0.574968\pi\) | |||||||
\(692\) | −126.376 | −0.182625 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 195.771 | 0.282091 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 282.929i | − 0.405924i | ||||||||
\(698\) | 313.207 | 0.448720 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 574.441i | 0.819459i | 0.912207 | + | 0.409730i | \(0.134377\pi\) | ||||
−0.912207 | + | 0.409730i | \(0.865623\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1342.37i | 1.90949i | ||||||||
\(704\) | − 52.9346i | − 0.0751912i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 911.831 | 1.29154 | ||||||||
\(707\) | 263.876 | 0.373233 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1194.48 | 1.68474 | 0.842372 | − | 0.538896i | \(-0.181158\pi\) | ||||
0.842372 | + | 0.538896i | \(0.181158\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 17.2165i | − 0.0241805i | ||||||||
\(713\) | 508.779 | 0.713575 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 605.652i | 0.845883i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 607.513i | 0.846119i | ||||||||
\(719\) | 58.4935i | 0.0813539i | 0.999172 | + | 0.0406770i | \(0.0129515\pi\) | ||||
−0.999172 | + | 0.0406770i | \(0.987049\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −245.865 | −0.341006 | ||||||||
\(722\) | −275.190 | −0.381149 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 98.6201 | 0.136216 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 194.084i | 0.266965i | 0.991051 | + | 0.133483i | \(0.0426161\pi\) | ||||
−0.991051 | + | 0.133483i | \(0.957384\pi\) | |||||||
\(728\) | 46.5193 | 0.0639002 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 382.375i | 0.523085i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 690.669i | − 0.942250i | −0.882066 | − | 0.471125i | \(-0.843848\pi\) | ||||
0.882066 | − | 0.471125i | \(-0.156152\pi\) | |||||||
\(734\) | − 557.439i | − 0.759453i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 72.7963 | 0.0989080 | ||||||||
\(737\) | 455.446 | 0.617973 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.443737 | −0.000600456 0 | −0.000300228 | − | 1.00000i | \(-0.500096\pi\) | ||||
−0.000300228 | 1.00000i | \(0.500096\pi\) | ||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 149.961i | − 0.202104i | ||||||||
\(743\) | −723.574 | −0.973855 | −0.486927 | − | 0.873442i | \(-0.661882\pi\) | ||||
−0.486927 | + | 0.873442i | \(0.661882\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 32.7062i | 0.0438421i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 84.1403i | 0.112487i | ||||||||
\(749\) | 111.020i | 0.148224i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 923.228 | 1.22933 | 0.614666 | − | 0.788788i | \(-0.289291\pi\) | ||||
0.614666 | + | 0.788788i | \(0.289291\pi\) | |||||||
\(752\) | 82.4765 | 0.109676 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −190.834 | −0.253096 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1096.39i | − 1.44833i | −0.689627 | − | 0.724165i | \(-0.742225\pi\) | ||||
0.689627 | − | 0.724165i | \(-0.257775\pi\) | |||||||
\(758\) | 838.698 | 1.10646 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 913.964i | − 1.20100i | −0.799623 | − | 0.600502i | \(-0.794967\pi\) | ||||
0.799623 | − | 0.600502i | \(-0.205033\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 385.651i | − 0.505441i | ||||||||
\(764\) | − 84.9040i | − 0.111131i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 165.353 | 0.215866 | ||||||||
\(767\) | 158.435 | 0.206564 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −770.840 | −1.00239 | −0.501197 | − | 0.865333i | \(-0.667107\pi\) | ||||
−0.501197 | + | 0.865333i | \(0.667107\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 168.484i | − 0.218243i | ||||||||
\(773\) | 250.584 | 0.324171 | 0.162085 | − | 0.986777i | \(-0.448178\pi\) | ||||
0.162085 | + | 0.986777i | \(0.448178\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − 382.251i | − 0.492592i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 148.998i | 0.191514i | ||||||||
\(779\) | 1048.89i | 1.34646i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −374.715 | −0.479789 | ||||||||
\(782\) | −115.711 | −0.147968 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2.48249i | − 0.00315437i | −0.999999 | − | 0.00157719i | \(-0.999498\pi\) | ||||
0.999999 | − | 0.00157719i | \(-0.000502034\pi\) | |||||||
\(788\) | −376.197 | −0.477407 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 78.3568i | − 0.0990604i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 4.62326i | − 0.00583009i | ||||||||
\(794\) | 499.878i | 0.629570i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −73.9585 | −0.0929127 | ||||||||
\(797\) | −269.762 | −0.338471 | −0.169236 | − | 0.985576i | \(-0.554130\pi\) | ||||
−0.169236 | + | 0.985576i | \(0.554130\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −131.098 | −0.164077 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 1087.36i | − 1.35581i | ||||||||
\(803\) | 86.6805 | 0.107946 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 347.576i | 0.431236i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 282.095i | 0.349127i | ||||||||
\(809\) | 811.512i | 1.00311i | 0.865127 | + | 0.501553i | \(0.167238\pi\) | ||||
−0.865127 | + | 0.501553i | \(0.832762\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 891.278 | 1.09899 | 0.549493 | − | 0.835498i | \(-0.314821\pi\) | ||||
0.549493 | + | 0.835498i | \(0.314821\pi\) | |||||||
\(812\) | 114.863 | 0.141457 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −532.918 | −0.654691 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 1417.56i | − 1.73508i | ||||||||
\(818\) | 827.500 | 1.01161 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 814.161i | − 0.991670i | −0.868417 | − | 0.495835i | \(-0.834862\pi\) | ||||
0.868417 | − | 0.495835i | \(-0.165138\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1497.09i | − 1.81906i | −0.415640 | − | 0.909529i | \(-0.636442\pi\) | ||||
0.415640 | − | 0.909529i | \(-0.363558\pi\) | |||||||
\(824\) | − 262.841i | − 0.318982i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −95.3620 | −0.115450 | ||||||||
\(827\) | 538.871 | 0.651597 | 0.325798 | − | 0.945439i | \(-0.394367\pi\) | ||||
0.325798 | + | 0.945439i | \(0.394367\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1512.58 | 1.82459 | 0.912293 | − | 0.409539i | \(-0.134310\pi\) | ||||
0.912293 | + | 0.409539i | \(0.134310\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 49.7312i | 0.0597731i | ||||||||
\(833\) | 44.5064 | 0.0534291 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − 311.929i | − 0.373121i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 406.339i | 0.484892i | ||||||||
\(839\) | 999.083i | 1.19080i | 0.803429 | + | 0.595401i | \(0.203007\pi\) | ||||
−0.803429 | + | 0.595401i | \(0.796993\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 369.801 | 0.439715 | ||||||||
\(842\) | 618.774 | 0.734886 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −285.672 | −0.338474 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 204.299i | 0.241203i | ||||||||
\(848\) | 160.315 | 0.189051 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 732.875i | − 0.861192i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 94.6292i | − 0.110937i | −0.998460 | − | 0.0554685i | \(-0.982335\pi\) | ||||
0.998460 | − | 0.0554685i | \(-0.0176652\pi\) | |||||||
\(854\) | 2.78274i | 0.00325848i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −118.685 | −0.138651 | ||||||||
\(857\) | 1326.35 | 1.54766 | 0.773831 | − | 0.633392i | \(-0.218338\pi\) | ||||
0.773831 | + | 0.633392i | \(0.218338\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1366.84 | 1.59119 | 0.795597 | − | 0.605826i | \(-0.207157\pi\) | ||||
0.795597 | + | 0.605826i | \(0.207157\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 72.2490i | − 0.0838155i | ||||||||
\(863\) | −367.560 | −0.425909 | −0.212955 | − | 0.977062i | \(-0.568309\pi\) | ||||
−0.212955 | + | 0.977062i | \(0.568309\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − 175.392i | − 0.202531i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 209.206i | − 0.241021i | ||||||||
\(869\) | − 147.160i | − 0.169344i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −427.884 | −0.491256 | ||||||||
\(872\) | 412.278 | 0.472796 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 428.969 | 0.490811 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 252.803i | 0.288259i | 0.989559 | + | 0.144129i | \(0.0460382\pi\) | ||||
−0.989559 | + | 0.144129i | \(0.953962\pi\) | |||||||
\(878\) | −703.714 | −0.801496 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 927.007i | 1.05222i | 0.850416 | + | 0.526111i | \(0.176350\pi\) | ||||
−0.850416 | + | 0.526111i | \(0.823650\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 965.503i | − 1.09343i | −0.837317 | − | 0.546717i | \(-0.815877\pi\) | ||||
0.837317 | − | 0.546717i | \(-0.184123\pi\) | |||||||
\(884\) | − 79.0485i | − 0.0894214i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1164.58 | 1.31443 | ||||||||
\(887\) | 41.9639 | 0.0473099 | 0.0236549 | − | 0.999720i | \(-0.492470\pi\) | ||||
0.0236549 | + | 0.999720i | \(0.492470\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −565.479 | −0.636084 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 138.334i | − 0.155083i | ||||||||
\(893\) | 486.012 | 0.544246 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − 29.9333i | − 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 825.634i | 0.919414i | ||||||||
\(899\) | 858.218i | 0.954637i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −254.823 | −0.282823 | ||||||||
\(902\) | −416.407 | −0.461649 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 83.7669 | 0.0926625 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 356.488i | 0.393040i | 0.980500 | + | 0.196520i | \(0.0629641\pi\) | ||||
−0.980500 | + | 0.196520i | \(0.937036\pi\) | |||||||
\(908\) | −425.863 | −0.469012 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 277.860i | − 0.305006i | −0.988303 | − | 0.152503i | \(-0.951267\pi\) | ||||
0.988303 | − | 0.152503i | \(-0.0487334\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 999.611i | 1.09486i | ||||||||
\(914\) | − 449.002i | − 0.491249i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −773.137 | −0.844036 | ||||||||
\(917\) | 360.480 | 0.393108 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 271.756 | 0.295708 | 0.147854 | − | 0.989009i | \(-0.452763\pi\) | ||||
0.147854 | + | 0.989009i | \(0.452763\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 995.279i | − 1.07948i | ||||||||
\(923\) | 352.039 | 0.381407 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 419.995i | 0.453558i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 122.794i | 0.132321i | ||||||||
\(929\) | − 368.676i | − 0.396853i | −0.980116 | − | 0.198426i | \(-0.936417\pi\) | ||||
0.980116 | − | 0.198426i | \(-0.0635831\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −164.996 | −0.177225 | ||||||||
\(932\) | −440.783 | −0.472943 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1187.64 | 1.27156 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 601.796i | 0.642258i | 0.947035 | + | 0.321129i | \(0.104062\pi\) | ||||
−0.947035 | + | 0.321129i | \(0.895938\pi\) | |||||||
\(938\) | 257.544 | 0.274567 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 63.5278i | 0.0675109i | 0.999430 | + | 0.0337554i | \(0.0107467\pi\) | ||||
−0.999430 | + | 0.0337554i | \(0.989253\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 572.647i | − 0.607261i | ||||||||
\(944\) | − 101.946i | − 0.107994i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 562.769 | 0.594893 | ||||||||
\(947\) | −47.9984 | −0.0506847 | −0.0253424 | − | 0.999679i | \(-0.508068\pi\) | ||||
−0.0253424 | + | 0.999679i | \(0.508068\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −81.4350 | −0.0858113 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 47.5793i | 0.0499783i | ||||||||
\(953\) | 223.027 | 0.234026 | 0.117013 | − | 0.993130i | \(-0.462668\pi\) | ||||
0.117013 | + | 0.993130i | \(0.462668\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − 348.802i | − 0.364856i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 1189.06i | − 1.24119i | ||||||||
\(959\) | − 14.2001i | − 0.0148072i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 602.114 | 0.626550 | ||||||||
\(962\) | 500.668 | 0.520445 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 767.144 | 0.795793 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1382.98i | − 1.43017i | −0.699036 | − | 0.715087i | \(-0.746387\pi\) | ||||
0.699036 | − | 0.715087i | \(-0.253613\pi\) | |||||||
\(968\) | −218.404 | −0.225624 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 646.400i | 0.665706i | 0.942979 | + | 0.332853i | \(0.108011\pi\) | ||||
−0.942979 | + | 0.332853i | \(0.891989\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 357.672i | − 0.367597i | ||||||||
\(974\) | − 387.742i | − 0.398092i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.97488 | −0.00304803 | ||||||||
\(977\) | −265.222 | −0.271466 | −0.135733 | − | 0.990745i | \(-0.543339\pi\) | ||||
−0.135733 | + | 0.990745i | \(0.543339\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.2763 | 0.0411402 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 233.654i | 0.237937i | ||||||||
\(983\) | −1376.44 | −1.40024 | −0.700121 | − | 0.714024i | \(-0.746871\pi\) | ||||
−0.700121 | + | 0.714024i | \(0.746871\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − 195.183i | − 0.197954i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 293.053i | 0.296612i | ||||||||
\(989\) | 773.925i | 0.782533i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −80.2405 | −0.0809693 | −0.0404846 | − | 0.999180i | \(-0.512890\pi\) | ||||
−0.0404846 | + | 0.999180i | \(0.512890\pi\) | |||||||
\(992\) | 223.651 | 0.225454 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −211.892 | −0.213171 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 409.667i | 0.410899i | 0.978668 | + | 0.205450i | \(0.0658657\pi\) | ||||
−0.978668 | + | 0.205450i | \(0.934134\pi\) | |||||||
\(998\) | 86.2913 | 0.0864643 | ||||||||
\(999\) | 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 | 3150.3.c.f.449.5 | 16 | ||
3.2 | odd | 2 | inner | 3150.3.c.f.449.16 | 16 | ||
5.2 | odd | 4 | 630.3.e.b.71.3 | ✓ | 8 | ||
5.3 | odd | 4 | 3150.3.e.f.701.7 | 8 | |||
5.4 | even | 2 | inner | 3150.3.c.f.449.9 | 16 | ||
15.2 | even | 4 | 630.3.e.b.71.5 | yes | 8 | ||
15.8 | even | 4 | 3150.3.e.f.701.4 | 8 | |||
15.14 | odd | 2 | inner | 3150.3.c.f.449.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.3.e.b.71.3 | ✓ | 8 | 5.2 | odd | 4 | ||
630.3.e.b.71.5 | yes | 8 | 15.2 | even | 4 | ||
3150.3.c.f.449.4 | 16 | 15.14 | odd | 2 | inner | ||
3150.3.c.f.449.5 | 16 | 1.1 | even | 1 | trivial | ||
3150.3.c.f.449.9 | 16 | 5.4 | even | 2 | inner | ||
3150.3.c.f.449.16 | 16 | 3.2 | odd | 2 | inner | ||
3150.3.e.f.701.4 | 8 | 15.8 | even | 4 | |||
3150.3.e.f.701.7 | 8 | 5.3 | odd | 4 |