Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(485,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1089.485");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.b (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: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{15})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 16x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 485.4 | ||
Root | \(3.44572i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.485 |
Dual form | 1089.3.b.c.485.1 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.44572i | 1.72286i | 0.507877 | + | 0.861430i | \(0.330431\pi\) | ||||
−0.507877 | + | 0.861430i | \(0.669569\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.87298 | −1.96825 | ||||||||
\(5\) | − 6.27415i | − 1.25483i | −0.778685 | − | 0.627415i | \(-0.784113\pi\) | ||||
0.778685 | − | 0.627415i | \(-0.215887\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.87298 | −1.26757 | −0.633785 | − | 0.773510i | \(-0.718499\pi\) | ||||
−0.633785 | + | 0.773510i | \(0.718499\pi\) | |||||||
\(8\) | − 13.3452i | − 1.66815i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 21.6190 | 2.16190 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −24.7460 | −1.90354 | −0.951768 | − | 0.306819i | \(-0.900735\pi\) | ||||
−0.951768 | + | 0.306819i | \(0.900735\pi\) | |||||||
\(14\) | − 30.5738i | − 2.18384i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.4919 | 0.905746 | ||||||||
\(17\) | 4.68030i | 0.275312i | 0.990480 | + | 0.137656i | \(0.0439568\pi\) | ||||
−0.990480 | + | 0.137656i | \(0.956043\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.2379 | 1.53884 | 0.769418 | − | 0.638745i | \(-0.220546\pi\) | ||||
0.769418 | + | 0.638745i | \(0.220546\pi\) | |||||||
\(20\) | 49.3963i | 2.46981i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 27.7454i | − 1.20632i | −0.797620 | − | 0.603161i | \(-0.793908\pi\) | ||||
0.797620 | − | 0.603161i | \(-0.206092\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.3649 | −0.574597 | ||||||||
\(26\) | − 85.2677i | − 3.27953i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 69.8569 | 2.49489 | ||||||||
\(29\) | 34.5584i | 1.19167i | 0.803107 | + | 0.595835i | \(0.203179\pi\) | ||||
−0.803107 | + | 0.595835i | \(0.796821\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 24.7298 | 0.797737 | 0.398868 | − | 0.917008i | \(-0.369403\pi\) | ||||
0.398868 | + | 0.917008i | \(0.369403\pi\) | |||||||
\(32\) | − 3.44572i | − 0.107679i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −16.1270 | −0.474324 | ||||||||
\(35\) | 55.6704i | 1.59058i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.36492 | −0.0368896 | −0.0184448 | − | 0.999830i | \(-0.505872\pi\) | ||||
−0.0184448 | + | 0.999830i | \(0.505872\pi\) | |||||||
\(38\) | 100.746i | 2.65120i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −83.7298 | −2.09325 | ||||||||
\(41\) | 50.9673i | 1.24310i | 0.783373 | + | 0.621552i | \(0.213498\pi\) | ||||
−0.783373 | + | 0.621552i | \(0.786502\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 62.8407 | 1.46141 | 0.730706 | − | 0.682692i | \(-0.239191\pi\) | ||||
0.730706 | + | 0.682692i | \(0.239191\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 95.6028 | 2.07832 | ||||||||
\(47\) | − 23.5027i | − 0.500058i | −0.968238 | − | 0.250029i | \(-0.919560\pi\) | ||||
0.968238 | − | 0.250029i | \(-0.0804402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 29.7298 | 0.606731 | ||||||||
\(50\) | − 49.4975i | − 0.989949i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 194.825 | 3.74663 | ||||||||
\(53\) | 4.32105i | 0.0815292i | 0.999169 | + | 0.0407646i | \(0.0129794\pi\) | ||||
−0.999169 | + | 0.0407646i | \(0.987021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 118.412i | 2.11450i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −119.079 | −2.05308 | ||||||||
\(59\) | 69.2965i | 1.17452i | 0.809400 | + | 0.587258i | \(0.199793\pi\) | ||||
−0.809400 | + | 0.587258i | \(0.800207\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −36.9839 | −0.606293 | −0.303146 | − | 0.952944i | \(-0.598037\pi\) | ||||
−0.303146 | + | 0.952944i | \(0.598037\pi\) | |||||||
\(62\) | 85.2121i | 1.37439i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 69.8407 | 1.09126 | ||||||||
\(65\) | 155.260i | 2.38861i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.12702 | −0.136224 | −0.0681121 | − | 0.997678i | \(-0.521698\pi\) | ||||
−0.0681121 | + | 0.997678i | \(0.521698\pi\) | |||||||
\(68\) | − 36.8480i | − 0.541882i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −191.825 | −2.74035 | ||||||||
\(71\) | 33.2454i | 0.468245i | 0.972207 | + | 0.234123i | \(0.0752218\pi\) | ||||
−0.972207 | + | 0.234123i | \(0.924778\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.76210 | −0.120029 | −0.0600144 | − | 0.998198i | \(-0.519115\pi\) | ||||
−0.0600144 | + | 0.998198i | \(0.519115\pi\) | |||||||
\(74\) | − 4.70312i | − 0.0635557i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −230.190 | −3.02881 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.01613 | −0.0381789 | −0.0190895 | − | 0.999818i | \(-0.506077\pi\) | ||||
−0.0190895 | + | 0.999818i | \(0.506077\pi\) | |||||||
\(80\) | − 90.9245i | − 1.13656i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −175.619 | −2.14169 | ||||||||
\(83\) | 43.9746i | 0.529815i | 0.964274 | + | 0.264907i | \(0.0853414\pi\) | ||||
−0.964274 | + | 0.264907i | \(0.914659\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29.3649 | 0.345470 | ||||||||
\(86\) | 216.531i | 2.51781i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 105.449i | 1.18482i | 0.805638 | + | 0.592409i | \(0.201823\pi\) | ||||
−0.805638 | + | 0.592409i | \(0.798177\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 219.571 | 2.41286 | ||||||||
\(92\) | 218.439i | 2.37434i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 80.9839 | 0.861530 | ||||||||
\(95\) | − 183.443i | − 1.93098i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 102.095 | 1.05252 | 0.526262 | − | 0.850323i | \(-0.323593\pi\) | ||||
0.526262 | + | 0.850323i | \(0.323593\pi\) | |||||||
\(98\) | 102.441i | 1.04531i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 113.095 | 1.13095 | ||||||||
\(101\) | − 90.8461i | − 0.899466i | −0.893163 | − | 0.449733i | \(-0.851519\pi\) | ||||
0.893163 | − | 0.449733i | \(-0.148481\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.6351 | −0.171214 | −0.0856072 | − | 0.996329i | \(-0.527283\pi\) | ||||
−0.0856072 | + | 0.996329i | \(0.527283\pi\) | |||||||
\(104\) | 330.240i | 3.17539i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.8891 | −0.140463 | ||||||||
\(107\) | − 4.08583i | − 0.0381853i | −0.999818 | − | 0.0190927i | \(-0.993922\pi\) | ||||
0.999818 | − | 0.0190927i | \(-0.00607775\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 95.6976 | 0.877959 | 0.438980 | − | 0.898497i | \(-0.355340\pi\) | ||||
0.438980 | + | 0.898497i | \(0.355340\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −128.587 | −1.14810 | ||||||||
\(113\) | 118.804i | 1.05136i | 0.850682 | + | 0.525681i | \(0.176189\pi\) | ||||
−0.850682 | + | 0.525681i | \(0.823811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −174.079 | −1.51373 | ||||||||
\(116\) | − 272.078i | − 2.34550i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −238.776 | −2.02353 | ||||||||
\(119\) | − 41.5283i | − 0.348977i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − 127.436i | − 1.04456i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −194.698 | −1.57014 | ||||||||
\(125\) | − 66.7261i | − 0.533809i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 112.508 | 0.885890 | 0.442945 | − | 0.896549i | \(-0.353934\pi\) | ||||
0.442945 | + | 0.896549i | \(0.353934\pi\) | |||||||
\(128\) | 226.869i | 1.77241i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −534.982 | −4.11524 | ||||||||
\(131\) | 15.0403i | 0.114811i | 0.998351 | + | 0.0574056i | \(0.0182828\pi\) | ||||
−0.998351 | + | 0.0574056i | \(0.981717\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −259.427 | −1.95058 | ||||||||
\(134\) | − 31.4491i | − 0.234695i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 62.4597 | 0.459262 | ||||||||
\(137\) | − 199.470i | − 1.45598i | −0.685586 | − | 0.727991i | \(-0.740454\pi\) | ||||
0.685586 | − | 0.727991i | \(-0.259546\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 152.808 | 1.09934 | 0.549671 | − | 0.835381i | \(-0.314753\pi\) | ||||
0.549671 | + | 0.835381i | \(0.314753\pi\) | |||||||
\(140\) | − 438.292i | − 3.13066i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −114.554 | −0.806721 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 216.825 | 1.49534 | ||||||||
\(146\) | − 30.1917i | − 0.206793i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.7460 | 0.0726079 | ||||||||
\(149\) | − 270.664i | − 1.81653i | −0.418391 | − | 0.908267i | \(-0.637406\pi\) | ||||
0.418391 | − | 0.908267i | \(-0.362594\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 94.2863 | 0.624413 | 0.312206 | − | 0.950014i | \(-0.398932\pi\) | ||||
0.312206 | + | 0.950014i | \(0.398932\pi\) | |||||||
\(152\) | − 390.186i | − 2.56701i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 155.159i | − 1.00102i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 186.157 | 1.18571 | 0.592857 | − | 0.805307i | \(-0.298000\pi\) | ||||
0.592857 | + | 0.805307i | \(0.298000\pi\) | |||||||
\(158\) | − 10.3927i | − 0.0657769i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −21.6190 | −0.135118 | ||||||||
\(161\) | 246.184i | 1.52910i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −44.3327 | −0.271979 | −0.135990 | − | 0.990710i | \(-0.543421\pi\) | ||||
−0.135990 | + | 0.990710i | \(0.543421\pi\) | |||||||
\(164\) | − 401.265i | − 2.44673i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −151.524 | −0.912796 | ||||||||
\(167\) | 152.039i | 0.910415i | 0.890385 | + | 0.455208i | \(0.150435\pi\) | ||||
−0.890385 | + | 0.455208i | \(0.849565\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 443.363 | 2.62345 | ||||||||
\(170\) | 101.183i | 0.595196i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −494.744 | −2.87642 | ||||||||
\(173\) | − 256.038i | − 1.47999i | −0.672613 | − | 0.739995i | \(-0.734828\pi\) | ||||
0.672613 | − | 0.739995i | \(-0.265172\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 127.460 | 0.728341 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −363.347 | −2.04127 | ||||||||
\(179\) | 113.405i | 0.633548i | 0.948501 | + | 0.316774i | \(0.102600\pi\) | ||||
−0.948501 | + | 0.316774i | \(0.897400\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 160.270 | 0.885471 | 0.442735 | − | 0.896652i | \(-0.354008\pi\) | ||||
0.442735 | + | 0.896652i | \(0.354008\pi\) | |||||||
\(182\) | 756.579i | 4.15702i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −370.268 | −2.01233 | ||||||||
\(185\) | 8.56369i | 0.0462902i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 185.037i | 0.984238i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 632.093 | 3.32680 | ||||||||
\(191\) | − 75.0218i | − 0.392784i | −0.980525 | − | 0.196392i | \(-0.937077\pi\) | ||||
0.980525 | − | 0.196392i | \(-0.0629225\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −118.903 | −0.616079 | −0.308039 | − | 0.951374i | \(-0.599673\pi\) | ||||
−0.308039 | + | 0.951374i | \(0.599673\pi\) | |||||||
\(194\) | 351.790i | 1.81335i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −234.062 | −1.19420 | ||||||||
\(197\) | 187.271i | 0.950613i | 0.879820 | + | 0.475306i | \(0.157663\pi\) | ||||
−0.879820 | + | 0.475306i | \(0.842337\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −29.5706 | −0.148596 | −0.0742979 | − | 0.997236i | \(-0.523672\pi\) | ||||
−0.0742979 | + | 0.997236i | \(0.523672\pi\) | |||||||
\(200\) | 191.703i | 0.958514i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 313.030 | 1.54965 | ||||||||
\(203\) | − 306.636i | − 1.51052i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 319.776 | 1.55988 | ||||||||
\(206\) | − 60.7656i | − 0.294978i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −358.617 | −1.72412 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −393.825 | −1.86647 | −0.933234 | − | 0.359270i | \(-0.883026\pi\) | ||||
−0.933234 | + | 0.359270i | \(0.883026\pi\) | |||||||
\(212\) | − 34.0195i | − 0.160469i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.0786 | 0.0657879 | ||||||||
\(215\) | − 394.272i | − 1.83382i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −219.427 | −1.01119 | ||||||||
\(218\) | 329.747i | 1.51260i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 115.819i | − 0.524066i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −121.016 | −0.542673 | −0.271337 | − | 0.962485i | \(-0.587466\pi\) | ||||
−0.271337 | + | 0.962485i | \(0.587466\pi\) | |||||||
\(224\) | 30.5738i | 0.136490i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −409.365 | −1.81135 | ||||||||
\(227\) | 160.388i | 0.706554i | 0.935519 | + | 0.353277i | \(0.114933\pi\) | ||||
−0.935519 | + | 0.353277i | \(0.885067\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 201.000 | 0.877729 | 0.438865 | − | 0.898553i | \(-0.355381\pi\) | ||||
0.438865 | + | 0.898553i | \(0.355381\pi\) | |||||||
\(230\) | − 599.826i | − 2.60794i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 461.190 | 1.98789 | ||||||||
\(233\) | 66.7261i | 0.286378i | 0.989695 | + | 0.143189i | \(0.0457357\pi\) | ||||
−0.989695 | + | 0.143189i | \(0.954264\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −147.460 | −0.627488 | ||||||||
\(236\) | − 545.570i | − 2.31174i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 143.095 | 0.601238 | ||||||||
\(239\) | 337.726i | 1.41308i | 0.707673 | + | 0.706540i | \(0.249745\pi\) | ||||
−0.707673 | + | 0.706540i | \(0.750255\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.9516 | 0.0786373 | 0.0393187 | − | 0.999227i | \(-0.487481\pi\) | ||||
0.0393187 | + | 0.999227i | \(0.487481\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 291.173 | 1.19333 | ||||||||
\(245\) | − 186.529i | − 0.761344i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −723.520 | −2.92923 | ||||||||
\(248\) | − 330.025i | − 1.33075i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 229.919 | 0.919677 | ||||||||
\(251\) | − 247.487i | − 0.986005i | −0.870028 | − | 0.493003i | \(-0.835899\pi\) | ||||
0.870028 | − | 0.493003i | \(-0.164101\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 387.671i | 1.52626i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −502.363 | −1.96235 | ||||||||
\(257\) | − 330.733i | − 1.28690i | −0.765488 | − | 0.643450i | \(-0.777502\pi\) | ||||
0.765488 | − | 0.643450i | \(-0.222498\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.1109 | 0.0467602 | ||||||||
\(260\) | − 1222.36i | − 4.70138i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −51.8246 | −0.197804 | ||||||||
\(263\) | 275.658i | 1.04813i | 0.851679 | + | 0.524064i | \(0.175585\pi\) | ||||
−0.851679 | + | 0.524064i | \(0.824415\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.1109 | 0.102305 | ||||||||
\(266\) | − 893.914i | − 3.36058i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 71.8569 | 0.268123 | ||||||||
\(269\) | 141.004i | 0.524177i | 0.965044 | + | 0.262088i | \(0.0844112\pi\) | ||||
−0.965044 | + | 0.262088i | \(0.915589\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −47.3165 | −0.174600 | −0.0872998 | − | 0.996182i | \(-0.527824\pi\) | ||||
−0.0872998 | + | 0.996182i | \(0.527824\pi\) | |||||||
\(272\) | 67.8267i | 0.249363i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 687.317 | 2.50845 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 257.919 | 0.931117 | 0.465558 | − | 0.885017i | \(-0.345854\pi\) | ||||
0.465558 | + | 0.885017i | \(0.345854\pi\) | |||||||
\(278\) | 526.535i | 1.89401i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 742.933 | 2.65333 | ||||||||
\(281\) | − 111.455i | − 0.396637i | −0.980138 | − | 0.198318i | \(-0.936452\pi\) | ||||
0.980138 | − | 0.198318i | \(-0.0635480\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 116.490 | 0.411625 | 0.205813 | − | 0.978591i | \(-0.434016\pi\) | ||||
0.205813 | + | 0.978591i | \(0.434016\pi\) | |||||||
\(284\) | − 261.741i | − 0.921622i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 452.232i | − 1.57572i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 267.095 | 0.924203 | ||||||||
\(290\) | 747.117i | 2.57626i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 68.9839 | 0.236246 | ||||||||
\(293\) | − 274.233i | − 0.935950i | −0.883742 | − | 0.467975i | \(-0.844984\pi\) | ||||
0.883742 | − | 0.467975i | \(-0.155016\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 434.776 | 1.47382 | ||||||||
\(296\) | 18.2151i | 0.0615375i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 932.631 | 3.12963 | ||||||||
\(299\) | 686.586i | 2.29628i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −557.585 | −1.85244 | ||||||||
\(302\) | 324.884i | 1.07578i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 423.714 | 1.39380 | ||||||||
\(305\) | 232.042i | 0.760794i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −506.587 | −1.65012 | −0.825060 | − | 0.565045i | \(-0.808859\pi\) | ||||
−0.825060 | + | 0.565045i | \(0.808859\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 534.633 | 1.72462 | ||||||||
\(311\) | 522.247i | 1.67925i | 0.543166 | + | 0.839625i | \(0.317225\pi\) | ||||
−0.543166 | + | 0.839625i | \(0.682775\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.3186 | 0.0361616 | 0.0180808 | − | 0.999837i | \(-0.494244\pi\) | ||||
0.0180808 | + | 0.999837i | \(0.494244\pi\) | |||||||
\(314\) | 641.446i | 2.04282i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 23.7460 | 0.0751455 | ||||||||
\(317\) | 5.85640i | 0.0184745i | 0.999957 | + | 0.00923723i | \(0.00294034\pi\) | ||||
−0.999957 | + | 0.00923723i | \(0.997060\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − 438.191i | − 1.36935i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −848.282 | −2.63442 | ||||||||
\(323\) | 136.842i | 0.423660i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 355.474 | 1.09377 | ||||||||
\(326\) | − 152.758i | − 0.468582i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 680.169 | 2.07369 | ||||||||
\(329\) | 208.539i | 0.633859i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −599.617 | −1.81153 | −0.905766 | − | 0.423779i | \(-0.860703\pi\) | ||||
−0.905766 | + | 0.423779i | \(0.860703\pi\) | |||||||
\(332\) | − 346.211i | − 1.04281i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −523.885 | −1.56852 | ||||||||
\(335\) | 57.2642i | 0.170938i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 544.571 | 1.61594 | 0.807968 | − | 0.589226i | \(-0.200567\pi\) | ||||
0.807968 | + | 0.589226i | \(0.200567\pi\) | |||||||
\(338\) | 1527.70i | 4.51983i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −231.190 | −0.679969 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 170.984 | 0.498495 | ||||||||
\(344\) | − 838.623i | − 2.43786i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 882.236 | 2.54981 | ||||||||
\(347\) | 626.271i | 1.80482i | 0.430882 | + | 0.902408i | \(0.358203\pi\) | ||||
−0.430882 | + | 0.902408i | \(0.641797\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.25198 | 0.00645268 | 0.00322634 | − | 0.999995i | \(-0.498973\pi\) | ||||
0.00322634 | + | 0.999995i | \(0.498973\pi\) | |||||||
\(350\) | 439.190i | 1.25483i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 565.154i | 1.60100i | 0.599332 | + | 0.800501i | \(0.295433\pi\) | ||||
−0.599332 | + | 0.800501i | \(0.704567\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 208.587 | 0.587568 | ||||||||
\(356\) | − 830.196i | − 2.33201i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −390.762 | −1.09151 | ||||||||
\(359\) | − 151.210i | − 0.421197i | −0.977573 | − | 0.210598i | \(-0.932459\pi\) | ||||
0.977573 | − | 0.210598i | \(-0.0675412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 493.855 | 1.36802 | ||||||||
\(362\) | 552.246i | 1.52554i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1728.68 | −4.74911 | ||||||||
\(365\) | 54.9747i | 0.150616i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.45762 | −0.0230453 | −0.0115226 | − | 0.999934i | \(-0.503668\pi\) | ||||
−0.0115226 | + | 0.999934i | \(0.503668\pi\) | |||||||
\(368\) | − 402.084i | − 1.09262i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −29.5081 | −0.0797515 | ||||||||
\(371\) | − 38.3406i | − 0.103344i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 483.363 | 1.29588 | 0.647940 | − | 0.761692i | \(-0.275631\pi\) | ||||
0.647940 | + | 0.761692i | \(0.275631\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −313.649 | −0.834173 | ||||||||
\(377\) | − 855.181i | − 2.26839i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 412.458 | 1.08828 | 0.544139 | − | 0.838995i | \(-0.316856\pi\) | ||||
0.544139 | + | 0.838995i | \(0.316856\pi\) | |||||||
\(380\) | 1444.24i | 3.80064i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 258.504 | 0.676712 | ||||||||
\(383\) | − 529.141i | − 1.38157i | −0.723060 | − | 0.690785i | \(-0.757265\pi\) | ||||
0.723060 | − | 0.690785i | \(-0.242735\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 409.707i | − 1.06142i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −803.790 | −2.07162 | ||||||||
\(389\) | 606.884i | 1.56011i | 0.625709 | + | 0.780057i | \(0.284810\pi\) | ||||
−0.625709 | + | 0.780057i | \(0.715190\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 129.857 | 0.332115 | ||||||||
\(392\) | − 396.751i | − 1.01212i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −645.282 | −1.63777 | ||||||||
\(395\) | 18.9237i | 0.0479080i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 474.571 | 1.19539 | 0.597696 | − | 0.801723i | \(-0.296083\pi\) | ||||
0.597696 | + | 0.801723i | \(0.296083\pi\) | |||||||
\(398\) | − 101.892i | − 0.256010i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −208.175 | −0.520439 | ||||||||
\(401\) | 115.682i | 0.288483i | 0.989543 | + | 0.144242i | \(0.0460742\pi\) | ||||
−0.989543 | + | 0.144242i | \(0.953926\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −611.964 | −1.51852 | ||||||||
\(404\) | 715.230i | 1.77037i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1056.58 | 2.60242 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −56.9859 | −0.139330 | −0.0696649 | − | 0.997570i | \(-0.522193\pi\) | ||||
−0.0696649 | + | 0.997570i | \(0.522193\pi\) | |||||||
\(410\) | 1101.86i | 2.68746i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 138.841 | 0.336992 | ||||||||
\(413\) | − 614.866i | − 1.48878i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 275.903 | 0.664827 | ||||||||
\(416\) | 85.2677i | 0.204970i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 752.136i | 1.79507i | 0.440938 | + | 0.897537i | \(0.354646\pi\) | ||||
−0.440938 | + | 0.897537i | \(0.645354\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 137.129 | 0.325722 | 0.162861 | − | 0.986649i | \(-0.447928\pi\) | ||||
0.162861 | + | 0.986649i | \(0.447928\pi\) | |||||||
\(422\) | − 1357.01i | − 3.21566i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 57.6653 | 0.136003 | ||||||||
\(425\) | − 67.2322i | − 0.158193i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 328.157 | 0.768518 | ||||||||
\(428\) | 32.1677i | 0.0751581i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1358.55 | 3.15942 | ||||||||
\(431\) | 183.355i | 0.425416i | 0.977116 | + | 0.212708i | \(0.0682284\pi\) | ||||
−0.977116 | + | 0.212708i | \(0.931772\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.4274 | −0.0841279 | −0.0420640 | − | 0.999115i | \(-0.513393\pi\) | ||||
−0.0420640 | + | 0.999115i | \(0.513393\pi\) | |||||||
\(434\) | − 756.085i | − 1.74213i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −753.425 | −1.72804 | ||||||||
\(437\) | − 811.217i | − 1.85633i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 120.730 | 0.275011 | 0.137506 | − | 0.990501i | \(-0.456092\pi\) | ||||
0.137506 | + | 0.990501i | \(0.456092\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 399.079 | 0.902893 | ||||||||
\(443\) | − 543.277i | − 1.22636i | −0.789943 | − | 0.613180i | \(-0.789890\pi\) | ||||
0.789943 | − | 0.613180i | \(-0.210110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 661.601 | 1.48674 | ||||||||
\(446\) | − 416.988i | − 0.934950i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −619.696 | −1.38325 | ||||||||
\(449\) | 85.2677i | 0.189906i | 0.995482 | + | 0.0949529i | \(0.0302700\pi\) | ||||
−0.995482 | + | 0.0949529i | \(0.969730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 935.341i | − 2.06934i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −552.651 | −1.21729 | ||||||||
\(455\) | − 1377.62i | − 3.02773i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −291.554 | −0.637975 | −0.318987 | − | 0.947759i | \(-0.603343\pi\) | ||||
−0.318987 | + | 0.947759i | \(0.603343\pi\) | |||||||
\(458\) | 692.590i | 1.51220i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1370.52 | 2.97939 | ||||||||
\(461\) | − 61.4741i | − 0.133349i | −0.997775 | − | 0.0666747i | \(-0.978761\pi\) | ||||
0.997775 | − | 0.0666747i | \(-0.0212390\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 71.6633 | 0.154780 | 0.0773901 | − | 0.997001i | \(-0.475341\pi\) | ||||
0.0773901 | + | 0.997001i | \(0.475341\pi\) | |||||||
\(464\) | 500.818i | 1.07935i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −229.919 | −0.493389 | ||||||||
\(467\) | − 212.044i | − 0.454055i | −0.973888 | − | 0.227027i | \(-0.927099\pi\) | ||||
0.973888 | − | 0.227027i | \(-0.0729007\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 80.9839 | 0.172673 | ||||||||
\(470\) | − 508.105i | − 1.08107i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 924.776 | 1.95927 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −420.000 | −0.884211 | ||||||||
\(476\) | 326.951i | 0.686873i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1163.71 | −2.43454 | ||||||||
\(479\) | 8.84164i | 0.0184585i | 0.999957 | + | 0.00922927i | \(0.00293781\pi\) | ||||
−0.999957 | + | 0.00922927i | \(0.997062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.7762 | 0.0702208 | ||||||||
\(482\) | 65.3019i | 0.135481i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 640.557i | − 1.32074i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −483.252 | −0.992304 | −0.496152 | − | 0.868236i | \(-0.665254\pi\) | ||||
−0.496152 | + | 0.868236i | \(0.665254\pi\) | |||||||
\(488\) | 493.558i | 1.01139i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 642.728 | 1.31169 | ||||||||
\(491\) | − 317.006i | − 0.645634i | −0.946461 | − | 0.322817i | \(-0.895370\pi\) | ||||
0.946461 | − | 0.322817i | \(-0.104630\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −161.744 | −0.328081 | ||||||||
\(494\) | − 2493.05i | − 5.04665i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 358.383 | 0.722547 | ||||||||
\(497\) | − 294.986i | − 0.593533i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 503.631 | 1.00928 | 0.504640 | − | 0.863330i | \(-0.331625\pi\) | ||||
0.504640 | + | 0.863330i | \(0.331625\pi\) | |||||||
\(500\) | 525.333i | 1.05067i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 852.772 | 1.69875 | ||||||||
\(503\) | − 116.661i | − 0.231931i | −0.993253 | − | 0.115965i | \(-0.963004\pi\) | ||||
0.993253 | − | 0.115965i | \(-0.0369962\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −569.982 | −1.12868 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −885.774 | −1.74365 | ||||||||
\(509\) | − 293.193i | − 0.576017i | −0.957628 | − | 0.288009i | \(-0.907007\pi\) | ||||
0.957628 | − | 0.288009i | \(-0.0929932\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 77.7460 | 0.152145 | ||||||||
\(512\) | − 823.527i | − 1.60845i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1139.61 | 2.21715 | ||||||||
\(515\) | 110.645i | 0.214845i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 41.7307i | 0.0805612i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2071.98 | 3.98457 | ||||||||
\(521\) | 96.5030i | 0.185226i | 0.995702 | + | 0.0926132i | \(0.0295220\pi\) | ||||
−0.995702 | + | 0.0926132i | \(0.970478\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 201.427 | 0.385138 | 0.192569 | − | 0.981283i | \(-0.438318\pi\) | ||||
0.192569 | + | 0.981283i | \(0.438318\pi\) | |||||||
\(524\) | − 118.412i | − 0.225977i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −949.839 | −1.80578 | ||||||||
\(527\) | 115.743i | 0.219626i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −240.806 | −0.455211 | ||||||||
\(530\) | 93.4165i | 0.176258i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2042.47 | 3.83922 | ||||||||
\(533\) | − 1261.23i | − 2.36629i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.6351 | −0.0479160 | ||||||||
\(536\) | 121.802i | 0.227243i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −485.859 | −0.903083 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −866.375 | −1.60143 | −0.800716 | − | 0.599044i | \(-0.795547\pi\) | ||||
−0.800716 | + | 0.599044i | \(0.795547\pi\) | |||||||
\(542\) | − 163.039i | − 0.300811i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.1270 | 0.0296453 | ||||||||
\(545\) | − 600.421i | − 1.10169i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 461.145 | 0.843044 | 0.421522 | − | 0.906818i | \(-0.361496\pi\) | ||||
0.421522 | + | 0.906818i | \(0.361496\pi\) | |||||||
\(548\) | 1570.42i | 2.86573i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1010.42i | 1.83379i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.7621 | 0.0483944 | ||||||||
\(554\) | 888.718i | 1.60418i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1203.06 | −2.16377 | ||||||||
\(557\) | 285.694i | 0.512916i | 0.966555 | + | 0.256458i | \(0.0825555\pi\) | ||||
−0.966555 | + | 0.256458i | \(0.917445\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1555.05 | −2.78185 | ||||||||
\(560\) | 806.772i | 1.44066i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 384.042 | 0.683349 | ||||||||
\(563\) | − 321.739i | − 0.571473i | −0.958308 | − | 0.285736i | \(-0.907762\pi\) | ||||
0.958308 | − | 0.285736i | \(-0.0922382\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 745.393 | 1.31928 | ||||||||
\(566\) | 401.391i | 0.709172i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 443.667 | 0.781104 | ||||||||
\(569\) | 963.864i | 1.69396i | 0.531624 | + | 0.846980i | \(0.321582\pi\) | ||||
−0.531624 | + | 0.846980i | \(0.678418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1014.45 | −1.77663 | −0.888313 | − | 0.459238i | \(-0.848122\pi\) | ||||
−0.888313 | + | 0.459238i | \(0.848122\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1558.26 | 2.71475 | ||||||||
\(575\) | 398.560i | 0.693148i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 362.903 | 0.628948 | 0.314474 | − | 0.949266i | \(-0.398172\pi\) | ||||
0.314474 | + | 0.949266i | \(0.398172\pi\) | |||||||
\(578\) | 920.334i | 1.59227i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1707.06 | −2.94320 | ||||||||
\(581\) | − 390.186i | − 0.671577i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 116.932i | 0.200226i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 944.931 | 1.61251 | ||||||||
\(587\) | 567.835i | 0.967351i | 0.875247 | + | 0.483676i | \(0.160699\pi\) | ||||
−0.875247 | + | 0.483676i | \(0.839301\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 723.048 | 1.22759 | ||||||||
\(590\) | 1498.12i | 2.53918i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −19.7803 | −0.0334126 | ||||||||
\(593\) | 203.728i | 0.343555i | 0.985136 | + | 0.171777i | \(0.0549510\pi\) | ||||
−0.985136 | + | 0.171777i | \(0.945049\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −260.554 | −0.437907 | ||||||||
\(596\) | 2130.93i | 3.57539i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2365.78 | −3.95616 | ||||||||
\(599\) | 591.566i | 0.987589i | 0.869579 | + | 0.493795i | \(0.164391\pi\) | ||||
−0.869579 | + | 0.493795i | \(0.835609\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −719.157 | −1.19660 | −0.598301 | − | 0.801272i | \(-0.704157\pi\) | ||||
−0.598301 | + | 0.801272i | \(0.704157\pi\) | |||||||
\(602\) | − 1921.28i | − 3.19150i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −742.314 | −1.22900 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0000 | −0.0263591 | −0.0131796 | − | 0.999913i | \(-0.504195\pi\) | ||||
−0.0131796 | + | 0.999913i | \(0.504195\pi\) | |||||||
\(608\) | − 100.746i | − 0.165700i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −799.552 | −1.31074 | ||||||||
\(611\) | 581.598i | 0.951879i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −317.740 | −0.518336 | −0.259168 | − | 0.965832i | \(-0.583448\pi\) | ||||
−0.259168 | + | 0.965832i | \(0.583448\pi\) | |||||||
\(614\) | − 1745.56i | − 2.84292i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 629.469i | − 1.02021i | −0.860112 | − | 0.510105i | \(-0.829607\pi\) | ||||
0.860112 | − | 0.510105i | \(-0.170393\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 243.982 | 0.394155 | 0.197077 | − | 0.980388i | \(-0.436855\pi\) | ||||
0.197077 | + | 0.980388i | \(0.436855\pi\) | |||||||
\(620\) | 1221.56i | 1.97026i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1799.52 | −2.89311 | ||||||||
\(623\) | − 935.645i | − 1.50184i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −777.772 | −1.24444 | ||||||||
\(626\) | 39.0006i | 0.0623013i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1465.61 | −2.33378 | ||||||||
\(629\) | − 6.38823i | − 0.0101562i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 658.236 | 1.04316 | 0.521581 | − | 0.853201i | \(-0.325342\pi\) | ||||
0.521581 | + | 0.853201i | \(0.325342\pi\) | |||||||
\(632\) | 40.2509i | 0.0636882i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.1795 | −0.0318289 | ||||||||
\(635\) | − 705.892i | − 1.11164i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −735.693 | −1.15493 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1423.41 | 2.22407 | ||||||||
\(641\) | − 464.074i | − 0.723985i | −0.932181 | − | 0.361993i | \(-0.882097\pi\) | ||||
0.932181 | − | 0.361993i | \(-0.117903\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 218.000 | 0.339036 | 0.169518 | − | 0.985527i | \(-0.445779\pi\) | ||||
0.169518 | + | 0.985527i | \(0.445779\pi\) | |||||||
\(644\) | − 1938.21i | − 3.00964i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −471.520 | −0.729907 | ||||||||
\(647\) | − 1135.45i | − 1.75494i | −0.479629 | − | 0.877471i | \(-0.659229\pi\) | ||||
0.479629 | − | 0.877471i | \(-0.340771\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1224.86i | 1.88440i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 349.030 | 0.535322 | ||||||||
\(653\) | 793.419i | 1.21504i | 0.794305 | + | 0.607519i | \(0.207835\pi\) | ||||
−0.794305 | + | 0.607519i | \(0.792165\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 94.3649 | 0.144069 | ||||||||
\(656\) | 738.614i | 1.12594i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −718.569 | −1.09205 | ||||||||
\(659\) | 87.6613i | 0.133022i | 0.997786 | + | 0.0665109i | \(0.0211867\pi\) | ||||
−0.997786 | + | 0.0665109i | \(0.978813\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1071.04 | 1.62033 | 0.810165 | − | 0.586202i | \(-0.199377\pi\) | ||||
0.810165 | + | 0.586202i | \(0.199377\pi\) | |||||||
\(662\) | − 2066.11i | − 3.12101i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 586.851 | 0.883811 | ||||||||
\(665\) | 1627.69i | 2.44765i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 958.837 | 1.43754 | ||||||||
\(668\) | − 1197.00i | − 1.79192i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −197.317 | −0.294502 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −402.883 | −0.598637 | −0.299319 | − | 0.954153i | \(-0.596759\pi\) | ||||
−0.299319 | + | 0.954153i | \(0.596759\pi\) | |||||||
\(674\) | 1876.44i | 2.78403i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3490.59 | −5.16359 | ||||||||
\(677\) | − 123.859i | − 0.182953i | −0.995807 | − | 0.0914765i | \(-0.970841\pi\) | ||||
0.995807 | − | 0.0914765i | \(-0.0291586\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −905.885 | −1.33415 | ||||||||
\(680\) | − 391.881i | − 0.576296i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 621.918i | 0.910567i | 0.890346 | + | 0.455284i | \(0.150462\pi\) | ||||
−0.890346 | + | 0.455284i | \(0.849538\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1251.50 | −1.82701 | ||||||||
\(686\) | 589.162i | 0.858837i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 910.683 | 1.32367 | ||||||||
\(689\) | − 106.928i | − 0.155194i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1058.90 | 1.53242 | 0.766209 | − | 0.642591i | \(-0.222141\pi\) | ||||
0.766209 | + | 0.642591i | \(0.222141\pi\) | |||||||
\(692\) | 2015.78i | 2.91298i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2157.96 | −3.10945 | ||||||||
\(695\) | − 958.743i | − 1.37949i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −238.542 | −0.342242 | ||||||||
\(698\) | 7.75971i | 0.0111171i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1003.49 | −1.43355 | ||||||||
\(701\) | 875.810i | 1.24937i | 0.780876 | + | 0.624686i | \(0.214773\pi\) | ||||
−0.780876 | + | 0.624686i | \(0.785227\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39.9073 | −0.0567671 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1947.36 | −2.75830 | ||||||||
\(707\) | 806.076i | 1.14014i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 286.661 | 0.404318 | 0.202159 | − | 0.979353i | \(-0.435204\pi\) | ||||
0.202159 | + | 0.979353i | \(0.435204\pi\) | |||||||
\(710\) | 718.731i | 1.01230i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1407.24 | 1.97645 | ||||||||
\(713\) | − 686.139i | − 0.962326i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 892.836i | − 1.24698i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 521.026 | 0.725663 | ||||||||
\(719\) | 273.950i | 0.381015i | 0.981686 | + | 0.190507i | \(0.0610133\pi\) | ||||
−0.981686 | + | 0.190507i | \(0.938987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 156.476 | 0.217026 | ||||||||
\(722\) | 1701.69i | 2.35690i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1261.80 | −1.74282 | ||||||||
\(725\) | − 496.429i | − 0.684729i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1276.84 | 1.75631 | 0.878154 | − | 0.478377i | \(-0.158775\pi\) | ||||
0.878154 | + | 0.478377i | \(0.158775\pi\) | |||||||
\(728\) | − 2930.22i | − 4.02502i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −189.427 | −0.259490 | ||||||||
\(731\) | 294.114i | 0.402344i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1064.27 | −1.45193 | −0.725966 | − | 0.687731i | \(-0.758607\pi\) | ||||
−0.725966 | + | 0.687731i | \(0.758607\pi\) | |||||||
\(734\) | − 29.1426i | − 0.0397038i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −95.6028 | −0.129895 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −830.794 | −1.12421 | −0.562107 | − | 0.827064i | \(-0.690009\pi\) | ||||
−0.562107 | + | 0.827064i | \(0.690009\pi\) | |||||||
\(740\) | − 67.4218i | − 0.0911105i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 132.111 | 0.178047 | ||||||||
\(743\) | − 1335.35i | − 1.79724i | −0.438729 | − | 0.898619i | \(-0.644571\pi\) | ||||
0.438729 | − | 0.898619i | \(-0.355429\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1698.18 | −2.27944 | ||||||||
\(746\) | 1665.53i | 2.23262i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36.2535i | 0.0484025i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −877.917 | −1.16900 | −0.584499 | − | 0.811395i | \(-0.698709\pi\) | ||||
−0.584499 | + | 0.811395i | \(0.698709\pi\) | |||||||
\(752\) | − 340.600i | − 0.452926i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2946.72 | 3.90811 | ||||||||
\(755\) | − 591.566i | − 0.783531i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1075.54 | 1.42079 | 0.710394 | − | 0.703804i | \(-0.248517\pi\) | ||||
0.710394 | + | 0.703804i | \(0.248517\pi\) | |||||||
\(758\) | 1421.21i | 1.87495i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2448.08 | −3.22116 | ||||||||
\(761\) | 351.679i | 0.462127i | 0.972939 | + | 0.231064i | \(0.0742205\pi\) | ||||
−0.972939 | + | 0.231064i | \(0.925779\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −849.123 | −1.11287 | ||||||||
\(764\) | 590.645i | 0.773096i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1823.27 | 2.38025 | ||||||||
\(767\) | − 1714.81i | − 2.23573i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −466.423 | −0.606532 | −0.303266 | − | 0.952906i | \(-0.598077\pi\) | ||||
−0.303266 | + | 0.952906i | \(0.598077\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 936.123 | 1.21259 | ||||||||
\(773\) | 258.978i | 0.335030i | 0.985870 | + | 0.167515i | \(0.0535742\pi\) | ||||
−0.985870 | + | 0.167515i | \(0.946426\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −355.242 | −0.458377 | ||||||||
\(776\) | − 1362.48i | − 1.75577i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2091.15 | −2.68786 | ||||||||
\(779\) | 1490.18i | 1.91293i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 447.450i | 0.572187i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 430.843 | 0.549544 | ||||||||
\(785\) | − 1167.98i | − 1.48787i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 169.270 | 0.215083 | 0.107541 | − | 0.994201i | \(-0.465702\pi\) | ||||
0.107541 | + | 0.994201i | \(0.465702\pi\) | |||||||
\(788\) | − 1474.38i | − 1.87104i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −65.2056 | −0.0825388 | ||||||||
\(791\) | − 1054.15i | − 1.33267i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 915.202 | 1.15410 | ||||||||
\(794\) | 1635.24i | 2.05949i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 232.808 | 0.292473 | ||||||||
\(797\) | 888.999i | 1.11543i | 0.830032 | + | 0.557716i | \(0.188322\pi\) | ||||
−0.830032 | + | 0.557716i | \(0.811678\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 110.000 | 0.137672 | ||||||||
\(800\) | 49.4975i | 0.0618718i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −398.607 | −0.497016 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1544.60 | 1.91875 | ||||||||
\(806\) | − 2108.66i | − 2.61620i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1212.36 | −1.50045 | ||||||||
\(809\) | 998.765i | 1.23457i | 0.786740 | + | 0.617284i | \(0.211767\pi\) | ||||
−0.786740 | + | 0.617284i | \(0.788233\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 514.097 | 0.633905 | 0.316952 | − | 0.948441i | \(-0.397340\pi\) | ||||
0.316952 | + | 0.948441i | \(0.397340\pi\) | |||||||
\(812\) | 2414.14i | 2.97308i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 278.150i | 0.341288i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1837.33 | 2.24887 | ||||||||
\(818\) | − 196.357i | − 0.240046i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2517.59 | −3.07023 | ||||||||
\(821\) | 984.093i | 1.19865i | 0.800505 | + | 0.599326i | \(0.204565\pi\) | ||||
−0.800505 | + | 0.599326i | \(0.795435\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −636.083 | −0.772883 | −0.386442 | − | 0.922314i | \(-0.626296\pi\) | ||||
−0.386442 | + | 0.922314i | \(0.626296\pi\) | |||||||
\(824\) | 235.344i | 0.285612i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2118.66 | 2.56496 | ||||||||
\(827\) | 994.996i | 1.20314i | 0.798820 | + | 0.601570i | \(0.205458\pi\) | ||||
−0.798820 | + | 0.601570i | \(0.794542\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −768.996 | −0.927619 | −0.463809 | − | 0.885935i | \(-0.653518\pi\) | ||||
−0.463809 | + | 0.885935i | \(0.653518\pi\) | |||||||
\(830\) | 950.685i | 1.14540i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1728.28 | −2.07725 | ||||||||
\(833\) | 139.145i | 0.167040i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 953.917 | 1.14242 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2591.65 | −3.09266 | ||||||||
\(839\) | − 927.065i | − 1.10496i | −0.833525 | − | 0.552482i | \(-0.813681\pi\) | ||||
0.833525 | − | 0.552482i | \(-0.186319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −353.284 | −0.420076 | ||||||||
\(842\) | 472.508i | 0.561174i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3100.57 | 3.67367 | ||||||||
\(845\) | − 2781.72i | − 3.29198i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 62.6203i | 0.0738447i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 231.663 | 0.272545 | ||||||||
\(851\) | 37.8701i | 0.0445008i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 160.889 | 0.188616 | 0.0943078 | − | 0.995543i | \(-0.469936\pi\) | ||||
0.0943078 | + | 0.995543i | \(0.469936\pi\) | |||||||
\(854\) | 1130.74i | 1.32405i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −54.5262 | −0.0636989 | ||||||||
\(857\) | − 808.391i | − 0.943280i | −0.881791 | − | 0.471640i | \(-0.843662\pi\) | ||||
0.881791 | − | 0.471640i | \(-0.156338\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1311.06 | −1.52627 | −0.763133 | − | 0.646241i | \(-0.776340\pi\) | ||||
−0.763133 | + | 0.646241i | \(0.776340\pi\) | |||||||
\(860\) | 3104.10i | 3.60941i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −631.788 | −0.732933 | ||||||||
\(863\) | 183.805i | 0.212984i | 0.994314 | + | 0.106492i | \(0.0339618\pi\) | ||||
−0.994314 | + | 0.106492i | \(0.966038\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1606.42 | −1.85713 | ||||||||
\(866\) | − 125.519i | − 0.144941i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1727.55 | 1.99026 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 225.857 | 0.259308 | ||||||||
\(872\) | − 1277.10i | − 1.46457i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2795.23 | 3.19820 | ||||||||
\(875\) | 592.059i | 0.676639i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1049.04 | 1.19617 | 0.598083 | − | 0.801434i | \(-0.295929\pi\) | ||||
0.598083 | + | 0.801434i | \(0.295929\pi\) | |||||||
\(878\) | 416.001i | 0.473805i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 624.821i | − 0.709218i | −0.935015 | − | 0.354609i | \(-0.884614\pi\) | ||||
0.935015 | − | 0.354609i | \(-0.115386\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1336.79 | −1.51391 | −0.756957 | − | 0.653465i | \(-0.773315\pi\) | ||||
−0.756957 | + | 0.653465i | \(0.773315\pi\) | |||||||
\(884\) | 911.838i | 1.03149i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1871.98 | 2.11285 | ||||||||
\(887\) | − 1268.64i | − 1.43025i | −0.698995 | − | 0.715127i | \(-0.746369\pi\) | ||||
0.698995 | − | 0.715127i | \(-0.253631\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −998.282 | −1.12293 | ||||||||
\(890\) | 2279.69i | 2.56145i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 952.758 | 1.06811 | ||||||||
\(893\) | − 687.171i | − 0.769508i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 711.520 | 0.794995 | ||||||||
\(896\) | − 2013.00i | − 2.24665i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −293.808 | −0.327181 | ||||||||
\(899\) | 854.624i | 0.950638i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.2238 | −0.0224460 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1585.46 | 1.75383 | ||||||||
\(905\) | − 1005.56i | − 1.11111i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1470.26 | 1.62102 | 0.810509 | − | 0.585726i | \(-0.199190\pi\) | ||||
0.810509 | + | 0.585726i | \(0.199190\pi\) | |||||||
\(908\) | − 1262.73i | − 1.39067i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4746.88 | 5.21636 | ||||||||
\(911\) | 1344.21i | 1.47554i | 0.675055 | + | 0.737768i | \(0.264120\pi\) | ||||
−0.675055 | + | 0.737768i | \(0.735880\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − 1004.61i | − 1.09914i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1582.47 | −1.72759 | ||||||||
\(917\) | − 133.452i | − 0.145531i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1013.26 | −1.10256 | −0.551282 | − | 0.834319i | \(-0.685861\pi\) | ||||
−0.551282 | + | 0.834319i | \(0.685861\pi\) | |||||||
\(920\) | 2323.12i | 2.52513i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 211.823 | 0.229742 | ||||||||
\(923\) | − 822.690i | − 0.891322i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.6069 | 0.0211967 | ||||||||
\(926\) | 246.931i | 0.266665i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 119.079 | 0.128317 | ||||||||
\(929\) | − 578.763i | − 0.622995i | −0.950247 | − | 0.311498i | \(-0.899169\pi\) | ||||
0.950247 | − | 0.311498i | \(-0.100831\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 869.238 | 0.933660 | ||||||||
\(932\) | − 525.333i | − 0.563662i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 730.643 | 0.782273 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −679.472 | −0.725157 | −0.362578 | − | 0.931953i | \(-0.618103\pi\) | ||||
−0.362578 | + | 0.931953i | \(0.618103\pi\) | |||||||
\(938\) | 279.048i | 0.297492i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1160.95 | 1.23505 | ||||||||
\(941\) | 1046.59i | 1.11221i | 0.831112 | + | 0.556106i | \(0.187705\pi\) | ||||
−0.831112 | + | 0.556106i | \(0.812295\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1414.11 | 1.49958 | ||||||||
\(944\) | 1004.24i | 1.06381i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 377.752i | − 0.398893i | −0.979909 | − | 0.199447i | \(-0.936086\pi\) | ||||
0.979909 | − | 0.199447i | \(-0.0639144\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 216.827 | 0.228479 | ||||||||
\(950\) | − 1447.20i | − 1.52337i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −554.204 | −0.582147 | ||||||||
\(953\) | 939.364i | 0.985692i | 0.870117 | + | 0.492846i | \(0.164043\pi\) | ||||
−0.870117 | + | 0.492846i | \(0.835957\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −470.698 | −0.492877 | ||||||||
\(956\) | − 2658.91i | − 2.78129i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −30.4658 | −0.0318015 | ||||||||
\(959\) | 1769.89i | 1.84556i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −349.435 | −0.363616 | ||||||||
\(962\) | 116.383i | 0.120981i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −149.206 | −0.154778 | ||||||||
\(965\) | 746.016i | 0.773074i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −519.663 | −0.537397 | −0.268699 | − | 0.963224i | \(-0.586594\pi\) | ||||
−0.268699 | + | 0.963224i | \(0.586594\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2207.18 | 2.27544 | ||||||||
\(971\) | − 461.769i | − 0.475560i | −0.971319 | − | 0.237780i | \(-0.923580\pi\) | ||||
0.971319 | − | 0.237780i | \(-0.0764198\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1355.87 | −1.39349 | ||||||||
\(974\) | − 1665.15i | − 1.70960i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −535.968 | −0.549147 | ||||||||
\(977\) | 1613.28i | 1.65126i | 0.564211 | + | 0.825631i | \(0.309181\pi\) | ||||
−0.564211 | + | 0.825631i | \(0.690819\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1468.54i | 1.49851i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1092.31 | 1.11234 | ||||||||
\(983\) | − 1662.92i | − 1.69168i | −0.533437 | − | 0.845840i | \(-0.679100\pi\) | ||||
0.533437 | − | 0.845840i | \(-0.320900\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1174.96 | 1.19286 | ||||||||
\(986\) | − 557.324i | − 0.565238i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5696.26 | 5.76545 | ||||||||
\(989\) | − 1743.54i | − 1.76293i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −68.7903 | −0.0694150 | −0.0347075 | − | 0.999398i | \(-0.511050\pi\) | ||||
−0.0347075 | + | 0.999398i | \(0.511050\pi\) | |||||||
\(992\) | − 85.2121i | − 0.0858993i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1016.44 | 1.02257 | ||||||||
\(995\) | 185.530i | 0.186462i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −758.510 | −0.760792 | −0.380396 | − | 0.924824i | \(-0.624212\pi\) | ||||
−0.380396 | + | 0.924824i | \(0.624212\pi\) | |||||||
\(998\) | 1735.37i | 1.73885i | ||||||||
\(999\) | 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 | 1089.3.b.c.485.4 | yes | 4 | |
3.2 | odd | 2 | inner | 1089.3.b.c.485.1 | ✓ | 4 | |
11.10 | odd | 2 | 1089.3.b.d.485.1 | yes | 4 | ||
33.32 | even | 2 | 1089.3.b.d.485.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1089.3.b.c.485.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
1089.3.b.c.485.4 | yes | 4 | 1.1 | even | 1 | trivial | |
1089.3.b.d.485.1 | yes | 4 | 11.10 | odd | 2 | ||
1089.3.b.d.485.4 | yes | 4 | 33.32 | even | 2 |