Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(197,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, 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("882.197");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.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: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{37})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 13x^{2} + 14x + 123 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.4 | ||
Root | \(3.54138 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.197 |
Dual form | 882.3.b.g.197.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 8.60233i | 1.72047i | 0.509902 | + | 0.860233i | \(0.329682\pi\) | ||||
−0.509902 | + | 0.860233i | \(0.670318\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 2.82843i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −12.1655 | −1.21655 | ||||||||
\(11\) | − 2.82843i | − 0.257130i | −0.991701 | − | 0.128565i | \(-0.958963\pi\) | ||||
0.991701 | − | 0.128565i | \(-0.0410371\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.1655 | 0.935810 | 0.467905 | − | 0.883779i | \(-0.345009\pi\) | ||||
0.467905 | + | 0.883779i | \(0.345009\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 25.8070i | 1.51806i | 0.651057 | + | 0.759029i | \(0.274326\pi\) | ||||
−0.651057 | + | 0.759029i | \(0.725674\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −24.3311 | −1.28058 | −0.640291 | − | 0.768133i | \(-0.721186\pi\) | ||||
−0.640291 | + | 0.768133i | \(0.721186\pi\) | |||||||
\(20\) | − 17.2047i | − 0.860233i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000 | 0.181818 | ||||||||
\(23\) | 42.4264i | 1.84463i | 0.386443 | + | 0.922313i | \(0.373704\pi\) | ||||
−0.386443 | + | 0.922313i | \(0.626296\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −49.0000 | −1.96000 | ||||||||
\(26\) | 17.2047i | 0.661717i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 15.5563i | − 0.536426i | −0.963360 | − | 0.268213i | \(-0.913567\pi\) | ||||
0.963360 | − | 0.268213i | \(-0.0864331\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 24.3311 | 0.784873 | 0.392436 | − | 0.919779i | \(-0.371632\pi\) | ||||
0.392436 | + | 0.919779i | \(0.371632\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −36.4966 | −1.07343 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.162162 | −0.0810811 | − | 0.996708i | \(-0.525837\pi\) | ||||
−0.0810811 | + | 0.996708i | \(0.525837\pi\) | |||||||
\(38\) | − 34.4093i | − 0.905508i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 24.3311 | 0.608276 | ||||||||
\(41\) | 25.8070i | 0.629438i | 0.949185 | + | 0.314719i | \(0.101910\pi\) | ||||
−0.949185 | + | 0.314719i | \(0.898090\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −68.0000 | −1.58140 | −0.790698 | − | 0.612207i | \(-0.790282\pi\) | ||||
−0.790698 | + | 0.612207i | \(0.790282\pi\) | |||||||
\(44\) | 5.65685i | 0.128565i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −60.0000 | −1.30435 | ||||||||
\(47\) | − 68.8186i | − 1.46423i | −0.681183 | − | 0.732113i | \(-0.738534\pi\) | ||||
0.681183 | − | 0.732113i | \(-0.261466\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 69.2965i | − 1.38593i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −24.3311 | −0.467905 | ||||||||
\(53\) | − 41.0122i | − 0.773815i | −0.922119 | − | 0.386907i | \(-0.873543\pi\) | ||||
0.922119 | − | 0.386907i | \(-0.126457\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 24.3311 | 0.442383 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 22.0000 | 0.379310 | ||||||||
\(59\) | − 68.8186i | − 1.16642i | −0.812323 | − | 0.583208i | \(-0.801797\pi\) | ||||
0.812323 | − | 0.583208i | \(-0.198203\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 97.3242 | 1.59548 | 0.797739 | − | 0.603002i | \(-0.206029\pi\) | ||||
0.797739 | + | 0.603002i | \(0.206029\pi\) | |||||||
\(62\) | 34.4093i | 0.554989i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 104.652i | 1.61003i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −104.000 | −1.55224 | −0.776119 | − | 0.630586i | \(-0.782815\pi\) | ||||
−0.776119 | + | 0.630586i | \(0.782815\pi\) | |||||||
\(68\) | − 51.6140i | − 0.759029i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 70.7107i | − 0.995925i | −0.867199 | − | 0.497963i | \(-0.834082\pi\) | ||||
0.867199 | − | 0.497963i | \(-0.165918\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 60.8276 | 0.833255 | 0.416628 | − | 0.909077i | \(-0.363212\pi\) | ||||
0.416628 | + | 0.909077i | \(0.363212\pi\) | |||||||
\(74\) | − 8.48528i | − 0.114666i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 48.6621 | 0.640291 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −20.0000 | −0.253165 | −0.126582 | − | 0.991956i | \(-0.540401\pi\) | ||||
−0.126582 | + | 0.991956i | \(0.540401\pi\) | |||||||
\(80\) | 34.4093i | 0.430116i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −36.4966 | −0.445080 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −222.000 | −2.61176 | ||||||||
\(86\) | − 96.1665i | − 1.11822i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.00000 | −0.0909091 | ||||||||
\(89\) | 94.6256i | 1.06321i | 0.846993 | + | 0.531604i | \(0.178411\pi\) | ||||
−0.846993 | + | 0.531604i | \(0.821589\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 84.8528i | − 0.922313i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 97.3242 | 1.03536 | ||||||||
\(95\) | − 209.304i | − 2.20320i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −158.152 | −1.63043 | −0.815216 | − | 0.579158i | \(-0.803382\pi\) | ||||
−0.815216 | + | 0.579158i | \(0.803382\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 98.0000 | 0.980000 | ||||||||
\(101\) | 60.2163i | 0.596201i | 0.954535 | + | 0.298100i | \(0.0963530\pi\) | ||||
−0.954535 | + | 0.298100i | \(0.903647\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −170.317 | −1.65357 | −0.826783 | − | 0.562521i | \(-0.809832\pi\) | ||||
−0.826783 | + | 0.562521i | \(0.809832\pi\) | |||||||
\(104\) | − 34.4093i | − 0.330859i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 58.0000 | 0.547170 | ||||||||
\(107\) | 19.7990i | 0.185037i | 0.995711 | + | 0.0925186i | \(0.0294918\pi\) | ||||
−0.995711 | + | 0.0925186i | \(0.970508\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −56.0000 | −0.513761 | −0.256881 | − | 0.966443i | \(-0.582695\pi\) | ||||
−0.256881 | + | 0.966443i | \(0.582695\pi\) | |||||||
\(110\) | 34.4093i | 0.312812i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 159.806i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −364.966 | −3.17362 | ||||||||
\(116\) | 31.1127i | 0.268213i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 97.3242 | 0.824781 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 113.000 | 0.933884 | ||||||||
\(122\) | 137.637i | 1.12817i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −48.6621 | −0.392436 | ||||||||
\(125\) | − 206.456i | − 1.65165i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −76.0000 | −0.598425 | −0.299213 | − | 0.954186i | \(-0.596724\pi\) | ||||
−0.299213 | + | 0.954186i | \(0.596724\pi\) | |||||||
\(128\) | − 11.3137i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −148.000 | −1.13846 | ||||||||
\(131\) | 103.228i | 0.787999i | 0.919111 | + | 0.394000i | \(0.128909\pi\) | ||||
−0.919111 | + | 0.394000i | \(0.871091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 147.078i | − 1.09760i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 72.9932 | 0.536714 | ||||||||
\(137\) | − 100.409i | − 0.732914i | −0.930435 | − | 0.366457i | \(-0.880571\pi\) | ||||
0.930435 | − | 0.366457i | \(-0.119429\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 145.986 | 1.05026 | 0.525131 | − | 0.851022i | \(-0.324016\pi\) | ||||
0.525131 | + | 0.851022i | \(0.324016\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 100.000 | 0.704225 | ||||||||
\(143\) | − 34.4093i | − 0.240624i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 133.821 | 0.922902 | ||||||||
\(146\) | 86.0233i | 0.589200i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 12.0000 | 0.0810811 | ||||||||
\(149\) | − 41.0122i | − 0.275250i | −0.990484 | − | 0.137625i | \(-0.956053\pi\) | ||||
0.990484 | − | 0.137625i | \(-0.0439468\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 160.000 | 1.05960 | 0.529801 | − | 0.848122i | \(-0.322266\pi\) | ||||
0.529801 | + | 0.848122i | \(0.322266\pi\) | |||||||
\(152\) | 68.8186i | 0.452754i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 209.304i | 1.35035i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 194.648 | 1.23980 | 0.619899 | − | 0.784681i | \(-0.287173\pi\) | ||||
0.619899 | + | 0.784681i | \(0.287173\pi\) | |||||||
\(158\) | − 28.2843i | − 0.179014i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −48.6621 | −0.304138 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | − 51.6140i | − 0.314719i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 172.047i | 1.03022i | 0.857125 | + | 0.515109i | \(0.172249\pi\) | ||||
−0.857125 | + | 0.515109i | \(0.827751\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −21.0000 | −0.124260 | ||||||||
\(170\) | − 313.955i | − 1.84680i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 136.000 | 0.790698 | ||||||||
\(173\) | − 8.60233i | − 0.0497244i | −0.999691 | − | 0.0248622i | \(-0.992085\pi\) | ||||
0.999691 | − | 0.0248622i | \(-0.00791470\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 11.3137i | − 0.0642824i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −133.821 | −0.751802 | ||||||||
\(179\) | − 144.250i | − 0.805865i | −0.915230 | − | 0.402932i | \(-0.867991\pi\) | ||||
0.915230 | − | 0.402932i | \(-0.132009\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.1655 | −0.0672128 | −0.0336064 | − | 0.999435i | \(-0.510699\pi\) | ||||
−0.0336064 | + | 0.999435i | \(0.510699\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 120.000 | 0.652174 | ||||||||
\(185\) | − 51.6140i | − 0.278994i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 72.9932 | 0.390338 | ||||||||
\(188\) | 137.637i | 0.732113i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 296.000 | 1.55789 | ||||||||
\(191\) | 263.044i | 1.37719i | 0.725145 | + | 0.688596i | \(0.241773\pi\) | ||||
−0.725145 | + | 0.688596i | \(0.758227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 38.0000 | 0.196891 | 0.0984456 | − | 0.995142i | \(-0.468613\pi\) | ||||
0.0984456 | + | 0.995142i | \(0.468613\pi\) | |||||||
\(194\) | − 223.660i | − 1.15289i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 165.463i | 0.839914i | 0.907544 | + | 0.419957i | \(0.137955\pi\) | ||||
−0.907544 | + | 0.419957i | \(0.862045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 243.311 | 1.22267 | 0.611333 | − | 0.791374i | \(-0.290634\pi\) | ||||
0.611333 | + | 0.791374i | \(0.290634\pi\) | |||||||
\(200\) | 138.593i | 0.692965i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −85.1587 | −0.421578 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −222.000 | −1.08293 | ||||||||
\(206\) | − 240.865i | − 1.16925i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 48.6621 | 0.233952 | ||||||||
\(209\) | 68.8186i | 0.329276i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 44.0000 | 0.208531 | 0.104265 | − | 0.994550i | \(-0.466751\pi\) | ||||
0.104265 | + | 0.994550i | \(0.466751\pi\) | |||||||
\(212\) | 82.0244i | 0.386907i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −28.0000 | −0.130841 | ||||||||
\(215\) | − 584.958i | − 2.72074i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 79.1960i | − 0.363284i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −48.6621 | −0.221191 | ||||||||
\(221\) | 313.955i | 1.42061i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −194.648 | −0.872863 | −0.436431 | − | 0.899738i | \(-0.643758\pi\) | ||||
−0.436431 | + | 0.899738i | \(0.643758\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −226.000 | −1.00000 | ||||||||
\(227\) | − 34.4093i | − 0.151583i | −0.997124 | − | 0.0757914i | \(-0.975852\pi\) | ||||
0.997124 | − | 0.0757914i | \(-0.0241483\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.1655 | 0.0531246 | 0.0265623 | − | 0.999647i | \(-0.491544\pi\) | ||||
0.0265623 | + | 0.999647i | \(0.491544\pi\) | |||||||
\(230\) | − 516.140i | − 2.24408i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −44.0000 | −0.189655 | ||||||||
\(233\) | − 270.115i | − 1.15929i | −0.814869 | − | 0.579645i | \(-0.803191\pi\) | ||||
0.814869 | − | 0.579645i | \(-0.196809\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 592.000 | 2.51915 | ||||||||
\(236\) | 137.637i | 0.583208i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 76.3675i | 0.319529i | 0.987155 | + | 0.159765i | \(0.0510736\pi\) | ||||
−0.987155 | + | 0.159765i | \(0.948926\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 133.821 | 0.555273 | 0.277636 | − | 0.960686i | \(-0.410449\pi\) | ||||
0.277636 | + | 0.960686i | \(0.410449\pi\) | |||||||
\(242\) | 159.806i | 0.660356i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −194.648 | −0.797739 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −296.000 | −1.19838 | ||||||||
\(248\) | − 68.8186i | − 0.277494i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 291.973 | 1.16789 | ||||||||
\(251\) | 137.637i | 0.548355i | 0.961679 | + | 0.274178i | \(0.0884056\pi\) | ||||
−0.961679 | + | 0.274178i | \(0.911594\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 120.000 | 0.474308 | ||||||||
\(254\) | − 107.480i | − 0.423151i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 249.467i | 0.970690i | 0.874323 | + | 0.485345i | \(0.161306\pi\) | ||||
−0.874323 | + | 0.485345i | \(0.838694\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 209.304i | − 0.805014i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −145.986 | −0.557200 | ||||||||
\(263\) | 234.759i | 0.892621i | 0.894878 | + | 0.446311i | \(0.147262\pi\) | ||||
−0.894878 | + | 0.446311i | \(0.852738\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 352.800 | 1.33132 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 208.000 | 0.776119 | ||||||||
\(269\) | 215.058i | 0.799473i | 0.916630 | + | 0.399736i | \(0.130898\pi\) | ||||
−0.916630 | + | 0.399736i | \(0.869102\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −316.304 | −1.16717 | −0.583586 | − | 0.812051i | \(-0.698351\pi\) | ||||
−0.583586 | + | 0.812051i | \(0.698351\pi\) | |||||||
\(272\) | 103.228i | 0.379514i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 142.000 | 0.518248 | ||||||||
\(275\) | 138.593i | 0.503974i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 64.0000 | 0.231047 | 0.115523 | − | 0.993305i | \(-0.463145\pi\) | ||||
0.115523 | + | 0.993305i | \(0.463145\pi\) | |||||||
\(278\) | 206.456i | 0.742647i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 462.448i | 1.64572i | 0.568243 | + | 0.822861i | \(0.307623\pi\) | ||||
−0.568243 | + | 0.822861i | \(0.692377\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.3311 | 0.0859754 | 0.0429877 | − | 0.999076i | \(-0.486312\pi\) | ||||
0.0429877 | + | 0.999076i | \(0.486312\pi\) | |||||||
\(284\) | 141.421i | 0.497963i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 48.6621 | 0.170147 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −377.000 | −1.30450 | ||||||||
\(290\) | 189.251i | 0.652590i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −121.655 | −0.416628 | ||||||||
\(293\) | 283.877i | 0.968863i | 0.874829 | + | 0.484431i | \(0.160973\pi\) | ||||
−0.874829 | + | 0.484431i | \(0.839027\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 592.000 | 2.00678 | ||||||||
\(296\) | 16.9706i | 0.0573330i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 58.0000 | 0.194631 | ||||||||
\(299\) | 516.140i | 1.72622i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 226.274i | 0.749252i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −97.3242 | −0.320145 | ||||||||
\(305\) | 837.214i | 2.74497i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 316.304 | 1.03031 | 0.515153 | − | 0.857099i | \(-0.327735\pi\) | ||||
0.515153 | + | 0.857099i | \(0.327735\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −296.000 | −0.954839 | ||||||||
\(311\) | 275.274i | 0.885127i | 0.896737 | + | 0.442563i | \(0.145931\pi\) | ||||
−0.896737 | + | 0.442563i | \(0.854069\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −291.973 | −0.932820 | −0.466410 | − | 0.884569i | \(-0.654453\pi\) | ||||
−0.466410 | + | 0.884569i | \(0.654453\pi\) | |||||||
\(314\) | 275.274i | 0.876670i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 40.0000 | 0.126582 | ||||||||
\(317\) | 335.169i | 1.05731i | 0.848835 | + | 0.528657i | \(0.177304\pi\) | ||||
−0.848835 | + | 0.528657i | \(0.822696\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −44.0000 | −0.137931 | ||||||||
\(320\) | − 68.8186i | − 0.215058i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 627.911i | − 1.94400i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −596.111 | −1.83419 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 72.9932 | 0.222540 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −388.000 | −1.17221 | −0.586103 | − | 0.810237i | \(-0.699339\pi\) | ||||
−0.586103 | + | 0.810237i | \(0.699339\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −243.311 | −0.728475 | ||||||||
\(335\) | − 894.642i | − 2.67057i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −208.000 | −0.617211 | −0.308605 | − | 0.951190i | \(-0.599862\pi\) | ||||
−0.308605 | + | 0.951190i | \(0.599862\pi\) | |||||||
\(338\) | − 29.6985i | − 0.0878653i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 444.000 | 1.30588 | ||||||||
\(341\) | − 68.8186i | − 0.201814i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 192.333i | 0.559108i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.1655 | 0.0351605 | ||||||||
\(347\) | − 364.867i | − 1.05149i | −0.850642 | − | 0.525745i | \(-0.823787\pi\) | ||||
0.850642 | − | 0.525745i | \(-0.176213\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.0000 | 0.0454545 | ||||||||
\(353\) | − 25.8070i | − 0.0731076i | −0.999332 | − | 0.0365538i | \(-0.988362\pi\) | ||||
0.999332 | − | 0.0365538i | \(-0.0116380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 608.276 | 1.71345 | ||||||||
\(356\) | − 189.251i | − 0.531604i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 204.000 | 0.569832 | ||||||||
\(359\) | − 302.642i | − 0.843013i | −0.906825 | − | 0.421507i | \(-0.861501\pi\) | ||||
0.906825 | − | 0.421507i | \(-0.138499\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 231.000 | 0.639889 | ||||||||
\(362\) | − 17.2047i | − 0.0475267i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 523.259i | 1.43359i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 389.297 | 1.06075 | 0.530377 | − | 0.847762i | \(-0.322050\pi\) | ||||
0.530377 | + | 0.847762i | \(0.322050\pi\) | |||||||
\(368\) | 169.706i | 0.461157i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 72.9932 | 0.197279 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 706.000 | 1.89276 | 0.946381 | − | 0.323054i | \(-0.104709\pi\) | ||||
0.946381 | + | 0.323054i | \(0.104709\pi\) | |||||||
\(374\) | 103.228i | 0.276010i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −194.648 | −0.517682 | ||||||||
\(377\) | − 189.251i | − 0.501992i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 708.000 | 1.86807 | 0.934037 | − | 0.357176i | \(-0.116261\pi\) | ||||
0.934037 | + | 0.357176i | \(0.116261\pi\) | |||||||
\(380\) | 418.607i | 1.10160i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −372.000 | −0.973822 | ||||||||
\(383\) | 309.684i | 0.808574i | 0.914632 | + | 0.404287i | \(0.132480\pi\) | ||||
−0.914632 | + | 0.404287i | \(0.867520\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 53.7401i | 0.139223i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 316.304 | 0.815216 | ||||||||
\(389\) | 131.522i | 0.338102i | 0.985607 | + | 0.169051i | \(0.0540703\pi\) | ||||
−0.985607 | + | 0.169051i | \(0.945930\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1094.90 | −2.80025 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −234.000 | −0.593909 | ||||||||
\(395\) | − 172.047i | − 0.435561i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −97.3242 | −0.245149 | −0.122575 | − | 0.992459i | \(-0.539115\pi\) | ||||
−0.122575 | + | 0.992459i | \(0.539115\pi\) | |||||||
\(398\) | 344.093i | 0.864555i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −196.000 | −0.490000 | ||||||||
\(401\) | − 89.0955i | − 0.222183i | −0.993810 | − | 0.111092i | \(-0.964565\pi\) | ||||
0.993810 | − | 0.111092i | \(-0.0354347\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 296.000 | 0.734491 | ||||||||
\(404\) | − 120.433i | − 0.298100i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.9706i | 0.0416967i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −547.449 | −1.33851 | −0.669253 | − | 0.743035i | \(-0.733386\pi\) | ||||
−0.669253 | + | 0.743035i | \(0.733386\pi\) | |||||||
\(410\) | − 313.955i | − 0.765745i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 340.635 | 0.826783 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 68.8186i | 0.165429i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −97.3242 | −0.232833 | ||||||||
\(419\) | 653.777i | 1.56033i | 0.625576 | + | 0.780163i | \(0.284864\pi\) | ||||
−0.625576 | + | 0.780163i | \(0.715136\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 240.000 | 0.570071 | 0.285036 | − | 0.958517i | \(-0.407995\pi\) | ||||
0.285036 | + | 0.958517i | \(0.407995\pi\) | |||||||
\(422\) | 62.2254i | 0.147454i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −116.000 | −0.273585 | ||||||||
\(425\) | − 1264.54i | − 2.97539i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 39.5980i | − 0.0925186i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 827.256 | 1.92385 | ||||||||
\(431\) | − 14.1421i | − 0.0328124i | −0.999865 | − | 0.0164062i | \(-0.994778\pi\) | ||||
0.999865 | − | 0.0164062i | \(-0.00522249\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −389.297 | −0.899069 | −0.449534 | − | 0.893263i | \(-0.648410\pi\) | ||||
−0.449534 | + | 0.893263i | \(0.648410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 112.000 | 0.256881 | ||||||||
\(437\) | − 1032.28i | − 2.36219i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 291.973 | 0.665086 | 0.332543 | − | 0.943088i | \(-0.392093\pi\) | ||||
0.332543 | + | 0.943088i | \(0.392093\pi\) | |||||||
\(440\) | − 68.8186i | − 0.156406i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −444.000 | −1.00452 | ||||||||
\(443\) | 25.4558i | 0.0574624i | 0.999587 | + | 0.0287312i | \(0.00914668\pi\) | ||||
−0.999587 | + | 0.0287312i | \(0.990853\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −814.000 | −1.82921 | ||||||||
\(446\) | − 275.274i | − 0.617207i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 733.977i | − 1.63469i | −0.576147 | − | 0.817346i | \(-0.695444\pi\) | ||||
0.576147 | − | 0.817346i | \(-0.304556\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 72.9932 | 0.161847 | ||||||||
\(452\) | − 319.612i | − 0.707107i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 48.6621 | 0.107185 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 272.000 | 0.595186 | 0.297593 | − | 0.954693i | \(-0.403816\pi\) | ||||
0.297593 | + | 0.954693i | \(0.403816\pi\) | |||||||
\(458\) | 17.2047i | 0.0375647i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 729.932 | 1.58681 | ||||||||
\(461\) | 490.333i | 1.06363i | 0.846861 | + | 0.531814i | \(0.178489\pi\) | ||||
−0.846861 | + | 0.531814i | \(0.821511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −436.000 | −0.941685 | −0.470842 | − | 0.882217i | \(-0.656050\pi\) | ||||
−0.470842 | + | 0.882217i | \(0.656050\pi\) | |||||||
\(464\) | − 62.2254i | − 0.134106i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 382.000 | 0.819742 | ||||||||
\(467\) | 481.730i | 1.03154i | 0.856726 | + | 0.515771i | \(0.172495\pi\) | ||||
−0.856726 | + | 0.515771i | \(0.827505\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 837.214i | 1.78131i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −194.648 | −0.412391 | ||||||||
\(473\) | 192.333i | 0.406624i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1192.22 | 2.50994 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −108.000 | −0.225941 | ||||||||
\(479\) | − 103.228i | − 0.215507i | −0.994178 | − | 0.107754i | \(-0.965634\pi\) | ||||
0.994178 | − | 0.107754i | \(-0.0343657\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −72.9932 | −0.151753 | ||||||||
\(482\) | 189.251i | 0.392637i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −226.000 | −0.466942 | ||||||||
\(485\) | − 1360.47i | − 2.80510i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 232.000 | 0.476386 | 0.238193 | − | 0.971218i | \(-0.423445\pi\) | ||||
0.238193 | + | 0.971218i | \(0.423445\pi\) | |||||||
\(488\) | − 275.274i | − 0.564087i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 449.720i | − 0.915927i | −0.888971 | − | 0.457963i | \(-0.848579\pi\) | ||||
0.888971 | − | 0.457963i | \(-0.151421\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 401.462 | 0.814325 | ||||||||
\(494\) | − 418.607i | − 0.847383i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 97.3242 | 0.196218 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 756.000 | 1.51503 | 0.757515 | − | 0.652818i | \(-0.226413\pi\) | ||||
0.757515 | + | 0.652818i | \(0.226413\pi\) | |||||||
\(500\) | 412.912i | 0.825823i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −194.648 | −0.387746 | ||||||||
\(503\) | − 550.549i | − 1.09453i | −0.836959 | − | 0.547265i | \(-0.815669\pi\) | ||||
0.836959 | − | 0.547265i | \(-0.184331\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −518.000 | −1.02574 | ||||||||
\(506\) | 169.706i | 0.335387i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 152.000 | 0.299213 | ||||||||
\(509\) | − 8.60233i | − 0.0169004i | −0.999964 | − | 0.00845022i | \(-0.997310\pi\) | ||||
0.999964 | − | 0.00845022i | \(-0.00268982\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −352.800 | −0.686382 | ||||||||
\(515\) | − 1465.13i | − 2.84490i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −194.648 | −0.376496 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 296.000 | 0.569231 | ||||||||
\(521\) | 94.6256i | 0.181623i | 0.995868 | + | 0.0908115i | \(0.0289461\pi\) | ||||
−0.995868 | + | 0.0908115i | \(0.971054\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 924.580 | 1.76784 | 0.883920 | − | 0.467639i | \(-0.154895\pi\) | ||||
0.883920 | + | 0.467639i | \(0.154895\pi\) | |||||||
\(524\) | − 206.456i | − 0.394000i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −332.000 | −0.631179 | ||||||||
\(527\) | 627.911i | 1.19148i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1271.00 | −2.40265 | ||||||||
\(530\) | 498.935i | 0.941387i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 313.955i | 0.589035i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −170.317 | −0.318350 | ||||||||
\(536\) | 294.156i | 0.548799i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −304.138 | −0.565313 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 592.000 | 1.09427 | 0.547135 | − | 0.837044i | \(-0.315718\pi\) | ||||
0.547135 | + | 0.837044i | \(0.315718\pi\) | |||||||
\(542\) | − 447.321i | − 0.825315i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −145.986 | −0.268357 | ||||||||
\(545\) | − 481.730i | − 0.883909i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −416.000 | −0.760512 | −0.380256 | − | 0.924881i | \(-0.624164\pi\) | ||||
−0.380256 | + | 0.924881i | \(0.624164\pi\) | |||||||
\(548\) | 200.818i | 0.366457i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −196.000 | −0.356364 | ||||||||
\(551\) | 378.502i | 0.686937i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 90.5097i | 0.163375i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −291.973 | −0.525131 | ||||||||
\(557\) | 309.713i | 0.556037i | 0.960576 | + | 0.278019i | \(0.0896777\pi\) | ||||
−0.960576 | + | 0.278019i | \(0.910322\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −827.256 | −1.47988 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −654.000 | −1.16370 | ||||||||
\(563\) | 894.642i | 1.58906i | 0.607224 | + | 0.794531i | \(0.292283\pi\) | ||||
−0.607224 | + | 0.794531i | \(0.707717\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1374.70 | −2.43311 | ||||||||
\(566\) | 34.4093i | 0.0607938i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −200.000 | −0.352113 | ||||||||
\(569\) | − 733.977i | − 1.28994i | −0.764207 | − | 0.644971i | \(-0.776869\pi\) | ||||
0.764207 | − | 0.644971i | \(-0.223131\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 312.000 | 0.546410 | 0.273205 | − | 0.961956i | \(-0.411916\pi\) | ||||
0.273205 | + | 0.961956i | \(0.411916\pi\) | |||||||
\(572\) | 68.8186i | 0.120312i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 2078.89i | − 3.61547i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −194.648 | −0.337346 | −0.168673 | − | 0.985672i | \(-0.553948\pi\) | ||||
−0.168673 | + | 0.985672i | \(0.553948\pi\) | |||||||
\(578\) | − 533.159i | − 0.922420i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −267.642 | −0.461451 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −116.000 | −0.198971 | ||||||||
\(584\) | − 172.047i | − 0.294600i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −401.462 | −0.685089 | ||||||||
\(587\) | 447.321i | 0.762046i | 0.924566 | + | 0.381023i | \(0.124428\pi\) | ||||
−0.924566 | + | 0.381023i | \(0.875572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −592.000 | −1.00509 | ||||||||
\(590\) | 837.214i | 1.41901i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.0000 | −0.0405405 | ||||||||
\(593\) | 645.174i | 1.08798i | 0.839090 | + | 0.543992i | \(0.183088\pi\) | ||||
−0.839090 | + | 0.543992i | \(0.816912\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 82.0244i | 0.137625i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −729.932 | −1.22062 | ||||||||
\(599\) | − 687.308i | − 1.14743i | −0.819057 | − | 0.573713i | \(-0.805503\pi\) | ||||
0.819057 | − | 0.573713i | \(-0.194497\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1070.57 | 1.78131 | 0.890654 | − | 0.454682i | \(-0.150247\pi\) | ||||
0.890654 | + | 0.454682i | \(0.150247\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −320.000 | −0.529801 | ||||||||
\(605\) | 972.063i | 1.60672i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −729.932 | −1.20252 | −0.601262 | − | 0.799052i | \(-0.705335\pi\) | ||||
−0.601262 | + | 0.799052i | \(0.705335\pi\) | |||||||
\(608\) | − 137.637i | − 0.226377i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1184.00 | −1.94098 | ||||||||
\(611\) | − 837.214i | − 1.37024i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −514.000 | −0.838499 | −0.419250 | − | 0.907871i | \(-0.637707\pi\) | ||||
−0.419250 | + | 0.907871i | \(0.637707\pi\) | |||||||
\(614\) | 447.321i | 0.728536i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 202.233i | 0.327767i | 0.986480 | + | 0.163884i | \(0.0524022\pi\) | ||||
−0.986480 | + | 0.163884i | \(0.947598\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 681.269 | 1.10060 | 0.550298 | − | 0.834968i | \(-0.314514\pi\) | ||||
0.550298 | + | 0.834968i | \(0.314514\pi\) | |||||||
\(620\) | − 418.607i | − 0.675173i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −389.297 | −0.625879 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 551.000 | 0.881600 | ||||||||
\(626\) | − 412.912i | − 0.659603i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −389.297 | −0.619899 | ||||||||
\(629\) | − 154.842i | − 0.246171i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 636.000 | 1.00792 | 0.503962 | − | 0.863726i | \(-0.331875\pi\) | ||||
0.503962 | + | 0.863726i | \(0.331875\pi\) | |||||||
\(632\) | 56.5685i | 0.0895072i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −474.000 | −0.747634 | ||||||||
\(635\) | − 653.777i | − 1.02957i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 62.2254i | − 0.0975320i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 97.3242 | 0.152069 | ||||||||
\(641\) | − 77.7817i | − 0.121344i | −0.998158 | − | 0.0606722i | \(-0.980676\pi\) | ||||
0.998158 | − | 0.0606722i | \(-0.0193244\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 510.952 | 0.794638 | 0.397319 | − | 0.917681i | \(-0.369941\pi\) | ||||
0.397319 | + | 0.917681i | \(0.369941\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 888.000 | 1.37461 | ||||||||
\(647\) | 929.051i | 1.43594i | 0.696076 | + | 0.717968i | \(0.254928\pi\) | ||||
−0.696076 | + | 0.717968i | \(0.745072\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −194.648 | −0.299920 | ||||||||
\(650\) | − 843.028i | − 1.29697i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 637.810i | 0.976739i | 0.872637 | + | 0.488369i | \(0.162408\pi\) | ||||
−0.872637 | + | 0.488369i | \(0.837592\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −888.000 | −1.35573 | ||||||||
\(656\) | 103.228i | 0.157360i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 200.818i | − 0.304732i | −0.988324 | − | 0.152366i | \(-0.951311\pi\) | ||||
0.988324 | − | 0.152366i | \(-0.0486892\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −97.3242 | −0.147238 | −0.0736189 | − | 0.997286i | \(-0.523455\pi\) | ||||
−0.0736189 | + | 0.997286i | \(0.523455\pi\) | |||||||
\(662\) | − 548.715i | − 0.828874i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 660.000 | 0.989505 | ||||||||
\(668\) | − 344.093i | − 0.515109i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1265.21 | 1.88838 | ||||||||
\(671\) | − 275.274i | − 0.410245i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −250.000 | −0.371471 | −0.185736 | − | 0.982600i | \(-0.559467\pi\) | ||||
−0.185736 | + | 0.982600i | \(0.559467\pi\) | |||||||
\(674\) | − 294.156i | − 0.436434i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 42.0000 | 0.0621302 | ||||||||
\(677\) | 335.491i | 0.495555i | 0.968817 | + | 0.247777i | \(0.0797002\pi\) | ||||
−0.968817 | + | 0.247777i | \(0.920300\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 627.911i | 0.923398i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 97.3242 | 0.142704 | ||||||||
\(683\) | 291.328i | 0.426542i | 0.976993 | + | 0.213271i | \(0.0684117\pi\) | ||||
−0.976993 | + | 0.213271i | \(0.931588\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 863.752 | 1.26095 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −272.000 | −0.395349 | ||||||||
\(689\) | − 498.935i | − 0.724143i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 535.283 | 0.774650 | 0.387325 | − | 0.921943i | \(-0.373399\pi\) | ||||
0.387325 | + | 0.921943i | \(0.373399\pi\) | |||||||
\(692\) | 17.2047i | 0.0248622i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 516.000 | 0.743516 | ||||||||
\(695\) | 1255.82i | 1.80694i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −666.000 | −0.955524 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1045.10i | − 1.49088i | −0.666575 | − | 0.745438i | \(-0.732240\pi\) | ||||
0.666575 | − | 0.745438i | \(-0.267760\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 145.986 | 0.207662 | ||||||||
\(704\) | 22.6274i | 0.0321412i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 36.4966 | 0.0516949 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −488.000 | −0.688293 | −0.344147 | − | 0.938916i | \(-0.611832\pi\) | ||||
−0.344147 | + | 0.938916i | \(0.611832\pi\) | |||||||
\(710\) | 860.233i | 1.21160i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 267.642 | 0.375901 | ||||||||
\(713\) | 1032.28i | 1.44780i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 296.000 | 0.413986 | ||||||||
\(716\) | 288.500i | 0.402932i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 428.000 | 0.596100 | ||||||||
\(719\) | − 929.051i | − 1.29214i | −0.763277 | − | 0.646072i | \(-0.776411\pi\) | ||||
0.763277 | − | 0.646072i | \(-0.223589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 326.683i | 0.452470i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 24.3311 | 0.0336064 | ||||||||
\(725\) | 762.261i | 1.05139i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −900.249 | −1.23831 | −0.619153 | − | 0.785270i | \(-0.712524\pi\) | ||||
−0.619153 | + | 0.785270i | \(0.712524\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −740.000 | −1.01370 | ||||||||
\(731\) | − 1754.87i | − 2.40065i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1155.72 | 1.57671 | 0.788353 | − | 0.615224i | \(-0.210934\pi\) | ||||
0.788353 | + | 0.615224i | \(0.210934\pi\) | |||||||
\(734\) | 550.549i | 0.750067i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −240.000 | −0.326087 | ||||||||
\(737\) | 294.156i | 0.399127i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −920.000 | −1.24493 | −0.622463 | − | 0.782649i | \(-0.713868\pi\) | ||||
−0.622463 | + | 0.782649i | \(0.713868\pi\) | |||||||
\(740\) | 103.228i | 0.139497i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 755.190i | − 1.01641i | −0.861237 | − | 0.508203i | \(-0.830310\pi\) | ||||
0.861237 | − | 0.508203i | \(-0.169690\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 352.800 | 0.473557 | ||||||||
\(746\) | 998.435i | 1.33838i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −145.986 | −0.195169 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −120.000 | −0.159787 | −0.0798935 | − | 0.996803i | \(-0.525458\pi\) | ||||
−0.0798935 | + | 0.996803i | \(0.525458\pi\) | |||||||
\(752\) | − 275.274i | − 0.366056i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 267.642 | 0.354962 | ||||||||
\(755\) | 1376.37i | 1.82301i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1016.00 | −1.34214 | −0.671070 | − | 0.741394i | \(-0.734165\pi\) | ||||
−0.671070 | + | 0.741394i | \(0.734165\pi\) | |||||||
\(758\) | 1001.26i | 1.32093i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −592.000 | −0.778947 | ||||||||
\(761\) | − 43.0116i | − 0.0565199i | −0.999601 | − | 0.0282599i | \(-0.991003\pi\) | ||||
0.999601 | − | 0.0282599i | \(-0.00899662\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 526.087i | − 0.688596i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −437.959 | −0.571748 | ||||||||
\(767\) | − 837.214i | − 1.09154i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −681.269 | −0.885916 | −0.442958 | − | 0.896542i | \(-0.646071\pi\) | ||||
−0.442958 | + | 0.896542i | \(0.646071\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −76.0000 | −0.0984456 | ||||||||
\(773\) | − 1161.31i | − 1.50235i | −0.660105 | − | 0.751173i | \(-0.729488\pi\) | ||||
0.660105 | − | 0.751173i | \(-0.270512\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1192.22 | −1.53835 | ||||||||
\(776\) | 447.321i | 0.576444i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −186.000 | −0.239075 | ||||||||
\(779\) | − 627.911i | − 0.806047i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −200.000 | −0.256082 | ||||||||
\(782\) | − 1548.42i | − 1.98007i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1674.43i | 2.13303i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −194.648 | −0.247330 | −0.123665 | − | 0.992324i | \(-0.539465\pi\) | ||||
−0.123665 | + | 0.992324i | \(0.539465\pi\) | |||||||
\(788\) | − 330.926i | − 0.419957i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 243.311 | 0.307988 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1184.00 | 1.49306 | ||||||||
\(794\) | − 137.637i | − 0.173347i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −486.621 | −0.611333 | ||||||||
\(797\) | − 1109.70i | − 1.39235i | −0.717874 | − | 0.696173i | \(-0.754885\pi\) | ||||
0.717874 | − | 0.696173i | \(-0.245115\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1776.00 | 2.22278 | ||||||||
\(800\) | − 277.186i | − 0.346482i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 126.000 | 0.157107 | ||||||||
\(803\) | − 172.047i | − 0.214255i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 418.607i | 0.519364i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 170.317 | 0.210789 | ||||||||
\(809\) | 1030.96i | 1.27437i | 0.770713 | + | 0.637183i | \(0.219900\pi\) | ||||
−0.770713 | + | 0.637183i | \(0.780100\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −243.311 | −0.300013 | −0.150006 | − | 0.988685i | \(-0.547929\pi\) | ||||
−0.150006 | + | 0.988685i | \(0.547929\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −24.0000 | −0.0294840 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1654.51 | 2.02511 | ||||||||
\(818\) | − 774.209i | − 0.946466i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 444.000 | 0.541463 | ||||||||
\(821\) | 357.796i | 0.435805i | 0.975971 | + | 0.217903i | \(0.0699215\pi\) | ||||
−0.975971 | + | 0.217903i | \(0.930078\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1228.00 | 1.49210 | 0.746051 | − | 0.665889i | \(-0.231947\pi\) | ||||
0.746051 | + | 0.665889i | \(0.231947\pi\) | |||||||
\(824\) | 481.730i | 0.584624i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 195.161i | − 0.235987i | −0.993014 | − | 0.117994i | \(-0.962354\pi\) | ||||
0.993014 | − | 0.117994i | \(-0.0376462\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 790.759 | 0.953871 | 0.476936 | − | 0.878938i | \(-0.341748\pi\) | ||||
0.476936 | + | 0.878938i | \(0.341748\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −97.3242 | −0.116976 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1480.00 | −1.77246 | ||||||||
\(836\) | − 137.637i | − 0.164638i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −924.580 | −1.10332 | ||||||||
\(839\) | − 1238.73i | − 1.47644i | −0.674559 | − | 0.738221i | \(-0.735666\pi\) | ||||
0.674559 | − | 0.738221i | \(-0.264334\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 599.000 | 0.712247 | ||||||||
\(842\) | 339.411i | 0.403101i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −88.0000 | −0.104265 | ||||||||
\(845\) | − 180.649i | − 0.213786i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 164.049i | − 0.193454i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1788.33 | 2.10392 | ||||||||
\(851\) | − 254.558i | − 0.299129i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1557.19 | −1.82554 | −0.912771 | − | 0.408472i | \(-0.866062\pi\) | ||||
−0.912771 | + | 0.408472i | \(0.866062\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 56.0000 | 0.0654206 | ||||||||
\(857\) | 1471.00i | 1.71645i | 0.513274 | + | 0.858225i | \(0.328433\pi\) | ||||
−0.513274 | + | 0.858225i | \(0.671567\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −510.952 | −0.594822 | −0.297411 | − | 0.954750i | \(-0.596123\pi\) | ||||
−0.297411 | + | 0.954750i | \(0.596123\pi\) | |||||||
\(860\) | 1169.92i | 1.36037i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.0000 | 0.0232019 | ||||||||
\(863\) | 568.514i | 0.658765i | 0.944197 | + | 0.329382i | \(0.106840\pi\) | ||||
−0.944197 | + | 0.329382i | \(0.893160\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 74.0000 | 0.0855491 | ||||||||
\(866\) | − 550.549i | − 0.635738i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 56.5685i | 0.0650961i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1265.21 | −1.45260 | ||||||||
\(872\) | 158.392i | 0.181642i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1459.86 | 1.67032 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −882.000 | −1.00570 | −0.502851 | − | 0.864373i | \(-0.667715\pi\) | ||||
−0.502851 | + | 0.864373i | \(0.667715\pi\) | |||||||
\(878\) | 412.912i | 0.470287i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 97.3242 | 0.110596 | ||||||||
\(881\) | − 43.0116i | − 0.0488214i | −0.999702 | − | 0.0244107i | \(-0.992229\pi\) | ||||
0.999702 | − | 0.0244107i | \(-0.00777093\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −140.000 | −0.158550 | −0.0792752 | − | 0.996853i | \(-0.525261\pi\) | ||||
−0.0792752 | + | 0.996853i | \(0.525261\pi\) | |||||||
\(884\) | − 627.911i | − 0.710306i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.0000 | −0.0406321 | ||||||||
\(887\) | − 309.684i | − 0.349136i | −0.984645 | − | 0.174568i | \(-0.944147\pi\) | ||||
0.984645 | − | 0.174568i | \(-0.0558529\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 1151.17i | − 1.29345i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 389.297 | 0.436431 | ||||||||
\(893\) | 1674.43i | 1.87506i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1240.88 | 1.38646 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1038.00 | 1.15590 | ||||||||
\(899\) | − 378.502i | − 0.421026i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1058.40 | 1.17470 | ||||||||
\(902\) | 103.228i | 0.114443i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 452.000 | 0.500000 | ||||||||
\(905\) | − 104.652i | − 0.115637i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1228.00 | 1.35391 | 0.676957 | − | 0.736023i | \(-0.263298\pi\) | ||||
0.676957 | + | 0.736023i | \(0.263298\pi\) | |||||||
\(908\) | 68.8186i | 0.0757914i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 138.593i | 0.152133i | 0.997103 | + | 0.0760664i | \(0.0242361\pi\) | ||||
−0.997103 | + | 0.0760664i | \(0.975764\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 384.666i | 0.420860i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.3311 | −0.0265623 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1608.00 | −1.74973 | −0.874864 | − | 0.484369i | \(-0.839049\pi\) | ||||
−0.874864 | + | 0.484369i | \(0.839049\pi\) | |||||||
\(920\) | 1032.28i | 1.12204i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −693.435 | −0.752099 | ||||||||
\(923\) | − 860.233i | − 0.931996i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 294.000 | 0.317838 | ||||||||
\(926\) | − 616.597i | − 0.665872i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 88.0000 | 0.0948276 | ||||||||
\(929\) | 1419.38i | 1.52786i | 0.645298 | + | 0.763931i | \(0.276733\pi\) | ||||
−0.645298 | + | 0.763931i | \(0.723267\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 540.230i | 0.579645i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −681.269 | −0.729410 | ||||||||
\(935\) | 627.911i | 0.671562i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −291.973 | −0.311604 | −0.155802 | − | 0.987788i | \(-0.549796\pi\) | ||||
−0.155802 | + | 0.987788i | \(0.549796\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1184.00 | −1.25957 | ||||||||
\(941\) | 1367.77i | 1.45353i | 0.686887 | + | 0.726764i | \(0.258977\pi\) | ||||
−0.686887 | + | 0.726764i | \(0.741023\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1094.90 | −1.16108 | ||||||||
\(944\) | − 275.274i | − 0.291604i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −272.000 | −0.287526 | ||||||||
\(947\) | 591.141i | 0.624225i | 0.950045 | + | 0.312113i | \(0.101037\pi\) | ||||
−0.950045 | + | 0.312113i | \(0.898963\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 740.000 | 0.779768 | ||||||||
\(950\) | 1686.06i | 1.77480i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 352.139i | − 0.369506i | −0.982785 | − | 0.184753i | \(-0.940851\pi\) | ||||
0.982785 | − | 0.184753i | \(-0.0591485\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2262.79 | −2.36941 | ||||||||
\(956\) | − 152.735i | − 0.159765i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 145.986 | 0.152387 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −369.000 | −0.383975 | ||||||||
\(962\) | − 103.228i | − 0.107306i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −267.642 | −0.277636 | ||||||||
\(965\) | 326.888i | 0.338744i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −260.000 | −0.268873 | −0.134436 | − | 0.990922i | \(-0.542922\pi\) | ||||
−0.134436 | + | 0.990922i | \(0.542922\pi\) | |||||||
\(968\) | − 319.612i | − 0.330178i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1924.00 | 1.98351 | ||||||||
\(971\) | 1479.60i | 1.52379i | 0.647701 | + | 0.761895i | \(0.275731\pi\) | ||||
−0.647701 | + | 0.761895i | \(0.724269\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 328.098i | 0.336856i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 389.297 | 0.398870 | ||||||||
\(977\) | − 329.512i | − 0.337269i | −0.985679 | − | 0.168634i | \(-0.946064\pi\) | ||||
0.985679 | − | 0.168634i | \(-0.0539357\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 267.642 | 0.273383 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 636.000 | 0.647658 | ||||||||
\(983\) | − 997.870i | − 1.01513i | −0.861614 | − | 0.507563i | \(-0.830546\pi\) | ||||
0.861614 | − | 0.507563i | \(-0.169454\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1423.37 | −1.44504 | ||||||||
\(986\) | 567.753i | 0.575815i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 592.000 | 0.599190 | ||||||||
\(989\) | − 2885.00i | − 2.91708i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1496.00 | 1.50959 | 0.754793 | − | 0.655963i | \(-0.227737\pi\) | ||||
0.754793 | + | 0.655963i | \(0.227737\pi\) | |||||||
\(992\) | 137.637i | 0.138747i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2093.04i | 2.10355i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1557.19 | −1.56187 | −0.780936 | − | 0.624611i | \(-0.785258\pi\) | ||||
−0.780936 | + | 0.624611i | \(0.785258\pi\) | |||||||
\(998\) | 1069.15i | 1.07129i | ||||||||
\(999\) | 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 | 882.3.b.g.197.4 | yes | 4 | |
3.2 | odd | 2 | inner | 882.3.b.g.197.1 | ✓ | 4 | |
7.2 | even | 3 | 882.3.s.h.557.4 | 8 | |||
7.3 | odd | 6 | 882.3.s.h.863.2 | 8 | |||
7.4 | even | 3 | 882.3.s.h.863.1 | 8 | |||
7.5 | odd | 6 | 882.3.s.h.557.3 | 8 | |||
7.6 | odd | 2 | inner | 882.3.b.g.197.3 | yes | 4 | |
21.2 | odd | 6 | 882.3.s.h.557.1 | 8 | |||
21.5 | even | 6 | 882.3.s.h.557.2 | 8 | |||
21.11 | odd | 6 | 882.3.s.h.863.4 | 8 | |||
21.17 | even | 6 | 882.3.s.h.863.3 | 8 | |||
21.20 | even | 2 | inner | 882.3.b.g.197.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.3.b.g.197.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
882.3.b.g.197.2 | yes | 4 | 21.20 | even | 2 | inner | |
882.3.b.g.197.3 | yes | 4 | 7.6 | odd | 2 | inner | |
882.3.b.g.197.4 | yes | 4 | 1.1 | even | 1 | trivial | |
882.3.s.h.557.1 | 8 | 21.2 | odd | 6 | |||
882.3.s.h.557.2 | 8 | 21.5 | even | 6 | |||
882.3.s.h.557.3 | 8 | 7.5 | odd | 6 | |||
882.3.s.h.557.4 | 8 | 7.2 | even | 3 | |||
882.3.s.h.863.1 | 8 | 7.4 | even | 3 | |||
882.3.s.h.863.2 | 8 | 7.3 | odd | 6 | |||
882.3.s.h.863.3 | 8 | 21.17 | even | 6 | |||
882.3.s.h.863.4 | 8 | 21.11 | odd | 6 |