Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(604,1089)]
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([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.604");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.c (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: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 21x^{14} + 227x^{12} - 1488x^{10} + 24225x^{8} - 62832x^{6} + 64372x^{4} + 7986x^{2} + 14641 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 11^{4} \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 604.2 | ||
Root | \(3.67414 - 1.19380i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.604 |
Dual form | 1089.3.c.l.604.16 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.86322i | − 1.93161i | −0.259266 | − | 0.965806i | \(-0.583481\pi\) | ||||
0.259266 | − | 0.965806i | \(-0.416519\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −10.9245 | −2.73112 | ||||||||
\(5\) | 4.15040 | 0.830079 | 0.415040 | − | 0.909803i | \(-0.363768\pi\) | ||||
0.415040 | + | 0.909803i | \(0.363768\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.44465i | 1.06352i | 0.846895 | + | 0.531761i | \(0.178469\pi\) | ||||
−0.846895 | + | 0.531761i | \(0.821531\pi\) | |||||||
\(8\) | 26.7509i | 3.34386i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 16.0339i | − 1.60339i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 7.32428i | − 0.563406i | −0.959502 | − | 0.281703i | \(-0.909101\pi\) | ||||
0.959502 | − | 0.281703i | \(-0.0908993\pi\) | |||||||
\(14\) | 28.7603 | 2.05431 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 59.6467 | 3.72792 | ||||||||
\(17\) | 3.57908i | 0.210534i | 0.994444 | + | 0.105267i | \(0.0335697\pi\) | ||||
−0.994444 | + | 0.105267i | \(0.966430\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 29.9894i | − 1.57839i | −0.614142 | − | 0.789196i | \(-0.710498\pi\) | ||||
0.614142 | − | 0.789196i | \(-0.289502\pi\) | |||||||
\(20\) | −45.3410 | −2.26705 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −20.6531 | −0.897959 | −0.448980 | − | 0.893542i | \(-0.648212\pi\) | ||||
−0.448980 | + | 0.893542i | \(0.648212\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.77420 | −0.310968 | ||||||||
\(26\) | −28.2953 | −1.08828 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 81.3291i | − 2.90461i | ||||||||
\(29\) | − 17.1852i | − 0.592592i | −0.955096 | − | 0.296296i | \(-0.904248\pi\) | ||||
0.955096 | − | 0.296296i | \(-0.0957515\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 15.7747 | 0.508862 | 0.254431 | − | 0.967091i | \(-0.418112\pi\) | ||||
0.254431 | + | 0.967091i | \(0.418112\pi\) | |||||||
\(32\) | − 123.425i | − 3.85703i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.8268 | 0.406670 | ||||||||
\(35\) | 30.8983i | 0.882807i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −32.2745 | −0.872283 | −0.436141 | − | 0.899878i | \(-0.643655\pi\) | ||||
−0.436141 | + | 0.899878i | \(0.643655\pi\) | |||||||
\(38\) | −115.856 | −3.04884 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 111.027i | 2.77567i | ||||||||
\(41\) | − 16.2215i | − 0.395647i | −0.980238 | − | 0.197824i | \(-0.936613\pi\) | ||||
0.980238 | − | 0.197824i | \(-0.0633874\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 33.7299i | − 0.784415i | −0.919877 | − | 0.392208i | \(-0.871711\pi\) | ||||
0.919877 | − | 0.392208i | \(-0.128289\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 79.7874i | 1.73451i | ||||||||
\(47\) | −38.9036 | −0.827737 | −0.413868 | − | 0.910337i | \(-0.635823\pi\) | ||||
−0.413868 | + | 0.910337i | \(0.635823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.42281 | −0.131078 | ||||||||
\(50\) | 30.0335i | 0.600670i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 80.0141i | 1.53873i | ||||||||
\(53\) | −36.6137 | −0.690824 | −0.345412 | − | 0.938451i | \(-0.612261\pi\) | ||||
−0.345412 | + | 0.938451i | \(0.612261\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −199.151 | −3.55627 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −66.3902 | −1.14466 | ||||||||
\(59\) | −69.9524 | −1.18563 | −0.592817 | − | 0.805338i | \(-0.701984\pi\) | ||||
−0.592817 | + | 0.805338i | \(0.701984\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 22.7511i | 0.372968i | 0.982458 | + | 0.186484i | \(0.0597093\pi\) | ||||
−0.982458 | + | 0.186484i | \(0.940291\pi\) | |||||||
\(62\) | − 60.9413i | − 0.982925i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −238.231 | −3.72236 | ||||||||
\(65\) | − 30.3987i | − 0.467672i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −63.0682 | −0.941317 | −0.470658 | − | 0.882315i | \(-0.655984\pi\) | ||||
−0.470658 | + | 0.882315i | \(0.655984\pi\) | |||||||
\(68\) | − 39.0996i | − 0.574994i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 119.367 | 1.70524 | ||||||||
\(71\) | 31.5933 | 0.444976 | 0.222488 | − | 0.974935i | \(-0.428582\pi\) | ||||
0.222488 | + | 0.974935i | \(0.428582\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 103.388i | − 1.41628i | −0.706075 | − | 0.708138i | \(-0.749536\pi\) | ||||
0.706075 | − | 0.708138i | \(-0.250464\pi\) | |||||||
\(74\) | 124.683i | 1.68491i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 327.620i | 4.31078i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 18.2635i | − 0.231183i | −0.993297 | − | 0.115592i | \(-0.963124\pi\) | ||||
0.993297 | − | 0.115592i | \(-0.0368764\pi\) | |||||||
\(80\) | 247.557 | 3.09447 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −62.6675 | −0.764237 | ||||||||
\(83\) | − 118.991i | − 1.43362i | −0.697268 | − | 0.716811i | \(-0.745601\pi\) | ||||
0.697268 | − | 0.716811i | \(-0.254399\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.8546i | 0.174760i | ||||||||
\(86\) | −130.306 | −1.51519 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 154.739 | 1.73864 | 0.869320 | − | 0.494249i | \(-0.164557\pi\) | ||||
0.869320 | + | 0.494249i | \(0.164557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 54.5267 | 0.599195 | ||||||||
\(92\) | 225.624 | 2.45244 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 150.293i | 1.59887i | ||||||||
\(95\) | − 124.468i | − 1.31019i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −69.2168 | −0.713575 | −0.356788 | − | 0.934186i | \(-0.616128\pi\) | ||||
−0.356788 | + | 0.934186i | \(0.616128\pi\) | |||||||
\(98\) | 24.8128i | 0.253191i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 84.9293 | 0.849293 | ||||||||
\(101\) | − 137.148i | − 1.35790i | −0.734186 | − | 0.678948i | \(-0.762436\pi\) | ||||
0.734186 | − | 0.678948i | \(-0.237564\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 20.5216 | 0.199239 | 0.0996193 | − | 0.995026i | \(-0.468238\pi\) | ||||
0.0996193 | + | 0.995026i | \(0.468238\pi\) | |||||||
\(104\) | 195.931 | 1.88395 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 141.447i | 1.33440i | ||||||||
\(107\) | 59.3985i | 0.555127i | 0.960707 | + | 0.277563i | \(0.0895268\pi\) | ||||
−0.960707 | + | 0.277563i | \(0.910473\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 37.5085i | 0.344115i | 0.985087 | + | 0.172058i | \(0.0550415\pi\) | ||||
−0.985087 | + | 0.172058i | \(0.944958\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 444.049i | 3.96472i | ||||||||
\(113\) | −117.154 | −1.03676 | −0.518380 | − | 0.855151i | \(-0.673465\pi\) | ||||
−0.518380 | + | 0.855151i | \(0.673465\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −85.7184 | −0.745377 | ||||||||
\(116\) | 187.739i | 1.61844i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 270.242i | 2.29018i | ||||||||
\(119\) | −26.6450 | −0.223907 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 87.8925 | 0.720430 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −172.331 | −1.38977 | ||||||||
\(125\) | −136.026 | −1.08821 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 30.4604i | − 0.239846i | −0.992783 | − | 0.119923i | \(-0.961735\pi\) | ||||
0.992783 | − | 0.119923i | \(-0.0382648\pi\) | |||||||
\(128\) | 426.641i | 3.33313i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −117.437 | −0.903361 | ||||||||
\(131\) | 179.208i | 1.36800i | 0.729482 | + | 0.684000i | \(0.239761\pi\) | ||||
−0.729482 | + | 0.684000i | \(0.760239\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 223.261 | 1.67865 | ||||||||
\(134\) | 243.647i | 1.81826i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −95.7435 | −0.703996 | ||||||||
\(137\) | −192.096 | −1.40216 | −0.701080 | − | 0.713082i | \(-0.747299\pi\) | ||||
−0.701080 | + | 0.713082i | \(0.747299\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 24.5728i | 0.176783i | 0.996086 | + | 0.0883914i | \(0.0281726\pi\) | ||||
−0.996086 | + | 0.0883914i | \(0.971827\pi\) | |||||||
\(140\) | − 337.548i | − 2.41106i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 122.052i | − 0.859520i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 71.3253i | − 0.491899i | ||||||||
\(146\) | −399.411 | −2.73569 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 352.582 | 2.38231 | ||||||||
\(149\) | − 28.8346i | − 0.193521i | −0.995308 | − | 0.0967603i | \(-0.969152\pi\) | ||||
0.995308 | − | 0.0967603i | \(-0.0308480\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 140.463i | − 0.930218i | −0.885254 | − | 0.465109i | \(-0.846015\pi\) | ||||
0.885254 | − | 0.465109i | \(-0.153985\pi\) | |||||||
\(152\) | 802.244 | 5.27792 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 65.4714 | 0.422396 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 264.782 | 1.68651 | 0.843255 | − | 0.537514i | \(-0.180636\pi\) | ||||
0.843255 | + | 0.537514i | \(0.180636\pi\) | |||||||
\(158\) | −70.5559 | −0.446556 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 512.262i | − 3.20164i | ||||||||
\(161\) | − 153.755i | − 0.954999i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 64.2445 | 0.394138 | 0.197069 | − | 0.980390i | \(-0.436858\pi\) | ||||
0.197069 | + | 0.980390i | \(0.436858\pi\) | |||||||
\(164\) | 177.212i | 1.08056i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −459.687 | −2.76920 | ||||||||
\(167\) | 114.868i | 0.687830i | 0.939001 | + | 0.343915i | \(0.111753\pi\) | ||||
−0.939001 | + | 0.343915i | \(0.888247\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 115.355 | 0.682573 | ||||||||
\(170\) | 57.3866 | 0.337568 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 368.482i | 2.14234i | ||||||||
\(173\) | − 233.750i | − 1.35116i | −0.737288 | − | 0.675578i | \(-0.763894\pi\) | ||||
0.737288 | − | 0.675578i | \(-0.236106\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 57.8762i | − 0.330721i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 597.791i | − 3.35838i | ||||||||
\(179\) | −222.362 | −1.24225 | −0.621123 | − | 0.783713i | \(-0.713323\pi\) | ||||
−0.621123 | + | 0.783713i | \(0.713323\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 269.413 | 1.48847 | 0.744234 | − | 0.667920i | \(-0.232815\pi\) | ||||
0.744234 | + | 0.667920i | \(0.232815\pi\) | |||||||
\(182\) | − 210.649i | − 1.15741i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − 552.488i | − 3.00265i | ||||||||
\(185\) | −133.952 | −0.724064 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 425.003 | 2.26065 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −480.848 | −2.53078 | ||||||||
\(191\) | −244.952 | −1.28247 | −0.641236 | − | 0.767344i | \(-0.721578\pi\) | ||||
−0.641236 | + | 0.767344i | \(0.721578\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 263.453i | − 1.36504i | −0.730867 | − | 0.682520i | \(-0.760884\pi\) | ||||
0.730867 | − | 0.682520i | \(-0.239116\pi\) | |||||||
\(194\) | 267.400i | 1.37835i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 70.1660 | 0.357990 | ||||||||
\(197\) | 256.209i | 1.30055i | 0.759697 | + | 0.650277i | \(0.225347\pi\) | ||||
−0.759697 | + | 0.650277i | \(0.774653\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.63062 | −0.0383448 | −0.0191724 | − | 0.999816i | \(-0.506103\pi\) | ||||
−0.0191724 | + | 0.999816i | \(0.506103\pi\) | |||||||
\(200\) | − 207.967i | − 1.03983i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −529.832 | −2.62293 | ||||||||
\(203\) | 127.938 | 0.630235 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 67.3259i | − 0.328419i | ||||||||
\(206\) | − 79.2794i | − 0.384852i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 436.869i | − 2.10033i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 375.591i | 1.78005i | 0.455911 | + | 0.890025i | \(0.349313\pi\) | ||||
−0.455911 | + | 0.890025i | \(0.650687\pi\) | |||||||
\(212\) | 399.986 | 1.88673 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 229.470 | 1.07229 | ||||||||
\(215\) | − 139.992i | − 0.651127i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 117.437i | 0.541186i | ||||||||
\(218\) | 144.904 | 0.664697 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.2142 | 0.118616 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.1852 | −0.126391 | −0.0631955 | − | 0.998001i | \(-0.520129\pi\) | ||||
−0.0631955 | + | 0.998001i | \(0.520129\pi\) | |||||||
\(224\) | 918.855 | 4.10203 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 452.591i | 2.00262i | ||||||||
\(227\) | − 272.560i | − 1.20071i | −0.799735 | − | 0.600353i | \(-0.795027\pi\) | ||||
0.799735 | − | 0.600353i | \(-0.204973\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.590239 | 0.00257746 | 0.00128873 | − | 0.999999i | \(-0.499590\pi\) | ||||
0.00128873 | + | 0.999999i | \(0.499590\pi\) | |||||||
\(230\) | 331.149i | 1.43978i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 459.719 | 1.98155 | ||||||||
\(233\) | 185.559i | 0.796391i | 0.917301 | + | 0.398196i | \(0.130363\pi\) | ||||
−0.917301 | + | 0.398196i | \(0.869637\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −161.465 | −0.687087 | ||||||||
\(236\) | 764.194 | 3.23811 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 102.935i | 0.432502i | ||||||||
\(239\) | 269.209i | 1.12640i | 0.826322 | + | 0.563198i | \(0.190429\pi\) | ||||
−0.826322 | + | 0.563198i | \(0.809571\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 249.403i | − 1.03487i | −0.855723 | − | 0.517434i | \(-0.826887\pi\) | ||||
0.855723 | − | 0.517434i | \(-0.173113\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 248.544i | − 1.01862i | ||||||||
\(245\) | −26.6572 | −0.108805 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −219.651 | −0.889276 | ||||||||
\(248\) | 421.988i | 1.70156i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 525.499i | 2.10199i | ||||||||
\(251\) | −321.026 | −1.27899 | −0.639493 | − | 0.768797i | \(-0.720856\pi\) | ||||
−0.639493 | + | 0.768797i | \(0.720856\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −117.675 | −0.463289 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 695.285 | 2.71596 | ||||||||
\(257\) | 11.5105 | 0.0447878 | 0.0223939 | − | 0.999749i | \(-0.492871\pi\) | ||||
0.0223939 | + | 0.999749i | \(0.492871\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 240.272i | − 0.927692i | ||||||||
\(260\) | 332.090i | 1.27727i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 692.321 | 2.64245 | ||||||||
\(263\) | 184.999i | 0.703417i | 0.936110 | + | 0.351708i | \(0.114399\pi\) | ||||
−0.936110 | + | 0.351708i | \(0.885601\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −151.961 | −0.573439 | ||||||||
\(266\) | − 862.507i | − 3.24251i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 688.989 | 2.57085 | ||||||||
\(269\) | −242.153 | −0.900198 | −0.450099 | − | 0.892979i | \(-0.648611\pi\) | ||||
−0.450099 | + | 0.892979i | \(0.648611\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 243.989i | − 0.900329i | −0.892946 | − | 0.450164i | \(-0.851365\pi\) | ||||
0.892946 | − | 0.450164i | \(-0.148635\pi\) | |||||||
\(272\) | 213.480i | 0.784853i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 742.110i | 2.70843i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 144.134i | 0.520340i | 0.965563 | + | 0.260170i | \(0.0837785\pi\) | ||||
−0.965563 | + | 0.260170i | \(0.916221\pi\) | |||||||
\(278\) | 94.9303 | 0.341476 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −826.556 | −2.95198 | ||||||||
\(281\) | 359.273i | 1.27855i | 0.768977 | + | 0.639277i | \(0.220766\pi\) | ||||
−0.768977 | + | 0.639277i | \(0.779234\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 443.556i | − 1.56734i | −0.621180 | − | 0.783668i | \(-0.713346\pi\) | ||||
0.621180 | − | 0.783668i | \(-0.286654\pi\) | |||||||
\(284\) | −345.141 | −1.21528 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 120.764 | 0.420780 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 276.190 | 0.955675 | ||||||||
\(290\) | −275.546 | −0.950157 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1129.46i | 3.86802i | ||||||||
\(293\) | − 514.650i | − 1.75648i | −0.478217 | − | 0.878242i | \(-0.658717\pi\) | ||||
0.478217 | − | 0.878242i | \(-0.341283\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −290.330 | −0.984170 | ||||||||
\(296\) | − 863.371i | − 2.91679i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −111.394 | −0.373807 | ||||||||
\(299\) | 151.269i | 0.505916i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 251.107 | 0.834242 | ||||||||
\(302\) | −542.639 | −1.79682 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 1788.77i | − 5.88411i | ||||||||
\(305\) | 94.4260i | 0.309593i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 145.625i | 0.474349i | 0.971467 | + | 0.237175i | \(0.0762214\pi\) | ||||
−0.971467 | + | 0.237175i | \(0.923779\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 252.931i | − 0.815906i | ||||||||
\(311\) | −396.344 | −1.27442 | −0.637208 | − | 0.770692i | \(-0.719911\pi\) | ||||
−0.637208 | + | 0.770692i | \(0.719911\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −300.680 | −0.960638 | −0.480319 | − | 0.877094i | \(-0.659479\pi\) | ||||
−0.480319 | + | 0.877094i | \(0.659479\pi\) | |||||||
\(314\) | − 1022.91i | − 3.25768i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 199.519i | 0.631390i | ||||||||
\(317\) | 270.066 | 0.851943 | 0.425972 | − | 0.904737i | \(-0.359932\pi\) | ||||
0.425972 | + | 0.904737i | \(0.359932\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −988.754 | −3.08986 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −593.989 | −1.84469 | ||||||||
\(323\) | 107.334 | 0.332305 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 56.9405i | 0.175201i | ||||||||
\(326\) | − 248.191i | − 0.761321i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 433.941 | 1.32299 | ||||||||
\(329\) | − 289.624i | − 0.880316i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 172.536 | 0.521257 | 0.260629 | − | 0.965439i | \(-0.416070\pi\) | ||||
0.260629 | + | 0.965439i | \(0.416070\pi\) | |||||||
\(332\) | 1299.91i | 3.91540i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 443.760 | 1.32862 | ||||||||
\(335\) | −261.758 | −0.781368 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 276.335i | 0.819986i | 0.912089 | + | 0.409993i | \(0.134469\pi\) | ||||
−0.912089 | + | 0.409993i | \(0.865531\pi\) | |||||||
\(338\) | − 445.642i | − 1.31847i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − 162.279i | − 0.477291i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 316.972i | 0.924117i | ||||||||
\(344\) | 902.303 | 2.62298 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −903.029 | −2.60991 | ||||||||
\(347\) | − 144.475i | − 0.416354i | −0.978091 | − | 0.208177i | \(-0.933247\pi\) | ||||
0.978091 | − | 0.208177i | \(-0.0667530\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 147.891i | − 0.423755i | −0.977296 | − | 0.211878i | \(-0.932042\pi\) | ||||
0.977296 | − | 0.211878i | \(-0.0679578\pi\) | |||||||
\(350\) | −223.589 | −0.638825 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.8683 | 0.0704485 | 0.0352243 | − | 0.999379i | \(-0.488785\pi\) | ||||
0.0352243 | + | 0.999379i | \(0.488785\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 131.125 | 0.369365 | ||||||||
\(356\) | −1690.45 | −4.74844 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 859.034i | 2.39954i | ||||||||
\(359\) | 233.674i | 0.650902i | 0.945559 | + | 0.325451i | \(0.105516\pi\) | ||||
−0.945559 | + | 0.325451i | \(0.894484\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −538.366 | −1.49132 | ||||||||
\(362\) | − 1040.80i | − 2.87514i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −595.677 | −1.63648 | ||||||||
\(365\) | − 429.102i | − 1.17562i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −548.153 | −1.49361 | −0.746803 | − | 0.665046i | \(-0.768412\pi\) | ||||
−0.746803 | + | 0.665046i | \(0.768412\pi\) | |||||||
\(368\) | −1231.89 | −3.34752 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 517.486i | 1.39861i | ||||||||
\(371\) | − 272.576i | − 0.734706i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 84.3957i | 0.226262i | 0.993580 | + | 0.113131i | \(0.0360879\pi\) | ||||
−0.993580 | + | 0.113131i | \(0.963912\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 1040.71i | − 2.76784i | ||||||||
\(377\) | −125.869 | −0.333870 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 134.386 | 0.354580 | 0.177290 | − | 0.984159i | \(-0.443267\pi\) | ||||
0.177290 | + | 0.984159i | \(0.443267\pi\) | |||||||
\(380\) | 1359.75i | 3.57829i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 946.305i | 2.47724i | ||||||||
\(383\) | −413.818 | −1.08046 | −0.540232 | − | 0.841516i | \(-0.681664\pi\) | ||||
−0.540232 | + | 0.841516i | \(0.681664\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1017.78 | −2.63673 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 756.159 | 1.94886 | ||||||||
\(389\) | −214.844 | −0.552297 | −0.276148 | − | 0.961115i | \(-0.589058\pi\) | ||||
−0.276148 | + | 0.961115i | \(0.589058\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 73.9189i | − 0.189051i | ||||||||
\(392\) | − 171.816i | − 0.438306i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 989.793 | 2.51216 | ||||||||
\(395\) | − 75.8007i | − 0.191900i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 633.921 | 1.59678 | 0.798389 | − | 0.602142i | \(-0.205686\pi\) | ||||
0.798389 | + | 0.602142i | \(0.205686\pi\) | |||||||
\(398\) | 29.4788i | 0.0740673i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −463.705 | −1.15926 | ||||||||
\(401\) | 316.692 | 0.789756 | 0.394878 | − | 0.918733i | \(-0.370787\pi\) | ||||
0.394878 | + | 0.918733i | \(0.370787\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 115.539i | − 0.286696i | ||||||||
\(404\) | 1498.27i | 3.70858i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − 494.252i | − 1.21737i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 378.419i | − 0.925231i | −0.886559 | − | 0.462615i | \(-0.846911\pi\) | ||||
0.886559 | − | 0.462615i | \(-0.153089\pi\) | |||||||
\(410\) | −260.095 | −0.634378 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −224.188 | −0.544145 | ||||||||
\(413\) | − 520.771i | − 1.26095i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 493.858i | − 1.19002i | ||||||||
\(416\) | −903.998 | −2.17307 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 187.826 | 0.448273 | 0.224137 | − | 0.974558i | \(-0.428044\pi\) | ||||
0.224137 | + | 0.974558i | \(0.428044\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −153.479 | −0.364558 | −0.182279 | − | 0.983247i | \(-0.558347\pi\) | ||||
−0.182279 | + | 0.983247i | \(0.558347\pi\) | |||||||
\(422\) | 1450.99 | 3.43837 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − 979.449i | − 2.31002i | ||||||||
\(425\) | − 27.8245i | − 0.0654693i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −169.374 | −0.396660 | ||||||||
\(428\) | − 648.899i | − 1.51612i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −540.822 | −1.25772 | ||||||||
\(431\) | − 198.527i | − 0.460619i | −0.973117 | − | 0.230310i | \(-0.926026\pi\) | ||||
0.973117 | − | 0.230310i | \(-0.0739739\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 82.6034 | 0.190770 | 0.0953849 | − | 0.995440i | \(-0.469592\pi\) | ||||
0.0953849 | + | 0.995440i | \(0.469592\pi\) | |||||||
\(434\) | 453.687 | 1.04536 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − 409.762i | − 0.939821i | ||||||||
\(437\) | 619.374i | 1.41733i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 231.295i | 0.526868i | 0.964677 | + | 0.263434i | \(0.0848550\pi\) | ||||
−0.964677 | + | 0.263434i | \(0.915145\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 101.271i | − 0.229120i | ||||||||
\(443\) | 602.563 | 1.36019 | 0.680094 | − | 0.733125i | \(-0.261939\pi\) | ||||
0.680094 | + | 0.733125i | \(0.261939\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 642.228 | 1.44321 | ||||||||
\(446\) | 108.886i | 0.244138i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 1773.55i | − 3.95881i | ||||||||
\(449\) | 266.735 | 0.594065 | 0.297032 | − | 0.954867i | \(-0.404003\pi\) | ||||
0.297032 | + | 0.954867i | \(0.404003\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1279.85 | 2.83152 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1052.96 | −2.31930 | ||||||||
\(455\) | 226.308 | 0.497379 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 816.782i | − 1.78727i | −0.448796 | − | 0.893634i | \(-0.648147\pi\) | ||||
0.448796 | − | 0.893634i | \(-0.351853\pi\) | |||||||
\(458\) | − 2.28023i | − 0.00497866i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 936.431 | 2.03572 | ||||||||
\(461\) | 193.244i | 0.419185i | 0.977789 | + | 0.209592i | \(0.0672137\pi\) | ||||
−0.977789 | + | 0.209592i | \(0.932786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −530.341 | −1.14545 | −0.572723 | − | 0.819749i | \(-0.694113\pi\) | ||||
−0.572723 | + | 0.819749i | \(0.694113\pi\) | |||||||
\(464\) | − 1025.04i | − 2.20913i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 716.857 | 1.53832 | ||||||||
\(467\) | −101.521 | −0.217390 | −0.108695 | − | 0.994075i | \(-0.534667\pi\) | ||||
−0.108695 | + | 0.994075i | \(0.534667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 469.521i | − 1.00111i | ||||||||
\(470\) | 623.777i | 1.32719i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 1871.29i | − 3.96459i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 233.144i | 0.490829i | ||||||||
\(476\) | 291.083 | 0.611519 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1040.01 | 2.17576 | ||||||||
\(479\) | 471.107i | 0.983522i | 0.870730 | + | 0.491761i | \(0.163647\pi\) | ||||
−0.870730 | + | 0.491761i | \(0.836353\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 236.387i | 0.491450i | ||||||||
\(482\) | −963.501 | −1.99896 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −287.277 | −0.592324 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 716.246 | 1.47073 | 0.735366 | − | 0.677670i | \(-0.237010\pi\) | ||||
0.735366 | + | 0.677670i | \(0.237010\pi\) | |||||||
\(488\) | −608.611 | −1.24715 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 102.983i | 0.210169i | ||||||||
\(491\) | 802.375i | 1.63417i | 0.576520 | + | 0.817083i | \(0.304410\pi\) | ||||
−0.576520 | + | 0.817083i | \(0.695590\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 61.5071 | 0.124761 | ||||||||
\(494\) | 848.561i | 1.71774i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 940.910 | 1.89700 | ||||||||
\(497\) | 235.201i | 0.473241i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 178.361 | 0.357437 | 0.178719 | − | 0.983900i | \(-0.442805\pi\) | ||||
0.178719 | + | 0.983900i | \(0.442805\pi\) | |||||||
\(500\) | 1486.02 | 2.97203 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1240.19i | 2.47051i | ||||||||
\(503\) | − 452.616i | − 0.899833i | −0.893071 | − | 0.449916i | \(-0.851454\pi\) | ||||
0.893071 | − | 0.449916i | \(-0.148546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 569.217i | − 1.12716i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 332.765i | 0.655049i | ||||||||
\(509\) | 908.282 | 1.78444 | 0.892222 | − | 0.451597i | \(-0.149146\pi\) | ||||
0.892222 | + | 0.451597i | \(0.149146\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 769.688 | 1.50624 | ||||||||
\(512\) | − 979.477i | − 1.91304i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 44.4675i | − 0.0865127i | ||||||||
\(515\) | 85.1727 | 0.165384 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −928.225 | −1.79194 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 813.192 | 1.56383 | ||||||||
\(521\) | 257.259 | 0.493779 | 0.246889 | − | 0.969044i | \(-0.420592\pi\) | ||||
0.246889 | + | 0.969044i | \(0.420592\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 212.744i | 0.406776i | 0.979098 | + | 0.203388i | \(0.0651953\pi\) | ||||
−0.979098 | + | 0.203388i | \(0.934805\pi\) | |||||||
\(524\) | − 1957.76i | − 3.73618i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 714.691 | 1.35873 | ||||||||
\(527\) | 56.4590i | 0.107133i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −102.451 | −0.193669 | ||||||||
\(530\) | 587.061i | 1.10766i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2439.01 | −4.58461 | ||||||||
\(533\) | −118.811 | −0.222910 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 246.528i | 0.460799i | ||||||||
\(536\) | − 1687.13i | − 3.14763i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 935.492i | 1.73883i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 59.5988i | − 0.110164i | −0.998482 | − | 0.0550821i | \(-0.982458\pi\) | ||||
0.998482 | − | 0.0550821i | \(-0.0175420\pi\) | |||||||
\(542\) | −942.585 | −1.73909 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 441.747 | 0.812035 | ||||||||
\(545\) | 155.675i | 0.285643i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 535.776i | 0.979481i | 0.871868 | + | 0.489740i | \(0.162908\pi\) | ||||
−0.871868 | + | 0.489740i | \(0.837092\pi\) | |||||||
\(548\) | 2098.55 | 3.82947 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −515.374 | −0.935343 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 135.965 | 0.245868 | ||||||||
\(554\) | 556.822 | 1.00509 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 268.446i | − 0.482816i | ||||||||
\(557\) | 431.831i | 0.775281i | 0.921811 | + | 0.387640i | \(0.126710\pi\) | ||||
−0.921811 | + | 0.387640i | \(0.873290\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −247.047 | −0.441945 | ||||||||
\(560\) | 1842.98i | 3.29103i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1387.95 | 2.46967 | ||||||||
\(563\) | 155.811i | 0.276751i | 0.990380 | + | 0.138376i | \(0.0441882\pi\) | ||||
−0.990380 | + | 0.138376i | \(0.955812\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −486.235 | −0.860593 | ||||||||
\(566\) | −1713.56 | −3.02749 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 845.148i | 1.48794i | ||||||||
\(569\) | − 622.591i | − 1.09419i | −0.837072 | − | 0.547093i | \(-0.815735\pi\) | ||||
0.837072 | − | 0.547093i | \(-0.184265\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 327.913i | − 0.574279i | −0.957889 | − | 0.287139i | \(-0.907296\pi\) | ||||
0.957889 | − | 0.287139i | \(-0.0927043\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − 466.537i | − 0.812783i | ||||||||
\(575\) | 160.561 | 0.279237 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −731.904 | −1.26846 | −0.634232 | − | 0.773143i | \(-0.718684\pi\) | ||||
−0.634232 | + | 0.773143i | \(0.718684\pi\) | |||||||
\(578\) | − 1066.98i | − 1.84599i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 779.193i | 1.34344i | ||||||||
\(581\) | 885.843 | 1.52469 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2765.72 | 4.73583 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1988.21 | −3.39284 | ||||||||
\(587\) | −109.316 | −0.186228 | −0.0931142 | − | 0.995655i | \(-0.529682\pi\) | ||||
−0.0931142 | + | 0.995655i | \(0.529682\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 473.075i | − 0.803184i | ||||||||
\(590\) | 1121.61i | 1.90103i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1925.06 | −3.25180 | ||||||||
\(593\) | − 903.281i | − 1.52324i | −0.648024 | − | 0.761620i | \(-0.724404\pi\) | ||||
0.648024 | − | 0.761620i | \(-0.275596\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −110.587 | −0.185861 | ||||||||
\(596\) | 315.003i | 0.528529i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 584.385 | 0.977233 | ||||||||
\(599\) | 779.269 | 1.30095 | 0.650475 | − | 0.759528i | \(-0.274570\pi\) | ||||
0.650475 | + | 0.759528i | \(0.274570\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 564.553i | − 0.939356i | −0.882838 | − | 0.469678i | \(-0.844370\pi\) | ||||
0.882838 | − | 0.469678i | \(-0.155630\pi\) | |||||||
\(602\) | − 970.082i | − 1.61143i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1534.49i | 2.54054i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 134.510i | − 0.221597i | −0.993843 | − | 0.110799i | \(-0.964659\pi\) | ||||
0.993843 | − | 0.110799i | \(-0.0353409\pi\) | |||||||
\(608\) | −3701.44 | −6.08790 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 364.789 | 0.598014 | ||||||||
\(611\) | 284.941i | 0.466352i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 540.234i | − 0.881295i | −0.897680 | − | 0.440648i | \(-0.854749\pi\) | ||||
0.897680 | − | 0.440648i | \(-0.145251\pi\) | |||||||
\(614\) | 562.583 | 0.916259 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −684.941 | −1.11011 | −0.555057 | − | 0.831812i | \(-0.687304\pi\) | ||||
−0.555057 | + | 0.831812i | \(0.687304\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1089.66 | 1.76035 | 0.880177 | − | 0.474646i | \(-0.157424\pi\) | ||||
0.880177 | + | 0.474646i | \(0.157424\pi\) | |||||||
\(620\) | −715.242 | −1.15362 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1531.16i | 2.46168i | ||||||||
\(623\) | 1151.98i | 1.84908i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −370.207 | −0.592331 | ||||||||
\(626\) | 1161.59i | 1.85558i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2892.61 | −4.60607 | ||||||||
\(629\) | − 115.513i | − 0.183645i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 858.142 | 1.35997 | 0.679986 | − | 0.733225i | \(-0.261986\pi\) | ||||
0.679986 | + | 0.733225i | \(0.261986\pi\) | |||||||
\(632\) | 488.564 | 0.773044 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − 1043.33i | − 1.64562i | ||||||||
\(635\) | − 126.423i | − 0.199091i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 47.0425i | 0.0738501i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1770.73i | 2.76677i | ||||||||
\(641\) | −703.848 | −1.09805 | −0.549024 | − | 0.835807i | \(-0.685000\pi\) | ||||
−0.549024 | + | 0.835807i | \(0.685000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −484.714 | −0.753833 | −0.376916 | − | 0.926247i | \(-0.623016\pi\) | ||||
−0.376916 | + | 0.926247i | \(0.623016\pi\) | |||||||
\(644\) | 1679.69i | 2.60822i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − 414.657i | − 0.641884i | ||||||||
\(647\) | 762.533 | 1.17857 | 0.589283 | − | 0.807926i | \(-0.299410\pi\) | ||||
0.589283 | + | 0.807926i | \(0.299410\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 219.974 | 0.338421 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −701.839 | −1.07644 | ||||||||
\(653\) | 297.917 | 0.456229 | 0.228114 | − | 0.973634i | \(-0.426744\pi\) | ||||
0.228114 | + | 0.973634i | \(0.426744\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 743.784i | 1.13555i | ||||||||
\(656\) | − 967.561i | − 1.47494i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1118.88 | −1.70043 | ||||||||
\(659\) | − 622.572i | − 0.944722i | −0.881405 | − | 0.472361i | \(-0.843402\pi\) | ||||
0.881405 | − | 0.472361i | \(-0.156598\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1201.96 | 1.81840 | 0.909199 | − | 0.416361i | \(-0.136695\pi\) | ||||
0.909199 | + | 0.416361i | \(0.136695\pi\) | |||||||
\(662\) | − 666.546i | − 1.00687i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3183.10 | 4.79383 | ||||||||
\(665\) | 926.621 | 1.39342 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 354.927i | 0.532124i | ||||||||
\(668\) | − 1254.87i | − 1.87855i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1011.23i | 1.50930i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 293.533i | 0.436156i | 0.975931 | + | 0.218078i | \(0.0699788\pi\) | ||||
−0.975931 | + | 0.218078i | \(0.930021\pi\) | |||||||
\(674\) | 1067.55 | 1.58390 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1260.19 | −1.86419 | ||||||||
\(677\) | − 171.767i | − 0.253718i | −0.991921 | − | 0.126859i | \(-0.959510\pi\) | ||||
0.991921 | − | 0.126859i | \(-0.0404896\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 515.295i | − 0.758903i | ||||||||
\(680\) | −397.373 | −0.584373 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 371.395 | 0.543770 | 0.271885 | − | 0.962330i | \(-0.412353\pi\) | ||||
0.271885 | + | 0.962330i | \(0.412353\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −797.275 | −1.16390 | ||||||||
\(686\) | 1224.53 | 1.78504 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 2011.87i | − 2.92423i | ||||||||
\(689\) | 268.169i | 0.389215i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 473.877 | 0.685785 | 0.342892 | − | 0.939375i | \(-0.388593\pi\) | ||||
0.342892 | + | 0.939375i | \(0.388593\pi\) | |||||||
\(692\) | 2553.60i | 3.69018i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −558.138 | −0.804234 | ||||||||
\(695\) | 101.987i | 0.146744i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 58.0582 | 0.0832972 | ||||||||
\(698\) | −571.334 | −0.818531 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 632.269i | 0.903241i | ||||||||
\(701\) | 528.656i | 0.754145i | 0.926184 | + | 0.377073i | \(0.123069\pi\) | ||||
−0.926184 | + | 0.377073i | \(0.876931\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 967.893i | 1.37680i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 96.0719i | − 0.136079i | ||||||||
\(707\) | 1021.02 | 1.44415 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1077.52 | −1.51978 | −0.759888 | − | 0.650054i | \(-0.774746\pi\) | ||||
−0.759888 | + | 0.650054i | \(0.774746\pi\) | |||||||
\(710\) | − 506.564i | − 0.713470i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4139.41i | 5.81377i | ||||||||
\(713\) | −325.797 | −0.456938 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2429.19 | 3.39273 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 902.734 | 1.25729 | ||||||||
\(719\) | 1230.24 | 1.71104 | 0.855522 | − | 0.517766i | \(-0.173236\pi\) | ||||
0.855522 | + | 0.517766i | \(0.173236\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 152.776i | 0.211895i | ||||||||
\(722\) | 2079.83i | 2.88065i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2943.20 | −4.06519 | ||||||||
\(725\) | 133.601i | 0.184277i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −389.945 | −0.536376 | −0.268188 | − | 0.963367i | \(-0.586425\pi\) | ||||
−0.268188 | + | 0.963367i | \(0.586425\pi\) | |||||||
\(728\) | 1458.64i | 2.00362i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1657.72 | −2.27084 | ||||||||
\(731\) | 120.722 | 0.165146 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 187.861i | − 0.256290i | −0.991755 | − | 0.128145i | \(-0.959098\pi\) | ||||
0.991755 | − | 0.128145i | \(-0.0409024\pi\) | |||||||
\(734\) | 2117.64i | 2.88507i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2549.10i | 3.46345i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 735.434i | 0.995175i | 0.867414 | + | 0.497588i | \(0.165781\pi\) | ||||
−0.867414 | + | 0.497588i | \(0.834219\pi\) | |||||||
\(740\) | 1463.36 | 1.97751 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1053.02 | −1.41917 | ||||||||
\(743\) | 335.749i | 0.451884i | 0.974141 | + | 0.225942i | \(0.0725459\pi\) | ||||
−0.974141 | + | 0.225942i | \(0.927454\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 119.675i | − 0.160637i | ||||||||
\(746\) | 326.039 | 0.437050 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −442.201 | −0.590389 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 373.497 | 0.497333 | 0.248666 | − | 0.968589i | \(-0.420008\pi\) | ||||
0.248666 | + | 0.968589i | \(0.420008\pi\) | |||||||
\(752\) | −2320.47 | −3.08573 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 486.260i | 0.644908i | ||||||||
\(755\) | − 582.977i | − 0.772155i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1248.69 | 1.64952 | 0.824762 | − | 0.565480i | \(-0.191309\pi\) | ||||
0.824762 | + | 0.565480i | \(0.191309\pi\) | |||||||
\(758\) | − 519.163i | − 0.684912i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3329.63 | 4.38109 | ||||||||
\(761\) | − 274.084i | − 0.360162i | −0.983652 | − | 0.180081i | \(-0.942364\pi\) | ||||
0.983652 | − | 0.180081i | \(-0.0576360\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −279.238 | −0.365974 | ||||||||
\(764\) | 2675.98 | 3.50259 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1598.67i | 2.08704i | ||||||||
\(767\) | 512.351i | 0.667993i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 1313.03i | − 1.70745i | −0.520722 | − | 0.853726i | \(-0.674337\pi\) | ||||
0.520722 | − | 0.853726i | \(-0.325663\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2878.09i | 3.72809i | ||||||||
\(773\) | 573.729 | 0.742211 | 0.371105 | − | 0.928591i | \(-0.378979\pi\) | ||||
0.371105 | + | 0.928591i | \(0.378979\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −122.636 | −0.158240 | ||||||||
\(776\) | − 1851.61i | − 2.38610i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 829.989i | 1.06682i | ||||||||
\(779\) | −486.475 | −0.624487 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −285.565 | −0.365173 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −383.099 | −0.488647 | ||||||||
\(785\) | 1098.95 | 1.39994 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 274.155i | − 0.348354i | −0.984714 | − | 0.174177i | \(-0.944273\pi\) | ||||
0.984714 | − | 0.174177i | \(-0.0557266\pi\) | |||||||
\(788\) | − 2798.95i | − 3.55197i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −292.835 | −0.370677 | ||||||||
\(791\) | − 872.169i | − 1.10262i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 166.635 | 0.210133 | ||||||||
\(794\) | − 2448.98i | − 3.08436i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 83.3607 | 0.104724 | ||||||||
\(797\) | 343.282 | 0.430718 | 0.215359 | − | 0.976535i | \(-0.430908\pi\) | ||||
0.215359 | + | 0.976535i | \(0.430908\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 139.239i | − 0.174267i | ||||||||
\(800\) | 959.530i | 1.19941i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 1223.45i | − 1.52550i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 638.144i | − 0.792725i | ||||||||
\(806\) | −446.351 | −0.553786 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3668.82 | 4.54062 | ||||||||
\(809\) | 565.999i | 0.699628i | 0.936819 | + | 0.349814i | \(0.113755\pi\) | ||||
−0.936819 | + | 0.349814i | \(0.886245\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 15.6724i | − 0.0193248i | −0.999953 | − | 0.00966241i | \(-0.996924\pi\) | ||||
0.999953 | − | 0.00966241i | \(-0.00307569\pi\) | |||||||
\(812\) | −1397.65 | −1.72125 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 266.640 | 0.327166 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1011.54 | −1.23811 | ||||||||
\(818\) | −1461.92 | −1.78719 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 735.501i | 0.896953i | ||||||||
\(821\) | 1400.47i | 1.70581i | 0.522067 | + | 0.852904i | \(0.325161\pi\) | ||||
−0.522067 | + | 0.852904i | \(0.674839\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 593.743 | 0.721437 | 0.360719 | − | 0.932675i | \(-0.382531\pi\) | ||||
0.360719 | + | 0.932675i | \(0.382531\pi\) | |||||||
\(824\) | 548.970i | 0.666226i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2011.85 | −2.43566 | ||||||||
\(827\) | − 544.028i | − 0.657833i | −0.944359 | − | 0.328916i | \(-0.893317\pi\) | ||||
0.944359 | − | 0.328916i | \(-0.106683\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 586.695 | 0.707714 | 0.353857 | − | 0.935300i | \(-0.384870\pi\) | ||||
0.353857 | + | 0.935300i | \(0.384870\pi\) | |||||||
\(830\) | −1907.88 | −2.29866 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1744.87i | 2.09720i | ||||||||
\(833\) | − 22.9877i | − 0.0275963i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 476.747i | 0.570954i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 725.615i | − 0.865889i | ||||||||
\(839\) | −661.038 | −0.787888 | −0.393944 | − | 0.919134i | \(-0.628890\pi\) | ||||
−0.393944 | + | 0.919134i | \(0.628890\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 545.670 | 0.648834 | ||||||||
\(842\) | 592.923i | 0.704184i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − 4103.14i | − 4.86154i | ||||||||
\(845\) | 478.769 | 0.566590 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2183.88 | −2.57534 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −107.492 | −0.126461 | ||||||||
\(851\) | 666.567 | 0.783275 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 473.383i | − 0.554962i | −0.960731 | − | 0.277481i | \(-0.910500\pi\) | ||||
0.960731 | − | 0.277481i | \(-0.0894996\pi\) | |||||||
\(854\) | 654.329i | 0.766193i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1588.96 | −1.85627 | ||||||||
\(857\) | − 461.983i | − 0.539070i | −0.962991 | − | 0.269535i | \(-0.913130\pi\) | ||||
0.962991 | − | 0.269535i | \(-0.0868701\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −787.819 | −0.917135 | −0.458567 | − | 0.888660i | \(-0.651637\pi\) | ||||
−0.458567 | + | 0.888660i | \(0.651637\pi\) | |||||||
\(860\) | 1529.35i | 1.77831i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −766.954 | −0.889738 | ||||||||
\(863\) | −864.133 | −1.00131 | −0.500657 | − | 0.865646i | \(-0.666908\pi\) | ||||
−0.500657 | + | 0.865646i | \(0.666908\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 970.156i | − 1.12157i | ||||||||
\(866\) | − 319.115i | − 0.368493i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 1282.94i | − 1.47805i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 461.930i | 0.530344i | ||||||||
\(872\) | −1003.39 | −1.15067 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2392.78 | 2.73773 | ||||||||
\(875\) | − 1012.67i | − 1.15733i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 75.2272i | − 0.0857779i | −0.999080 | − | 0.0428889i | \(-0.986344\pi\) | ||||
0.999080 | − | 0.0428889i | \(-0.0136562\pi\) | |||||||
\(878\) | 893.544 | 1.01770 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 405.703 | 0.460503 | 0.230252 | − | 0.973131i | \(-0.426045\pi\) | ||||
0.230252 | + | 0.973131i | \(0.426045\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −136.243 | −0.154296 | −0.0771480 | − | 0.997020i | \(-0.524581\pi\) | ||||
−0.0771480 | + | 0.997020i | \(0.524581\pi\) | |||||||
\(884\) | −286.377 | −0.323955 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − 2327.84i | − 2.62735i | ||||||||
\(887\) | − 71.2823i | − 0.0803634i | −0.999192 | − | 0.0401817i | \(-0.987206\pi\) | ||||
0.999192 | − | 0.0401817i | \(-0.0127937\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 226.767 | 0.255081 | ||||||||
\(890\) | − 2481.07i | − 2.78772i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 307.909 | 0.345189 | ||||||||
\(893\) | 1166.70i | 1.30649i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −922.891 | −1.03116 | ||||||||
\(896\) | −3176.19 | −3.54486 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 1030.46i | − 1.14750i | ||||||||
\(899\) | − 271.092i | − 0.301548i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 131.043i | − 0.145442i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − 3133.97i | − 3.46678i | ||||||||
\(905\) | 1118.17 | 1.23555 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 597.914 | 0.659221 | 0.329611 | − | 0.944117i | \(-0.393083\pi\) | ||||
0.329611 | + | 0.944117i | \(0.393083\pi\) | |||||||
\(908\) | 2977.58i | 3.27928i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | − 874.277i | − 0.960744i | ||||||||
\(911\) | 1753.01 | 1.92427 | 0.962136 | − | 0.272571i | \(-0.0878740\pi\) | ||||
0.962136 | + | 0.272571i | \(0.0878740\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −3155.41 | −3.45231 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.44806 | −0.00703937 | ||||||||
\(917\) | −1334.14 | −1.45490 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 556.541i | − 0.605595i | −0.953055 | − | 0.302797i | \(-0.902079\pi\) | ||||
0.953055 | − | 0.302797i | \(-0.0979205\pi\) | |||||||
\(920\) | − 2293.04i | − 2.49244i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 746.545 | 0.809702 | ||||||||
\(923\) | − 231.398i | − 0.250702i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 250.908 | 0.271252 | ||||||||
\(926\) | 2048.83i | 2.21256i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2121.08 | −2.28564 | ||||||||
\(929\) | −703.792 | −0.757580 | −0.378790 | − | 0.925483i | \(-0.623660\pi\) | ||||
−0.378790 | + | 0.925483i | \(0.623660\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 192.617i | 0.206892i | ||||||||
\(932\) | − 2027.14i | − 2.17504i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 392.199i | 0.419913i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 407.451i | − 0.434846i | −0.976077 | − | 0.217423i | \(-0.930235\pi\) | ||||
0.976077 | − | 0.217423i | \(-0.0697651\pi\) | |||||||
\(938\) | −1813.86 | −1.93376 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1763.93 | 1.87652 | ||||||||
\(941\) | 467.484i | 0.496795i | 0.968658 | + | 0.248398i | \(0.0799040\pi\) | ||||
−0.968658 | + | 0.248398i | \(0.920096\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 335.025i | 0.355275i | ||||||||
\(944\) | −4172.42 | −4.41994 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1795.45 | −1.89594 | −0.947969 | − | 0.318363i | \(-0.896867\pi\) | ||||
−0.947969 | + | 0.318363i | \(0.896867\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −757.243 | −0.797938 | ||||||||
\(950\) | 900.687 | 0.948092 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 712.777i | − 0.748715i | ||||||||
\(953\) | 456.624i | 0.479144i | 0.970879 | + | 0.239572i | \(0.0770071\pi\) | ||||
−0.970879 | + | 0.239572i | \(0.922993\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1016.65 | −1.06455 | ||||||||
\(956\) | − 2940.97i | − 3.07633i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1819.99 | 1.89978 | ||||||||
\(959\) | − 1430.09i | − 1.49123i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −712.158 | −0.741059 | ||||||||
\(962\) | 913.217 | 0.949290 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2724.61i | 2.82636i | ||||||||
\(965\) | − 1093.43i | − 1.13309i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 42.6322i | − 0.0440871i | −0.999757 | − | 0.0220436i | \(-0.992983\pi\) | ||||
0.999757 | − | 0.0220436i | \(-0.00701725\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1109.82i | 1.14414i | ||||||||
\(971\) | 570.592 | 0.587633 | 0.293816 | − | 0.955862i | \(-0.405075\pi\) | ||||
0.293816 | + | 0.955862i | \(0.405075\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −182.936 | −0.188012 | ||||||||
\(974\) | − 2767.02i | − 2.84088i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1357.03i | 1.39040i | ||||||||
\(977\) | −1604.15 | −1.64191 | −0.820956 | − | 0.570992i | \(-0.806559\pi\) | ||||
−0.820956 | + | 0.570992i | \(0.806559\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 291.217 | 0.297160 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3099.76 | 3.15657 | ||||||||
\(983\) | −1274.76 | −1.29680 | −0.648401 | − | 0.761299i | \(-0.724562\pi\) | ||||
−0.648401 | + | 0.761299i | \(0.724562\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1063.37i | 1.07956i | ||||||||
\(986\) | − 237.616i | − 0.240989i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2399.58 | 2.42872 | ||||||||
\(989\) | 696.625i | 0.704373i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1336.90 | −1.34904 | −0.674519 | − | 0.738258i | \(-0.735649\pi\) | ||||
−0.674519 | + | 0.738258i | \(0.735649\pi\) | |||||||
\(992\) | − 1946.99i | − 1.96270i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 908.634 | 0.914118 | ||||||||
\(995\) | −31.6701 | −0.0318292 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1800.83i | 1.80625i | 0.429383 | + | 0.903123i | \(0.358731\pi\) | ||||
−0.429383 | + | 0.903123i | \(0.641269\pi\) | |||||||
\(998\) | − 689.049i | − 0.690430i | ||||||||
\(999\) | 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.c.l.604.2 | 16 | ||
3.2 | odd | 2 | inner | 1089.3.c.l.604.15 | 16 | ||
11.2 | odd | 10 | 99.3.k.b.73.4 | yes | 16 | ||
11.5 | even | 5 | 99.3.k.b.19.4 | yes | 16 | ||
11.10 | odd | 2 | inner | 1089.3.c.l.604.16 | 16 | ||
33.2 | even | 10 | 99.3.k.b.73.1 | yes | 16 | ||
33.5 | odd | 10 | 99.3.k.b.19.1 | ✓ | 16 | ||
33.32 | even | 2 | inner | 1089.3.c.l.604.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.3.k.b.19.1 | ✓ | 16 | 33.5 | odd | 10 | ||
99.3.k.b.19.4 | yes | 16 | 11.5 | even | 5 | ||
99.3.k.b.73.1 | yes | 16 | 33.2 | even | 10 | ||
99.3.k.b.73.4 | yes | 16 | 11.2 | odd | 10 | ||
1089.3.c.l.604.1 | 16 | 33.32 | even | 2 | inner | ||
1089.3.c.l.604.2 | 16 | 1.1 | even | 1 | trivial | ||
1089.3.c.l.604.15 | 16 | 3.2 | odd | 2 | inner | ||
1089.3.c.l.604.16 | 16 | 11.10 | odd | 2 | inner |