Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,4,Mod(649,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.6525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 270) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.649 |
Dual form | 1350.4.c.i.649.2 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.0000i | 1.18789i | 0.804506 | + | 0.593944i | \(0.202430\pi\) | ||||
−0.804506 | + | 0.593944i | \(0.797570\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.0000 | −0.328921 | −0.164461 | − | 0.986384i | \(-0.552588\pi\) | ||||
−0.164461 | + | 0.986384i | \(0.552588\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.0000i | 0.810716i | 0.914158 | + | 0.405358i | \(0.132853\pi\) | ||||
−0.914158 | + | 0.405358i | \(0.867147\pi\) | |||||||
\(14\) | 44.0000 | 0.839964 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 105.000i | 1.49801i | 0.662562 | + | 0.749007i | \(0.269469\pi\) | ||||
−0.662562 | + | 0.749007i | \(0.730531\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 157.000 | 1.89570 | 0.947849 | − | 0.318719i | \(-0.103253\pi\) | ||||
0.947849 | + | 0.318719i | \(0.103253\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 24.0000i | 0.232583i | ||||||||
\(23\) | − 117.000i | − 1.06070i | −0.847778 | − | 0.530352i | \(-0.822060\pi\) | ||||
0.847778 | − | 0.530352i | \(-0.177940\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 76.0000 | 0.573263 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 88.0000i | − 0.593944i | ||||||||
\(29\) | −66.0000 | −0.422617 | −0.211308 | − | 0.977419i | \(-0.567772\pi\) | ||||
−0.211308 | + | 0.977419i | \(0.567772\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −25.0000 | −0.144843 | −0.0724215 | − | 0.997374i | \(-0.523073\pi\) | ||||
−0.0724215 | + | 0.997374i | \(0.523073\pi\) | |||||||
\(32\) | − 32.0000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 210.000 | 1.05926 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 314.000i | − 1.39517i | −0.716502 | − | 0.697585i | \(-0.754258\pi\) | ||||
0.716502 | − | 0.697585i | \(-0.245742\pi\) | |||||||
\(38\) | − 314.000i | − 1.34046i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −504.000 | −1.91979 | −0.959897 | − | 0.280352i | \(-0.909549\pi\) | ||||
−0.959897 | + | 0.280352i | \(0.909549\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 380.000i | 1.34766i | 0.738886 | + | 0.673831i | \(0.235352\pi\) | ||||
−0.738886 | + | 0.673831i | \(0.764648\pi\) | |||||||
\(44\) | 48.0000 | 0.164461 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −234.000 | −0.750031 | ||||||||
\(47\) | 252.000i | 0.782085i | 0.920373 | + | 0.391042i | \(0.127885\pi\) | ||||
−0.920373 | + | 0.391042i | \(0.872115\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −141.000 | −0.411079 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 152.000i | − 0.405358i | ||||||||
\(53\) | 3.00000i | 0.00777513i | 0.999992 | + | 0.00388756i | \(0.00123745\pi\) | ||||
−0.999992 | + | 0.00388756i | \(0.998763\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −176.000 | −0.419982 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 132.000i | 0.298835i | ||||||||
\(59\) | 318.000 | 0.701696 | 0.350848 | − | 0.936432i | \(-0.385893\pi\) | ||||
0.350848 | + | 0.936432i | \(0.385893\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 293.000 | 0.614997 | 0.307498 | − | 0.951549i | \(-0.400508\pi\) | ||||
0.307498 | + | 0.951549i | \(0.400508\pi\) | |||||||
\(62\) | 50.0000i | 0.102419i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 322.000i | 0.587143i | 0.955937 | + | 0.293571i | \(0.0948438\pi\) | ||||
−0.955937 | + | 0.293571i | \(0.905156\pi\) | |||||||
\(68\) | − 420.000i | − 0.749007i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −120.000 | −0.200583 | −0.100291 | − | 0.994958i | \(-0.531978\pi\) | ||||
−0.100291 | + | 0.994958i | \(0.531978\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 44.0000i | 0.0705453i | 0.999378 | + | 0.0352727i | \(0.0112300\pi\) | ||||
−0.999378 | + | 0.0352727i | \(0.988770\pi\) | |||||||
\(74\) | −628.000 | −0.986534 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −628.000 | −0.947849 | ||||||||
\(77\) | − 264.000i | − 0.390722i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −917.000 | −1.30596 | −0.652978 | − | 0.757377i | \(-0.726481\pi\) | ||||
−0.652978 | + | 0.757377i | \(0.726481\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1008.00i | 1.35750i | ||||||||
\(83\) | 309.000i | 0.408640i | 0.978904 | + | 0.204320i | \(0.0654984\pi\) | ||||
−0.978904 | + | 0.204320i | \(0.934502\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 760.000 | 0.952941 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 96.0000i | − 0.116291i | ||||||||
\(89\) | −1272.00 | −1.51496 | −0.757482 | − | 0.652856i | \(-0.773570\pi\) | ||||
−0.757482 | + | 0.652856i | \(0.773570\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −836.000 | −0.963040 | ||||||||
\(92\) | 468.000i | 0.530352i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 504.000 | 0.553017 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1328.00i | − 1.39008i | −0.718970 | − | 0.695041i | \(-0.755386\pi\) | ||||
0.718970 | − | 0.695041i | \(-0.244614\pi\) | |||||||
\(98\) | 282.000i | 0.290677i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −492.000 | −0.484711 | −0.242356 | − | 0.970187i | \(-0.577920\pi\) | ||||
−0.242356 | + | 0.970187i | \(0.577920\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 548.000i | 0.524233i | 0.965036 | + | 0.262117i | \(0.0844205\pi\) | ||||
−0.965036 | + | 0.262117i | \(0.915579\pi\) | |||||||
\(104\) | −304.000 | −0.286631 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.00549784 | ||||||||
\(107\) | − 732.000i | − 0.661356i | −0.943744 | − | 0.330678i | \(-0.892723\pi\) | ||||
0.943744 | − | 0.330678i | \(-0.107277\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 907.000 | 0.797017 | 0.398508 | − | 0.917165i | \(-0.369528\pi\) | ||||
0.398508 | + | 0.917165i | \(0.369528\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 352.000i | 0.296972i | ||||||||
\(113\) | − 1542.00i | − 1.28371i | −0.766826 | − | 0.641855i | \(-0.778165\pi\) | ||||
0.766826 | − | 0.641855i | \(-0.221835\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 264.000 | 0.211308 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 636.000i | − 0.496174i | ||||||||
\(119\) | −2310.00 | −1.77947 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | − 586.000i | − 0.434868i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 100.000 | 0.0724215 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2554.00i | 1.78449i | 0.451547 | + | 0.892247i | \(0.350872\pi\) | ||||
−0.451547 | + | 0.892247i | \(0.649128\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −150.000 | −0.100042 | −0.0500212 | − | 0.998748i | \(-0.515929\pi\) | ||||
−0.0500212 | + | 0.998748i | \(0.515929\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3454.00i | 2.25188i | ||||||||
\(134\) | 644.000 | 0.415173 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −840.000 | −0.529628 | ||||||||
\(137\) | − 1653.00i | − 1.03084i | −0.856937 | − | 0.515421i | \(-0.827636\pi\) | ||||
0.856937 | − | 0.515421i | \(-0.172364\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1124.00 | −0.685874 | −0.342937 | − | 0.939358i | \(-0.611422\pi\) | ||||
−0.342937 | + | 0.939358i | \(0.611422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 240.000i | 0.141833i | ||||||||
\(143\) | − 456.000i | − 0.266662i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 88.0000 | 0.0498831 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1256.00i | 0.697585i | ||||||||
\(149\) | −1608.00 | −0.884111 | −0.442055 | − | 0.896988i | \(-0.645751\pi\) | ||||
−0.442055 | + | 0.896988i | \(0.645751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2488.00 | −1.34086 | −0.670432 | − | 0.741971i | \(-0.733891\pi\) | ||||
−0.670432 | + | 0.741971i | \(0.733891\pi\) | |||||||
\(152\) | 1256.00i | 0.670231i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −528.000 | −0.276282 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2968.00i | 1.50874i | 0.656449 | + | 0.754370i | \(0.272058\pi\) | ||||
−0.656449 | + | 0.754370i | \(0.727942\pi\) | |||||||
\(158\) | 1834.00i | 0.923451i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2574.00 | 1.26000 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3170.00i | 1.52327i | 0.648004 | + | 0.761637i | \(0.275604\pi\) | ||||
−0.648004 | + | 0.761637i | \(0.724396\pi\) | |||||||
\(164\) | 2016.00 | 0.959897 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 618.000 | 0.288952 | ||||||||
\(167\) | − 327.000i | − 0.151521i | −0.997126 | − | 0.0757605i | \(-0.975862\pi\) | ||||
0.997126 | − | 0.0757605i | \(-0.0241385\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 753.000 | 0.342740 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 1520.00i | − 0.673831i | ||||||||
\(173\) | 1305.00i | 0.573510i | 0.958004 | + | 0.286755i | \(0.0925766\pi\) | ||||
−0.958004 | + | 0.286755i | \(0.907423\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −192.000 | −0.0822304 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2544.00i | 1.07124i | ||||||||
\(179\) | 4044.00 | 1.68862 | 0.844309 | − | 0.535856i | \(-0.180011\pi\) | ||||
0.844309 | + | 0.535856i | \(0.180011\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1051.00 | −0.431603 | −0.215802 | − | 0.976437i | \(-0.569236\pi\) | ||||
−0.215802 | + | 0.976437i | \(0.569236\pi\) | |||||||
\(182\) | 1672.00i | 0.680972i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 936.000 | 0.375015 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1260.00i | − 0.492729i | ||||||||
\(188\) | − 1008.00i | − 0.391042i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2598.00 | −0.984213 | −0.492106 | − | 0.870535i | \(-0.663773\pi\) | ||||
−0.492106 | + | 0.870535i | \(0.663773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4370.00i | 1.62984i | 0.579572 | + | 0.814921i | \(0.303220\pi\) | ||||
−0.579572 | + | 0.814921i | \(0.696780\pi\) | |||||||
\(194\) | −2656.00 | −0.982937 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 564.000 | 0.205539 | ||||||||
\(197\) | 2943.00i | 1.06437i | 0.846629 | + | 0.532183i | \(0.178628\pi\) | ||||
−0.846629 | + | 0.532183i | \(0.821372\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4768.00 | 1.69847 | 0.849233 | − | 0.528019i | \(-0.177065\pi\) | ||||
0.849233 | + | 0.528019i | \(0.177065\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 984.000i | 0.342743i | ||||||||
\(203\) | − 1452.00i | − 0.502022i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1096.00 | 0.370689 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 608.000i | 0.202679i | ||||||||
\(209\) | −1884.00 | −0.623536 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1267.00 | −0.413383 | −0.206692 | − | 0.978406i | \(-0.566270\pi\) | ||||
−0.206692 | + | 0.978406i | \(0.566270\pi\) | |||||||
\(212\) | − 12.0000i | − 0.00388756i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1464.00 | −0.467649 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 550.000i | − 0.172057i | ||||||||
\(218\) | − 1814.00i | − 0.563576i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3990.00 | −1.21446 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2986.00i | − 0.896670i | −0.893866 | − | 0.448335i | \(-0.852017\pi\) | ||||
0.893866 | − | 0.448335i | \(-0.147983\pi\) | |||||||
\(224\) | 704.000 | 0.209991 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3084.00 | −0.907720 | ||||||||
\(227\) | − 5409.00i | − 1.58153i | −0.612118 | − | 0.790766i | \(-0.709682\pi\) | ||||
0.612118 | − | 0.790766i | \(-0.290318\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4331.00 | −1.24978 | −0.624892 | − | 0.780711i | \(-0.714857\pi\) | ||||
−0.624892 | + | 0.780711i | \(0.714857\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 528.000i | − 0.149418i | ||||||||
\(233\) | 2586.00i | 0.727101i | 0.931575 | + | 0.363550i | \(0.118436\pi\) | ||||
−0.931575 | + | 0.363550i | \(0.881564\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1272.00 | −0.350848 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4620.00i | 1.25828i | ||||||||
\(239\) | −510.000 | −0.138030 | −0.0690150 | − | 0.997616i | \(-0.521986\pi\) | ||||
−0.0690150 | + | 0.997616i | \(0.521986\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −205.000 | −0.0547934 | −0.0273967 | − | 0.999625i | \(-0.508722\pi\) | ||||
−0.0273967 | + | 0.999625i | \(0.508722\pi\) | |||||||
\(242\) | 2374.00i | 0.630605i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1172.00 | −0.307498 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5966.00i | 1.53687i | ||||||||
\(248\) | − 200.000i | − 0.0512097i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4680.00 | −1.17689 | −0.588444 | − | 0.808538i | \(-0.700259\pi\) | ||||
−0.588444 | + | 0.808538i | \(0.700259\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1404.00i | 0.348888i | ||||||||
\(254\) | 5108.00 | 1.26183 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 6159.00i | 1.49489i | 0.664321 | + | 0.747447i | \(0.268721\pi\) | ||||
−0.664321 | + | 0.747447i | \(0.731279\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6908.00 | 1.65731 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 300.000i | 0.0707407i | ||||||||
\(263\) | − 6240.00i | − 1.46302i | −0.681829 | − | 0.731511i | \(-0.738815\pi\) | ||||
0.681829 | − | 0.731511i | \(-0.261185\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6908.00 | 1.59232 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 1288.00i | − 0.293571i | ||||||||
\(269\) | 7758.00 | 1.75841 | 0.879207 | − | 0.476439i | \(-0.158073\pi\) | ||||
0.879207 | + | 0.476439i | \(0.158073\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7345.00 | −1.64641 | −0.823205 | − | 0.567745i | \(-0.807816\pi\) | ||||
−0.823205 | + | 0.567745i | \(0.807816\pi\) | |||||||
\(272\) | 1680.00i | 0.374504i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3306.00 | −0.728915 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3004.00i | 0.651599i | 0.945439 | + | 0.325799i | \(0.105633\pi\) | ||||
−0.945439 | + | 0.325799i | \(0.894367\pi\) | |||||||
\(278\) | 2248.00i | 0.484986i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2046.00 | 0.434356 | 0.217178 | − | 0.976132i | \(-0.430315\pi\) | ||||
0.217178 | + | 0.976132i | \(0.430315\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 5488.00i | − 1.15275i | −0.817186 | − | 0.576374i | \(-0.804467\pi\) | ||||
0.817186 | − | 0.576374i | \(-0.195533\pi\) | |||||||
\(284\) | 480.000 | 0.100291 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −912.000 | −0.188558 | ||||||||
\(287\) | − 11088.0i | − 2.28050i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6112.00 | −1.24405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 176.000i | − 0.0352727i | ||||||||
\(293\) | 333.000i | 0.0663961i | 0.999449 | + | 0.0331981i | \(0.0105692\pi\) | ||||
−0.999449 | + | 0.0331981i | \(0.989431\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2512.00 | 0.493267 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3216.00i | 0.625161i | ||||||||
\(299\) | 4446.00 | 0.859929 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8360.00 | −1.60087 | ||||||||
\(302\) | 4976.00i | 0.948135i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2512.00 | 0.473925 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2918.00i | − 0.542472i | −0.962513 | − | 0.271236i | \(-0.912568\pi\) | ||||
0.962513 | − | 0.271236i | \(-0.0874325\pi\) | |||||||
\(308\) | 1056.00i | 0.195361i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5754.00 | −1.04913 | −0.524565 | − | 0.851370i | \(-0.675772\pi\) | ||||
−0.524565 | + | 0.851370i | \(0.675772\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3368.00i | 0.608213i | 0.952638 | + | 0.304106i | \(0.0983578\pi\) | ||||
−0.952638 | + | 0.304106i | \(0.901642\pi\) | |||||||
\(314\) | 5936.00 | 1.06684 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3668.00 | 0.652978 | ||||||||
\(317\) | − 2871.00i | − 0.508680i | −0.967115 | − | 0.254340i | \(-0.918142\pi\) | ||||
0.967115 | − | 0.254340i | \(-0.0818582\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 792.000 | 0.139008 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 5148.00i | − 0.890953i | ||||||||
\(323\) | 16485.0i | 2.83978i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6340.00 | 1.07712 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 4032.00i | − 0.678750i | ||||||||
\(329\) | −5544.00 | −0.929029 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10540.0 | −1.75024 | −0.875122 | − | 0.483902i | \(-0.839219\pi\) | ||||
−0.875122 | + | 0.483902i | \(0.839219\pi\) | |||||||
\(332\) | − 1236.00i | − 0.204320i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −654.000 | −0.107142 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 5006.00i | − 0.809182i | −0.914498 | − | 0.404591i | \(-0.867414\pi\) | ||||
0.914498 | − | 0.404591i | \(-0.132586\pi\) | |||||||
\(338\) | − 1506.00i | − 0.242354i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 300.000 | 0.0476420 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4444.00i | 0.699573i | ||||||||
\(344\) | −3040.00 | −0.476470 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2610.00 | 0.405533 | ||||||||
\(347\) | 36.0000i | 0.00556940i | 0.999996 | + | 0.00278470i | \(0.000886398\pi\) | ||||
−0.999996 | + | 0.00278470i | \(0.999114\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6715.00 | 1.02993 | 0.514965 | − | 0.857211i | \(-0.327805\pi\) | ||||
0.514965 | + | 0.857211i | \(0.327805\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 384.000i | 0.0581456i | ||||||||
\(353\) | 12822.0i | 1.93328i | 0.256148 | + | 0.966638i | \(0.417547\pi\) | ||||
−0.256148 | + | 0.966638i | \(0.582453\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5088.00 | 0.757482 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 8088.00i | − 1.19403i | ||||||||
\(359\) | −5478.00 | −0.805342 | −0.402671 | − | 0.915345i | \(-0.631918\pi\) | ||||
−0.402671 | + | 0.915345i | \(0.631918\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17790.0 | 2.59367 | ||||||||
\(362\) | 2102.00i | 0.305190i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3344.00 | 0.481520 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2446.00i | 0.347902i | 0.984754 | + | 0.173951i | \(0.0556535\pi\) | ||||
−0.984754 | + | 0.173951i | \(0.944347\pi\) | |||||||
\(368\) | − 1872.00i | − 0.265176i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −66.0000 | −0.00923598 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11696.0i | 1.62358i | 0.583948 | + | 0.811791i | \(0.301507\pi\) | ||||
−0.583948 | + | 0.811791i | \(0.698493\pi\) | |||||||
\(374\) | −2520.00 | −0.348412 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2016.00 | −0.276509 | ||||||||
\(377\) | − 2508.00i | − 0.342622i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2095.00 | 0.283939 | 0.141970 | − | 0.989871i | \(-0.454656\pi\) | ||||
0.141970 | + | 0.989871i | \(0.454656\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5196.00i | 0.695944i | ||||||||
\(383\) | − 11313.0i | − 1.50931i | −0.656119 | − | 0.754657i | \(-0.727803\pi\) | ||||
0.656119 | − | 0.754657i | \(-0.272197\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8740.00 | 1.15247 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5312.00i | 0.695041i | ||||||||
\(389\) | −2124.00 | −0.276841 | −0.138420 | − | 0.990374i | \(-0.544203\pi\) | ||||
−0.138420 | + | 0.990374i | \(0.544203\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12285.0 | 1.58895 | ||||||||
\(392\) | − 1128.00i | − 0.145338i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5886.00 | 0.752620 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 6410.00i | − 0.810349i | −0.914239 | − | 0.405175i | \(-0.867211\pi\) | ||||
0.914239 | − | 0.405175i | \(-0.132789\pi\) | |||||||
\(398\) | − 9536.00i | − 1.20100i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9882.00 | −1.23063 | −0.615316 | − | 0.788280i | \(-0.710972\pi\) | ||||
−0.615316 | + | 0.788280i | \(0.710972\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 950.000i | − 0.117426i | ||||||||
\(404\) | 1968.00 | 0.242356 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2904.00 | −0.354983 | ||||||||
\(407\) | 3768.00i | 0.458901i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5897.00 | −0.712929 | −0.356464 | − | 0.934309i | \(-0.616018\pi\) | ||||
−0.356464 | + | 0.934309i | \(0.616018\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 2192.00i | − 0.262117i | ||||||||
\(413\) | 6996.00i | 0.833537i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1216.00 | 0.143316 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3768.00i | 0.440906i | ||||||||
\(419\) | −6852.00 | −0.798907 | −0.399454 | − | 0.916753i | \(-0.630800\pi\) | ||||
−0.399454 | + | 0.916753i | \(0.630800\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 323.000 | 0.0373921 | 0.0186960 | − | 0.999825i | \(-0.494049\pi\) | ||||
0.0186960 | + | 0.999825i | \(0.494049\pi\) | |||||||
\(422\) | 2534.00i | 0.292306i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −24.0000 | −0.00274892 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6446.00i | 0.730548i | ||||||||
\(428\) | 2928.00i | 0.330678i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10242.0 | 1.14464 | 0.572320 | − | 0.820030i | \(-0.306044\pi\) | ||||
0.572320 | + | 0.820030i | \(0.306044\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 14398.0i | − 1.59798i | −0.601347 | − | 0.798988i | \(-0.705369\pi\) | ||||
0.601347 | − | 0.798988i | \(-0.294631\pi\) | |||||||
\(434\) | −1100.00 | −0.121663 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3628.00 | −0.398508 | ||||||||
\(437\) | − 18369.0i | − 2.01077i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4079.00 | −0.443463 | −0.221731 | − | 0.975108i | \(-0.571171\pi\) | ||||
−0.221731 | + | 0.975108i | \(0.571171\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7980.00i | 0.858755i | ||||||||
\(443\) | 5781.00i | 0.620008i | 0.950735 | + | 0.310004i | \(0.100330\pi\) | ||||
−0.950735 | + | 0.310004i | \(0.899670\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5972.00 | −0.634041 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 1408.00i | − 0.148486i | ||||||||
\(449\) | 15078.0 | 1.58480 | 0.792400 | − | 0.610002i | \(-0.208832\pi\) | ||||
0.792400 | + | 0.610002i | \(0.208832\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6048.00 | 0.631462 | ||||||||
\(452\) | 6168.00i | 0.641855i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10818.0 | −1.11831 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 4268.00i | − 0.436868i | −0.975852 | − | 0.218434i | \(-0.929905\pi\) | ||||
0.975852 | − | 0.218434i | \(-0.0700948\pi\) | |||||||
\(458\) | 8662.00i | 0.883731i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5634.00 | −0.569201 | −0.284600 | − | 0.958646i | \(-0.591861\pi\) | ||||
−0.284600 | + | 0.958646i | \(0.591861\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4526.00i | 0.454300i | 0.973860 | + | 0.227150i | \(0.0729408\pi\) | ||||
−0.973860 | + | 0.227150i | \(0.927059\pi\) | |||||||
\(464\) | −1056.00 | −0.105654 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5172.00 | 0.514138 | ||||||||
\(467\) | − 969.000i | − 0.0960171i | −0.998847 | − | 0.0480085i | \(-0.984713\pi\) | ||||
0.998847 | − | 0.0480085i | \(-0.0152875\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7084.00 | −0.697460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2544.00i | 0.248087i | ||||||||
\(473\) | − 4560.00i | − 0.443275i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9240.00 | 0.889737 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1020.00i | 0.0976019i | ||||||||
\(479\) | −9756.00 | −0.930612 | −0.465306 | − | 0.885150i | \(-0.654056\pi\) | ||||
−0.465306 | + | 0.885150i | \(0.654056\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11932.0 | 1.13109 | ||||||||
\(482\) | 410.000i | 0.0387448i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4748.00 | 0.445905 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 8768.00i | − 0.815844i | −0.913017 | − | 0.407922i | \(-0.866254\pi\) | ||||
0.913017 | − | 0.407922i | \(-0.133746\pi\) | |||||||
\(488\) | 2344.00i | 0.217434i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2274.00 | −0.209011 | −0.104505 | − | 0.994524i | \(-0.533326\pi\) | ||||
−0.104505 | + | 0.994524i | \(0.533326\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 6930.00i | − 0.633086i | ||||||||
\(494\) | 11932.0 | 1.08673 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −400.000 | −0.0362107 | ||||||||
\(497\) | − 2640.00i | − 0.238270i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1969.00 | 0.176642 | 0.0883212 | − | 0.996092i | \(-0.471850\pi\) | ||||
0.0883212 | + | 0.996092i | \(0.471850\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9360.00i | 0.832186i | ||||||||
\(503\) | − 10701.0i | − 0.948577i | −0.880370 | − | 0.474288i | \(-0.842705\pi\) | ||||
0.880370 | − | 0.474288i | \(-0.157295\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2808.00 | 0.246701 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 10216.0i | − 0.892247i | ||||||||
\(509\) | −12420.0 | −1.08155 | −0.540773 | − | 0.841169i | \(-0.681868\pi\) | ||||
−0.540773 | + | 0.841169i | \(0.681868\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −968.000 | −0.0838000 | ||||||||
\(512\) | − 512.000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12318.0 | 1.05705 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 3024.00i | − 0.257244i | ||||||||
\(518\) | − 13816.0i | − 1.17189i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18816.0 | −1.58223 | −0.791117 | − | 0.611665i | \(-0.790500\pi\) | ||||
−0.791117 | + | 0.611665i | \(0.790500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 16798.0i | − 1.40445i | −0.711957 | − | 0.702223i | \(-0.752191\pi\) | ||||
0.711957 | − | 0.702223i | \(-0.247809\pi\) | |||||||
\(524\) | 600.000 | 0.0500212 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12480.0 | −1.03451 | ||||||||
\(527\) | − 2625.00i | − 0.216977i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1522.00 | −0.125092 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 13816.0i | − 1.12594i | ||||||||
\(533\) | − 19152.0i | − 1.55641i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2576.00 | −0.207586 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 15516.0i | − 1.24339i | ||||||||
\(539\) | 1692.00 | 0.135213 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5890.00 | −0.468079 | −0.234040 | − | 0.972227i | \(-0.575195\pi\) | ||||
−0.234040 | + | 0.972227i | \(0.575195\pi\) | |||||||
\(542\) | 14690.0i | 1.16419i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3360.00 | 0.264814 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 5516.00i | − 0.431165i | −0.976486 | − | 0.215582i | \(-0.930835\pi\) | ||||
0.976486 | − | 0.215582i | \(-0.0691650\pi\) | |||||||
\(548\) | 6612.00i | 0.515421i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10362.0 | −0.801154 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 20174.0i | − 1.55133i | ||||||||
\(554\) | 6008.00 | 0.460750 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4496.00 | 0.342937 | ||||||||
\(557\) | − 4146.00i | − 0.315389i | −0.987488 | − | 0.157694i | \(-0.949594\pi\) | ||||
0.987488 | − | 0.157694i | \(-0.0504061\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14440.0 | −1.09257 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 4092.00i | − 0.307136i | ||||||||
\(563\) | − 21444.0i | − 1.60525i | −0.596483 | − | 0.802626i | \(-0.703436\pi\) | ||||
0.596483 | − | 0.802626i | \(-0.296564\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10976.0 | −0.815116 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 960.000i | − 0.0709167i | ||||||||
\(569\) | −14778.0 | −1.08880 | −0.544399 | − | 0.838826i | \(-0.683242\pi\) | ||||
−0.544399 | + | 0.838826i | \(0.683242\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9131.00 | 0.669213 | 0.334606 | − | 0.942358i | \(-0.391397\pi\) | ||||
0.334606 | + | 0.942358i | \(0.391397\pi\) | |||||||
\(572\) | 1824.00i | 0.133331i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −22176.0 | −1.61256 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2344.00i | 0.169120i | 0.996418 | + | 0.0845598i | \(0.0269484\pi\) | ||||
−0.996418 | + | 0.0845598i | \(0.973052\pi\) | |||||||
\(578\) | 12224.0i | 0.879674i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6798.00 | −0.485419 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 36.0000i | − 0.00255741i | ||||||||
\(584\) | −352.000 | −0.0249415 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 666.000 | 0.0469492 | ||||||||
\(587\) | 26829.0i | 1.88646i | 0.332142 | + | 0.943229i | \(0.392229\pi\) | ||||
−0.332142 | + | 0.943229i | \(0.607771\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3925.00 | −0.274579 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 5024.00i | − 0.348792i | ||||||||
\(593\) | 8181.00i | 0.566532i | 0.959041 | + | 0.283266i | \(0.0914179\pi\) | ||||
−0.959041 | + | 0.283266i | \(0.908582\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6432.00 | 0.442055 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 8892.00i | − 0.608062i | ||||||||
\(599\) | −24078.0 | −1.64240 | −0.821202 | − | 0.570637i | \(-0.806696\pi\) | ||||
−0.821202 | + | 0.570637i | \(0.806696\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22565.0 | 1.53152 | 0.765762 | − | 0.643124i | \(-0.222362\pi\) | ||||
0.765762 | + | 0.643124i | \(0.222362\pi\) | |||||||
\(602\) | 16720.0i | 1.13199i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9952.00 | 0.670432 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14716.0i | 0.984026i | 0.870588 | + | 0.492013i | \(0.163739\pi\) | ||||
−0.870588 | + | 0.492013i | \(0.836261\pi\) | |||||||
\(608\) | − 5024.00i | − 0.335115i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9576.00 | −0.634048 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 7552.00i | − 0.497590i | −0.968556 | − | 0.248795i | \(-0.919966\pi\) | ||||
0.968556 | − | 0.248795i | \(-0.0800345\pi\) | |||||||
\(614\) | −5836.00 | −0.383586 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2112.00 | 0.138141 | ||||||||
\(617\) | 3981.00i | 0.259755i | 0.991530 | + | 0.129878i | \(0.0414585\pi\) | ||||
−0.991530 | + | 0.129878i | \(0.958542\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13928.0 | −0.904384 | −0.452192 | − | 0.891921i | \(-0.649358\pi\) | ||||
−0.452192 | + | 0.891921i | \(0.649358\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11508.0i | 0.741847i | ||||||||
\(623\) | − 27984.0i | − 1.79961i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6736.00 | 0.430071 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 11872.0i | − 0.754370i | ||||||||
\(629\) | 32970.0 | 2.08998 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18605.0 | 1.17378 | 0.586889 | − | 0.809668i | \(-0.300353\pi\) | ||||
0.586889 | + | 0.809668i | \(0.300353\pi\) | |||||||
\(632\) | − 7336.00i | − 0.461725i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5742.00 | −0.359691 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 5358.00i | − 0.333268i | ||||||||
\(638\) | − 1584.00i | − 0.0982934i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14928.0 | 0.919845 | 0.459922 | − | 0.887959i | \(-0.347877\pi\) | ||||
0.459922 | + | 0.887959i | \(0.347877\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 6082.00i | − 0.373018i | −0.982453 | − | 0.186509i | \(-0.940283\pi\) | ||||
0.982453 | − | 0.186509i | \(-0.0597174\pi\) | |||||||
\(644\) | −10296.0 | −0.629999 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 32970.0 | 2.00803 | ||||||||
\(647\) | − 4875.00i | − 0.296223i | −0.988971 | − | 0.148111i | \(-0.952681\pi\) | ||||
0.988971 | − | 0.148111i | \(-0.0473194\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3816.00 | −0.230803 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 12680.0i | − 0.761637i | ||||||||
\(653\) | − 5157.00i | − 0.309049i | −0.987989 | − | 0.154525i | \(-0.950615\pi\) | ||||
0.987989 | − | 0.154525i | \(-0.0493846\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8064.00 | −0.479949 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11088.0i | 0.656923i | ||||||||
\(659\) | 1506.00 | 0.0890219 | 0.0445109 | − | 0.999009i | \(-0.485827\pi\) | ||||
0.0445109 | + | 0.999009i | \(0.485827\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2386.00 | −0.140400 | −0.0702002 | − | 0.997533i | \(-0.522364\pi\) | ||||
−0.0702002 | + | 0.997533i | \(0.522364\pi\) | |||||||
\(662\) | 21080.0i | 1.23761i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2472.00 | −0.144476 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7722.00i | 0.448271i | ||||||||
\(668\) | 1308.00i | 0.0757605i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3516.00 | −0.202286 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21158.0i | 1.21186i | 0.795518 | + | 0.605929i | \(0.207199\pi\) | ||||
−0.795518 | + | 0.605929i | \(0.792801\pi\) | |||||||
\(674\) | −10012.0 | −0.572178 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3012.00 | −0.171370 | ||||||||
\(677\) | − 26826.0i | − 1.52291i | −0.648220 | − | 0.761453i | \(-0.724486\pi\) | ||||
0.648220 | − | 0.761453i | \(-0.275514\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29216.0 | 1.65126 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 600.000i | − 0.0336880i | ||||||||
\(683\) | 32493.0i | 1.82037i | 0.414206 | + | 0.910183i | \(0.364059\pi\) | ||||
−0.414206 | + | 0.910183i | \(0.635941\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8888.00 | 0.494673 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6080.00i | 0.336915i | ||||||||
\(689\) | −114.000 | −0.00630342 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7531.00 | −0.414606 | −0.207303 | − | 0.978277i | \(-0.566469\pi\) | ||||
−0.207303 | + | 0.978277i | \(0.566469\pi\) | |||||||
\(692\) | − 5220.00i | − 0.286755i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 72.0000 | 0.00393816 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 52920.0i | − 2.87588i | ||||||||
\(698\) | − 13430.0i | − 0.728271i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24306.0 | 1.30959 | 0.654797 | − | 0.755805i | \(-0.272754\pi\) | ||||
0.654797 | + | 0.755805i | \(0.272754\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 49298.0i | − 2.64482i | ||||||||
\(704\) | 768.000 | 0.0411152 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25644.0 | 1.36703 | ||||||||
\(707\) | − 10824.0i | − 0.575783i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27454.0 | 1.45424 | 0.727120 | − | 0.686510i | \(-0.240858\pi\) | ||||
0.727120 | + | 0.686510i | \(0.240858\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 10176.0i | − 0.535620i | ||||||||
\(713\) | 2925.00i | 0.153635i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16176.0 | −0.844309 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10956.0i | 0.569463i | ||||||||
\(719\) | 5334.00 | 0.276668 | 0.138334 | − | 0.990386i | \(-0.455825\pi\) | ||||
0.138334 | + | 0.990386i | \(0.455825\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12056.0 | −0.622731 | ||||||||
\(722\) | − 35580.0i | − 1.83400i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4204.00 | 0.215802 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 26048.0i | − 1.32884i | −0.747359 | − | 0.664420i | \(-0.768679\pi\) | ||||
0.747359 | − | 0.664420i | \(-0.231321\pi\) | |||||||
\(728\) | − 6688.00i | − 0.340486i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39900.0 | −2.01882 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 33136.0i | − 1.66972i | −0.550461 | − | 0.834861i | \(-0.685548\pi\) | ||||
0.550461 | − | 0.834861i | \(-0.314452\pi\) | |||||||
\(734\) | 4892.00 | 0.246004 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3744.00 | −0.187508 | ||||||||
\(737\) | − 3864.00i | − 0.193124i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11599.0 | 0.577370 | 0.288685 | − | 0.957424i | \(-0.406782\pi\) | ||||
0.288685 | + | 0.957424i | \(0.406782\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 132.000i | 0.00653083i | ||||||||
\(743\) | 26424.0i | 1.30471i | 0.757912 | + | 0.652357i | \(0.226220\pi\) | ||||
−0.757912 | + | 0.652357i | \(0.773780\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 23392.0 | 1.14805 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5040.00i | 0.246365i | ||||||||
\(749\) | 16104.0 | 0.785617 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13661.0 | 0.663778 | 0.331889 | − | 0.943319i | \(-0.392314\pi\) | ||||
0.331889 | + | 0.943319i | \(0.392314\pi\) | |||||||
\(752\) | 4032.00i | 0.195521i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5016.00 | −0.242270 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22846.0i | 1.09690i | 0.836184 | + | 0.548449i | \(0.184782\pi\) | ||||
−0.836184 | + | 0.548449i | \(0.815218\pi\) | |||||||
\(758\) | − 4190.00i | − 0.200775i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20862.0 | 0.993754 | 0.496877 | − | 0.867821i | \(-0.334480\pi\) | ||||
0.496877 | + | 0.867821i | \(0.334480\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19954.0i | 0.946767i | ||||||||
\(764\) | 10392.0 | 0.492106 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22626.0 | −1.06725 | ||||||||
\(767\) | 12084.0i | 0.568876i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22219.0 | 1.04192 | 0.520961 | − | 0.853581i | \(-0.325574\pi\) | ||||
0.520961 | + | 0.853581i | \(0.325574\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 17480.0i | − 0.814921i | ||||||||
\(773\) | 17619.0i | 0.819808i | 0.912129 | + | 0.409904i | \(0.134438\pi\) | ||||
−0.912129 | + | 0.409904i | \(0.865562\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10624.0 | 0.491468 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4248.00i | 0.195756i | ||||||||
\(779\) | −79128.0 | −3.63935 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1440.00 | 0.0659760 | ||||||||
\(782\) | − 24570.0i | − 1.12356i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2256.00 | −0.102770 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 15584.0i | − 0.705857i | −0.935650 | − | 0.352929i | \(-0.885186\pi\) | ||||
0.935650 | − | 0.352929i | \(-0.114814\pi\) | |||||||
\(788\) | − 11772.0i | − 0.532183i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33924.0 | 1.52490 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11134.0i | 0.498588i | ||||||||
\(794\) | −12820.0 | −0.573003 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19072.0 | −0.849233 | ||||||||
\(797\) | 13023.0i | 0.578793i | 0.957209 | + | 0.289397i | \(0.0934547\pi\) | ||||
−0.957209 | + | 0.289397i | \(0.906545\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26460.0 | −1.17157 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19764.0i | 0.870188i | ||||||||
\(803\) | − 528.000i | − 0.0232039i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1900.00 | −0.0830331 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 3936.00i | − 0.171371i | ||||||||
\(809\) | 25872.0 | 1.12436 | 0.562182 | − | 0.827013i | \(-0.309962\pi\) | ||||
0.562182 | + | 0.827013i | \(0.309962\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22052.0 | 0.954809 | 0.477405 | − | 0.878684i | \(-0.341578\pi\) | ||||
0.477405 | + | 0.878684i | \(0.341578\pi\) | |||||||
\(812\) | 5808.00i | 0.251011i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7536.00 | 0.324492 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 59660.0i | 2.55476i | ||||||||
\(818\) | 11794.0i | 0.504117i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1914.00 | 0.0813630 | 0.0406815 | − | 0.999172i | \(-0.487047\pi\) | ||||
0.0406815 | + | 0.999172i | \(0.487047\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 11068.0i | − 0.468780i | −0.972143 | − | 0.234390i | \(-0.924691\pi\) | ||||
0.972143 | − | 0.234390i | \(-0.0753093\pi\) | |||||||
\(824\) | −4384.00 | −0.185345 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13992.0 | 0.589399 | ||||||||
\(827\) | 21405.0i | 0.900030i | 0.893021 | + | 0.450015i | \(0.148581\pi\) | ||||
−0.893021 | + | 0.450015i | \(0.851419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40042.0 | 1.67758 | 0.838791 | − | 0.544453i | \(-0.183263\pi\) | ||||
0.838791 | + | 0.544453i | \(0.183263\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 2432.00i | − 0.101339i | ||||||||
\(833\) | − 14805.0i | − 0.615802i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7536.00 | 0.311768 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13704.0i | 0.564913i | ||||||||
\(839\) | −17904.0 | −0.736728 | −0.368364 | − | 0.929682i | \(-0.620082\pi\) | ||||
−0.368364 | + | 0.929682i | \(0.620082\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20033.0 | −0.821395 | ||||||||
\(842\) | − 646.000i | − 0.0264402i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5068.00 | 0.206692 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 26114.0i | − 1.05937i | ||||||||
\(848\) | 48.0000i | 0.00194378i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36738.0 | −1.47986 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 21580.0i | − 0.866219i | −0.901341 | − | 0.433110i | \(-0.857416\pi\) | ||||
0.901341 | − | 0.433110i | \(-0.142584\pi\) | |||||||
\(854\) | 12892.0 | 0.516575 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5856.00 | 0.233825 | ||||||||
\(857\) | − 17151.0i | − 0.683625i | −0.939768 | − | 0.341813i | \(-0.888959\pi\) | ||||
0.939768 | − | 0.341813i | \(-0.111041\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33425.0 | −1.32764 | −0.663822 | − | 0.747891i | \(-0.731067\pi\) | ||||
−0.663822 | + | 0.747891i | \(0.731067\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 20484.0i | − 0.809383i | ||||||||
\(863\) | 6603.00i | 0.260450i | 0.991484 | + | 0.130225i | \(0.0415700\pi\) | ||||
−0.991484 | + | 0.130225i | \(0.958430\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −28796.0 | −1.12994 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2200.00i | 0.0860286i | ||||||||
\(869\) | 11004.0 | 0.429557 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12236.0 | −0.476006 | ||||||||
\(872\) | 7256.00i | 0.281788i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −36738.0 | −1.42183 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43384.0i | 1.67044i | 0.549918 | + | 0.835219i | \(0.314659\pi\) | ||||
−0.549918 | + | 0.835219i | \(0.685341\pi\) | |||||||
\(878\) | 8158.00i | 0.313575i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12726.0 | 0.486663 | 0.243331 | − | 0.969943i | \(-0.421760\pi\) | ||||
0.243331 | + | 0.969943i | \(0.421760\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2786.00i | 0.106179i | 0.998590 | + | 0.0530897i | \(0.0169069\pi\) | ||||
−0.998590 | + | 0.0530897i | \(0.983093\pi\) | |||||||
\(884\) | 15960.0 | 0.607232 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11562.0 | 0.438412 | ||||||||
\(887\) | 4389.00i | 0.166142i | 0.996544 | + | 0.0830711i | \(0.0264729\pi\) | ||||
−0.996544 | + | 0.0830711i | \(0.973527\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −56188.0 | −2.11978 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11944.0i | 0.448335i | ||||||||
\(893\) | 39564.0i | 1.48260i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2816.00 | −0.104995 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 30156.0i | − 1.12062i | ||||||||
\(899\) | 1650.00 | 0.0612131 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −315.000 | −0.0116472 | ||||||||
\(902\) | − 12096.0i | − 0.446511i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12336.0 | 0.453860 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24868.0i | 0.910395i | 0.890390 | + | 0.455198i | \(0.150431\pi\) | ||||
−0.890390 | + | 0.455198i | \(0.849569\pi\) | |||||||
\(908\) | 21636.0i | 0.790766i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −126.000 | −0.00458240 | −0.00229120 | − | 0.999997i | \(-0.500729\pi\) | ||||
−0.00229120 | + | 0.999997i | \(0.500729\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 3708.00i | − 0.134411i | ||||||||
\(914\) | −8536.00 | −0.308912 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17324.0 | 0.624892 | ||||||||
\(917\) | − 3300.00i | − 0.118839i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16144.0 | 0.579479 | 0.289740 | − | 0.957106i | \(-0.406431\pi\) | ||||
0.289740 | + | 0.957106i | \(0.406431\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11268.0i | 0.402486i | ||||||||
\(923\) | − 4560.00i | − 0.162616i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9052.00 | 0.321239 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2112.00i | 0.0747088i | ||||||||
\(929\) | 42192.0 | 1.49007 | 0.745035 | − | 0.667026i | \(-0.232433\pi\) | ||||
0.745035 | + | 0.667026i | \(0.232433\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22137.0 | −0.779281 | ||||||||
\(932\) | − 10344.0i | − 0.363550i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1938.00 | −0.0678943 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 3272.00i | − 0.114079i | −0.998372 | − | 0.0570393i | \(-0.981834\pi\) | ||||
0.998372 | − | 0.0570393i | \(-0.0181660\pi\) | |||||||
\(938\) | 14168.0i | 0.493179i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20838.0 | 0.721891 | 0.360945 | − | 0.932587i | \(-0.382454\pi\) | ||||
0.360945 | + | 0.932587i | \(0.382454\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58968.0i | 2.03633i | ||||||||
\(944\) | 5088.00 | 0.175424 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9120.00 | −0.313443 | ||||||||
\(947\) | − 13353.0i | − 0.458199i | −0.973403 | − | 0.229099i | \(-0.926422\pi\) | ||||
0.973403 | − | 0.229099i | \(-0.0735781\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1672.00 | −0.0571922 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 18480.0i | − 0.629139i | ||||||||
\(953\) | 13098.0i | 0.445211i | 0.974909 | + | 0.222605i | \(0.0714561\pi\) | ||||
−0.974909 | + | 0.222605i | \(0.928544\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2040.00 | 0.0690150 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19512.0i | 0.658042i | ||||||||
\(959\) | 36366.0 | 1.22452 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29166.0 | −0.979021 | ||||||||
\(962\) | − 23864.0i | − 0.799799i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 820.000 | 0.0273967 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 19826.0i | − 0.659319i | −0.944100 | − | 0.329659i | \(-0.893066\pi\) | ||||
0.944100 | − | 0.329659i | \(-0.106934\pi\) | |||||||
\(968\) | − 9496.00i | − 0.315303i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23322.0 | 0.770792 | 0.385396 | − | 0.922751i | \(-0.374065\pi\) | ||||
0.385396 | + | 0.922751i | \(0.374065\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 24728.0i | − 0.814741i | ||||||||
\(974\) | −17536.0 | −0.576889 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4688.00 | 0.153749 | ||||||||
\(977\) | 47346.0i | 1.55039i | 0.631721 | + | 0.775196i | \(0.282349\pi\) | ||||
−0.631721 | + | 0.775196i | \(0.717651\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15264.0 | 0.498304 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4548.00i | 0.147793i | ||||||||
\(983\) | − 33033.0i | − 1.07181i | −0.844278 | − | 0.535905i | \(-0.819971\pi\) | ||||
0.844278 | − | 0.535905i | \(-0.180029\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −13860.0 | −0.447660 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 23864.0i | − 0.768436i | ||||||||
\(989\) | 44460.0 | 1.42947 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6017.00 | 0.192872 | 0.0964361 | − | 0.995339i | \(-0.469256\pi\) | ||||
0.0964361 | + | 0.995339i | \(0.469256\pi\) | |||||||
\(992\) | 800.000i | 0.0256049i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5280.00 | −0.168482 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34216.0i | 1.08689i | 0.839444 | + | 0.543446i | \(0.182881\pi\) | ||||
−0.839444 | + | 0.543446i | \(0.817119\pi\) | |||||||
\(998\) | − 3938.00i | − 0.124905i | ||||||||
\(999\) | 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 | 1350.4.c.i.649.1 | 2 | ||
3.2 | odd | 2 | 1350.4.c.l.649.2 | 2 | |||
5.2 | odd | 4 | 270.4.a.g.1.1 | yes | 1 | ||
5.3 | odd | 4 | 1350.4.a.l.1.1 | 1 | |||
5.4 | even | 2 | inner | 1350.4.c.i.649.2 | 2 | ||
15.2 | even | 4 | 270.4.a.c.1.1 | ✓ | 1 | ||
15.8 | even | 4 | 1350.4.a.z.1.1 | 1 | |||
15.14 | odd | 2 | 1350.4.c.l.649.1 | 2 | |||
20.7 | even | 4 | 2160.4.a.i.1.1 | 1 | |||
45.2 | even | 12 | 810.4.e.s.271.1 | 2 | |||
45.7 | odd | 12 | 810.4.e.k.271.1 | 2 | |||
45.22 | odd | 12 | 810.4.e.k.541.1 | 2 | |||
45.32 | even | 12 | 810.4.e.s.541.1 | 2 | |||
60.47 | odd | 4 | 2160.4.a.r.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.4.a.c.1.1 | ✓ | 1 | 15.2 | even | 4 | ||
270.4.a.g.1.1 | yes | 1 | 5.2 | odd | 4 | ||
810.4.e.k.271.1 | 2 | 45.7 | odd | 12 | |||
810.4.e.k.541.1 | 2 | 45.22 | odd | 12 | |||
810.4.e.s.271.1 | 2 | 45.2 | even | 12 | |||
810.4.e.s.541.1 | 2 | 45.32 | even | 12 | |||
1350.4.a.l.1.1 | 1 | 5.3 | odd | 4 | |||
1350.4.a.z.1.1 | 1 | 15.8 | even | 4 | |||
1350.4.c.i.649.1 | 2 | 1.1 | even | 1 | trivial | ||
1350.4.c.i.649.2 | 2 | 5.4 | even | 2 | inner | ||
1350.4.c.l.649.1 | 2 | 15.14 | odd | 2 | |||
1350.4.c.l.649.2 | 2 | 3.2 | odd | 2 | |||
2160.4.a.i.1.1 | 1 | 20.7 | even | 4 | |||
2160.4.a.r.1.1 | 1 | 60.47 | odd | 4 |