Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (of order \(3\), degree \(2\), 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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{3}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.361 |
Dual form | 441.4.e.t.226.2 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.32288 | + | 2.29129i | 0.467707 | + | 0.810093i | 0.999319 | − | 0.0368954i | \(-0.0117469\pi\) |
−0.531612 | + | 0.846988i | \(0.678414\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.0625000 | − | 0.108253i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 23.8118 | 1.05234 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.2288 | − | 22.9129i | 0.362602 | − | 0.628045i | −0.625786 | − | 0.779994i | \(-0.715222\pi\) |
0.988388 | + | 0.151950i | \(0.0485552\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 27.5000 | + | 47.6314i | 0.429688 | + | 0.744241i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 70.0000 | 0.678366 | ||||||||
\(23\) | −108.476 | − | 187.886i | −0.983425 | − | 1.70334i | −0.648737 | − | 0.761012i | \(-0.724703\pi\) |
−0.334687 | − | 0.942329i | \(-0.608631\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.5000 | − | 108.253i | 0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 264.575 | 1.69415 | 0.847075 | − | 0.531473i | \(-0.178361\pi\) | ||||
0.847075 | + | 0.531473i | \(0.178361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | 22.4889 | − | 38.9519i | 0.124235 | − | 0.215181i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 225.000 | + | 389.711i | 0.999724 | + | 1.73157i | 0.520223 | + | 0.854030i | \(0.325849\pi\) |
0.479500 | + | 0.877542i | \(0.340818\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 180.000 | 0.638366 | 0.319183 | − | 0.947693i | \(-0.396592\pi\) | ||||
0.319183 | + | 0.947693i | \(0.396592\pi\) | |||||||
\(44\) | −13.2288 | − | 22.9129i | −0.0453252 | − | 0.0785056i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 287.000 | − | 497.099i | 0.919910 | − | 1.59333i | ||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 330.719 | 0.935414 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 248.701 | − | 430.762i | 0.644560 | − | 1.11641i | −0.339843 | − | 0.940482i | \(-0.610374\pi\) |
0.984403 | − | 0.175928i | \(-0.0562926\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 350.000 | + | 606.218i | 0.792366 | + | 1.37242i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 559.000 | 1.09180 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 370.000 | − | 640.859i | 0.674667 | − | 1.16856i | −0.301899 | − | 0.953340i | \(-0.597621\pi\) |
0.976566 | − | 0.215218i | \(-0.0690461\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −978.928 | −1.63630 | −0.818151 | − | 0.575004i | \(-0.805000\pi\) | ||||
−0.818151 | + | 0.575004i | \(0.805000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(74\) | −595.294 | + | 1031.08i | −0.935156 | + | 1.61974i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 692.000 | + | 1198.58i | 0.985520 | + | 1.70697i | 0.639602 | + | 0.768706i | \(0.279099\pi\) |
0.345918 | + | 0.938265i | \(0.387568\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 238.118 | + | 412.432i | 0.298568 | + | 0.517136i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 315.000 | − | 545.596i | 0.381581 | − | 0.660917i | ||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −216.952 | −0.245856 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −62.5000 | − | 108.253i | −0.0625000 | − | 0.108253i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1316.00 | 1.20586 | ||||||||
\(107\) | 775.205 | + | 1342.69i | 0.700392 | + | 1.21311i | 0.968329 | + | 0.249678i | \(0.0803246\pi\) |
−0.267937 | + | 0.963436i | \(0.586342\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −27.0000 | + | 46.7654i | −0.0237260 | + | 0.0410946i | −0.877645 | − | 0.479312i | \(-0.840886\pi\) |
0.853919 | + | 0.520407i | \(0.174220\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2307.10 | −1.92065 | −0.960324 | − | 0.278886i | \(-0.910035\pi\) | ||||
−0.960324 | + | 0.278886i | \(0.910035\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 132.288 | − | 229.129i | 0.105884 | − | 0.183397i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 315.500 | + | 546.462i | 0.237040 | + | 0.410565i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2000.00 | −1.39741 | −0.698706 | − | 0.715409i | \(-0.746240\pi\) | ||||
−0.698706 | + | 0.715409i | \(0.746240\pi\) | |||||||
\(128\) | 559.576 | + | 969.215i | 0.386407 | + | 0.669276i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1957.86 | 1.26219 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 391.571 | − | 678.221i | 0.244191 | − | 0.422951i | −0.717713 | − | 0.696339i | \(-0.754811\pi\) |
0.961904 | + | 0.273388i | \(0.0881442\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1295.00 | − | 2243.01i | −0.765310 | − | 1.32556i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 450.000 | 0.249931 | ||||||||
\(149\) | −1772.65 | − | 3070.33i | −0.974640 | − | 1.68813i | −0.681117 | − | 0.732175i | \(-0.738505\pi\) |
−0.293524 | − | 0.955952i | \(-0.594828\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1476.00 | + | 2556.51i | −0.795465 | + | 1.37779i | 0.127079 | + | 0.991893i | \(0.459440\pi\) |
−0.922544 | + | 0.385893i | \(0.873893\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(158\) | −1830.86 | + | 3171.14i | −0.921870 | + | 1.59672i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −890.000 | − | 1541.53i | −0.427670 | − | 0.740746i | 0.568996 | − | 0.822340i | \(-0.307332\pi\) |
−0.996666 | + | 0.0815946i | \(0.973999\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2197.00 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 90.0000 | − | 155.885i | 0.0398979 | − | 0.0691052i | ||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1455.16 | 0.623222 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2156.29 | − | 3734.80i | 0.900383 | − | 1.55951i | 0.0733844 | − | 0.997304i | \(-0.476620\pi\) |
0.826998 | − | 0.562205i | \(-0.190047\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2583.00 | − | 4473.89i | −1.03490 | − | 1.79250i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1680.05 | − | 2909.94i | −0.636462 | − | 1.10239i | −0.986203 | − | 0.165539i | \(-0.947064\pi\) |
0.349741 | − | 0.936846i | \(-0.386270\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2295.00 | + | 3975.06i | −0.855947 | + | 1.48254i | 0.0198172 | + | 0.999804i | \(0.493692\pi\) |
−0.875764 | + | 0.482740i | \(0.839642\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5069.26 | 1.83335 | 0.916675 | − | 0.399634i | \(-0.130863\pi\) | ||||
0.916675 | + | 0.399634i | \(0.130863\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | 1488.24 | − | 2577.70i | 0.526171 | − | 0.911354i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5868.00 | −1.91455 | −0.957274 | − | 0.289181i | \(-0.906617\pi\) | ||||
−0.957274 | + | 0.289181i | \(0.906617\pi\) | |||||||
\(212\) | −248.701 | − | 430.762i | −0.0805699 | − | 0.139551i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2051.00 | + | 3552.44i | −0.655156 | + | 1.13476i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −142.871 | −0.0443872 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3052.00 | − | 5286.22i | −0.898301 | − | 1.55590i | ||||
\(227\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6300.00 | 1.78282 | ||||||||
\(233\) | 2656.33 | + | 4600.91i | 0.746877 | + | 1.29363i | 0.949313 | + | 0.314333i | \(0.101781\pi\) |
−0.202436 | + | 0.979295i | \(0.564886\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 449.778 | 0.121731 | 0.0608655 | − | 0.998146i | \(-0.480614\pi\) | ||||
0.0608655 | + | 0.998146i | \(0.480614\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(242\) | −834.735 | + | 1445.80i | −0.221730 | + | 0.384048i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5740.00 | −1.42637 | ||||||||
\(254\) | −2645.75 | − | 4582.58i | −0.653580 | − | 1.13203i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 755.500 | − | 1308.56i | 0.184448 | − | 0.319474i | ||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2013.42 | + | 3487.34i | −0.472063 | + | 0.817637i | −0.999489 | − | 0.0319637i | \(-0.989824\pi\) |
0.527426 | + | 0.849601i | \(0.323157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −370.000 | − | 640.859i | −0.0843334 | − | 0.146070i | ||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2072.00 | 0.456840 | ||||||||
\(275\) | −1653.59 | − | 2864.11i | −0.362602 | − | 0.628045i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3655.00 | + | 6330.65i | −0.792807 | + | 1.37318i | 0.131415 | + | 0.991327i | \(0.458048\pi\) |
−0.924222 | + | 0.381855i | \(0.875285\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8360.57 | −1.77491 | −0.887456 | − | 0.460893i | \(-0.847529\pi\) | ||||
−0.887456 | + | 0.460893i | \(0.847529\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(284\) | −489.464 | + | 847.777i | −0.102269 | + | 0.177135i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2456.50 | + | 4254.78i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5357.65 | + | 9279.72i | 1.05205 | + | 1.82220i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4690.00 | − | 8123.32i | 0.911693 | − | 1.57910i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7810.26 | −1.48818 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1384.00 | 0.246380 | ||||||||
\(317\) | 4439.57 | + | 7689.56i | 0.786597 | + | 1.36243i | 0.928041 | + | 0.372479i | \(0.121492\pi\) |
−0.141444 | + | 0.989946i | \(0.545175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3500.00 | − | 6062.18i | 0.614302 | − | 1.06400i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2354.72 | − | 4078.49i | 0.400048 | − | 0.692904i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5454.00 | + | 9446.61i | 0.905677 | + | 1.56868i | 0.820006 | + | 0.572354i | \(0.193970\pi\) |
0.0856702 | + | 0.996324i | \(0.472697\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3330.00 | 0.538269 | 0.269135 | − | 0.963103i | \(-0.413262\pi\) | ||||
0.269135 | + | 0.963103i | \(0.413262\pi\) | |||||||
\(338\) | −2906.36 | − | 5033.96i | −0.467707 | − | 0.810093i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4286.12 | 0.671779 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6130.21 | + | 10617.8i | −0.948377 | + | 1.64264i | −0.199532 | + | 0.979891i | \(0.563942\pi\) |
−0.748845 | + | 0.662745i | \(0.769391\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −595.000 | − | 1030.57i | −0.0900955 | − | 0.156050i | ||||
\(353\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11410.0 | 1.68446 | ||||||||
\(359\) | 5463.48 | + | 9463.02i | 0.803207 | + | 1.39120i | 0.917495 | + | 0.397747i | \(0.130208\pi\) |
−0.114288 | + | 0.993448i | \(0.536459\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3429.50 | − | 5940.07i | 0.500000 | − | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(368\) | 5966.17 | − | 10333.7i | 0.845131 | − | 1.46381i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6985.00 | + | 12098.4i | 0.969624 | + | 1.67944i | 0.696643 | + | 0.717418i | \(0.254676\pi\) |
0.272980 | + | 0.962020i | \(0.411991\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11916.0 | −1.61500 | −0.807498 | − | 0.589870i | \(-0.799179\pi\) | ||||
−0.807498 | + | 0.589870i | \(0.799179\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4445.00 | − | 7698.97i | 0.595356 | − | 1.03119i | ||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12144.0 | −1.60133 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5582.54 | + | 9669.23i | −0.727624 | + | 1.26028i | 0.230261 | + | 0.973129i | \(0.426042\pi\) |
−0.957885 | + | 0.287153i | \(0.907291\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6706.00 | + | 11615.1i | 0.857471 | + | 1.48518i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6875.00 | 0.859375 | ||||||||
\(401\) | −7990.17 | − | 13839.4i | −0.995037 | − | 1.72346i | −0.583690 | − | 0.811977i | \(-0.698392\pi\) |
−0.411348 | − | 0.911478i | \(-0.634942\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11905.9 | 1.45001 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15262.0 | 1.76680 | 0.883402 | − | 0.468616i | \(-0.155247\pi\) | ||||
0.883402 | + | 0.468616i | \(0.155247\pi\) | |||||||
\(422\) | −7762.63 | − | 13445.3i | −0.895448 | − | 1.55096i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5922.00 | − | 10257.2i | 0.678297 | − | 1.17484i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1550.41 | 0.175098 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7844.65 | − | 13587.3i | 0.876714 | − | 1.51851i | 0.0217878 | − | 0.999763i | \(-0.493064\pi\) |
0.854926 | − | 0.518750i | \(-0.173602\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 27.0000 | + | 46.7654i | 0.00296575 | + | 0.00513682i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −796.371 | − | 1379.36i | −0.0854102 | − | 0.147935i | 0.820156 | − | 0.572140i | \(-0.193887\pi\) |
−0.905566 | + | 0.424205i | \(0.860553\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18837.7 | 1.97997 | 0.989987 | − | 0.141158i | \(-0.0450827\pi\) | ||||
0.989987 | + | 0.141158i | \(0.0450827\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −1153.55 | + | 1998.00i | −0.120041 | + | 0.207916i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4005.00 | + | 6936.86i | 0.409947 | + | 0.710050i | 0.994883 | − | 0.101030i | \(-0.0322137\pi\) |
−0.584936 | + | 0.811079i | \(0.698880\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8440.00 | −0.847171 | −0.423585 | − | 0.905856i | \(-0.639229\pi\) | ||||
−0.423585 | + | 0.905856i | \(0.639229\pi\) | |||||||
\(464\) | 7275.82 | + | 12602.1i | 0.727955 | + | 1.26086i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7028.00 | + | 12172.9i | −0.698639 | + | 1.21008i | ||||
\(467\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2381.18 | − | 4124.32i | 0.231473 | − | 0.400923i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 595.000 | + | 1030.57i | 0.0569344 | + | 0.0986134i | ||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 631.000 | 0.0592600 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10620.0 | − | 18394.4i | 0.988169 | − | 1.71156i | 0.361261 | − | 0.932465i | \(-0.382346\pi\) |
0.626908 | − | 0.779094i | \(-0.284320\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7646.22 | 0.702788 | 0.351394 | − | 0.936228i | \(-0.385708\pi\) | ||||
0.351394 | + | 0.936228i | \(0.385708\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3618.00 | − | 6266.56i | −0.324577 | − | 0.562184i | 0.656850 | − | 0.754022i | \(-0.271889\pi\) |
−0.981427 | + | 0.191838i | \(0.938555\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7593.31 | − | 13152.0i | −0.667122 | − | 1.15549i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1000.00 | + | 1732.05i | −0.0873382 | + | 0.151274i | ||||
\(509\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 12951.0 | 1.11788 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10654.0 | −0.883149 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17450.5 | + | 30225.2i | −1.43425 | + | 2.48419i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8810.35 | − | 15260.0i | 0.709980 | − | 1.22972i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7939.00 | − | 13750.8i | −0.630914 | − | 1.09277i | −0.987365 | − | 0.158461i | \(-0.949347\pi\) |
0.356452 | − | 0.934314i | \(-0.383986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12980.0 | 1.01460 | 0.507299 | − | 0.861770i | \(-0.330644\pi\) | ||||
0.507299 | + | 0.861770i | \(0.330644\pi\) | |||||||
\(548\) | −391.571 | − | 678.221i | −0.0305239 | − | 0.0528689i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4375.00 | − | 7577.72i | 0.339183 | − | 0.587482i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −19340.4 | −1.48321 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8249.45 | + | 14288.5i | −0.627541 | + | 1.08693i | 0.360502 | + | 0.932758i | \(0.382605\pi\) |
−0.988044 | + | 0.154175i | \(0.950728\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11060.0 | − | 19156.5i | −0.830139 | − | 1.43784i | ||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −23310.0 | −1.72195 | ||||||||
\(569\) | 1799.11 | + | 3116.15i | 0.132553 | + | 0.229589i | 0.924660 | − | 0.380794i | \(-0.124349\pi\) |
−0.792107 | + | 0.610382i | \(0.791016\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3394.00 | − | 5878.58i | 0.248747 | − | 0.430842i | −0.714431 | − | 0.699705i | \(-0.753315\pi\) |
0.963178 | + | 0.268863i | \(0.0866479\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27119.0 | −1.96685 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(578\) | −6499.29 | + | 11257.1i | −0.467707 | + | 0.810093i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6580.00 | − | 11396.9i | −0.467437 | − | 0.809625i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12375.0 | + | 21434.1i | −0.859137 | + | 1.48807i | ||||
\(593\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3545.31 | −0.243660 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7871.11 | + | 13633.2i | −0.536903 | + | 0.929943i | 0.462166 | + | 0.886794i | \(0.347073\pi\) |
−0.999069 | + | 0.0431495i | \(0.986261\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1476.00 | + | 2556.51i | 0.0994331 | + | 0.172223i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7505.00 | + | 12999.0i | −0.494493 | + | 0.856487i | −0.999980 | − | 0.00634752i | \(-0.997980\pi\) |
0.505487 | + | 0.862834i | \(0.331313\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2497.59 | 0.162965 | 0.0814823 | − | 0.996675i | \(-0.474035\pi\) | ||||
0.0814823 | + | 0.996675i | \(0.474035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7812.50 | − | 13531.6i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26192.0 | −1.65244 | −0.826218 | − | 0.563351i | \(-0.809512\pi\) | ||||
−0.826218 | + | 0.563351i | \(0.809512\pi\) | |||||||
\(632\) | 16477.7 | + | 28540.3i | 1.03710 | + | 1.79632i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11746.0 | + | 20344.7i | −0.735794 | + | 1.27443i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 18520.3 | 1.14925 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15609.9 | − | 27037.2i | 0.961865 | − | 1.66600i | 0.244052 | − | 0.969762i | \(-0.421523\pi\) |
0.717813 | − | 0.696236i | \(-0.245143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1780.00 | −0.106917 | ||||||||
\(653\) | 9773.41 | + | 16928.0i | 0.585701 | + | 1.01446i | 0.994788 | + | 0.101969i | \(0.0325141\pi\) |
−0.409086 | + | 0.912496i | \(0.634153\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33786.2 | −1.99716 | −0.998578 | − | 0.0533186i | \(-0.983020\pi\) | ||||
−0.998578 | + | 0.0533186i | \(0.983020\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(662\) | −14429.9 | + | 24993.4i | −0.847183 | + | 1.46736i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28700.0 | − | 49709.9i | −1.66607 | − | 2.88572i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33570.0 | 1.92278 | 0.961388 | − | 0.275196i | \(-0.0887428\pi\) | ||||
0.961388 | + | 0.275196i | \(0.0887428\pi\) | |||||||
\(674\) | 4405.18 | + | 7629.99i | 0.251752 | + | 0.436048i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1098.50 | + | 1902.66i | −0.0625000 | + | 0.108253i | ||||
\(677\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5347.06 | + | 9261.39i | −0.299560 | + | 0.518854i | −0.976035 | − | 0.217612i | \(-0.930173\pi\) |
0.676475 | + | 0.736466i | \(0.263507\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4950.00 | + | 8573.65i | 0.274298 | + | 0.475098i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32438.0 | −1.77425 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36881.8 | −1.98717 | −0.993584 | − | 0.113093i | \(-0.963924\pi\) | ||||
−0.993584 | + | 0.113093i | \(0.963924\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 7394.87 | − | 12808.3i | 0.395888 | − | 0.685697i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6273.00 | + | 10865.2i | 0.332281 | + | 0.575528i | 0.982959 | − | 0.183826i | \(-0.0588483\pi\) |
−0.650677 | + | 0.759354i | \(0.725515\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2156.29 | − | 3734.80i | −0.112548 | − | 0.194939i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14455.0 | + | 25036.8i | −0.751331 | + | 1.30134i | ||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18147.2 | 0.935414 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16535.9 | − | 28641.1i | 0.847075 | − | 1.46718i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9758.00 | −0.488702 | ||||||||
\(737\) | −9789.28 | − | 16955.5i | −0.489271 | − | 0.847442i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12662.0 | − | 21931.2i | 0.630283 | − | 1.09168i | −0.357211 | − | 0.934024i | \(-0.616272\pi\) |
0.987494 | − | 0.157658i | \(-0.0503945\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31743.7 | 1.56738 | 0.783691 | − | 0.621151i | \(-0.213335\pi\) | ||||
0.783691 | + | 0.621151i | \(0.213335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −18480.6 | + | 32009.3i | −0.907000 | + | 1.57097i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1224.00 | − | 2120.03i | −0.0594732 | − | 0.103011i | 0.834756 | − | 0.550620i | \(-0.185609\pi\) |
−0.894229 | + | 0.447610i | \(0.852275\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34830.0 | 1.67228 | 0.836141 | − | 0.548514i | \(-0.184806\pi\) | ||||
0.836141 | + | 0.548514i | \(0.184806\pi\) | |||||||
\(758\) | −15763.4 | − | 27303.0i | −0.755346 | − | 1.30830i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3360.10 | −0.159116 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2295.00 | + | 3975.06i | 0.106993 | + | 0.185318i | ||||
\(773\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −29540.0 | −1.36126 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12950.0 | + | 22430.1i | −0.593326 | + | 1.02767i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(788\) | 2534.63 | − | 4390.11i | 0.114584 | − | 0.198466i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −2811.11 | − | 4868.99i | −0.124235 | − | 0.215181i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21140.0 | − | 36615.6i | 0.930772 | − | 1.61214i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13440.4 | + | 23279.5i | −0.584104 | + | 1.01170i | 0.410883 | + | 0.911688i | \(0.365221\pi\) |
−0.994987 | + | 0.100009i | \(0.968113\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15750.0 | + | 27279.8i | 0.678178 | + | 1.17464i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8916.18 | − | 15443.3i | −0.379022 | − | 0.656485i | 0.611898 | − | 0.790936i | \(-0.290406\pi\) |
−0.990920 | + | 0.134451i | \(0.957073\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23120.0 | − | 40045.0i | 0.979238 | − | 1.69609i | 0.314062 | − | 0.949403i | \(-0.398310\pi\) |
0.665176 | − | 0.746687i | \(-0.268357\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41077.9 | 1.72723 | 0.863615 | − | 0.504151i | \(-0.168195\pi\) | ||||
0.863615 | + | 0.504151i | \(0.168195\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45611.0 | 1.87015 | ||||||||
\(842\) | 20189.7 | + | 34969.6i | 0.826347 | + | 1.43127i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2934.00 | + | 5081.84i | −0.119659 | + | 0.207256i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 27357.1 | 1.10784 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48814.1 | − | 84548.5i | 1.96631 | − | 3.40574i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18459.0 | + | 31971.9i | 0.737051 | + | 1.27661i | ||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 41510.0 | 1.64018 | ||||||||
\(863\) | −23253.5 | − | 40276.3i | −0.917217 | − | 1.58867i | −0.803622 | − | 0.595140i | \(-0.797097\pi\) |
−0.113595 | − | 0.993527i | \(-0.536237\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36617.2 | 1.42941 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −642.918 | + | 1113.57i | −0.0249678 | + | 0.0432455i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3275.00 | + | 5672.47i | 0.126099 | + | 0.218410i | 0.922162 | − | 0.386804i | \(-0.126421\pi\) |
−0.796063 | + | 0.605214i | \(0.793088\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30060.0 | −1.14564 | −0.572820 | − | 0.819681i | \(-0.694150\pi\) | ||||
−0.572820 | + | 0.819681i | \(0.694150\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2107.00 | − | 3649.43i | 0.0798940 | − | 0.138380i | ||||
\(887\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24920.0 | + | 43162.7i | 0.926048 | + | 1.60396i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −54936.0 | −2.02118 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26370.0 | − | 45674.2i | 0.965382 | − | 1.67209i | 0.256797 | − | 0.966465i | \(-0.417333\pi\) |
0.708585 | − | 0.705625i | \(-0.249334\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38125.3 | −1.38655 | −0.693275 | − | 0.720673i | \(-0.743833\pi\) | ||||
−0.693275 | + | 0.720673i | \(0.743833\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −10596.2 | + | 18353.2i | −0.383471 | + | 0.664191i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10872.0 | + | 18830.9i | 0.390244 | + | 0.675922i | 0.992482 | − | 0.122395i | \(-0.0390573\pi\) |
−0.602238 | + | 0.798317i | \(0.705724\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 56250.0 | 1.99945 | ||||||||
\(926\) | −11165.1 | − | 19338.5i | −0.396228 | − | 0.686287i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5950.00 | − | 10305.7i | 0.210472 | − | 0.364549i | ||||
\(929\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5312.67 | 0.186719 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12600.0 | 0.433046 | ||||||||
\(947\) | 15919.5 | + | 27573.4i | 0.546266 | + | 0.946160i | 0.998526 | + | 0.0542742i | \(0.0172845\pi\) |
−0.452260 | + | 0.891886i | \(0.649382\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51031.3 | −1.73459 | −0.867295 | − | 0.497794i | \(-0.834143\pi\) | ||||
−0.867295 | + | 0.497794i | \(0.834143\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 224.889 | − | 389.519i | 0.00760819 | − | 0.0131778i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14895.5 | + | 25799.8i | 0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52040.0 | 1.73060 | 0.865302 | − | 0.501251i | \(-0.167127\pi\) | ||||
0.865302 | + | 0.501251i | \(0.167127\pi\) | |||||||
\(968\) | 7512.61 | + | 13012.2i | 0.249447 | + | 0.432054i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 56195.8 | 1.84869 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24108.1 | + | 41756.4i | −0.789443 | + | 1.36736i | 0.136865 | + | 0.990590i | \(0.456297\pi\) |
−0.926308 | + | 0.376766i | \(0.877036\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10115.0 | + | 17519.7i | 0.328699 | + | 0.569324i | ||||
\(983\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19525.6 | − | 33819.4i | −0.627785 | − | 1.08736i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28764.0 | − | 49820.7i | 0.922017 | − | 1.59698i | 0.125727 | − | 0.992065i | \(-0.459874\pi\) |
0.796290 | − | 0.604915i | \(-0.206793\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(998\) | 9572.33 | − | 16579.8i | 0.303614 | − | 0.525875i | ||||
\(999\) | 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 | 441.4.e.t.361.2 | 4 | ||
3.2 | odd | 2 | inner | 441.4.e.t.361.1 | 4 | ||
7.2 | even | 3 | inner | 441.4.e.t.226.2 | 4 | ||
7.3 | odd | 6 | 441.4.a.p.1.1 | ✓ | 2 | ||
7.4 | even | 3 | 441.4.a.p.1.1 | ✓ | 2 | ||
7.5 | odd | 6 | inner | 441.4.e.t.226.2 | 4 | ||
7.6 | odd | 2 | CM | 441.4.e.t.361.2 | 4 | ||
21.2 | odd | 6 | inner | 441.4.e.t.226.1 | 4 | ||
21.5 | even | 6 | inner | 441.4.e.t.226.1 | 4 | ||
21.11 | odd | 6 | 441.4.a.p.1.2 | yes | 2 | ||
21.17 | even | 6 | 441.4.a.p.1.2 | yes | 2 | ||
21.20 | even | 2 | inner | 441.4.e.t.361.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.4.a.p.1.1 | ✓ | 2 | 7.3 | odd | 6 | ||
441.4.a.p.1.1 | ✓ | 2 | 7.4 | even | 3 | ||
441.4.a.p.1.2 | yes | 2 | 21.11 | odd | 6 | ||
441.4.a.p.1.2 | yes | 2 | 21.17 | even | 6 | ||
441.4.e.t.226.1 | 4 | 21.2 | odd | 6 | inner | ||
441.4.e.t.226.1 | 4 | 21.5 | even | 6 | inner | ||
441.4.e.t.226.2 | 4 | 7.2 | even | 3 | inner | ||
441.4.e.t.226.2 | 4 | 7.5 | odd | 6 | inner | ||
441.4.e.t.361.1 | 4 | 3.2 | odd | 2 | inner | ||
441.4.e.t.361.1 | 4 | 21.20 | even | 2 | inner | ||
441.4.e.t.361.2 | 4 | 1.1 | even | 1 | trivial | ||
441.4.e.t.361.2 | 4 | 7.6 | odd | 2 | CM |