Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(80,441)]
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([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.80");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.p (of order \(6\), 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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.12745506816.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 215.3 | ||
Root | \(-1.00781 - 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.215 |
Dual form | 441.4.p.b.80.3 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.44168 | + | 0.832353i | 0.509710 | + | 0.294281i | 0.732714 | − | 0.680536i | \(-0.238253\pi\) |
−0.223005 | + | 0.974817i | \(0.571586\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.61438 | − | 4.52824i | −0.326797 | − | 0.566030i | ||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 22.0220i | − | 0.973243i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −25.4395 | + | 14.6875i | −0.697299 | + | 0.402586i | −0.806341 | − | 0.591451i | \(-0.798555\pi\) |
0.109042 | + | 0.994037i | \(0.465222\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.58497 | + | 4.47731i | −0.0403902 | + | 0.0699579i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −48.9007 | −0.473894 | ||||||||
\(23\) | −157.350 | − | 90.8461i | −1.42651 | − | 0.823597i | −0.429668 | − | 0.902987i | \(-0.641369\pi\) |
−0.996844 | + | 0.0793904i | \(0.974703\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.5000 | + | 108.253i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 304.463i | 1.94956i | 0.223165 | + | 0.974781i | \(0.428361\pi\) | ||||
−0.223165 | + | 0.974781i | \(0.571639\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(32\) | −160.026 | + | 92.3911i | −0.884028 | + | 0.510394i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.29150 | − | 9.16515i | 0.0235113 | − | 0.0407227i | −0.854030 | − | 0.520223i | \(-0.825849\pi\) |
0.877542 | + | 0.479500i | \(0.159182\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −534.442 | −1.89539 | −0.947693 | − | 0.319183i | \(-0.896592\pi\) | ||||
−0.947693 | + | 0.319183i | \(0.896592\pi\) | |||||||
\(44\) | 133.017 | + | 76.7973i | 0.455751 | + | 0.263128i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −151.232 | − | 261.942i | −0.484738 | − | 0.839591i | ||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 208.088i | 0.588562i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −665.895 | + | 384.454i | −1.72580 | + | 0.996394i | −0.820478 | + | 0.571678i | \(0.806293\pi\) |
−0.905327 | + | 0.424716i | \(0.860374\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −253.420 | + | 438.937i | −0.573719 | + | 0.993711i | ||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −266.248 | −0.520016 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −370.000 | − | 640.859i | −0.674667 | − | 1.16856i | −0.976566 | − | 0.215218i | \(-0.930954\pi\) |
0.301899 | − | 0.953340i | \(-0.402379\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1178.70i | 1.97022i | 0.171931 | + | 0.985109i | \(0.445000\pi\) | ||||
−0.171931 | + | 0.985109i | \(0.555000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(74\) | 15.2573 | − | 8.80879i | 0.0239679 | − | 0.0138379i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 692.000 | − | 1198.58i | 0.985520 | − | 1.70697i | 0.345918 | − | 0.938265i | \(-0.387568\pi\) |
0.639602 | − | 0.768706i | \(-0.279099\pi\) | |||||||
\(80\) | 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 | ||||||||
\(86\) | −770.492 | − | 444.844i | −0.966097 | − | 0.557776i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 323.448 | + | 560.228i | 0.391814 | + | 0.678642i | ||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 950.024i | 1.07660i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 326.797 | − | 566.030i | 0.326797 | − | 0.566030i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1280.01 | −1.17288 | ||||||||
\(107\) | 18.1199 | + | 10.4615i | 0.0163712 | + | 0.00945193i | 0.508163 | − | 0.861261i | \(-0.330325\pi\) |
−0.491792 | + | 0.870713i | \(0.663658\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1137.67 | − | 1970.51i | −0.999718 | − | 1.73156i | −0.520407 | − | 0.853919i | \(-0.674220\pi\) |
−0.479312 | − | 0.877645i | \(-0.659114\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1157.60i | − | 0.963699i | −0.876254 | − | 0.481849i | \(-0.839965\pi\) | ||
0.876254 | − | 0.481849i | \(-0.160035\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1378.68 | − | 795.980i | 1.10351 | − | 0.637111i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −234.055 | + | 405.396i | −0.175849 | + | 0.304580i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2000.00 | 1.39741 | 0.698706 | − | 0.715409i | \(-0.253760\pi\) | ||||
0.698706 | + | 0.715409i | \(0.253760\pi\) | |||||||
\(128\) | 896.365 | + | 517.517i | 0.618970 | + | 0.357363i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 1231.88i | − | 0.794167i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2384.05 | + | 1376.43i | −1.48674 | + | 0.858370i | −0.999886 | − | 0.0151133i | \(-0.995189\pi\) |
−0.486854 | + | 0.873483i | \(0.661856\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −981.091 | + | 1699.30i | −0.579798 | + | 1.00424i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −55.3360 | −0.0307337 | ||||||||
\(149\) | 1672.58 | + | 965.663i | 0.919616 | + | 0.530941i | 0.883513 | − | 0.468407i | \(-0.155172\pi\) |
0.0361037 | + | 0.999348i | \(0.488505\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1124.44 | + | 1947.59i | 0.606000 | + | 1.04962i | 0.991893 | + | 0.127079i | \(0.0405601\pi\) |
−0.385893 | + | 0.922544i | \(0.626107\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(158\) | 1995.28 | − | 1151.98i | 1.00466 | − | 0.580040i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 890.000 | − | 1541.53i | 0.427670 | − | 0.740746i | −0.568996 | − | 0.822340i | \(-0.692668\pi\) |
0.996666 | + | 0.0815946i | \(0.0260013\pi\) | |||||||
\(164\) | 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 | ||||||||
\(172\) | 1397.23 | + | 2420.08i | 0.619407 | + | 1.07284i | ||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 151.867i | − | 0.0650421i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1364.72 | − | 787.920i | 0.569854 | − | 0.329005i | −0.187237 | − | 0.982315i | \(-0.559953\pi\) |
0.757091 | + | 0.653310i | \(0.226620\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2000.61 | + | 3465.16i | −0.801560 | + | 1.38834i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4551.22 | − | 2627.65i | −1.72416 | − | 0.995444i | −0.909755 | − | 0.415146i | \(-0.863730\pi\) |
−0.814405 | − | 0.580298i | \(-0.802936\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1386.37 | + | 2401.27i | 0.517064 | + | 0.895581i | 0.999804 | + | 0.0198172i | \(0.00630844\pi\) |
−0.482740 | + | 0.875764i | \(0.660358\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5147.21i | − | 1.86154i | −0.365603 | − | 0.930771i | \(-0.619137\pi\) | ||
0.365603 | − | 0.930771i | \(-0.380863\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(200\) | 2383.95 | − | 1376.37i | 0.842853 | − | 0.486622i | ||||
\(201\) | 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 | ||||||||
\(211\) | −1772.65 | −0.578363 | −0.289181 | − | 0.957274i | \(-0.593383\pi\) | ||||
−0.289181 | + | 0.957274i | \(0.593383\pi\) | |||||||
\(212\) | 3481.80 | + | 2010.22i | 1.12798 | + | 0.651238i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.4154 | + | 30.1644i | 0.00556305 | + | 0.00963548i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 3787.78i | − | 1.17679i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 963.532 | − | 1668.89i | 0.283598 | − | 0.491207i | ||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6704.87 | 1.89740 | ||||||||
\(233\) | −356.810 | − | 206.004i | −0.100324 | − | 0.0579219i | 0.448999 | − | 0.893532i | \(-0.351781\pi\) |
−0.549322 | + | 0.835611i | \(0.685114\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5533.66i | − | 1.49767i | −0.662757 | − | 0.748834i | \(-0.730614\pi\) | ||
0.662757 | − | 0.748834i | \(-0.269386\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(242\) | −674.865 | + | 389.633i | −0.179264 | + | 0.103498i | ||||
\(243\) | 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 | ||||||||
\(253\) | 5337.20 | 1.32627 | ||||||||
\(254\) | 2883.35 | + | 1664.71i | 0.712274 | + | 0.411232i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1926.51 | + | 3336.81i | 0.470338 | + | 0.814650i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2139.12 | + | 1235.02i | −0.501535 | + | 0.289561i | −0.729347 | − | 0.684144i | \(-0.760176\pi\) |
0.227812 | + | 0.973705i | \(0.426843\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1934.64 | + | 3350.89i | −0.440959 | + | 0.763763i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4582.71 | −1.01041 | ||||||||
\(275\) | −3179.93 | − | 1835.94i | −0.697299 | − | 0.402586i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3655.00 | − | 6330.65i | −0.792807 | − | 1.37318i | −0.924222 | − | 0.381855i | \(-0.875285\pi\) |
0.131415 | − | 0.991327i | \(-0.458048\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8982.08i | 1.90685i | 0.301625 | + | 0.953427i | \(0.402471\pi\) | ||||
−0.301625 | + | 0.953427i | \(0.597529\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(284\) | 5337.41 | − | 3081.56i | 1.11520 | − | 0.643862i | ||||
\(285\) | 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 | ||||||||
\(296\) | −201.835 | − | 116.529i | −0.0396331 | − | 0.0228822i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1607.54 | + | 2784.35i | 0.312492 | + | 0.541251i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3743.74i | 0.713337i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7236.60 | −1.28826 | ||||||||
\(317\) | 1169.11 | + | 674.983i | 0.207140 | + | 0.119593i | 0.599982 | − | 0.800014i | \(-0.295175\pi\) |
−0.392841 | + | 0.919606i | \(0.628508\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4471.79 | − | 7745.37i | −0.784866 | − | 1.35943i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2566.19 | − | 1481.59i | 0.435975 | − | 0.251710i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2553.15 | − | 4422.19i | 0.423969 | − | 0.734336i | −0.572354 | − | 0.820006i | \(-0.693970\pi\) |
0.996324 | + | 0.0856702i | \(0.0273031\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11916.5 | −1.92621 | −0.963103 | − | 0.269135i | \(-0.913262\pi\) | ||||
−0.963103 | + | 0.269135i | \(0.913262\pi\) | |||||||
\(338\) | 3167.36 | + | 1828.68i | 0.509710 | + | 0.294281i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11769.5i | 1.84467i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10018.7 | + | 5784.28i | −1.54994 | + | 0.894860i | −0.551798 | + | 0.833978i | \(0.686058\pi\) |
−0.998145 | + | 0.0608819i | \(0.980609\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2713.99 | − | 4700.76i | 0.410955 | − | 0.711794i | ||||
\(353\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2623.31 | 0.387280 | ||||||||
\(359\) | 1728.70 | + | 998.065i | 0.254143 | + | 0.146729i | 0.621660 | − | 0.783287i | \(-0.286459\pi\) |
−0.367517 | + | 0.930017i | \(0.619792\pi\) | |||||||
\(360\) | 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 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(368\) | 813.492 | − | 469.670i | 0.115234 | − | 0.0665305i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6985.00 | + | 12098.4i | −0.969624 | + | 1.67944i | −0.272980 | + | 0.962020i | \(0.588009\pi\) |
−0.696643 | + | 0.717418i | \(0.745324\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8704.52 | 1.17974 | 0.589870 | − | 0.807498i | \(-0.299179\pi\) | ||||
0.589870 | + | 0.807498i | \(0.299179\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4374.26 | − | 7576.43i | −0.585881 | − | 1.01477i | ||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4615.81i | 0.608649i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13283.0 | + | 7668.95i | −1.73130 | + | 0.999566i | −0.850925 | + | 0.525287i | \(0.823958\pi\) |
−0.880375 | + | 0.474279i | \(0.842709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4284.30 | − | 7420.62i | 0.547817 | − | 0.948846i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −646.243 | −0.0807804 | ||||||||
\(401\) | −8807.35 | − | 5084.92i | −1.09680 | − | 0.633239i | −0.161423 | − | 0.986885i | \(-0.551608\pi\) |
−0.935379 | + | 0.353646i | \(0.884942\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 310.876i | 0.0378612i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(410\) | 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 | \(-0.844753\pi\) | ||||
−0.883402 | + | 0.468616i | \(0.844753\pi\) | |||||||
\(422\) | −2555.59 | − | 1475.47i | −0.294797 | − | 0.170201i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8466.45 | + | 14664.3i | 0.969734 | + | 1.67963i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 109.402i | − | 0.0123555i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4336.40 | + | 2503.62i | −0.484633 | + | 0.279803i | −0.722345 | − | 0.691533i | \(-0.756936\pi\) |
0.237712 | + | 0.971336i | \(0.423602\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5948.62 | + | 10303.3i | −0.653411 | + | 1.13174i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10402.5 | − | 6005.90i | −1.11566 | − | 0.644129i | −0.175373 | − | 0.984502i | \(-0.556113\pi\) |
−0.940290 | + | 0.340373i | \(0.889447\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15219.6i | 1.59968i | 0.600213 | + | 0.799841i | \(0.295083\pi\) | ||||
−0.600213 | + | 0.799841i | \(0.704917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5241.89 | + | 3026.41i | −0.545482 | + | 0.314934i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8910.89 | − | 15434.1i | 0.912109 | − | 1.57982i | 0.101030 | − | 0.994883i | \(-0.467786\pi\) |
0.811079 | − | 0.584936i | \(-0.198880\pi\) | |||||||
\(458\) | 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 | \(0.639229\pi\) | |||||||
\(464\) | −1363.17 | − | 787.028i | −0.136387 | − | 0.0787432i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −342.937 | − | 593.984i | −0.0340906 | − | 0.0590467i | ||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13595.9 | − | 7849.61i | 1.32165 | − | 0.763056i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4605.96 | − | 7977.75i | 0.440735 | − | 0.763376i | ||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2447.64 | 0.229868 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1648.30 | + | 2854.94i | 0.153371 | + | 0.265647i | 0.932465 | − | 0.361261i | \(-0.117654\pi\) |
−0.779094 | + | 0.626908i | \(0.784320\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8998.48i | − | 0.827079i | −0.910486 | − | 0.413540i | \(-0.864292\pi\) | ||
0.910486 | − | 0.413540i | \(-0.135708\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10543.3 | + | 18261.6i | −0.945859 | + | 1.63828i | −0.191838 | + | 0.981427i | \(0.561445\pi\) |
−0.754022 | + | 0.656850i | \(0.771889\pi\) | |||||||
\(500\) | 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 | ||||||||
\(506\) | 7694.52 | + | 4442.44i | 0.676015 | + | 0.390297i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5228.76 | − | 9056.47i | −0.456670 | − | 0.790976i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1866.13i | − | 0.161079i | ||||||
\(513\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4111.89 | −0.340850 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10422.5 | + | 18052.4i | 0.856623 | + | 1.48371i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14113.0 | + | 8148.13i | −1.13729 | + | 0.656615i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7939.00 | + | 13750.8i | −0.630914 | + | 1.09277i | 0.356452 | + | 0.934314i | \(0.383986\pi\) |
−0.987365 | + | 0.158461i | \(0.949347\pi\) | |||||||
\(542\) | 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 | \(0.330644\pi\) | |||||||
\(548\) | 12465.6 | + | 7197.04i | 0.971725 | + | 0.561026i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3056.29 | − | 5293.65i | −0.236947 | − | 0.410404i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 12169.0i | − | 0.933233i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2431.79 | − | 1403.99i | 0.184988 | − | 0.106803i | −0.404646 | − | 0.914473i | \(-0.632605\pi\) |
0.589634 | + | 0.807671i | \(0.299272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7476.25 | + | 12949.3i | −0.561151 | + | 0.971942i | ||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 25957.2 | 1.91750 | ||||||||
\(569\) | 14273.0 | + | 8240.54i | 1.05159 | + | 0.607138i | 0.923095 | − | 0.384572i | \(-0.125651\pi\) |
0.128499 | + | 0.991710i | \(0.458984\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3394.00 | − | 5878.58i | −0.248747 | − | 0.430842i | 0.714431 | − | 0.699705i | \(-0.246685\pi\) |
−0.963178 | + | 0.268863i | \(0.913352\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 22711.5i | − | 1.64719i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(578\) | 7082.96 | − | 4089.35i | 0.509710 | − | 0.294281i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11293.3 | − | 19560.6i | 0.802268 | − | 1.38957i | ||||
\(584\) | 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 | ||||||||
\(592\) | 27.3568 | + | 47.3834i | 0.00189925 | + | 0.00328960i | ||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 10098.4i | − | 0.694040i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24787.7 | − | 14311.2i | 1.69082 | − | 0.976194i | 0.736960 | − | 0.675937i | \(-0.236261\pi\) |
0.953858 | − | 0.300257i | \(-0.0970725\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5879.45 | − | 10183.5i | 0.396078 | − | 0.686028i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 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 | \(-0.00202049\pi\) |
−0.505487 | + | 0.862834i | \(0.668687\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19836.0i | 1.29428i | 0.762372 | + | 0.647139i | \(0.224035\pi\) | ||||
−0.762372 | + | 0.647139i | \(0.775965\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(620\) | 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 | \(-0.190488\pi\) | ||||
0.826218 | + | 0.563351i | \(0.190488\pi\) | |||||||
\(632\) | −26395.1 | − | 15239.2i | −1.66130 | − | 0.959151i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1123.65 | + | 1946.22i | 0.0703877 | + | 0.121915i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 14888.4i | − | 0.923885i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24554.8 | − | 14176.7i | 1.51304 | − | 0.873553i | 0.513154 | − | 0.858296i | \(-0.328477\pi\) |
0.999884 | − | 0.0152566i | \(-0.00485652\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9307.19 | −0.559045 | ||||||||
\(653\) | 28534.6 | + | 16474.5i | 1.71002 | + | 0.987282i | 0.934500 | + | 0.355964i | \(0.115847\pi\) |
0.775524 | + | 0.631318i | \(0.217486\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 22614.9i | − | 1.33680i | −0.743803 | − | 0.668399i | \(-0.766980\pi\) | ||
0.743803 | − | 0.668399i | \(-0.233020\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(662\) | 7361.64 | − | 4250.24i | 0.432203 | − | 0.249532i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27659.2 | − | 47907.2i | 1.60565 | − | 2.78107i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9609.37 | 0.550392 | 0.275196 | − | 0.961388i | \(-0.411257\pi\) | ||||
0.275196 | + | 0.961388i | \(0.411257\pi\) | |||||||
\(674\) | −17179.7 | − | 9918.70i | −0.981806 | − | 0.566846i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5743.79 | − | 9948.53i | −0.326797 | − | 0.566030i | ||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27406.2 | − | 15823.0i | 1.53539 | − | 0.886456i | 0.536286 | − | 0.844036i | \(-0.319827\pi\) |
0.999100 | − | 0.0424197i | \(-0.0135066\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1381.52 | − | 2392.86i | 0.0765551 | − | 0.132597i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19258.2 | −1.05336 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23110.9i | − | 1.24520i | −0.782539 | − | 0.622602i | \(-0.786076\pi\) | ||
0.782539 | − | 0.622602i | \(-0.213924\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 6773.22 | − | 3910.52i | 0.362607 | − | 0.209351i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17805.9 | + | 30840.7i | −0.943180 | + | 1.63364i | −0.183826 | + | 0.982959i | \(0.558848\pi\) |
−0.759354 | + | 0.650677i | \(0.774485\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7135.78 | − | 4119.84i | −0.372453 | − | 0.215036i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1661.48 | + | 2877.77i | 0.0863593 | + | 0.149579i | ||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 11418.2i | − | 0.588562i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −32959.0 | + | 19028.9i | −1.68837 | + | 0.974781i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 33573.5 | 1.68143 | ||||||||
\(737\) | 18825.2 | + | 10868.7i | 0.940889 | + | 0.543223i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12662.0 | + | 21931.2i | 0.630283 | + | 1.09168i | 0.987494 | + | 0.157658i | \(0.0503945\pi\) |
−0.357211 | + | 0.934024i | \(0.616272\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4655.40i | 0.229865i | 0.993373 | + | 0.114933i | \(0.0366652\pi\) | ||||
−0.993373 | + | 0.114933i | \(0.963335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20140.2 | + | 11628.0i | −0.988453 | + | 0.570684i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20544.3 | + | 35583.7i | −0.998230 | + | 1.72898i | −0.447610 | + | 0.894229i | \(0.647725\pi\) |
−0.550620 | + | 0.834756i | \(0.685609\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22848.7 | 1.09703 | 0.548514 | − | 0.836141i | \(-0.315194\pi\) | ||||
0.548514 | + | 0.836141i | \(0.315194\pi\) | |||||||
\(758\) | 12549.1 | + | 7245.23i | 0.601325 | + | 0.347175i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 27478.6i | 1.30123i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7249.01 | − | 12555.7i | 0.337950 | − | 0.585347i | ||||
\(773\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25533.1 | −1.17661 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17312.1 | − | 29985.4i | −0.793182 | − | 1.37383i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(788\) | −23307.8 | + | 13456.8i | −1.05369 | + | 0.608347i | ||||
\(789\) | 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 | ||||||||
\(800\) | −20003.3 | − | 11548.9i | −0.884028 | − | 0.510394i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8464.90 | − | 14661.6i | −0.372701 | − | 0.645537i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6413.48 | − | 3702.82i | 0.278722 | − | 0.160920i | −0.354123 | − | 0.935199i | \(-0.615221\pi\) |
0.632845 | + | 0.774279i | \(0.281887\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −258.758 | + | 448.182i | −0.0111418 | + | 0.0192982i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37581.5 | + | 21697.7i | 1.59757 | + | 0.922357i | 0.991954 | + | 0.126599i | \(0.0404061\pi\) |
0.605615 | + | 0.795758i | \(0.292927\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23120.0 | + | 40045.0i | 0.979238 | + | 1.69609i | 0.665176 | + | 0.746687i | \(0.268357\pi\) |
0.314062 | + | 0.949403i | \(0.398310\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46002.9i | 1.93431i | 0.254179 | + | 0.967157i | \(0.418195\pi\) | ||||
−0.254179 | + | 0.967157i | \(0.581805\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(830\) | 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 | ||||||||
\(841\) | −68308.5 | −2.80079 | ||||||||
\(842\) | −22002.9 | − | 12703.4i | −0.900557 | − | 0.519937i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4634.39 | + | 8026.99i | 0.189007 | + | 0.327370i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 3975.22i | − | 0.160978i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1665.24 | + | 961.425i | −0.0670782 | + | 0.0387276i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 230.384 | − | 399.037i | 0.00919902 | − | 0.0159332i | ||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8335.58 | −0.329363 | ||||||||
\(863\) | −40849.5 | − | 23584.5i | −1.61128 | − | 0.930273i | −0.989074 | − | 0.147419i | \(-0.952903\pi\) |
−0.622206 | − | 0.782854i | \(-0.713763\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40655.0i | 1.58703i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −43394.5 | + | 25053.8i | −1.68523 | + | 0.972969i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3275.00 | − | 5672.47i | 0.126099 | − | 0.218410i | −0.796063 | − | 0.605214i | \(-0.793088\pi\) |
0.922162 | + | 0.386804i | \(0.126421\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43014.6 | −1.63936 | −0.819681 | − | 0.572820i | \(-0.805850\pi\) | ||||
−0.819681 | + | 0.572820i | \(0.805850\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9998.06 | − | 17317.1i | −0.379110 | − | 0.656637i | ||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 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 | ||||||||
\(898\) | −12668.1 | + | 21941.7i | −0.470756 | + | 0.815373i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −25492.7 | −0.937913 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7125.01 | + | 12340.9i | 0.260840 | + | 0.451788i | 0.966465 | − | 0.256797i | \(-0.0826671\pi\) |
−0.705625 | + | 0.708585i | \(0.749334\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1065.41i | − | 0.0387473i | −0.999812 | − | 0.0193736i | \(-0.993833\pi\) | ||
0.999812 | − | 0.0193736i | \(-0.00616720\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 25693.3 | − | 14834.0i | 0.929822 | − | 0.536833i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25650.6 | − | 44428.1i | 0.920711 | − | 1.59472i | 0.122395 | − | 0.992482i | \(-0.460943\pi\) |
0.798317 | − | 0.602238i | \(-0.205724\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1322.88 | 0.0470226 | ||||||||
\(926\) | −12167.8 | − | 7025.06i | −0.431811 | − | 0.249306i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −28129.6 | − | 48722.0i | −0.995044 | − | 1.72347i | ||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2154.29i | 0.0757149i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26134.6 | 0.898211 | ||||||||
\(947\) | −49393.3 | − | 28517.3i | −1.69490 | − | 0.978549i | −0.950455 | − | 0.310862i | \(-0.899382\pi\) |
−0.744442 | − | 0.667687i | \(-0.767285\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56795.7i | 1.93053i | 0.261276 | + | 0.965264i | \(0.415857\pi\) | ||||
−0.261276 | + | 0.965264i | \(0.584143\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −25057.7 | + | 14467.1i | −0.847724 | + | 0.489434i | ||||
\(957\) | 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 | \(0.167127\pi\) | |||||||
\(968\) | 8927.62 | + | 5154.36i | 0.296430 | + | 0.171144i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5487.88i | 0.180537i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52484.1 | + | 30301.7i | −1.71864 | + | 0.992259i | −0.797231 | + | 0.603674i | \(0.793703\pi\) |
−0.921413 | + | 0.388585i | \(0.872964\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7489.91 | − | 12972.9i | 0.243394 | − | 0.421570i | ||||
\(983\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 84094.5 | + | 48552.0i | 2.70379 | + | 1.56103i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12077.9 | + | 20919.5i | 0.387150 | + | 0.670564i | 0.992065 | − | 0.125727i | \(-0.0401262\pi\) |
−0.604915 | + | 0.796290i | \(0.706793\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(998\) | −30400.1 | + | 17551.5i | −0.964227 | + | 0.556697i | ||||
\(999\) | 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.p.b.215.3 | 8 | ||
3.2 | odd | 2 | inner | 441.4.p.b.215.2 | 8 | ||
7.2 | even | 3 | 63.4.c.a.62.2 | ✓ | 4 | ||
7.3 | odd | 6 | inner | 441.4.p.b.80.2 | 8 | ||
7.4 | even | 3 | inner | 441.4.p.b.80.2 | 8 | ||
7.5 | odd | 6 | 63.4.c.a.62.2 | ✓ | 4 | ||
7.6 | odd | 2 | CM | 441.4.p.b.215.3 | 8 | ||
21.2 | odd | 6 | 63.4.c.a.62.3 | yes | 4 | ||
21.5 | even | 6 | 63.4.c.a.62.3 | yes | 4 | ||
21.11 | odd | 6 | inner | 441.4.p.b.80.3 | 8 | ||
21.17 | even | 6 | inner | 441.4.p.b.80.3 | 8 | ||
21.20 | even | 2 | inner | 441.4.p.b.215.2 | 8 | ||
28.19 | even | 6 | 1008.4.k.a.881.2 | 4 | |||
28.23 | odd | 6 | 1008.4.k.a.881.2 | 4 | |||
84.23 | even | 6 | 1008.4.k.a.881.1 | 4 | |||
84.47 | odd | 6 | 1008.4.k.a.881.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.c.a.62.2 | ✓ | 4 | 7.2 | even | 3 | ||
63.4.c.a.62.2 | ✓ | 4 | 7.5 | odd | 6 | ||
63.4.c.a.62.3 | yes | 4 | 21.2 | odd | 6 | ||
63.4.c.a.62.3 | yes | 4 | 21.5 | even | 6 | ||
441.4.p.b.80.2 | 8 | 7.3 | odd | 6 | inner | ||
441.4.p.b.80.2 | 8 | 7.4 | even | 3 | inner | ||
441.4.p.b.80.3 | 8 | 21.11 | odd | 6 | inner | ||
441.4.p.b.80.3 | 8 | 21.17 | even | 6 | inner | ||
441.4.p.b.215.2 | 8 | 3.2 | odd | 2 | inner | ||
441.4.p.b.215.2 | 8 | 21.20 | even | 2 | inner | ||
441.4.p.b.215.3 | 8 | 1.1 | even | 1 | trivial | ||
441.4.p.b.215.3 | 8 | 7.6 | odd | 2 | CM | ||
1008.4.k.a.881.1 | 4 | 84.23 | even | 6 | |||
1008.4.k.a.881.1 | 4 | 84.47 | odd | 6 | |||
1008.4.k.a.881.2 | 4 | 28.19 | even | 6 | |||
1008.4.k.a.881.2 | 4 | 28.23 | odd | 6 |