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 | 80.1 | ||
Root | \(-2.23256 + 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.80 |
Dual form | 441.4.p.b.215.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.68205 | + | 2.70318i | −1.65535 | + | 0.955719i | −0.680536 | + | 0.732714i | \(0.738253\pi\) |
−0.974817 | + | 0.223005i | \(0.928414\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 10.6144 | − | 18.3846i | 1.32680 | − | 2.29808i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 71.5195i | 3.16074i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 57.8432 | + | 33.3958i | 1.58549 | + | 0.915382i | 0.994037 | + | 0.109042i | \(0.0347782\pi\) |
0.591451 | + | 0.806341i | \(0.298555\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −108.415 | − | 187.780i | −1.69398 | − | 2.93407i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −361.099 | −3.49939 | ||||||||
\(23\) | −108.360 | + | 62.5618i | −0.982377 | + | 0.567176i | −0.902987 | − | 0.429668i | \(-0.858631\pi\) |
−0.0793904 | + | 0.996844i | \(0.525297\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.5000 | − | 108.253i | 0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 69.7031i | − | 0.446329i | −0.974781 | − | 0.223165i | \(-0.928361\pi\) | ||
0.974781 | − | 0.223165i | \(-0.0716388\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(32\) | 519.707 | + | 300.053i | 2.87100 | + | 1.65757i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.29150 | − | 9.16515i | −0.0235113 | − | 0.0407227i | 0.854030 | − | 0.520223i | \(-0.174151\pi\) |
−0.877542 | + | 0.479500i | \(0.840818\pi\) | |||||||
\(38\) | 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 | \(-0.103408\pi\) | ||||
0.947693 | + | 0.319183i | \(0.103408\pi\) | |||||||
\(44\) | 1227.94 | − | 708.951i | 4.20724 | − | 2.42905i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 338.232 | − | 585.835i | 1.08412 | − | 1.87775i | ||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 675.795i | 1.91144i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 56.7049 | + | 32.7386i | 0.146963 | + | 0.0848489i | 0.571678 | − | 0.820478i | \(-0.306293\pi\) |
−0.424716 | + | 0.905327i | \(0.639626\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 188.420 | + | 326.353i | 0.426565 | + | 0.738833i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1509.75 | −2.94873 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −370.000 | + | 640.859i | −0.674667 | + | 1.16856i | 0.301899 | + | 0.953340i | \(0.402379\pi\) |
−0.976566 | + | 0.215218i | \(0.930954\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 205.717i | − | 0.343861i | −0.985109 | − | 0.171931i | \(-0.945000\pi\) | ||
0.985109 | − | 0.171931i | \(-0.0550005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(74\) | 49.5501 | + | 28.6078i | 0.0778390 | + | 0.0449404i | ||||
\(75\) | 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 | ||||||||
\(86\) | −2502.28 | + | 1444.69i | −3.13753 | + | 1.81146i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2388.45 | + | 4136.91i | −2.89329 | + | 5.01132i | ||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2656.22i | 3.01011i | ||||||||
\(93\) | 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 | ||||||||
\(100\) | −1326.80 | − | 2298.08i | −1.32680 | − | 2.29808i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −353.994 | −0.324367 | ||||||||
\(107\) | −1916.98 | + | 1106.77i | −1.73197 | + | 0.999955i | −0.861261 | + | 0.508163i | \(0.830325\pi\) |
−0.870713 | + | 0.491792i | \(0.836342\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1137.67 | − | 1970.51i | 0.999718 | − | 1.73156i | 0.479312 | − | 0.877645i | \(-0.340886\pi\) |
0.520407 | − | 0.853919i | \(-0.325780\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2105.12i | 1.75251i | 0.481849 | + | 0.876254i | \(0.339965\pi\) | ||||
−0.481849 | + | 0.876254i | \(0.660035\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1281.47 | − | 739.856i | −1.02570 | − | 0.592188i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1565.06 | + | 2710.76i | 1.17585 | + | 2.03663i | ||||
\(122\) | 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 | \(0.253760\pi\) | |||||||
\(128\) | 2911.07 | − | 1680.71i | 2.01019 | − | 1.16059i | ||||
\(129\) | 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 | ||||||||
\(134\) | − | 4000.71i | − | 2.57917i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1424.90 | + | 822.668i | 0.888596 | + | 0.513031i | 0.873483 | − | 0.486854i | \(-0.161856\pi\) |
0.0151133 | + | 0.999886i | \(0.495189\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 556.091 | + | 963.177i | 0.328635 | + | 0.569212i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −224.664 | −0.124779 | ||||||||
\(149\) | 2669.52 | − | 1541.25i | 1.46776 | − | 0.847409i | 0.468407 | − | 0.883513i | \(-0.344828\pi\) |
0.999348 | + | 0.0361037i | \(0.0114947\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1124.44 | + | 1947.59i | −0.606000 | + | 1.04962i | 0.385893 | + | 0.922544i | \(0.373893\pi\) |
−0.991893 | + | 0.127079i | \(0.959440\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(158\) | −6479.95 | − | 3741.20i | −3.26277 | − | 1.88376i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 890.000 | + | 1541.53i | 0.427670 | + | 0.740746i | 0.996666 | − | 0.0815946i | \(-0.0260013\pi\) |
−0.568996 | + | 0.822340i | \(0.692668\pi\) | |||||||
\(164\) | 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 | ||||||||
\(172\) | 5672.77 | − | 9825.52i | 2.51479 | − | 4.35575i | ||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 14482.4i | − | 6.20257i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3917.09 | + | 2261.53i | 1.63562 | + | 0.944328i | 0.982315 | + | 0.187237i | \(0.0599533\pi\) |
0.653310 | + | 0.757091i | \(0.273380\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4474.39 | − | 7749.87i | −1.79270 | − | 3.10504i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 435.945 | − | 251.693i | 0.165151 | − | 0.0953502i | −0.415146 | − | 0.909755i | \(-0.636270\pi\) |
0.580298 | + | 0.814405i | \(0.302936\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1386.37 | + | 2401.27i | −0.517064 | + | 0.895581i | 0.482740 | + | 0.875764i | \(0.339642\pi\) |
−0.999804 | + | 0.0198172i | \(0.993692\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2021.80i | 0.731205i | 0.930771 | + | 0.365603i | \(0.119137\pi\) | ||||
−0.930771 | + | 0.365603i | \(0.880863\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(200\) | 7742.21 | + | 4469.97i | 2.73728 | + | 1.58037i | ||||
\(201\) | 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 | \(-0.406617\pi\) | ||||
0.289181 | + | 0.957274i | \(0.406617\pi\) | |||||||
\(212\) | 1203.78 | − | 695.000i | 0.389979 | − | 0.225155i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5983.58 | − | 10363.9i | 1.91135 | − | 3.31056i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 12301.3i | 3.82180i | ||||||||
\(219\) | 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 | ||||||||
\(226\) | −5690.53 | − | 9856.29i | −1.67491 | − | 2.90102i | ||||
\(227\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4985.13 | 1.41073 | ||||||||
\(233\) | −6149.85 | + | 3550.62i | −1.72914 | + | 0.998321i | −0.835611 | + | 0.549322i | \(0.814886\pi\) |
−0.893532 | + | 0.448999i | \(0.851781\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4897.58i | − | 1.32551i | −0.748834 | − | 0.662757i | \(-0.769386\pi\) | ||
0.748834 | − | 0.662757i | \(-0.230614\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(242\) | −14655.3 | − | 8461.26i | −3.89289 | − | 2.24756i | ||||
\(243\) | 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 | ||||||||
\(253\) | −8357.20 | −2.07673 | ||||||||
\(254\) | −9364.09 | + | 5406.36i | −2.31321 | + | 1.33553i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3047.51 | + | 5278.44i | −0.744020 | + | 1.28868i | ||||
\(257\) | 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 | ||||||||
\(263\) | 7070.96 | + | 4082.42i | 1.65785 | + | 0.957159i | 0.973705 | + | 0.227812i | \(0.0731572\pi\) |
0.684144 | + | 0.729347i | \(0.260176\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7854.64 | + | 13604.6i | 1.79029 | + | 3.10088i | ||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8895.29 | −1.96126 | ||||||||
\(275\) | 7230.40 | − | 4174.47i | 1.58549 | − | 0.915382i | ||||
\(276\) | 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 | ||||||||
\(281\) | − | 2841.56i | − | 0.603250i | −0.953427 | − | 0.301625i | \(-0.902471\pi\) | ||
0.953427 | − | 0.301625i | \(-0.0975291\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(284\) | −3782.04 | − | 2183.56i | −0.790220 | − | 0.456234i | ||||
\(285\) | 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 | ||||||||
\(296\) | 655.487 | − | 378.445i | 0.128714 | − | 0.0743131i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8332.54 | + | 14432.4i | −1.61977 | + | 2.80552i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 12158.3i | − | 2.31666i | ||||||
\(303\) | 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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 29380.6 | 5.23034 | ||||||||
\(317\) | 9705.58 | − | 5603.52i | 1.71962 | − | 0.992823i | 0.800014 | − | 0.599982i | \(-0.204825\pi\) |
0.919606 | − | 0.392841i | \(-0.128508\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2327.79 | − | 4031.85i | 0.408562 | − | 0.707650i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8334.04 | − | 4811.66i | −1.41589 | − | 0.817464i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2553.15 | − | 4422.19i | −0.423969 | − | 0.734336i | 0.572354 | − | 0.820006i | \(-0.306030\pi\) |
−0.996324 | + | 0.0856702i | \(0.972697\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11916.5 | 1.92621 | 0.963103 | − | 0.269135i | \(-0.0867376\pi\) | ||||
0.963103 | + | 0.269135i | \(0.0867376\pi\) | |||||||
\(338\) | −10286.5 | + | 5938.89i | −1.65535 | + | 0.955719i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 38223.0i | 5.99083i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4997.21 | − | 2885.14i | −0.773096 | − | 0.446347i | 0.0608819 | − | 0.998145i | \(-0.480609\pi\) |
−0.833978 | + | 0.551798i | \(0.813942\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20041.0 | + | 34712.1i | 3.03463 | + | 5.25613i | ||||
\(353\) | 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 | ||||||||
\(358\) | −24453.3 | −3.61005 | ||||||||
\(359\) | 11654.0 | − | 6728.46i | 1.71330 | − | 0.989177i | 0.783287 | − | 0.621660i | \(-0.213541\pi\) |
0.930017 | − | 0.367517i | \(-0.119792\pi\) | |||||||
\(360\) | 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 | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(368\) | 23495.8 | + | 13565.3i | 3.32826 | + | 1.92157i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6985.00 | − | 12098.4i | −0.969624 | − | 1.67944i | −0.696643 | − | 0.717418i | \(-0.745324\pi\) |
−0.272980 | − | 0.962020i | \(-0.588009\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8704.52 | −1.17974 | −0.589870 | − | 0.807498i | \(-0.700821\pi\) | ||||
−0.589870 | + | 0.807498i | \(0.700821\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1360.74 | + | 2356.88i | −0.182256 | + | 0.315676i | ||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 14990.5i | − | 1.97667i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −391.349 | − | 225.946i | −0.0510082 | − | 0.0294496i | 0.474279 | − | 0.880375i | \(-0.342709\pi\) |
−0.525287 | + | 0.850925i | \(0.676042\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5465.30 | − | 9466.17i | −0.698827 | − | 1.21040i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −27103.8 | −3.38797 | ||||||||
\(401\) | −10764.5 | + | 6214.88i | −1.34053 | + | 0.773956i | −0.986885 | − | 0.161423i | \(-0.948392\pi\) |
−0.353646 | + | 0.935379i | \(0.615058\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 706.855i | − | 0.0860873i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(410\) | 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 | \(0.844753\pi\) | |||||||
\(422\) | −8299.65 | + | 4791.80i | −0.957395 | + | 0.552752i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2341.45 | + | 4055.51i | −0.268186 | + | 0.464511i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 46990.6i | 5.30695i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14879.0 | − | 8590.39i | −1.66287 | − | 0.960057i | −0.971336 | − | 0.237712i | \(-0.923602\pi\) |
−0.691533 | − | 0.722345i | \(-0.743064\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −24151.4 | − | 41831.4i | −2.65285 | − | 4.59487i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12353.2 | − | 7132.14i | 1.32488 | − | 0.764917i | 0.340373 | − | 0.940290i | \(-0.389447\pi\) |
0.984502 | + | 0.175373i | \(0.0561132\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 11421.0i | − | 1.20043i | −0.799841 | − | 0.600213i | \(-0.795083\pi\) | ||
0.799841 | − | 0.600213i | \(-0.204917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 38702.0 | + | 22344.6i | 4.02740 | + | 2.32522i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8910.89 | − | 15434.1i | −0.912109 | − | 1.57982i | −0.811079 | − | 0.584936i | \(-0.801120\pi\) |
−0.101030 | − | 0.994883i | \(-0.532214\pi\) | |||||||
\(458\) | 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 | \(0.639229\pi\) | |||||||
\(464\) | −13088.9 | + | 7556.87i | −1.30956 | + | 0.756075i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19195.9 | − | 33248.3i | 1.90823 | − | 3.30515i | ||||
\(467\) | 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 | ||||||||
\(473\) | 30913.8 | + | 17848.1i | 3.00511 | + | 1.73500i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13239.0 | + | 22930.7i | 1.26682 | + | 2.19420i | ||||
\(479\) | 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 | ||||||||
\(484\) | 66448.4 | 6.24045 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1648.30 | + | 2854.94i | −0.153371 | + | 0.265647i | −0.932465 | − | 0.361261i | \(-0.882346\pi\) |
0.779094 | + | 0.626908i | \(0.215680\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19811.9i | − | 1.82097i | −0.413540 | − | 0.910486i | \(-0.635708\pi\) | ||
0.413540 | − | 0.910486i | \(-0.364292\pi\) | |||||||
\(492\) | 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 | 0.754022 | + | 0.656850i | \(0.228111\pi\) |
0.191838 | + | 0.981427i | \(0.438555\pi\) | |||||||
\(500\) | 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 | ||||||||
\(506\) | 39128.8 | − | 22591.0i | 3.43772 | − | 1.98477i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 21228.8 | − | 36769.3i | 1.85408 | − | 3.21136i | ||||
\(509\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 6060.53i | − | 0.523125i | ||||||
\(513\) | 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 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −44142.1 | −3.65910 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1744.47 | − | 3021.51i | 0.143377 | − | 0.248336i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −45833.9 | − | 26462.2i | −3.69351 | − | 2.13245i | ||||
\(537\) | 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 | \(0.330644\pi\) | |||||||
\(548\) | 30248.9 | − | 17464.2i | 2.35797 | − | 1.36138i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −22568.7 | + | 39090.1i | −1.74970 | + | 3.03056i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 39520.5i | − | 3.03080i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22638.7 | − | 13070.5i | −1.72214 | − | 0.994280i | −0.914473 | − | 0.404646i | \(-0.867395\pi\) |
−0.807671 | − | 0.589634i | \(-0.799272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7681.25 | + | 13304.3i | 0.576538 | + | 0.998593i | ||||
\(563\) | 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 | ||||||||
\(568\) | 14712.8 | 1.08686 | ||||||||
\(569\) | −18679.9 | + | 10784.9i | −1.37628 | + | 0.794596i | −0.991710 | − | 0.128499i | \(-0.958984\pi\) |
−0.384572 | + | 0.923095i | \(0.625651\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3394.00 | + | 5878.58i | −0.248747 | + | 0.430842i | −0.963178 | − | 0.268863i | \(-0.913352\pi\) |
0.714431 | + | 0.699705i | \(0.246685\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15640.5i | 1.13435i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(578\) | −23002.9 | − | 13280.7i | −1.65535 | − | 0.955719i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2186.66 | + | 3787.41i | 0.155338 | + | 0.269054i | ||||
\(584\) | 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 | ||||||||
\(592\) | −1147.36 | + | 1987.28i | −0.0796555 | + | 0.137967i | ||||
\(593\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 65437.5i | − | 4.49736i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5507.54 | − | 3179.78i | −0.375680 | − | 0.216899i | 0.300257 | − | 0.953858i | \(-0.402927\pi\) |
−0.675937 | + | 0.736960i | \(0.736261\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 23870.6 | + | 41345.0i | 1.60808 | + | 2.78527i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7505.00 | − | 12999.0i | 0.494493 | − | 0.856487i | −0.505487 | − | 0.862834i | \(-0.668687\pi\) |
0.999980 | + | 0.00634752i | \(0.00202049\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23368.2i | 1.52474i | 0.647139 | + | 0.762372i | \(0.275965\pi\) | ||||
−0.647139 | + | 0.762372i | \(0.724035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(620\) | 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 | \(0.190488\pi\) | |||||||
\(632\) | −85721.7 | + | 49491.5i | −5.39530 | + | 3.11498i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −30294.6 | + | 52471.9i | −1.89772 | + | 3.28695i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 25169.8i | 1.56188i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13681.5 | + | 7899.04i | 0.843040 | + | 0.486729i | 0.858296 | − | 0.513154i | \(-0.171523\pi\) |
−0.0152566 | + | 0.999884i | \(0.504857\pi\) | |||||||
\(642\) | 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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 37787.2 | 2.26972 | ||||||||
\(653\) | −4594.75 | + | 2652.78i | −0.275354 | + | 0.158976i | −0.631318 | − | 0.775524i | \(-0.717486\pi\) |
0.355964 | + | 0.934500i | \(0.384153\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25166.1i | 1.48761i | 0.668399 | + | 0.743803i | \(0.266980\pi\) | ||||
−0.668399 | + | 0.743803i | \(0.733020\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(662\) | 23907.9 | + | 13803.3i | 1.40364 | + | 0.810391i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4360.76 | + | 7553.05i | 0.253147 | + | 0.438464i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9609.37 | −0.550392 | −0.275196 | − | 0.961388i | \(-0.588743\pi\) | ||||
−0.275196 | + | 0.961388i | \(0.588743\pi\) | |||||||
\(674\) | −55793.4 | + | 32212.4i | −3.18855 | + | 1.84091i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23319.8 | − | 40391.1i | 1.32680 | − | 2.29808i | ||||
\(677\) | 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 | ||||||||
\(683\) | −14308.6 | − | 8261.08i | −0.801616 | − | 0.462813i | 0.0424197 | − | 0.999100i | \(-0.486493\pi\) |
−0.844036 | + | 0.536286i | \(0.819827\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −57941.5 | − | 100358.i | −3.21076 | − | 5.56119i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31196.2 | 1.70633 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29047.8i | 1.56508i | 0.622602 | + | 0.782539i | \(0.286076\pi\) | ||||
−0.622602 | + | 0.782539i | \(0.713924\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −87328.8 | − | 50419.3i | −4.67518 | − | 2.69922i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17805.9 | + | 30840.7i | 0.943180 | + | 1.63364i | 0.759354 | + | 0.650677i | \(0.225515\pi\) |
0.183826 | + | 0.982959i | \(0.441152\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 83154.9 | − | 48009.5i | 4.34028 | − | 2.50586i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −36376.5 | + | 63005.9i | −1.89075 | + | 3.27487i | ||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 37082.2i | − | 1.91144i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7545.59 | − | 4356.45i | −0.386532 | − | 0.223165i | ||||
\(726\) | 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 | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −75087.5 | −3.76055 | ||||||||
\(737\) | −42804.0 | + | 24712.9i | −2.13935 | + | 1.23516i | ||||
\(738\) | 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 | ||||||||
\(743\) | − | 40237.0i | − | 1.98675i | −0.114933 | − | 0.993373i | \(-0.536665\pi\) | ||
0.114933 | − | 0.993373i | \(-0.463335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 65408.2 | + | 37763.4i | 3.21014 | + | 1.85338i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20544.3 | + | 35583.7i | 0.998230 | + | 1.72898i | 0.550620 | + | 0.834756i | \(0.314391\pi\) |
0.447610 | + | 0.894229i | \(0.352275\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22848.7 | −1.09703 | −0.548514 | − | 0.836141i | \(-0.684806\pi\) | ||||
−0.548514 | + | 0.836141i | \(0.684806\pi\) | |||||||
\(758\) | 40755.0 | − | 23529.9i | 1.95289 | − | 1.12750i | ||||
\(759\) | 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 | ||||||||
\(764\) | − | 10686.3i | − | 0.506041i | ||||||
\(765\) | 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 | ||||||||
\(772\) | 29431.0 | + | 50976.0i | 1.37208 | + | 2.37651i | ||||
\(773\) | 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 | ||||||||
\(778\) | 2443.09 | 0.112582 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6870.08 | − | 11899.3i | 0.314764 | − | 0.545188i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(788\) | 37170.1 | + | 21460.2i | 1.68037 | + | 0.970161i | ||||
\(789\) | 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 | ||||||||
\(800\) | 64963.4 | − | 37506.6i | 2.87100 | − | 1.65757i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 33599.9 | − | 58196.7i | 1.47937 | − | 2.56234i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39335.6 | − | 22710.4i | −1.70948 | − | 0.986967i | −0.935199 | − | 0.354123i | \(-0.884779\pi\) |
−0.774279 | − | 0.632845i | \(-0.781887\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1910.76 | + | 3309.53i | 0.0822752 | + | 0.142505i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15741.4 | + | 9088.31i | −0.669159 | + | 0.386339i | −0.795758 | − | 0.605615i | \(-0.792927\pi\) |
0.126599 | + | 0.991954i | \(0.459594\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | − | 12090.1i | − | 0.508359i | −0.967157 | − | 0.254179i | \(-0.918195\pi\) | ||
0.967157 | − | 0.254179i | \(-0.0818054\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(830\) | 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 | ||||||||
\(841\) | 19530.5 | 0.800790 | ||||||||
\(842\) | 71457.4 | − | 41256.0i | 2.92469 | − | 1.68857i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18815.6 | − | 32589.6i | 0.767370 | − | 1.32912i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 14197.4i | − | 0.574931i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1146.78 | + | 662.092i | 0.0461939 | + | 0.0266701i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −79155.4 | − | 137101.i | −3.16060 | − | 5.47432i | ||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 92885.6 | 3.67018 | ||||||||
\(863\) | −16109.7 | + | 9300.93i | −0.635435 | + | 0.366868i | −0.782854 | − | 0.622206i | \(-0.786237\pi\) |
0.147419 | + | 0.989074i | \(0.452903\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 92439.5i | 3.60851i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 140930. | + | 81365.8i | 5.47303 | + | 3.15985i | ||||
\(873\) | 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 | ||||||||
\(883\) | 43014.6 | 1.63936 | 0.819681 | − | 0.572820i | \(-0.194150\pi\) | ||||
0.819681 | + | 0.572820i | \(0.194150\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38558.9 | + | 66786.0i | −1.46209 | + | 2.53242i | ||||
\(887\) | 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 | ||||||||
\(898\) | 30873.1 | + | 53473.7i | 1.14727 | + | 1.98713i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −150557. | −5.53923 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7125.01 | + | 12340.9i | −0.260840 | + | 0.451788i | −0.966465 | − | 0.256797i | \(-0.917333\pi\) |
0.705625 | + | 0.708585i | \(0.250666\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 54982.7i | − | 1.99962i | −0.0193736 | − | 0.999812i | \(-0.506167\pi\) | ||
0.0193736 | − | 0.999812i | \(-0.493833\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 83442.4 | + | 48175.5i | 3.01973 | + | 1.74344i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25650.6 | − | 44428.1i | −0.920711 | − | 1.59472i | −0.798317 | − | 0.602238i | \(-0.794276\pi\) |
−0.122395 | − | 0.992482i | \(-0.539057\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1322.88 | −0.0470226 | ||||||||
\(926\) | 39516.5 | − | 22814.9i | 1.40237 | − | 0.809657i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 20914.6 | − | 36225.2i | 0.739824 | − | 1.28141i | ||||
\(929\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 150750.i | 5.29828i | ||||||||
\(933\) | 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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −192987. | −6.63270 | ||||||||
\(947\) | 10398.7 | − | 6003.70i | 0.356824 | − | 0.206013i | −0.310862 | − | 0.950455i | \(-0.600618\pi\) |
0.667687 | + | 0.744442i | \(0.267285\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 15373.4i | − | 0.522553i | −0.965264 | − | 0.261276i | \(-0.915857\pi\) | ||
0.965264 | − | 0.261276i | \(-0.0841434\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −90040.2 | − | 51984.8i | −3.04614 | − | 1.75869i | ||||
\(957\) | 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 | \(0.167127\pi\) | |||||||
\(968\) | −193872. | + | 111932.i | −6.43727 | + | 3.71656i | ||||
\(969\) | 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 | ||||||||
\(974\) | − | 17822.6i | − | 0.586319i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6568.41 | − | 3792.27i | −0.215089 | − | 0.124182i | 0.388585 | − | 0.921413i | \(-0.372964\pi\) |
−0.603674 | + | 0.797231i | \(0.706297\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 53555.1 | + | 92760.1i | 1.74034 | + | 3.01435i | ||||
\(983\) | 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 | ||||||||
\(989\) | −57912.3 | + | 33435.7i | −1.86198 | + | 1.07502i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12077.9 | + | 20919.5i | −0.387150 | + | 0.670564i | −0.992065 | − | 0.125727i | \(-0.959874\pi\) |
0.604915 | + | 0.796290i | \(0.293207\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(998\) | −98728.6 | − | 57001.0i | −3.13146 | − | 1.80795i | ||||
\(999\) | 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.80.1 | 8 | ||
3.2 | odd | 2 | inner | 441.4.p.b.80.4 | 8 | ||
7.2 | even | 3 | inner | 441.4.p.b.215.4 | 8 | ||
7.3 | odd | 6 | 63.4.c.a.62.1 | ✓ | 4 | ||
7.4 | even | 3 | 63.4.c.a.62.1 | ✓ | 4 | ||
7.5 | odd | 6 | inner | 441.4.p.b.215.4 | 8 | ||
7.6 | odd | 2 | CM | 441.4.p.b.80.1 | 8 | ||
21.2 | odd | 6 | inner | 441.4.p.b.215.1 | 8 | ||
21.5 | even | 6 | inner | 441.4.p.b.215.1 | 8 | ||
21.11 | odd | 6 | 63.4.c.a.62.4 | yes | 4 | ||
21.17 | even | 6 | 63.4.c.a.62.4 | yes | 4 | ||
21.20 | even | 2 | inner | 441.4.p.b.80.4 | 8 | ||
28.3 | even | 6 | 1008.4.k.a.881.4 | 4 | |||
28.11 | odd | 6 | 1008.4.k.a.881.4 | 4 | |||
84.11 | even | 6 | 1008.4.k.a.881.3 | 4 | |||
84.59 | odd | 6 | 1008.4.k.a.881.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.c.a.62.1 | ✓ | 4 | 7.3 | odd | 6 | ||
63.4.c.a.62.1 | ✓ | 4 | 7.4 | even | 3 | ||
63.4.c.a.62.4 | yes | 4 | 21.11 | odd | 6 | ||
63.4.c.a.62.4 | yes | 4 | 21.17 | even | 6 | ||
441.4.p.b.80.1 | 8 | 1.1 | even | 1 | trivial | ||
441.4.p.b.80.1 | 8 | 7.6 | odd | 2 | CM | ||
441.4.p.b.80.4 | 8 | 3.2 | odd | 2 | inner | ||
441.4.p.b.80.4 | 8 | 21.20 | even | 2 | inner | ||
441.4.p.b.215.1 | 8 | 21.2 | odd | 6 | inner | ||
441.4.p.b.215.1 | 8 | 21.5 | even | 6 | inner | ||
441.4.p.b.215.4 | 8 | 7.2 | even | 3 | inner | ||
441.4.p.b.215.4 | 8 | 7.5 | odd | 6 | inner | ||
1008.4.k.a.881.3 | 4 | 84.11 | even | 6 | |||
1008.4.k.a.881.3 | 4 | 84.59 | odd | 6 | |||
1008.4.k.a.881.4 | 4 | 28.3 | even | 6 | |||
1008.4.k.a.881.4 | 4 | 28.11 | odd | 6 |