Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(17,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 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("336.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bc (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: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.257 |
Dual form | 336.4.bc.a.17.1 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −4.50000 | + | 2.59808i | −0.866025 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.5000 | + | 0.866025i | −0.998906 | + | 0.0467610i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 13.5000 | − | 23.3827i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 29.4449i | − | 0.628195i | −0.949391 | − | 0.314098i | \(-0.898298\pi\) | ||
0.949391 | − | 0.314098i | \(-0.101702\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −25.5000 | − | 14.7224i | −0.307900 | − | 0.177766i | 0.338086 | − | 0.941115i | \(-0.390220\pi\) |
−0.645986 | + | 0.763349i | \(0.723554\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 81.0000 | − | 51.9615i | 0.841698 | − | 0.539949i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.5000 | + | 108.253i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 140.296i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 298.500 | − | 172.339i | 1.72943 | − | 0.998484i | 0.837192 | − | 0.546908i | \(-0.184195\pi\) |
0.892233 | − | 0.451576i | \(-0.149138\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −216.500 | + | 374.989i | −0.961956 | + | 1.66616i | −0.244377 | + | 0.969680i | \(0.578583\pi\) |
−0.717579 | + | 0.696477i | \(0.754750\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 76.5000 | + | 132.502i | 0.314098 | + | 0.544033i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 449.000 | 1.59237 | 0.796184 | − | 0.605054i | \(-0.206849\pi\) | ||||
0.796184 | + | 0.605054i | \(0.206849\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 341.500 | − | 32.0429i | 0.995627 | − | 0.0934196i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 153.000 | 0.355532 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 810.000 | + | 467.654i | 1.70016 | + | 0.981589i | 0.945584 | + | 0.325379i | \(0.105492\pi\) |
0.754578 | + | 0.656210i | \(0.227842\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −229.500 | + | 444.271i | −0.458957 | + | 0.888459i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 503.500 | + | 872.088i | 0.918094 | + | 1.59019i | 0.802307 | + | 0.596912i | \(0.203606\pi\) |
0.115787 | + | 0.993274i | \(0.463061\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 730.500 | − | 421.754i | 1.17121 | − | 0.676200i | 0.217248 | − | 0.976117i | \(-0.430292\pi\) |
0.953966 | + | 0.299916i | \(0.0969588\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −562.500 | − | 324.760i | −0.866025 | − | 0.500000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 251.500 | − | 435.611i | 0.358177 | − | 0.620380i | −0.629480 | − | 0.777017i | \(-0.716732\pi\) |
0.987656 | + | 0.156637i | \(0.0500652\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −364.500 | − | 631.333i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.5000 | + | 544.730i | 0.0293750 | + | 0.627508i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −895.500 | + | 1551.05i | −0.998484 | + | 1.72943i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1371.78i | − | 1.43591i | −0.696088 | − | 0.717957i | \(-0.745078\pi\) | ||
0.696088 | − | 0.717957i | \(-0.254922\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1810.50 | − | 1045.29i | −1.73198 | − | 0.999959i | −0.870534 | − | 0.492109i | \(-0.836226\pi\) |
−0.861446 | − | 0.507850i | \(-0.830440\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −783.500 | − | 1357.06i | −0.688493 | − | 1.19250i | −0.972325 | − | 0.233630i | \(-0.924939\pi\) |
0.283833 | − | 0.958874i | \(-0.408394\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2249.93i | − | 1.92391i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −688.500 | − | 397.506i | −0.544033 | − | 0.314098i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −665.500 | + | 1152.68i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2647.00 | 1.84947 | 0.924737 | − | 0.380606i | \(-0.124285\pi\) | ||||
0.924737 | + | 0.380606i | \(0.124285\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2020.50 | + | 1166.54i | −1.37903 | + | 0.796184i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 484.500 | + | 250.281i | 0.315876 | + | 0.163174i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1217.63i | 0.743008i | 0.928431 | + | 0.371504i | \(0.121158\pi\) | ||||
−0.928431 | + | 0.371504i | \(0.878842\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1453.50 | + | 1031.44i | −0.815528 | + | 0.578717i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −874.000 | − | 1513.81i | −0.471027 | − | 0.815843i | 0.528424 | − | 0.848981i | \(-0.322783\pi\) |
−0.999451 | + | 0.0331378i | \(0.989450\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 702.000 | − | 405.300i | 0.356852 | − | 0.206028i | −0.310847 | − | 0.950460i | \(-0.600613\pi\) |
0.667699 | + | 0.744432i | \(0.267279\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1700.00 | + | 2944.49i | −0.816897 | + | 1.41491i | 0.0910600 | + | 0.995845i | \(0.470974\pi\) |
−0.907957 | + | 0.419062i | \(0.862359\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1330.00 | 0.605371 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −688.500 | + | 397.506i | −0.307900 | + | 0.177766i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1250.00 | − | 1948.56i | −0.539949 | − | 0.841698i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4709.45i | − | 1.93398i | −0.254814 | − | 0.966990i | \(-0.582014\pi\) | ||
0.254814 | − | 0.966990i | \(-0.417986\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4860.00 | −1.96318 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −121.500 | − | 2595.48i | −0.0467610 | − | 0.998906i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2555.50 | + | 4426.26i | 0.953103 | + | 1.65082i | 0.738650 | + | 0.674089i | \(0.235464\pi\) |
0.214453 | + | 0.976734i | \(0.431203\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1755.00 | − | 1013.25i | 0.625169 | − | 0.360942i | −0.153710 | − | 0.988116i | \(-0.549122\pi\) |
0.778879 | + | 0.627175i | \(0.215789\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4531.50 | − | 2616.26i | −1.59019 | − | 0.918094i | ||||
\(202\) | 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 | ||||||||
\(211\) | 6032.00 | 1.96806 | 0.984028 | − | 0.178011i | \(-0.0569664\pi\) | ||||
0.984028 | + | 0.178011i | \(0.0569664\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5373.00 | + | 3446.78i | −1.68084 | + | 1.07826i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2191.50 | + | 3795.79i | −0.676200 | + | 1.17121i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5830.08i | − | 1.75072i | −0.483469 | − | 0.875362i | \(-0.660623\pi\) | ||
0.483469 | − | 0.875362i | \(-0.339377\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3375.00 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1054.50 | + | 608.816i | 0.304294 | + | 0.175684i | 0.644370 | − | 0.764714i | \(-0.277120\pi\) |
−0.340076 | + | 0.940398i | \(0.610453\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2613.66i | 0.716353i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1080.00 | − | 623.538i | 0.288668 | − | 0.166662i | −0.348673 | − | 0.937244i | \(-0.613368\pi\) |
0.637341 | + | 0.770582i | \(0.280034\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3280.50 | + | 1894.00i | 0.866025 | + | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −433.500 | + | 750.844i | −0.111672 | + | 0.193421i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3680.50 | − | 7124.79i | 0.882993 | − | 1.70932i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7695.00 | + | 4442.71i | 1.72486 | + | 0.995850i | 0.907935 | + | 0.419111i | \(0.137658\pi\) |
0.816928 | + | 0.576739i | \(0.195675\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1530.00 | − | 2385.03i | −0.339193 | − | 0.528750i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2583.50 | + | 4474.75i | 0.560388 | + | 0.970620i | 0.997462 | + | 0.0711951i | \(0.0226813\pi\) |
−0.437074 | + | 0.899425i | \(0.643985\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 9306.31i | − | 1.99697i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7534.50 | + | 4350.05i | −1.58261 | + | 0.913722i | −0.588137 | + | 0.808761i | \(0.700138\pi\) |
−0.994476 | + | 0.104961i | \(0.966528\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2456.50 | − | 4254.78i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3564.00 | + | 6173.03i | 0.717957 | + | 1.24354i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8306.50 | + | 388.845i | −1.59063 | + | 0.0744607i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8419.50i | 1.56523i | 0.622505 | + | 0.782616i | \(0.286115\pi\) | ||||
−0.622505 | + | 0.782616i | \(0.713885\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10863.0 | 1.99992 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9559.50 | + | 5519.18i | 1.72631 | + | 0.996685i | 0.903832 | + | 0.427888i | \(0.140742\pi\) |
0.822478 | + | 0.568797i | \(0.192591\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3187.50 | − | 1840.30i | 0.544033 | − | 0.314098i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7051.50 | + | 4071.19i | 1.19250 | + | 0.688493i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4949.50 | + | 8572.79i | −0.821901 | + | 1.42357i | 0.0823644 | + | 0.996602i | \(0.473753\pi\) |
−0.904265 | + | 0.426971i | \(0.859580\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5845.50 | + | 10124.7i | 0.961956 | + | 1.66616i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7363.00 | 1.19017 | 0.595086 | − | 0.803662i | \(-0.297118\pi\) | ||||
0.595086 | + | 0.803662i | \(0.297118\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6290.00 | + | 888.542i | −0.990169 | + | 0.139874i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5300.08i | − | 0.812913i | −0.913670 | − | 0.406456i | \(-0.866764\pi\) | ||
0.913670 | − | 0.406456i | \(-0.133236\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4131.00 | 0.628195 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 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 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2996.00 | − | 5189.22i | −0.436798 | − | 0.756557i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 6916.08i | − | 1.00000i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2536.50 | + | 1464.45i | −0.360774 | + | 0.208293i | −0.669420 | − | 0.742884i | \(-0.733457\pi\) |
0.308646 | + | 0.951177i | \(0.400124\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −125.500 | + | 217.372i | −0.0174213 | + | 0.0301746i | −0.874605 | − | 0.484837i | \(-0.838879\pi\) |
0.857183 | + | 0.515011i | \(0.172212\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14687.0 | 1.99056 | 0.995278 | − | 0.0970683i | \(-0.0309465\pi\) | ||||
0.995278 | + | 0.0970683i | \(0.0309465\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11911.5 | + | 6877.11i | −1.60169 | + | 0.924737i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6061.50 | − | 10498.8i | 0.796184 | − | 1.37903i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7723.50 | − | 4459.16i | −0.976401 | − | 0.563726i | −0.0752196 | − | 0.997167i | \(-0.523966\pi\) |
−0.901182 | + | 0.433441i | \(0.857299\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2830.50 | + | 132.502i | −0.355143 | + | 0.0166250i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5074.50 | − | 8789.29i | −0.627243 | − | 1.08642i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12394.5 | + | 7155.97i | −1.49846 | + | 0.865134i | −0.999998 | − | 0.00177990i | \(-0.999433\pi\) |
−0.498458 | + | 0.866914i | \(0.666100\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3163.50 | − | 5479.34i | −0.371504 | − | 0.643464i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10459.0 | −1.21078 | −0.605392 | − | 0.795927i | \(-0.706984\pi\) | ||||
−0.605392 | + | 0.795927i | \(0.706984\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15390.0 | − | 7950.11i | −1.74420 | − | 0.901014i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 11159.6i | − | 1.23856i | −0.785170 | − | 0.619280i | \(-0.787425\pi\) | ||
0.785170 | − | 0.619280i | \(-0.212575\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9315.00 | − | 5378.02i | −1.01271 | − | 0.584690i | −0.100728 | − | 0.994914i | \(-0.532117\pi\) |
−0.911985 | + | 0.410224i | \(0.865450\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3861.00 | − | 8417.77i | 0.416910 | − | 0.908948i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7866.00 | + | 4541.44i | 0.815843 | + | 0.471027i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9603.50 | + | 16633.7i | −0.983004 | + | 1.70261i | −0.332513 | + | 0.943099i | \(0.607897\pi\) |
−0.650491 | + | 0.759514i | \(0.725437\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7811.00 | −0.784034 | −0.392017 | − | 0.919958i | \(-0.628223\pi\) | ||||
−0.392017 | + | 0.919958i | \(0.628223\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10070.0 | − | 15697.6i | −0.991449 | − | 1.54552i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2106.00 | + | 3647.70i | −0.206028 | + | 0.356852i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3680.61i | − | 0.355532i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11041.5 | + | 6374.81i | 1.04667 | + | 0.604296i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7398.50 | + | 12814.6i | 0.688415 | + | 1.19237i | 0.972351 | + | 0.233526i | \(0.0750265\pi\) |
−0.283936 | + | 0.958843i | \(0.591640\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 17666.9i | − | 1.63379i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3303.50 | − | 5721.83i | 0.296363 | − | 0.513315i | −0.678938 | − | 0.734195i | \(-0.737560\pi\) |
0.975301 | + | 0.220880i | \(0.0708930\pi\) | |||||||
\(500\) | 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 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5985.00 | + | 3455.44i | −0.524267 | + | 0.302685i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13149.0 | + | 8435.09i | −1.13831 | + | 0.730228i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2065.50 | − | 3577.55i | 0.177766 | − | 0.307900i | ||||
\(514\) | 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 | ||||||||
\(523\) | −17980.5 | − | 10381.0i | −1.50331 | − | 0.867938i | −0.999993 | − | 0.00383755i | \(-0.998778\pi\) |
−0.503320 | − | 0.864100i | \(-0.667888\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10687.5 | + | 5520.91i | 0.888459 | + | 0.458957i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6083.50 | − | 10536.9i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10394.5 | + | 18003.8i | −0.826053 | + | 1.43077i | 0.0750596 | + | 0.997179i | \(0.476085\pi\) |
−0.901112 | + | 0.433586i | \(0.857248\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12235.5 | + | 21192.5i | 0.966990 | + | 1.67488i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1640.00 | −0.128193 | −0.0640963 | − | 0.997944i | \(-0.520416\pi\) | ||||
−0.0640963 | + | 0.997944i | \(0.520416\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 21870.0 | − | 12626.7i | 1.70016 | − | 0.981589i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4275.50 | + | 8276.60i | −0.328775 | + | 0.636450i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13220.7i | − | 1.00032i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 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 | ||||||||
\(567\) | 7290.00 | + | 11364.0i | 0.539949 | + | 0.841698i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 314.500 | + | 544.730i | 0.0230498 | + | 0.0399234i | 0.877320 | − | 0.479905i | \(-0.159329\pi\) |
−0.854270 | + | 0.519829i | \(0.825996\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4048.50 | − | 2337.40i | 0.292099 | − | 0.168644i | −0.346789 | − | 0.937943i | \(-0.612728\pi\) |
0.638888 | + | 0.769300i | \(0.279395\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22999.5 | − | 13278.8i | −1.65082 | − | 0.953103i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10149.0 | −0.709987 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5265.00 | + | 9119.25i | −0.360942 | + | 0.625169i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26935.1i | 1.82813i | 0.405567 | + | 0.914065i | \(0.367074\pi\) | ||||
−0.405567 | + | 0.914065i | \(0.632926\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27189.0 | 1.83619 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17278.5 | + | 9975.75i | 1.15538 | + | 0.667056i | 0.950191 | − | 0.311667i | \(-0.100887\pi\) |
0.205184 | + | 0.978723i | \(0.434221\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8695.00 | − | 15060.2i | −0.572900 | − | 0.992292i | −0.996266 | − | 0.0863334i | \(-0.972485\pi\) |
0.423366 | − | 0.905959i | \(-0.360848\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26674.5 | − | 15400.5i | 1.73205 | − | 0.999999i | 0.865424 | − | 0.501040i | \(-0.167049\pi\) |
0.866625 | − | 0.498959i | \(-0.166284\pi\) | |||||||
\(620\) | 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 | ||||||||
\(631\) | −1892.00 | −0.119365 | −0.0596825 | − | 0.998217i | \(-0.519009\pi\) | ||||
−0.0596825 | + | 0.998217i | \(0.519009\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −27144.0 | + | 15671.6i | −1.70439 | + | 0.984028i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −943.500 | − | 10055.4i | −0.0586858 | − | 0.625448i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3521.26i | 0.215964i | 0.994153 | + | 0.107982i | \(0.0344389\pi\) | ||||
−0.994153 | + | 0.107982i | \(0.965561\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | 15223.5 | − | 29470.0i | 0.916522 | − | 1.77422i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 22774.7i | − | 1.35240i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27106.5 | − | 15649.9i | 1.59504 | − | 0.920896i | 0.602615 | − | 0.798032i | \(-0.294125\pi\) |
0.992423 | − | 0.122864i | \(-0.0392080\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15147.0 | + | 26235.4i | 0.875362 | + | 1.51617i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33949.0 | 1.94448 | 0.972242 | − | 0.233977i | \(-0.0751742\pi\) | ||||
0.972242 | + | 0.233977i | \(0.0751742\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15187.5 | + | 8768.51i | −0.866025 | + | 0.500000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1188.00 | + | 25378.0i | 0.0671447 | + | 1.43434i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6327.00 | −0.351368 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2053.50 | + | 1185.59i | 0.113052 | + | 0.0652705i | 0.555460 | − | 0.831543i | \(-0.312542\pi\) |
−0.442408 | + | 0.896814i | \(0.645876\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11041.5 | − | 6374.81i | 0.592373 | − | 0.342007i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18073.0 | − | 31303.4i | 0.957328 | − | 1.65814i | 0.228381 | − | 0.973572i | \(-0.426657\pi\) |
0.728948 | − | 0.684569i | \(-0.240010\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6790.50 | − | 11761.5i | −0.358177 | − | 0.620380i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34399.5 | + | 17770.0i | 1.77684 | + | 0.917876i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3240.00 | + | 5611.84i | −0.166662 | + | 0.288668i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28182.2i | 1.43772i | 0.695157 | + | 0.718858i | \(0.255335\pi\) | ||||
−0.695157 | + | 0.718858i | \(0.744665\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19683.0 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27190.5 | − | 15698.4i | −1.37013 | − | 0.791044i | −0.379184 | − | 0.925321i | \(-0.623795\pi\) |
−0.990944 | + | 0.134277i | \(0.957129\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18711.5 | − | 32409.3i | −0.931412 | − | 1.61325i | −0.780910 | − | 0.624644i | \(-0.785244\pi\) |
−0.150502 | − | 0.988610i | \(-0.548089\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 4505.06i | − | 0.223344i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20510.5 | + | 35525.2i | −0.996590 | + | 1.72614i | −0.426832 | + | 0.904331i | \(0.640370\pi\) |
−0.569757 | + | 0.821813i | \(0.692963\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41470.0 | 1.99109 | 0.995543 | − | 0.0943039i | \(-0.0300625\pi\) | ||||
0.995543 | + | 0.0943039i | \(0.0300625\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 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 | ||||||||
\(763\) | 15670.0 | + | 24427.1i | 0.743502 | + | 1.15901i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17211.4i | 0.807098i | 0.914958 | + | 0.403549i | \(0.132224\pi\) | ||||
−0.914958 | + | 0.403549i | \(0.867776\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37312.5 | + | 21542.4i | 1.72943 | + | 0.998484i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1948.50 | + | 41623.8i | 0.0899640 | + | 1.92181i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7047.00 | − | 4068.59i | 0.319185 | − | 0.184281i | −0.331844 | − | 0.943334i | \(-0.607671\pi\) |
0.651029 | + | 0.759053i | \(0.274338\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13770.0 | − | 23850.3i | 0.616629 | − | 1.06803i | ||||
\(794\) | 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 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 24162.1i | − | 1.04617i | −0.852280 | − | 0.523087i | \(-0.824780\pi\) | ||
0.852280 | − | 0.523087i | \(-0.175220\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −46170.0 | −1.99170 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11449.5 | − | 6610.37i | −0.490290 | − | 0.283069i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13081.5 | + | 6757.60i | 0.558125 | + | 0.288314i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6110.00 | − | 10582.8i | −0.258786 | − | 0.448231i | 0.707131 | − | 0.707083i | \(-0.249989\pi\) |
−0.965917 | + | 0.258852i | \(0.916656\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6505.50 | − | 3755.95i | 0.272552 | − | 0.157358i | −0.357495 | − | 0.933915i | \(-0.616369\pi\) |
0.630047 | + | 0.776557i | \(0.283036\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23251.5 | − | 13424.3i | −0.970620 | − | 0.560388i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24178.5 | + | 41878.4i | 0.998484 | + | 1.72943i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24389.0 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11313.5 | − | 21900.9i | 0.458957 | − | 0.888459i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22603.5 | − | 39150.4i | 0.913722 | − | 1.58261i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31736.4i | 1.27390i | 0.770907 | + | 0.636948i | \(0.219803\pi\) | ||||
−0.770907 | + | 0.636948i | \(0.780197\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34155.0 | + | 19719.4i | 1.35664 | + | 0.783256i | 0.989169 | − | 0.146779i | \(-0.0468906\pi\) |
0.367470 | + | 0.930035i | \(0.380224\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25528.7i | 1.00000i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25678.5 | − | 14825.5i | 0.998947 | − | 0.576742i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −32076.0 | − | 18519.1i | −1.24354 | − | 0.717957i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25075.0 | + | 43431.2i | −0.965476 | + | 1.67225i | −0.257146 | + | 0.966373i | \(0.582782\pi\) |
−0.708330 | + | 0.705881i | \(0.750551\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31429.0 | −1.19781 | −0.598907 | − | 0.800818i | \(-0.704398\pi\) | ||||
−0.598907 | + | 0.800818i | \(0.704398\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48969.5 | + | 2292.37i | −1.84745 | + | 0.0864832i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36369.0 | − | 23330.7i | 1.34029 | − | 0.859798i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2303.50 | − | 3989.78i | −0.0843291 | − | 0.146062i | 0.820776 | − | 0.571250i | \(-0.193541\pi\) |
−0.905105 | + | 0.425188i | \(0.860208\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24786.5 | − | 42931.5i | 0.889697 | − | 1.54100i | 0.0494625 | − | 0.998776i | \(-0.484249\pi\) |
0.840234 | − | 0.542224i | \(-0.182417\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21874.5 | − | 37887.7i | −0.782616 | − | 1.35553i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −54125.0 | −1.92391 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −48883.5 | + | 28222.9i | −1.73198 | + | 0.999959i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9180.00 | − | 4210.62i | −0.323160 | − | 0.148225i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55306.1i | 1.92825i | 0.265445 | + | 0.964126i | \(0.414481\pi\) | ||||
−0.265445 | + | 0.964126i | \(0.585519\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −57357.0 | −1.99337 | ||||||||
\(940\) | 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 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12418.5 | − | 21509.5i | −0.424786 | − | 0.735750i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44506.0 | − | 77086.7i | 1.49394 | − | 2.58758i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53927.0 | −1.79336 | −0.896678 | − | 0.442683i | \(-0.854027\pi\) | ||||
−0.896678 | + | 0.442683i | \(0.854027\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 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 | ||||||||
\(973\) | −1054.50 | − | 22526.2i | −0.0347438 | − | 0.742196i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9562.50 | + | 16562.7i | −0.314098 | + | 0.544033i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42309.0 | −1.37699 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 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 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29834.5 | − | 51674.9i | −0.956331 | − | 1.65641i | −0.731292 | − | 0.682064i | \(-0.761082\pi\) |
−0.225039 | − | 0.974350i | \(-0.572251\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 51436.7i | − | 1.64380i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45901.5 | − | 26501.2i | 1.45809 | − | 0.841828i | 0.459172 | − | 0.888347i | \(-0.348146\pi\) |
0.998917 | + | 0.0465191i | \(0.0148128\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −52609.5 | − | 30374.1i | −1.66616 | − | 0.961956i |
(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 | 336.4.bc.a.257.1 | 2 | ||
3.2 | odd | 2 | CM | 336.4.bc.a.257.1 | 2 | ||
4.3 | odd | 2 | 84.4.k.b.5.1 | ✓ | 2 | ||
7.3 | odd | 6 | inner | 336.4.bc.a.17.1 | 2 | ||
12.11 | even | 2 | 84.4.k.b.5.1 | ✓ | 2 | ||
21.17 | even | 6 | inner | 336.4.bc.a.17.1 | 2 | ||
28.3 | even | 6 | 84.4.k.b.17.1 | yes | 2 | ||
28.11 | odd | 6 | 588.4.k.a.521.1 | 2 | |||
28.19 | even | 6 | 588.4.f.b.293.1 | 2 | |||
28.23 | odd | 6 | 588.4.f.b.293.2 | 2 | |||
28.27 | even | 2 | 588.4.k.a.509.1 | 2 | |||
84.11 | even | 6 | 588.4.k.a.521.1 | 2 | |||
84.23 | even | 6 | 588.4.f.b.293.2 | 2 | |||
84.47 | odd | 6 | 588.4.f.b.293.1 | 2 | |||
84.59 | odd | 6 | 84.4.k.b.17.1 | yes | 2 | ||
84.83 | odd | 2 | 588.4.k.a.509.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.k.b.5.1 | ✓ | 2 | 4.3 | odd | 2 | ||
84.4.k.b.5.1 | ✓ | 2 | 12.11 | even | 2 | ||
84.4.k.b.17.1 | yes | 2 | 28.3 | even | 6 | ||
84.4.k.b.17.1 | yes | 2 | 84.59 | odd | 6 | ||
336.4.bc.a.17.1 | 2 | 7.3 | odd | 6 | inner | ||
336.4.bc.a.17.1 | 2 | 21.17 | even | 6 | inner | ||
336.4.bc.a.257.1 | 2 | 1.1 | even | 1 | trivial | ||
336.4.bc.a.257.1 | 2 | 3.2 | odd | 2 | CM | ||
588.4.f.b.293.1 | 2 | 28.19 | even | 6 | |||
588.4.f.b.293.1 | 2 | 84.47 | odd | 6 | |||
588.4.f.b.293.2 | 2 | 28.23 | odd | 6 | |||
588.4.f.b.293.2 | 2 | 84.23 | even | 6 | |||
588.4.k.a.509.1 | 2 | 28.27 | even | 2 | |||
588.4.k.a.509.1 | 2 | 84.83 | odd | 2 | |||
588.4.k.a.521.1 | 2 | 28.11 | odd | 6 | |||
588.4.k.a.521.1 | 2 | 84.11 | even | 6 |