Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [24,4,Mod(11,24)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("24.11");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.f (of order \(2\), degree \(1\), 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: | \(1.41604584014\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(-1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 24.11 |
Dual form | 24.4.f.a.11.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(13\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.82843i | − | 1.00000i | ||||||
\(3\) | 5.00000 | − | 1.41421i | 0.962250 | − | 0.272166i | ||||
\(4\) | −8.00000 | −1.00000 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | −4.00000 | − | 14.1421i | −0.272166 | − | 0.962250i | ||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 22.6274i | 1.00000i | ||||||||
\(9\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 70.7107i | 1.93819i | 0.246691 | + | 0.969094i | \(0.420657\pi\) | ||||
−0.246691 | + | 0.969094i | \(0.579343\pi\) | |||||||
\(12\) | −40.0000 | + | 11.3137i | −0.962250 | + | 0.272166i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 1.00000 | ||||||||
\(17\) | − | 107.480i | − | 1.53340i | −0.642006 | − | 0.766700i | \(-0.721898\pi\) | ||
0.642006 | − | 0.766700i | \(-0.278102\pi\) | |||||||
\(18\) | −40.0000 | − | 65.0538i | −0.523783 | − | 0.851852i | ||||
\(19\) | −106.000 | −1.27990 | −0.639949 | − | 0.768417i | \(-0.721045\pi\) | ||||
−0.639949 | + | 0.768417i | \(0.721045\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 200.000 | 1.93819 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 32.0000 | + | 113.137i | 0.272166 | + | 0.962250i | ||||
\(25\) | −125.000 | −1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 95.0000 | − | 103.238i | 0.677139 | − | 0.735855i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | − | 181.019i | − | 1.00000i | ||||||
\(33\) | 100.000 | + | 353.553i | 0.527508 | + | 1.86502i | ||||
\(34\) | −304.000 | −1.53340 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −184.000 | + | 113.137i | −0.851852 | + | 0.523783i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 299.813i | 1.27990i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 56.5685i | − | 0.215476i | −0.994179 | − | 0.107738i | \(-0.965639\pi\) | ||
0.994179 | − | 0.107738i | \(-0.0343608\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 290.000 | 1.02848 | 0.514239 | − | 0.857647i | \(-0.328074\pi\) | ||||
0.514239 | + | 0.857647i | \(0.328074\pi\) | |||||||
\(44\) | − | 565.685i | − | 1.93819i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 320.000 | − | 90.5097i | 0.962250 | − | 0.272166i | ||||
\(49\) | 343.000 | 1.00000 | ||||||||
\(50\) | 353.553i | 1.00000i | ||||||||
\(51\) | −152.000 | − | 537.401i | −0.417338 | − | 1.47551i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −292.000 | − | 268.701i | −0.735855 | − | 0.677139i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −530.000 | + | 149.907i | −1.23158 | + | 0.348344i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 325.269i | 0.717736i | 0.933388 | + | 0.358868i | \(0.116837\pi\) | ||||
−0.933388 | + | 0.358868i | \(0.883163\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1000.00 | − | 282.843i | 1.86502 | − | 0.527508i | ||||
\(67\) | −70.0000 | −0.127640 | −0.0638199 | − | 0.997961i | \(-0.520328\pi\) | ||||
−0.0638199 | + | 0.997961i | \(0.520328\pi\) | |||||||
\(68\) | 859.842i | 1.53340i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 320.000 | + | 520.431i | 0.523783 | + | 0.851852i | ||||
\(73\) | −430.000 | −0.689420 | −0.344710 | − | 0.938709i | \(-0.612023\pi\) | ||||
−0.344710 | + | 0.938709i | \(0.612023\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −625.000 | + | 176.777i | −0.962250 | + | 0.272166i | ||||
\(76\) | 848.000 | 1.27990 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 329.000 | − | 650.538i | 0.451303 | − | 0.892371i | ||||
\(82\) | −160.000 | −0.215476 | ||||||||
\(83\) | 681.651i | 0.901457i | 0.892661 | + | 0.450728i | \(0.148836\pi\) | ||||
−0.892661 | + | 0.450728i | \(0.851164\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 820.244i | − | 1.02848i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1600.00 | −1.93819 | ||||||||
\(89\) | − | 1329.36i | − | 1.58328i | −0.610988 | − | 0.791640i | \(-0.709227\pi\) | ||
0.610988 | − | 0.791640i | \(-0.290773\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −256.000 | − | 905.097i | −0.272166 | − | 0.962250i | ||||
\(97\) | 1910.00 | 1.99929 | 0.999645 | − | 0.0266459i | \(-0.00848265\pi\) | ||||
0.999645 | + | 0.0266459i | \(0.00848265\pi\) | |||||||
\(98\) | − | 970.151i | − | 1.00000i | ||||||
\(99\) | 1000.00 | + | 1626.35i | 1.01519 | + | 1.65105i | ||||
\(100\) | 1000.00 | 1.00000 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | −1520.00 | + | 429.921i | −1.47551 | + | 0.417338i | ||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1405.73i | − | 1.27006i | −0.772486 | − | 0.635032i | \(-0.780987\pi\) | ||
0.772486 | − | 0.635032i | \(-0.219013\pi\) | |||||||
\(108\) | −760.000 | + | 825.901i | −0.677139 | + | 0.735855i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2387.19i | 1.98733i | 0.112387 | + | 0.993665i | \(0.464150\pi\) | ||||
−0.112387 | + | 0.993665i | \(0.535850\pi\) | |||||||
\(114\) | 424.000 | + | 1499.07i | 0.348344 | + | 1.23158i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 920.000 | 0.717736 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3669.00 | −2.75657 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −80.0000 | − | 282.843i | −0.0586452 | − | 0.207342i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 1448.15i | 1.00000i | ||||||||
\(129\) | 1450.00 | − | 410.122i | 0.989654 | − | 0.279916i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2729.43i | − | 1.82039i | −0.414176 | − | 0.910197i | \(-0.635930\pi\) | ||
0.414176 | − | 0.910197i | \(-0.364070\pi\) | |||||||
\(132\) | −800.000 | − | 2828.43i | −0.527508 | − | 1.86502i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 197.990i | 0.127640i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2432.00 | 1.53340 | ||||||||
\(137\) | 2285.37i | 1.42520i | 0.701571 | + | 0.712599i | \(0.252482\pi\) | ||||
−0.701571 | + | 0.712599i | \(0.747518\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1474.00 | −0.899446 | −0.449723 | − | 0.893168i | \(-0.648477\pi\) | ||||
−0.449723 | + | 0.893168i | \(0.648477\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1472.00 | − | 905.097i | 0.851852 | − | 0.523783i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1216.22i | 0.689420i | ||||||||
\(147\) | 1715.00 | − | 485.075i | 0.962250 | − | 0.272166i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 500.000 | + | 1767.77i | 0.272166 | + | 0.962250i | ||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | − | 2398.51i | − | 1.27990i | ||||||
\(153\) | −1520.00 | − | 2472.05i | −0.803168 | − | 1.30623i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1840.00 | − | 930.553i | −0.892371 | − | 0.451303i | ||||
\(163\) | −970.000 | −0.466112 | −0.233056 | − | 0.972463i | \(-0.574873\pi\) | ||||
−0.233056 | + | 0.972463i | \(0.574873\pi\) | |||||||
\(164\) | 452.548i | 0.215476i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1928.00 | 0.901457 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2197.00 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2438.00 | + | 1499.07i | −1.09028 | + | 0.670389i | ||||
\(172\) | −2320.00 | −1.02848 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4525.48i | 1.93819i | ||||||||
\(177\) | 460.000 | + | 1626.35i | 0.195343 | + | 0.690642i | ||||
\(178\) | −3760.00 | −1.58328 | ||||||||
\(179\) | 2870.85i | 1.19876i | 0.800465 | + | 0.599379i | \(0.204586\pi\) | ||||
−0.800465 | + | 0.599379i | \(0.795414\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7600.00 | 2.97202 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | −2560.00 | + | 724.077i | −0.962250 | + | 0.272166i | ||||
\(193\) | 2090.00 | 0.779490 | 0.389745 | − | 0.920923i | \(-0.372563\pi\) | ||||
0.389745 | + | 0.920923i | \(0.372563\pi\) | |||||||
\(194\) | − | 5402.30i | − | 1.99929i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2744.00 | −1.00000 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 4600.00 | − | 2828.43i | 1.65105 | − | 1.01519i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | − | 2828.43i | − | 1.00000i | ||||||
\(201\) | −350.000 | + | 98.9949i | −0.122821 | + | 0.0347391i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1216.00 | + | 4299.21i | 0.417338 | + | 1.47551i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 7495.33i | − | 2.48068i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6118.00 | −1.99612 | −0.998058 | − | 0.0622910i | \(-0.980159\pi\) | ||||
−0.998058 | + | 0.0622910i | \(0.980159\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3976.00 | −1.27006 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2336.00 | + | 2149.60i | 0.735855 | + | 0.677139i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2150.00 | + | 608.112i | −0.663395 | + | 0.187636i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2875.00 | + | 1767.77i | −0.851852 | + | 0.523783i | ||||
\(226\) | 6752.00 | 1.98733 | ||||||||
\(227\) | 1903.53i | 0.556572i | 0.960498 | + | 0.278286i | \(0.0897663\pi\) | ||||
−0.960498 | + | 0.278286i | \(0.910234\pi\) | |||||||
\(228\) | 4240.00 | − | 1199.25i | 1.23158 | − | 0.348344i | ||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3773.12i | − | 1.06088i | −0.847722 | − | 0.530441i | \(-0.822026\pi\) | ||
0.847722 | − | 0.530441i | \(-0.177974\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 2602.15i | − | 0.717736i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1222.00 | −0.326622 | −0.163311 | − | 0.986575i | \(-0.552217\pi\) | ||||
−0.163311 | + | 0.986575i | \(0.552217\pi\) | |||||||
\(242\) | 10377.5i | 2.75657i | ||||||||
\(243\) | 725.000 | − | 3717.97i | 0.191394 | − | 0.981513i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −800.000 | + | 226.274i | −0.207342 | + | 0.0586452i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 964.000 | + | 3408.25i | 0.245345 | + | 0.867427i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6689.23i | 1.68215i | 0.540916 | + | 0.841077i | \(0.318078\pi\) | ||||
−0.540916 | + | 0.841077i | \(0.681922\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 7274.71i | 1.76570i | 0.469658 | + | 0.882849i | \(0.344377\pi\) | ||||
−0.469658 | + | 0.882849i | \(0.655623\pi\) | |||||||
\(258\) | −1160.00 | − | 4101.22i | −0.279916 | − | 0.989654i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7720.00 | −1.82039 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | −8000.00 | + | 2262.74i | −1.86502 | + | 0.527508i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1880.00 | − | 6646.80i | −0.430914 | − | 1.52351i | ||||
\(268\) | 560.000 | 0.127640 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | − | 6878.73i | − | 1.53340i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6464.00 | 1.42520 | ||||||||
\(275\) | − | 8838.83i | − | 1.93819i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 4169.10i | 0.899446i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1216.22i | 0.258199i | 0.991632 | + | 0.129099i | \(0.0412086\pi\) | ||||
−0.991632 | + | 0.129099i | \(0.958791\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8030.00 | 1.68669 | 0.843346 | − | 0.537371i | \(-0.180582\pi\) | ||||
0.843346 | + | 0.537371i | \(0.180582\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2560.00 | − | 4163.44i | −0.523783 | − | 0.851852i | ||||
\(289\) | −6639.00 | −1.35131 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9550.00 | − | 2701.15i | 1.92382 | − | 0.544138i | ||||
\(292\) | 3440.00 | 0.689420 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | −1372.00 | − | 4850.75i | −0.272166 | − | 0.962250i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7300.00 | + | 6717.51i | 1.42623 | + | 1.31242i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5000.00 | − | 1414.21i | 0.962250 | − | 0.272166i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6784.00 | −1.27990 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6992.00 | + | 4299.21i | −1.30623 | + | 0.803168i | ||||
\(307\) | −7990.00 | −1.48539 | −0.742693 | − | 0.669632i | \(-0.766452\pi\) | ||||
−0.742693 | + | 0.669632i | \(0.766452\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8390.00 | 1.51511 | 0.757557 | − | 0.652769i | \(-0.226393\pi\) | ||||
0.757557 | + | 0.652769i | \(0.226393\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1988.00 | − | 7028.64i | −0.345668 | − | 1.22212i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11392.9i | 1.96259i | ||||||||
\(324\) | −2632.00 | + | 5204.31i | −0.451303 | + | 0.892371i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2743.57i | 0.466112i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1280.00 | 0.215476 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8242.00 | −1.36864 | −0.684322 | − | 0.729180i | \(-0.739902\pi\) | ||||
−0.684322 | + | 0.729180i | \(0.739902\pi\) | |||||||
\(332\) | − | 5453.21i | − | 0.901457i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11410.0 | −1.84434 | −0.922170 | − | 0.386786i | \(-0.873585\pi\) | ||||
−0.922170 | + | 0.386786i | \(0.873585\pi\) | |||||||
\(338\) | − | 6214.05i | − | 1.00000i | ||||||
\(339\) | 3376.00 | + | 11936.0i | 0.540882 | + | 1.91231i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4240.00 | + | 6895.71i | 0.670389 | + | 1.09028i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6561.95i | 1.02848i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 11435.3i | − | 1.76911i | −0.466437 | − | 0.884554i | \(-0.654463\pi\) | ||
0.466437 | − | 0.884554i | \(-0.345537\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12800.0 | 1.93819 | ||||||||
\(353\) | − | 12377.2i | − | 1.86621i | −0.359605 | − | 0.933104i | \(-0.617089\pi\) | ||
0.359605 | − | 0.933104i | \(-0.382911\pi\) | |||||||
\(354\) | 4600.00 | − | 1301.08i | 0.690642 | − | 0.195343i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10634.9i | 1.58328i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8120.00 | 1.19876 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4377.00 | 0.638140 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18345.0 | + | 5188.75i | −2.65251 | + | 0.750244i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −800.000 | − | 1301.08i | −0.112863 | − | 0.183554i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | − | 21496.0i | − | 2.97202i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11666.0 | 1.58111 | 0.790557 | − | 0.612389i | \(-0.209791\pi\) | ||||
0.790557 | + | 0.612389i | \(0.209791\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 2048.00 | + | 7240.77i | 0.272166 | + | 0.962250i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 5911.41i | − | 0.779490i | ||||||
\(387\) | 6670.00 | − | 4101.22i | 0.876112 | − | 0.538699i | ||||
\(388\) | −15280.0 | −1.99929 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 7761.20i | 1.00000i | ||||||||
\(393\) | −3860.00 | − | 13647.2i | −0.495448 | − | 1.75167i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8000.00 | − | 13010.8i | −1.01519 | − | 1.65105i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8000.00 | −1.00000 | ||||||||
\(401\) | 14453.3i | 1.79990i | 0.435989 | + | 0.899952i | \(0.356399\pi\) | ||||
−0.435989 | + | 0.899952i | \(0.643601\pi\) | |||||||
\(402\) | 280.000 | + | 989.949i | 0.0347391 | + | 0.122821i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 12160.0 | − | 3439.37i | 1.47551 | − | 0.417338i | ||||
\(409\) | 16346.0 | 1.97618 | 0.988090 | − | 0.153877i | \(-0.0491758\pi\) | ||||
0.988090 | + | 0.153877i | \(0.0491758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3232.00 | + | 11426.8i | 0.387890 | + | 1.37140i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7370.00 | + | 2084.55i | −0.865493 | + | 0.244798i | ||||
\(418\) | −21200.0 | −2.48068 | ||||||||
\(419\) | − | 3493.11i | − | 0.407278i | −0.979046 | − | 0.203639i | \(-0.934723\pi\) | ||
0.979046 | − | 0.203639i | \(-0.0652769\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 17304.3i | 1.99612i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13435.0i | 1.53340i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11245.8i | 1.27006i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 6080.00 | − | 6607.21i | 0.677139 | − | 0.735855i | ||||
\(433\) | 5510.00 | 0.611533 | 0.305766 | − | 0.952107i | \(-0.401087\pi\) | ||||
0.305766 | + | 0.952107i | \(0.401087\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 1720.00 | + | 6081.12i | 0.187636 | + | 0.663395i | ||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7889.00 | − | 4850.75i | 0.851852 | − | 0.523783i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3736.35i | 0.400721i | 0.979722 | + | 0.200361i | \(0.0642114\pi\) | ||||
−0.979722 | + | 0.200361i | \(0.935789\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 7438.76i | − | 0.781864i | −0.920420 | − | 0.390932i | \(-0.872153\pi\) | ||
0.920420 | − | 0.390932i | \(-0.127847\pi\) | |||||||
\(450\) | 5000.00 | + | 8131.73i | 0.523783 | + | 0.851852i | ||||
\(451\) | 4000.00 | 0.417633 | ||||||||
\(452\) | − | 19097.5i | − | 1.98733i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5384.00 | 0.556572 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3392.00 | − | 11992.5i | −0.348344 | − | 1.23158i | ||||
\(457\) | −18070.0 | −1.84963 | −0.924813 | − | 0.380422i | \(-0.875779\pi\) | ||||
−0.924813 | + | 0.380422i | \(0.875779\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11096.0 | − | 10210.6i | −1.12836 | − | 1.03832i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10672.0 | −1.06088 | ||||||||
\(467\) | − | 13471.8i | − | 1.33490i | −0.744653 | − | 0.667452i | \(-0.767385\pi\) | ||
0.744653 | − | 0.667452i | \(-0.232615\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7360.00 | −0.717736 | ||||||||
\(473\) | 20506.1i | 1.99339i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13250.0 | 1.27990 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3456.34i | 0.326622i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 29352.0 | 2.75657 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10516.0 | − | 2050.61i | −0.981513 | − | 0.191394i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4850.00 | + | 1371.79i | −0.448517 | + | 0.126860i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 18002.9i | − | 1.65471i | −0.561681 | − | 0.827354i | \(-0.689845\pi\) | ||
0.561681 | − | 0.827354i | \(-0.310155\pi\) | |||||||
\(492\) | 640.000 | + | 2262.74i | 0.0586452 | + | 0.207342i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 9640.00 | − | 2726.60i | 0.867427 | − | 0.245345i | ||||
\(499\) | −18214.0 | −1.63401 | −0.817005 | − | 0.576631i | \(-0.804367\pi\) | ||||
−0.817005 | + | 0.576631i | \(0.804367\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18920.0 | 1.68215 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10985.0 | − | 3107.03i | 0.962250 | − | 0.272166i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 11585.2i | − | 1.00000i | ||||||
\(513\) | −10070.0 | + | 10943.2i | −0.866669 | + | 0.941819i | ||||
\(514\) | 20576.0 | 1.76570 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11600.0 | + | 3280.98i | −0.989654 | + | 0.279916i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 21948.6i | − | 1.84565i | −0.385215 | − | 0.922827i | \(-0.625873\pi\) | ||
0.385215 | − | 0.922827i | \(-0.374127\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4750.00 | −0.397138 | −0.198569 | − | 0.980087i | \(-0.563629\pi\) | ||||
−0.198569 | + | 0.980087i | \(0.563629\pi\) | |||||||
\(524\) | 21835.5i | 1.82039i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 6400.00 | + | 22627.4i | 0.527508 | + | 1.86502i | ||||
\(529\) | −12167.0 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4600.00 | + | 7481.19i | 0.375938 | + | 0.611405i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −18800.0 | + | 5317.44i | −1.52351 | + | 0.430914i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 1583.92i | − | 0.127640i | ||||||
\(537\) | 4060.00 | + | 14354.3i | 0.326261 | + | 1.15351i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24253.8i | 1.93819i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −19456.0 | −1.53340 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21850.0 | −1.70793 | −0.853966 | − | 0.520329i | \(-0.825809\pi\) | ||||
−0.853966 | + | 0.520329i | \(0.825809\pi\) | |||||||
\(548\) | − | 18283.0i | − | 1.42520i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −25000.0 | −1.93819 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11792.0 | 0.899446 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 38000.0 | − | 10748.0i | 2.85982 | − | 0.808880i | ||||
\(562\) | 3440.00 | 0.258199 | ||||||||
\(563\) | 12391.3i | 0.927589i | 0.885943 | + | 0.463795i | \(0.153512\pi\) | ||||
−0.885943 | + | 0.463795i | \(0.846488\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 22712.3i | − | 1.68669i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 27039.8i | − | 1.99221i | −0.0881913 | − | 0.996104i | \(-0.528109\pi\) | ||
0.0881913 | − | 0.996104i | \(-0.471891\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27038.0 | 1.98162 | 0.990810 | − | 0.135261i | \(-0.0431872\pi\) | ||||
0.990810 | + | 0.135261i | \(0.0431872\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11776.0 | + | 7240.77i | −0.851852 | + | 0.523783i | ||||
\(577\) | 19550.0 | 1.41053 | 0.705266 | − | 0.708943i | \(-0.250827\pi\) | ||||
0.705266 | + | 0.708943i | \(0.250827\pi\) | |||||||
\(578\) | 18777.9i | 1.35131i | ||||||||
\(579\) | 10450.0 | − | 2955.71i | 0.750064 | − | 0.212150i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −7640.00 | − | 27011.5i | −0.544138 | − | 1.92382i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 9729.79i | − | 0.689420i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26493.9i | 1.86289i | 0.363876 | + | 0.931447i | \(0.381453\pi\) | ||||
−0.363876 | + | 0.931447i | \(0.618547\pi\) | |||||||
\(588\) | −13720.0 | + | 3880.60i | −0.962250 | + | 0.272166i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 12173.6i | − | 0.843015i | −0.906825 | − | 0.421507i | \(-0.861501\pi\) | ||
0.906825 | − | 0.421507i | \(-0.138499\pi\) | |||||||
\(594\) | 19000.0 | − | 20647.5i | 1.31242 | − | 1.42623i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | −4000.00 | − | 14142.1i | −0.272166 | − | 0.962250i | ||||
\(601\) | −14398.0 | −0.977216 | −0.488608 | − | 0.872503i | \(-0.662495\pi\) | ||||
−0.488608 | + | 0.872503i | \(0.662495\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1610.00 | + | 989.949i | −0.108730 | + | 0.0668555i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(608\) | 19188.0i | 1.27990i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 12160.0 | + | 19776.4i | 0.803168 | + | 1.30623i | ||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 22599.1i | 1.48539i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 11206.2i | − | 0.731192i | −0.930774 | − | 0.365596i | \(-0.880865\pi\) | ||
0.930774 | − | 0.365596i | \(-0.119135\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30706.0 | −1.99383 | −0.996913 | − | 0.0785136i | \(-0.974983\pi\) | ||||
−0.996913 | + | 0.0785136i | \(0.974983\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15625.0 | 1.00000 | ||||||||
\(626\) | − | 23730.5i | − | 1.51511i | ||||||
\(627\) | −10600.0 | − | 37476.7i | −0.675157 | − | 2.38704i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −30590.0 | + | 8652.16i | −1.92076 | + | 0.543274i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31763.2i | 1.95721i | 0.205745 | + | 0.978606i | \(0.434038\pi\) | ||||
−0.205745 | + | 0.978606i | \(0.565962\pi\) | |||||||
\(642\) | −19880.0 | + | 5622.91i | −1.22212 | + | 0.345668i | ||||
\(643\) | 28550.0 | 1.75101 | 0.875507 | − | 0.483205i | \(-0.160528\pi\) | ||||
0.875507 | + | 0.483205i | \(0.160528\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 32224.0 | 1.96259 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 14720.0 | + | 7444.42i | 0.892371 | + | 0.451303i | ||||
\(649\) | −23000.0 | −1.39111 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7760.00 | 0.466112 | ||||||||
\(653\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 3620.39i | − | 0.215476i | ||||||
\(657\) | −9890.00 | + | 6081.12i | −0.587284 | + | 0.361107i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16107.9i | 0.952161i | 0.879402 | + | 0.476081i | \(0.157943\pi\) | ||||
−0.879402 | + | 0.476081i | \(0.842057\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 23311.9i | 1.36864i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15424.0 | −0.901457 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19190.0 | 1.09914 | 0.549569 | − | 0.835448i | \(-0.314792\pi\) | ||||
0.549569 | + | 0.835448i | \(0.314792\pi\) | |||||||
\(674\) | 32272.4i | 1.84434i | ||||||||
\(675\) | −11875.0 | + | 12904.7i | −0.677139 | + | 0.735855i | ||||
\(676\) | −17576.0 | −1.00000 | ||||||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | 33760.0 | − | 9548.77i | 1.91231 | − | 0.540882i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2692.00 | + | 9517.66i | 0.151480 | + | 0.535562i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 33632.8i | − | 1.88422i | −0.335300 | − | 0.942112i | \(-0.608838\pi\) | ||
0.335300 | − | 0.942112i | \(-0.391162\pi\) | |||||||
\(684\) | 19504.0 | − | 11992.5i | 1.09028 | − | 0.670389i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 18560.0 | 1.02848 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1978.00 | −0.108895 | −0.0544477 | − | 0.998517i | \(-0.517340\pi\) | ||||
−0.0544477 | + | 0.998517i | \(0.517340\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32344.0 | −1.76911 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6080.00 | −0.330411 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5336.00 | − | 18865.6i | −0.288735 | − | 1.02083i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | − | 36203.9i | − | 1.93819i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −35008.0 | −1.86621 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3680.00 | − | 13010.8i | −0.195343 | − | 0.690642i | ||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 30080.0 | 1.58328 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 22966.8i | − | 1.19876i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 12380.0i | − | 0.638140i | ||||||
\(723\) | −6110.00 | + | 1728.17i | −0.314292 | + | 0.0888953i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 14676.0 | + | 51887.5i | 0.750244 | + | 2.65251i | ||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1633.00 | − | 19615.1i | −0.0829650 | − | 0.996552i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 31169.3i | − | 1.57707i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4949.75i | − | 0.247390i | ||||||
\(738\) | −3680.00 | + | 2262.74i | −0.183554 | + | 0.112863i | ||||
\(739\) | 36074.0 | 1.79567 | 0.897837 | − | 0.440327i | \(-0.145138\pi\) | ||||
0.897837 | + | 0.440327i | \(0.145138\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9640.00 | + | 15678.0i | 0.472168 | + | 0.767908i | ||||
\(748\) | −60800.0 | −2.97202 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9460.00 | + | 33446.2i | 0.457824 | + | 1.61865i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | − | 32996.4i | − | 1.58111i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24381.0i | 1.16138i | 0.814124 | + | 0.580691i | \(0.197218\pi\) | ||||
−0.814124 | + | 0.580691i | \(0.802782\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 20480.0 | − | 5792.62i | 0.962250 | − | 0.272166i | ||||
\(769\) | 40106.0 | 1.88070 | 0.940351 | − | 0.340207i | \(-0.110497\pi\) | ||||
0.940351 | + | 0.340207i | \(0.110497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10288.0 | + | 36373.6i | 0.480562 | + | 1.69904i | ||||
\(772\) | −16720.0 | −0.779490 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | −11600.0 | − | 18865.6i | −0.538699 | − | 0.876112i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 43218.4i | 1.99929i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5996.27i | 0.275788i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21952.0 | 1.00000 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −38600.0 | + | 10917.7i | −1.75167 | + | 0.495448i | ||||
\(787\) | 6950.00 | 0.314791 | 0.157396 | − | 0.987536i | \(-0.449690\pi\) | ||||
0.157396 | + | 0.987536i | \(0.449690\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −36800.0 | + | 22627.4i | −1.65105 | + | 1.01519i | ||||
\(793\) | 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 | ||||||||
\(800\) | 22627.4i | 1.00000i | ||||||||
\(801\) | −18800.0 | − | 30575.3i | −0.829295 | − | 1.34872i | ||||
\(802\) | 40880.0 | 1.79990 | ||||||||
\(803\) | − | 30405.6i | − | 1.33623i | ||||||
\(804\) | 2800.00 | − | 791.960i | 0.122821 | − | 0.0347391i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43727.5i | 1.90034i | 0.311730 | + | 0.950171i | \(0.399092\pi\) | ||||
−0.311730 | + | 0.950171i | \(0.600908\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37582.0 | −1.62723 | −0.813614 | − | 0.581405i | \(-0.802503\pi\) | ||||
−0.813614 | + | 0.581405i | \(0.802503\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −9728.00 | − | 34393.7i | −0.417338 | − | 1.47551i | ||||
\(817\) | −30740.0 | −1.31635 | ||||||||
\(818\) | − | 46233.5i | − | 1.97618i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(822\) | 32320.0 | − | 9141.48i | 1.37140 | − | 0.387890i | ||||
\(823\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12500.0 | − | 44194.2i | −0.527508 | − | 1.86502i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41360.1i | 1.73909i | 0.493850 | + | 0.869547i | \(0.335589\pi\) | ||||
−0.493850 | + | 0.869547i | \(0.664411\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 36865.7i | − | 1.53340i | ||||||
\(834\) | 5896.00 | + | 20845.5i | 0.244798 | + | 0.865493i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 59962.7i | 2.48068i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9880.00 | −0.407278 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24389.0 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1720.00 | + | 6081.12i | 0.0702728 | + | 0.248452i | ||||
\(844\) | 48944.0 | 1.99612 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40150.0 | − | 11356.1i | 1.62302 | − | 0.459060i | ||||
\(850\) | 38000.0 | 1.53340 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 31808.0 | 1.27006 | ||||||||
\(857\) | − | 46589.9i | − | 1.85704i | −0.371289 | − | 0.928518i | \(-0.621084\pi\) | ||
0.371289 | − | 0.928518i | \(-0.378916\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45646.0 | −1.81306 | −0.906532 | − | 0.422138i | \(-0.861280\pi\) | ||||
−0.906532 | + | 0.422138i | \(0.861280\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | −18688.0 | − | 17196.8i | −0.735855 | − | 0.677139i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 15584.6i | − | 0.611533i | ||||||
\(867\) | −33195.0 | + | 9388.96i | −1.30030 | + | 0.367781i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 43930.0 | − | 27011.5i | 1.70310 | − | 1.04719i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 17200.0 | − | 4864.89i | 0.663395 | − | 0.187636i | ||||
\(877\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31508.7i | 1.20494i | 0.798141 | + | 0.602471i | \(0.205817\pi\) | ||||
−0.798141 | + | 0.602471i | \(0.794183\pi\) | |||||||
\(882\) | −13720.0 | − | 22313.5i | −0.523783 | − | 0.851852i | ||||
\(883\) | −5290.00 | −0.201611 | −0.100806 | − | 0.994906i | \(-0.532142\pi\) | ||||
−0.100806 | + | 0.994906i | \(0.532142\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10568.0 | 0.400721 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 46000.0 | + | 23263.8i | 1.72958 | + | 0.874711i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21040.0 | −0.781864 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 23000.0 | − | 14142.1i | 0.851852 | − | 0.523783i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | − | 11313.7i | − | 0.417633i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −54016.0 | −1.98733 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26210.0 | 0.959525 | 0.479762 | − | 0.877399i | \(-0.340723\pi\) | ||||
0.479762 | + | 0.877399i | \(0.340723\pi\) | |||||||
\(908\) | − | 15228.3i | − | 0.556572i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | −33920.0 | + | 9594.02i | −1.23158 | + | 0.348344i | ||||
\(913\) | −48200.0 | −1.74719 | ||||||||
\(914\) | 51109.7i | 1.84963i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −28880.0 | + | 31384.2i | −1.03832 | + | 1.12836i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −39950.0 | + | 11299.6i | −1.42931 | + | 0.404271i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56200.8i | 1.98481i | 0.123007 | + | 0.992406i | \(0.460746\pi\) | ||||
−0.123007 | + | 0.992406i | \(0.539254\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36358.0 | −1.27990 | ||||||||
\(932\) | 30185.0i | 1.06088i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −38104.0 | −1.33490 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56270.0 | 1.96186 | 0.980929 | − | 0.194367i | \(-0.0622652\pi\) | ||||
0.980929 | + | 0.194367i | \(0.0622652\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 41950.0 | − | 11865.3i | 1.45792 | − | 0.412362i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 20817.2i | 0.717736i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 58000.0 | 1.99339 | ||||||||
\(947\) | − | 2525.79i | − | 0.0866705i | −0.999061 | − | 0.0433353i | \(-0.986202\pi\) | ||
0.999061 | − | 0.0433353i | \(-0.0137984\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | − | 37476.7i | − | 1.27990i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36701.7i | 1.24752i | 0.781617 | + | 0.623759i | \(0.214395\pi\) | ||||
−0.781617 | + | 0.623759i | \(0.785605\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29791.0 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19880.0 | − | 32331.8i | −0.665238 | − | 1.08191i | ||||
\(964\) | 9776.00 | 0.326622 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | − | 83020.0i | − | 2.75657i | ||||||
\(969\) | 16112.0 | + | 56964.5i | 0.534151 | + | 1.88851i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 60514.2i | − | 1.99999i | −0.00267705 | − | 0.999996i | \(-0.500852\pi\) | ||
0.00267705 | − | 0.999996i | \(-0.499148\pi\) | |||||||
\(972\) | −5800.00 | + | 29743.7i | −0.191394 | + | 0.981513i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 58554.1i | − | 1.91741i | −0.284399 | − | 0.958706i | \(-0.591794\pi\) | ||
0.284399 | − | 0.958706i | \(-0.408206\pi\) | |||||||
\(978\) | 3880.00 | + | 13717.9i | 0.126860 | + | 0.448517i | ||||
\(979\) | 94000.0 | 3.06870 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −50920.0 | −1.65471 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 6400.00 | − | 1810.19i | 0.207342 | − | 0.0586452i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −41210.0 | + | 11655.9i | −1.31698 | + | 0.372498i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7712.00 | − | 27266.0i | −0.245345 | − | 0.867427i | ||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | 51517.0i | 1.63401i | ||||||||
\(999\) | 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 | 24.4.f.a.11.1 | ✓ | 2 | |
3.2 | odd | 2 | inner | 24.4.f.a.11.2 | yes | 2 | |
4.3 | odd | 2 | 96.4.f.a.47.2 | 2 | |||
8.3 | odd | 2 | CM | 24.4.f.a.11.1 | ✓ | 2 | |
8.5 | even | 2 | 96.4.f.a.47.2 | 2 | |||
12.11 | even | 2 | 96.4.f.a.47.1 | 2 | |||
16.3 | odd | 4 | 768.4.c.l.767.1 | 4 | |||
16.5 | even | 4 | 768.4.c.l.767.1 | 4 | |||
16.11 | odd | 4 | 768.4.c.l.767.4 | 4 | |||
16.13 | even | 4 | 768.4.c.l.767.4 | 4 | |||
24.5 | odd | 2 | 96.4.f.a.47.1 | 2 | |||
24.11 | even | 2 | inner | 24.4.f.a.11.2 | yes | 2 | |
48.5 | odd | 4 | 768.4.c.l.767.3 | 4 | |||
48.11 | even | 4 | 768.4.c.l.767.2 | 4 | |||
48.29 | odd | 4 | 768.4.c.l.767.2 | 4 | |||
48.35 | even | 4 | 768.4.c.l.767.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.4.f.a.11.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
24.4.f.a.11.1 | ✓ | 2 | 8.3 | odd | 2 | CM | |
24.4.f.a.11.2 | yes | 2 | 3.2 | odd | 2 | inner | |
24.4.f.a.11.2 | yes | 2 | 24.11 | even | 2 | inner | |
96.4.f.a.47.1 | 2 | 12.11 | even | 2 | |||
96.4.f.a.47.1 | 2 | 24.5 | odd | 2 | |||
96.4.f.a.47.2 | 2 | 4.3 | odd | 2 | |||
96.4.f.a.47.2 | 2 | 8.5 | even | 2 | |||
768.4.c.l.767.1 | 4 | 16.3 | odd | 4 | |||
768.4.c.l.767.1 | 4 | 16.5 | even | 4 | |||
768.4.c.l.767.2 | 4 | 48.11 | even | 4 | |||
768.4.c.l.767.2 | 4 | 48.29 | odd | 4 | |||
768.4.c.l.767.3 | 4 | 48.5 | odd | 4 | |||
768.4.c.l.767.3 | 4 | 48.35 | even | 4 | |||
768.4.c.l.767.4 | 4 | 16.11 | odd | 4 | |||
768.4.c.l.767.4 | 4 | 16.13 | even | 4 |