Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,4,Mod(5,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.f (of order \(4\), degree \(2\), 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: | \(2.30107449022\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.5 |
Dual form | 39.4.f.a.8.1 |
$q$-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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(3\) | −5.19615 | −1.00000 | ||||||||
\(4\) | − | 8.00000i | − | 1.00000i | ||||||
\(5\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −25.5885 | − | 25.5885i | −1.38165 | − | 1.38165i | −0.841698 | − | 0.539949i | \(-0.818443\pi\) |
−0.539949 | − | 0.841698i | \(-0.681557\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 27.0000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(12\) | 41.5692i | 1.00000i | ||||||||
\(13\) | 31.1769 | + | 35.0000i | 0.665148 | + | 0.746712i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −64.0000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 49.9423 | − | 49.9423i | 0.603029 | − | 0.603029i | −0.338086 | − | 0.941115i | \(-0.609780\pi\) |
0.941115 | + | 0.338086i | \(0.109780\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 132.962 | + | 132.962i | 1.38165 | + | 1.38165i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 125.000i | − | 1.00000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −140.296 | −1.00000 | ||||||||
\(28\) | −204.708 | + | 204.708i | −1.38165 | + | 1.38165i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 231.942 | − | 231.942i | 1.34381 | − | 1.34381i | 0.451576 | − | 0.892233i | \(-0.350862\pi\) |
0.892233 | − | 0.451576i | \(-0.149138\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 216.000i | − | 1.00000i | ||||||
\(37\) | −163.238 | − | 163.238i | −0.725303 | − | 0.725303i | 0.244377 | − | 0.969680i | \(-0.421417\pi\) |
−0.969680 | + | 0.244377i | \(0.921417\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −162.000 | − | 181.865i | −0.665148 | − | 0.746712i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 218.238i | 0.773978i | 0.922084 | + | 0.386989i | \(0.126485\pi\) | ||||
−0.922084 | + | 0.386989i | \(0.873515\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | 332.554 | 1.00000 | ||||||||
\(49\) | 966.538i | 2.81790i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 280.000 | − | 249.415i | 0.746712 | − | 0.665148i | ||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −259.508 | + | 259.508i | −0.603029 | + | 0.603029i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 935.307 | 1.96318 | 0.981589 | − | 0.191006i | \(-0.0611749\pi\) | ||||
0.981589 | + | 0.191006i | \(0.0611749\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −690.888 | − | 690.888i | −1.38165 | − | 1.38165i | ||||
\(64\) | 512.000i | 1.00000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 112.642 | − | 112.642i | 0.205395 | − | 0.205395i | −0.596912 | − | 0.802307i | \(-0.703606\pi\) |
0.802307 | + | 0.596912i | \(0.203606\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −407.939 | − | 407.939i | −0.654049 | − | 0.654049i | 0.299916 | − | 0.953966i | \(-0.403041\pi\) |
−0.953966 | + | 0.299916i | \(0.903041\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 649.519i | 1.00000i | ||||||||
\(76\) | −399.538 | − | 399.538i | −0.603029 | − | 0.603029i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1091.19 | −1.55403 | −0.777017 | − | 0.629480i | \(-0.783268\pi\) | ||||
−0.777017 | + | 0.629480i | \(0.783268\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | 1063.69 | − | 1063.69i | 1.38165 | − | 1.38165i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 97.8269 | − | 1693.37i | 0.112693 | − | 1.95069i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1205.21 | + | 1205.21i | −1.34381 | + | 1.34381i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 20.8921 | − | 20.8921i | 0.0218688 | − | 0.0218688i | −0.696088 | − | 0.717957i | \(-0.745078\pi\) |
0.717957 | + | 0.696088i | \(0.245078\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1000.00 | −1.00000 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1028.84i | 0.984218i | 0.870534 | + | 0.492109i | \(0.163774\pi\) | ||||
−0.870534 | + | 0.492109i | \(0.836226\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 1122.37i | 1.00000i | ||||||||
\(109\) | 1414.19 | − | 1414.19i | 1.24271 | − | 1.24271i | 0.283833 | − | 0.958874i | \(-0.408394\pi\) |
0.958874 | − | 0.283833i | \(-0.0916061\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 848.212 | + | 848.212i | 0.725303 | + | 0.725303i | ||||
\(112\) | 1637.66 | + | 1637.66i | 1.38165 | + | 1.38165i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 841.777 | + | 945.000i | 0.665148 | + | 0.746712i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1331.00i | 1.00000i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1855.54 | − | 1855.54i | −1.34381 | − | 1.34381i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 380.000i | − | 0.265508i | −0.991149 | − | 0.132754i | \(-0.957618\pi\) | ||
0.991149 | − | 0.132754i | \(-0.0423821\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1134.00i | − | 0.773978i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2555.89 | −1.66635 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2576.00 | 1.57190 | 0.785948 | − | 0.618293i | \(-0.212175\pi\) | ||||
0.785948 | + | 0.618293i | \(0.212175\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1728.00 | −1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 5022.28i | − | 2.81790i | ||||||
\(148\) | −1305.91 | + | 1305.91i | −0.725303 | + | 0.725303i | ||||
\(149\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −762.788 | − | 762.788i | −0.411091 | − | 0.411091i | 0.471027 | − | 0.882119i | \(-0.343883\pi\) |
−0.882119 | + | 0.471027i | \(0.843883\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1454.92 | + | 1296.00i | −0.746712 | + | 0.665148i | ||||
\(157\) | 3850.00 | 1.95709 | 0.978546 | − | 0.206028i | \(-0.0660539\pi\) | ||||
0.978546 | + | 0.206028i | \(0.0660539\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −499.689 | − | 499.689i | −0.240114 | − | 0.240114i | 0.576783 | − | 0.816897i | \(-0.304308\pi\) |
−0.816897 | + | 0.576783i | \(0.804308\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −253.000 | + | 2182.38i | −0.115157 | + | 0.993347i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1348.44 | − | 1348.44i | 0.603029 | − | 0.603029i | ||||
\(172\) | 1745.91 | 0.773978 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3198.56 | + | 3198.56i | −1.38165 | + | 1.38165i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3429.46i | − | 1.40834i | −0.710031 | − | 0.704171i | \(-0.751319\pi\) | ||
0.710031 | − | 0.704171i | \(-0.248681\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4860.00 | −1.96318 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3589.96 | + | 3589.96i | 1.38165 | + | 1.38165i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | − | 2660.43i | − | 1.00000i | ||||||
\(193\) | 3193.86 | + | 3193.86i | 1.19119 | + | 1.19119i | 0.976734 | + | 0.214453i | \(0.0687968\pi\) |
0.214453 | + | 0.976734i | \(0.431203\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7732.31 | 2.81790 | ||||||||
\(197\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5236.00i | 1.86518i | 0.360942 | + | 0.932588i | \(0.382455\pi\) | ||||
−0.360942 | + | 0.932588i | \(0.617545\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −585.307 | + | 585.307i | −0.205395 | + | 0.205395i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1995.32 | − | 2240.00i | −0.665148 | − | 0.746712i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1091.19 | −0.356023 | −0.178011 | − | 0.984028i | \(-0.556966\pi\) | ||||
−0.178011 | + | 0.984028i | \(0.556966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11870.1 | −3.71334 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2119.71 | + | 2119.71i | 0.654049 | + | 0.654049i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4525.04 | − | 4525.04i | 1.35883 | − | 1.35883i | 0.483469 | − | 0.875362i | \(-0.339377\pi\) |
0.875362 | − | 0.483469i | \(-0.160623\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 3375.00i | − | 1.00000i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(228\) | 2076.06 | + | 2076.06i | 0.603029 | + | 0.603029i | ||||
\(229\) | −4883.04 | − | 4883.04i | −1.40908 | − | 1.40908i | −0.764714 | − | 0.644370i | \(-0.777120\pi\) |
−0.644370 | − | 0.764714i | \(-0.722880\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5670.00 | 1.55403 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4312.54 | − | 4312.54i | −1.15268 | − | 1.15268i | −0.986014 | − | 0.166662i | \(-0.946701\pi\) |
−0.166662 | − | 0.986014i | \(-0.553299\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3788.00 | −1.00000 | ||||||||
\(244\) | − | 7482.46i | − | 1.96318i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3305.03 | + | 190.934i | 0.851392 | + | 0.0491855i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −5527.11 | + | 5527.11i | −1.38165 | + | 1.38165i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8354.04i | 2.00423i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −901.139 | − | 901.139i | −0.205395 | − | 0.205395i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4848.71 | + | 4848.71i | 1.08686 | + | 1.08686i | 0.995850 | + | 0.0910064i | \(0.0290084\pi\) |
0.0910064 | + | 0.995850i | \(0.470992\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −508.323 | + | 8798.98i | −0.112693 | + | 1.95069i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 8293.06i | − | 1.79885i | −0.437074 | − | 0.899425i | \(-0.643985\pi\) | ||
0.437074 | − | 0.899425i | \(-0.356015\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6262.44 | − | 6262.44i | 1.34381 | − | 1.34381i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5600.00i | 1.17627i | 0.808761 | + | 0.588137i | \(0.200138\pi\) | ||||
−0.808761 | + | 0.588137i | \(0.799862\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4913.00 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −108.559 | + | 108.559i | −0.0218688 | + | 0.0218688i | ||||
\(292\) | −3263.51 | + | 3263.51i | −0.654049 | + | 0.654049i | ||||
\(293\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5196.15 | 1.00000 | ||||||||
\(301\) | 5584.38 | − | 5584.38i | 1.06936 | − | 1.06936i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3196.31 | + | 3196.31i | −0.603029 | + | 0.603029i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6115.01 | + | 6115.01i | 1.13681 | + | 1.13681i | 0.989018 | + | 0.147797i | \(0.0472182\pi\) |
0.147797 | + | 0.989018i | \(0.452782\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 5346.00i | − | 0.984218i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4738.89 | −0.855776 | −0.427888 | − | 0.903832i | \(-0.640742\pi\) | ||||
−0.427888 | + | 0.903832i | \(0.640742\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8729.54i | 1.55403i | ||||||||
\(317\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 5832.00i | − | 1.00000i | ||||||
\(325\) | 4375.00 | − | 3897.11i | 0.746712 | − | 0.665148i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7348.36 | + | 7348.36i | −1.24271 | + | 1.24271i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6497.56 | + | 6497.56i | −1.07897 | + | 1.07897i | −0.0823644 | + | 0.996602i | \(0.526247\pi\) |
−0.996602 | + | 0.0823644i | \(0.973753\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4407.44 | − | 4407.44i | −0.725303 | − | 0.725303i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −8509.54 | − | 8509.54i | −1.38165 | − | 1.38165i | ||||
\(337\) | − | 4930.00i | − | 0.796897i | −0.917191 | − | 0.398448i | \(-0.869549\pi\) | ||
0.917191 | − | 0.398448i | \(-0.130451\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15955.4 | − | 15955.4i | 2.51169 | − | 2.51169i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3306.96 | + | 3306.96i | 0.507214 | + | 0.507214i | 0.913670 | − | 0.406456i | \(-0.133236\pi\) |
−0.406456 | + | 0.913670i | \(0.633236\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4374.00 | − | 4910.36i | −0.665148 | − | 0.746712i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1870.54i | 0.272713i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 6916.08i | − | 1.00000i | ||||||
\(364\) | −13546.9 | − | 782.615i | −1.95069 | − | 0.112693i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4340.00 | −0.617292 | −0.308646 | − | 0.951177i | \(-0.599876\pi\) | ||||
−0.308646 | + | 0.951177i | \(0.599876\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9641.66 | + | 9641.66i | 1.34381 | + | 1.34381i | ||||
\(373\) | 7420.11 | 1.03002 | 0.515011 | − | 0.857183i | \(-0.327788\pi\) | ||||
0.515011 | + | 0.857183i | \(0.327788\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10293.6 | + | 10293.6i | −1.39510 | + | 1.39510i | −0.581702 | + | 0.813402i | \(0.697613\pi\) |
−0.813402 | + | 0.581702i | \(0.802387\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1974.54i | 0.265508i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5892.44i | 0.773978i | ||||||||
\(388\) | −167.137 | − | 167.137i | −0.0218688 | − | 0.0218688i | ||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7292.76 | + | 7292.76i | 0.921947 | + | 0.921947i | 0.997167 | − | 0.0752196i | \(-0.0239658\pi\) |
−0.0752196 | + | 0.997167i | \(0.523966\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13280.8 | 1.66635 | ||||||||
\(400\) | 8000.00i | 1.00000i | ||||||||
\(401\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15349.2 | + | 886.735i | 1.89727 | + | 0.109607i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3047.69 | − | 3047.69i | 0.368456 | − | 0.368456i | −0.498458 | − | 0.866914i | \(-0.666100\pi\) |
0.866914 | + | 0.498458i | \(0.166100\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8230.71 | 0.984218 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13385.3 | −1.57190 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7477.81 | + | 7477.81i | −0.865668 | + | 0.865668i | −0.991989 | − | 0.126322i | \(-0.959683\pi\) |
0.126322 | + | 0.991989i | \(0.459683\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23933.1 | − | 23933.1i | −2.71242 | − | 2.71242i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(432\) | 8978.95 | 1.00000 | ||||||||
\(433\) | − | 2590.00i | − | 0.287454i | −0.989617 | − | 0.143727i | \(-0.954091\pi\) | ||
0.989617 | − | 0.143727i | \(-0.0459087\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11313.5 | − | 11313.5i | −1.24271 | − | 1.24271i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10756.0i | 1.16938i | 0.811257 | + | 0.584690i | \(0.198784\pi\) | ||||
−0.811257 | + | 0.584690i | \(0.801216\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 26096.5i | 2.81790i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | 6785.69 | − | 6785.69i | 0.725303 | − | 0.725303i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13101.3 | − | 13101.3i | 1.38165 | − | 1.38165i | ||||
\(449\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3963.56 | + | 3963.56i | 0.411091 | + | 0.411091i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1065.11 | + | 1065.11i | −0.109023 | + | 0.109023i | −0.759514 | − | 0.650491i | \(-0.774563\pi\) |
0.650491 | + | 0.759514i | \(0.274563\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8689.69 | − | 8689.69i | −0.872233 | − | 0.872233i | 0.120482 | − | 0.992716i | \(-0.461556\pi\) |
−0.992716 | + | 0.120482i | \(0.961556\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 7560.00 | − | 6734.21i | 0.746712 | − | 0.665148i | ||||
\(469\) | −5764.69 | −0.567566 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20005.2 | −1.95709 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6242.79 | − | 6242.79i | −0.603029 | − | 0.603029i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 624.074 | − | 10802.6i | 0.0591587 | − | 1.02403i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10648.0 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12959.7 | − | 12959.7i | 1.20588 | − | 1.20588i | 0.233526 | − | 0.972351i | \(-0.424974\pi\) |
0.972351 | − | 0.233526i | \(-0.0750265\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2596.46 | + | 2596.46i | 0.240114 | + | 0.240114i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14844.3 | + | 14844.3i | −1.34381 | + | 1.34381i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 615.940 | − | 615.940i | 0.0552570 | − | 0.0552570i | −0.678938 | − | 0.734195i | \(-0.737560\pi\) |
0.734195 | + | 0.678938i | \(0.237560\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1314.63 | − | 11340.0i | 0.115157 | − | 0.993347i | ||||
\(508\) | −3040.00 | −0.265508 | ||||||||
\(509\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20877.0i | 1.80733i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7006.71 | + | 7006.71i | −0.603029 | + | 0.603029i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9072.00 | −0.773978 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12040.0 | 1.00664 | 0.503320 | − | 0.864100i | \(-0.332112\pi\) | ||||
0.503320 | + | 0.864100i | \(0.332112\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16620.2 | − | 16620.2i | 1.38165 | − | 1.38165i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12167.0 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 20447.1i | 1.66635i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16795.0 | + | 16795.0i | 1.33470 | + | 1.33470i | 0.901112 | + | 0.433586i | \(0.142752\pi\) |
0.433586 | + | 0.901112i | \(0.357248\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17820.0i | 1.40834i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1640.00 | 0.128193 | 0.0640963 | − | 0.997944i | \(-0.479584\pi\) | ||||
0.0640963 | + | 0.997944i | \(0.479584\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25253.3 | 1.96318 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27921.9 | + | 27921.9i | 2.14713 | + | 2.14713i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 20608.0i | − | 1.57190i | ||||||
\(557\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7638.34 | + | 6804.00i | −0.577938 | + | 0.514810i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18654.0 | − | 18654.0i | −1.38165 | − | 1.38165i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 23312.0i | − | 1.70854i | −0.519829 | − | 0.854270i | \(-0.674004\pi\) | ||
0.519829 | − | 0.854270i | \(-0.325996\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 13824.0i | 1.00000i | ||||||||
\(577\) | −19517.5 | + | 19517.5i | −1.40819 | + | 1.40819i | −0.638888 | + | 0.769300i | \(0.720605\pi\) |
−0.769300 | + | 0.638888i | \(0.779395\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16595.8 | − | 16595.8i | −1.19119 | − | 1.19119i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(588\) | −40178.2 | −2.81790 | ||||||||
\(589\) | − | 23167.5i | − | 1.62071i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10447.3 | + | 10447.3i | 0.725303 | + | 0.725303i | ||||
\(593\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 27207.1i | − | 1.86518i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3117.69 | −0.211603 | −0.105801 | − | 0.994387i | \(-0.533741\pi\) | ||||
−0.105801 | + | 0.994387i | \(0.533741\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3041.34 | − | 3041.34i | 0.205395 | − | 0.205395i | ||||
\(604\) | −6102.30 | + | 6102.30i | −0.411091 | + | 0.411091i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28420.0 | 1.90038 | 0.950191 | − | 0.311667i | \(-0.100887\pi\) | ||||
0.950191 | + | 0.311667i | \(0.100887\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21134.6 | − | 21134.6i | 1.39253 | − | 1.39253i | 0.572900 | − | 0.819625i | \(-0.305818\pi\) |
0.819625 | − | 0.572900i | \(-0.194182\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5611.71 | + | 5611.71i | 0.364384 | + | 0.364384i | 0.865424 | − | 0.501040i | \(-0.167049\pi\) |
−0.501040 | + | 0.865424i | \(0.667049\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 10368.0 | + | 11639.4i | 0.665148 | + | 0.746712i | ||||
\(625\) | −15625.0 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 30800.0i | − | 1.95709i | ||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16768.3 | − | 16768.3i | −1.05790 | − | 1.05790i | −0.998217 | − | 0.0596825i | \(-0.980991\pi\) |
−0.0596825 | − | 0.998217i | \(-0.519009\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5670.00 | 0.356023 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33828.8 | + | 30133.7i | −2.10416 | + | 1.87432i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21498.2 | + | 21498.2i | −1.31851 | + | 1.31851i | −0.403561 | + | 0.914953i | \(0.632228\pi\) |
−0.914953 | + | 0.403561i | \(0.867772\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 61678.8 | 3.71334 | ||||||||
\(652\) | −3997.51 | + | 3997.51i | −0.240114 | + | 0.240114i | ||||
\(653\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11014.3 | − | 11014.3i | −0.654049 | − | 0.654049i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3320.96 | + | 3320.96i | 0.195416 | + | 0.195416i | 0.798032 | − | 0.602615i | \(-0.205875\pi\) |
−0.602615 | + | 0.798032i | \(0.705875\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23512.8 | + | 23512.8i | −1.35883 | + | 1.35883i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 25315.7i | − | 1.45000i | −0.688751 | − | 0.724998i | \(-0.741841\pi\) | ||
0.688751 | − | 0.724998i | \(-0.258159\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17537.0i | 1.00000i | ||||||||
\(676\) | 17459.1 | + | 2024.00i | 0.993347 | + | 0.115157i | ||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1069.19 | −0.0604299 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(684\) | −10787.5 | − | 10787.5i | −0.603029 | − | 0.603029i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25373.0 | + | 25373.0i | 1.40908 | + | 1.40908i | ||||
\(688\) | − | 13967.3i | − | 0.773978i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8253.94 | − | 8253.94i | 0.454406 | − | 0.454406i | −0.442408 | − | 0.896814i | \(-0.645876\pi\) |
0.896814 | + | 0.442408i | \(0.145876\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 25588.5 | + | 25588.5i | 1.38165 | + | 1.38165i | ||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16305.0 | −0.874758 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23529.0 | + | 23529.0i | 1.24633 | + | 1.24633i | 0.957328 | + | 0.289003i | \(0.0933236\pi\) |
0.289003 | + | 0.957328i | \(0.406676\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29462.2 | −1.55403 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26326.4 | − | 26326.4i | 1.35984 | − | 1.35984i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22408.6 | + | 22408.6i | 1.15268 | + | 1.15268i | ||||
\(724\) | −27435.7 | −1.40834 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 10780.0i | − | 0.549942i | −0.961452 | − | 0.274971i | \(-0.911332\pi\) | ||
0.961452 | − | 0.274971i | \(-0.0886683\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19683.0 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 38880.0i | 1.96318i | ||||||||
\(733\) | −10838.2 | + | 10838.2i | −0.546137 | + | 0.546137i | −0.925321 | − | 0.379184i | \(-0.876205\pi\) |
0.379184 | + | 0.925321i | \(0.376205\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3139.29 | − | 3139.29i | −0.156266 | − | 0.156266i | 0.624644 | − | 0.780910i | \(-0.285244\pi\) |
−0.780910 | + | 0.624644i | \(0.785244\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17173.4 | − | 992.120i | −0.851392 | − | 0.0491855i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 33827.0i | − | 1.64363i | −0.569757 | − | 0.821813i | \(-0.692963\pi\) | ||
0.569757 | − | 0.821813i | \(-0.307037\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 28719.7 | − | 28719.7i | 1.38165 | − | 1.38165i | ||||
\(757\) | −3928.29 | −0.188608 | −0.0943039 | − | 0.995543i | \(-0.530063\pi\) | ||||
−0.0943039 | + | 0.995543i | \(0.530063\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −72374.0 | −3.43396 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −21283.4 | −1.00000 | ||||||||
\(769\) | −23503.3 | + | 23503.3i | −1.10215 | + | 1.10215i | −0.107995 | + | 0.994151i | \(0.534443\pi\) |
−0.994151 | + | 0.107995i | \(0.965557\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 25550.9 | − | 25550.9i | 1.19119 | − | 1.19119i | ||||
\(773\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28992.8 | − | 28992.8i | −1.34381 | − | 1.34381i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 43408.9i | − | 2.00423i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 61858.5i | − | 2.81790i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17631.4 | + | 17631.4i | 0.798592 | + | 0.798592i | 0.982874 | − | 0.184281i | \(-0.0589958\pi\) |
−0.184281 | + | 0.982874i | \(0.558996\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29160.0 | + | 32735.8i | 1.30580 | + | 1.46593i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 41888.0 | 1.86518 | ||||||||
\(797\) | 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 | ||||||||
\(804\) | 4682.46 | + | 4682.46i | 0.205395 | + | 0.205395i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31765.1 | + | 31765.1i | −1.37537 | + | 1.37537i | −0.523087 | + | 0.852280i | \(0.675220\pi\) |
−0.852280 | + | 0.523087i | \(0.824780\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25194.6 | − | 25194.6i | −1.08686 | − | 1.08686i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10899.3 | + | 10899.3i | 0.466731 | + | 0.466731i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2641.33 | − | 45720.9i | 0.112693 | − | 1.95069i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45611.8i | 1.93187i | 0.258786 | + | 0.965935i | \(0.416677\pi\) | ||||
−0.258786 | + | 0.965935i | \(0.583323\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17066.0i | 0.714990i | 0.933915 | + | 0.357495i | \(0.116369\pi\) | ||||
−0.933915 | + | 0.357495i | \(0.883631\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43092.0i | 1.79885i | ||||||||
\(832\) | −17920.0 | + | 15962.6i | −0.746712 | + | 0.665148i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32540.6 | + | 32540.6i | −1.34381 | + | 1.34381i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24389.0 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8729.54i | 0.356023i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34058.2 | − | 34058.2i | 1.38165 | − | 1.38165i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 29098.5i | − | 1.17627i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14646.6 | − | 14646.6i | −0.587915 | − | 0.587915i | 0.349151 | − | 0.937066i | \(-0.386470\pi\) |
−0.937066 | + | 0.349151i | \(0.886470\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39438.8 | 1.56651 | 0.783256 | − | 0.621699i | \(-0.213557\pi\) | ||||
0.783256 | + | 0.621699i | \(0.213557\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25528.7 | 1.00000 | ||||||||
\(868\) | 94960.7i | 3.71334i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7454.33 | + | 430.642i | 0.289989 | + | 0.0167528i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 564.087 | − | 564.087i | 0.0218688 | − | 0.0218688i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16957.7 | − | 16957.7i | 0.654049 | − | 0.654049i | ||||
\(877\) | 31840.4 | − | 31840.4i | 1.22597 | − | 1.22597i | 0.260491 | − | 0.965476i | \(-0.416115\pi\) |
0.965476 | − | 0.260491i | \(-0.0838846\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20680.0i | 0.788151i | 0.919078 | + | 0.394076i | \(0.128935\pi\) | ||||
−0.919078 | + | 0.394076i | \(0.871065\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9723.61 | + | 9723.61i | −0.366839 | + | 0.366839i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −36200.3 | − | 36200.3i | −1.35883 | − | 1.35883i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −27000.0 | −1.00000 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −29017.3 | + | 29017.3i | −1.06936 | + | 1.06936i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 44840.0i | − | 1.64155i | −0.571250 | − | 0.820776i | \(-0.693541\pi\) | ||
0.571250 | − | 0.820776i | \(-0.306459\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 16608.5 | − | 16608.5i | 0.603029 | − | 0.603029i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −39064.3 | + | 39064.3i | −1.40908 | + | 1.40908i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55650.8 | 1.99755 | 0.998776 | − | 0.0494625i | \(-0.0157508\pi\) | ||||
0.998776 | + | 0.0494625i | \(0.0157508\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31774.5 | − | 31774.5i | −1.13681 | − | 1.13681i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20404.8 | + | 20404.8i | −0.725303 | + | 0.725303i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 27778.6i | 0.984218i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 48271.1 | + | 48271.1i | 1.69927 | + | 1.69927i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14466.1 | −0.504361 | −0.252181 | − | 0.967680i | \(-0.581148\pi\) | ||||
−0.252181 | + | 0.967680i | \(0.581148\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24624.0 | 0.855776 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(948\) | − | 45360.0i | − | 1.55403i | ||||||
\(949\) | 1559.58 | − | 26996.1i | 0.0533469 | − | 0.923426i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 77803.4i | − | 2.61164i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −34500.3 | + | 34500.3i | −1.15268 | + | 1.15268i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41705.2 | − | 41705.2i | 1.38692 | − | 1.38692i | 0.555204 | − | 0.831714i | \(-0.312640\pi\) |
0.831714 | − | 0.555204i | \(-0.187360\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | 30304.0i | 1.00000i | ||||||||
\(973\) | −65915.9 | − | 65915.9i | −2.17180 | − | 2.17180i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22733.2 | + | 20250.0i | −0.746712 | + | 0.665148i | ||||
\(976\) | −59859.7 | −1.96318 | ||||||||
\(977\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38183.2 | − | 38183.2i | 1.24271 | − | 1.24271i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1527.47 | − | 26440.2i | 0.0491855 | − | 0.851392i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45628.0 | −1.46258 | −0.731292 | − | 0.682064i | \(-0.761082\pi\) | ||||
−0.731292 | + | 0.682064i | \(0.761082\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33762.3 | − | 33762.3i | 1.07897 | − | 1.07897i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28910.0 | −0.918344 | −0.459172 | − | 0.888347i | \(-0.651854\pi\) | ||||
−0.459172 | + | 0.888347i | \(0.651854\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22901.7 | + | 22901.7i | 0.725303 | + | 0.725303i |
(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 | 39.4.f.a.5.1 | ✓ | 4 | |
3.2 | odd | 2 | CM | 39.4.f.a.5.1 | ✓ | 4 | |
13.8 | odd | 4 | inner | 39.4.f.a.8.1 | yes | 4 | |
39.8 | even | 4 | inner | 39.4.f.a.8.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.f.a.5.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
39.4.f.a.5.1 | ✓ | 4 | 3.2 | odd | 2 | CM | |
39.4.f.a.8.1 | yes | 4 | 13.8 | odd | 4 | inner | |
39.4.f.a.8.1 | yes | 4 | 39.8 | even | 4 | inner |