Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [387,3,Mod(343,387)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(387, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("387.343");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 387 = 3^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 387.b (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: | \(10.5449862307\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 20x^{4} + 121x^{2} + 214 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 343.3 | ||
Root | \(-1.77533i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 387.343 |
Dual form | 387.3.b.c.343.4 |
$q$-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 \(\left(\mathbb{Z}/387\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(173\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.77533i | − | 0.887663i | −0.896110 | − | 0.443832i | \(-0.853619\pi\) | ||
0.896110 | − | 0.443832i | \(-0.146381\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.848217 | 0.212054 | ||||||||
\(5\) | 2.98959i | 0.597919i | 0.954266 | + | 0.298959i | \(0.0966395\pi\) | ||||
−0.954266 | + | 0.298959i | \(0.903360\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.83184i | 0.975977i | 0.872850 | + | 0.487989i | \(0.162269\pi\) | ||||
−0.872850 | + | 0.487989i | \(0.837731\pi\) | |||||||
\(8\) | − | 8.60717i | − | 1.07590i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.30751 | 0.530751 | ||||||||
\(11\) | −6.88766 | −0.626151 | −0.313075 | − | 0.949728i | \(-0.601359\pi\) | ||||
−0.313075 | + | 0.949728i | \(0.601359\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.4014 | 0.953953 | 0.476977 | − | 0.878916i | \(-0.341733\pi\) | ||||
0.476977 | + | 0.878916i | \(0.341733\pi\) | |||||||
\(14\) | 12.1287 | 0.866339 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −11.8877 | −0.742979 | ||||||||
\(17\) | 15.8212 | 0.930661 | 0.465331 | − | 0.885137i | \(-0.345935\pi\) | ||||
0.465331 | + | 0.885137i | \(0.345935\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.2112i | 1.01112i | 0.862792 | + | 0.505559i | \(0.168714\pi\) | ||||
−0.862792 | + | 0.505559i | \(0.831286\pi\) | |||||||
\(20\) | 2.53583i | 0.126791i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.2278i | 0.555811i | ||||||||
\(23\) | 33.2226 | 1.44446 | 0.722231 | − | 0.691652i | \(-0.243117\pi\) | ||||
0.722231 | + | 0.691652i | \(0.243117\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 16.0623 | 0.642493 | ||||||||
\(26\) | − | 22.0165i | − | 0.846789i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.79488i | 0.206960i | ||||||||
\(29\) | 45.8411i | 1.58073i | 0.612637 | + | 0.790364i | \(0.290109\pi\) | ||||
−0.612637 | + | 0.790364i | \(0.709891\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 14.7278 | 0.475092 | 0.237546 | − | 0.971376i | \(-0.423657\pi\) | ||||
0.237546 | + | 0.971376i | \(0.423657\pi\) | |||||||
\(32\) | − | 13.3242i | − | 0.416381i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 28.0879i | − | 0.826114i | ||||||
\(35\) | −20.4244 | −0.583555 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 13.1726i | − | 0.356017i | −0.984029 | − | 0.178009i | \(-0.943034\pi\) | ||
0.984029 | − | 0.178009i | \(-0.0569655\pi\) | |||||||
\(38\) | 34.1062 | 0.897532 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 25.7319 | 0.643298 | ||||||||
\(41\) | 2.49085 | 0.0607525 | 0.0303762 | − | 0.999539i | \(-0.490329\pi\) | ||||
0.0303762 | + | 0.999539i | \(0.490329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −40.8836 | − | 13.3242i | −0.950781 | − | 0.309865i | ||||
\(44\) | −5.84223 | −0.132778 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 58.9810i | − | 1.28220i | ||||||
\(47\) | 10.2595 | 0.218288 | 0.109144 | − | 0.994026i | \(-0.465189\pi\) | ||||
0.109144 | + | 0.994026i | \(0.465189\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.32596 | 0.0474685 | ||||||||
\(50\) | − | 28.5159i | − | 0.570317i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.5191 | 0.202290 | ||||||||
\(53\) | 31.2780 | 0.590151 | 0.295075 | − | 0.955474i | \(-0.404655\pi\) | ||||
0.295075 | + | 0.955474i | \(0.404655\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 20.5913i | − | 0.374387i | ||||||
\(56\) | 58.8028 | 1.05005 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 81.3829 | 1.40315 | ||||||||
\(59\) | −64.4112 | −1.09171 | −0.545857 | − | 0.837878i | \(-0.683796\pi\) | ||||
−0.545857 | + | 0.837878i | \(0.683796\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 78.1922i | − | 1.28184i | −0.767608 | − | 0.640920i | \(-0.778553\pi\) | ||
0.767608 | − | 0.640920i | \(-0.221447\pi\) | |||||||
\(62\) | − | 26.1467i | − | 0.421721i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −71.2054 | −1.11258 | ||||||||
\(65\) | 37.0751i | 0.570387i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −89.3657 | −1.33382 | −0.666908 | − | 0.745140i | \(-0.732383\pi\) | ||||
−0.666908 | + | 0.745140i | \(0.732383\pi\) | |||||||
\(68\) | 13.4198 | 0.197351 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 36.2600i | 0.518000i | ||||||||
\(71\) | − | 35.5065i | − | 0.500092i | −0.968234 | − | 0.250046i | \(-0.919554\pi\) | ||
0.968234 | − | 0.250046i | \(-0.0804457\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 35.9603i | 0.492607i | 0.969193 | + | 0.246303i | \(0.0792160\pi\) | ||||
−0.969193 | + | 0.246303i | \(0.920784\pi\) | |||||||
\(74\) | −23.3857 | −0.316024 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 16.2953i | 0.214412i | ||||||||
\(77\) | − | 47.0554i | − | 0.611109i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 50.1103 | 0.634308 | 0.317154 | − | 0.948374i | \(-0.397273\pi\) | ||||
0.317154 | + | 0.948374i | \(0.397273\pi\) | |||||||
\(80\) | − | 35.5393i | − | 0.444241i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 4.42207i | − | 0.0539277i | ||||||
\(83\) | 10.3645 | 0.124873 | 0.0624367 | − | 0.998049i | \(-0.480113\pi\) | ||||
0.0624367 | + | 0.998049i | \(0.480113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 47.2991i | 0.556460i | ||||||||
\(86\) | −23.6548 | + | 72.5817i | −0.275056 | + | 0.843973i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 59.2832i | 0.673673i | ||||||||
\(89\) | 13.4900i | 0.151573i | 0.997124 | + | 0.0757865i | \(0.0241468\pi\) | ||||
−0.997124 | + | 0.0757865i | \(0.975853\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 84.7243i | 0.931037i | ||||||||
\(92\) | 28.1800 | 0.306304 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 18.2140i | − | 0.193766i | ||||||
\(95\) | −57.4338 | −0.604566 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 66.6322 | 0.686930 | 0.343465 | − | 0.939165i | \(-0.388399\pi\) | ||||
0.343465 | + | 0.939165i | \(0.388399\pi\) | |||||||
\(98\) | − | 4.12933i | − | 0.0421360i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 13.6243 | 0.136243 | ||||||||
\(101\) | −73.3449 | −0.726187 | −0.363094 | − | 0.931753i | \(-0.618279\pi\) | ||||
−0.363094 | + | 0.931753i | \(0.618279\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −34.7405 | −0.337286 | −0.168643 | − | 0.985677i | \(-0.553939\pi\) | ||||
−0.168643 | + | 0.985677i | \(0.553939\pi\) | |||||||
\(104\) | − | 106.741i | − | 1.02635i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 55.5286i | − | 0.523855i | ||||||
\(107\) | −120.519 | −1.12635 | −0.563173 | − | 0.826339i | \(-0.690420\pi\) | ||||
−0.563173 | + | 0.826339i | \(0.690420\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −81.5825 | −0.748464 | −0.374232 | − | 0.927335i | \(-0.622094\pi\) | ||||
−0.374232 | + | 0.927335i | \(0.622094\pi\) | |||||||
\(110\) | −36.5563 | −0.332330 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 81.2146i | − | 0.725130i | ||||||
\(113\) | − | 58.7443i | − | 0.519861i | −0.965627 | − | 0.259931i | \(-0.916300\pi\) | ||
0.965627 | − | 0.259931i | \(-0.0836997\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 99.3222i | 0.863671i | ||||||||
\(116\) | 38.8832i | 0.335200i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 114.351i | 0.969075i | ||||||||
\(119\) | 108.088i | 0.908304i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −73.5601 | −0.607935 | ||||||||
\(122\) | −138.817 | −1.13784 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.4924 | 0.100745 | ||||||||
\(125\) | 122.760i | 0.982078i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.9828 | −0.141597 | −0.0707984 | − | 0.997491i | \(-0.522555\pi\) | ||||
−0.0707984 | + | 0.997491i | \(0.522555\pi\) | |||||||
\(128\) | 73.1161i | 0.571219i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 65.8205 | 0.506311 | ||||||||
\(131\) | − | 103.364i | − | 0.789039i | −0.918887 | − | 0.394520i | \(-0.870911\pi\) | ||
0.918887 | − | 0.394520i | \(-0.129089\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −131.248 | −0.986827 | ||||||||
\(134\) | 158.653i | 1.18398i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 136.176i | − | 1.00129i | ||||||
\(137\) | 140.446i | 1.02516i | 0.858641 | + | 0.512578i | \(0.171309\pi\) | ||||
−0.858641 | + | 0.512578i | \(0.828691\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 248.580 | 1.78834 | 0.894172 | − | 0.447725i | \(-0.147765\pi\) | ||||
0.894172 | + | 0.447725i | \(0.147765\pi\) | |||||||
\(140\) | −17.3244 | −0.123745 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −63.0357 | −0.443913 | ||||||||
\(143\) | −85.4166 | −0.597319 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −137.046 | −0.945147 | ||||||||
\(146\) | 63.8412 | 0.437269 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 11.1733i | − | 0.0754950i | ||||||
\(149\) | − | 95.0589i | − | 0.637979i | −0.947758 | − | 0.318990i | \(-0.896656\pi\) | ||
0.947758 | − | 0.318990i | \(-0.103344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 122.926i | 0.814076i | 0.913411 | + | 0.407038i | \(0.133438\pi\) | ||||
−0.913411 | + | 0.407038i | \(0.866562\pi\) | |||||||
\(152\) | 165.354 | 1.08786 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −83.5387 | −0.542459 | ||||||||
\(155\) | 44.0303i | 0.284066i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 189.332i | − | 1.20594i | −0.797765 | − | 0.602969i | \(-0.793984\pi\) | ||
0.797765 | − | 0.602969i | \(-0.206016\pi\) | |||||||
\(158\) | − | 88.9621i | − | 0.563051i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 39.8339 | 0.248962 | ||||||||
\(161\) | 226.972i | 1.40976i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 264.440i | 1.62233i | 0.584817 | + | 0.811165i | \(0.301166\pi\) | ||||
−0.584817 | + | 0.811165i | \(0.698834\pi\) | |||||||
\(164\) | 2.11278 | 0.0128828 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 18.4004i | − | 0.110845i | ||||||
\(167\) | −40.0299 | −0.239700 | −0.119850 | − | 0.992792i | \(-0.538241\pi\) | ||||
−0.119850 | + | 0.992792i | \(0.538241\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.2054 | −0.0899729 | ||||||||
\(170\) | 83.9713 | 0.493949 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −34.6781 | − | 11.3018i | −0.201617 | − | 0.0657082i | ||||
\(173\) | −181.497 | −1.04912 | −0.524559 | − | 0.851374i | \(-0.675770\pi\) | ||||
−0.524559 | + | 0.851374i | \(0.675770\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 109.735i | 0.627059i | ||||||||
\(176\) | 81.8782 | 0.465217 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 23.9492 | 0.134546 | ||||||||
\(179\) | − | 62.5972i | − | 0.349705i | −0.984595 | − | 0.174852i | \(-0.944055\pi\) | ||
0.984595 | − | 0.174852i | \(-0.0559448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7178 | 0.0923638 | 0.0461819 | − | 0.998933i | \(-0.485295\pi\) | ||||
0.0461819 | + | 0.998933i | \(0.485295\pi\) | |||||||
\(182\) | 150.413 | 0.826447 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 285.953i | − | 1.55409i | ||||||
\(185\) | 39.3809 | 0.212870 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −108.971 | −0.582734 | ||||||||
\(188\) | 8.70231 | 0.0462889 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 101.964i | 0.536651i | ||||||||
\(191\) | − | 44.7333i | − | 0.234206i | −0.993120 | − | 0.117103i | \(-0.962639\pi\) | ||
0.993120 | − | 0.117103i | \(-0.0373607\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 135.200 | 0.700516 | 0.350258 | − | 0.936653i | \(-0.386094\pi\) | ||||
0.350258 | + | 0.936653i | \(0.386094\pi\) | |||||||
\(194\) | − | 118.294i | − | 0.609763i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.97292 | 0.0100659 | ||||||||
\(197\) | −145.802 | −0.740109 | −0.370055 | − | 0.929010i | \(-0.620661\pi\) | ||||
−0.370055 | + | 0.929010i | \(0.620661\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 280.657i | − | 1.41034i | −0.709039 | − | 0.705169i | \(-0.750871\pi\) | ||
0.709039 | − | 0.705169i | \(-0.249129\pi\) | |||||||
\(200\) | − | 138.251i | − | 0.691256i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 130.211i | 0.644609i | ||||||||
\(203\) | −313.179 | −1.54275 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.44664i | 0.0363251i | ||||||||
\(206\) | 61.6757i | 0.299396i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −147.424 | −0.708767 | ||||||||
\(209\) | − | 132.320i | − | 0.633112i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 181.131i | − | 0.858439i | −0.903200 | − | 0.429219i | \(-0.858789\pi\) | ||
0.903200 | − | 0.429219i | \(-0.141211\pi\) | |||||||
\(212\) | 26.5305 | 0.125144 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 213.961i | 0.999816i | ||||||||
\(215\) | 39.8339 | − | 122.225i | 0.185274 | − | 0.568490i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 100.618i | 0.463679i | ||||||||
\(218\) | 144.836i | 0.664384i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 17.4659i | − | 0.0793905i | ||||||
\(221\) | 196.205 | 0.887807 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 107.757i | − | 0.483213i | −0.970374 | − | 0.241607i | \(-0.922326\pi\) | ||
0.970374 | − | 0.241607i | \(-0.0776744\pi\) | |||||||
\(224\) | 91.0288 | 0.406378 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −104.290 | −0.461461 | ||||||||
\(227\) | − | 139.742i | − | 0.615603i | −0.951451 | − | 0.307801i | \(-0.900407\pi\) | ||
0.951451 | − | 0.307801i | \(-0.0995932\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 308.655 | 1.34784 | 0.673919 | − | 0.738805i | \(-0.264610\pi\) | ||||
0.673919 | + | 0.738805i | \(0.264610\pi\) | |||||||
\(230\) | 176.329 | 0.766649 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 394.562 | 1.70070 | ||||||||
\(233\) | − | 301.133i | − | 1.29242i | −0.763161 | − | 0.646209i | \(-0.776354\pi\) | ||
0.763161 | − | 0.646209i | \(-0.223646\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 30.6719i | 0.130519i | ||||||||
\(236\) | −54.6346 | −0.231503 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 191.892 | 0.806268 | ||||||||
\(239\) | 122.039 | 0.510625 | 0.255312 | − | 0.966859i | \(-0.417822\pi\) | ||||
0.255312 | + | 0.966859i | \(0.417822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 475.092i | − | 1.97133i | −0.168701 | − | 0.985667i | \(-0.553957\pi\) | ||
0.168701 | − | 0.985667i | \(-0.446043\pi\) | |||||||
\(242\) | 130.593i | 0.539642i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 66.3240i | − | 0.271820i | ||||||
\(245\) | 6.95367i | 0.0283823i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 238.246i | 0.964559i | ||||||||
\(248\) | − | 126.765i | − | 0.511149i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 217.939 | 0.871754 | ||||||||
\(251\) | 35.9930 | 0.143399 | 0.0716993 | − | 0.997426i | \(-0.477158\pi\) | ||||
0.0716993 | + | 0.997426i | \(0.477158\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −228.826 | −0.904451 | ||||||||
\(254\) | 31.9253i | 0.125690i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −155.017 | −0.605534 | ||||||||
\(257\) | − | 62.7857i | − | 0.244302i | −0.992512 | − | 0.122151i | \(-0.961021\pi\) | ||
0.992512 | − | 0.122151i | \(-0.0389793\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 89.9934 | 0.347465 | ||||||||
\(260\) | 31.4478i | 0.120953i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −183.505 | −0.700401 | ||||||||
\(263\) | − | 17.1841i | − | 0.0653386i | −0.999466 | − | 0.0326693i | \(-0.989599\pi\) | ||
0.999466 | − | 0.0326693i | \(-0.0104008\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 93.5085i | 0.352862i | ||||||||
\(266\) | 233.008i | 0.875970i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −75.8015 | −0.282842 | ||||||||
\(269\) | 407.934 | 1.51648 | 0.758242 | − | 0.651974i | \(-0.226059\pi\) | ||||
0.758242 | + | 0.651974i | \(0.226059\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −316.274 | −1.16706 | −0.583532 | − | 0.812090i | \(-0.698330\pi\) | ||||
−0.583532 | + | 0.812090i | \(0.698330\pi\) | |||||||
\(272\) | −188.078 | −0.691461 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 249.338 | 0.909993 | ||||||||
\(275\) | −110.632 | −0.402298 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 209.408i | 0.755984i | 0.925809 | + | 0.377992i | \(0.123385\pi\) | ||||
−0.925809 | + | 0.377992i | \(0.876615\pi\) | |||||||
\(278\) | − | 441.310i | − | 1.58745i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 175.796i | 0.627845i | ||||||||
\(281\) | −36.4182 | −0.129602 | −0.0648011 | − | 0.997898i | \(-0.520641\pi\) | ||||
−0.0648011 | + | 0.997898i | \(0.520641\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.3124 | −0.0541074 | −0.0270537 | − | 0.999634i | \(-0.508613\pi\) | ||||
−0.0270537 | + | 0.999634i | \(0.508613\pi\) | |||||||
\(284\) | − | 30.1172i | − | 0.106047i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 151.642i | 0.530218i | ||||||||
\(287\) | 17.0171i | 0.0592930i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −38.6884 | −0.133870 | ||||||||
\(290\) | 243.302i | 0.838972i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 30.5021i | 0.104459i | ||||||||
\(293\) | 421.851 | 1.43976 | 0.719882 | − | 0.694097i | \(-0.244196\pi\) | ||||
0.719882 | + | 0.694097i | \(0.244196\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 192.563i | − | 0.652757i | ||||||
\(296\) | −113.379 | −0.383038 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −168.761 | −0.566311 | ||||||||
\(299\) | 412.007 | 1.37795 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 91.0288 | − | 279.310i | 0.302421 | − | 0.927940i | ||||
\(302\) | 218.233 | 0.722625 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 228.377i | − | 0.751239i | ||||||
\(305\) | 233.763 | 0.766436 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −239.260 | −0.779349 | −0.389674 | − | 0.920953i | \(-0.627412\pi\) | ||||
−0.389674 | + | 0.920953i | \(0.627412\pi\) | |||||||
\(308\) | − | 39.9132i | − | 0.129588i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 78.1681 | 0.252155 | ||||||||
\(311\) | −565.399 | −1.81800 | −0.909001 | − | 0.416793i | \(-0.863154\pi\) | ||||
−0.909001 | + | 0.416793i | \(0.863154\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 340.149i | − | 1.08674i | −0.839493 | − | 0.543370i | \(-0.817148\pi\) | ||
0.839493 | − | 0.543370i | \(-0.182852\pi\) | |||||||
\(314\) | −336.126 | −1.07047 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 42.5044 | 0.134508 | ||||||||
\(317\) | 470.259 | 1.48347 | 0.741733 | − | 0.670695i | \(-0.234004\pi\) | ||||
0.741733 | + | 0.670695i | \(0.234004\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 315.738i | − | 0.989774i | ||||||
\(320\) | − | 212.875i | − | 0.665235i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 402.949 | 1.25139 | ||||||||
\(323\) | 303.945i | 0.941008i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 199.195 | 0.612908 | ||||||||
\(326\) | 469.467 | 1.44008 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 21.4392i | − | 0.0653633i | ||||||
\(329\) | 70.0915i | 0.213044i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 297.506i | 0.898809i | 0.893328 | + | 0.449405i | \(0.148364\pi\) | ||||
−0.893328 | + | 0.449405i | \(0.851636\pi\) | |||||||
\(332\) | 8.79134 | 0.0264799 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 71.0662i | 0.212773i | ||||||||
\(335\) | − | 267.167i | − | 0.797514i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 488.152 | 1.44852 | 0.724261 | − | 0.689526i | \(-0.242181\pi\) | ||||
0.724261 | + | 0.689526i | \(0.242181\pi\) | |||||||
\(338\) | 26.9946i | 0.0798657i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 40.1199i | 0.118000i | ||||||||
\(341\) | −101.440 | −0.297479 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 350.651i | 1.02231i | ||||||||
\(344\) | −114.684 | + | 351.892i | −0.333382 | + | 1.02294i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 322.217i | 0.931263i | ||||||||
\(347\) | 620.235i | 1.78742i | 0.448646 | + | 0.893710i | \(0.351907\pi\) | ||||
−0.448646 | + | 0.893710i | \(0.648093\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 97.1065i | − | 0.278242i | −0.990275 | − | 0.139121i | \(-0.955572\pi\) | ||
0.990275 | − | 0.139121i | \(-0.0444277\pi\) | |||||||
\(350\) | 194.816 | 0.556617 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 91.7725i | 0.260717i | ||||||||
\(353\) | −355.666 | −1.00755 | −0.503776 | − | 0.863834i | \(-0.668056\pi\) | ||||
−0.503776 | + | 0.863834i | \(0.668056\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 106.150 | 0.299014 | ||||||||
\(356\) | 11.4425i | 0.0321417i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −111.130 | −0.310420 | ||||||||
\(359\) | −185.120 | −0.515655 | −0.257827 | − | 0.966191i | \(-0.583007\pi\) | ||||
−0.257827 | + | 0.966191i | \(0.583007\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.07135 | −0.0223583 | ||||||||
\(362\) | − | 29.6796i | − | 0.0819879i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 71.8646i | 0.197430i | ||||||||
\(365\) | −107.507 | −0.294539 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −379.616 | −1.03438 | −0.517188 | − | 0.855872i | \(-0.673021\pi\) | ||||
−0.517188 | + | 0.855872i | \(0.673021\pi\) | |||||||
\(368\) | −394.939 | −1.07320 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 69.9139i | − | 0.188956i | ||||||
\(371\) | 213.686i | 0.575974i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 190.307i | 0.510206i | 0.966914 | + | 0.255103i | \(0.0821094\pi\) | ||||
−0.966914 | + | 0.255103i | \(0.917891\pi\) | |||||||
\(374\) | 193.460i | 0.517272i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 88.3055i | − | 0.234855i | ||||||
\(377\) | 568.494i | 1.50794i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −542.592 | −1.43164 | −0.715820 | − | 0.698285i | \(-0.753947\pi\) | ||||
−0.715820 | + | 0.698285i | \(0.753947\pi\) | |||||||
\(380\) | −48.7163 | −0.128201 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −79.4161 | −0.207896 | ||||||||
\(383\) | 126.903i | 0.331340i | 0.986181 | + | 0.165670i | \(0.0529786\pi\) | ||||
−0.986181 | + | 0.165670i | \(0.947021\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 140.677 | 0.365394 | ||||||||
\(386\) | − | 240.024i | − | 0.621823i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 56.5186 | 0.145667 | ||||||||
\(389\) | − | 689.167i | − | 1.77164i | −0.464031 | − | 0.885819i | \(-0.653597\pi\) | ||
0.464031 | − | 0.885819i | \(-0.346403\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 525.623 | 1.34430 | ||||||||
\(392\) | − | 20.0199i | − | 0.0510712i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 258.845i | 0.656968i | ||||||||
\(395\) | 149.809i | 0.379264i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −422.076 | −1.06316 | −0.531582 | − | 0.847007i | \(-0.678402\pi\) | ||||
−0.531582 | + | 0.847007i | \(0.678402\pi\) | |||||||
\(398\) | −498.258 | −1.25191 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −190.943 | −0.477359 | ||||||||
\(401\) | 393.635 | 0.981632 | 0.490816 | − | 0.871263i | \(-0.336699\pi\) | ||||
0.490816 | + | 0.871263i | \(0.336699\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 182.646 | 0.453215 | ||||||||
\(404\) | −62.2124 | −0.153991 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 555.995i | 1.36945i | ||||||||
\(407\) | 90.7287i | 0.222921i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 319.833i | 0.781988i | 0.920393 | + | 0.390994i | \(0.127869\pi\) | ||||
−0.920393 | + | 0.390994i | \(0.872131\pi\) | |||||||
\(410\) | 13.2202 | 0.0322444 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −29.4675 | −0.0715229 | ||||||||
\(413\) | − | 440.047i | − | 1.06549i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.9856i | 0.0746642i | ||||||||
\(416\) | − | 165.239i | − | 0.397208i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −234.912 | −0.561990 | ||||||||
\(419\) | − | 334.413i | − | 0.798121i | −0.916925 | − | 0.399061i | \(-0.869336\pi\) | ||
0.916925 | − | 0.399061i | \(-0.130664\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 332.902i | − | 0.790740i | −0.918522 | − | 0.395370i | \(-0.870616\pi\) | ||
0.918522 | − | 0.395370i | \(-0.129384\pi\) | |||||||
\(422\) | −321.566 | −0.762005 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 269.215i | − | 0.634941i | ||||||
\(425\) | 254.126 | 0.597943 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 534.197 | 1.25105 | ||||||||
\(428\) | −102.226 | −0.238847 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −216.990 | − | 70.7182i | −0.504627 | − | 0.164461i | ||||
\(431\) | 163.406 | 0.379132 | 0.189566 | − | 0.981868i | \(-0.439292\pi\) | ||||
0.189566 | + | 0.981868i | \(0.439292\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 190.232i | 0.439335i | 0.975575 | + | 0.219668i | \(0.0704973\pi\) | ||||
−0.975575 | + | 0.219668i | \(0.929503\pi\) | |||||||
\(434\) | 178.630 | 0.411590 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −69.1997 | −0.158715 | ||||||||
\(437\) | 638.248i | 1.46052i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −343.705 | −0.782927 | −0.391463 | − | 0.920194i | \(-0.628031\pi\) | ||||
−0.391463 | + | 0.920194i | \(0.628031\pi\) | |||||||
\(440\) | −177.233 | −0.402802 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 348.329i | − | 0.788074i | ||||||
\(443\) | −515.530 | −1.16373 | −0.581863 | − | 0.813287i | \(-0.697676\pi\) | ||||
−0.581863 | + | 0.813287i | \(0.697676\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −40.3296 | −0.0906284 | ||||||||
\(446\) | −191.303 | −0.428931 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 486.464i | − | 1.08586i | ||||||
\(449\) | − | 598.611i | − | 1.33321i | −0.745411 | − | 0.666605i | \(-0.767747\pi\) | ||
0.745411 | − | 0.666605i | \(-0.232253\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.1561 | −0.0380402 | ||||||||
\(452\) | − | 49.8279i | − | 0.110239i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −248.087 | −0.546448 | ||||||||
\(455\) | −253.291 | −0.556684 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 459.459i | 1.00538i | 0.864467 | + | 0.502690i | \(0.167656\pi\) | ||||
−0.864467 | + | 0.502690i | \(0.832344\pi\) | |||||||
\(458\) | − | 547.963i | − | 1.19643i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 84.2468i | 0.183145i | ||||||||
\(461\) | −334.655 | −0.725933 | −0.362967 | − | 0.931802i | \(-0.618236\pi\) | ||||
−0.362967 | + | 0.931802i | \(0.618236\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 696.646i | − | 1.50464i | −0.658801 | − | 0.752318i | \(-0.728936\pi\) | ||
0.658801 | − | 0.752318i | \(-0.271064\pi\) | |||||||
\(464\) | − | 544.944i | − | 1.17445i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −534.610 | −1.14723 | ||||||||
\(467\) | − | 123.292i | − | 0.264009i | −0.991249 | − | 0.132004i | \(-0.957859\pi\) | ||
0.991249 | − | 0.132004i | \(-0.0421413\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 610.532i | − | 1.30177i | ||||||
\(470\) | 54.4525 | 0.115856 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 554.398i | 1.17457i | ||||||||
\(473\) | 281.592 | + | 91.7725i | 0.595332 | + | 0.194022i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 308.577i | 0.649636i | ||||||||
\(476\) | 91.6822i | 0.192610i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 216.660i | − | 0.453263i | ||||||
\(479\) | −201.938 | −0.421583 | −0.210791 | − | 0.977531i | \(-0.567604\pi\) | ||||
−0.210791 | + | 0.977531i | \(0.567604\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 163.359i | − | 0.339624i | ||||||
\(482\) | −843.443 | −1.74988 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −62.3950 | −0.128915 | ||||||||
\(485\) | 199.203i | 0.410729i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 151.294 | 0.310666 | 0.155333 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155333 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(488\) | −673.014 | −1.37913 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 12.3450 | 0.0251939 | ||||||||
\(491\) | − | 56.4377i | − | 0.114944i | −0.998347 | − | 0.0574722i | \(-0.981696\pi\) | ||
0.998347 | − | 0.0574722i | \(-0.0183041\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 725.263i | 1.47112i | ||||||||
\(494\) | 422.964 | 0.856203 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −175.080 | −0.352983 | ||||||||
\(497\) | 242.575 | 0.488078 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 337.720i | − | 0.676793i | −0.941004 | − | 0.338396i | \(-0.890116\pi\) | ||
0.941004 | − | 0.338396i | \(-0.109884\pi\) | |||||||
\(500\) | 104.127i | 0.208254i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 63.8994i | − | 0.127290i | ||||||
\(503\) | 124.026i | 0.246573i | 0.992371 | + | 0.123287i | \(0.0393434\pi\) | ||||
−0.992371 | + | 0.123287i | \(0.960657\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 219.272i | − | 0.434201i | ||||||
\(506\) | 406.241i | 0.802848i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.2533 | −0.0300262 | ||||||||
\(509\) | −229.831 | −0.451535 | −0.225767 | − | 0.974181i | \(-0.572489\pi\) | ||||
−0.225767 | + | 0.974181i | \(0.572489\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −245.675 | −0.480773 | ||||||||
\(512\) | 567.670i | 1.10873i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −111.465 | −0.216858 | ||||||||
\(515\) | − | 103.860i | − | 0.201670i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −70.6642 | −0.136681 | ||||||||
\(518\) | − | 159.768i | − | 0.308432i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 319.112 | 0.613677 | ||||||||
\(521\) | 335.813i | 0.644555i | 0.946645 | + | 0.322278i | \(0.104448\pi\) | ||||
−0.946645 | + | 0.322278i | \(0.895552\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 630.020i | 1.20463i | 0.798259 | + | 0.602314i | \(0.205754\pi\) | ||||
−0.798259 | + | 0.602314i | \(0.794246\pi\) | |||||||
\(524\) | − | 87.6752i | − | 0.167319i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.5073 | −0.0579987 | ||||||||
\(527\) | 233.013 | 0.442149 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 574.743 | 1.08647 | ||||||||
\(530\) | 166.008 | 0.313223 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −111.327 | −0.209261 | ||||||||
\(533\) | 30.8900 | 0.0579550 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 360.303i | − | 0.673464i | ||||||
\(536\) | 769.186i | 1.43505i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 724.216i | − | 1.34613i | ||||||
\(539\) | −16.0204 | −0.0297224 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 579.942 | 1.07198 | 0.535991 | − | 0.844224i | \(-0.319938\pi\) | ||||
0.535991 | + | 0.844224i | \(0.319938\pi\) | |||||||
\(542\) | 561.490i | 1.03596i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 210.805i | − | 0.387510i | ||||||
\(545\) | − | 243.899i | − | 0.447521i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 276.106 | 0.504764 | 0.252382 | − | 0.967628i | \(-0.418786\pi\) | ||||
0.252382 | + | 0.967628i | \(0.418786\pi\) | |||||||
\(548\) | 119.129i | 0.217389i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 196.408i | 0.357105i | ||||||||
\(551\) | −880.664 | −1.59830 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 342.346i | 0.619070i | ||||||||
\(554\) | 371.767 | 0.671059 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 210.850 | 0.379226 | ||||||||
\(557\) | 1.44850 | 0.00260054 | 0.00130027 | − | 0.999999i | \(-0.499586\pi\) | ||||
0.00130027 | + | 0.999999i | \(0.499586\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −507.013 | − | 165.239i | −0.907000 | − | 0.295597i | ||||
\(560\) | 242.799 | 0.433569 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 64.6542i | 0.115043i | ||||||||
\(563\) | 87.6035 | 0.155601 | 0.0778006 | − | 0.996969i | \(-0.475210\pi\) | ||||
0.0778006 | + | 0.996969i | \(0.475210\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 175.622 | 0.310835 | ||||||||
\(566\) | 27.1845i | 0.0480292i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −305.611 | −0.538047 | ||||||||
\(569\) | 657.323 | 1.15522 | 0.577612 | − | 0.816311i | \(-0.303985\pi\) | ||||
0.577612 | + | 0.816311i | \(0.303985\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 321.145i | − | 0.562426i | −0.959645 | − | 0.281213i | \(-0.909263\pi\) | ||
0.959645 | − | 0.281213i | \(-0.0907368\pi\) | |||||||
\(572\) | −72.4518 | −0.126664 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 30.2109 | 0.0526322 | ||||||||
\(575\) | 533.633 | 0.928057 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 440.527i | 0.763479i | 0.924270 | + | 0.381740i | \(0.124675\pi\) | ||||
−0.924270 | + | 0.381740i | \(0.875325\pi\) | |||||||
\(578\) | 68.6845i | 0.118831i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −116.245 | −0.200423 | ||||||||
\(581\) | 70.8085i | 0.121874i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −215.432 | −0.369523 | ||||||||
\(584\) | 309.516 | 0.529994 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 748.923i | − | 1.27803i | ||||||
\(587\) | − | 975.567i | − | 1.66195i | −0.556307 | − | 0.830977i | \(-0.687782\pi\) | ||
0.556307 | − | 0.830977i | \(-0.312218\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 282.940i | 0.480373i | ||||||||
\(590\) | −341.863 | −0.579428 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 156.592i | 0.264513i | ||||||||
\(593\) | 14.4319i | 0.0243370i | 0.999926 | + | 0.0121685i | \(0.00387345\pi\) | ||||
−0.999926 | + | 0.0121685i | \(0.996127\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −323.140 | −0.543092 | ||||||||
\(596\) | − | 80.6306i | − | 0.135286i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 731.447i | − | 1.22316i | ||||||
\(599\) | 947.716 | 1.58216 | 0.791082 | − | 0.611710i | \(-0.209518\pi\) | ||||
0.791082 | + | 0.611710i | \(0.209518\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1115.25i | 1.85565i | 0.373016 | + | 0.927825i | \(0.378324\pi\) | ||||
−0.373016 | + | 0.927825i | \(0.621676\pi\) | |||||||
\(602\) | −495.866 | − | 161.606i | −0.823698 | − | 0.268448i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 104.268i | 0.172628i | ||||||||
\(605\) | − | 219.915i | − | 0.363496i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 297.682i | − | 0.490416i | −0.969471 | − | 0.245208i | \(-0.921144\pi\) | ||
0.969471 | − | 0.245208i | \(-0.0788562\pi\) | |||||||
\(608\) | 255.974 | 0.421010 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 415.006i | − | 0.680337i | ||||||
\(611\) | 127.233 | 0.208237 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 382.944 | 0.624705 | 0.312352 | − | 0.949966i | \(-0.398883\pi\) | ||||
0.312352 | + | 0.949966i | \(0.398883\pi\) | |||||||
\(614\) | 424.765i | 0.691799i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −405.014 | −0.657490 | ||||||||
\(617\) | 702.287 | 1.13823 | 0.569114 | − | 0.822258i | \(-0.307286\pi\) | ||||
0.569114 | + | 0.822258i | \(0.307286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −680.743 | −1.09975 | −0.549873 | − | 0.835248i | \(-0.685324\pi\) | ||||
−0.549873 | + | 0.835248i | \(0.685324\pi\) | |||||||
\(620\) | 37.3472i | 0.0602375i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1003.77i | 1.61377i | ||||||||
\(623\) | −92.1616 | −0.147932 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 34.5564 | 0.0552903 | ||||||||
\(626\) | −603.876 | −0.964659 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 160.595i | − | 0.255724i | ||||||
\(629\) | − | 208.408i | − | 0.331332i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1019.35i | − | 1.61546i | −0.589555 | − | 0.807728i | \(-0.700697\pi\) | ||
0.589555 | − | 0.807728i | \(-0.299303\pi\) | |||||||
\(632\) | − | 431.308i | − | 0.682449i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 834.863i | − | 1.31682i | ||||||
\(635\) | − | 53.7613i | − | 0.0846634i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.8451 | 0.0452827 | ||||||||
\(638\) | −560.538 | −0.878586 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −218.587 | −0.341543 | ||||||||
\(641\) | − | 815.451i | − | 1.27215i | −0.771625 | − | 0.636077i | \(-0.780556\pi\) | ||
0.771625 | − | 0.636077i | \(-0.219444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 661.567 | 1.02888 | 0.514438 | − | 0.857528i | \(-0.328001\pi\) | ||||
0.514438 | + | 0.857528i | \(0.328001\pi\) | |||||||
\(644\) | 192.521i | 0.298946i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 539.602 | 0.835298 | ||||||||
\(647\) | 1013.73i | 1.56681i | 0.621512 | + | 0.783405i | \(0.286519\pi\) | ||||
−0.621512 | + | 0.783405i | \(0.713481\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 443.642 | 0.683578 | ||||||||
\(650\) | − | 353.636i | − | 0.544056i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 224.302i | 0.344022i | ||||||||
\(653\) | 812.108i | 1.24366i | 0.783153 | + | 0.621829i | \(0.213610\pi\) | ||||
−0.783153 | + | 0.621829i | \(0.786390\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 309.017 | 0.471782 | ||||||||
\(656\) | −29.6104 | −0.0451378 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 124.435 | 0.189111 | ||||||||
\(659\) | 1106.83 | 1.67955 | 0.839777 | − | 0.542932i | \(-0.182686\pi\) | ||||
0.839777 | + | 0.542932i | \(0.182686\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 523.333 | 0.791729 | 0.395865 | − | 0.918309i | \(-0.370445\pi\) | ||||
0.395865 | + | 0.918309i | \(0.370445\pi\) | |||||||
\(662\) | 528.170 | 0.797840 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 89.2089i | − | 0.134351i | ||||||
\(665\) | − | 392.378i | − | 0.590043i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1522.96i | 2.28330i | ||||||||
\(668\) | −33.9541 | −0.0508295 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −474.309 | −0.707924 | ||||||||
\(671\) | 538.562i | 0.802625i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 320.300i | 0.475929i | 0.971274 | + | 0.237965i | \(0.0764803\pi\) | ||||
−0.971274 | + | 0.237965i | \(0.923520\pi\) | |||||||
\(674\) | − | 866.629i | − | 1.28580i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.8975 | −0.0190791 | ||||||||
\(677\) | − | 854.967i | − | 1.26288i | −0.775426 | − | 0.631438i | \(-0.782465\pi\) | ||
0.775426 | − | 0.631438i | \(-0.217535\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 455.221i | 0.670428i | ||||||||
\(680\) | 407.111 | 0.598693 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 180.090i | 0.264061i | ||||||||
\(683\) | −1331.16 | −1.94898 | −0.974492 | − | 0.224420i | \(-0.927951\pi\) | ||||
−0.974492 | + | 0.224420i | \(0.927951\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −419.877 | −0.612960 | ||||||||
\(686\) | 622.519 | 0.907463 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 486.010 | + | 158.393i | 0.706410 | + | 0.230223i | ||||
\(689\) | 387.891 | 0.562976 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 568.600i | 0.822866i | 0.911440 | + | 0.411433i | \(0.134972\pi\) | ||||
−0.911440 | + | 0.411433i | \(0.865028\pi\) | |||||||
\(692\) | −153.949 | −0.222470 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1101.12 | 1.58663 | ||||||||
\(695\) | 743.152i | 1.06928i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.4084 | 0.0565400 | ||||||||
\(698\) | −172.396 | −0.246985 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 93.0793i | 0.132970i | ||||||||
\(701\) | −369.079 | −0.526504 | −0.263252 | − | 0.964727i | \(-0.584795\pi\) | ||||
−0.263252 | + | 0.964727i | \(0.584795\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 253.063 | 0.359975 | ||||||||
\(704\) | 490.439 | 0.696646 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 631.423i | 0.894367i | ||||||||
\(707\) | − | 501.081i | − | 0.708742i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −656.495 | −0.925945 | −0.462972 | − | 0.886373i | \(-0.653217\pi\) | ||||
−0.462972 | + | 0.886373i | \(0.653217\pi\) | |||||||
\(710\) | − | 188.451i | − | 0.265424i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 116.111 | 0.163077 | ||||||||
\(713\) | 489.298 | 0.686252 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 255.361i | − | 0.357148i | ||||||
\(716\) | − | 53.0960i | − | 0.0741564i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 328.649i | 0.457728i | ||||||||
\(719\) | 497.631 | 0.692115 | 0.346057 | − | 0.938213i | \(-0.387520\pi\) | ||||
0.346057 | + | 0.938213i | \(0.387520\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 237.341i | − | 0.329183i | ||||||
\(722\) | 14.3293i | 0.0198466i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.1804 | 0.0195861 | ||||||||
\(725\) | 736.315i | 1.01561i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1020.14i | − | 1.40322i | −0.712559 | − | 0.701612i | \(-0.752464\pi\) | ||
0.712559 | − | 0.701612i | \(-0.247536\pi\) | |||||||
\(728\) | 729.237 | 1.00170 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 190.859i | 0.261451i | ||||||||
\(731\) | −646.829 | − | 210.805i | −0.884855 | − | 0.288379i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 310.797i | 0.424007i | 0.977269 | + | 0.212003i | \(0.0679987\pi\) | ||||
−0.977269 | + | 0.212003i | \(0.932001\pi\) | |||||||
\(734\) | 673.942i | 0.918177i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 442.665i | − | 0.601447i | ||||||
\(737\) | 615.521 | 0.835171 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1188.34i | 1.60804i | 0.594603 | + | 0.804020i | \(0.297309\pi\) | ||||
−0.594603 | + | 0.804020i | \(0.702691\pi\) | |||||||
\(740\) | 33.4035 | 0.0451399 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 379.363 | 0.511271 | ||||||||
\(743\) | 258.515i | 0.347934i | 0.984752 | + | 0.173967i | \(0.0556585\pi\) | ||||
−0.984752 | + | 0.173967i | \(0.944341\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 284.188 | 0.381460 | ||||||||
\(746\) | 337.857 | 0.452891 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −92.4313 | −0.123571 | ||||||||
\(749\) | − | 823.367i | − | 1.09929i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 816.888i | 1.08773i | 0.839171 | + | 0.543867i | \(0.183040\pi\) | ||||
−0.839171 | + | 0.543867i | \(0.816960\pi\) | |||||||
\(752\) | −121.962 | −0.162183 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1009.26 | 1.33854 | ||||||||
\(755\) | −367.497 | −0.486752 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 807.752i | − | 1.06704i | −0.845786 | − | 0.533522i | \(-0.820868\pi\) | ||
0.845786 | − | 0.533522i | \(-0.179132\pi\) | |||||||
\(758\) | 963.277i | 1.27081i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 494.342i | 0.650450i | ||||||||
\(761\) | − | 589.286i | − | 0.774358i | −0.922005 | − | 0.387179i | \(-0.873450\pi\) | ||
0.922005 | − | 0.387179i | \(-0.126550\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 557.359i | − | 0.730483i | ||||||
\(764\) | − | 37.9435i | − | 0.0496643i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 225.294 | 0.294118 | ||||||||
\(767\) | −798.788 | −1.04144 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1272.87 | 1.65522 | 0.827612 | − | 0.561300i | \(-0.189699\pi\) | ||||
0.827612 | + | 0.561300i | \(0.189699\pi\) | |||||||
\(770\) | − | 249.747i | − | 0.324346i | ||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 114.679 | 0.148547 | ||||||||
\(773\) | − | 176.192i | − | 0.227933i | −0.993485 | − | 0.113967i | \(-0.963644\pi\) | ||
0.993485 | − | 0.113967i | \(-0.0363557\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 236.563 | 0.305243 | ||||||||
\(776\) | − | 573.515i | − | 0.739065i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1223.50 | −1.57262 | ||||||||
\(779\) | 47.8523i | 0.0614279i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 244.557i | 0.313133i | ||||||||
\(782\) | − | 933.153i | − | 1.19329i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −27.6502 | −0.0352681 | ||||||||
\(785\) | 566.026 | 0.721053 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1120.38 | −1.42361 | −0.711804 | − | 0.702379i | \(-0.752121\pi\) | ||||
−0.711804 | + | 0.702379i | \(0.752121\pi\) | |||||||
\(788\) | −123.671 | −0.156943 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 265.961 | 0.336659 | ||||||||
\(791\) | 401.332 | 0.507373 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 969.693i | − | 1.22282i | ||||||
\(794\) | 749.323i | 0.943732i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 238.058i | − | 0.299068i | ||||||
\(797\) | 872.371 | 1.09457 | 0.547284 | − | 0.836947i | \(-0.315662\pi\) | ||||
0.547284 | + | 0.836947i | \(0.315662\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 162.319 | 0.203152 | ||||||||
\(800\) | − | 214.018i | − | 0.267522i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 698.830i | − | 0.871359i | ||||||
\(803\) | − | 247.682i | − | 0.308446i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −678.553 | −0.842924 | ||||||||
\(806\) | − | 324.256i | − | 0.402303i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 631.292i | 0.781302i | ||||||||
\(809\) | −273.069 | −0.337539 | −0.168770 | − | 0.985656i | \(-0.553979\pi\) | ||||
−0.168770 | + | 0.985656i | \(0.553979\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1420.64i | − | 1.75171i | −0.482576 | − | 0.875854i | \(-0.660299\pi\) | ||
0.482576 | − | 0.875854i | \(-0.339701\pi\) | |||||||
\(812\) | −265.644 | −0.327148 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 161.073 | 0.197878 | ||||||||
\(815\) | −790.568 | −0.970022 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 255.974 | − | 785.424i | 0.313310 | − | 0.961351i | ||||
\(818\) | 567.808 | 0.694142 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.31636i | 0.00770288i | ||||||||
\(821\) | −1163.98 | −1.41775 | −0.708877 | − | 0.705332i | \(-0.750798\pi\) | ||||
−0.708877 | + | 0.705332i | \(0.750798\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.3698 | 0.0575574 | 0.0287787 | − | 0.999586i | \(-0.490838\pi\) | ||||
0.0287787 | + | 0.999586i | \(0.490838\pi\) | |||||||
\(824\) | 299.017i | 0.362885i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −781.227 | −0.945795 | ||||||||
\(827\) | 662.925 | 0.801602 | 0.400801 | − | 0.916165i | \(-0.368732\pi\) | ||||
0.400801 | + | 0.916165i | \(0.368732\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 952.975i | − | 1.14955i | −0.818312 | − | 0.574774i | \(-0.805090\pi\) | ||
0.818312 | − | 0.574774i | \(-0.194910\pi\) | |||||||
\(830\) | 55.0096 | 0.0662766 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −883.047 | −1.06135 | ||||||||
\(833\) | 36.7995 | 0.0441771 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 119.673i | − | 0.143321i | ||||||
\(836\) | − | 112.236i | − | 0.134254i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −593.692 | −0.708463 | ||||||||
\(839\) | − | 218.560i | − | 0.260501i | −0.991481 | − | 0.130250i | \(-0.958422\pi\) | ||
0.991481 | − | 0.130250i | \(-0.0415781\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1260.41 | −1.49870 | ||||||||
\(842\) | −591.009 | −0.701911 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 153.638i | − | 0.182036i | ||||||
\(845\) | − | 45.4581i | − | 0.0537965i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 502.551i | − | 0.593331i | ||||||
\(848\) | −371.822 | −0.438469 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 451.156i | − | 0.530772i | ||||||
\(851\) | − | 437.630i | − | 0.514254i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1445.29 | −1.69436 | −0.847180 | − | 0.531306i | \(-0.821701\pi\) | ||||
−0.847180 | + | 0.531306i | \(0.821701\pi\) | |||||||
\(854\) | − | 948.374i | − | 1.11051i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1037.33i | 1.21183i | ||||||||
\(857\) | 92.3800 | 0.107795 | 0.0538973 | − | 0.998546i | \(-0.482836\pi\) | ||||
0.0538973 | + | 0.998546i | \(0.482836\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 786.473i | − | 0.915568i | −0.889064 | − | 0.457784i | \(-0.848643\pi\) | ||
0.889064 | − | 0.457784i | \(-0.151357\pi\) | |||||||
\(860\) | 33.7878 | − | 103.674i | 0.0392882 | − | 0.120551i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 290.099i | − | 0.336542i | ||||||
\(863\) | 1277.18i | 1.47993i | 0.672646 | + | 0.739965i | \(0.265158\pi\) | ||||
−0.672646 | + | 0.739965i | \(0.734842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 542.603i | − | 0.627287i | ||||||
\(866\) | 337.724 | 0.389982 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 85.3461i | 0.0983250i | ||||||||
\(869\) | −345.143 | −0.397172 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1108.26 | −1.27240 | ||||||||
\(872\) | 702.194i | 0.805269i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1133.10 | 1.29645 | ||||||||
\(875\) | −838.675 | −0.958485 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1081.16 | 1.23279 | 0.616396 | − | 0.787436i | \(-0.288592\pi\) | ||||
0.616396 | + | 0.787436i | \(0.288592\pi\) | |||||||
\(878\) | 610.188i | 0.694975i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 244.782i | 0.278162i | ||||||||
\(881\) | 575.591 | 0.653338 | 0.326669 | − | 0.945139i | \(-0.394074\pi\) | ||||
0.326669 | + | 0.945139i | \(0.394074\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1401.90 | 1.58766 | 0.793828 | − | 0.608143i | \(-0.208085\pi\) | ||||
0.793828 | + | 0.608143i | \(0.208085\pi\) | |||||||
\(884\) | 166.425 | 0.188263 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 915.234i | 1.03300i | ||||||||
\(887\) | 205.103i | 0.231232i | 0.993294 | + | 0.115616i | \(0.0368842\pi\) | ||||
−0.993294 | + | 0.115616i | \(0.963116\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 122.856i | − | 0.138195i | ||||||
\(890\) | 71.5983i | 0.0804475i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 91.4010i | − | 0.102467i | ||||||
\(893\) | 197.098i | 0.220715i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 187.140 | 0.209095 | ||||||||
\(896\) | −499.517 | −0.557497 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1062.73 | −1.18344 | ||||||||
\(899\) | 675.141i | 0.750991i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 494.857 | 0.549230 | ||||||||
\(902\) | 30.4577i | 0.0337669i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −505.622 | −0.559316 | ||||||||
\(905\) | 49.9796i | 0.0552260i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −252.284 | −0.278152 | −0.139076 | − | 0.990282i | \(-0.544413\pi\) | ||||
−0.139076 | + | 0.990282i | \(0.544413\pi\) | |||||||
\(908\) | − | 118.531i | − | 0.130541i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 449.675i | 0.494148i | ||||||||
\(911\) | 1367.68i | 1.50130i | 0.660702 | + | 0.750649i | \(0.270259\pi\) | ||||
−0.660702 | + | 0.750649i | \(0.729741\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −71.3871 | −0.0781896 | ||||||||
\(914\) | 815.689 | 0.892439 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 261.806 | 0.285815 | ||||||||
\(917\) | 706.167 | 0.770084 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −270.734 | −0.294597 | −0.147298 | − | 0.989092i | \(-0.547058\pi\) | ||||
−0.147298 | + | 0.989092i | \(0.547058\pi\) | |||||||
\(920\) | 854.883 | 0.929220 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 594.122i | 0.644384i | ||||||||
\(923\) | − | 440.330i | − | 0.477064i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 211.583i | − | 0.228739i | ||||||
\(926\) | −1236.77 | −1.33561 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 610.796 | 0.658185 | ||||||||
\(929\) | − | 791.662i | − | 0.852165i | −0.904684 | − | 0.426083i | \(-0.859893\pi\) | ||
0.904684 | − | 0.426083i | \(-0.140107\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 44.6845i | 0.0479962i | ||||||||
\(932\) | − | 255.426i | − | 0.274063i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −218.884 | −0.234351 | ||||||||
\(935\) | − | 325.780i | − | 0.348428i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1025.37i | − | 1.09431i | −0.837030 | − | 0.547157i | \(-0.815710\pi\) | ||
0.837030 | − | 0.547157i | \(-0.184290\pi\) | |||||||
\(938\) | −1083.89 | −1.15554 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 26.0164i | 0.0276770i | ||||||||
\(941\) | −1515.52 | −1.61054 | −0.805271 | − | 0.592907i | \(-0.797980\pi\) | ||||
−0.805271 | + | 0.592907i | \(0.797980\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 82.7527 | 0.0877547 | ||||||||
\(944\) | 765.698 | 0.811121 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 162.926 | − | 499.918i | 0.172226 | − | 0.528454i | ||||
\(947\) | −804.042 | −0.849042 | −0.424521 | − | 0.905418i | \(-0.639557\pi\) | ||||
−0.424521 | + | 0.905418i | \(0.639557\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 445.958i | 0.469924i | ||||||||
\(950\) | 547.825 | 0.576658 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 930.333 | 0.977241 | ||||||||
\(953\) | 1307.06i | 1.37152i | 0.727828 | + | 0.685760i | \(0.240530\pi\) | ||||
−0.727828 | + | 0.685760i | \(0.759470\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 133.734 | 0.140036 | ||||||||
\(956\) | 103.516 | 0.108280 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 358.506i | 0.374224i | ||||||||
\(959\) | −959.507 | −1.00053 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −744.091 | −0.774288 | ||||||||
\(962\) | −290.016 | −0.301472 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 402.981i | − | 0.418030i | ||||||
\(965\) | 404.192i | 0.418852i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1273.66 | −1.31713 | −0.658563 | − | 0.752525i | \(-0.728836\pi\) | ||||
−0.658563 | + | 0.752525i | \(0.728836\pi\) | |||||||
\(968\) | 633.144i | 0.654075i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 353.651 | 0.364589 | ||||||||
\(971\) | −1511.12 | −1.55625 | −0.778123 | − | 0.628112i | \(-0.783828\pi\) | ||||
−0.778123 | + | 0.628112i | \(0.783828\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1698.26i | 1.74538i | ||||||||
\(974\) | − | 268.597i | − | 0.275767i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 929.523i | 0.952380i | ||||||||
\(977\) | −1275.34 | −1.30537 | −0.652684 | − | 0.757630i | \(-0.726357\pi\) | ||||
−0.652684 | + | 0.757630i | \(0.726357\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 92.9146i | − | 0.0949076i | ||||||
\(980\) | 5.89822i | 0.00601859i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −100.195 | −0.102032 | ||||||||
\(983\) | 643.947i | 0.655084i | 0.944837 | + | 0.327542i | \(0.106220\pi\) | ||||
−0.944837 | + | 0.327542i | \(0.893780\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 435.887i | − | 0.442525i | ||||||
\(986\) | 1287.58 | 1.30586 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 202.084i | 0.204539i | ||||||||
\(989\) | −1358.26 | − | 442.665i | −1.37337 | − | 0.447588i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 778.474i | 0.785544i | 0.919636 | + | 0.392772i | \(0.128484\pi\) | ||||
−0.919636 | + | 0.392772i | \(0.871516\pi\) | |||||||
\(992\) | − | 196.237i | − | 0.197819i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 430.650i | − | 0.433249i | ||||||
\(995\) | 839.052 | 0.843268 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 457.177i | 0.458552i | 0.973361 | + | 0.229276i | \(0.0736359\pi\) | ||||
−0.973361 | + | 0.229276i | \(0.926364\pi\) | |||||||
\(998\) | −599.562 | −0.600764 | ||||||||
\(999\) | 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 | 387.3.b.c.343.3 | 6 | ||
3.2 | odd | 2 | 43.3.b.b.42.4 | yes | 6 | ||
12.11 | even | 2 | 688.3.b.e.257.6 | 6 | |||
43.42 | odd | 2 | inner | 387.3.b.c.343.4 | 6 | ||
129.128 | even | 2 | 43.3.b.b.42.3 | ✓ | 6 | ||
516.515 | odd | 2 | 688.3.b.e.257.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.3.b.b.42.3 | ✓ | 6 | 129.128 | even | 2 | ||
43.3.b.b.42.4 | yes | 6 | 3.2 | odd | 2 | ||
387.3.b.c.343.3 | 6 | 1.1 | even | 1 | trivial | ||
387.3.b.c.343.4 | 6 | 43.42 | odd | 2 | inner | ||
688.3.b.e.257.1 | 6 | 516.515 | odd | 2 | |||
688.3.b.e.257.6 | 6 | 12.11 | even | 2 |