Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [688,3,Mod(257,688)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(688, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("688.257");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.7466421880\) |
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 | 257.6 | ||
Root | \(-1.77533i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 688.257 |
Dual form | 688.3.b.e.257.1 |
$q$-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 \(\left(\mathbb{Z}/688\mathbb{Z}\right)^\times\).
\(n\) | \(431\) | \(433\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 5.61757i | 1.87252i | 0.351302 | + | 0.936262i | \(0.385739\pi\) | ||||
−0.351302 | + | 0.936262i | \(0.614261\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.98959i | − | 0.597919i | −0.954266 | − | 0.298959i | \(-0.903360\pi\) | ||
0.954266 | − | 0.298959i | \(-0.0966395\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 6.83184i | − | 0.975977i | −0.872850 | − | 0.487989i | \(-0.837731\pi\) | ||
0.872850 | − | 0.487989i | \(-0.162269\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −22.5571 | −2.50635 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −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 | \(0.341733\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 16.7943 | 1.11962 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −15.8212 | −0.930661 | −0.465331 | − | 0.885137i | \(-0.654065\pi\) | ||||
−0.465331 | + | 0.885137i | \(0.654065\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 19.2112i | − | 1.01112i | −0.862792 | − | 0.505559i | \(-0.831286\pi\) | ||
0.862792 | − | 0.505559i | \(-0.168714\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 38.3784 | 1.82754 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 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 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 76.1581i | − | 2.82067i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 45.8411i | − | 1.58073i | −0.612637 | − | 0.790364i | \(-0.709891\pi\) | ||
0.612637 | − | 0.790364i | \(-0.290109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14.7278 | −0.475092 | −0.237546 | − | 0.971376i | \(-0.576343\pi\) | ||||
−0.237546 | + | 0.971376i | \(0.576343\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 38.6919i | − | 1.17248i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −20.4244 | −0.583555 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 13.1726i | − | 0.356017i | −0.984029 | − | 0.178009i | \(-0.943034\pi\) | ||
0.984029 | − | 0.178009i | \(-0.0569655\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 69.6657i | 1.78630i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.49085 | −0.0607525 | −0.0303762 | − | 0.999539i | \(-0.509671\pi\) | ||||
−0.0303762 | + | 0.999539i | \(0.509671\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 40.8836 | + | 13.3242i | 0.950781 | + | 0.309865i | ||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 67.4366i | 1.49859i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 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 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 88.8770i | − | 1.74269i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −31.2780 | −0.590151 | −0.295075 | − | 0.955474i | \(-0.595345\pi\) | ||||
−0.295075 | + | 0.955474i | \(0.595345\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 20.5913i | 0.374387i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 107.920 | 1.89334 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −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 | \(-0.221447\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 154.107i | 2.44614i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 37.0751i | − | 0.570387i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 89.3657 | 1.33382 | 0.666908 | − | 0.745140i | \(-0.267617\pi\) | ||||
0.666908 | + | 0.745140i | \(0.267617\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 186.631i | 2.70479i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 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 | \(0.920784\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 90.2313i | 1.20308i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 47.0554i | 0.611109i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −50.1103 | −0.634308 | −0.317154 | − | 0.948374i | \(-0.602727\pi\) | ||||
−0.317154 | + | 0.948374i | \(0.602727\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 224.809 | 2.77543 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 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 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 257.516 | 2.95995 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 13.4900i | − | 0.151573i | −0.997124 | − | 0.0757865i | \(-0.975853\pi\) | ||
0.997124 | − | 0.0757865i | \(-0.0241468\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 84.7243i | − | 0.931037i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 82.7347i | − | 0.889621i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −57.4338 | −0.604566 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 66.6322 | 0.686930 | 0.343465 | − | 0.939165i | \(-0.388399\pi\) | ||||
0.343465 | + | 0.939165i | \(0.388399\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 155.366 | 1.56935 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 73.3449 | 0.726187 | 0.363094 | − | 0.931753i | \(-0.381721\pi\) | ||||
0.363094 | + | 0.931753i | \(0.381721\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 34.7405 | 0.337286 | 0.168643 | − | 0.985677i | \(-0.446061\pi\) | ||||
0.168643 | + | 0.985677i | \(0.446061\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 114.736i | − | 1.09272i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −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 | \(0.622094\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 73.9983 | 0.666651 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 58.7443i | 0.519861i | 0.965627 | + | 0.259931i | \(0.0836997\pi\) | ||||
−0.965627 | + | 0.259931i | \(0.916300\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 99.3222i | − | 0.863671i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −279.740 | −2.39094 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 108.088i | 0.908304i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −73.5601 | −0.607935 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 13.9925i | − | 0.113760i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 122.760i | − | 0.982078i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.9828 | 0.141597 | 0.0707984 | − | 0.997491i | \(-0.477445\pi\) | ||||
0.0707984 | + | 0.997491i | \(0.477445\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −74.8496 | + | 229.666i | −0.580230 | + | 1.78036i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 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 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −227.682 | −1.68653 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 140.446i | − | 1.02516i | −0.858641 | − | 0.512578i | \(-0.828691\pi\) | ||
0.858641 | − | 0.512578i | \(-0.171309\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −248.580 | −1.78834 | −0.894172 | − | 0.447725i | \(-0.852235\pi\) | ||||
−0.894172 | + | 0.447725i | \(0.852235\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 57.6337i | 0.408750i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −85.4166 | −0.597319 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −137.046 | −0.945147 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.0662i | 0.0888859i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 95.0589i | 0.637979i | 0.947758 | + | 0.318990i | \(0.103344\pi\) | ||||
−0.947758 | + | 0.318990i | \(0.896656\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 122.926i | − | 0.814076i | −0.913411 | − | 0.407038i | \(-0.866562\pi\) | ||
0.913411 | − | 0.407038i | \(-0.133438\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 356.882 | 2.33256 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 44.0303i | 0.284066i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 189.332i | − | 1.20594i | −0.797765 | − | 0.602969i | \(-0.793984\pi\) | ||
0.797765 | − | 0.602969i | \(-0.206016\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 175.706i | − | 1.10507i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 226.972i | − | 1.40976i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 264.440i | − | 1.62233i | −0.584817 | − | 0.811165i | \(-0.698834\pi\) | ||
0.584817 | − | 0.811165i | \(-0.301166\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −115.673 | −0.701049 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −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 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 433.350i | 2.53421i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 181.497 | 1.04912 | 0.524559 | − | 0.851374i | \(-0.324230\pi\) | ||||
0.524559 | + | 0.851374i | \(0.324230\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 109.735i | − | 0.627059i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 361.834i | − | 2.04426i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 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 | \(0.485295\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 439.251 | 2.40028 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −39.3809 | −0.212870 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 108.971 | 0.582734 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −520.300 | −2.75291 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 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 | \(0.386094\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 208.272 | 1.06806 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 145.802 | 0.740109 | 0.370055 | − | 0.929010i | \(-0.379339\pi\) | ||||
0.370055 | + | 0.929010i | \(0.379339\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 280.657i | 1.41034i | 0.709039 | + | 0.705169i | \(0.249129\pi\) | ||||
−0.709039 | + | 0.705169i | \(0.750871\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 502.018i | 2.49760i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −313.179 | −1.54275 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.44664i | 0.0363251i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −749.407 | −3.62032 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 132.320i | 0.633112i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 181.131i | 0.858439i | 0.903200 | + | 0.429219i | \(0.141211\pi\) | ||||
−0.903200 | + | 0.429219i | \(0.858789\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 199.460 | 0.936434 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 39.8339 | − | 122.225i | 0.185274 | − | 0.568490i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 100.618i | 0.463679i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −202.010 | −0.922418 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −196.205 | −0.887807 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 107.757i | 0.483213i | 0.970374 | + | 0.241607i | \(0.0776744\pi\) | ||||
−0.970374 | + | 0.241607i | \(0.922326\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −362.320 | −1.61031 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 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 | \(0.264610\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −264.337 | −1.14432 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 301.133i | 1.29242i | 0.763161 | + | 0.646209i | \(0.223646\pi\) | ||||
−0.763161 | + | 0.646209i | \(0.776354\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 30.6719i | − | 0.130519i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 281.498i | − | 1.18776i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 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 | \(-0.446043\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 577.461i | 2.37638i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 6.95367i | − | 0.0283823i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 238.246i | − | 0.964559i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 58.2233i | 0.233828i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 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 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −265.706 | −1.04198 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 62.7857i | 0.244302i | 0.992512 | + | 0.122151i | \(0.0389793\pi\) | ||||
−0.992512 | + | 0.122151i | \(0.961021\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −89.9934 | −0.347465 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1034.04i | 3.96185i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 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 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 75.7811 | 0.283824 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −407.934 | −1.51648 | −0.758242 | − | 0.651974i | \(-0.773941\pi\) | ||||
−0.758242 | + | 0.651974i | \(0.773941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 316.274 | 1.16706 | 0.583532 | − | 0.812090i | \(-0.301670\pi\) | ||||
0.583532 | + | 0.812090i | \(0.301670\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 475.945 | 1.74339 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −110.632 | −0.402298 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 209.408i | 0.755984i | 0.925809 | + | 0.377992i | \(0.123385\pi\) | ||||
−0.925809 | + | 0.377992i | \(0.876615\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 332.218 | 1.19074 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 36.4182 | 0.129602 | 0.0648011 | − | 0.997898i | \(-0.479359\pi\) | ||||
0.0648011 | + | 0.997898i | \(0.479359\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3124 | 0.0541074 | 0.0270537 | − | 0.999634i | \(-0.491387\pi\) | ||||
0.0270537 | + | 0.999634i | \(0.491387\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 322.638i | − | 1.13206i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.0171i | 0.0592930i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −38.6884 | −0.133870 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 374.311i | 1.28629i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −421.851 | −1.43976 | −0.719882 | − | 0.694097i | \(-0.755804\pi\) | ||||
−0.719882 | + | 0.694097i | \(0.755804\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 192.563i | 0.652757i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 524.551i | 1.76616i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 412.007 | 1.37795 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 91.0288 | − | 279.310i | 0.302421 | − | 0.927940i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 412.020i | 1.35980i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −233.763 | −0.766436 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 239.260 | 0.779349 | 0.389674 | − | 0.920953i | \(-0.372588\pi\) | ||||
0.389674 | + | 0.920953i | \(0.372588\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 195.157i | 0.631576i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −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 | \(-0.182852\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 460.716 | 1.46259 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −470.259 | −1.48347 | −0.741733 | − | 0.670695i | \(-0.765996\pi\) | ||||
−0.741733 | + | 0.670695i | \(0.765996\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 315.738i | 0.989774i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 677.025i | − | 2.10911i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 303.945i | 0.941008i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 199.195 | 0.612908 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 458.296i | − | 1.40152i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 70.0915i | − | 0.213044i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 297.506i | − | 0.898809i | −0.893328 | − | 0.449405i | \(-0.851636\pi\) | ||
0.893328 | − | 0.449405i | \(-0.148364\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 297.137i | 0.892303i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 267.167i | − | 0.797514i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 488.152 | 1.44852 | 0.724261 | − | 0.689526i | \(-0.242181\pi\) | ||||
0.724261 | + | 0.689526i | \(0.242181\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −330.000 | −0.973452 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 101.440 | 0.297479 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 350.651i | − | 1.02231i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 557.950 | 1.61725 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 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 | \(-0.0444277\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 944.466i | − | 2.69079i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 355.666 | 1.00755 | 0.503776 | − | 0.863834i | \(-0.331944\pi\) | ||||
0.503776 | + | 0.863834i | \(0.331944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −106.150 | −0.299014 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −607.193 | −1.70082 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 413.229i | − | 1.13837i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 107.507 | 0.294539 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 379.616 | 1.03438 | 0.517188 | − | 0.855872i | \(-0.326979\pi\) | ||||
0.517188 | + | 0.855872i | \(0.326979\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 56.1864 | 0.152267 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 213.686i | 0.575974i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 190.307i | 0.510206i | 0.966914 | + | 0.255103i | \(0.0821094\pi\) | ||||
−0.966914 | + | 0.255103i | \(0.917891\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 689.611 | 1.83896 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 568.494i | − | 1.50794i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 542.592 | 1.43164 | 0.715820 | − | 0.698285i | \(-0.246053\pi\) | ||||
0.715820 | + | 0.698285i | \(0.246053\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 101.020i | 0.265143i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 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 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −922.215 | − | 300.555i | −2.38299 | − | 0.776629i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 689.167i | 1.77164i | 0.464031 | + | 0.885819i | \(0.346403\pi\) | ||||
−0.464031 | + | 0.885819i | \(0.653597\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −525.623 | −1.34430 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 580.656 | 1.47750 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 149.809i | 0.379264i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −422.076 | −1.06316 | −0.531582 | − | 0.847007i | \(-0.678402\pi\) | ||||
−0.531582 | + | 0.847007i | \(0.678402\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 737.295i | − | 1.84786i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −393.635 | −0.981632 | −0.490816 | − | 0.871263i | \(-0.663301\pi\) | ||||
−0.490816 | + | 0.871263i | \(0.663301\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −182.646 | −0.453215 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 672.089i | − | 1.65948i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 90.7287i | 0.222921i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 319.833i | 0.781988i | 0.920393 | + | 0.390994i | \(0.127869\pi\) | ||||
−0.920393 | + | 0.390994i | \(0.872131\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 788.967 | 1.91963 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 440.047i | 1.06549i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 30.9856i | − | 0.0746642i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1396.41i | − | 3.34872i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 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 | \(-0.129384\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −231.426 | −0.547105 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −254.126 | −0.597943 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −534.197 | −1.25105 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 479.834i | − | 1.11849i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 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 | \(0.929503\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 769.868i | − | 1.76981i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 638.248i | − | 1.46052i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 343.705 | 0.782927 | 0.391463 | − | 0.920194i | \(-0.371969\pi\) | ||||
0.391463 | + | 0.920194i | \(0.371969\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −52.4669 | −0.118973 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −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 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −534.000 | −1.19463 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 598.611i | 1.33321i | 0.745411 | + | 0.666605i | \(0.232253\pi\) | ||||
−0.745411 | + | 0.666605i | \(0.767747\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.1561 | 0.0380402 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 690.543 | 1.52438 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −253.291 | −0.556684 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 459.459i | 1.00538i | 0.864467 | + | 0.502690i | \(0.167656\pi\) | ||||
−0.864467 | + | 0.502690i | \(0.832344\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1204.92i | 2.62509i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 334.655 | 0.725933 | 0.362967 | − | 0.931802i | \(-0.381764\pi\) | ||||
0.362967 | + | 0.931802i | \(0.381764\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 696.646i | 1.50464i | 0.658801 | + | 0.752318i | \(0.271064\pi\) | ||||
−0.658801 | + | 0.752318i | \(0.728936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −247.343 | −0.531921 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 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 | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1063.59 | 2.25815 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −281.592 | − | 91.7725i | −0.595332 | − | 0.194022i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 308.577i | − | 0.649636i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 705.541 | 1.47912 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −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 | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1275.03 | 2.63981 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 199.203i | − | 0.410729i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −151.294 | −0.310666 | −0.155333 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155333 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1485.51 | 3.03785 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 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 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 464.481i | − | 0.938345i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −242.575 | −0.488078 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 337.720i | 0.676793i | 0.941004 | + | 0.338396i | \(0.109884\pi\) | ||||
−0.941004 | + | 0.338396i | \(0.890116\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 224.871i | − | 0.448844i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 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 | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 85.4176i | − | 0.168476i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 229.831 | 0.451535 | 0.225767 | − | 0.974181i | \(-0.427511\pi\) | ||||
0.225767 | + | 0.974181i | \(0.427511\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 245.675 | 0.480773 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1463.09 | −2.85203 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 103.860i | − | 0.201670i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −70.6642 | −0.136681 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1019.57i | 1.96450i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 335.813i | − | 0.644555i | −0.946645 | − | 0.322278i | \(-0.895552\pi\) | ||
0.946645 | − | 0.322278i | \(-0.104448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 630.020i | − | 1.20463i | −0.798259 | − | 0.602314i | \(-0.794246\pi\) | ||
0.798259 | − | 0.602314i | \(-0.205754\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 616.446 | 1.17418 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 233.013 | 0.442149 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 574.743 | 1.08647 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1452.93 | 2.73621 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.8900 | −0.0579550 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 360.303i | 0.673464i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 351.644 | 0.654831 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.0204 | −0.0297224 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 579.942 | 1.07198 | 0.535991 | − | 0.844224i | \(-0.319938\pi\) | ||||
0.535991 | + | 0.844224i | \(0.319938\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 93.9137i | 0.172953i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 243.899i | 0.447521i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −276.106 | −0.504764 | −0.252382 | − | 0.967628i | \(-0.581214\pi\) | ||||
−0.252382 | + | 0.967628i | \(0.581214\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1763.79i | 3.21273i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −880.664 | −1.59830 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 342.346i | 0.619070i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 221.225i | − | 0.398603i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.44850 | −0.00260054 | −0.00130027 | − | 0.999999i | \(-0.500414\pi\) | ||||
−0.00130027 | + | 0.999999i | \(0.500414\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 507.013 | + | 165.239i | 0.907000 | + | 0.295597i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 612.154i | 1.09118i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 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 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1535.86i | − | 2.70875i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −657.323 | −1.15522 | −0.577612 | − | 0.816311i | \(-0.696015\pi\) | ||||
−0.577612 | + | 0.816311i | \(0.696015\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 321.145i | 0.562426i | 0.959645 | + | 0.281213i | \(0.0907368\pi\) | ||||
−0.959645 | + | 0.281213i | \(0.909263\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 251.292 | 0.438556 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 533.633 | 0.928057 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 440.527i | 0.763479i | 0.924270 | + | 0.381740i | \(0.124675\pi\) | ||||
−0.924270 | + | 0.381740i | \(0.875325\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 759.494i | 1.31173i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 70.8085i | − | 0.121874i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 215.432 | 0.369523 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 836.308i | 1.42959i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 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 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 819.051i | 1.38587i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 14.4319i | − | 0.0243370i | −0.999926 | − | 0.0121685i | \(-0.996127\pi\) | ||
0.999926 | − | 0.0121685i | \(-0.00387345\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 323.140 | 0.543092 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1576.61 | −2.64089 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 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 | \(0.621676\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2015.83 | −3.34301 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 219.915i | 0.363496i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 297.682i | 0.490416i | 0.969471 | + | 0.245208i | \(0.0788562\pi\) | ||||
−0.969471 | + | 0.245208i | \(0.921144\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 1759.31i | − | 2.88885i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 127.233 | 0.208237 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 382.944 | 0.624705 | 0.312352 | − | 0.949966i | \(-0.398883\pi\) | ||||
0.312352 | + | 0.949966i | \(0.398883\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −41.8320 | −0.0680195 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −702.287 | −1.13823 | −0.569114 | − | 0.822258i | \(-0.692714\pi\) | ||||
−0.569114 | + | 0.822258i | \(0.692714\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 680.743 | 1.09975 | 0.549873 | − | 0.835248i | \(-0.314676\pi\) | ||||
0.549873 | + | 0.835248i | \(0.314676\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 2530.17i | − | 4.07435i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −92.1616 | −0.147932 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 34.5564 | 0.0552903 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −743.319 | −1.18552 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 208.408i | 0.331332i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1019.35i | 1.61546i | 0.589555 | + | 0.807728i | \(0.299303\pi\) | ||||
−0.589555 | + | 0.807728i | \(0.700697\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1017.51 | −1.60745 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 53.7613i | − | 0.0846634i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.8451 | 0.0452827 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 800.925i | 1.25340i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 815.451i | 1.27215i | 0.771625 | + | 0.636077i | \(0.219444\pi\) | ||||
−0.771625 | + | 0.636077i | \(0.780556\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −661.567 | −1.02888 | −0.514438 | − | 0.857528i | \(-0.671999\pi\) | ||||
−0.514438 | + | 0.857528i | \(0.671999\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 686.609 | + | 223.770i | 1.06451 | + | 0.346930i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 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 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −565.230 | −0.868249 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 812.108i | − | 1.24366i | −0.783153 | − | 0.621829i | \(-0.786390\pi\) | ||
0.783153 | − | 0.621829i | \(-0.213610\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −309.017 | −0.471782 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 811.160i | − | 1.23464i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 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 | \(0.370445\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1102.20i | − | 1.66244i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 392.378i | 0.590043i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1522.96i | − | 2.28330i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −605.330 | −0.904828 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 538.562i | 0.802625i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 320.300i | 0.475929i | 0.971274 | + | 0.237965i | \(0.0764803\pi\) | ||||
−0.971274 | + | 0.237965i | \(0.923520\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 1223.28i | − | 1.81226i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 854.967i | 1.26288i | 0.775426 | + | 0.631438i | \(0.217535\pi\) | ||||
−0.775426 | + | 0.631438i | \(0.782465\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 455.221i | − | 0.670428i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 785.010 | 1.15273 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −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 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1733.89i | 2.52386i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −387.891 | −0.562976 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 568.600i | − | 0.822866i | −0.911440 | − | 0.411433i | \(-0.865028\pi\) | ||
0.911440 | − | 0.411433i | \(-0.134972\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 1061.43i | − | 1.53165i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 743.152i | 1.06928i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.4084 | 0.0565400 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1691.64 | −2.42008 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 369.079 | 0.526504 | 0.263252 | − | 0.964727i | \(-0.415205\pi\) | ||||
0.263252 | + | 0.964727i | \(0.415205\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −253.063 | −0.359975 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 172.301 | 0.244399 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 501.081i | − | 0.708742i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −656.495 | −0.925945 | −0.462972 | − | 0.886373i | \(-0.653217\pi\) | ||||
−0.462972 | + | 0.886373i | \(0.653217\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1130.34 | 1.58979 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −489.298 | −0.686252 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 255.361i | 0.357148i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 685.564i | 0.956157i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 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 | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2668.86 | 3.69137 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 736.315i | − | 1.01561i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1020.14i | 1.40322i | 0.712559 | + | 0.701612i | \(0.247536\pi\) | ||||
−0.712559 | + | 0.701612i | \(0.752464\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1220.64 | −1.67441 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −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 | \(0.932001\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 39.0627 | 0.0531466 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −615.521 | −0.835171 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1188.34i | − | 1.60804i | −0.594603 | − | 0.804020i | \(-0.702691\pi\) | ||
0.594603 | − | 0.804020i | \(-0.297309\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1338.36 | 1.80616 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 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 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −233.793 | −0.312976 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 823.367i | 1.09929i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 816.888i | − | 1.08773i | −0.839171 | − | 0.543867i | \(-0.816960\pi\) | ||
0.839171 | − | 0.543867i | \(-0.183040\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 202.193i | 0.268517i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −367.497 | −0.486752 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 807.752i | − | 1.06704i | −0.845786 | − | 0.533522i | \(-0.820868\pi\) | ||
0.845786 | − | 0.533522i | \(-0.179132\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1285.45i | − | 1.69361i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 589.286i | 0.774358i | 0.922005 | + | 0.387179i | \(0.126550\pi\) | ||||
−0.922005 | + | 0.387179i | \(0.873450\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 557.359i | 0.730483i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 1066.93i | − | 1.39468i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −798.788 | −1.04144 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1272.87 | 1.65522 | 0.827612 | − | 0.561300i | \(-0.189699\pi\) | ||||
0.827612 | + | 0.561300i | \(0.189699\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −352.703 | −0.457462 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 176.192i | 0.227933i | 0.993485 | + | 0.113967i | \(0.0363557\pi\) | ||||
−0.993485 | + | 0.113967i | \(0.963644\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −236.563 | −0.305243 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 505.544i | − | 0.650636i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 47.8523i | 0.0614279i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 244.557i | 0.313133i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3491.17 | −4.45871 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −566.026 | −0.721053 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1120.38 | 1.42361 | 0.711804 | − | 0.702379i | \(-0.247879\pi\) | ||||
0.711804 | + | 0.702379i | \(0.247879\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 96.5327 | 0.122348 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 401.332 | 0.507373 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 969.693i | − | 1.22282i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −525.291 | −0.660743 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −872.371 | −1.09457 | −0.547284 | − | 0.836947i | \(-0.684338\pi\) | ||||
−0.547284 | + | 0.836947i | \(0.684338\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −162.319 | −0.203152 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 304.296i | 0.379895i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 247.682i | − | 0.308446i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −678.553 | −0.842924 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 2291.60i | − | 2.83965i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 273.069 | 0.337539 | 0.168770 | − | 0.985656i | \(-0.446021\pi\) | ||||
0.168770 | + | 0.985656i | \(0.446021\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1420.64i | 1.75171i | 0.482576 | + | 0.875854i | \(0.339701\pi\) | ||||
−0.482576 | + | 0.875854i | \(0.660299\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1776.69i | 2.18536i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −790.568 | −0.970022 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 255.974 | − | 785.424i | 0.313310 | − | 0.961351i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1911.14i | 2.33350i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1163.98 | 1.41775 | 0.708877 | − | 0.705332i | \(-0.249202\pi\) | ||||
0.708877 | + | 0.705332i | \(0.249202\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.3698 | −0.0575574 | −0.0287787 | − | 0.999586i | \(-0.509162\pi\) | ||||
−0.0287787 | + | 0.999586i | \(0.509162\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 621.482i | − | 0.753312i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 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 | \(-0.194910\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1176.36 | −1.41560 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −36.7995 | −0.0441771 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 119.673i | 0.143321i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1121.64i | 1.34008i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 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 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 204.582i | 0.242683i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 45.4581i | 0.0537965i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 502.551i | 0.593331i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 86.0185i | 0.101317i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 437.630i | − | 0.514254i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1445.29 | −1.69436 | −0.847180 | − | 0.531306i | \(-0.821701\pi\) | ||||
−0.847180 | + | 0.531306i | \(0.821701\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1295.54 | 1.51525 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −92.3800 | −0.107795 | −0.0538973 | − | 0.998546i | \(-0.517164\pi\) | ||||
−0.0538973 | + | 0.998546i | \(0.517164\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 786.473i | 0.915568i | 0.889064 | + | 0.457784i | \(0.151357\pi\) | ||||
−0.889064 | + | 0.457784i | \(0.848643\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −95.5948 | −0.111028 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 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 | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 217.335i | − | 0.250674i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 345.143 | 0.397172 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1108.26 | 1.27240 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1503.03 | −1.72169 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −838.675 | −0.958485 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1081.16 | 1.23279 | 0.616396 | − | 0.787436i | \(-0.288592\pi\) | ||||
0.616396 | + | 0.787436i | \(0.288592\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 2369.78i | − | 2.69599i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −575.591 | −0.653338 | −0.326669 | − | 0.945139i | \(-0.605926\pi\) | ||||
−0.326669 | + | 0.945139i | \(0.605926\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1401.90 | −1.58766 | −0.793828 | − | 0.608143i | \(-0.791915\pi\) | ||||
−0.793828 | + | 0.608143i | \(0.791915\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1081.74 | −1.22230 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 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 | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1548.41 | −1.73783 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 197.098i | − | 0.220715i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −187.140 | −0.209095 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2314.48i | 2.58024i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 675.141i | 0.750991i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 494.857 | 0.549230 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1569.04 | + | 511.361i | 1.73759 | + | 0.566291i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 49.9796i | − | 0.0552260i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 252.284 | 0.278152 | 0.139076 | − | 0.990282i | \(-0.455587\pi\) | ||||
0.139076 | + | 0.990282i | \(0.455587\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1654.45 | −1.82008 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 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 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 1313.18i | − | 1.43517i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −706.167 | −0.770084 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 270.734 | 0.294597 | 0.147298 | − | 0.989092i | \(-0.452942\pi\) | ||||
0.147298 | + | 0.989092i | \(0.452942\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1344.06i | 1.45935i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 440.330i | − | 0.477064i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 211.583i | − | 0.228739i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −783.645 | −0.845356 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 791.662i | 0.852165i | 0.904684 | + | 0.426083i | \(0.140107\pi\) | ||||
−0.904684 | + | 0.426083i | \(0.859893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 44.6845i | − | 0.0479962i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 3176.17i | − | 3.40425i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 325.780i | − | 0.348428i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1025.37i | − | 1.09431i | −0.837030 | − | 0.547157i | \(-0.815710\pi\) | ||
0.837030 | − | 0.547157i | \(-0.184290\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1910.81 | 2.03495 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1515.52 | 1.61054 | 0.805271 | − | 0.592907i | \(-0.202020\pi\) | ||||
0.805271 | + | 0.592907i | \(0.202020\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −82.7527 | −0.0877547 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1555.49i | 1.64602i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −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 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 2641.71i | − | 2.77783i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1307.06i | − | 1.37152i | −0.727828 | − | 0.685760i | \(-0.759470\pi\) | ||
0.727828 | − | 0.685760i | \(-0.240530\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −133.734 | −0.140036 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1773.68 | −1.85338 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −959.507 | −1.00053 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −744.091 | −0.774288 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2718.56 | 2.82301 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 404.192i | − | 0.418852i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1273.66 | 1.31713 | 0.658563 | − | 0.752525i | \(-0.271164\pi\) | ||||
0.658563 | + | 0.752525i | \(0.271164\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1707.44 | −1.76206 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −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 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1118.99i | 1.14769i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1275.34 | 1.30537 | 0.652684 | − | 0.757630i | \(-0.273643\pi\) | ||||
0.652684 | + | 0.757630i | \(0.273643\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 92.9146i | 0.0949076i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1840.27 | 1.87591 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 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 | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 393.744 | 0.398930 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1358.26 | + | 442.665i | 1.37337 | + | 0.447588i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 778.474i | − | 0.785544i | −0.919636 | − | 0.392772i | \(-0.871516\pi\) | ||
0.919636 | − | 0.392772i | \(-0.128484\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1671.26 | 1.68304 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 839.052 | 0.843268 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 457.177i | 0.458552i | 0.973361 | + | 0.229276i | \(0.0736359\pi\) | ||||
−0.973361 | + | 0.229276i | \(0.926364\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1003.20 | −1.00421 |
(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 | 688.3.b.e.257.6 | 6 | ||
4.3 | odd | 2 | 43.3.b.b.42.4 | yes | 6 | ||
12.11 | even | 2 | 387.3.b.c.343.3 | 6 | |||
43.42 | odd | 2 | inner | 688.3.b.e.257.1 | 6 | ||
172.171 | even | 2 | 43.3.b.b.42.3 | ✓ | 6 | ||
516.515 | odd | 2 | 387.3.b.c.343.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.3.b.b.42.3 | ✓ | 6 | 172.171 | even | 2 | ||
43.3.b.b.42.4 | yes | 6 | 4.3 | odd | 2 | ||
387.3.b.c.343.3 | 6 | 12.11 | even | 2 | |||
387.3.b.c.343.4 | 6 | 516.515 | odd | 2 | |||
688.3.b.e.257.1 | 6 | 43.42 | odd | 2 | inner | ||
688.3.b.e.257.6 | 6 | 1.1 | even | 1 | trivial |