Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(145,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.145");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.r (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + 64 x^{2} - 128 x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.4 | ||
Root | \(-1.34532 - 0.436011i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 864.145 |
Dual form | 864.2.r.b.721.4 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.602794 | − | 0.348023i | −0.269578 | − | 0.155641i | 0.359118 | − | 0.933292i | \(-0.383078\pi\) |
−0.628696 | + | 0.777651i | \(0.716411\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.795065 | − | 1.37709i | −0.300506 | − | 0.520492i | 0.675745 | − | 0.737136i | \(-0.263822\pi\) |
−0.976251 | + | 0.216644i | \(0.930489\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.37222 | + | 1.36960i | −0.715252 | + | 0.412951i | −0.813003 | − | 0.582260i | \(-0.802169\pi\) |
0.0977506 | + | 0.995211i | \(0.468835\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.76780 | + | 2.75269i | 1.32235 | + | 0.763460i | 0.984103 | − | 0.177597i | \(-0.0568325\pi\) |
0.338248 | + | 0.941057i | \(0.390166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.65175 | 1.37075 | 0.685375 | − | 0.728190i | \(-0.259638\pi\) | ||||
0.685375 | + | 0.728190i | \(0.259638\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.963328i | − | 0.221003i | −0.993876 | − | 0.110501i | \(-0.964754\pi\) | ||
0.993876 | − | 0.110501i | \(-0.0352457\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.28857 | − | 5.69597i | 0.685714 | − | 1.18769i | −0.287498 | − | 0.957781i | \(-0.592823\pi\) |
0.973212 | − | 0.229910i | \(-0.0738432\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.25776 | − | 3.91055i | −0.451552 | − | 0.782111i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.85076 | − | 1.64589i | 0.529373 | − | 0.305634i | −0.211388 | − | 0.977402i | \(-0.567798\pi\) |
0.740761 | + | 0.671768i | \(0.234465\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.69844 | − | 6.40589i | 0.664259 | − | 1.15053i | −0.315226 | − | 0.949017i | \(-0.602080\pi\) |
0.979486 | − | 0.201514i | \(-0.0645863\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.10680i | 0.187084i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.25538i | − | 1.02838i | −0.857677 | − | 0.514189i | \(-0.828093\pi\) | ||
0.857677 | − | 0.514189i | \(-0.171907\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.931886 | − | 1.61407i | 0.145536 | − | 0.252076i | −0.784037 | − | 0.620714i | \(-0.786843\pi\) |
0.929573 | + | 0.368639i | \(0.120176\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.99838 | + | 1.73111i | −0.457248 | + | 0.263992i | −0.710886 | − | 0.703307i | \(-0.751706\pi\) |
0.253638 | + | 0.967299i | \(0.418373\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.85668 | + | 6.67997i | 0.562555 | + | 0.974374i | 0.997273 | + | 0.0738070i | \(0.0235149\pi\) |
−0.434717 | + | 0.900567i | \(0.643152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.23574 | − | 3.87242i | 0.319392 | − | 0.553203i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.54179i | 0.349141i | 0.984645 | + | 0.174571i | \(0.0558537\pi\) | ||||
−0.984645 | + | 0.174571i | \(0.944146\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.90662 | 0.257088 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.62019 | + | 2.66747i | 0.601498 | + | 0.347275i | 0.769631 | − | 0.638489i | \(-0.220440\pi\) |
−0.168133 | + | 0.985764i | \(0.553774\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.93715 | + | 4.58252i | −1.01625 | + | 0.586731i | −0.913015 | − | 0.407926i | \(-0.866252\pi\) |
−0.103233 | + | 0.994657i | \(0.532919\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.91600 | − | 3.31861i | −0.237651 | − | 0.411623i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.95780 | + | 3.43974i | 0.727861 | + | 0.420231i | 0.817639 | − | 0.575731i | \(-0.195283\pi\) |
−0.0897783 | + | 0.995962i | \(0.528616\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.68351 | 0.437153 | 0.218576 | − | 0.975820i | \(-0.429859\pi\) | ||||
0.218576 | + | 0.975820i | \(0.429859\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.83201 | 0.331461 | 0.165731 | − | 0.986171i | \(-0.447002\pi\) | ||||
0.165731 | + | 0.986171i | \(0.447002\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.77214 | + | 2.17785i | 0.429875 | + | 0.248189i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.87870 | − | 4.98605i | −0.323879 | − | 0.560975i | 0.657406 | − | 0.753537i | \(-0.271654\pi\) |
−0.981285 | + | 0.192562i | \(0.938320\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.74968 | − | 3.31958i | 0.631110 | − | 0.364371i | −0.150072 | − | 0.988675i | \(-0.547951\pi\) |
0.781182 | + | 0.624304i | \(0.214617\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.40684 | − | 1.96694i | −0.369524 | − | 0.213345i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.98701 | 0.316622 | 0.158311 | − | 0.987389i | \(-0.449395\pi\) | ||||
0.158311 | + | 0.987389i | \(0.449395\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 8.75427i | − | 0.917697i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.335261 | + | 0.580689i | −0.0343970 | + | 0.0595774i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.24837 | − | 2.16224i | −0.126753 | − | 0.219543i | 0.795664 | − | 0.605738i | \(-0.207122\pi\) |
−0.922417 | + | 0.386196i | \(0.873789\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.22136 | + | 4.74661i | −0.818056 | + | 0.472305i | −0.849746 | − | 0.527193i | \(-0.823245\pi\) |
0.0316896 | + | 0.999498i | \(0.489911\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.37220 | + | 12.7690i | −0.726405 | + | 1.25817i | 0.231989 | + | 0.972719i | \(0.425477\pi\) |
−0.958393 | + | 0.285451i | \(0.907857\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 7.83384i | − | 0.757325i | −0.925535 | − | 0.378663i | \(-0.876384\pi\) | ||
0.925535 | − | 0.378663i | \(-0.123616\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.242400i | 0.0232177i | 0.999933 | + | 0.0116089i | \(0.00369529\pi\) | ||||
−0.999933 | + | 0.0116089i | \(0.996305\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.34789 | + | 7.53076i | −0.409015 | + | 0.708435i | −0.994780 | − | 0.102046i | \(-0.967461\pi\) |
0.585765 | + | 0.810481i | \(0.300794\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.96466 | + | 2.28900i | −0.369706 | + | 0.213450i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.49350 | − | 7.78298i | −0.411919 | − | 0.713464i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.74837 | + | 3.02827i | −0.158943 | + | 0.275297i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.62325i | 0.592401i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.72754 | 0.153295 | 0.0766473 | − | 0.997058i | \(-0.475578\pi\) | ||||
0.0766473 | + | 0.997058i | \(0.475578\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.74968 | − | 3.31958i | −0.502352 | − | 0.290033i | 0.227332 | − | 0.973817i | \(-0.427000\pi\) |
−0.729684 | + | 0.683784i | \(0.760333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.32659 | + | 0.765908i | −0.115030 | + | 0.0664127i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.81325 | − | 3.14063i | −0.154916 | − | 0.268322i | 0.778112 | − | 0.628125i | \(-0.216177\pi\) |
−0.933028 | + | 0.359803i | \(0.882844\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.9919 | + | 8.65556i | 1.27159 | + | 0.734155i | 0.975288 | − | 0.220937i | \(-0.0709117\pi\) |
0.296307 | + | 0.955093i | \(0.404245\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.0804 | −1.26109 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.29123 | −0.190276 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.7251 | − | 10.8109i | −1.53402 | − | 0.885665i | −0.999171 | − | 0.0407158i | \(-0.987036\pi\) |
−0.534846 | − | 0.844949i | \(-0.679631\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.35019 | + | 10.9988i | 0.516771 | + | 0.895073i | 0.999810 | + | 0.0194749i | \(0.00619944\pi\) |
−0.483039 | + | 0.875599i | \(0.660467\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.45880 | + | 2.57429i | −0.358139 | + | 0.206772i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.1285 | + | 8.73443i | 1.20738 | + | 0.697083i | 0.962187 | − | 0.272390i | \(-0.0878140\pi\) |
0.245197 | + | 0.969473i | \(0.421147\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.4585 | −0.824245 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.56748i | − | 0.671057i | −0.942030 | − | 0.335528i | \(-0.891085\pi\) | ||
0.942030 | − | 0.335528i | \(-0.108915\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.97532 | + | 10.3496i | −0.462384 | + | 0.800873i | −0.999079 | − | 0.0429032i | \(-0.986339\pi\) |
0.536695 | + | 0.843776i | \(0.319673\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.65464 | + | 14.9903i | 0.665741 | + | 1.15310i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.2973 | − | 6.52248i | 0.858916 | − | 0.495895i | −0.00473326 | − | 0.999989i | \(-0.501507\pi\) |
0.863649 | + | 0.504094i | \(0.168173\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.59013 | + | 6.21829i | −0.271388 | + | 0.470058i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.31875i | 0.248055i | 0.992279 | + | 0.124028i | \(0.0395811\pi\) | ||||
−0.992279 | + | 0.124028i | \(0.960419\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.9128i | − | 1.10846i | −0.832363 | − | 0.554231i | \(-0.813013\pi\) | ||
0.832363 | − | 0.554231i | \(-0.186987\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.17702 | + | 3.77070i | −0.160058 | + | 0.277228i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.4072 | + | 7.74065i | −0.980432 | + | 0.566053i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.65884 | + | 6.33729i | 0.264744 | + | 0.458550i | 0.967497 | − | 0.252884i | \(-0.0813792\pi\) |
−0.702752 | + | 0.711434i | \(0.748046\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.2354 | + | 17.7282i | −0.736759 | + | 1.27610i | 0.217189 | + | 0.976130i | \(0.430311\pi\) |
−0.953947 | + | 0.299974i | \(0.903022\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.5437i | − | 1.46368i | −0.681479 | − | 0.731838i | \(-0.738663\pi\) | ||
0.681479 | − | 0.731838i | \(-0.261337\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.95597 | −0.138655 | −0.0693275 | − | 0.997594i | \(-0.522085\pi\) | ||||
−0.0693275 | + | 0.997594i | \(0.522085\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.53308 | − | 2.61718i | −0.318160 | − | 0.183690i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.12347 | + | 0.648636i | −0.0784666 | + | 0.0453027i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.31938 | + | 2.28523i | 0.0912633 | + | 0.158073i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.10981 | − | 5.25955i | −0.627145 | − | 0.362082i | 0.152501 | − | 0.988303i | \(-0.451267\pi\) |
−0.779646 | + | 0.626221i | \(0.784601\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.40987 | 0.164352 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.7620 | −0.798456 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.9464 | + | 15.5575i | 1.81261 | + | 1.04651i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.93129 | − | 3.34510i | −0.129329 | − | 0.224004i | 0.794088 | − | 0.607803i | \(-0.207949\pi\) |
−0.923417 | + | 0.383799i | \(0.874616\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.9183 | + | 8.03574i | −0.923790 | + | 0.533351i | −0.884842 | − | 0.465891i | \(-0.845734\pi\) |
−0.0389481 | + | 0.999241i | \(0.512401\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.46319 | − | 4.30888i | −0.493182 | − | 0.284739i | 0.232712 | − | 0.972546i | \(-0.425240\pi\) |
−0.725893 | + | 0.687807i | \(0.758573\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.1535 | −1.58235 | −0.791176 | − | 0.611589i | \(-0.790531\pi\) | ||||
−0.791176 | + | 0.611589i | \(0.790531\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 5.36886i | − | 0.350226i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.01493 | + | 3.48996i | −0.130335 | + | 0.225746i | −0.923806 | − | 0.382862i | \(-0.874939\pi\) |
0.793471 | + | 0.608608i | \(0.208272\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.81649 | + | 4.87830i | 0.181426 | + | 0.314239i | 0.942366 | − | 0.334583i | \(-0.108595\pi\) |
−0.760940 | + | 0.648822i | \(0.775262\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.69539 | + | 1.55618i | −0.172202 | + | 0.0994209i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.65175 | − | 4.59296i | 0.168727 | − | 0.292243i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.8828i | 0.876276i | 0.898908 | + | 0.438138i | \(0.144362\pi\) | ||||
−0.898908 | + | 0.438138i | \(0.855638\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0161i | 1.13267i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.42539 | − | 9.39705i | 0.338427 | − | 0.586172i | −0.645710 | − | 0.763582i | \(-0.723439\pi\) |
0.984137 | + | 0.177410i | \(0.0567720\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.61423 | + | 4.97343i | −0.535262 | + | 0.309034i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.6051 | − | 20.1005i | −0.715598 | − | 1.23945i | −0.962728 | − | 0.270470i | \(-0.912821\pi\) |
0.247130 | − | 0.968982i | \(-0.420513\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.884601 | − | 1.53217i | 0.0543406 | − | 0.0941207i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 4.01966i | − | 0.245083i | −0.992463 | − | 0.122541i | \(-0.960896\pi\) | ||
0.992463 | − | 0.122541i | \(-0.0391044\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.75621 | 0.410411 | 0.205205 | − | 0.978719i | \(-0.434214\pi\) | ||||
0.205205 | + | 0.978719i | \(0.434214\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.7118 | + | 6.18447i | 0.645947 | + | 0.372938i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.83595 | + | 1.05999i | −0.110312 | + | 0.0636885i | −0.554141 | − | 0.832423i | \(-0.686953\pi\) |
0.443829 | + | 0.896111i | \(0.353620\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.0580 | + | 22.6171i | 0.778976 | + | 1.34923i | 0.932533 | + | 0.361086i | \(0.117594\pi\) |
−0.153557 | + | 0.988140i | \(0.549073\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.5376 | − | 9.54799i | −0.983058 | − | 0.567569i | −0.0798661 | − | 0.996806i | \(-0.525449\pi\) |
−0.903192 | + | 0.429237i | \(0.858783\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.96364 | −0.174938 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.9423 | 0.878956 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.07116 | − | 2.92784i | −0.296261 | − | 0.171046i | 0.344501 | − | 0.938786i | \(-0.388048\pi\) |
−0.640762 | + | 0.767740i | \(0.721381\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.85668 | − | 3.21587i | −0.108100 | − | 0.187235i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 31.3585 | − | 18.1048i | 1.81351 | − | 1.04703i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.76780 | + | 2.75269i | 0.274812 | + | 0.158663i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.37929 | 0.365277 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.7071i | 0.782305i | 0.920326 | + | 0.391152i | \(0.127923\pi\) | ||||
−0.920326 | + | 0.391152i | \(0.872077\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.57980 | + | 16.5927i | −0.543221 | + | 0.940886i | 0.455496 | + | 0.890238i | \(0.349462\pi\) |
−0.998717 | + | 0.0506479i | \(0.983871\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.6102 | − | 21.8416i | −0.712773 | − | 1.23456i | −0.963812 | − | 0.266582i | \(-0.914106\pi\) |
0.251039 | − | 0.967977i | \(-0.419228\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.13931 | − | 1.23513i | 0.120156 | − | 0.0693719i | −0.438718 | − | 0.898625i | \(-0.644567\pi\) |
0.558873 | + | 0.829253i | \(0.311234\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.50843 | + | 7.80883i | −0.252424 | + | 0.437211i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.44449i | − | 0.302939i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 24.8597i | − | 1.37897i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.13262 | − | 10.6220i | 0.338103 | − | 0.585611i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.4404 | − | 14.1107i | 1.34336 | − | 0.775592i | 0.356065 | − | 0.934461i | \(-0.384118\pi\) |
0.987300 | + | 0.158869i | \(0.0507848\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.39422 | − | 4.14691i | −0.130810 | − | 0.226570i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.60565 | − | 9.70927i | 0.305359 | − | 0.528897i | −0.671982 | − | 0.740567i | \(-0.734557\pi\) |
0.977341 | + | 0.211670i | \(0.0678902\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.2616i | 1.09723i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.2411 | −0.984929 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.8303 | − | 10.2943i | −0.957180 | − | 0.552628i | −0.0618763 | − | 0.998084i | \(-0.519708\pi\) |
−0.895304 | + | 0.445455i | \(0.853042\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.93968 | + | 1.69723i | −0.157358 | + | 0.0908505i | −0.576611 | − | 0.817019i | \(-0.695625\pi\) |
0.419253 | + | 0.907869i | \(0.362292\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.503241 | + | 0.871639i | 0.0267848 | + | 0.0463926i | 0.879107 | − | 0.476624i | \(-0.158140\pi\) |
−0.852322 | + | 0.523017i | \(0.824806\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.22040 | − | 1.28195i | −0.117847 | − | 0.0680388i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.4772 | 1.66131 | 0.830653 | − | 0.556791i | \(-0.187968\pi\) | ||||
0.830653 | + | 0.556791i | \(0.187968\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0720 | 0.951158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.70712 | − | 0.985604i | −0.0893546 | − | 0.0515889i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.66667 | + | 15.0111i | 0.452397 | + | 0.783574i | 0.998534 | − | 0.0541214i | \(-0.0172358\pi\) |
−0.546138 | + | 0.837695i | \(0.683902\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.50027 | − | 2.02088i | 0.181725 | − | 0.104919i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.2742 | − | 6.50917i | −0.583757 | − | 0.337032i | 0.178868 | − | 0.983873i | \(-0.442756\pi\) |
−0.762625 | + | 0.646841i | \(0.776090\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.1225 | 0.933357 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.8643i | 1.17446i | 0.809421 | + | 0.587229i | \(0.199781\pi\) | ||||
−0.809421 | + | 0.587229i | \(0.800219\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.0117 | − | 26.0010i | 0.767061 | − | 1.32859i | −0.172089 | − | 0.985081i | \(-0.555052\pi\) |
0.939150 | − | 0.343508i | \(-0.111615\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.51588 | − | 2.62559i | −0.0772565 | − | 0.133812i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.9474 | + | 19.0222i | −1.67050 | + | 0.964463i | −0.703140 | + | 0.711051i | \(0.748220\pi\) |
−0.967358 | + | 0.253412i | \(0.918447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.5862 | − | 32.1922i | 0.939943 | − | 1.62803i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00742i | 0.201635i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.4510i | 1.87961i | 0.341709 | + | 0.939806i | \(0.388994\pi\) | ||||
−0.341709 | + | 0.939806i | \(0.611006\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.35402 | − | 4.07728i | 0.117554 | − | 0.203610i | −0.801244 | − | 0.598338i | \(-0.795828\pi\) |
0.918798 | + | 0.394728i | \(0.129161\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.2669 | − | 20.3613i | 1.75677 | − | 1.01427i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.56739 | + | 14.8391i | 0.424670 | + | 0.735549i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.36377 | − | 9.29032i | 0.265221 | − | 0.459377i | −0.702400 | − | 0.711782i | \(-0.747888\pi\) |
0.967622 | + | 0.252405i | \(0.0812216\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 8.48324i | − | 0.417433i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.62117 | −0.226844 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.57600 | + | 2.06460i | 0.174699 | + | 0.100863i | 0.584800 | − | 0.811178i | \(-0.301173\pi\) |
−0.410101 | + | 0.912040i | \(0.634506\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7321 | − | 7.92824i | 0.669262 | − | 0.386399i | −0.126535 | − | 0.991962i | \(-0.540386\pi\) |
0.795797 | + | 0.605563i | \(0.207052\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.7603 | − | 22.1015i | −0.618965 | − | 1.07208i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.6211 | + | 7.28679i | 0.610778 | + | 0.352633i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.1853 | 0.779619 | 0.389810 | − | 0.920895i | \(-0.372541\pi\) | ||||
0.389810 | + | 0.920895i | \(0.372541\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.8306 | −1.57774 | −0.788868 | − | 0.614563i | \(-0.789332\pi\) | ||||
−0.788868 | + | 0.614563i | \(0.789332\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.48709 | − | 3.16797i | −0.262483 | − | 0.151545i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.9273 | − | 18.9267i | −0.521533 | − | 0.903321i | −0.999686 | − | 0.0250450i | \(-0.992027\pi\) |
0.478154 | − | 0.878276i | \(-0.341306\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.4500 | + | 17.5803i | −1.44672 | + | 0.835265i | −0.998284 | − | 0.0585501i | \(-0.981352\pi\) |
−0.448436 | + | 0.893815i | \(0.648019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.80055 | − | 1.03955i | −0.0853543 | − | 0.0492793i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.21851 | −0.151891 | −0.0759453 | − | 0.997112i | \(-0.524197\pi\) | ||||
−0.0759453 | + | 0.997112i | \(0.524197\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.10526i | 0.240397i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.04669 | + | 5.27703i | −0.142831 | + | 0.247391i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.05512 | + | 7.02368i | 0.189691 | + | 0.328554i | 0.945147 | − | 0.326645i | \(-0.105918\pi\) |
−0.755456 | + | 0.655199i | \(0.772585\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.1813 | − | 10.4970i | 0.846789 | − | 0.488894i | −0.0127771 | − | 0.999918i | \(-0.504067\pi\) |
0.859566 | + | 0.511024i | \(0.170734\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.45005 | − | 7.70772i | 0.206812 | − | 0.358208i | −0.743897 | − | 0.668294i | \(-0.767025\pi\) |
0.950708 | + | 0.310086i | \(0.100358\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 26.0527i | − | 1.20557i | −0.797902 | − | 0.602787i | \(-0.794057\pi\) | ||
0.797902 | − | 0.602787i | \(-0.205943\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 10.9392i | − | 0.505128i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.74188 | − | 8.21317i | 0.218032 | − | 0.377642i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.76715 | + | 2.17496i | −0.172849 | + | 0.0997942i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.71143 | + | 15.0886i | 0.398035 | + | 0.689418i | 0.993483 | − | 0.113976i | \(-0.0363588\pi\) |
−0.595448 | + | 0.803394i | \(0.703025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.2191 | − | 29.8244i | 0.785125 | − | 1.35988i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.73785i | 0.0789118i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.7367 | 1.34750 | 0.673750 | − | 0.738959i | \(-0.264682\pi\) | ||||
0.673750 | + | 0.738959i | \(0.264682\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.6346 | + | 11.9134i | 0.931229 | + | 0.537645i | 0.887200 | − | 0.461385i | \(-0.152647\pi\) |
0.0440286 | + | 0.999030i | \(0.485981\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.1118 | − | 9.30215i | 0.725639 | − | 0.418948i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.92863 | − | 5.07254i | −0.131367 | − | 0.227534i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.8622 | + | 9.73540i | 0.754856 | + | 0.435816i | 0.827446 | − | 0.561546i | \(-0.189793\pi\) |
−0.0725899 | + | 0.997362i | \(0.523126\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.23494 | 0.0550631 | 0.0275316 | − | 0.999621i | \(-0.491235\pi\) | ||||
0.0275316 | + | 0.999621i | \(0.491235\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.60772 | 0.294040 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.392870 | − | 0.226823i | −0.0174136 | − | 0.0100538i | 0.491268 | − | 0.871009i | \(-0.336534\pi\) |
−0.508682 | + | 0.860955i | \(0.669867\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.25163 | − | 3.89993i | −0.0996061 | − | 0.172523i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.88784 | − | 5.13140i | 0.391645 | − | 0.226116i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.2978 | − | 10.5643i | −0.804737 | − | 0.464615i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.0873 | 1.27434 | 0.637170 | − | 0.770724i | \(-0.280105\pi\) | ||||
0.637170 | + | 0.770724i | \(0.280105\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.95874i | 0.129377i | 0.997906 | + | 0.0646883i | \(0.0206053\pi\) | ||||
−0.997906 | + | 0.0646883i | \(0.979395\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.9026 | − | 36.2044i | 0.910534 | − | 1.57709i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.1294 | − | 17.5446i | −0.440407 | − | 0.762808i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.88610 | − | 5.13039i | 0.384900 | − | 0.222222i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.72636 | + | 4.72219i | −0.117871 | + | 0.204158i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.2483i | 0.527573i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.9753i | 0.643838i | 0.946767 | + | 0.321919i | \(0.104328\pi\) | ||||
−0.946767 | + | 0.321919i | \(0.895672\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.0843608 | − | 0.146117i | 0.00361362 | − | 0.00625897i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.7731 | + | 9.10661i | −0.674409 | + | 0.389370i | −0.797745 | − | 0.602995i | \(-0.793974\pi\) |
0.123336 | + | 0.992365i | \(0.460641\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.58553 | − | 2.74622i | −0.0675459 | − | 0.116993i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.57750 | + | 7.92846i | −0.194655 | + | 0.337153i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.7359i | 1.51418i | 0.653310 | + | 0.757090i | \(0.273380\pi\) | ||||
−0.653310 | + | 0.757090i | \(0.726620\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.0609 | −0.806190 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.04256 | − | 4.64337i | −0.338953 | − | 0.195695i | 0.320856 | − | 0.947128i | \(-0.396030\pi\) |
−0.659809 | + | 0.751433i | \(0.729363\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.24176 | − | 3.02633i | 0.220523 | − | 0.127319i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.66727 | + | 9.81599i | 0.237584 | + | 0.411508i | 0.960021 | − | 0.279930i | \(-0.0903111\pi\) |
−0.722436 | + | 0.691437i | \(0.756978\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.7843 | − | 21.8148i | −1.58122 | − | 0.912920i | −0.994681 | − | 0.103002i | \(-0.967155\pi\) |
−0.586543 | − | 0.809918i | \(-0.699511\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −29.6992 | −1.23854 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.98123 | 0.290632 | 0.145316 | − | 0.989385i | \(-0.453580\pi\) | ||||
0.145316 | + | 0.989385i | \(0.453580\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.14274 | − | 5.27856i | −0.379305 | − | 0.218992i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.48124 | − | 6.02968i | −0.144178 | − | 0.249724i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.34574 | − | 4.24107i | 0.303191 | − | 0.175048i | −0.340684 | − | 0.940178i | \(-0.610659\pi\) |
0.643876 | + | 0.765130i | \(0.277325\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.17097 | − | 3.56281i | −0.254270 | − | 0.146803i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.40869 | 0.386368 | 0.193184 | − | 0.981163i | \(-0.438119\pi\) | ||||
0.193184 | + | 0.981163i | \(0.438119\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.25538i | 0.256445i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.9623 | + | 25.9155i | −0.611344 | + | 1.05888i | 0.379670 | + | 0.925122i | \(0.376038\pi\) |
−0.991014 | + | 0.133757i | \(0.957296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.81973 | + | 3.15186i | 0.0742282 | + | 0.128567i | 0.900750 | − | 0.434337i | \(-0.143017\pi\) |
−0.826522 | + | 0.562904i | \(0.809684\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.10782 | − | 1.21695i | 0.0856950 | − | 0.0494760i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.63358 | + | 6.29355i | −0.147482 | + | 0.255447i | −0.930296 | − | 0.366809i | \(-0.880450\pi\) |
0.782814 | + | 0.622256i | \(0.213784\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 42.4651i | 1.71795i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.6469i | 1.31859i | 0.751882 | + | 0.659297i | \(0.229146\pi\) | ||||
−0.751882 | + | 0.659297i | \(0.770854\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.6751 | + | 27.1501i | −0.631056 | + | 1.09302i | 0.356280 | + | 0.934379i | \(0.384045\pi\) |
−0.987336 | + | 0.158642i | \(0.949288\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.72589 | + | 0.996445i | −0.0693695 | + | 0.0400505i | −0.534284 | − | 0.845305i | \(-0.679419\pi\) |
0.464914 | + | 0.885356i | \(0.346085\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.37486 | − | 4.11339i | −0.0951469 | − | 0.164799i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.98375 | + | 15.5603i | −0.359350 | + | 0.622413i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 35.3538i | − | 1.40965i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.4643 | 0.615623 | 0.307812 | − | 0.951447i | \(-0.400403\pi\) | ||||
0.307812 | + | 0.951447i | \(0.400403\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.04135 | − | 0.601225i | −0.0413248 | − | 0.0238589i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.3192 | − | 12.3086i | 0.844697 | − | 0.487686i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.3638 | + | 21.4147i | 0.488340 | + | 0.845829i | 0.999910 | − | 0.0134123i | \(-0.00426940\pi\) |
−0.511570 | + | 0.859241i | \(0.670936\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.0176 | − | 23.1042i | −1.57814 | − | 0.911141i | −0.995119 | − | 0.0986850i | \(-0.968536\pi\) |
−0.583023 | − | 0.812456i | \(-0.698130\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.36971 | −0.250419 | −0.125210 | − | 0.992130i | \(-0.539960\pi\) | ||||
−0.125210 | + | 0.992130i | \(0.539960\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.6135 | −0.573630 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.8848 | + | 18.4087i | 1.24775 | + | 0.720389i | 0.970660 | − | 0.240455i | \(-0.0772968\pi\) |
0.277090 | + | 0.960844i | \(0.410630\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.31058 | + | 4.00205i | 0.0902820 | + | 0.156373i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.46565 | + | 3.73294i | −0.251866 | + | 0.145415i | −0.620618 | − | 0.784113i | \(-0.713118\pi\) |
0.368752 | + | 0.929528i | \(0.379785\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.51984 | − | 1.45483i | −0.0980102 | − | 0.0565862i | 0.450194 | − | 0.892931i | \(-0.351355\pi\) |
−0.548204 | + | 0.836345i | \(0.684688\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.06622 | 0.0413461 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 21.6505i | − | 0.838310i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.5525 | − | 21.7415i | 0.484582 | − | 0.839321i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.0527 | + | 36.4643i | 0.811522 | + | 1.40560i | 0.911799 | + | 0.410637i | \(0.134694\pi\) |
−0.100277 | + | 0.994960i | \(0.531973\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.9941 | − | 19.0492i | 1.26807 | − | 0.732119i | 0.293445 | − | 0.955976i | \(-0.405198\pi\) |
0.974622 | + | 0.223858i | \(0.0718650\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.98507 | + | 3.43825i | −0.0761801 | + | 0.131948i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 47.0728i | − | 1.80119i | −0.434659 | − | 0.900595i | \(-0.643131\pi\) | ||
0.434659 | − | 0.900595i | \(-0.356869\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.52421i | 0.0964450i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.99676 | + | 12.1187i | −0.266555 | + | 0.461687i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.38522 | − | 1.95446i | 0.128780 | − | 0.0743512i | −0.434226 | − | 0.900804i | \(-0.642978\pi\) |
0.563006 | + | 0.826453i | \(0.309645\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.02468 | − | 10.4350i | −0.228529 | − | 0.395824i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.26678 | − | 9.12234i | 0.199494 | − | 0.345533i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 16.4480i | − | 0.621231i | −0.950536 | − | 0.310615i | \(-0.899465\pi\) | ||
0.950536 | − | 0.310615i | \(-0.100535\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.02598 | −0.227274 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.0730 | + | 7.54772i | 0.491662 | + | 0.283861i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.84805 | − | 3.95372i | 0.257184 | − | 0.148485i | −0.365865 | − | 0.930668i | \(-0.619227\pi\) |
0.623049 | + | 0.782183i | \(0.285894\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.3251 | − | 42.1324i | −0.910984 | − | 1.57787i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.09037 | + | 5.24833i | 0.339961 | + | 0.196276i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.0556 | −1.38194 | −0.690970 | − | 0.722884i | \(-0.742816\pi\) | ||||
−0.690970 | + | 0.722884i | \(0.742816\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.4455 | 0.873156 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.8727 | − | 7.43204i | −0.478079 | − | 0.276019i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.83467 | − | 4.90979i | −0.105132 | − | 0.182094i | 0.808660 | − | 0.588276i | \(-0.200193\pi\) |
−0.913792 | + | 0.406182i | \(0.866860\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.9461 | + | 9.78381i | −0.626773 | + | 0.361867i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.8544 | − | 6.26677i | −0.400915 | − | 0.231469i | 0.285964 | − | 0.958240i | \(-0.407686\pi\) |
−0.686879 | + | 0.726772i | \(0.741020\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.8443 | −0.694139 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.83358i | − | 0.0674492i | −0.999431 | − | 0.0337246i | \(-0.989263\pi\) | ||
0.999431 | − | 0.0337246i | \(-0.0107369\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.6588 | + | 27.1219i | −0.574467 | + | 0.995006i | 0.421632 | + | 0.906767i | \(0.361457\pi\) |
−0.996099 | + | 0.0882391i | \(0.971876\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.52491 | + | 13.0335i | 0.275691 | + | 0.477511i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.7879 | + | 6.22841i | −0.394182 | + | 0.227581i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.64466 | + | 6.31274i | −0.132996 | + | 0.230355i | −0.924830 | − | 0.380381i | \(-0.875793\pi\) |
0.791834 | + | 0.610736i | \(0.209126\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 8.84005i | − | 0.321722i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.8156i | 0.465792i | 0.972502 | + | 0.232896i | \(0.0748202\pi\) | ||||
−0.972502 | + | 0.232896i | \(0.925180\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.5800 | + | 21.7892i | −0.456025 | + | 0.789859i | −0.998747 | − | 0.0500541i | \(-0.984061\pi\) |
0.542721 | + | 0.839913i | \(0.317394\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.333807 | − | 0.192724i | 0.0120846 | − | 0.00697706i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.6854 | + | 25.4359i | 0.530261 | + | 0.918439i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.7318 | + | 18.5880i | −0.386998 | + | 0.670300i | −0.992044 | − | 0.125890i | \(-0.959821\pi\) |
0.605046 | + | 0.796190i | \(0.293155\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.2122i | 0.726981i | 0.931598 | + | 0.363491i | \(0.118415\pi\) | ||||
−0.931598 | + | 0.363491i | \(0.881585\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.4007 | −1.19979 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.55488 | − | 0.897712i | −0.0557095 | − | 0.0321639i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.73811 | + | 5.04495i | −0.312674 | + | 0.180523i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.07957 | − | 10.5301i | −0.216989 | − | 0.375836i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.5726 | + | 10.1455i | 0.626395 | + | 0.361649i | 0.779355 | − | 0.626583i | \(-0.215547\pi\) |
−0.152960 | + | 0.988232i | \(0.548880\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.8274 | 0.491646 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −50.4570 | −1.79178 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.8758 | − | 16.6715i | −1.02283 | − | 0.590533i | −0.107910 | − | 0.994161i | \(-0.534416\pi\) |
−0.914924 | + | 0.403627i | \(0.867749\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.7970 | + | 37.7535i | 0.771122 | + | 1.33562i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.71815 | + | 3.87873i | −0.237078 | + | 0.136877i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.30432 | + | 3.63980i | 0.222198 | + | 0.128286i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.6920 | −1.07907 | −0.539536 | − | 0.841962i | \(-0.681400\pi\) | ||||
−0.539536 | + | 0.841962i | \(0.681400\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.5457i | 1.73978i | 0.493241 | + | 0.869892i | \(0.335812\pi\) | ||||
−0.493241 | + | 0.869892i | \(0.664188\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.98168 | + | 5.16443i | −0.104444 | + | 0.180902i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.66763 | + | 2.88842i | 0.0583430 | + | 0.101053i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.9739 | + | 19.0375i | −1.15080 | + | 0.664414i | −0.949082 | − | 0.315030i | \(-0.897985\pi\) |
−0.201716 | + | 0.979444i | \(0.564652\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.2626 | + | 19.5074i | −0.392589 | + | 0.679984i | −0.992790 | − | 0.119865i | \(-0.961754\pi\) |
0.600201 | + | 0.799849i | \(0.295087\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.5317i | 1.16601i | 0.812468 | + | 0.583006i | \(0.198124\pi\) | ||||
−0.812468 | + | 0.583006i | \(0.801876\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 37.7559i | − | 1.31132i | −0.755058 | − | 0.655658i | \(-0.772391\pi\) | ||
0.755058 | − | 0.655658i | \(-0.227609\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.6359 | − | 21.8860i | 0.437807 | − | 0.758304i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.20378 | − | 4.15910i | 0.249297 | − | 0.143932i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.90604 | − | 17.1578i | −0.341994 | − | 0.592352i | 0.642809 | − | 0.766027i | \(-0.277769\pi\) |
−0.984803 | + | 0.173675i | \(0.944436\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.08210 | + | 15.7307i | −0.313176 | + | 0.542436i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 12.0481i | − | 0.414466i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.56028 | 0.191053 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −35.6304 | − | 20.5712i | −1.22140 | − | 0.705173i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.95424 | − | 3.43768i | 0.203869 | − | 0.117704i | −0.394590 | − | 0.918857i | \(-0.629113\pi\) |
0.598459 | + | 0.801153i | \(0.295780\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.87316 | + | 6.70851i | 0.132305 | + | 0.229158i | 0.924565 | − | 0.381025i | \(-0.124429\pi\) |
−0.792260 | + | 0.610184i | \(0.791096\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.594592 | + | 0.343288i | 0.0202872 | + | 0.0117128i | 0.510109 | − | 0.860110i | \(-0.329605\pi\) |
−0.489822 | + | 0.871822i | \(0.662938\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.9194 | −1.46099 | −0.730496 | − | 0.682917i | \(-0.760711\pi\) | ||||
−0.730496 | + | 0.682917i | \(0.760711\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.07991 | −0.308726 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.6578 | + | 7.88535i | 0.463310 | + | 0.267492i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.9371 | + | 32.8000i | 0.641658 | + | 1.11138i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.12082 | − | 5.26591i | 0.308340 | − | 0.178020i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.7508 | − | 8.51640i | −0.498100 | − | 0.287578i | 0.229828 | − | 0.973231i | \(-0.426183\pi\) |
−0.727929 | + | 0.685653i | \(0.759517\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.90546 | 0.266342 | 0.133171 | − | 0.991093i | \(-0.457484\pi\) | ||||
0.133171 | + | 0.991093i | \(0.457484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.53298i | 0.253505i | 0.991934 | + | 0.126752i | \(0.0404554\pi\) | ||||
−0.991934 | + | 0.126752i | \(0.959545\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.02719 | − | 12.1715i | 0.235950 | − | 0.408677i | −0.723598 | − | 0.690221i | \(-0.757513\pi\) |
0.959548 | + | 0.281544i | \(0.0908465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.37351 | − | 2.37899i | −0.0460660 | − | 0.0797886i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.43501 | − | 3.71525i | 0.215339 | − | 0.124326i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.15500 | − | 2.00052i | 0.0386075 | − | 0.0668701i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 24.3489i | − | 0.812081i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.3655i | 0.478585i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.19001 | + | 8.98936i | −0.172522 | + | 0.298816i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.7958 | − | 22.9761i | 1.32140 | − | 0.762910i | 0.337447 | − | 0.941345i | \(-0.390437\pi\) |
0.983952 | + | 0.178435i | \(0.0571034\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.7911 | + | 44.6715i | 0.854497 | + | 1.48003i | 0.877111 | + | 0.480288i | \(0.159468\pi\) |
−0.0226136 | + | 0.999744i | \(0.507199\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.09302 | + | 15.7496i | −0.300935 | + | 0.521235i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.5571i | 0.348627i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.2048 | 0.699481 | 0.349741 | − | 0.936847i | \(-0.386270\pi\) | ||||
0.349741 | + | 0.936847i | \(0.386270\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.5623 | + | 10.1396i | 0.578069 | + | 0.333748i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.4620 | + | 14.1231i | −0.804305 | + | 0.464366i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.70516 | − | 2.95343i | −0.0559446 | − | 0.0968989i | 0.836697 | − | 0.547666i | \(-0.184484\pi\) |
−0.892641 | + | 0.450767i | \(0.851150\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.73042 | − | 2.15376i | −0.122259 | − | 0.0705865i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.7757 | 0.352403 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.4448 | 0.961919 | 0.480959 | − | 0.876743i | \(-0.340288\pi\) | ||||
0.480959 | + | 0.876743i | \(0.340288\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.5880 | − | 23.4335i | −1.32313 | − | 0.763910i | −0.338904 | − | 0.940821i | \(-0.610056\pi\) |
−0.984227 | + | 0.176911i | \(0.943389\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.12914 | − | 10.6160i | −0.199592 | − | 0.345704i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.5821 | − | 18.2340i | 1.02628 | − | 0.592524i | 0.110365 | − | 0.993891i | \(-0.464798\pi\) |
0.915917 | + | 0.401367i | \(0.131465\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.5024 | + | 7.79564i | 0.438308 | + | 0.253057i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.0590 | −1.23285 | −0.616426 | − | 0.787413i | \(-0.711420\pi\) | ||||
−0.616426 | + | 0.787413i | \(0.711420\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 5.09344i | − | 0.164820i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.88330 | + | 4.99401i | −0.0931065 | + | 0.161265i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.8569 | − | 20.5368i | −0.382481 | − | 0.662477i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.3397 | − | 7.12430i | 0.397228 | − | 0.229339i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.4864 | + | 19.8951i | −0.369378 | + | 0.639782i | −0.989468 | − | 0.144749i | \(-0.953763\pi\) |
0.620090 | + | 0.784531i | \(0.287096\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 53.8829i | − | 1.72919i | −0.502474 | − | 0.864593i | \(-0.667577\pi\) | ||
0.502474 | − | 0.864593i | \(-0.332423\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 27.5269i | − | 0.882473i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.1024 | + | 33.0863i | −0.611140 | + | 1.05853i | 0.379909 | + | 0.925024i | \(0.375955\pi\) |
−0.991049 | + | 0.133501i | \(0.957378\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.08585 | + | 4.09102i | −0.226465 | + | 0.130749i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.3307 | − | 42.1420i | −0.776028 | − | 1.34412i | −0.934215 | − | 0.356711i | \(-0.883898\pi\) |
0.158186 | − | 0.987409i | \(-0.449435\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.14968 | + | 12.3836i | −0.227808 | + | 0.394574i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.7715i | 0.724093i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.7822 | 0.406040 | 0.203020 | − | 0.979175i | \(-0.434924\pi\) | ||||
0.203020 | + | 0.979175i | \(0.434924\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.17905 | + | 0.680723i | 0.0373783 | + | 0.0215804i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.1161 | + | 12.1914i | −0.668752 | + | 0.386104i | −0.795604 | − | 0.605817i | \(-0.792846\pi\) |
0.126851 | + | 0.991922i | \(0.459513\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 864.2.r.b.145.4 | 16 | ||
3.2 | odd | 2 | 288.2.r.b.49.7 | 16 | |||
4.3 | odd | 2 | 216.2.n.b.37.2 | 16 | |||
8.3 | odd | 2 | 216.2.n.b.37.8 | 16 | |||
8.5 | even | 2 | inner | 864.2.r.b.145.5 | 16 | ||
9.2 | odd | 6 | 288.2.r.b.241.2 | 16 | |||
9.4 | even | 3 | 2592.2.d.k.1297.5 | 8 | |||
9.5 | odd | 6 | 2592.2.d.j.1297.4 | 8 | |||
9.7 | even | 3 | inner | 864.2.r.b.721.5 | 16 | ||
12.11 | even | 2 | 72.2.n.b.13.7 | yes | 16 | ||
24.5 | odd | 2 | 288.2.r.b.49.2 | 16 | |||
24.11 | even | 2 | 72.2.n.b.13.1 | ✓ | 16 | ||
36.7 | odd | 6 | 216.2.n.b.181.8 | 16 | |||
36.11 | even | 6 | 72.2.n.b.61.1 | yes | 16 | ||
36.23 | even | 6 | 648.2.d.j.325.6 | 8 | |||
36.31 | odd | 6 | 648.2.d.k.325.3 | 8 | |||
72.5 | odd | 6 | 2592.2.d.j.1297.5 | 8 | |||
72.11 | even | 6 | 72.2.n.b.61.7 | yes | 16 | ||
72.13 | even | 6 | 2592.2.d.k.1297.4 | 8 | |||
72.29 | odd | 6 | 288.2.r.b.241.7 | 16 | |||
72.43 | odd | 6 | 216.2.n.b.181.2 | 16 | |||
72.59 | even | 6 | 648.2.d.j.325.5 | 8 | |||
72.61 | even | 6 | inner | 864.2.r.b.721.4 | 16 | ||
72.67 | odd | 6 | 648.2.d.k.325.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.n.b.13.1 | ✓ | 16 | 24.11 | even | 2 | ||
72.2.n.b.13.7 | yes | 16 | 12.11 | even | 2 | ||
72.2.n.b.61.1 | yes | 16 | 36.11 | even | 6 | ||
72.2.n.b.61.7 | yes | 16 | 72.11 | even | 6 | ||
216.2.n.b.37.2 | 16 | 4.3 | odd | 2 | |||
216.2.n.b.37.8 | 16 | 8.3 | odd | 2 | |||
216.2.n.b.181.2 | 16 | 72.43 | odd | 6 | |||
216.2.n.b.181.8 | 16 | 36.7 | odd | 6 | |||
288.2.r.b.49.2 | 16 | 24.5 | odd | 2 | |||
288.2.r.b.49.7 | 16 | 3.2 | odd | 2 | |||
288.2.r.b.241.2 | 16 | 9.2 | odd | 6 | |||
288.2.r.b.241.7 | 16 | 72.29 | odd | 6 | |||
648.2.d.j.325.5 | 8 | 72.59 | even | 6 | |||
648.2.d.j.325.6 | 8 | 36.23 | even | 6 | |||
648.2.d.k.325.3 | 8 | 36.31 | odd | 6 | |||
648.2.d.k.325.4 | 8 | 72.67 | odd | 6 | |||
864.2.r.b.145.4 | 16 | 1.1 | even | 1 | trivial | ||
864.2.r.b.145.5 | 16 | 8.5 | even | 2 | inner | ||
864.2.r.b.721.4 | 16 | 72.61 | even | 6 | inner | ||
864.2.r.b.721.5 | 16 | 9.7 | even | 3 | inner | ||
2592.2.d.j.1297.4 | 8 | 9.5 | odd | 6 | |||
2592.2.d.j.1297.5 | 8 | 72.5 | odd | 6 | |||
2592.2.d.k.1297.4 | 8 | 72.13 | even | 6 | |||
2592.2.d.k.1297.5 | 8 | 9.4 | even | 3 |