Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(577,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.s (of order \(3\), 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1368) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1873.4 | ||
Root | \(0.643668 + 1.11487i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1873 |
Dual form | 2736.2.s.bc.577.4 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.95872 | − | 3.39260i | 0.875966 | − | 1.51722i | 0.0202354 | − | 0.999795i | \(-0.493558\pi\) |
0.855730 | − | 0.517422i | \(-0.173108\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.04306 | −0.772204 | −0.386102 | − | 0.922456i | \(-0.626179\pi\) | ||||
−0.386102 | + | 0.922456i | \(0.626179\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.91744 | 0.578129 | 0.289065 | − | 0.957310i | \(-0.406656\pi\) | ||||
0.289065 | + | 0.957310i | \(0.406656\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.13010 | + | 3.68945i | 0.590784 | + | 1.02327i | 0.994127 | + | 0.108219i | \(0.0345148\pi\) |
−0.403343 | + | 0.915049i | \(0.632152\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.04306 | − | 5.27073i | 0.738050 | − | 1.27834i | −0.215322 | − | 0.976543i | \(-0.569080\pi\) |
0.953372 | − | 0.301797i | \(-0.0975865\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.33039 | − | 0.497680i | −0.993461 | − | 0.114176i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.42711 | − | 5.93592i | −0.714601 | − | 1.23773i | −0.963113 | − | 0.269096i | \(-0.913275\pi\) |
0.248512 | − | 0.968629i | \(-0.420058\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.17316 | − | 8.96018i | −1.03463 | − | 1.79204i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.34277 | + | 2.32574i | 0.249345 | + | 0.431879i | 0.963344 | − | 0.268268i | \(-0.0864512\pi\) |
−0.713999 | + | 0.700147i | \(0.753118\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.46839 | 0.263730 | 0.131865 | − | 0.991268i | \(-0.457903\pi\) | ||||
0.131865 | + | 0.991268i | \(0.457903\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00178 | + | 6.93128i | −0.676424 | + | 1.17160i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.93677 | 0.647202 | 0.323601 | − | 0.946194i | \(-0.395107\pi\) | ||||
0.323601 | + | 0.946194i | \(0.395107\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.70029 | − | 2.94499i | 0.265541 | − | 0.459930i | −0.702164 | − | 0.712015i | \(-0.747783\pi\) |
0.967705 | + | 0.252085i | \(0.0811161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.77725 | − | 6.54239i | 0.576026 | − | 0.997705i | −0.419904 | − | 0.907569i | \(-0.637936\pi\) |
0.995929 | − | 0.0901369i | \(-0.0287304\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.96050 | + | 8.59183i | 0.723563 | + | 1.25325i | 0.959563 | + | 0.281494i | \(0.0908301\pi\) |
−0.236000 | + | 0.971753i | \(0.575837\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.82591 | −0.403702 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.91922 | − | 8.52033i | −0.675706 | − | 1.17036i | −0.976262 | − | 0.216593i | \(-0.930505\pi\) |
0.300556 | − | 0.953764i | \(-0.402828\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.75572 | − | 6.50510i | 0.506422 | − | 0.877148i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.61595 | + | 2.79891i | −0.210379 | + | 0.364387i | −0.951833 | − | 0.306616i | \(-0.900803\pi\) |
0.741454 | + | 0.671004i | \(0.234136\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.70477 | − | 8.14891i | −0.602385 | − | 1.04336i | −0.992459 | − | 0.122577i | \(-0.960884\pi\) |
0.390074 | − | 0.920783i | \(-0.372449\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.6891 | 2.07003 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.28173 | + | 9.14823i | 0.645266 | + | 1.11763i | 0.984240 | + | 0.176838i | \(0.0565870\pi\) |
−0.338973 | + | 0.940796i | \(0.610080\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.21715 | − | 3.84021i | 0.263127 | − | 0.455749i | −0.703944 | − | 0.710255i | \(-0.748580\pi\) |
0.967071 | + | 0.254506i | \(0.0819129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.33488 | + | 10.9723i | −0.741441 | + | 1.28421i | 0.210398 | + | 0.977616i | \(0.432524\pi\) |
−0.951839 | + | 0.306598i | \(0.900809\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.91744 | −0.446434 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.52601 | − | 11.3034i | 0.734234 | − | 1.27173i | −0.220825 | − | 0.975313i | \(-0.570875\pi\) |
0.955059 | − | 0.296417i | \(-0.0957917\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.43429 | −0.486727 | −0.243363 | − | 0.969935i | \(-0.578251\pi\) | ||||
−0.243363 | + | 0.969935i | \(0.578251\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.9210 | − | 20.6478i | −1.29301 | − | 2.23956i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.47016 | + | 6.01050i | 0.367837 | + | 0.637112i | 0.989227 | − | 0.146389i | \(-0.0467652\pi\) |
−0.621390 | + | 0.783501i | \(0.713432\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.35192 | − | 7.53775i | −0.456206 | − | 0.790171i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.1705 | + | 13.7165i | −1.04347 | + | 1.40728i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.58704 | − | 4.48089i | 0.262675 | − | 0.454966i | −0.704277 | − | 0.709925i | \(-0.748729\pi\) |
0.966952 | + | 0.254959i | \(0.0820621\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.79182 | − | 8.29967i | −0.476804 | − | 0.825848i | 0.522843 | − | 0.852429i | \(-0.324871\pi\) |
−0.999647 | + | 0.0265808i | \(0.991538\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.7128 | −1.74530 | −0.872648 | − | 0.488351i | \(-0.837599\pi\) | ||||
−0.872648 | + | 0.488351i | \(0.837599\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.8578 | −1.04966 | −0.524830 | − | 0.851207i | \(-0.675871\pi\) | ||||
−0.524830 | + | 0.851207i | \(0.675871\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.41296 | − | 5.91141i | 0.326902 | − | 0.566211i | −0.654994 | − | 0.755634i | \(-0.727329\pi\) |
0.981895 | + | 0.189424i | \(0.0606620\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.16868 | 0.580300 | 0.290150 | − | 0.956981i | \(-0.406295\pi\) | ||||
0.290150 | + | 0.956981i | \(0.406295\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −26.8510 | −2.50386 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.21715 | + | 10.7684i | −0.569925 | + | 0.987139i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.32343 | −0.665766 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −20.9439 | −1.87328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.4095 | − | 18.0299i | −0.923698 | − | 1.59989i | −0.793642 | − | 0.608385i | \(-0.791818\pi\) |
−0.130056 | − | 0.991507i | \(-0.541516\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.61773 | + | 2.80199i | −0.141342 | + | 0.244811i | −0.928002 | − | 0.372575i | \(-0.878475\pi\) |
0.786660 | + | 0.617386i | \(0.211808\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.84725 | + | 1.01679i | 0.767154 | + | 0.0881669i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.405993 | + | 0.703200i | 0.0346863 | + | 0.0600785i | 0.882847 | − | 0.469660i | \(-0.155623\pi\) |
−0.848161 | + | 0.529738i | \(0.822290\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.77725 | − | 3.07829i | −0.150745 | − | 0.261097i | 0.780757 | − | 0.624835i | \(-0.214834\pi\) |
−0.931501 | + | 0.363738i | \(0.881500\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.08434 | + | 7.07428i | 0.341550 | + | 0.591581i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.5204 | 0.873672 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.3445 | + | 17.9173i | −0.847458 | + | 1.46784i | 0.0360112 | + | 0.999351i | \(0.488535\pi\) |
−0.883469 | + | 0.468489i | \(0.844799\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.0408 | 1.38676 | 0.693381 | − | 0.720571i | \(-0.256120\pi\) | ||||
0.693381 | + | 0.720571i | \(0.256120\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.87616 | − | 4.98165i | 0.231019 | − | 0.400136i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.62918 | − | 16.6782i | 0.768492 | − | 1.33107i | −0.169889 | − | 0.985463i | \(-0.554341\pi\) |
0.938381 | − | 0.345604i | \(-0.112326\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.00178 | + | 12.1274i | 0.551817 | + | 0.955776i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.32801 | 0.104018 | 0.0520088 | − | 0.998647i | \(-0.483438\pi\) | ||||
0.0520088 | + | 0.998647i | \(0.483438\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.49033 | − | 11.2416i | −0.502237 | − | 0.869900i | −0.999997 | − | 0.00258498i | \(-0.999177\pi\) |
0.497760 | − | 0.867315i | \(-0.334156\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.57467 | + | 4.45946i | −0.198052 | + | 0.343036i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.49211 | + | 4.31646i | −0.189472 | + | 0.328174i | −0.945074 | − | 0.326856i | \(-0.894011\pi\) |
0.755603 | + | 0.655030i | \(0.227344\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.5691 | + | 18.3062i | 0.798947 | + | 1.38382i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.6101 | 1.24150 | 0.620748 | − | 0.784010i | \(-0.286829\pi\) | ||||
0.620748 | + | 0.784010i | \(0.286829\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.52382 | + | 6.10343i | 0.261923 | + | 0.453664i | 0.966753 | − | 0.255712i | \(-0.0823099\pi\) |
−0.704830 | + | 0.709377i | \(0.748977\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.71103 | − | 13.3559i | 0.566926 | − | 0.981945i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.83488 | − | 10.1063i | 0.426688 | − | 0.739046i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.1687 | 1.16992 | 0.584962 | − | 0.811061i | \(-0.301109\pi\) | ||||
0.584962 | + | 0.811061i | \(0.301109\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.32250 | + | 14.4150i | −0.599067 | + | 1.03761i | 0.393892 | + | 0.919157i | \(0.371128\pi\) |
−0.992959 | + | 0.118458i | \(0.962205\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.23191 | −0.657746 | −0.328873 | − | 0.944374i | \(-0.606669\pi\) | ||||
−0.328873 | + | 0.944374i | \(0.606669\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.82031 | − | 11.8131i | −0.483479 | − | 0.837410i | 0.516341 | − | 0.856383i | \(-0.327294\pi\) |
−0.999820 | + | 0.0189729i | \(0.993960\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.74335 | − | 4.75162i | −0.192545 | − | 0.333499i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.66079 | − | 11.5368i | −0.465210 | − | 0.805767i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.30326 | − | 0.954271i | −0.574349 | − | 0.0660083i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.10068 | + | 3.63849i | −0.144617 | + | 0.250484i | −0.929230 | − | 0.369502i | \(-0.879528\pi\) |
0.784613 | + | 0.619986i | \(0.212862\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.7972 | − | 25.6294i | −1.00916 | − | 1.74791i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | −0.203653 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.9281 | 1.74411 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.82927 | + | 13.5607i | −0.524287 | + | 0.908092i | 0.475313 | + | 0.879817i | \(0.342335\pi\) |
−0.999600 | + | 0.0282750i | \(0.990999\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.1758 | 1.87009 | 0.935046 | − | 0.354525i | \(-0.115358\pi\) | ||||
0.935046 | + | 0.354525i | \(0.115358\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.23731 | 0.478255 | 0.239128 | − | 0.970988i | \(-0.423139\pi\) | ||||
0.239128 | + | 0.970988i | \(0.423139\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.96405 | + | 15.5262i | −0.587255 | + | 1.01715i | 0.407336 | + | 0.913279i | \(0.366458\pi\) |
−0.994590 | + | 0.103876i | \(0.966875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 38.8649 | 2.53527 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.08256 | 0.134710 | 0.0673549 | − | 0.997729i | \(-0.478544\pi\) | ||||
0.0673549 | + | 0.997729i | \(0.478544\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.90955 | + | 10.2356i | 0.380667 | + | 0.659335i | 0.991158 | − | 0.132688i | \(-0.0423609\pi\) |
−0.610490 | + | 0.792024i | \(0.709028\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.53517 | + | 9.58719i | −0.353629 | + | 0.612503i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.38802 | − | 17.0369i | −0.470088 | − | 1.08403i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.434292 | + | 0.752216i | 0.0274123 | + | 0.0474795i | 0.879406 | − | 0.476072i | \(-0.157940\pi\) |
−0.851994 | + | 0.523552i | \(0.824607\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.57126 | − | 11.3818i | −0.413132 | − | 0.715565i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.85243 | − | 10.1367i | −0.365065 | − | 0.632311i | 0.623722 | − | 0.781646i | \(-0.285620\pi\) |
−0.988787 | + | 0.149336i | \(0.952287\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.04306 | −0.499771 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.7038 | − | 27.1999i | 0.968341 | − | 1.67722i | 0.267982 | − | 0.963424i | \(-0.413643\pi\) |
0.700358 | − | 0.713791i | \(-0.253024\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −38.5414 | −2.36758 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.68731 | − | 13.3148i | 0.468704 | − | 0.811818i | −0.530657 | − | 0.847587i | \(-0.678055\pi\) |
0.999360 | + | 0.0357685i | \(0.0113879\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.94574 | + | 17.2265i | −0.604161 | + | 1.04644i | 0.388023 | + | 0.921650i | \(0.373158\pi\) |
−0.992184 | + | 0.124787i | \(0.960175\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.91922 | − | 17.1806i | −0.598151 | − | 1.03603i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.19698 | 0.252172 | 0.126086 | − | 0.992019i | \(-0.459758\pi\) | ||||
0.126086 | + | 0.992019i | \(0.459758\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.95872 | + | 13.7849i | 0.474777 | + | 0.822339i | 0.999583 | − | 0.0288837i | \(-0.00919524\pi\) |
−0.524805 | + | 0.851222i | \(0.675862\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.76269 | + | 6.51716i | −0.223668 | + | 0.387405i | −0.955919 | − | 0.293630i | \(-0.905137\pi\) |
0.732251 | + | 0.681035i | \(0.238470\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.47380 | + | 6.01679i | −0.205052 | + | 0.355160i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0204 | − | 17.3559i | −0.589436 | − | 1.02093i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.7962 | 1.27335 | 0.636674 | − | 0.771133i | \(-0.280310\pi\) | ||||
0.636674 | + | 0.771133i | \(0.280310\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.33039 | + | 10.9646i | 0.368570 | + | 0.638382i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.6002 | − | 25.2882i | 0.844350 | − | 1.46246i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.71715 | + | 13.3665i | −0.444809 | + | 0.770432i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −36.8613 | −2.11067 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.3394 | − | 26.5685i | 0.875463 | − | 1.51635i | 0.0191951 | − | 0.999816i | \(-0.493890\pi\) |
0.856268 | − | 0.516531i | \(-0.172777\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.0530439 | 0.00300784 | 0.00150392 | − | 0.999999i | \(-0.499521\pi\) | ||||
0.00150392 | + | 0.999999i | \(0.499521\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.07374 | + | 7.05593i | 0.230262 | + | 0.398825i | 0.957885 | − | 0.287152i | \(-0.0927085\pi\) |
−0.727623 | + | 0.685977i | \(0.759375\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.1126 | − | 22.7118i | −0.736479 | − | 1.27562i | −0.954071 | − | 0.299580i | \(-0.903154\pi\) |
0.217592 | − | 0.976040i | \(-0.430180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.57467 | + | 4.45946i | 0.144154 | + | 0.249682i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.8008 | + | 21.3099i | −0.879179 | + | 1.18571i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.0387 | − | 38.1722i | 1.22249 | − | 2.11741i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.1346 | − | 17.5536i | −0.558738 | − | 0.967762i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.359379 | −0.0197533 | −0.00987664 | − | 0.999951i | \(-0.503144\pi\) | ||||
−0.00987664 | + | 0.999951i | \(0.503144\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 41.3817 | 2.26093 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.3454 | + | 24.8470i | −0.781443 | + | 1.35350i | 0.149657 | + | 0.988738i | \(0.452183\pi\) |
−0.931101 | + | 0.364762i | \(0.881150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.81554 | 0.152470 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0749 | 1.08394 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.64781 | − | 13.2464i | 0.410556 | − | 0.711103i | −0.584395 | − | 0.811469i | \(-0.698668\pi\) |
0.994951 | + | 0.100366i | \(0.0320014\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.75772 | −0.308204 | −0.154102 | − | 0.988055i | \(-0.549248\pi\) | ||||
−0.154102 | + | 0.988055i | \(0.549248\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.8950 | 0.739558 | 0.369779 | − | 0.929120i | \(-0.379433\pi\) | ||||
0.369779 | + | 0.929120i | \(0.379433\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.68553 | − | 15.0438i | −0.460980 | − | 0.798441i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.936774 | + | 1.62254i | −0.0494410 | + | 0.0856344i | −0.889687 | − | 0.456571i | \(-0.849077\pi\) |
0.840246 | + | 0.542206i | \(0.182411\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5046 | + | 4.31030i | 0.973928 | + | 0.226858i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.8165 | + | 42.9834i | 1.29895 | + | 2.24985i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.526011 | − | 0.911078i | −0.0274576 | − | 0.0475579i | 0.851970 | − | 0.523590i | \(-0.175408\pi\) |
−0.879428 | + | 0.476033i | \(0.842074\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.0502 | + | 17.4075i | 0.521783 | + | 0.903754i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.6908 | 1.74444 | 0.872221 | − | 0.489111i | \(-0.162679\pi\) | ||||
0.872221 | + | 0.489111i | \(0.162679\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.72046 | + | 9.90813i | −0.294619 | + | 0.510295i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.1157 | −1.80377 | −0.901887 | − | 0.431972i | \(-0.857818\pi\) | ||||
−0.901887 | + | 0.431972i | \(0.857818\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.75054 | + | 13.4243i | −0.396034 | + | 0.685951i | −0.993233 | − | 0.116142i | \(-0.962947\pi\) |
0.597199 | + | 0.802093i | \(0.296280\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.67316 | + | 13.2903i | −0.391060 | + | 0.677337i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.28215 | + | 10.8810i | 0.318518 | + | 0.551689i | 0.980179 | − | 0.198114i | \(-0.0634817\pi\) |
−0.661661 | + | 0.749803i | \(0.730148\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −41.7155 | −2.10965 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −25.5652 | − | 44.2803i | −1.28633 | − | 2.22798i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.01924 | − | 5.22948i | 0.151531 | − | 0.262460i | −0.780259 | − | 0.625456i | \(-0.784913\pi\) |
0.931791 | + | 0.362996i | \(0.118246\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.1557 | + | 17.5902i | −0.507151 | + | 0.878412i | 0.492814 | + | 0.870134i | \(0.335968\pi\) |
−0.999966 | + | 0.00827741i | \(0.997365\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.12781 | + | 5.41753i | 0.155808 | + | 0.269867i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.54852 | 0.374166 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.0580 | + | 29.5453i | 0.843462 | + | 1.46092i | 0.886950 | + | 0.461865i | \(0.152820\pi\) |
−0.0434881 | + | 0.999054i | \(0.513847\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.30149 | − | 5.71834i | 0.162455 | − | 0.281381i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.68553 | + | 15.0438i | −0.426356 | + | 0.738470i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.326693 | 0.0159600 | 0.00797999 | − | 0.999968i | \(-0.497460\pi\) | ||||
0.00797999 | + | 0.999968i | \(0.497460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0195 | + | 17.3543i | −0.488320 | + | 0.845795i | −0.999910 | − | 0.0134352i | \(-0.995723\pi\) |
0.511590 | + | 0.859230i | \(0.329057\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −62.9689 | −3.05444 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.61213 | + | 16.6487i | 0.465163 | + | 0.805687i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.2297 | − | 29.8427i | −0.829924 | − | 1.43747i | −0.898097 | − | 0.439797i | \(-0.855051\pi\) |
0.0681736 | − | 0.997673i | \(-0.478283\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.10993 | − | 10.5827i | −0.293625 | − | 0.508573i | 0.681039 | − | 0.732247i | \(-0.261528\pi\) |
−0.974664 | + | 0.223674i | \(0.928195\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.8865 | + | 27.4105i | 0.568610 | + | 1.31122i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.93356 | + | 10.2772i | −0.283193 | + | 0.490505i | −0.972169 | − | 0.234279i | \(-0.924727\pi\) |
0.688976 | + | 0.724784i | \(0.258060\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.154752 | − | 0.268039i | −0.00735250 | − | 0.0127349i | 0.862326 | − | 0.506354i | \(-0.169007\pi\) |
−0.869678 | + | 0.493619i | \(0.835674\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.1883 | 1.28885 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.5275 | −1.06314 | −0.531570 | − | 0.847015i | \(-0.678398\pi\) | ||||
−0.531570 | + | 0.847015i | \(0.678398\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.26020 | − | 5.64684i | 0.153517 | − | 0.265899i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −34.0968 | −1.59848 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.6679 | 1.38781 | 0.693903 | − | 0.720069i | \(-0.255890\pi\) | ||||
0.693903 | + | 0.720069i | \(0.255890\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.2530 | − | 19.4908i | 0.524105 | − | 0.907777i | −0.475501 | − | 0.879715i | \(-0.657733\pi\) |
0.999606 | − | 0.0280618i | \(-0.00893351\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.7041 | 1.42694 | 0.713471 | − | 0.700685i | \(-0.247122\pi\) | ||||
0.713471 | + | 0.700685i | \(0.247122\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 38.0932 | 1.76274 | 0.881372 | − | 0.472423i | \(-0.156620\pi\) | ||||
0.881372 | + | 0.472423i | \(0.156620\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.7909 | − | 18.6904i | −0.498277 | − | 0.863041i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.24265 | − | 12.5446i | 0.333017 | − | 0.576803i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.9425 | + | 41.3757i | 0.823259 | + | 1.89845i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.4755 | + | 21.6082i | 0.570020 | + | 0.987304i | 0.996563 | + | 0.0828364i | \(0.0263979\pi\) |
−0.426543 | + | 0.904467i | \(0.640269\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.38573 | + | 14.5245i | 0.382356 | + | 0.662261i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.1346 | − | 17.5536i | −0.460188 | − | 0.797069i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.6747 | 0.755603 | 0.377802 | − | 0.925887i | \(-0.376680\pi\) | ||||
0.377802 | + | 0.925887i | \(0.376680\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.6881 | + | 21.9764i | −0.572604 | + | 0.991780i | 0.423693 | + | 0.905806i | \(0.360734\pi\) |
−0.996297 | + | 0.0859741i | \(0.972600\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.3445 | 0.736118 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.52976 | + | 7.84577i | −0.203187 | + | 0.351931i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.92421 | − | 10.2610i | 0.265204 | − | 0.459347i | −0.702413 | − | 0.711770i | \(-0.747894\pi\) |
0.967617 | + | 0.252423i | \(0.0812274\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.0125 | + | 19.0742i | 0.491024 | + | 0.850478i | 0.999947 | − | 0.0103338i | \(-0.00328942\pi\) |
−0.508923 | + | 0.860812i | \(0.669956\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −37.5433 | −1.67065 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.16512 | + | 14.1424i | 0.361913 | + | 0.626851i | 0.988276 | − | 0.152680i | \(-0.0487905\pi\) |
−0.626363 | + | 0.779532i | \(0.715457\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.9425 | − | 22.4171i | 0.572543 | − | 0.991674i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −34.6944 | + | 60.0925i | −1.52882 | + | 2.64799i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.51145 | + | 16.4743i | 0.418313 | + | 0.724539i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.3180 | 1.54731 | 0.773655 | − | 0.633607i | \(-0.218426\pi\) | ||||
0.773655 | + | 0.633607i | \(0.218426\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.22971 | + | 10.7902i | 0.272406 | + | 0.471821i | 0.969477 | − | 0.245180i | \(-0.0788472\pi\) |
−0.697071 | + | 0.717002i | \(0.745514\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.46839 | − | 7.73947i | 0.194646 | − | 0.337137i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.9901 | + | 20.7675i | −0.521309 | + | 0.902934i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.4872 | 0.627510 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.2673 | + | 36.8361i | −0.919466 | + | 1.59256i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.41851 | −0.233392 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.6629 | + | 20.2007i | 0.501427 | + | 0.868496i | 0.999999 | + | 0.00164801i | \(0.000524577\pi\) |
−0.498572 | + | 0.866848i | \(0.666142\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.3700 | − | 23.1576i | −0.572710 | − | 0.991962i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.26581 | + | 3.92449i | 0.0968789 | + | 0.167799i | 0.910391 | − | 0.413749i | \(-0.135781\pi\) |
−0.813512 | + | 0.581548i | \(0.802447\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.65723 | − | 10.7396i | −0.198405 | − | 0.457524i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.3330 | + | 23.0935i | −0.566978 | + | 0.982034i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.05782 | − | 10.4924i | −0.256678 | − | 0.444579i | 0.708672 | − | 0.705538i | \(-0.249295\pi\) |
−0.965350 | + | 0.260959i | \(0.915961\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.1837 | 1.36123 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.3553 | 0.605003 | 0.302502 | − | 0.953149i | \(-0.402178\pi\) | ||||
0.302502 | + | 0.953149i | \(0.402178\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.0827 | − | 20.9279i | 0.508323 | − | 0.880442i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.69927 | −0.238926 | −0.119463 | − | 0.992839i | \(-0.538117\pi\) | ||||
−0.119463 | + | 0.992839i | \(0.538117\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.20155 | −0.133981 | −0.0669904 | − | 0.997754i | \(-0.521340\pi\) | ||||
−0.0669904 | + | 0.997754i | \(0.521340\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −35.4579 | + | 61.4150i | −1.47870 | + | 2.56118i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.4957 | 0.769985 | 0.384992 | − | 0.922920i | \(-0.374204\pi\) | ||||
0.384992 | + | 0.922920i | \(0.374204\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.05952 | 0.375852 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.43229 | − | 16.3372i | −0.390646 | − | 0.676618i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.7487 | − | 18.6173i | 0.443646 | − | 0.768417i | −0.554311 | − | 0.832310i | \(-0.687018\pi\) |
0.997957 | + | 0.0638928i | \(0.0203516\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.35869 | − | 0.730787i | −0.262005 | − | 0.0301116i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.2225 | + | 40.2225i | 0.953633 | + | 1.65174i | 0.737466 | + | 0.675384i | \(0.236022\pi\) |
0.216167 | + | 0.976356i | \(0.430644\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.3553 | + | 42.1846i | 0.998469 | + | 1.72940i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.23013 | + | 2.13064i | 0.0502617 | + | 0.0870557i | 0.890062 | − | 0.455840i | \(-0.150661\pi\) |
−0.839800 | + | 0.542896i | \(0.817328\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.4329 | −1.77167 | −0.885833 | − | 0.464004i | \(-0.846412\pi\) | ||||
−0.885833 | + | 0.464004i | \(0.846412\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.3445 | + | 24.8455i | −0.583189 | + | 1.01011i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.2875 | 0.579911 | 0.289956 | − | 0.957040i | \(-0.406359\pi\) | ||||
0.289956 | + | 0.957040i | \(0.406359\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.1327 | + | 36.6030i | −0.854939 | + | 1.48080i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.03526 | + | 8.72133i | −0.203372 | + | 0.352251i | −0.949613 | − | 0.313425i | \(-0.898524\pi\) |
0.746241 | + | 0.665676i | \(0.231857\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.72579 | − | 4.72121i | −0.109736 | − | 0.190069i | 0.805927 | − | 0.592015i | \(-0.201667\pi\) |
−0.915663 | + | 0.401946i | \(0.868334\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.48602 | −0.0597282 | −0.0298641 | − | 0.999554i | \(-0.509507\pi\) | ||||
−0.0298641 | + | 0.999554i | \(0.509507\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.08975 | − | 12.2798i | −0.284045 | − | 0.491980i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.1574 | + | 26.2534i | −0.606295 | + | 1.05013i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.9798 | − | 20.7497i | 0.477667 | − | 0.827344i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.28173 | + | 14.3444i | 0.329691 | + | 0.571041i | 0.982450 | − | 0.186524i | \(-0.0597222\pi\) |
−0.652760 | + | 0.757565i | \(0.726389\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −81.5575 | −3.23651 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.01948 | − | 10.4260i | −0.238501 | − | 0.413095i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.598395 | − | 1.03645i | 0.0236352 | − | 0.0409373i | −0.853966 | − | 0.520329i | \(-0.825809\pi\) |
0.877601 | + | 0.479392i | \(0.159143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.91067 | + | 10.2376i | −0.233094 | + | 0.403731i | −0.958717 | − | 0.284362i | \(-0.908218\pi\) |
0.725623 | + | 0.688092i | \(0.241552\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.6540 | 1.59827 | 0.799136 | − | 0.601150i | \(-0.205291\pi\) | ||||
0.799136 | + | 0.601150i | \(0.205291\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.09849 | + | 5.36674i | −0.121626 | + | 0.210663i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.4522 | −0.722091 | −0.361046 | − | 0.932548i | \(-0.617580\pi\) | ||||
−0.361046 | + | 0.932548i | \(0.617580\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.33736 | + | 10.9766i | 0.247621 | + | 0.428892i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.9429 | + | 24.1499i | 0.543140 | + | 0.940746i | 0.998721 | + | 0.0505517i | \(0.0160980\pi\) |
−0.455582 | + | 0.890194i | \(0.650569\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.33736 | + | 12.7087i | 0.285390 | + | 0.494310i | 0.972704 | − | 0.232051i | \(-0.0745435\pi\) |
−0.687314 | + | 0.726361i | \(0.741210\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.7788 | − | 28.0236i | 0.805769 | − | 1.08671i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.20361 | − | 15.9411i | 0.356365 | − | 0.617242i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.02111 | − | 15.6250i | −0.348256 | − | 0.603197i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.5272 | −0.598531 | −0.299265 | − | 0.954170i | \(-0.596742\pi\) | ||||
−0.299265 | + | 0.954170i | \(0.596742\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.9734 | −0.421742 | −0.210871 | − | 0.977514i | \(-0.567630\pi\) | ||||
−0.210871 | + | 0.977514i | \(0.567630\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.28548 | + | 9.15472i | −0.202838 | + | 0.351326i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.5032 | 1.32023 | 0.660115 | − | 0.751165i | \(-0.270508\pi\) | ||||
0.660115 | + | 0.751165i | \(0.270508\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.18090 | 0.121536 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.9569 | − | 36.2984i | 0.798393 | − | 1.38286i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.2359 | −1.22631 | −0.613157 | − | 0.789961i | \(-0.710101\pi\) | ||||
−0.613157 | + | 0.789961i | \(0.710101\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.9245 | −0.528188 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.3482 | − | 17.9236i | −0.391965 | − | 0.678903i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.4261 | − | 24.9867i | 0.544866 | − | 0.943735i | −0.453750 | − | 0.891129i | \(-0.649914\pi\) |
0.998615 | − | 0.0526059i | \(-0.0167527\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.0478 | − | 1.95925i | −0.642969 | − | 0.0738947i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.78996 | + | 16.9567i | 0.368189 | + | 0.637723i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5486 | + | 26.9310i | 0.583940 | + | 1.01141i | 0.995007 | + | 0.0998090i | \(0.0318232\pi\) |
−0.411066 | + | 0.911606i | \(0.634843\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.03232 | − | 8.71623i | −0.188462 | − | 0.326425i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.0003 | 1.19674 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.78108 | − | 13.4772i | 0.290185 | − | 0.502615i | −0.683668 | − | 0.729793i | \(-0.739616\pi\) |
0.973853 | + | 0.227178i | \(0.0729498\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.1883 | 1.34772 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.8927 | − | 24.0629i | 0.515962 | − | 0.893672i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.05762 | + | 1.83186i | −0.0392251 | + | 0.0679399i | −0.884971 | − | 0.465645i | \(-0.845822\pi\) |
0.845746 | + | 0.533585i | \(0.179156\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.9888 | − | 39.8178i | −0.850271 | − | 1.47271i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.5909 | −1.35152 | −0.675759 | − | 0.737123i | \(-0.736184\pi\) | ||||
−0.675759 | + | 0.737123i | \(0.736184\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.1274 | + | 17.5412i | 0.373047 | + | 0.646137i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.62533 | + | 11.4754i | −0.243717 | + | 0.422130i | −0.961770 | − | 0.273858i | \(-0.911700\pi\) |
0.718053 | + | 0.695988i | \(0.245033\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.63427 | + | 14.9550i | −0.316761 | + | 0.548645i | −0.979810 | − | 0.199930i | \(-0.935928\pi\) |
0.663050 | + | 0.748575i | \(0.269262\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.5241 | + | 70.1898i | 1.48469 | + | 2.57156i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.1831 | 0.810551 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.32703 | + | 5.76259i | 0.121405 | + | 0.210280i | 0.920322 | − | 0.391162i | \(-0.127927\pi\) |
−0.798917 | + | 0.601441i | \(0.794593\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.3782 | − | 57.8127i | 1.21476 | − | 2.10402i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.7980 | − | 39.4873i | 0.828607 | − | 1.43519i | −0.0705234 | − | 0.997510i | \(-0.522467\pi\) |
0.899131 | − | 0.437680i | \(-0.144200\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.47448 | 0.162200 | 0.0810998 | − | 0.996706i | \(-0.474157\pi\) | ||||
0.0810998 | + | 0.996706i | \(0.474157\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.97287 | + | 12.0774i | −0.252435 | + | 0.437230i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.7686 | −0.497155 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.310132 | + | 0.537164i | 0.0111836 | + | 0.0193706i | 0.871563 | − | 0.490283i | \(-0.163107\pi\) |
−0.860379 | + | 0.509654i | \(0.829773\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.0219 | − | 26.0186i | −0.540299 | − | 0.935825i | −0.998887 | − | 0.0471762i | \(-0.984978\pi\) |
0.458588 | − | 0.888649i | \(-0.348356\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.59620 | − | 13.1570i | −0.272864 | − | 0.472614i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.82860 | + | 11.9068i | −0.316317 | + | 0.426604i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.25124 | − | 7.36336i | 0.152121 | − | 0.263482i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −37.7217 | − | 65.3359i | −1.34635 | − | 2.33194i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.7810 | −1.48933 | −0.744666 | − | 0.667437i | \(-0.767391\pi\) | ||||
−0.744666 | + | 0.667437i | \(0.767391\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.6030 | −0.448110 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.0433 | − | 34.7160i | 0.711758 | − | 1.23280i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.9231 | 0.882823 | 0.441411 | − | 0.897305i | \(-0.354478\pi\) | ||||
0.441411 | + | 0.897305i | \(0.354478\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 60.3803 | 2.13610 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.1467 | + | 21.0388i | −0.428649 | + | 0.742442i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 54.8581 | 1.93349 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.5993 | 0.724232 | 0.362116 | − | 0.932133i | \(-0.382055\pi\) | ||||
0.362116 | + | 0.932133i | \(0.382055\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.2831 | + | 24.7390i | 0.501547 | + | 0.868705i | 0.999998 | + | 0.00178759i | \(0.000569009\pi\) |
−0.498451 | + | 0.866918i | \(0.666098\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.60119 | − | 4.50540i | 0.0911158 | − | 0.157817i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.6130 | + | 26.4513i | −0.686172 | + | 0.925413i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.18475 | − | 8.98026i | −0.180949 | − | 0.313413i | 0.761255 | − | 0.648453i | \(-0.224584\pi\) |
−0.942204 | + | 0.335040i | \(0.891250\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.9457 | − | 31.0829i | −0.625549 | − | 1.08348i | −0.988434 | − | 0.151649i | \(-0.951542\pi\) |
0.362885 | − | 0.931834i | \(-0.381792\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.5782 | + | 39.1066i | 0.785122 | + | 1.35987i | 0.928926 | + | 0.370265i | \(0.120733\pi\) |
−0.143804 | + | 0.989606i | \(0.545934\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.6047 | 1.06294 | 0.531472 | − | 0.847076i | \(-0.321639\pi\) | ||||
0.531472 | + | 0.847076i | \(0.321639\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.59942 | + | 14.8946i | −0.297952 | + | 0.516068i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −50.8510 | −1.75977 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.0089 | − | 17.3359i | 0.345545 | − | 0.598502i | −0.639907 | − | 0.768452i | \(-0.721027\pi\) |
0.985453 | + | 0.169950i | \(0.0543607\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8940 | − | 18.8689i | 0.375654 | − | 0.650651i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.0861 | + | 17.4697i | 0.346973 | + | 0.600975i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.9622 | 0.514107 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.4917 | − | 23.3684i | −0.462491 | − | 0.801058i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.71715 | − | 8.17034i | 0.161512 | − | 0.279747i | −0.773899 | − | 0.633309i | \(-0.781696\pi\) |
0.935411 | + | 0.353562i | \(0.115030\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.330247 | − | 0.572005i | 0.0112810 | − | 0.0195393i | −0.860330 | − | 0.509738i | \(-0.829742\pi\) |
0.871611 | + | 0.490199i | \(0.163076\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.34992 | + | 9.26634i | 0.182537 | + | 0.316163i | 0.942744 | − | 0.333518i | \(-0.108236\pi\) |
−0.760207 | + | 0.649681i | \(0.774902\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 52.3471 | 1.78192 | 0.890958 | − | 0.454086i | \(-0.150034\pi\) | ||||
0.890958 | + | 0.454086i | \(0.150034\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.76269 | + | 16.9095i | 0.331941 | + | 0.574939i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.5132 | − | 21.6735i | 0.424482 | − | 0.735224i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.5013 | + | 38.9733i | −0.762426 | + | 1.32056i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 42.7896 | 1.44655 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.5362 | − | 47.6942i | 0.929833 | − | 1.61052i | 0.146234 | − | 0.989250i | \(-0.453285\pi\) |
0.783598 | − | 0.621268i | \(-0.213382\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 59.0183 | 1.98838 | 0.994188 | − | 0.107660i | \(-0.0343357\pi\) | ||||
0.994188 | + | 0.107660i | \(0.0343357\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.8835 | − | 25.7790i | −0.500871 | − | 0.867534i | −0.999999 | − | 0.00100591i | \(-0.999680\pi\) |
0.499129 | − | 0.866528i | \(-0.333654\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.74074 | + | 6.47915i | 0.125602 | + | 0.217549i | 0.921968 | − | 0.387266i | \(-0.126581\pi\) |
−0.796366 | + | 0.604815i | \(0.793247\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.2673 | + | 36.8361i | 0.713283 | + | 1.23544i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.2049 | − | 39.6748i | −0.575741 | − | 1.32767i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.5345 | − | 56.3514i | 1.08751 | − | 1.88362i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.97170 | + | 3.41509i | 0.0657599 | + | 0.113899i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −59.8778 | −1.99482 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.6087 | 0.917743 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.0071 | − | 31.1892i | 0.597916 | − | 1.03562i | −0.395212 | − | 0.918590i | \(-0.629329\pi\) |
0.993128 | − | 0.117031i | \(-0.0373378\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.2605 | −1.36702 | −0.683511 | − | 0.729941i | \(-0.739548\pi\) | ||||
−0.683511 | + | 0.729941i | \(0.739548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.50248 | −0.281391 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.30512 | − | 5.72463i | 0.109145 | − | 0.189044i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −57.0889 | −1.88319 | −0.941595 | − | 0.336747i | \(-0.890673\pi\) | ||||
−0.941595 | + | 0.336747i | \(0.890673\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.8910 | 0.621805 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.3656 | − | 35.2742i | −0.669616 | − | 1.15981i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.19418 | + | 12.4607i | −0.236033 | + | 0.408822i | −0.959572 | − | 0.281462i | \(-0.909181\pi\) |
0.723539 | + | 0.690283i | \(0.242514\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.2373 | + | 1.40640i | 0.401062 | + | 0.0460929i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.8578 | − | 39.5908i | −0.747529 | − | 1.29476i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.78836 | + | 3.09753i | 0.0584231 | + | 0.101192i | 0.893758 | − | 0.448550i | \(-0.148059\pi\) |
−0.835335 | + | 0.549742i | \(0.814726\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.70842 | + | 9.88728i | 0.186089 | + | 0.322316i | 0.943943 | − | 0.330108i | \(-0.107085\pi\) |
−0.757854 | + | 0.652424i | \(0.773752\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.3083 | −0.759023 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.7671 | − | 25.5773i | 0.479865 | − | 0.831151i | −0.519868 | − | 0.854247i | \(-0.674019\pi\) |
0.999733 | + | 0.0230954i | \(0.00735216\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −53.9757 | −1.75213 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.7483 | + | 25.5448i | −0.477744 | + | 0.827477i | −0.999675 | − | 0.0255109i | \(-0.991879\pi\) |
0.521930 | + | 0.852988i | \(0.325212\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.6699 | − | 54.8539i | 1.02481 | − | 1.77503i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.829467 | − | 1.43668i | −0.0267849 | − | 0.0463928i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8438 | −0.930446 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.6029 | + | 56.4699i | 1.04952 | + | 1.81783i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.0446 | + | 31.2541i | −0.580274 | + | 1.00506i | 0.415172 | + | 0.909743i | \(0.363721\pi\) |
−0.995447 | + | 0.0953215i | \(0.969612\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.68637 | + | 6.38497i | −0.118301 | + | 0.204904i | −0.919095 | − | 0.394037i | \(-0.871078\pi\) |
0.800793 | + | 0.598941i | \(0.204411\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.63103 | + | 6.28913i | 0.116405 | + | 0.201620i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.9705 | 1.08681 | 0.543406 | − | 0.839470i | \(-0.317134\pi\) | ||||
0.543406 | + | 0.839470i | \(0.317134\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.65383 | + | 11.5248i | 0.212657 | + | 0.368333i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.0857 | + | 38.2535i | −0.704423 | + | 1.22010i | 0.262476 | + | 0.964938i | \(0.415461\pi\) |
−0.966899 | + | 0.255158i | \(0.917873\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.0827 | + | 31.3202i | −0.576163 | + | 0.997944i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −51.7802 | −1.64651 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.70048 | − | 13.3376i | 0.244614 | − | 0.423684i | −0.717409 | − | 0.696652i | \(-0.754672\pi\) |
0.962023 | + | 0.272968i | \(0.0880054\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −53.4363 | −1.69404 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.3218 | − | 47.3228i | −0.865291 | − | 1.49873i | −0.866758 | − | 0.498728i | \(-0.833800\pi\) |
0.00146761 | − | 0.999999i | \(-0.499533\pi\) | |||||||
\(998\) | 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 | 2736.2.s.bc.1873.4 | 8 | ||
3.2 | odd | 2 | 2736.2.s.ba.1873.1 | 8 | |||
4.3 | odd | 2 | 1368.2.s.m.505.4 | yes | 8 | ||
12.11 | even | 2 | 1368.2.s.l.505.1 | ✓ | 8 | ||
19.7 | even | 3 | inner | 2736.2.s.bc.577.4 | 8 | ||
57.26 | odd | 6 | 2736.2.s.ba.577.1 | 8 | |||
76.7 | odd | 6 | 1368.2.s.m.577.4 | yes | 8 | ||
228.83 | even | 6 | 1368.2.s.l.577.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.s.l.505.1 | ✓ | 8 | 12.11 | even | 2 | ||
1368.2.s.l.577.1 | yes | 8 | 228.83 | even | 6 | ||
1368.2.s.m.505.4 | yes | 8 | 4.3 | odd | 2 | ||
1368.2.s.m.577.4 | yes | 8 | 76.7 | odd | 6 | ||
2736.2.s.ba.577.1 | 8 | 57.26 | odd | 6 | |||
2736.2.s.ba.1873.1 | 8 | 3.2 | odd | 2 | |||
2736.2.s.bc.577.4 | 8 | 19.7 | even | 3 | inner | ||
2736.2.s.bc.1873.4 | 8 | 1.1 | even | 1 | trivial |