Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.9 | ||
Character | \(\chi\) | \(=\) | 3024.2305 |
Dual form | 3024.2.q.l.2881.9 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.38590 | + | 2.40045i | 0.619793 | + | 1.07351i | 0.989523 | + | 0.144373i | \(0.0461167\pi\) |
−0.369731 | + | 0.929139i | \(0.620550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.74026 | − | 1.99286i | −0.657757 | − | 0.753230i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.71972 | − | 2.97864i | 0.518515 | − | 0.898094i | −0.481254 | − | 0.876581i | \(-0.659819\pi\) |
0.999769 | − | 0.0215124i | \(-0.00684814\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.429164 | + | 0.743335i | −0.119029 | + | 0.206164i | −0.919383 | − | 0.393363i | \(-0.871311\pi\) |
0.800354 | + | 0.599527i | \(0.204645\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.405132 | + | 0.701710i | 0.0982590 | + | 0.170190i | 0.910964 | − | 0.412486i | \(-0.135339\pi\) |
−0.812705 | + | 0.582675i | \(0.802006\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.750215 | + | 1.29941i | −0.172111 | + | 0.298105i | −0.939158 | − | 0.343486i | \(-0.888392\pi\) |
0.767047 | + | 0.641591i | \(0.221725\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.82465 | − | 6.62449i | −0.797495 | − | 1.38130i | −0.921243 | − | 0.388988i | \(-0.872825\pi\) |
0.123748 | − | 0.992314i | \(-0.460508\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.34143 | + | 2.32343i | −0.268286 | + | 0.464685i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.99696 | − | 6.92294i | −0.742217 | − | 1.28556i | −0.951484 | − | 0.307700i | \(-0.900441\pi\) |
0.209266 | − | 0.977859i | \(-0.432893\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.21156 | 1.29524 | 0.647618 | − | 0.761965i | \(-0.275765\pi\) | ||||
0.647618 | + | 0.761965i | \(0.275765\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.37193 | − | 6.93931i | 0.400929 | − | 1.17296i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.458211 | − | 0.793644i | 0.0753294 | − | 0.130474i | −0.825900 | − | 0.563817i | \(-0.809333\pi\) |
0.901229 | + | 0.433342i | \(0.142666\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.67577 | + | 2.90251i | −0.261711 | + | 0.453297i | −0.966697 | − | 0.255925i | \(-0.917620\pi\) |
0.704986 | + | 0.709221i | \(0.250953\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.20465 | − | 2.08652i | −0.183708 | − | 0.318191i | 0.759433 | − | 0.650586i | \(-0.225477\pi\) |
−0.943140 | + | 0.332395i | \(0.892143\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.615039 | −0.0897127 | −0.0448564 | − | 0.998993i | \(-0.514283\pi\) | ||||
−0.0448564 | + | 0.998993i | \(0.514283\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.942983 | + | 6.93619i | −0.134712 | + | 0.990885i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.31646 | − | 10.9404i | −0.867633 | − | 1.50278i | −0.864409 | − | 0.502789i | \(-0.832307\pi\) |
−0.00322332 | − | 0.999995i | \(-0.501026\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.53342 | 1.28549 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.46938 | 0.191297 | 0.0956485 | − | 0.995415i | \(-0.469508\pi\) | ||||
0.0956485 | + | 0.995415i | \(0.469508\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4327 | 1.46381 | 0.731904 | − | 0.681408i | \(-0.238632\pi\) | ||||
0.731904 | + | 0.681408i | \(0.238632\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.37911 | −0.295093 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16.2012 | −1.97929 | −0.989647 | − | 0.143522i | \(-0.954157\pi\) | ||||
−0.989647 | + | 0.143522i | \(0.954157\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.4177 | 1.71106 | 0.855532 | − | 0.517749i | \(-0.173230\pi\) | ||||
0.855532 | + | 0.517749i | \(0.173230\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.16893 | − | 7.22079i | −0.487936 | − | 0.845130i | 0.511968 | − | 0.859005i | \(-0.328917\pi\) |
−0.999904 | + | 0.0138749i | \(0.995583\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.92877 | + | 1.75645i | −1.01753 | + | 0.200166i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.75171 | 0.309592 | 0.154796 | − | 0.987946i | \(-0.450528\pi\) | ||||
0.154796 | + | 0.987946i | \(0.450528\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.75814 | − | 9.97340i | −0.632038 | − | 1.09472i | −0.987134 | − | 0.159893i | \(-0.948885\pi\) |
0.355096 | − | 0.934830i | \(-0.384448\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.12294 | + | 1.94500i | −0.121800 | + | 0.210965i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.11395 | − | 8.85763i | 0.542078 | − | 0.938907i | −0.456707 | − | 0.889617i | \(-0.650971\pi\) |
0.998785 | − | 0.0492892i | \(-0.0156956\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.22822 | − | 0.438331i | 0.233581 | − | 0.0459496i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.15889 | −0.426693 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.82852 | + | 6.63119i | 0.388727 | + | 0.673296i | 0.992279 | − | 0.124029i | \(-0.0395814\pi\) |
−0.603551 | + | 0.797324i | \(0.706248\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.84302 | + | 3.19220i | −0.183387 | + | 0.317635i | −0.943032 | − | 0.332703i | \(-0.892039\pi\) |
0.759645 | + | 0.650338i | \(0.225373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.06026 | − | 13.9608i | −0.794201 | − | 1.37560i | −0.923346 | − | 0.383970i | \(-0.874557\pi\) |
0.129145 | − | 0.991626i | \(-0.458777\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.16767 | − | 5.48656i | 0.306230 | − | 0.530405i | −0.671305 | − | 0.741182i | \(-0.734266\pi\) |
0.977534 | + | 0.210776i | \(0.0675991\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.89477 | + | 8.47799i | 0.468834 | + | 0.812044i | 0.999365 | − | 0.0356213i | \(-0.0113410\pi\) |
−0.530532 | + | 0.847665i | \(0.678008\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.06963 | + | 7.04881i | −0.382839 | + | 0.663096i | −0.991467 | − | 0.130360i | \(-0.958387\pi\) |
0.608628 | + | 0.793456i | \(0.291720\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.6012 | − | 18.3617i | 0.988563 | − | 1.71224i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.693374 | − | 2.02853i | 0.0635615 | − | 0.185955i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.414862 | − | 0.718563i | −0.0377148 | − | 0.0653239i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.42264 | 0.574459 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.5658 | 1.11504 | 0.557518 | − | 0.830165i | \(-0.311754\pi\) | ||||
0.557518 | + | 0.830165i | \(0.311754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.792752 | − | 1.37309i | −0.0692631 | − | 0.119967i | 0.829314 | − | 0.558783i | \(-0.188731\pi\) |
−0.898577 | + | 0.438816i | \(0.855398\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.89511 | − | 0.766240i | 0.337749 | − | 0.0664414i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.46394 | − | 4.26767i | 0.210508 | − | 0.364611i | −0.741365 | − | 0.671102i | \(-0.765821\pi\) |
0.951874 | + | 0.306490i | \(0.0991547\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.12999 | + | 7.15336i | −0.350301 | + | 0.606740i | −0.986302 | − | 0.164949i | \(-0.947254\pi\) |
0.636001 | + | 0.771688i | \(0.280588\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.47608 | + | 2.55665i | 0.123436 | + | 0.213798i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.0788 | − | 19.1890i | 0.920042 | − | 1.59356i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.95698 | − | 12.0498i | −0.569938 | − | 0.987161i | −0.996571 | − | 0.0827368i | \(-0.973634\pi\) |
0.426634 | − | 0.904425i | \(-0.359699\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.4964 | − | 19.9123i | 0.935561 | − | 1.62044i | 0.161930 | − | 0.986802i | \(-0.448228\pi\) |
0.773631 | − | 0.633637i | \(-0.218439\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.99450 | + | 17.3110i | 0.802777 | + | 1.39045i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.5804 | 1.48288 | 0.741441 | − | 0.671019i | \(-0.234143\pi\) | ||||
0.741441 | + | 0.671019i | \(0.234143\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.54579 | + | 19.1503i | −0.515880 | + | 1.50926i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.45194 | − | 4.24688i | 0.192050 | − | 0.332641i | −0.753879 | − | 0.657013i | \(-0.771820\pi\) |
0.945930 | + | 0.324372i | \(0.105153\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.47493 | + | 9.48286i | −0.423663 | + | 0.733805i | −0.996295 | − | 0.0860073i | \(-0.972589\pi\) |
0.572632 | + | 0.819813i | \(0.305923\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.13164 | + | 10.6203i | 0.471664 | + | 0.816947i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.4054 | 1.01920 | 0.509598 | − | 0.860413i | \(-0.329794\pi\) | ||||
0.509598 | + | 0.860413i | \(0.329794\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.96470 | − | 1.37008i | 0.526482 | − | 0.103569i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.64888 | − | 11.5162i | −0.496961 | − | 0.860761i | 0.503033 | − | 0.864267i | \(-0.332217\pi\) |
−0.999994 | + | 0.00350600i | \(0.998884\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9190 | −0.811601 | −0.405801 | − | 0.913962i | \(-0.633007\pi\) | ||||
−0.405801 | + | 0.913962i | \(0.633007\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.54013 | 0.186754 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.78685 | 0.203795 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.6111 | −1.34665 | −0.673325 | − | 0.739347i | \(-0.735134\pi\) | ||||
−0.673325 | + | 0.739347i | \(0.735134\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.92940 | 0.210863 | 0.105431 | − | 0.994427i | \(-0.466378\pi\) | ||||
0.105431 | + | 0.994427i | \(0.466378\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.5050 | 1.31843 | 0.659214 | − | 0.751956i | \(-0.270889\pi\) | ||||
0.659214 | + | 0.751956i | \(0.270889\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.793836 | − | 1.37496i | −0.0562736 | − | 0.0974687i | 0.836516 | − | 0.547942i | \(-0.184589\pi\) |
−0.892790 | + | 0.450473i | \(0.851255\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.84070 | + | 20.0131i | −0.480123 | + | 1.40465i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.28977 | −0.648826 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.58032 | + | 4.46924i | 0.178484 | + | 0.309144i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.3436 | + | 21.3798i | −0.849770 | + | 1.47184i | 0.0316443 | + | 0.999499i | \(0.489926\pi\) |
−0.881414 | + | 0.472345i | \(0.843408\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.33905 | − | 5.78340i | 0.227721 | − | 0.394425i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.5500 | − | 14.3716i | −0.851950 | − | 0.975611i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.695474 | −0.0467826 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.78468 | + | 16.9476i | 0.655231 | + | 1.13489i | 0.981836 | + | 0.189732i | \(0.0607619\pi\) |
−0.326605 | + | 0.945161i | \(0.605905\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.32404 | + | 7.48945i | −0.286996 | + | 0.497092i | −0.973091 | − | 0.230420i | \(-0.925990\pi\) |
0.686095 | + | 0.727512i | \(0.259323\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.77136 | − | 9.99630i | −0.381382 | − | 0.660574i | 0.609878 | − | 0.792496i | \(-0.291219\pi\) |
−0.991260 | + | 0.131922i | \(0.957885\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.12745 | − | 14.0772i | 0.532447 | − | 0.922225i | −0.466835 | − | 0.884344i | \(-0.654606\pi\) |
0.999282 | − | 0.0378811i | \(-0.0120608\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.852382 | − | 1.47637i | −0.0556033 | − | 0.0963077i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.4336 | − | 21.5355i | 0.804260 | − | 1.39302i | −0.112530 | − | 0.993648i | \(-0.535895\pi\) |
0.916790 | − | 0.399371i | \(-0.130771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.51814 | − | 16.4859i | 0.613117 | − | 1.06195i | −0.377595 | − | 0.925971i | \(-0.623249\pi\) |
0.990712 | − | 0.135979i | \(-0.0434180\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.9568 | + | 7.34928i | −1.14722 | + | 0.469528i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.643931 | − | 1.11532i | −0.0409724 | − | 0.0709662i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.980433 | −0.0618844 | −0.0309422 | − | 0.999521i | \(-0.509851\pi\) | ||||
−0.0309422 | + | 0.999521i | \(0.509851\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.3093 | −1.65405 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.18362 | + | 3.78215i | 0.136211 | + | 0.235924i | 0.926059 | − | 0.377378i | \(-0.123174\pi\) |
−0.789849 | + | 0.613302i | \(0.789841\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.37903 | + | 0.467998i | −0.147826 | + | 0.0290800i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.24212 | − | 10.8117i | 0.384905 | − | 0.666676i | −0.606851 | − | 0.794816i | \(-0.707567\pi\) |
0.991756 | + | 0.128140i | \(0.0409007\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.5079 | − | 30.3247i | 1.07550 | − | 1.86283i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.29270 | − | 14.3634i | −0.505615 | − | 0.875750i | −0.999979 | − | 0.00649532i | \(-0.997932\pi\) |
0.494364 | − | 0.869255i | \(-0.335401\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.9814 | + | 22.4845i | −0.788566 | + | 1.36584i | 0.138279 | + | 0.990393i | \(0.455843\pi\) |
−0.926845 | + | 0.375444i | \(0.877490\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.61376 | + | 7.99127i | 0.278220 | + | 0.481892i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.980373 | − | 1.69806i | 0.0589049 | − | 0.102026i | −0.835069 | − | 0.550145i | \(-0.814572\pi\) |
0.893974 | + | 0.448119i | \(0.147906\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.42057 | − | 16.3169i | −0.561984 | − | 0.973385i | −0.997323 | − | 0.0731185i | \(-0.976705\pi\) |
0.435339 | − | 0.900267i | \(-0.356628\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.4844 | 1.39600 | 0.698002 | − | 0.716095i | \(-0.254072\pi\) | ||||
0.698002 | + | 0.716095i | \(0.254072\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.70058 | − | 1.71156i | 0.513579 | − | 0.101030i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.17174 | − | 14.1539i | 0.480690 | − | 0.832580i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.00384 | − | 1.73871i | 0.0586452 | − | 0.101576i | −0.835212 | − | 0.549928i | \(-0.814655\pi\) |
0.893857 | + | 0.448351i | \(0.147989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.03641 | + | 3.52717i | 0.118564 | + | 0.205360i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.56561 | 0.379699 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.06173 | + | 6.03179i | −0.118836 | + | 0.347666i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.8446 | + | 27.4436i | 0.907257 | + | 1.57142i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.7633 | −1.86990 | −0.934951 | − | 0.354777i | \(-0.884557\pi\) | ||||
−0.934951 | + | 0.354777i | \(0.884557\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.0996 | −0.799514 | −0.399757 | − | 0.916621i | \(-0.630906\pi\) | ||||
−0.399757 | + | 0.916621i | \(0.630906\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −34.1539 | −1.93049 | −0.965245 | − | 0.261345i | \(-0.915834\pi\) | ||||
−0.965245 | + | 0.261345i | \(0.915834\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.58117 | 0.0888074 | 0.0444037 | − | 0.999014i | \(-0.485861\pi\) | ||||
0.0444037 | + | 0.999014i | \(0.485861\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.4946 | −1.53940 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.21575 | −0.0676459 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.15139 | − | 1.99426i | −0.0638675 | − | 0.110622i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.07033 | + | 1.22569i | 0.0590092 | + | 0.0675743i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.7372 | −0.755067 | −0.377533 | − | 0.925996i | \(-0.623228\pi\) | ||||
−0.377533 | + | 0.925996i | \(0.623228\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −22.4533 | − | 38.8902i | −1.22675 | − | 2.12480i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.72318 | + | 15.1090i | −0.475182 | + | 0.823039i | −0.999596 | − | 0.0284243i | \(-0.990951\pi\) |
0.524414 | + | 0.851463i | \(0.324284\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.4019 | − | 21.4807i | 0.671598 | − | 1.16324i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4639 | − | 10.1916i | 0.834972 | − | 0.550292i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.83104 | 0.205661 | 0.102830 | − | 0.994699i | \(-0.467210\pi\) | ||||
0.102830 | + | 0.994699i | \(0.467210\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.69984 | + | 2.94421i | 0.0909903 | + | 0.157600i | 0.907928 | − | 0.419126i | \(-0.137663\pi\) |
−0.816938 | + | 0.576726i | \(0.804330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.27841 | − | 10.8745i | 0.334166 | − | 0.578793i | −0.649158 | − | 0.760653i | \(-0.724879\pi\) |
0.983324 | + | 0.181861i | \(0.0582120\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.9815 | + | 34.6089i | 1.06051 | + | 1.83685i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.02209 | + | 10.4306i | −0.317834 | + | 0.550504i | −0.980036 | − | 0.198821i | \(-0.936289\pi\) |
0.662202 | + | 0.749325i | \(0.269622\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.37435 | + | 14.5048i | 0.440756 | + | 0.763411i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.5554 | − | 20.0146i | 0.604838 | − | 1.04761i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.01257 | + | 1.75382i | −0.0528557 | + | 0.0915487i | −0.891243 | − | 0.453527i | \(-0.850166\pi\) |
0.838387 | + | 0.545075i | \(0.183499\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.8105 | + | 31.6270i | −0.561251 | + | 1.64199i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.8130 | − | 18.7286i | −0.559874 | − | 0.969731i | −0.997506 | − | 0.0705766i | \(-0.977516\pi\) |
0.437632 | − | 0.899154i | \(-0.355817\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.86142 | 0.353381 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.76701 | 0.347598 | 0.173799 | − | 0.984781i | \(-0.444396\pi\) | ||||
0.173799 | + | 0.984781i | \(0.444396\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.82822 | + | 6.63068i | 0.195613 | + | 0.338812i | 0.947101 | − | 0.320935i | \(-0.103997\pi\) |
−0.751488 | + | 0.659747i | \(0.770664\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.5906 | − | 18.9988i | −0.845537 | − | 0.968267i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.5781 | + | 18.3218i | −0.536329 | + | 0.928950i | 0.462768 | + | 0.886479i | \(0.346856\pi\) |
−0.999098 | + | 0.0424705i | \(0.986477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.09898 | − | 5.36759i | 0.156722 | − | 0.271451i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.81360 | + | 6.60534i | 0.191883 | + | 0.332351i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.02642 | − | 6.97396i | 0.202080 | − | 0.350013i | −0.747118 | − | 0.664691i | \(-0.768563\pi\) |
0.949199 | + | 0.314678i | \(0.101896\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.88886 | − | 6.73571i | −0.194201 | − | 0.336365i | 0.752438 | − | 0.658664i | \(-0.228878\pi\) |
−0.946638 | + | 0.322298i | \(0.895545\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.09495 | + | 5.36061i | −0.154170 | + | 0.267031i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.57599 | − | 2.72969i | −0.0781188 | − | 0.135306i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.5265 | 0.965526 | 0.482763 | − | 0.875751i | \(-0.339633\pi\) | ||||
0.482763 | + | 0.875751i | \(0.339633\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.55710 | − | 2.92827i | −0.125827 | − | 0.144091i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.9604 | − | 27.6442i | 0.783466 | − | 1.35700i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.5259 | + | 21.6955i | −0.611932 | + | 1.05990i | 0.378983 | + | 0.925404i | \(0.376274\pi\) |
−0.990915 | + | 0.134493i | \(0.957059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0746 | + | 31.3061i | 0.880902 | + | 1.52577i | 0.850340 | + | 0.526234i | \(0.176396\pi\) |
0.0305620 | + | 0.999533i | \(0.490270\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.17383 | −0.105446 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.8959 | − | 22.7838i | −0.962829 | − | 1.10258i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.95636 | − | 3.38852i | −0.0942346 | − | 0.163219i | 0.815054 | − | 0.579385i | \(-0.196707\pi\) |
−0.909289 | + | 0.416165i | \(0.863374\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.2929 | −0.686872 | −0.343436 | − | 0.939176i | \(-0.611591\pi\) | ||||
−0.343436 | + | 0.939176i | \(0.611591\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.4772 | 0.549031 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.78469 | 0.228361 | 0.114180 | − | 0.993460i | \(-0.463576\pi\) | ||||
0.114180 | + | 0.993460i | \(0.463576\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.26427 | −0.392647 | −0.196324 | − | 0.980539i | \(-0.562900\pi\) | ||||
−0.196324 | + | 0.980539i | \(0.562900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.3497 | 1.34390 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.6036 | 0.972346 | 0.486173 | − | 0.873863i | \(-0.338392\pi\) | ||||
0.486173 | + | 0.873863i | \(0.338392\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.76370 | + | 9.98301i | 0.271402 | + | 0.470082i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.14028 | + | 4.74124i | 0.194099 | + | 0.222273i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.9644 | −0.840339 | −0.420170 | − | 0.907446i | \(-0.638029\pi\) | ||||
−0.420170 | + | 0.907446i | \(0.638029\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.03501 | − | 6.98885i | −0.187929 | − | 0.325503i | 0.756630 | − | 0.653843i | \(-0.226844\pi\) |
−0.944560 | + | 0.328340i | \(0.893511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.50704 | − | 4.34232i | 0.116512 | − | 0.201805i | −0.801871 | − | 0.597497i | \(-0.796162\pi\) |
0.918383 | + | 0.395692i | \(0.129495\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.1673 | + | 22.8063i | −0.609308 | + | 1.05535i | 0.382047 | + | 0.924143i | \(0.375219\pi\) |
−0.991355 | + | 0.131209i | \(0.958114\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.1944 | + | 32.2868i | 1.30189 | + | 1.49086i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.28665 | −0.381020 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.01272 | − | 3.48614i | −0.0923500 | − | 0.159955i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.6222 | − | 21.8623i | 0.576724 | − | 0.998916i | −0.419128 | − | 0.907927i | \(-0.637664\pi\) |
0.995852 | − | 0.0909886i | \(-0.0290027\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.393295 | + | 0.681208i | 0.0179327 | + | 0.0310604i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.6119 | + | 18.3803i | −0.481861 | + | 0.834608i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.36124 | − | 2.35774i | −0.0616837 | − | 0.106839i | 0.833534 | − | 0.552468i | \(-0.186314\pi\) |
−0.895218 | + | 0.445628i | \(0.852980\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.8020 | + | 27.3698i | −0.713134 | + | 1.23518i | 0.250541 | + | 0.968106i | \(0.419391\pi\) |
−0.963675 | + | 0.267078i | \(0.913942\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.23860 | − | 5.60942i | 0.145859 | − | 0.252635i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.0905 | − | 28.7324i | −1.12546 | − | 1.28883i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.97445 | + | 5.15190i | 0.133155 | + | 0.230631i | 0.924891 | − | 0.380232i | \(-0.124156\pi\) |
−0.791736 | + | 0.610863i | \(0.790823\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.6905 | −1.23466 | −0.617329 | − | 0.786705i | \(-0.711785\pi\) | ||||
−0.617329 | + | 0.786705i | \(0.711785\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.2169 | −0.454647 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.6443 | + | 32.2928i | 0.826392 | + | 1.43135i | 0.900850 | + | 0.434129i | \(0.142944\pi\) |
−0.0744581 | + | 0.997224i | \(0.523723\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.13501 | + | 20.8741i | −0.315634 | + | 0.923418i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.3414 | − | 38.6964i | 0.984480 | − | 1.70517i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.05769 | + | 1.83198i | −0.0465174 | + | 0.0805704i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.1271 | − | 31.3971i | −0.794163 | − | 1.37553i | −0.923370 | − | 0.383912i | \(-0.874577\pi\) |
0.129207 | − | 0.991618i | \(-0.458757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.2931 | + | 17.8282i | −0.450086 | + | 0.779572i | −0.998391 | − | 0.0567068i | \(-0.981940\pi\) |
0.548305 | + | 0.836278i | \(0.315273\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.92164 | + | 5.06043i | 0.127269 | + | 0.220436i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.7559 | + | 30.7541i | −0.771996 | + | 1.33714i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.43836 | − | 2.49131i | −0.0623023 | − | 0.107911i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.5603 | 0.759196 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.0388 | + | 14.7371i | 0.820057 | + | 0.634772i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.649192 | + | 1.12443i | −0.0279109 | + | 0.0483432i | −0.879643 | − | 0.475634i | \(-0.842219\pi\) |
0.851733 | + | 0.523977i | \(0.175552\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.5673 | + | 23.4993i | −0.581159 | + | 1.00660i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8412 | + | 23.9736i | 0.591805 | + | 1.02504i | 0.993989 | + | 0.109478i | \(0.0349180\pi\) |
−0.402184 | + | 0.915559i | \(0.631749\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.9943 | 0.510976 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.78870 | − | 5.48378i | −0.203636 | − | 0.233194i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.72089 | + | 13.3730i | 0.327145 | + | 0.566631i | 0.981944 | − | 0.189172i | \(-0.0605802\pi\) |
−0.654799 | + | 0.755803i | \(0.727247\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.06797 | 0.0874660 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.91343 | 0.0806414 | 0.0403207 | − | 0.999187i | \(-0.487162\pi\) | ||||
0.0403207 | + | 0.999187i | \(0.487162\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.5604 | −0.949122 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.7628 | 0.618887 | 0.309444 | − | 0.950918i | \(-0.399857\pi\) | ||||
0.309444 | + | 0.950918i | \(0.399857\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.56417 | −0.107307 | −0.0536535 | − | 0.998560i | \(-0.517087\pi\) | ||||
−0.0536535 | + | 0.998560i | \(0.517087\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.5220 | 0.855827 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.01283 | + | 12.1466i | 0.291948 | + | 0.505669i | 0.974270 | − | 0.225383i | \(-0.0723632\pi\) |
−0.682322 | + | 0.731052i | \(0.739030\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.85491 | + | 28.8315i | −0.408851 | + | 1.19613i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −43.4501 | −1.79952 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.7666 | + | 27.3085i | 0.650756 | + | 1.12714i | 0.982940 | + | 0.183928i | \(0.0588813\pi\) |
−0.332183 | + | 0.943215i | \(0.607785\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.41022 | + | 9.37078i | −0.222924 | + | 0.386116i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.72311 | − | 9.91272i | 0.235020 | − | 0.407067i | −0.724258 | − | 0.689529i | \(-0.757818\pi\) |
0.959279 | + | 0.282462i | \(0.0911511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.83033 | − | 1.14693i | 0.239020 | − | 0.0470196i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.61368 | 0.229369 | 0.114684 | − | 0.993402i | \(-0.463414\pi\) | ||||
0.114684 | + | 0.993402i | \(0.463414\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.2223 | + | 33.2940i | 0.784094 | + | 1.35809i | 0.929539 | + | 0.368725i | \(0.120205\pi\) |
−0.145444 | + | 0.989366i | \(0.546461\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.14991 | − | 1.99171i | 0.0467507 | − | 0.0809745i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.17187 | − | 14.1541i | −0.331686 | − | 0.574497i | 0.651157 | − | 0.758943i | \(-0.274284\pi\) |
−0.982843 | + | 0.184446i | \(0.940951\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.263953 | − | 0.457180i | 0.0106784 | − | 0.0184955i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.19332 | − | 10.7272i | −0.250146 | − | 0.433266i | 0.713420 | − | 0.700737i | \(-0.247145\pi\) |
−0.963566 | + | 0.267471i | \(0.913812\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.9853 | + | 36.3476i | −0.844836 | + | 1.46330i | 0.0409280 | + | 0.999162i | \(0.486969\pi\) |
−0.885764 | + | 0.464136i | \(0.846365\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.9473 | + | 31.0856i | −0.721361 | + | 1.24943i | 0.239093 | + | 0.970997i | \(0.423150\pi\) |
−0.960454 | + | 0.278438i | \(0.910183\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −26.5516 | + | 5.22319i | −1.06377 | + | 0.209263i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6083 | + | 27.0343i | 0.624331 | + | 1.08137i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.742544 | 0.0296072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.5519 | 0.778349 | 0.389175 | − | 0.921164i | \(-0.372760\pi\) | ||||
0.389175 | + | 0.921164i | \(0.372760\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.4149 | + | 30.1636i | 0.691091 | + | 1.19700i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.75122 | − | 3.67772i | −0.188250 | − | 0.145717i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.30132 | + | 12.6463i | −0.288385 | + | 0.499497i | −0.973424 | − | 0.229009i | \(-0.926452\pi\) |
0.685040 | + | 0.728506i | \(0.259785\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.96942 | − | 10.3393i | 0.235411 | − | 0.407744i | −0.723981 | − | 0.689820i | \(-0.757690\pi\) |
0.959392 | + | 0.282076i | \(0.0910231\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.92060 | − | 3.32658i | −0.0755067 | − | 0.130781i | 0.825800 | − | 0.563963i | \(-0.190724\pi\) |
−0.901306 | + | 0.433182i | \(0.857391\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.52692 | − | 4.37675i | 0.0991903 | − | 0.171803i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.9959 | + | 34.6339i | 0.782501 | + | 1.35533i | 0.930481 | + | 0.366340i | \(0.119389\pi\) |
−0.147980 | + | 0.988990i | \(0.547277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.19735 | − | 3.80592i | 0.0858575 | − | 0.148710i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.60101 | + | 2.77303i | 0.0623665 | + | 0.108022i | 0.895523 | − | 0.445016i | \(-0.146802\pi\) |
−0.833156 | + | 0.553038i | \(0.813469\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.3030 | −1.68429 | −0.842146 | − | 0.539250i | \(-0.818708\pi\) | ||||
−0.842146 | + | 0.539250i | \(0.818708\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.23755 | + | 8.28808i | 0.280660 | + | 0.321398i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.5740 | + | 52.9557i | −1.18383 | + | 2.05045i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.6610 | − | 34.0539i | 0.759006 | − | 1.31464i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2936 | + | 21.2931i | 0.473883 | + | 0.820790i | 0.999553 | − | 0.0298991i | \(-0.00951859\pi\) |
−0.525670 | + | 0.850689i | \(0.676185\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.4188 | 1.47655 | 0.738276 | − | 0.674498i | \(-0.235640\pi\) | ||||
0.738276 | + | 0.674498i | \(0.235640\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.55242 | − | 19.1697i | 0.251459 | − | 0.735666i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.122464 | − | 0.212113i | −0.00468594 | − | 0.00811629i | 0.863673 | − | 0.504053i | \(-0.168158\pi\) |
−0.868359 | + | 0.495936i | \(0.834825\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.6591 | 0.521886 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.8432 | 0.413093 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.30292 | 0.277816 | 0.138908 | − | 0.990305i | \(-0.455641\pi\) | ||||
0.138908 | + | 0.990305i | \(0.455641\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.8950 | −0.868457 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.71563 | −0.102862 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.3889 | −1.22331 | −0.611656 | − | 0.791124i | \(-0.709496\pi\) | ||||
−0.611656 | + | 0.791124i | \(0.709496\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.687513 | + | 1.19081i | 0.0259301 | + | 0.0449122i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.56893 | − | 1.88238i | 0.359877 | − | 0.0707943i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.92274 | 0.109766 | 0.0548828 | − | 0.998493i | \(-0.482521\pi\) | ||||
0.0548828 | + | 0.998493i | \(0.482521\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.5817 | − | 47.7729i | −1.03294 | − | 1.78911i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.09141 | + | 7.08652i | −0.153010 | + | 0.265021i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.78527 | − | 15.2165i | 0.327635 | − | 0.567481i | −0.654407 | − | 0.756143i | \(-0.727082\pi\) |
0.982042 | + | 0.188662i | \(0.0604150\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.7949 | + | 40.3584i | −0.513750 | + | 1.50302i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.4466 | 0.796506 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.0486 | − | 34.7252i | −0.743561 | − | 1.28789i | −0.950864 | − | 0.309609i | \(-0.899802\pi\) |
0.207303 | − | 0.978277i | \(-0.433531\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.976087 | − | 1.69063i | 0.0361019 | − | 0.0625303i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.56234 | + | 6.17016i | 0.131578 | + | 0.227900i | 0.924285 | − | 0.381703i | \(-0.124662\pi\) |
−0.792707 | + | 0.609603i | \(0.791329\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27.8615 | + | 48.2576i | −1.02629 | + | 1.77759i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.13570 | + | 3.69914i | 0.0785631 | + | 0.136075i | 0.902630 | − | 0.430417i | \(-0.141633\pi\) |
−0.824067 | + | 0.566492i | \(0.808300\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.108257 | − | 0.187507i | 0.00397157 | − | 0.00687896i | −0.864033 | − | 0.503436i | \(-0.832069\pi\) |
0.868004 | + | 0.496557i | \(0.165402\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.2833 | − | 33.3997i | 0.706487 | − | 1.22367i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.4465 | + | 3.23533i | −0.600942 | + | 0.118216i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.7920 | + | 20.4244i | 0.430297 | + | 0.745296i | 0.996899 | − | 0.0786955i | \(-0.0250755\pi\) |
−0.566602 | + | 0.823992i | \(0.691742\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 63.7312 | 2.31942 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0176 | −0.800242 | −0.400121 | − | 0.916462i | \(-0.631032\pi\) | ||||
−0.400121 | + | 0.916462i | \(0.631032\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.05699 | − | 15.6872i | −0.328316 | − | 0.568659i | 0.653862 | − | 0.756614i | \(-0.273148\pi\) |
−0.982178 | + | 0.187954i | \(0.939814\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.37727 | − | 24.5085i | 0.303277 | − | 0.887267i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.630606 | + | 1.09224i | −0.0227699 | + | 0.0394385i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.16710 | − | 5.48558i | 0.114209 | − | 0.197815i | −0.803255 | − | 0.595636i | \(-0.796900\pi\) |
0.917463 | + | 0.397821i | \(0.130233\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.10740 | − | 5.38218i | −0.111765 | − | 0.193584i | 0.804717 | − | 0.593659i | \(-0.202317\pi\) |
−0.916482 | + | 0.400076i | \(0.868984\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.67381 | + | 16.7555i | −0.347494 | + | 0.601876i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.51437 | − | 4.35502i | −0.0900867 | − | 0.156035i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.7944 | − | 42.9451i | 0.887212 | − | 1.53670i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.7506 | + | 44.6014i | 0.919079 | + | 1.59189i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.3183 | 0.688624 | 0.344312 | − | 0.938855i | \(-0.388112\pi\) | ||||
0.344312 | + | 0.938855i | \(0.388112\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.1295 | − | 4.15656i | 0.751279 | − | 0.147790i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.90651 | + | 8.49832i | −0.174235 | + | 0.301784i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.09519 | − | 8.82513i | 0.180481 | − | 0.312602i | −0.761563 | − | 0.648090i | \(-0.775568\pi\) |
0.942044 | + | 0.335488i | \(0.108901\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.249172 | − | 0.431579i | −0.00881509 | − | 0.0152682i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −28.6775 | −1.01201 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −55.0412 | + | 10.8276i | −1.93995 | + | 0.381623i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.7068 | + | 41.0613i | 0.833485 | + | 1.44364i | 0.895258 | + | 0.445548i | \(0.146991\pi\) |
−0.0617729 | + | 0.998090i | \(0.519675\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.4177 | −1.66506 | −0.832531 | − | 0.553979i | \(-0.813109\pi\) | ||||
−0.832531 | + | 0.553979i | \(0.813109\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.5925 | 0.476126 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.61499 | 0.126473 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −53.6353 | −1.87189 | −0.935943 | − | 0.352152i | \(-0.885450\pi\) | ||||
−0.935943 | + | 0.352152i | \(0.885450\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.950384 | 0.0331283 | 0.0165641 | − | 0.999863i | \(-0.494727\pi\) | ||||
0.0165641 | + | 0.999863i | \(0.494727\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.7813 | 0.722636 | 0.361318 | − | 0.932443i | \(-0.382327\pi\) | ||||
0.361318 | + | 0.932443i | \(0.382327\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.1615 | + | 21.0644i | 0.422387 | + | 0.731596i | 0.996172 | − | 0.0874096i | \(-0.0278589\pi\) |
−0.573785 | + | 0.819006i | \(0.694526\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.24923 | + | 2.14838i | −0.181875 | + | 0.0744368i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.3508 | −1.05033 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.7367 | − | 27.2567i | −0.543290 | − | 0.941006i | −0.998712 | − | 0.0507305i | \(-0.983845\pi\) |
0.455422 | − | 0.890276i | \(-0.349488\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.4514 | + | 30.2268i | −0.601774 | + | 1.04230i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.9957 | + | 29.4373i | −0.584668 | + | 1.01268i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.710026 | + | 2.07725i | −0.0243968 | + | 0.0713751i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.00998 | −0.240299 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.6959 | − | 46.2386i | −0.914049 | − | 1.58318i | −0.808287 | − | 0.588788i | \(-0.799605\pi\) |
−0.105762 | − | 0.994391i | \(-0.533728\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.8149 | − | 18.7319i | 0.369428 | − | 0.639869i | −0.620048 | − | 0.784564i | \(-0.712887\pi\) |
0.989476 | + | 0.144695i | \(0.0462202\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.2144 | − | 29.8162i | −0.587348 | − | 1.01732i | −0.994578 | − | 0.103991i | \(-0.966839\pi\) |
0.407230 | − | 0.913326i | \(-0.366495\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.4262 | + | 23.2548i | −0.457033 | + | 0.791604i | −0.998803 | − | 0.0489229i | \(-0.984421\pi\) |
0.541770 | + | 0.840527i | \(0.317754\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.5786 | + | 32.1790i | 0.631690 | + | 1.09412i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.73217 | − | 8.19636i | 0.160528 | − | 0.278043i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.95299 | − | 12.0429i | 0.235593 | − | 0.408059i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.1771 | − | 12.7994i | −0.377854 | − | 0.432700i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.2034 | − | 28.0651i | −0.547150 | − | 0.947692i | −0.998468 | − | 0.0553291i | \(-0.982379\pi\) |
0.451318 | − | 0.892363i | \(-0.350954\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.0404 | 1.31530 | 0.657652 | − | 0.753322i | \(-0.271550\pi\) | ||||
0.657652 | + | 0.753322i | \(0.271550\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.8079 | 0.464672 | 0.232336 | − | 0.972636i | \(-0.425363\pi\) | ||||
0.232336 | + | 0.972636i | \(0.425363\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.9778 | − | 20.7461i | −0.402174 | − | 0.696586i | 0.591814 | − | 0.806074i | \(-0.298412\pi\) |
−0.993988 | + | 0.109489i | \(0.965079\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.8678 | − | 25.0419i | −0.733422 | − | 0.839879i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.461412 | − | 0.799189i | 0.0154406 | − | 0.0267438i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.4293 | − | 31.9206i | 0.616025 | − | 1.06699i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.8244 | − | 49.9253i | −0.961346 | − | 1.66510i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.11801 | − | 8.86465i | 0.170505 | − | 0.295324i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.1326 | − | 26.2104i | −0.503025 | − | 0.871264i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.35064 | − | 4.07143i | 0.0780517 | − | 0.135190i | −0.824358 | − | 0.566069i | \(-0.808463\pi\) |
0.902409 | + | 0.430880i | \(0.141797\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.0884 | + | 36.5262i | 0.698689 | + | 1.21017i | 0.968921 | + | 0.247370i | \(0.0795663\pi\) |
−0.270232 | + | 0.962795i | \(0.587100\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.6095 | −1.31088 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.35677 | + | 3.96937i | −0.0448046 | + | 0.131080i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.1071 | − | 34.8265i | 0.663271 | − | 1.14882i | −0.316480 | − | 0.948599i | \(-0.602501\pi\) |
0.979751 | − | 0.200220i | \(-0.0641656\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.18756 | + | 10.7172i | −0.203666 | + | 0.352760i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.22932 | + | 2.12924i | 0.0404196 | + | 0.0700089i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.1424 | 0.988938 | 0.494469 | − | 0.869195i | \(-0.335362\pi\) | ||||
0.494469 | + | 0.869195i | \(0.335362\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.30552 | − | 6.42896i | −0.272203 | − | 0.210701i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.86230 | + | 6.68970i | 0.126311 | + | 0.218776i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.1550 | 1.14846 | 0.574231 | − | 0.818693i | \(-0.305301\pi\) | ||||
0.574231 | + | 0.818693i | \(0.305301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.04326 | 0.0992075 | 0.0496038 | − | 0.998769i | \(-0.484204\pi\) | ||||
0.0496038 | + | 0.998769i | \(0.484204\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.6369 | 0.834852 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.6781 | 0.411983 | 0.205991 | − | 0.978554i | \(-0.433958\pi\) | ||||
0.205991 | + | 0.978554i | \(0.433958\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.15662 | 0.232314 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.0052 | −0.745212 | −0.372606 | − | 0.927990i | \(-0.621536\pi\) | ||||
−0.372606 | + | 0.927990i | \(0.621536\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.7930 | − | 44.6749i | −0.834643 | − | 1.44564i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.7928 | + | 2.51657i | −0.413100 | + | 0.0812642i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.0067 | 0.677634 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.05985 | + | 7.03187i | 0.130691 | + | 0.226364i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.617767 | − | 1.07000i | 0.0198660 | − | 0.0344090i | −0.855921 | − | 0.517106i | \(-0.827009\pi\) |
0.875788 | + | 0.482697i | \(0.160343\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.01657 | + | 12.1530i | −0.225172 | + | 0.390010i | −0.956371 | − | 0.292155i | \(-0.905628\pi\) |
0.731199 | + | 0.682164i | \(0.238961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.4429 | − | 4.21821i | 0.687428 | − | 0.135230i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.2603 | −0.712169 | −0.356084 | − | 0.934454i | \(-0.615888\pi\) | ||||
−0.356084 | + | 0.934454i | \(0.615888\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.5891 | − | 30.4652i | −0.562151 | − | 0.973673i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.8671 | + | 29.2146i | −0.537976 | + | 0.931801i | 0.461037 | + | 0.887381i | \(0.347478\pi\) |
−0.999013 | + | 0.0444206i | \(0.985856\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.6461 | + | 44.4203i | 0.817152 | + | 1.41535i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.21474 | + | 15.9604i | −0.293012 | + | 0.507511i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.87364 | − | 11.9055i | −0.218348 | − | 0.378191i | 0.735955 | − | 0.677031i | \(-0.236734\pi\) |
−0.954303 | + | 0.298840i | \(0.903400\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.20035 | − | 3.81112i | 0.0697559 | − | 0.120821i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.6283 | + | 32.2651i | −0.589963 | + | 1.02185i | 0.404273 | + | 0.914638i | \(0.367524\pi\) |
−0.994237 | + | 0.107208i | \(0.965809\pi\) | |||||||
\(998\) | 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 | 3024.2.q.l.2305.9 | 22 | ||
3.2 | odd | 2 | 1008.2.q.l.625.4 | 22 | |||
4.3 | odd | 2 | 1512.2.q.d.793.9 | 22 | |||
7.4 | even | 3 | 3024.2.t.k.1873.3 | 22 | |||
9.2 | odd | 6 | 1008.2.t.l.961.10 | 22 | |||
9.7 | even | 3 | 3024.2.t.k.289.3 | 22 | |||
12.11 | even | 2 | 504.2.q.c.121.8 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.t.l.193.10 | 22 | |||
28.11 | odd | 6 | 1512.2.t.c.361.3 | 22 | |||
36.7 | odd | 6 | 1512.2.t.c.289.3 | 22 | |||
36.11 | even | 6 | 504.2.t.c.457.2 | yes | 22 | ||
63.11 | odd | 6 | 1008.2.q.l.529.4 | 22 | |||
63.25 | even | 3 | inner | 3024.2.q.l.2881.9 | 22 | ||
84.11 | even | 6 | 504.2.t.c.193.2 | yes | 22 | ||
252.11 | even | 6 | 504.2.q.c.25.8 | ✓ | 22 | ||
252.151 | odd | 6 | 1512.2.q.d.1369.9 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.8 | ✓ | 22 | 252.11 | even | 6 | ||
504.2.q.c.121.8 | yes | 22 | 12.11 | even | 2 | ||
504.2.t.c.193.2 | yes | 22 | 84.11 | even | 6 | ||
504.2.t.c.457.2 | yes | 22 | 36.11 | even | 6 | ||
1008.2.q.l.529.4 | 22 | 63.11 | odd | 6 | |||
1008.2.q.l.625.4 | 22 | 3.2 | odd | 2 | |||
1008.2.t.l.193.10 | 22 | 21.11 | odd | 6 | |||
1008.2.t.l.961.10 | 22 | 9.2 | odd | 6 | |||
1512.2.q.d.793.9 | 22 | 4.3 | odd | 2 | |||
1512.2.q.d.1369.9 | 22 | 252.151 | odd | 6 | |||
1512.2.t.c.289.3 | 22 | 36.7 | odd | 6 | |||
1512.2.t.c.361.3 | 22 | 28.11 | odd | 6 | |||
3024.2.q.l.2305.9 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.q.l.2881.9 | 22 | 63.25 | even | 3 | inner | ||
3024.2.t.k.289.3 | 22 | 9.7 | even | 3 | |||
3024.2.t.k.1873.3 | 22 | 7.4 | even | 3 |