Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(289,3024)]
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, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.t (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 | 289.3 | ||
Character | \(\chi\) | \(=\) | 3024.289 |
Dual form | 3024.2.t.k.1873.3 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | −2.77180 | −1.23959 | −0.619793 | − | 0.784766i | \(-0.712783\pi\) | ||||
−0.619793 | + | 0.784766i | \(0.712783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.855737 | + | 2.50354i | −0.323438 | + | 0.946249i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.43944 | −1.03703 | −0.518515 | − | 0.855069i | \(-0.673515\pi\) | ||||
−0.518515 | + | 0.855069i | \(0.673515\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.429164 | − | 0.743335i | −0.119029 | − | 0.206164i | 0.800354 | − | 0.599527i | \(-0.204645\pi\) |
−0.919383 | + | 0.393363i | \(0.871311\pi\) | |||||||
\(14\) | 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 | ||||||||
\(23\) | 7.64930 | 1.59499 | 0.797495 | − | 0.603326i | \(-0.206158\pi\) | ||||
0.797495 | + | 0.603326i | \(0.206158\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.68286 | 0.536572 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.99696 | + | 6.92294i | −0.742217 | + | 1.28556i | 0.209266 | + | 0.977859i | \(0.432893\pi\) |
−0.951484 | + | 0.307700i | \(0.900441\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.60578 | + | 6.24540i | −0.647618 | + | 1.12171i | 0.336073 | + | 0.941836i | \(0.390901\pi\) |
−0.983690 | + | 0.179871i | \(0.942432\pi\) | |||||||
\(32\) | 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 | 0.704986 | − | 0.709221i | \(-0.250953\pi\) |
−0.966697 | + | 0.255925i | \(0.917620\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.20465 | + | 2.08652i | −0.183708 | + | 0.318191i | −0.943140 | − | 0.332395i | \(-0.892143\pi\) |
0.759433 | + | 0.650586i | \(0.225477\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.307520 | + | 0.532640i | 0.0448564 | + | 0.0776935i | 0.887582 | − | 0.460650i | \(-0.152384\pi\) |
−0.842726 | + | 0.538343i | \(0.819050\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.53543 | − | 4.28474i | −0.790775 | − | 0.612106i | ||||
\(50\) | 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 | ||||||||
\(59\) | −0.734690 | + | 1.27252i | −0.0956485 | + | 0.165668i | −0.909879 | − | 0.414874i | \(-0.863826\pi\) |
0.814231 | + | 0.580542i | \(0.197159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.71635 | − | 9.90101i | −0.731904 | − | 1.26769i | −0.956069 | − | 0.293143i | \(-0.905299\pi\) |
0.224165 | − | 0.974551i | \(-0.428035\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.18956 | + | 2.06037i | 0.147546 | + | 0.255558i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.10061 | − | 14.0307i | 0.989647 | − | 1.71412i | 0.370530 | − | 0.928820i | \(-0.379176\pi\) |
0.619117 | − | 0.785299i | \(-0.287491\pi\) | |||||||
\(68\) | 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 | ||||||||
\(77\) | 2.94325 | − | 8.61077i | 0.335415 | − | 0.981288i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.37586 | − | 2.38305i | −0.154796 | − | 0.268115i | 0.778189 | − | 0.628031i | \(-0.216139\pi\) |
−0.932985 | + | 0.359916i | \(0.882805\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.75814 | + | 9.97340i | −0.632038 | + | 1.09472i | 0.355096 | + | 0.934830i | \(0.384448\pi\) |
−0.987134 | + | 0.159893i | \(0.948885\pi\) | |||||||
\(84\) | 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 | ||||||||
\(95\) | 2.07944 | − | 3.60170i | 0.213346 | − | 0.369527i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.82852 | − | 6.63119i | 0.388727 | − | 0.673296i | −0.603551 | − | 0.797324i | \(-0.706248\pi\) |
0.992279 | + | 0.124029i | \(0.0395814\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.68603 | 0.366774 | 0.183387 | − | 0.983041i | \(-0.441294\pi\) | ||||
0.183387 | + | 0.983041i | \(0.441294\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.1205 | 1.58840 | 0.794201 | − | 0.607656i | \(-0.207890\pi\) | ||||
0.794201 | + | 0.607656i | \(0.207890\pi\) | |||||||
\(104\) | 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 | 0.608628 | − | 0.793456i | \(-0.291720\pi\) |
−0.991467 | + | 0.130360i | \(0.958387\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.2023 | −1.97713 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.10345 | + | 0.413786i | −0.192823 | + | 0.0379317i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.829725 | 0.0754295 | ||||||||
\(122\) | 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 | ||||||||
\(131\) | 1.58550 | 0.138526 | 0.0692631 | − | 0.997598i | \(-0.477935\pi\) | ||||
0.0692631 | + | 0.997598i | \(0.477935\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.61114 | − | 2.99015i | −0.226415 | − | 0.259279i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.92788 | −0.421017 | −0.210508 | − | 0.977592i | \(-0.567512\pi\) | ||||
−0.210508 | + | 0.977592i | \(0.567512\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.12999 | − | 7.15336i | −0.350301 | − | 0.606740i | 0.636001 | − | 0.771688i | \(-0.280588\pi\) |
−0.986302 | + | 0.164949i | \(0.947254\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | 13.9140 | 1.13988 | 0.569938 | − | 0.821688i | \(-0.306967\pi\) | ||||
0.569938 | + | 0.821688i | \(0.306967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.9927 | −1.87112 | −0.935561 | − | 0.353166i | \(-0.885105\pi\) | ||||
−0.935561 | + | 0.353166i | \(0.885105\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.99450 | − | 17.3110i | 0.802777 | − | 1.39045i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.29022 | + | 16.0911i | −0.741441 | + | 1.28421i | 0.210399 | + | 0.977616i | \(0.432524\pi\) |
−0.951839 | + | 0.306597i | \(0.900810\pi\) | |||||||
\(158\) | 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 | 0.572632 | − | 0.819813i | \(-0.305923\pi\) |
−0.996295 | + | 0.0860073i | \(0.972589\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.13164 | − | 10.6203i | 0.471664 | − | 0.816947i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.70271 | − | 11.6094i | −0.509598 | − | 0.882649i | −0.999938 | − | 0.0111184i | \(-0.996461\pi\) |
0.490340 | − | 0.871531i | \(-0.336873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.29582 | + | 6.71665i | −0.173548 | + | 0.507731i | ||||
\(176\) | 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 | ||||||||
\(185\) | −1.27007 | + | 2.19982i | −0.0933772 | + | 0.161734i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.39343 | − | 2.41349i | −0.101897 | − | 0.176492i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.30553 | + | 16.1177i | 0.673325 | + | 1.16623i | 0.976956 | + | 0.213443i | \(0.0684677\pi\) |
−0.303631 | + | 0.952790i | \(0.598199\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.46470 | + | 2.53693i | −0.105431 | + | 0.182613i | −0.913914 | − | 0.405907i | \(-0.866956\pi\) |
0.808483 | + | 0.588520i | \(0.200289\pi\) | |||||||
\(194\) | 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 | ||||||||
\(203\) | −13.9115 | − | 15.9308i | −0.976397 | − | 1.11812i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.64489 | + | 8.04518i | 0.324413 | + | 0.561900i | ||||
\(206\) | 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 | −0.881414 | − | 0.472345i | \(-0.843408\pi\) |
0.0316443 | − | 0.999499i | \(-0.489926\pi\) | |||||||
\(212\) | 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 | ||||||||
\(221\) | 0.347737 | − | 0.602298i | 0.0233913 | − | 0.0405149i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.78468 | − | 16.9476i | 0.655231 | − | 1.13489i | −0.326605 | − | 0.945161i | \(-0.605905\pi\) |
0.981836 | − | 0.189732i | \(-0.0607619\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.64808 | 0.573993 | 0.286996 | − | 0.957932i | \(-0.407343\pi\) | ||||
0.286996 | + | 0.957932i | \(0.407343\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.5427 | 0.762765 | 0.381382 | − | 0.924417i | \(-0.375448\pi\) | ||||
0.381382 | + | 0.924417i | \(0.375448\pi\) | |||||||
\(230\) | 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 | 0.916790 | + | 0.399371i | \(0.130771\pi\) |
−0.112530 | + | 0.993648i | \(0.535895\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.0363 | −1.22623 | −0.613117 | − | 0.789992i | \(-0.710085\pi\) | ||||
−0.613117 | + | 0.789992i | \(0.710085\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.3431 | + | 11.8764i | 0.980234 | + | 0.758758i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.28786 | 0.0819447 | ||||||||
\(248\) | 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 | ||||||||
\(257\) | −4.36725 | −0.272421 | −0.136211 | − | 0.990680i | \(-0.543492\pi\) | ||||
−0.136211 | + | 0.990680i | \(0.543492\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.59481 | + | 1.82630i | 0.0990968 | + | 0.113481i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.4842 | −0.769811 | −0.384905 | − | 0.922956i | \(-0.625766\pi\) | ||||
−0.384905 | + | 0.922956i | \(0.625766\pi\) | |||||||
\(264\) | 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 | ||||||||
\(275\) | −9.22753 | −0.556441 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.96075 | −0.117810 | −0.0589049 | − | 0.998264i | \(-0.518761\pi\) | ||||
−0.0589049 | + | 0.998264i | \(0.518761\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.42057 | + | 16.3169i | −0.561984 | + | 0.973385i | 0.435339 | + | 0.900267i | \(0.356628\pi\) |
−0.997323 | + | 0.0731185i | \(0.976705\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.7422 | + | 20.3381i | −0.698002 | + | 1.20898i | 0.271156 | + | 0.962536i | \(0.412594\pi\) |
−0.969158 | + | 0.246440i | \(0.920739\pi\) | |||||||
\(284\) | 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 | 0.893857 | − | 0.448351i | \(-0.147989\pi\) |
−0.835212 | + | 0.549928i | \(0.814655\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.03641 | − | 3.52717i | 0.118564 | − | 0.205360i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.28281 | − | 5.68599i | −0.189850 | − | 0.328829i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.19282 | − | 4.80140i | −0.241670 | − | 0.276748i | ||||
\(302\) | 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 | ||||||||
\(311\) | 7.04979 | − | 12.2106i | 0.399757 | − | 0.692400i | −0.593939 | − | 0.804510i | \(-0.702428\pi\) |
0.993696 | + | 0.112111i | \(0.0357611\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.0769 | + | 29.5781i | 0.965245 | + | 1.67185i | 0.708954 | + | 0.705255i | \(0.249167\pi\) |
0.256291 | + | 0.966600i | \(0.417499\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.790586 | − | 1.36933i | −0.0444037 | − | 0.0769095i | 0.842969 | − | 0.537962i | \(-0.180805\pi\) |
−0.887373 | + | 0.461052i | \(0.847472\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.7473 | − | 23.8110i | 0.769701 | − | 1.33316i | ||||
\(320\) | 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 | ||||||||
\(329\) | −1.59664 | + | 0.314088i | −0.0880257 | + | 0.0173163i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.86862 | + | 11.8968i | 0.377533 | + | 0.653907i | 0.990703 | − | 0.136044i | \(-0.0434390\pi\) |
−0.613169 | + | 0.789951i | \(0.710106\pi\) | |||||||
\(332\) | 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 | 0.524414 | − | 0.851463i | \(-0.324284\pi\) |
−0.999596 | + | 0.0284243i | \(0.990951\pi\) | |||||||
\(338\) | 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 | ||||||||
\(347\) | −1.91552 | + | 3.31778i | −0.102830 | + | 0.178108i | −0.912850 | − | 0.408296i | \(-0.866123\pi\) |
0.810019 | + | 0.586403i | \(0.199457\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.69984 | − | 2.94421i | 0.0909903 | − | 0.157600i | −0.816938 | − | 0.576726i | \(-0.804330\pi\) |
0.907928 | + | 0.419126i | \(0.137663\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.5568 | −0.668332 | −0.334166 | − | 0.942514i | \(-0.608455\pi\) | ||||
−0.334166 | + | 0.942514i | \(0.608455\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −39.9629 | −2.12101 | ||||||||
\(356\) | 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 | ||||||||
\(367\) | 2.02514 | 0.105711 | 0.0528557 | − | 0.998602i | \(-0.483168\pi\) | ||||
0.0528557 | + | 0.998602i | \(0.483168\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 32.7950 | − | 6.45138i | 1.70263 | − | 0.334939i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.6259 | 1.11975 | 0.559874 | − | 0.828578i | \(-0.310849\pi\) | ||||
0.559874 | + | 0.828578i | \(0.310849\pi\) | |||||||
\(374\) | 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 | ||||||||
\(383\) | −7.65645 | −0.391226 | −0.195613 | − | 0.980681i | \(-0.562670\pi\) | ||||
−0.195613 | + | 0.980681i | \(0.562670\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.15810 | + | 23.8673i | −0.415775 | + | 1.21639i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.1561 | 1.07266 | 0.536329 | − | 0.844009i | \(-0.319811\pi\) | ||||
0.536329 | + | 0.844009i | \(0.319811\pi\) | |||||||
\(390\) | 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 | ||||||||
\(401\) | 7.77773 | 0.388401 | 0.194201 | − | 0.980962i | \(-0.437789\pi\) | ||||
0.194201 | + | 0.980962i | \(0.437789\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.18989 | 0.308341 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.57599 | + | 2.72969i | −0.0781188 | + | 0.135306i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.76327 | + | 16.9105i | −0.482763 | + | 0.836170i | −0.999804 | − | 0.0197907i | \(-0.993700\pi\) |
0.517041 | + | 0.855960i | \(0.327033\pi\) | |||||||
\(410\) | 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 | −0.990915 | − | 0.134493i | \(-0.957059\pi\) |
0.378983 | − | 0.925404i | \(-0.376274\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0746 | − | 31.3061i | 0.880902 | − | 1.52577i | 0.0305620 | − | 0.999533i | \(-0.490270\pi\) |
0.850340 | − | 0.526234i | \(-0.176396\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.08691 | + | 1.88259i | 0.0527231 | + | 0.0913190i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.6793 | − | 5.83845i | 1.43628 | − | 0.282543i | ||||
\(428\) | 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 | ||||||||
\(437\) | −5.73862 | + | 9.93958i | −0.274515 | + | 0.475475i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.39235 | − | 4.14367i | −0.114180 | − | 0.197766i | 0.803271 | − | 0.595613i | \(-0.203091\pi\) |
−0.917452 | + | 0.397847i | \(0.869758\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.13213 | + | 7.15707i | 0.196324 | + | 0.340042i | 0.947334 | − | 0.320248i | \(-0.103766\pi\) |
−0.751010 | + | 0.660291i | \(0.770433\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.1748 | + | 24.5515i | −0.671952 | + | 1.16385i | ||||
\(446\) | 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 | ||||||||
\(455\) | −6.17617 | + | 1.21497i | −0.289543 | + | 0.0569585i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.98220 | + | 15.5576i | 0.420170 | + | 0.727755i | 0.995956 | − | 0.0898451i | \(-0.0286372\pi\) |
−0.575786 | + | 0.817600i | \(0.695304\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.03501 | + | 6.98885i | −0.187929 | + | 0.325503i | −0.944560 | − | 0.328340i | \(-0.893511\pi\) |
0.756630 | + | 0.653843i | \(0.226844\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.50704 | + | 4.34232i | 0.116512 | + | 0.201805i | 0.918383 | − | 0.395692i | \(-0.129495\pi\) |
−0.801871 | + | 0.597497i | \(0.796162\pi\) | |||||||
\(464\) | 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 | ||||||||
\(473\) | 4.14332 | − | 7.17645i | 0.190510 | − | 0.329973i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.01272 | + | 3.48614i | −0.0923500 | + | 0.159955i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.2445 | −1.15345 | −0.576724 | − | 0.816939i | \(-0.695669\pi\) | ||||
−0.576724 | + | 0.816939i | \(0.695669\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.786591 | −0.0358655 | ||||||||
\(482\) | 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 | −0.963675 | − | 0.267078i | \(-0.913942\pi\) |
0.250541 | − | 0.968106i | \(-0.419391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.47720 | −0.291718 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.3377 | + | 36.0953i | −0.553424 | + | 1.61909i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.94890 | −0.266309 | −0.133155 | − | 0.991095i | \(-0.542511\pi\) | ||||
−0.133155 | + | 0.991095i | \(0.542511\pi\) | |||||||
\(500\) | 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 | ||||||||
\(509\) | −37.2885 | −1.65278 | −0.826392 | − | 0.563095i | \(-0.809611\pi\) | ||||
−0.826392 | + | 0.563095i | \(0.809611\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.6450 | − | 4.25798i | 0.957521 | − | 0.188362i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −44.6828 | −1.96896 | ||||||||
\(516\) | 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 | ||||||||
\(527\) | −5.84328 | −0.254537 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.5118 | 1.54399 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.43836 | + | 2.49131i | −0.0623023 | + | 0.107911i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.78013 | + | 15.2076i | −0.379598 | + | 0.657483i | ||||
\(536\) | 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 | −0.402184 | − | 0.915559i | \(-0.631749\pi\) |
0.993989 | − | 0.109478i | \(-0.0349180\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.99716 | − | 10.3874i | −0.255488 | − | 0.442518i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.14344 | − | 1.40525i | 0.303770 | − | 0.0597571i | ||||
\(554\) | 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 | ||||||||
\(563\) | −0.956715 | + | 1.65708i | −0.0403207 | + | 0.0698375i | −0.885482 | − | 0.464675i | \(-0.846171\pi\) |
0.845161 | + | 0.534512i | \(0.179505\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.2802 | + | 19.5379i | 0.474561 | + | 0.821964i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.38138 | − | 12.7849i | −0.309444 | − | 0.535972i | 0.668797 | − | 0.743445i | \(-0.266809\pi\) |
−0.978241 | + | 0.207473i | \(0.933476\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.28208 | − | 2.22063i | 0.0536535 | − | 0.0929306i | −0.837951 | − | 0.545745i | \(-0.816247\pi\) |
0.891605 | + | 0.452814i | \(0.149580\pi\) | |||||||
\(572\) | 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 | ||||||||
\(581\) | −20.0413 | − | 22.9504i | −0.831455 | − | 0.952141i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.7251 | + | 37.6289i | 0.899760 | + | 1.55843i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.7666 | − | 27.3085i | 0.650756 | − | 1.12714i | −0.332183 | − | 0.943215i | \(-0.607785\pi\) |
0.982940 | − | 0.183928i | \(-0.0588813\pi\) | |||||||
\(588\) | 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 | ||||||||
\(599\) | −2.80684 | + | 4.86159i | −0.114684 | + | 0.198639i | −0.917654 | − | 0.397381i | \(-0.869919\pi\) |
0.802969 | + | 0.596021i | \(0.203252\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.2223 | − | 33.2940i | 0.784094 | − | 1.35809i | −0.145444 | − | 0.989366i | \(-0.546461\pi\) |
0.929539 | − | 0.368725i | \(-0.120205\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.29983 | −0.0935013 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.3437 | 0.663372 | 0.331686 | − | 0.943390i | \(-0.392383\pi\) | ||||
0.331686 | + | 0.943390i | \(0.392383\pi\) | |||||||
\(608\) | 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 | −0.885764 | − | 0.464136i | \(-0.846365\pi\) |
0.0409280 | − | 0.999162i | \(-0.486969\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.8945 | 1.44272 | 0.721361 | − | 0.692559i | \(-0.243517\pi\) | ||||
0.721361 | + | 0.692559i | \(0.243517\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.7992 | + | 20.3828i | 0.713111 | + | 0.816619i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2166 | −1.24866 | ||||||||
\(626\) | 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 | ||||||||
\(635\) | −34.8299 | −1.38218 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.809390 | + | 5.95353i | −0.0320692 | + | 0.235888i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.6026 | 0.576769 | 0.288385 | − | 0.957515i | \(-0.406882\pi\) | ||||
0.288385 | + | 0.957515i | \(0.406882\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.96942 | + | 10.3393i | 0.235411 | + | 0.407744i | 0.959392 | − | 0.282076i | \(-0.0910231\pi\) |
−0.723981 | + | 0.689820i | \(0.757690\pi\) | |||||||
\(644\) | 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 | ||||||||
\(653\) | −39.9918 | −1.56500 | −0.782501 | − | 0.622650i | \(-0.786056\pi\) | ||||
−0.782501 | + | 0.622650i | \(0.786056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.39469 | −0.171715 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.60101 | − | 2.77303i | 0.0623665 | − | 0.108022i | −0.833156 | − | 0.553038i | \(-0.813469\pi\) |
0.895523 | + | 0.445016i | \(0.146802\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.6515 | − | 37.5015i | 0.842146 | − | 1.45864i | −0.0459311 | − | 0.998945i | \(-0.514625\pi\) |
0.888077 | − | 0.459695i | \(-0.152041\pi\) | |||||||
\(662\) | 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 | −0.525670 | − | 0.850689i | \(-0.676185\pi\) |
0.999553 | + | 0.0298991i | \(0.00951859\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.2094 | − | 33.2716i | −0.738276 | − | 1.27873i | −0.953271 | − | 0.302117i | \(-0.902307\pi\) |
0.214994 | − | 0.976615i | \(-0.431027\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.3253 | + | 15.2594i | 0.511376 | + | 0.585603i | ||||
\(680\) | 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 | ||||||||
\(689\) | −5.42160 | + | 9.39049i | −0.206547 | + | 0.357749i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.65146 | − | 6.32452i | −0.138908 | − | 0.240596i | 0.788175 | − | 0.615451i | \(-0.211026\pi\) |
−0.927084 | + | 0.374855i | \(0.877693\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.4475 | + | 19.8277i | 0.434229 | + | 0.752106i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.35782 | − | 2.35181i | 0.0514309 | − | 0.0890810i | ||||
\(698\) | 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 | ||||||||
\(707\) | −3.15427 | + | 9.22813i | −0.118629 | + | 0.347059i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.46137 | − | 2.53116i | −0.0548828 | − | 0.0950599i | 0.837279 | − | 0.546776i | \(-0.184145\pi\) |
−0.892162 | + | 0.451716i | \(0.850812\pi\) | |||||||
\(710\) | 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 | ||||||||
\(725\) | −10.7233 | + | 18.5733i | −0.398253 | + | 0.689795i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.0486 | + | 34.7252i | −0.743561 | + | 1.28789i | 0.207303 | + | 0.978277i | \(0.433531\pi\) |
−0.950864 | + | 0.309609i | \(0.899802\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.95217 | −0.0722037 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.12469 | −0.263156 | −0.131578 | − | 0.991306i | \(-0.542004\pi\) | ||||
−0.131578 | + | 0.991306i | \(0.542004\pi\) | |||||||
\(734\) | 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 | 0.868004 | − | 0.496557i | \(-0.165402\pi\) |
−0.864033 | + | 0.503436i | \(0.832069\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.5667 | −1.41297 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.0251 | + | 12.6254i | 0.402849 | + | 0.461323i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.5840 | −0.860594 | −0.430297 | − | 0.902687i | \(-0.641591\pi\) | ||||
−0.430297 | + | 0.902687i | \(0.641591\pi\) | |||||||
\(752\) | 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 | ||||||||
\(761\) | 18.1140 | 0.656631 | 0.328316 | − | 0.944568i | \(-0.393519\pi\) | ||||
0.328316 | + | 0.944568i | \(0.393519\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.4136 | + | 4.99932i | −0.920035 | + | 0.180988i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.26121 | 0.0455397 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.16710 | + | 5.48558i | 0.114209 | + | 0.197815i | 0.917463 | − | 0.397821i | \(-0.130233\pi\) |
−0.803255 | + | 0.595636i | \(0.796900\pi\) | |||||||
\(770\) | 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 | ||||||||
\(779\) | 5.02874 | 0.180173 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −49.5887 | −1.77442 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.7506 | − | 44.6014i | 0.919079 | − | 1.59189i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.65916 | + | 16.7302i | −0.344312 | + | 0.596366i | −0.985229 | − | 0.171245i | \(-0.945221\pi\) |
0.640917 | + | 0.767611i | \(0.278554\pi\) | |||||||
\(788\) | 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 | 0.942044 | − | 0.335488i | \(-0.108901\pi\) |
−0.761563 | + | 0.648090i | \(0.775568\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.249172 | + | 0.431579i | −0.00881509 | + | 0.0152682i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.3388 | + | 24.8355i | 0.506004 | + | 0.876424i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.1436 | − | 53.0808i | 0.639478 | − | 1.87085i | ||||
\(806\) | 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 | ||||||||
\(815\) | −6.79627 | + | 11.7715i | −0.238063 | + | 0.412337i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.80750 | − | 3.13067i | −0.0632363 | − | 0.109528i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.8177 | + | 46.4495i | 0.935943 | + | 1.62110i | 0.772944 | + | 0.634474i | \(0.218783\pi\) |
0.162998 | + | 0.986626i | \(0.447883\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.475192 | + | 0.823057i | −0.0165641 | + | 0.0286899i | −0.874189 | − | 0.485586i | \(-0.838606\pi\) |
0.857625 | + | 0.514276i | \(0.171939\pi\) | |||||||
\(824\) | 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 | ||||||||
\(833\) | 0.764066 | − | 5.62015i | 0.0264733 | − | 0.194727i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.1754 | + | 26.2846i | 0.525166 | + | 0.909615i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.7367 | + | 27.2567i | −0.543290 | + | 0.941006i | 0.455422 | + | 0.890276i | \(0.349488\pi\) |
−0.998712 | + | 0.0507305i | \(0.983845\pi\) | |||||||
\(840\) | 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 | ||||||||
\(851\) | 3.50499 | − | 6.07082i | 0.120150 | − | 0.208105i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.6959 | + | 46.2386i | −0.914049 | + | 1.58318i | −0.105762 | + | 0.994391i | \(0.533728\pi\) |
−0.808287 | + | 0.588788i | \(0.799605\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.6297 | −0.738857 | −0.369428 | − | 0.929259i | \(-0.620446\pi\) | ||||
−0.369428 | + | 0.929259i | \(0.620446\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.4288 | 1.17470 | 0.587348 | − | 0.809334i | \(-0.300172\pi\) | ||||
0.587348 | + | 0.809334i | \(0.300172\pi\) | |||||||
\(860\) | 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 | ||||||||
\(871\) | −13.9060 | −0.471186 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.49609 | + | 16.0793i | −0.185802 | + | 0.543581i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.4068 | 1.09430 | 0.547150 | − | 0.837034i | \(-0.315713\pi\) | ||||
0.547150 | + | 0.837034i | \(0.315713\pi\) | |||||||
\(878\) | 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 | ||||||||
\(887\) | 23.9555 | 0.804348 | 0.402174 | − | 0.915563i | \(-0.368255\pi\) | ||||
0.402174 | + | 0.915563i | \(0.368255\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.7530 | + | 31.4590i | −0.360645 | + | 1.05510i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.922824 | −0.0308811 | ||||||||
\(894\) | 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 | ||||||||
\(905\) | 30.2652 | 1.00605 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.70128 | −0.156103 | −0.0780517 | − | 0.996949i | \(-0.524870\pi\) | ||||
−0.0780517 | + | 0.996949i | \(0.524870\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.0884 | − | 36.5262i | 0.698689 | − | 1.21017i | −0.270232 | − | 0.962795i | \(-0.587100\pi\) |
0.968921 | − | 0.247370i | \(-0.0795663\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.8048 | − | 34.3029i | 0.655442 | − | 1.13526i | ||||
\(914\) | 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 | ||||||||
\(929\) | −15.0712 | − | 26.1040i | −0.494469 | − | 0.856446i | 0.505510 | − | 0.862820i | \(-0.331304\pi\) |
−0.999980 | + | 0.00637464i | \(0.997971\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.72040 | − | 3.97831i | 0.318573 | − | 0.130384i | ||||
\(932\) | 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 | ||||||||
\(941\) | −1.52163 | + | 2.63554i | −0.0496038 | + | 0.0859162i | −0.889761 | − | 0.456426i | \(-0.849129\pi\) |
0.840157 | + | 0.542343i | \(0.182463\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.8184 | − | 22.2022i | −0.417426 | − | 0.723003i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.33905 | − | 10.9796i | −0.205991 | − | 0.356788i | 0.744457 | − | 0.667671i | \(-0.232709\pi\) |
−0.950448 | + | 0.310883i | \(0.899375\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.57831 | + | 6.19781i | −0.116157 | + | 0.201190i | ||||
\(950\) | 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 | ||||||||
\(959\) | 4.21697 | − | 12.3371i | 0.136173 | − | 0.398387i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.5033 | − | 18.1923i | −0.338817 | − | 0.586849i | ||||
\(962\) | 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 | 0.875788 | − | 0.482697i | \(-0.160343\pi\) |
−0.855921 | + | 0.517106i | \(0.827009\pi\) | |||||||
\(968\) | 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 | ||||||||
\(977\) | 11.1301 | − | 19.2780i | 0.356084 | − | 0.616756i | −0.631218 | − | 0.775605i | \(-0.717445\pi\) |
0.987303 | + | 0.158849i | \(0.0507782\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.5891 | + | 30.4652i | −0.562151 | + | 0.973673i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.7341 | 1.07595 | 0.537976 | − | 0.842960i | \(-0.319189\pi\) | ||||
0.537976 | + | 0.842960i | \(0.319189\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −51.2921 | −1.63430 | ||||||||
\(986\) | 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 | ||||||||
\(997\) | 37.2565 | 1.17993 | 0.589963 | − | 0.807430i | \(-0.299142\pi\) | ||||
0.589963 | + | 0.807430i | \(0.299142\pi\) | |||||||
\(998\) | 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.t.k.289.3 | 22 | ||
3.2 | odd | 2 | 1008.2.t.l.961.10 | 22 | |||
4.3 | odd | 2 | 1512.2.t.c.289.3 | 22 | |||
7.4 | even | 3 | 3024.2.q.l.2881.9 | 22 | |||
9.4 | even | 3 | 3024.2.q.l.2305.9 | 22 | |||
9.5 | odd | 6 | 1008.2.q.l.625.4 | 22 | |||
12.11 | even | 2 | 504.2.t.c.457.2 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.q.l.529.4 | 22 | |||
28.11 | odd | 6 | 1512.2.q.d.1369.9 | 22 | |||
36.23 | even | 6 | 504.2.q.c.121.8 | yes | 22 | ||
36.31 | odd | 6 | 1512.2.q.d.793.9 | 22 | |||
63.4 | even | 3 | inner | 3024.2.t.k.1873.3 | 22 | ||
63.32 | odd | 6 | 1008.2.t.l.193.10 | 22 | |||
84.11 | even | 6 | 504.2.q.c.25.8 | ✓ | 22 | ||
252.67 | odd | 6 | 1512.2.t.c.361.3 | 22 | |||
252.95 | even | 6 | 504.2.t.c.193.2 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.8 | ✓ | 22 | 84.11 | even | 6 | ||
504.2.q.c.121.8 | yes | 22 | 36.23 | even | 6 | ||
504.2.t.c.193.2 | yes | 22 | 252.95 | even | 6 | ||
504.2.t.c.457.2 | yes | 22 | 12.11 | even | 2 | ||
1008.2.q.l.529.4 | 22 | 21.11 | odd | 6 | |||
1008.2.q.l.625.4 | 22 | 9.5 | odd | 6 | |||
1008.2.t.l.193.10 | 22 | 63.32 | odd | 6 | |||
1008.2.t.l.961.10 | 22 | 3.2 | odd | 2 | |||
1512.2.q.d.793.9 | 22 | 36.31 | odd | 6 | |||
1512.2.q.d.1369.9 | 22 | 28.11 | odd | 6 | |||
1512.2.t.c.289.3 | 22 | 4.3 | odd | 2 | |||
1512.2.t.c.361.3 | 22 | 252.67 | odd | 6 | |||
3024.2.q.l.2305.9 | 22 | 9.4 | even | 3 | |||
3024.2.q.l.2881.9 | 22 | 7.4 | even | 3 | |||
3024.2.t.k.289.3 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.t.k.1873.3 | 22 | 63.4 | even | 3 | inner |