Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(31,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.p (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.31 |
Dual form | 784.2.p.e.607.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 1.00000 | − | 1.73205i | 0.577350 | − | 1.00000i | −0.418432 | − | 0.908248i | \(-0.637420\pi\) |
0.995782 | − | 0.0917517i | \(-0.0292466\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.00000 | + | 1.73205i | −1.34164 | + | 0.774597i | −0.987048 | − | 0.160424i | \(-0.948714\pi\) |
−0.354593 | + | 0.935021i | \(0.615380\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | + | 1.73205i | 0.904534 | + | 0.522233i | 0.878668 | − | 0.477432i | \(-0.158432\pi\) |
0.0258656 | + | 0.999665i | \(0.491766\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.92820i | 1.78885i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | − | 1.73205i | 0.625543 | − | 0.361158i | −0.153481 | − | 0.988152i | \(-0.549048\pi\) |
0.779024 | + | 0.626994i | \(0.215715\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.50000 | − | 6.06218i | 0.700000 | − | 1.21244i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | + | 6.92820i | −0.718421 | + | 1.24434i | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.00000 | − | 3.46410i | 1.04447 | − | 0.603023i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | + | 1.73205i | 0.164399 | + | 0.284747i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.00000 | + | 3.46410i | 0.960769 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.92820i | − | 1.08200i | −0.841021 | − | 0.541002i | \(-0.818045\pi\) | ||
0.841021 | − | 0.541002i | \(-0.181955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.3923i | 1.58481i | 0.609994 | + | 0.792406i | \(0.291172\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | + | 1.73205i | 0.447214 | + | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.00000 | + | 5.19615i | −0.412082 | + | 0.713746i | −0.995117 | − | 0.0987002i | \(-0.968532\pi\) |
0.583036 | + | 0.812447i | \(0.301865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.0000 | −1.61808 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | − | 5.19615i | 0.390567 | − | 0.676481i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | − | 1.73205i | 0.384111 | − | 0.221766i | −0.295495 | − | 0.955344i | \(-0.595484\pi\) |
0.679605 | + | 0.733578i | \(0.262151\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.00000 | − | 10.3923i | −0.744208 | − | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.00000 | + | 1.73205i | 0.366508 | + | 0.211604i | 0.671932 | − | 0.740613i | \(-0.265465\pi\) |
−0.305424 | + | 0.952217i | \(0.598798\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.92820i | − | 0.834058i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.46410i | − | 0.411113i | −0.978645 | − | 0.205557i | \(-0.934100\pi\) | ||
0.978645 | − | 0.205557i | \(-0.0659005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | − | 3.46410i | −0.702247 | − | 0.405442i | 0.105937 | − | 0.994373i | \(-0.466216\pi\) |
−0.808184 | + | 0.588930i | \(0.799549\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.00000 | − | 12.1244i | −0.808290 | − | 1.40000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.00000 | + | 1.73205i | −0.337526 | + | 0.194871i | −0.659178 | − | 0.751987i | \(-0.729095\pi\) |
0.321651 | + | 0.946858i | \(0.395762\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.00000 | − | 10.3923i | 0.643268 | − | 1.11417i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | + | 3.46410i | −0.635999 | + | 0.367194i | −0.783072 | − | 0.621932i | \(-0.786348\pi\) |
0.147073 | + | 0.989126i | \(0.453015\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.00000 | + | 13.8564i | 0.829561 | + | 1.43684i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.00000 | − | 3.46410i | −0.615587 | − | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.8564i | 1.40690i | 0.710742 | + | 0.703452i | \(0.248359\pi\) | ||||
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.46410i | − | 0.348155i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.00000 | − | 5.19615i | −0.895533 | − | 0.517036i | −0.0197851 | − | 0.999804i | \(-0.506298\pi\) |
−0.875748 | + | 0.482768i | \(0.839632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | + | 3.46410i | 0.197066 | + | 0.341328i | 0.947576 | − | 0.319531i | \(-0.103525\pi\) |
−0.750510 | + | 0.660859i | \(0.770192\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.00000 | − | 5.19615i | 0.870063 | − | 0.502331i | 0.00269372 | − | 0.999996i | \(-0.499143\pi\) |
0.867369 | + | 0.497665i | \(0.165809\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | + | 12.1244i | −0.670478 | + | 1.16130i | 0.307290 | + | 0.951616i | \(0.400578\pi\) |
−0.977769 | + | 0.209687i | \(0.932756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.00000 | + | 10.3923i | −0.559503 | + | 0.969087i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.00000 | − | 1.73205i | 0.277350 | − | 0.160128i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.0000 | − | 6.92820i | −1.08200 | − | 0.624695i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.3923i | − | 0.922168i | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||
0.887357 | − | 0.461084i | \(-0.152539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18.0000 | + | 10.3923i | 1.58481 | + | 0.914991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.00000 | + | 15.5885i | 0.786334 | + | 1.36197i | 0.928199 | + | 0.372084i | \(0.121357\pi\) |
−0.141865 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.0000 | + | 6.92820i | −1.03280 | + | 0.596285i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.00000 | − | 5.19615i | 0.256307 | − | 0.443937i | −0.708942 | − | 0.705266i | \(-0.750827\pi\) |
0.965250 | + | 0.261329i | \(0.0841608\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | 0.169638 | 0.0848189 | − | 0.996396i | \(-0.472969\pi\) | ||||
0.0848189 | + | 0.996396i | \(0.472969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.00000 | + | 10.3923i | −0.501745 | + | 0.869048i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.0000 | + | 10.3923i | −1.49482 | + | 0.863034i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.00000 | − | 1.73205i | −0.244137 | − | 0.140952i | 0.372940 | − | 0.927855i | \(-0.378350\pi\) |
−0.617076 | + | 0.786903i | \(0.711683\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 27.7128i | − | 2.22595i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | + | 5.19615i | 0.718278 | + | 0.414698i | 0.814119 | − | 0.580699i | \(-0.197221\pi\) |
−0.0958404 | + | 0.995397i | \(0.530554\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.00000 | + | 10.3923i | 0.475831 | + | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.0000 | + | 8.66025i | −1.17489 | + | 0.678323i | −0.954827 | − | 0.297162i | \(-0.903960\pi\) |
−0.220064 | + | 0.975486i | \(0.570626\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.0000 | + | 20.7846i | −0.934199 | + | 1.61808i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | − | 1.73205i | 0.0764719 | − | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.00000 | − | 1.73205i | 0.228086 | − | 0.131685i | −0.381603 | − | 0.924326i | \(-0.624628\pi\) |
0.609689 | + | 0.792641i | \(0.291294\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.00000 | − | 10.3923i | −0.450988 | − | 0.781133i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.00000 | − | 5.19615i | −0.672692 | − | 0.388379i | 0.124404 | − | 0.992232i | \(-0.460298\pi\) |
−0.797096 | + | 0.603853i | \(0.793631\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 17.3205i | − | 1.28742i | −0.765268 | − | 0.643712i | \(-0.777394\pi\) | ||
0.765268 | − | 0.643712i | \(-0.222606\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 6.92820i | − | 0.512148i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | − | 3.46410i | −0.441129 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.0000 | − | 12.1244i | 1.51951 | − | 0.877288i | 0.519771 | − | 0.854306i | \(-0.326017\pi\) |
0.999736 | − | 0.0229818i | \(-0.00731599\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.00000 | − | 1.73205i | 0.0719816 | − | 0.124676i | −0.827788 | − | 0.561041i | \(-0.810401\pi\) |
0.899770 | + | 0.436365i | \(0.143734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −24.0000 | −1.71868 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000 | − | 17.3205i | 0.708881 | − | 1.22782i | −0.256391 | − | 0.966573i | \(-0.582534\pi\) |
0.965272 | − | 0.261245i | \(-0.0841331\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.00000 | − | 3.46410i | 0.423207 | − | 0.244339i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.0000 | + | 20.7846i | 0.838116 | + | 1.45166i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.00000 | − | 1.73205i | −0.208514 | − | 0.120386i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.92820i | 0.479234i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.46410i | − | 0.238479i | −0.992866 | − | 0.119239i | \(-0.961954\pi\) | ||
0.992866 | − | 0.119239i | \(-0.0380456\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.00000 | − | 3.46410i | −0.411113 | − | 0.237356i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.0000 | − | 31.1769i | −1.22759 | − | 2.12625i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.0000 | + | 6.92820i | −0.810885 | + | 0.468165i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000 | 1.07144 | 0.535720 | − | 0.844396i | \(-0.320040\pi\) | ||||
0.535720 | + | 0.844396i | \(0.320040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.00000 | −0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.00000 | + | 5.19615i | −0.199117 | + | 0.344881i | −0.948242 | − | 0.317547i | \(-0.897141\pi\) |
0.749125 | + | 0.662428i | \(0.230474\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.00000 | − | 5.19615i | 0.594737 | − | 0.343371i | −0.172231 | − | 0.985057i | \(-0.555098\pi\) |
0.766968 | + | 0.641685i | \(0.221764\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.00000 | + | 5.19615i | 0.196537 | + | 0.340411i | 0.947403 | − | 0.320043i | \(-0.103697\pi\) |
−0.750867 | + | 0.660454i | \(0.770364\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.92820i | 0.450035i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336111i | \(-0.109112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.0000 | − | 13.8564i | −1.54598 | − | 0.892570i | −0.998443 | − | 0.0557856i | \(-0.982234\pi\) |
−0.547533 | − | 0.836784i | \(-0.684433\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.00000 | − | 8.66025i | −0.320750 | − | 0.555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | + | 3.46410i | −0.381771 | + | 0.220416i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | − | 10.3923i | 0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.0000 | −1.89358 | −0.946792 | − | 0.321847i | \(-0.895696\pi\) | ||||
−0.946792 | + | 0.321847i | \(0.895696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.0000 | − | 13.8564i | 1.49708 | − | 0.864339i | 0.497085 | − | 0.867702i | \(-0.334404\pi\) |
0.999994 | + | 0.00336324i | \(0.00107055\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.0000 | − | 12.1244i | −1.29492 | − | 0.747620i | −0.315394 | − | 0.948961i | \(-0.602137\pi\) |
−0.979521 | + | 0.201341i | \(0.935470\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 20.7846i | − | 1.27679i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.8564i | 0.847998i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.00000 | − | 1.73205i | −0.182913 | − | 0.105605i | 0.405747 | − | 0.913985i | \(-0.367011\pi\) |
−0.588661 | + | 0.808380i | \(0.700345\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | − | 6.92820i | −0.242983 | − | 0.420858i | 0.718580 | − | 0.695444i | \(-0.244792\pi\) |
−0.961563 | + | 0.274586i | \(0.911459\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.0000 | − | 12.1244i | 1.26635 | − | 0.731126i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.00000 | − | 1.73205i | 0.0600842 | − | 0.104069i | −0.834419 | − | 0.551131i | \(-0.814196\pi\) |
0.894503 | + | 0.447062i | \(0.147530\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.00000 | − | 12.1244i | 0.416107 | − | 0.720718i | −0.579437 | − | 0.815017i | \(-0.696728\pi\) |
0.995544 | + | 0.0942988i | \(0.0300609\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.0000 | + | 6.92820i | −0.710819 | + | 0.410391i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.50000 | − | 14.7224i | −0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.0000 | + | 13.8564i | 1.40690 | + | 0.812277i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.3923i | 0.607125i | 0.952812 | + | 0.303562i | \(0.0981761\pi\) | ||||
−0.952812 | + | 0.303562i | \(0.901824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.7846i | 1.21013i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.0000 | + | 6.92820i | 0.696311 | + | 0.402015i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.00000 | + | 10.3923i | 0.346989 | + | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.0000 | + | 10.3923i | −1.03407 | + | 0.597022i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.00000 | + | 10.3923i | −0.343559 | + | 0.595062i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.0000 | 1.25561 | 0.627803 | − | 0.778372i | \(-0.283954\pi\) | ||||
0.627803 | + | 0.778372i | \(0.283954\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.00000 | + | 10.3923i | −0.340229 | + | 0.589294i | −0.984475 | − | 0.175525i | \(-0.943838\pi\) |
0.644246 | + | 0.764818i | \(0.277171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | − | 3.46410i | 0.339140 | − | 0.195803i | −0.320752 | − | 0.947163i | \(-0.603935\pi\) |
0.659892 | + | 0.751361i | \(0.270602\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.00000 | − | 5.19615i | −0.168497 | − | 0.291845i | 0.769395 | − | 0.638774i | \(-0.220558\pi\) |
−0.937892 | + | 0.346929i | \(0.887225\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.0000 | + | 10.3923i | 1.00781 | + | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 20.7846i | − | 1.16008i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.0000 | + | 12.1244i | 1.16487 | + | 0.672538i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.0000 | + | 24.2487i | 0.774202 | + | 1.34096i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.00000 | + | 1.73205i | −0.164895 | + | 0.0952021i | −0.580176 | − | 0.814491i | \(-0.697016\pi\) |
0.415282 | + | 0.909693i | \(0.363683\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.00000 | − | 1.73205i | 0.0547997 | − | 0.0949158i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.0000 | + | 31.1769i | −0.977626 | + | 1.69330i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.0000 | + | 13.8564i | −1.29967 | + | 0.750366i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.0000 | + | 20.7846i | 0.646058 | + | 1.11901i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.0000 | + | 8.66025i | 0.805242 | + | 0.464907i | 0.845301 | − | 0.534291i | \(-0.179421\pi\) |
−0.0400587 | + | 0.999197i | \(0.512754\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.46410i | 0.185429i | 0.995693 | + | 0.0927146i | \(0.0295544\pi\) | ||||
−0.995693 | + | 0.0927146i | \(0.970446\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.8564i | 0.739600i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.0000 | + | 13.8564i | 1.27739 | + | 0.737502i | 0.976368 | − | 0.216115i | \(-0.0693385\pi\) |
0.301023 | + | 0.953617i | \(0.402672\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | + | 10.3923i | 0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.0000 | − | 15.5885i | 1.42501 | − | 0.822727i | 0.428285 | − | 0.903644i | \(-0.359118\pi\) |
0.996721 | + | 0.0809166i | \(0.0257847\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.00000 | 0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.0000 | 1.25622 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00000 | − | 6.92820i | 0.208798 | − | 0.361649i | −0.742538 | − | 0.669804i | \(-0.766378\pi\) |
0.951336 | + | 0.308155i | \(0.0997115\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.00000 | + | 3.46410i | −0.312348 | + | 0.180334i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.00000 | − | 12.1244i | −0.362446 | − | 0.627775i | 0.625917 | − | 0.779890i | \(-0.284725\pi\) |
−0.988363 | + | 0.152115i | \(0.951392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0000 | + | 6.92820i | 0.619677 | + | 0.357771i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.7846i | 1.07046i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.2487i | 1.24557i | 0.782392 | + | 0.622786i | \(0.213999\pi\) | ||||
−0.782392 | + | 0.622786i | \(0.786001\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.0000 | − | 10.3923i | −0.922168 | − | 0.532414i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0000 | + | 20.7846i | 0.613171 | + | 1.06204i | 0.990702 | + | 0.136047i | \(0.0434398\pi\) |
−0.377531 | + | 0.925997i | \(0.623227\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.00000 | − | 5.19615i | 0.457496 | − | 0.264135i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.00000 | − | 15.5885i | 0.456318 | − | 0.790366i | −0.542445 | − | 0.840091i | \(-0.682501\pi\) |
0.998763 | + | 0.0497253i | \(0.0158346\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 36.0000 | 1.81596 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.00000 | − | 10.3923i | 0.301893 | − | 0.522894i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.00000 | + | 5.19615i | −0.451697 | + | 0.260787i | −0.708547 | − | 0.705664i | \(-0.750649\pi\) |
0.256850 | + | 0.966451i | \(0.417315\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0000 | − | 25.9808i | −0.749064 | − | 1.29742i | −0.948272 | − | 0.317460i | \(-0.897170\pi\) |
0.199207 | − | 0.979957i | \(-0.436163\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.0000 | − | 13.8564i | −1.19553 | − | 0.690237i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 38.1051i | 1.89346i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.92820i | 0.343418i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.00000 | − | 3.46410i | −0.296681 | − | 0.171289i | 0.344270 | − | 0.938871i | \(-0.388126\pi\) |
−0.640951 | + | 0.767582i | \(0.721460\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | − | 10.3923i | −0.295958 | − | 0.512615i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.0000 | + | 10.3923i | −0.883585 | + | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.00000 | − | 3.46410i | 0.0979404 | − | 0.169638i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.0000 | 1.46560 | 0.732798 | − | 0.680446i | \(-0.238214\pi\) | ||||
0.732798 | + | 0.680446i | \(0.238214\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.0000 | −1.26716 | −0.633581 | − | 0.773676i | \(-0.718416\pi\) | ||||
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.0000 | + | 20.7846i | 0.579365 | + | 1.00349i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.0000 | + | 19.0526i | 1.58955 | + | 0.917729i | 0.993380 | + | 0.114874i | \(0.0366465\pi\) |
0.596174 | + | 0.802855i | \(0.296687\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 41.5692i | 1.99309i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.00000 | + | 3.46410i | 0.287019 | + | 0.165710i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.0000 | − | 24.2487i | −0.668184 | − | 1.15733i | −0.978412 | − | 0.206666i | \(-0.933739\pi\) |
0.310228 | − | 0.950662i | \(-0.399595\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.00000 | + | 1.73205i | −0.142534 | + | 0.0822922i | −0.569571 | − | 0.821942i | \(-0.692891\pi\) |
0.427037 | + | 0.904234i | \(0.359557\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | − | 20.7846i | 0.568855 | − | 0.985285i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.0000 | −0.567581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | − | 20.7846i | 0.565058 | − | 0.978709i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.00000 | + | 3.46410i | −0.281905 | + | 0.162758i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.0000 | + | 29.4449i | 0.795226 | + | 1.37737i | 0.922695 | + | 0.385530i | \(0.125981\pi\) |
−0.127469 | + | 0.991843i | \(0.540685\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 38.1051i | − | 1.77473i | −0.461065 | − | 0.887366i | \(-0.652533\pi\) | ||
0.461065 | − | 0.887366i | \(-0.347467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.2487i | 1.12693i | 0.826139 | + | 0.563467i | \(0.190533\pi\) | ||||
−0.826139 | + | 0.563467i | \(0.809467\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −48.0000 | − | 27.7128i | −2.22595 | − | 1.28515i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.0000 | − | 25.9808i | −0.694117 | − | 1.20225i | −0.970477 | − | 0.241192i | \(-0.922462\pi\) |
0.276360 | − | 0.961054i | \(-0.410872\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.0000 | − | 10.3923i | 0.829396 | − | 0.478852i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.0000 | + | 31.1769i | −0.827641 | + | 1.43352i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.0000 | 0.642364 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.0000 | − | 20.7846i | 0.548294 | − | 0.949673i | −0.450098 | − | 0.892979i | \(-0.648611\pi\) |
0.998392 | − | 0.0566937i | \(-0.0180558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | + | 3.46410i | −0.273576 | + | 0.157949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −24.0000 | − | 41.5692i | −1.08978 | − | 1.88756i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.0000 | + | 12.1244i | 0.951601 | + | 0.549407i | 0.893578 | − | 0.448908i | \(-0.148187\pi\) |
0.0580230 | + | 0.998315i | \(0.481520\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 34.6410i | 1.56652i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 17.3205i | − | 0.781664i | −0.920462 | − | 0.390832i | \(-0.872187\pi\) | ||
0.920462 | − | 0.390832i | \(-0.127813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.00000 | + | 10.3923i | 0.269680 | + | 0.467099i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.00000 | − | 5.19615i | 0.402895 | − | 0.232612i | −0.284837 | − | 0.958576i | \(-0.591940\pi\) |
0.687733 | + | 0.725964i | \(0.258606\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0000 | − | 20.7846i | 0.536120 | − | 0.928588i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.0000 | −1.60516 | −0.802580 | − | 0.596544i | \(-0.796540\pi\) | ||||
−0.802580 | + | 0.596544i | \(0.796540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0000 | 1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | − | 1.73205i | 0.0444116 | − | 0.0769231i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.0000 | − | 15.5885i | 1.19675 | − | 0.690946i | 0.236924 | − | 0.971528i | \(-0.423861\pi\) |
0.959830 | + | 0.280582i | \(0.0905275\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.00000 | + | 6.92820i | 0.176604 | + | 0.305888i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.0000 | − | 6.92820i | −0.528783 | − | 0.305293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 6.92820i | − | 0.304114i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.0000 | + | 17.3205i | 1.31432 | + | 0.758825i | 0.982809 | − | 0.184625i | \(-0.0591070\pi\) |
0.331515 | + | 0.943450i | \(0.392440\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.00000 | − | 1.73205i | −0.0437269 | − | 0.0757373i | 0.843334 | − | 0.537390i | \(-0.180590\pi\) |
−0.887061 | + | 0.461653i | \(0.847256\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.50000 | + | 9.52628i | −0.239130 | + | 0.414186i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.0000 | 1.03956 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0000 | + | 31.1769i | −0.778208 | + | 1.34790i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.0000 | + | 10.3923i | −0.776757 | + | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.00000 | + | 1.73205i | 0.0429934 | + | 0.0744667i | 0.886721 | − | 0.462304i | \(-0.152977\pi\) |
−0.843728 | + | 0.536771i | \(0.819644\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −30.0000 | − | 17.3205i | −1.28742 | − | 0.743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 48.4974i | − | 2.07740i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 17.3205i | − | 0.740571i | −0.928918 | − | 0.370286i | \(-0.879260\pi\) | ||
0.928918 | − | 0.370286i | \(-0.120740\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.00000 | − | 1.73205i | −0.128037 | − | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | + | 10.3923i | 0.255609 | + | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.0000 | + | 6.92820i | −0.509372 | + | 0.294086i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.00000 | − | 15.5885i | 0.381342 | − | 0.660504i | −0.609912 | − | 0.792469i | \(-0.708795\pi\) |
0.991254 | + | 0.131965i | \(0.0421286\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.0000 | −1.52264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.00000 | − | 15.5885i | 0.379305 | − | 0.656975i | −0.611656 | − | 0.791123i | \(-0.709497\pi\) |
0.990961 | + | 0.134148i | \(0.0428299\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 54.0000 | − | 31.1769i | 2.27180 | − | 1.31162i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.00000 | + | 15.5885i | 0.377300 | + | 0.653502i | 0.990668 | − | 0.136295i | \(-0.0435194\pi\) |
−0.613369 | + | 0.789797i | \(0.710186\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.0000 | + | 22.5167i | 1.63210 | + | 0.942293i | 0.983444 | + | 0.181210i | \(0.0580014\pi\) |
0.648655 | + | 0.761083i | \(0.275332\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 48.4974i | − | 2.02601i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 24.2487i | − | 1.01124i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.0000 | + | 13.8564i | 0.999133 | + | 0.576850i | 0.907992 | − | 0.418988i | \(-0.137615\pi\) |
0.0911414 | + | 0.995838i | \(0.470948\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.00000 | − | 3.46410i | −0.0831172 | − | 0.143963i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0000 | + | 10.3923i | −0.745484 | + | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.00000 | + | 10.3923i | −0.248069 | + | 0.429669i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.0000 | 0.742940 | 0.371470 | − | 0.928445i | \(-0.378854\pi\) | ||||
0.371470 | + | 0.928445i | \(0.378854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | −0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.0000 | + | 31.1769i | −0.740421 | + | 1.28245i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.0000 | + | 6.92820i | −0.492781 | + | 0.284507i | −0.725727 | − | 0.687982i | \(-0.758497\pi\) |
0.232946 | + | 0.972490i | \(0.425163\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.0000 | − | 34.6410i | −0.818546 | − | 1.41776i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.0000 | − | 12.1244i | −0.858037 | − | 0.495388i | 0.00531761 | − | 0.999986i | \(-0.498307\pi\) |
−0.863354 | + | 0.504598i | \(0.831641\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.7846i | 0.847822i | 0.905704 | + | 0.423911i | \(0.139343\pi\) | ||||
−0.905704 | + | 0.423911i | \(0.860657\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 3.46410i | − | 0.141069i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.00000 | − | 1.73205i | −0.121967 | − | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.00000 | − | 13.8564i | −0.324710 | − | 0.562414i | 0.656744 | − | 0.754114i | \(-0.271933\pi\) |
−0.981454 | + | 0.191700i | \(0.938600\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0000 | + | 32.9090i | −0.767403 | + | 1.32918i | 0.171564 | + | 0.985173i | \(0.445118\pi\) |
−0.938967 | + | 0.344008i | \(0.888215\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 48.0000 | 1.93555 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.0000 | −0.724653 | −0.362326 | − | 0.932051i | \(-0.618017\pi\) | ||||
−0.362326 | + | 0.932051i | \(0.618017\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.0000 | + | 22.5167i | −0.522514 | + | 0.905021i | 0.477143 | + | 0.878826i | \(0.341672\pi\) |
−0.999657 | + | 0.0261952i | \(0.991661\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.0000 | − | 6.92820i | 0.481543 | − | 0.278019i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.0000 | + | 6.92820i | 0.479234 | + | 0.276686i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 3.46410i | − | 0.137904i | −0.997620 | − | 0.0689519i | \(-0.978035\pi\) | ||
0.997620 | − | 0.0689519i | \(-0.0219655\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.00000 | − | 3.46410i | −0.238479 | − | 0.137686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.0000 | + | 31.1769i | 0.714308 | + | 1.23722i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.00000 | + | 1.73205i | −0.118678 | + | 0.0685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.0000 | + | 25.9808i | −0.592464 | + | 1.02618i | 0.401435 | + | 0.915888i | \(0.368512\pi\) |
−0.993899 | + | 0.110291i | \(0.964822\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.0000 | −1.02534 | −0.512670 | − | 0.858586i | \(-0.671344\pi\) | ||||
−0.512670 | + | 0.858586i | \(0.671344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −72.0000 | −2.83500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.00000 | + | 10.3923i | −0.235884 | + | 0.408564i | −0.959529 | − | 0.281609i | \(-0.909132\pi\) |
0.723645 | + | 0.690172i | \(0.242465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.0000 | − | 10.3923i | 0.706562 | − | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.00000 | + | 15.5885i | 0.352197 | + | 0.610023i | 0.986634 | − | 0.162951i | \(-0.0521013\pi\) |
−0.634437 | + | 0.772975i | \(0.718768\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −54.0000 | − | 31.1769i | −2.10995 | − | 1.21818i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.92820i | 0.270295i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 3.46410i | − | 0.134942i | −0.997721 | − | 0.0674711i | \(-0.978507\pi\) | ||
0.997721 | − | 0.0674711i | \(-0.0214931\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.00000 | + | 1.73205i | 0.116686 | + | 0.0673690i | 0.557207 | − | 0.830373i | \(-0.311873\pi\) |
−0.440521 | + | 0.897742i | \(0.645206\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.0000 | − | 10.3923i | 0.696963 | − | 0.402392i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.0000 | − | 27.7128i | 0.618596 | − | 1.07144i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.0000 | −0.539660 | −0.269830 | − | 0.962908i | \(-0.586968\pi\) | ||||
−0.269830 | + | 0.962908i | \(0.586968\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.0000 | − | 24.2487i | 0.538860 | − | 0.933333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.00000 | + | 1.73205i | −0.115299 | + | 0.0665681i | −0.556541 | − | 0.830820i | \(-0.687872\pi\) |
0.441241 | + | 0.897389i | \(0.354538\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | + | 10.3923i | 0.229920 | + | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.0000 | − | 19.0526i | −1.26271 | − | 0.729026i | −0.289112 | − | 0.957295i | \(-0.593360\pi\) |
−0.973598 | + | 0.228269i | \(0.926693\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.7846i | 0.794139i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 20.7846i | − | 0.792982i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.0000 | − | 10.3923i | −0.685745 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.00000 | + | 8.66025i | 0.190209 | + | 0.329452i | 0.945319 | − | 0.326146i | \(-0.105750\pi\) |
−0.755110 | + | 0.655598i | \(0.772417\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.00000 | + | 3.46410i | −0.227593 | + | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.0000 | 0.453882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.00000 | + | 3.46410i | −0.0754314 | + | 0.130651i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | + | 8.66025i | 0.187779 | + | 0.325243i | 0.944509 | − | 0.328484i | \(-0.106538\pi\) |
−0.756730 | + | 0.653727i | \(0.773204\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.00000 | + | 1.73205i | 0.112509 | + | 0.0649570i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.7128i | 1.03785i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 41.5692i | − | 1.55460i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.0000 | − | 10.3923i | −0.672222 | − | 0.388108i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0000 | − | 41.5692i | −0.895049 | − | 1.55027i | −0.833744 | − | 0.552151i | \(-0.813807\pi\) |
−0.0613050 | − | 0.998119i | \(-0.519526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −48.0000 | + | 27.7128i | −1.78514 | + | 1.03065i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.0000 | − | 36.3731i | 0.779920 | − | 1.35086i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.0000 | −1.03846 | −0.519231 | − | 0.854634i | \(-0.673782\pi\) | ||||
−0.519231 | + | 0.854634i | \(0.673782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.0000 | + | 25.9808i | −1.66211 | + | 0.959621i | −0.690409 | + | 0.723419i | \(0.742569\pi\) |
−0.971704 | + | 0.236202i | \(0.924097\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.00000 | + | 10.3923i | 0.221013 | + | 0.382805i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.00000 | − | 5.19615i | −0.331070 | − | 0.191144i | 0.325246 | − | 0.945629i | \(-0.394553\pi\) |
−0.656316 | + | 0.754486i | \(0.727886\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.8564i | 0.509028i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 24.2487i | − | 0.889599i | −0.895630 | − | 0.444799i | \(-0.853275\pi\) | ||
0.895630 | − | 0.444799i | \(-0.146725\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.0000 | + | 10.3923i | 0.659469 | + | 0.380745i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.00000 | − | 5.19615i | −0.109764 | − | 0.190117i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.0000 | − | 22.5167i | 1.42313 | − | 0.821645i | 0.426565 | − | 0.904457i | \(-0.359724\pi\) |
0.996565 | + | 0.0828123i | \(0.0263902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −30.0000 | + | 51.9615i | −1.09326 | + | 1.89358i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | 0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.0000 | − | 20.7846i | 0.435572 | − | 0.754434i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0000 | + | 10.3923i | −0.652499 | + | 0.376721i | −0.789413 | − | 0.613862i | \(-0.789615\pi\) |
0.136914 | + | 0.990583i | \(0.456282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.0000 | + | 10.3923i | 0.649942 | + | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.8564i | 0.499675i | 0.968288 | + | 0.249837i | \(0.0803772\pi\) | ||||
−0.968288 | + | 0.249837i | \(0.919623\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 55.4256i | − | 1.99611i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.00000 | + | 1.73205i | 0.107903 | + | 0.0622975i | 0.552980 | − | 0.833194i | \(-0.313491\pi\) |
−0.445078 | + | 0.895492i | \(0.646824\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.0000 | + | 48.4974i | 1.00579 | + | 1.74208i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.0000 | − | 6.92820i | 0.429945 | − | 0.248229i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | − | 10.3923i | 0.214697 | − | 0.371866i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.0000 | 0.857690 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.0000 | −1.28490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.0000 | − | 29.4449i | 0.605985 | − | 1.04960i | −0.385911 | − | 0.922536i | \(-0.626113\pi\) |
0.991895 | − | 0.127060i | \(-0.0405540\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −42.0000 | + | 24.2487i | −1.49524 | + | 0.863277i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00000 | + | 10.3923i | 0.213066 | + | 0.369042i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −36.0000 | − | 20.7846i | −1.27679 | − | 0.737154i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.3205i | 0.613524i | 0.951786 | + | 0.306762i | \(0.0992455\pi\) | ||||
−0.951786 | + | 0.306762i | \(0.900754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | + | 3.46410i | 0.212000 | + | 0.122398i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.0000 | − | 20.7846i | −0.423471 | − | 0.733473i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.00000 | + | 3.46410i | −0.211210 | + | 0.121942i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.0000 | + | 25.9808i | −0.527372 | + | 0.913435i | 0.472119 | + | 0.881535i | \(0.343489\pi\) |
−0.999491 | + | 0.0319002i | \(0.989844\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.0000 | −0.772524 | −0.386262 | − | 0.922389i | \(-0.626234\pi\) | ||||
−0.386262 | + | 0.922389i | \(0.626234\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 30.0000 | − | 51.9615i | 1.05085 | − | 1.82013i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.0000 | + | 10.3923i | −0.629740 | + | 0.363581i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0000 | − | 25.9808i | −0.523504 | − | 0.906735i | −0.999626 | − | 0.0273557i | \(-0.991291\pi\) |
0.476122 | − | 0.879379i | \(-0.342042\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.00000 | + | 1.73205i | 0.104573 | + | 0.0603755i | 0.551375 | − | 0.834258i | \(-0.314104\pi\) |
−0.446801 | + | 0.894633i | \(0.647437\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 48.4974i | − | 1.68846i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.2487i | 0.843210i | 0.906780 | + | 0.421605i | \(0.138533\pi\) | ||||
−0.906780 | + | 0.421605i | \(0.861467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.00000 | − | 1.73205i | −0.104194 | − | 0.0601566i | 0.446997 | − | 0.894535i | \(-0.352493\pi\) |
−0.551192 | + | 0.834379i | \(0.685827\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.00000 | − | 3.46410i | −0.0693792 | − | 0.120168i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −36.0000 | + | 20.7846i | −1.24583 | + | 0.719281i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.0000 | + | 27.7128i | −0.553041 | + | 0.957895i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.0000 | 0.414286 | 0.207143 | − | 0.978311i | \(-0.433583\pi\) | ||||
0.207143 | + | 0.978311i | \(0.433583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.00000 | + | 10.3923i | −0.206651 | + | 0.357930i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.00000 | + | 1.73205i | −0.103203 | + | 0.0595844i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.0000 | − | 24.2487i | −0.480479 | − | 0.832214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.00000 | + | 3.46410i | 0.205677 | + | 0.118748i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.46410i | − | 0.118609i | −0.998240 | − | 0.0593043i | \(-0.981112\pi\) | ||
0.998240 | − | 0.0593043i | \(-0.0188882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.92820i | 0.236940i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.0000 | − | 17.3205i | −1.02478 | − | 0.591657i | −0.109295 | − | 0.994009i | \(-0.534859\pi\) |
−0.915485 | + | 0.402352i | \(0.868193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.00000 | + | 12.1244i | 0.238837 | + | 0.413678i | 0.960381 | − | 0.278691i | \(-0.0899005\pi\) |
−0.721544 | + | 0.692369i | \(0.756567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.0000 | + | 15.5885i | −0.919091 | + | 0.530637i | −0.883345 | − | 0.468724i | \(-0.844714\pi\) |
−0.0357458 | + | 0.999361i | \(0.511381\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | + | 10.3923i | −0.204006 | + | 0.353349i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −34.0000 | −1.15470 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0000 | −0.407072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.00000 | + | 10.3923i | −0.203302 | + | 0.352130i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.0000 | − | 6.92820i | 0.406138 | − | 0.234484i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.0000 | − | 32.9090i | −0.641584 | − | 1.11126i | −0.985079 | − | 0.172102i | \(-0.944944\pi\) |
0.343495 | − | 0.939155i | \(-0.388389\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.0000 | + | 10.3923i | 0.607125 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.8564i | 0.466834i | 0.972377 | + | 0.233417i | \(0.0749907\pi\) | ||||
−0.972377 | + | 0.233417i | \(0.925009\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 3.46410i | − | 0.116576i | −0.998300 | − | 0.0582882i | \(-0.981436\pi\) | ||
0.998300 | − | 0.0582882i | \(-0.0185642\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.0000 | + | 20.7846i | 1.21013 | + | 0.698667i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.00000 | + | 10.3923i | 0.201460 | + | 0.348939i | 0.948999 | − | 0.315279i | \(-0.102098\pi\) |
−0.747539 | + | 0.664218i | \(0.768765\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.0000 | − | 19.0526i | 1.10554 | − | 0.638285i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.0000 | 1.20335 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.0000 | 0.801337 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.0000 | + | 41.5692i | −0.800445 | + | 1.38641i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.0000 | + | 51.9615i | 0.997234 | + | 1.72726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.0000 | − | 12.1244i | −0.697294 | − | 0.402583i | 0.109045 | − | 0.994037i | \(-0.465221\pi\) |
−0.806339 | + | 0.591454i | \(0.798554\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.3923i | 0.344691i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 10.3923i | − | 0.344312i | −0.985070 | − | 0.172156i | \(-0.944927\pi\) | ||
0.985070 | − | 0.172156i | \(-0.0550734\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | + | 10.3923i | 0.595713 | + | 0.343935i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.0000 | + | 20.7846i | 0.396708 | + | 0.687118i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.0000 | + | 15.5885i | −0.890648 | + | 0.514216i | −0.874154 | − | 0.485648i | \(-0.838584\pi\) |
−0.0164935 | + | 0.999864i | \(0.505250\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.0000 | − | 38.1051i | 0.724925 | − | 1.25561i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0000 | 0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000 | 0.460317 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.00000 | − | 3.46410i | 0.0656886 | − | 0.113776i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.0000 | − | 20.7846i | 1.18112 | − | 0.681921i | 0.224848 | − | 0.974394i | \(-0.427811\pi\) |
0.956274 | + | 0.292473i | \(0.0944781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.0000 | + | 20.7846i | 0.392862 | + | 0.680458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 48.4974i | − | 1.58434i | −0.610299 | − | 0.792171i | \(-0.708951\pi\) | ||
0.610299 | − | 0.792171i | \(-0.291049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 13.8564i | − | 0.452187i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.0000 | + | 12.1244i | 0.684580 | + | 0.395243i | 0.801579 | − | 0.597889i | \(-0.203994\pi\) |
−0.116998 | + | 0.993132i | \(0.537327\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.0000 | − | 20.7846i | −0.390774 | − | 0.676840i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.0000 | − | 12.1244i | 0.682408 | − | 0.393989i | −0.118354 | − | 0.992972i | \(-0.537762\pi\) |
0.800762 | + | 0.598983i | \(0.204428\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0000 | − | 20.7846i | 0.389536 | − | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.0000 | −0.389127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.00000 | −0.194359 | −0.0971795 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971795 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.0000 | + | 72.7461i | −1.35909 | + | 2.35401i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 36.0000 | − | 20.7846i | 1.16371 | − | 0.671871i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.00000 | − | 5.19615i | −0.290021 | − | 0.167444i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.92820i | 0.223027i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 24.2487i | − | 0.779786i | −0.920860 | − | 0.389893i | \(-0.872512\pi\) | ||
0.920860 | − | 0.389893i | \(-0.127488\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.00000 | − | 15.5885i | −0.288824 | − | 0.500257i | 0.684706 | − | 0.728820i | \(-0.259931\pi\) |
−0.973529 | + | 0.228562i | \(0.926597\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 42.0000 | − | 24.2487i | 1.34508 | − | 0.776580i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.0000 | − | 25.9808i | 0.479893 | − | 0.831198i | −0.519841 | − | 0.854263i | \(-0.674009\pi\) |
0.999734 | + | 0.0230645i | \(0.00734232\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.0000 | −0.767043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.0000 | + | 31.1769i | −0.574111 | + | 0.994389i | 0.422027 | + | 0.906583i | \(0.361319\pi\) |
−0.996138 | + | 0.0878058i | \(0.972015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 54.0000 | − | 31.1769i | 1.72058 | − | 0.993379i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.0000 | + | 31.1769i | 0.572367 | + | 0.991368i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.00000 | + | 1.73205i | 0.0952981 | + | 0.0550204i | 0.546892 | − | 0.837203i | \(-0.315811\pi\) |
−0.451594 | + | 0.892224i | \(0.649144\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.92820i | 0.219860i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 69.2820i | 2.19639i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.0000 | − | 25.9808i | −1.42516 | − | 0.822819i | −0.428430 | − | 0.903575i | \(-0.640933\pi\) |
−0.996734 | + | 0.0807558i | \(0.974267\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.00000 | + | 6.92820i | 0.126554 | + | 0.219199i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))