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 | 607.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.607 |
Dual form | 784.2.p.e.31.1 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | 0.995782 | + | 0.0917517i | \(0.0292466\pi\) |
−0.418432 | + | 0.908248i | \(0.637420\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.00000 | − | 1.73205i | −1.34164 | − | 0.774597i | −0.354593 | − | 0.935021i | \(-0.615380\pi\) |
−0.987048 | + | 0.160424i | \(0.948714\pi\) | |||||||
\(6\) | 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 | 0.0258656 | − | 0.999665i | \(-0.491766\pi\) |
0.878668 | + | 0.477432i | \(0.158432\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.46410i | − | 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 6.92820i | − | 1.78885i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | − | 1.73205i | 0.229416 | − | 0.397360i | −0.728219 | − | 0.685344i | \(-0.759652\pi\) |
0.957635 | + | 0.287984i | \(0.0929851\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | + | 1.73205i | 0.625543 | + | 0.361158i | 0.779024 | − | 0.626994i | \(-0.215715\pi\) |
−0.153481 | + | 0.988152i | \(0.549048\pi\) | |||||||
\(24\) | 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 | −0.961625 | − | 0.274367i | \(-0.911532\pi\) |
0.243204 | − | 0.969975i | \(-0.421802\pi\) | |||||||
\(32\) | 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 | −0.772043 | − | 0.635571i | \(-0.780765\pi\) |
0.936442 | + | 0.350823i | \(0.114098\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.00000 | − | 3.46410i | 0.960769 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.92820i | 1.08200i | 0.841021 | + | 0.541002i | \(0.181955\pi\) | ||||
−0.841021 | + | 0.541002i | \(0.818045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.3923i | − | 1.58481i | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||
0.609994 | − | 0.792406i | \(-0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | − | 1.73205i | 0.447214 | − | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.00000 | − | 5.19615i | −0.412082 | − | 0.713746i | 0.583036 | − | 0.812447i | \(-0.301865\pi\) |
−0.995117 | + | 0.0987002i | \(0.968532\pi\) | |||||||
\(54\) | 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 | 0.992524 | − | 0.122047i | \(-0.0389457\pi\) |
−0.601958 | + | 0.798528i | \(0.705612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | + | 1.73205i | 0.384111 | + | 0.221766i | 0.679605 | − | 0.733578i | \(-0.262151\pi\) |
−0.295495 | + | 0.955344i | \(0.595484\pi\) | |||||||
\(62\) | 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 | −0.305424 | − | 0.952217i | \(-0.598798\pi\) |
0.671932 | + | 0.740613i | \(0.265465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.92820i | 0.834058i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.46410i | 0.411113i | 0.978645 | + | 0.205557i | \(0.0659005\pi\) | ||||
−0.978645 | + | 0.205557i | \(0.934100\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | + | 3.46410i | −0.702247 | + | 0.405442i | −0.808184 | − | 0.588930i | \(-0.799549\pi\) |
0.105937 | + | 0.994373i | \(0.466216\pi\) | |||||||
\(74\) | 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 | 0.321651 | − | 0.946858i | \(-0.395762\pi\) |
−0.659178 | + | 0.751987i | \(0.729095\pi\) | |||||||
\(80\) | 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 | 0.147073 | − | 0.989126i | \(-0.453015\pi\) |
−0.783072 | + | 0.621932i | \(0.786348\pi\) | |||||||
\(90\) | 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 | \(-0.751641\pi\) | ||
0.710742 | − | 0.703452i | \(-0.248359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.46410i | 0.348155i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.00000 | + | 5.19615i | −0.895533 | + | 0.517036i | −0.875748 | − | 0.482768i | \(-0.839632\pi\) |
−0.0197851 | + | 0.999804i | \(0.506298\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | − | 3.46410i | 0.197066 | − | 0.341328i | −0.750510 | − | 0.660859i | \(-0.770192\pi\) |
0.947576 | + | 0.319531i | \(0.103525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.00000 | + | 5.19615i | 0.870063 | + | 0.502331i | 0.867369 | − | 0.497665i | \(-0.165809\pi\) |
0.00269372 | + | 0.999996i | \(0.499143\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | − | 12.1244i | −0.670478 | − | 1.16130i | −0.977769 | − | 0.209687i | \(-0.932756\pi\) |
0.307290 | − | 0.951616i | \(-0.400578\pi\) | |||||||
\(110\) | 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 | \(0.152539\pi\) | ||||
−0.887357 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18.0000 | − | 10.3923i | 1.58481 | − | 0.914991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.00000 | − | 15.5885i | 0.786334 | − | 1.36197i | −0.141865 | − | 0.989886i | \(-0.545310\pi\) |
0.928199 | − | 0.372084i | \(-0.121357\pi\) | |||||||
\(132\) | 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 | 0.965250 | − | 0.261329i | \(-0.0841608\pi\) |
−0.708942 | + | 0.705266i | \(0.750827\pi\) | |||||||
\(138\) | 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 | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.00000 | + | 1.73205i | −0.244137 | + | 0.140952i | −0.617076 | − | 0.786903i | \(-0.711683\pi\) |
0.372940 | + | 0.927855i | \(0.378350\pi\) | |||||||
\(152\) | 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 | −0.0958404 | − | 0.995397i | \(-0.530554\pi\) |
0.814119 | + | 0.580699i | \(0.197221\pi\) | |||||||
\(158\) | 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 | −0.220064 | − | 0.975486i | \(-0.570626\pi\) |
−0.954827 | + | 0.297162i | \(0.903960\pi\) | |||||||
\(164\) | 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 | 0.609689 | − | 0.792641i | \(-0.291294\pi\) |
−0.381603 | + | 0.924326i | \(0.624628\pi\) | |||||||
\(174\) | 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 | −0.797096 | − | 0.603853i | \(-0.793631\pi\) |
0.124404 | + | 0.992232i | \(0.460298\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3205i | 1.28742i | 0.765268 | + | 0.643712i | \(0.222606\pi\) | ||||
−0.765268 | + | 0.643712i | \(0.777394\pi\) | |||||||
\(182\) | 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 | 0.999736 | + | 0.0229818i | \(0.00731599\pi\) |
0.519771 | + | 0.854306i | \(0.326017\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.00000 | + | 1.73205i | 0.0719816 | + | 0.124676i | 0.899770 | − | 0.436365i | \(-0.143734\pi\) |
−0.827788 | + | 0.561041i | \(0.810401\pi\) | |||||||
\(194\) | 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 | 0.965272 | + | 0.261245i | \(0.0841331\pi\) |
−0.256391 | + | 0.966573i | \(0.582534\pi\) | |||||||
\(200\) | 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 | \(0.0380456\pi\) | ||||
−0.992866 | + | 0.119239i | \(0.961954\pi\) | |||||||
\(212\) | 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 | 0.749125 | − | 0.662428i | \(-0.230474\pi\) |
−0.948242 | + | 0.317547i | \(0.897141\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.00000 | + | 5.19615i | 0.594737 | + | 0.343371i | 0.766968 | − | 0.641685i | \(-0.221764\pi\) |
−0.172231 | + | 0.985057i | \(0.555098\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.00000 | − | 5.19615i | 0.196537 | − | 0.340411i | −0.750867 | − | 0.660454i | \(-0.770364\pi\) |
0.947403 | + | 0.320043i | \(0.103697\pi\) | |||||||
\(234\) | 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 | \(0.109112\pi\) | ||||
−0.941822 | + | 0.336111i | \(0.890888\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.0000 | + | 13.8564i | −1.54598 | + | 0.892570i | −0.547533 | + | 0.836784i | \(0.684433\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 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 | 0.999994 | − | 0.00336324i | \(-0.00107055\pi\) |
0.497085 | + | 0.867702i | \(0.334404\pi\) | |||||||
\(258\) | 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 | −0.979521 | − | 0.201341i | \(-0.935470\pi\) |
−0.315394 | + | 0.948961i | \(0.602137\pi\) | |||||||
\(264\) | 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 | −0.588661 | − | 0.808380i | \(-0.700345\pi\) |
0.405747 | + | 0.913985i | \(0.367011\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | + | 6.92820i | −0.242983 | + | 0.420858i | −0.961563 | − | 0.274586i | \(-0.911459\pi\) |
0.718580 | + | 0.695444i | \(0.244792\pi\) | |||||||
\(272\) | 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 | 0.894503 | − | 0.447062i | \(-0.147530\pi\) |
−0.834419 | + | 0.551131i | \(0.814196\pi\) | |||||||
\(278\) | 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 | 0.995544 | − | 0.0942988i | \(-0.0300609\pi\) |
−0.579437 | + | 0.815017i | \(0.696728\pi\) | |||||||
\(284\) | 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 | \(-0.901824\pi\) | ||
0.952812 | − | 0.303562i | \(-0.0981761\pi\) | |||||||
\(294\) | 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 | 0.644246 | − | 0.764818i | \(-0.277171\pi\) |
−0.984475 | + | 0.175525i | \(0.943838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | + | 3.46410i | 0.339140 | + | 0.195803i | 0.659892 | − | 0.751361i | \(-0.270602\pi\) |
−0.320752 | + | 0.947163i | \(0.603935\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.00000 | + | 5.19615i | −0.168497 | + | 0.291845i | −0.937892 | − | 0.346929i | \(-0.887225\pi\) |
0.769395 | + | 0.638774i | \(0.220558\pi\) | |||||||
\(318\) | 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 | 0.415282 | − | 0.909693i | \(-0.363683\pi\) |
−0.580176 | + | 0.814491i | \(0.697016\pi\) | |||||||
\(332\) | 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 | −0.0400587 | − | 0.999197i | \(-0.512754\pi\) |
0.845301 | + | 0.534291i | \(0.179421\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.46410i | − | 0.185429i | −0.995693 | − | 0.0927146i | \(-0.970446\pi\) | ||
0.995693 | − | 0.0927146i | \(-0.0295544\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 13.8564i | − | 0.739600i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.0000 | − | 13.8564i | 1.27739 | − | 0.737502i | 0.301023 | − | 0.953617i | \(-0.402672\pi\) |
0.976368 | + | 0.216115i | \(0.0693385\pi\) | |||||||
\(354\) | 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 | 0.996721 | − | 0.0809166i | \(-0.0257847\pi\) |
0.428285 | + | 0.903644i | \(0.359118\pi\) | |||||||
\(360\) | 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 | 0.951336 | − | 0.308155i | \(-0.0997115\pi\) |
−0.742538 | + | 0.669804i | \(0.766378\pi\) | |||||||
\(368\) | 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 | −0.988363 | − | 0.152115i | \(-0.951392\pi\) |
0.625917 | + | 0.779890i | \(0.284725\pi\) | |||||||
\(374\) | 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 | \(-0.786001\pi\) | ||
0.782392 | − | 0.622786i | \(-0.213999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.0000 | + | 10.3923i | −0.922168 | + | 0.532414i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0000 | − | 20.7846i | 0.613171 | − | 1.06204i | −0.377531 | − | 0.925997i | \(-0.623227\pi\) |
0.990702 | − | 0.136047i | \(-0.0434398\pi\) | |||||||
\(384\) | 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 | 0.998763 | − | 0.0497253i | \(-0.0158346\pi\) |
−0.542445 | + | 0.840091i | \(0.682501\pi\) | |||||||
\(390\) | 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 | 0.256850 | − | 0.966451i | \(-0.417315\pi\) |
−0.708547 | + | 0.705664i | \(0.750649\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0000 | + | 25.9808i | −0.749064 | + | 1.29742i | 0.199207 | + | 0.979957i | \(0.436163\pi\) |
−0.948272 | + | 0.317460i | \(0.897170\pi\) | |||||||
\(402\) | 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 | −0.640951 | − | 0.767582i | \(-0.721460\pi\) |
0.344270 | + | 0.938871i | \(0.388126\pi\) | |||||||
\(410\) | 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 | 0.596174 | − | 0.802855i | \(-0.296687\pi\) |
0.993380 | − | 0.114874i | \(-0.0366465\pi\) | |||||||
\(432\) | 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 | 0.310228 | + | 0.950662i | \(0.399595\pi\) |
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.00000 | − | 1.73205i | −0.142534 | − | 0.0822922i | 0.427037 | − | 0.904234i | \(-0.359557\pi\) |
−0.569571 | + | 0.821942i | \(0.692891\pi\) | |||||||
\(444\) | 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 | −0.127469 | − | 0.991843i | \(-0.540685\pi\) |
0.922695 | − | 0.385530i | \(-0.125981\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.1051i | 1.77473i | 0.461065 | + | 0.887366i | \(0.347467\pi\) | ||||
−0.461065 | + | 0.887366i | \(0.652533\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.2487i | − | 1.12693i | −0.826139 | − | 0.563467i | \(-0.809467\pi\) | ||
0.826139 | − | 0.563467i | \(-0.190533\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −48.0000 | + | 27.7128i | −2.22595 | + | 1.28515i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.0000 | + | 25.9808i | −0.694117 | + | 1.20225i | 0.276360 | + | 0.961054i | \(0.410872\pi\) |
−0.970477 | + | 0.241192i | \(0.922462\pi\) | |||||||
\(468\) | 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 | 0.998392 | + | 0.0566937i | \(0.0180558\pi\) |
−0.450098 | + | 0.892979i | \(0.648611\pi\) | |||||||
\(480\) | 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 | 0.0580230 | − | 0.998315i | \(-0.481520\pi\) |
0.893578 | + | 0.448908i | \(0.148187\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 34.6410i | − | 1.56652i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.3205i | 0.781664i | 0.920462 | + | 0.390832i | \(0.127813\pi\) | ||||
−0.920462 | + | 0.390832i | \(0.872187\pi\) | |||||||
\(492\) | 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 | 0.687733 | − | 0.725964i | \(-0.258606\pi\) |
−0.284837 | + | 0.958576i | \(0.591940\pi\) | |||||||
\(500\) | 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 | 0.959830 | − | 0.280582i | \(-0.0905275\pi\) |
0.236924 | + | 0.971528i | \(0.423861\pi\) | |||||||
\(510\) | 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 | 0.331515 | − | 0.943450i | \(-0.392440\pi\) |
0.982809 | + | 0.184625i | \(0.0591070\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.00000 | + | 1.73205i | −0.0437269 | + | 0.0757373i | −0.887061 | − | 0.461653i | \(-0.847256\pi\) |
0.843334 | + | 0.537390i | \(0.180590\pi\) | |||||||
\(524\) | 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 | −0.843728 | − | 0.536771i | \(-0.819644\pi\) |
0.886721 | + | 0.462304i | \(0.152977\pi\) | |||||||
\(542\) | 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 | \(0.120740\pi\) | ||||
−0.928918 | + | 0.370286i | \(0.879260\pi\) | |||||||
\(548\) | 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 | 0.991254 | − | 0.131965i | \(-0.0421286\pi\) |
−0.609912 | + | 0.792469i | \(0.708795\pi\) | |||||||
\(558\) | 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 | 0.990961 | − | 0.134148i | \(-0.0428299\pi\) |
−0.611656 | + | 0.791123i | \(0.709497\pi\) | |||||||
\(564\) | 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 | −0.613369 | − | 0.789797i | \(-0.710186\pi\) |
0.990668 | + | 0.136295i | \(0.0435194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.0000 | − | 22.5167i | 1.63210 | − | 0.942293i | 0.648655 | − | 0.761083i | \(-0.275332\pi\) |
0.983444 | − | 0.181210i | \(-0.0580014\pi\) | |||||||
\(572\) | 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 | 0.0911414 | − | 0.995838i | \(-0.470948\pi\) |
0.907992 | + | 0.418988i | \(0.137615\pi\) | |||||||
\(578\) | 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 | 0.232946 | − | 0.972490i | \(-0.425163\pi\) |
−0.725727 | + | 0.687982i | \(0.758497\pi\) | |||||||
\(594\) | 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 | −0.863354 | − | 0.504598i | \(-0.831641\pi\) |
0.00531761 | + | 0.999986i | \(0.498307\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20.7846i | − | 0.847822i | −0.905704 | − | 0.423911i | \(-0.860657\pi\) | ||
0.905704 | − | 0.423911i | \(-0.139343\pi\) | |||||||
\(602\) | 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 | −0.981454 | − | 0.191700i | \(-0.938600\pi\) |
0.656744 | + | 0.754114i | \(0.271933\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0000 | − | 32.9090i | −0.767403 | − | 1.32918i | −0.938967 | − | 0.344008i | \(-0.888215\pi\) |
0.171564 | − | 0.985173i | \(-0.445118\pi\) | |||||||
\(614\) | 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 | −0.999657 | − | 0.0261952i | \(-0.991661\pi\) |
0.477143 | − | 0.878826i | \(-0.341672\pi\) | |||||||
\(620\) | 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 | \(0.0219655\pi\) | ||||
−0.997620 | + | 0.0689519i | \(0.978035\pi\) | |||||||
\(632\) | 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 | −0.993899 | − | 0.110291i | \(-0.964822\pi\) |
0.401435 | − | 0.915888i | \(-0.368512\pi\) | |||||||
\(642\) | 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 | 0.723645 | − | 0.690172i | \(-0.242465\pi\) |
−0.959529 | + | 0.281609i | \(0.909132\pi\) | |||||||
\(648\) | 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 | −0.634437 | − | 0.772975i | \(-0.718768\pi\) |
0.986634 | + | 0.162951i | \(0.0521013\pi\) | |||||||
\(654\) | 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 | \(0.0214931\pi\) | ||||
−0.997721 | + | 0.0674711i | \(0.978507\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.00000 | − | 1.73205i | 0.116686 | − | 0.0673690i | −0.440521 | − | 0.897742i | \(-0.645206\pi\) |
0.557207 | + | 0.830373i | \(0.311873\pi\) | |||||||
\(662\) | 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 | 0.441241 | − | 0.897389i | \(-0.354538\pi\) |
−0.556541 | + | 0.830820i | \(0.687872\pi\) | |||||||
\(678\) | 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 | −0.973598 | − | 0.228269i | \(-0.926693\pi\) |
−0.289112 | + | 0.957295i | \(0.593360\pi\) | |||||||
\(684\) | 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 | −0.755110 | − | 0.655598i | \(-0.772417\pi\) |
0.945319 | + | 0.326146i | \(0.105750\pi\) | |||||||
\(692\) | 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 | −0.756730 | − | 0.653727i | \(-0.773204\pi\) |
0.944509 | + | 0.328484i | \(0.106538\pi\) | |||||||
\(710\) | 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 | −0.0613050 | + | 0.998119i | \(0.519526\pi\) |
−0.833744 | + | 0.552151i | \(0.813807\pi\) | |||||||
\(720\) | 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 | −0.971704 | − | 0.236202i | \(-0.924097\pi\) |
−0.690409 | − | 0.723419i | \(-0.742569\pi\) | |||||||
\(734\) | 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 | −0.656316 | − | 0.754486i | \(-0.727886\pi\) |
0.325246 | + | 0.945629i | \(0.394553\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 13.8564i | − | 0.509028i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.2487i | 0.889599i | 0.895630 | + | 0.444799i | \(0.146725\pi\) | ||||
−0.895630 | + | 0.444799i | \(0.853275\pi\) | |||||||
\(744\) | 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 | 0.996565 | − | 0.0828123i | \(-0.0263902\pi\) |
0.426565 | + | 0.904457i | \(0.359724\pi\) | |||||||
\(752\) | 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 | 0.136914 | − | 0.990583i | \(-0.456282\pi\) |
−0.789413 | + | 0.613862i | \(0.789615\pi\) | |||||||
\(762\) | 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 | \(-0.919623\pi\) | ||
0.968288 | − | 0.249837i | \(-0.0803772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 55.4256i | 1.99611i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.00000 | − | 1.73205i | 0.107903 | − | 0.0622975i | −0.445078 | − | 0.895492i | \(-0.646824\pi\) |
0.552980 | + | 0.833194i | \(0.313491\pi\) | |||||||
\(774\) | 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 | 0.991895 | + | 0.127060i | \(0.0405540\pi\) |
−0.385911 | + | 0.922536i | \(0.626113\pi\) | |||||||
\(788\) | 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 | \(-0.900754\pi\) | ||
0.951786 | − | 0.306762i | \(-0.0992455\pi\) | |||||||
\(798\) | 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 | −0.999491 | − | 0.0319002i | \(-0.989844\pi\) |
0.472119 | − | 0.881535i | \(-0.343489\pi\) | |||||||
\(810\) | 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 | 0.476122 | + | 0.879379i | \(0.342042\pi\) |
−0.999626 | + | 0.0273557i | \(0.991291\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.00000 | − | 1.73205i | 0.104573 | − | 0.0603755i | −0.446801 | − | 0.894633i | \(-0.647437\pi\) |
0.551375 | + | 0.834258i | \(0.314104\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 48.4974i | 1.68846i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 24.2487i | − | 0.843210i | −0.906780 | − | 0.421605i | \(-0.861467\pi\) | ||
0.906780 | − | 0.421605i | \(-0.138533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.00000 | + | 1.73205i | −0.104194 | + | 0.0601566i | −0.551192 | − | 0.834379i | \(-0.685827\pi\) |
0.446997 | + | 0.894535i | \(0.352493\pi\) | |||||||
\(830\) | 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 | \(0.0188882\pi\) | ||||
−0.998240 | + | 0.0593043i | \(0.981112\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 6.92820i | − | 0.236940i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.0000 | + | 17.3205i | −1.02478 | + | 0.591657i | −0.915485 | − | 0.402352i | \(-0.868193\pi\) |
−0.109295 | + | 0.994009i | \(0.534859\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.00000 | − | 12.1244i | 0.238837 | − | 0.413678i | −0.721544 | − | 0.692369i | \(-0.756567\pi\) |
0.960381 | + | 0.278691i | \(0.0899005\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.0000 | − | 15.5885i | −0.919091 | − | 0.530637i | −0.0357458 | − | 0.999361i | \(-0.511381\pi\) |
−0.883345 | + | 0.468724i | \(0.844714\pi\) | |||||||
\(864\) | 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 | 0.343495 | + | 0.939155i | \(0.388389\pi\) |
−0.985079 | + | 0.172102i | \(0.944944\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.0000 | − | 10.3923i | 0.607125 | − | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 13.8564i | − | 0.466834i | −0.972377 | − | 0.233417i | \(-0.925009\pi\) | ||
0.972377 | − | 0.233417i | \(-0.0749907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.46410i | 0.116576i | 0.998300 | + | 0.0582882i | \(0.0185642\pi\) | ||||
−0.998300 | + | 0.0582882i | \(0.981436\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.0000 | − | 20.7846i | 1.21013 | − | 0.698667i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.00000 | − | 10.3923i | 0.201460 | − | 0.348939i | −0.747539 | − | 0.664218i | \(-0.768765\pi\) |
0.948999 | + | 0.315279i | \(0.102098\pi\) | |||||||
\(888\) | 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 | −0.806339 | − | 0.591454i | \(-0.798554\pi\) |
0.109045 | + | 0.994037i | \(0.465221\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 10.3923i | − | 0.344691i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.3923i | 0.344312i | 0.985070 | + | 0.172156i | \(0.0550734\pi\) | ||||
−0.985070 | + | 0.172156i | \(0.944927\pi\) | |||||||
\(912\) | 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 | −0.0164935 | − | 0.999864i | \(-0.505250\pi\) |
−0.874154 | + | 0.485648i | \(0.838584\pi\) | |||||||
\(920\) | 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 | 0.956274 | − | 0.292473i | \(-0.0944781\pi\) |
0.224848 | + | 0.974394i | \(0.427811\pi\) | |||||||
\(930\) | 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 | \(0.291049\pi\) | ||||
−0.610299 | + | 0.792171i | \(0.708951\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.8564i | 0.452187i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.0000 | − | 12.1244i | 0.684580 | − | 0.395243i | −0.116998 | − | 0.993132i | \(-0.537327\pi\) |
0.801579 | + | 0.597889i | \(0.203994\pi\) | |||||||
\(942\) | 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 | 0.800762 | − | 0.598983i | \(-0.204428\pi\) |
−0.118354 | + | 0.992972i | \(0.537762\pi\) | |||||||
\(948\) | 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 | \(0.127488\pi\) | ||||
−0.920860 | + | 0.389893i | \(0.872512\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.00000 | + | 15.5885i | −0.288824 | + | 0.500257i | −0.973529 | − | 0.228562i | \(-0.926597\pi\) |
0.684706 | + | 0.728820i | \(0.259931\pi\) | |||||||
\(972\) | 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 | 0.999734 | − | 0.0230645i | \(-0.00734232\pi\) |
−0.519841 | + | 0.854263i | \(0.674009\pi\) | |||||||
\(978\) | 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 | −0.996138 | − | 0.0878058i | \(-0.972015\pi\) |
0.422027 | − | 0.906583i | \(-0.361319\pi\) | |||||||
\(984\) | 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 | −0.451594 | − | 0.892224i | \(-0.649144\pi\) |
0.546892 | + | 0.837203i | \(0.315811\pi\) | |||||||
\(992\) | 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 | −0.996734 | − | 0.0807558i | \(-0.974267\pi\) |
−0.428430 | + | 0.903575i | \(0.640933\pi\) | |||||||
\(998\) | 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 \(a_p\))