Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,2,Mod(109,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.r (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: | \(12.9357651274\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.109 |
Dual form | 1620.2.r.d.1189.2 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23205 | + | 0.133975i | 0.998203 | + | 0.0599153i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.46410 | + | 2.00000i | −1.30931 | + | 0.755929i | −0.981981 | − | 0.188982i | \(-0.939481\pi\) |
−0.327327 | + | 0.944911i | \(0.606148\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | − | 3.46410i | −0.603023 | − | 1.04447i | −0.992361 | − | 0.123371i | \(-0.960630\pi\) |
0.389338 | − | 0.921095i | \(-0.372704\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00000i | 0.970143i | 0.874475 | + | 0.485071i | \(0.161206\pi\) | ||||
−0.874475 | + | 0.485071i | \(0.838794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.46410 | + | 2.00000i | 0.722315 | + | 0.417029i | 0.815604 | − | 0.578610i | \(-0.196405\pi\) |
−0.0932891 | + | 0.995639i | \(0.529738\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.96410 | + | 0.598076i | 0.992820 | + | 0.119615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.00000 | + | 4.00000i | −1.35225 | + | 0.676123i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.00000i | 1.31519i | 0.753371 | + | 0.657596i | \(0.228427\pi\) | ||||
−0.753371 | + | 0.657596i | \(0.771573\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.00000 | + | 8.66025i | −0.780869 | + | 1.35250i | 0.150567 | + | 0.988600i | \(0.451890\pi\) |
−0.931436 | + | 0.363905i | \(0.881443\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410 | − | 2.00000i | 0.528271 | − | 0.304997i | −0.212041 | − | 0.977261i | \(-0.568011\pi\) |
0.740312 | + | 0.672264i | \(0.234678\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.46410 | + | 2.00000i | −0.505291 | + | 0.291730i | −0.730896 | − | 0.682489i | \(-0.760898\pi\) |
0.225605 | + | 0.974219i | \(0.427564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.50000 | − | 7.79423i | 0.642857 | − | 1.11346i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.0000i | 1.64833i | 0.566352 | + | 0.824163i | \(0.308354\pi\) | ||||
−0.566352 | + | 0.824163i | \(0.691646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | − | 8.00000i | −0.539360 | − | 1.07872i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | − | 1.73205i | −0.128037 | − | 0.221766i | 0.794879 | − | 0.606768i | \(-0.207534\pi\) |
−0.922916 | + | 0.385002i | \(0.874201\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.46410 | − | 2.00000i | −0.423207 | − | 0.244339i | 0.273241 | − | 0.961946i | \(-0.411904\pi\) |
−0.696449 | + | 0.717607i | \(0.745238\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.00000i | − | 0.936329i | −0.883641 | − | 0.468165i | \(-0.844915\pi\) | ||
0.883641 | − | 0.468165i | \(-0.155085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.8564 | + | 8.00000i | 1.57908 | + | 0.911685i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.00000 | − | 10.3923i | −0.675053 | − | 1.16923i | −0.976453 | − | 0.215728i | \(-0.930788\pi\) |
0.301401 | − | 0.953498i | \(-0.402546\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.46410 | + | 2.00000i | −0.380235 | + | 0.219529i | −0.677920 | − | 0.735135i | \(-0.737119\pi\) |
0.297686 | + | 0.954664i | \(0.403785\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.535898 | + | 8.92820i | −0.0581263 | + | 0.968400i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.92820 | + | 4.00000i | −0.703452 | + | 0.406138i | −0.808632 | − | 0.588315i | \(-0.799792\pi\) |
0.105180 | + | 0.994453i | \(0.466458\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00000 | − | 1.73205i | −0.0995037 | − | 0.172345i | 0.811976 | − | 0.583691i | \(-0.198392\pi\) |
−0.911479 | + | 0.411346i | \(0.865059\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.46410 | + | 2.00000i | 0.341328 | + | 0.197066i | 0.660859 | − | 0.750510i | \(-0.270192\pi\) |
−0.319531 | + | 0.947576i | \(0.603525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000i | 1.16008i | 0.814587 | + | 0.580042i | \(0.196964\pi\) | ||||
−0.814587 | + | 0.580042i | \(0.803036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3923 | + | 6.00000i | 0.977626 | + | 0.564433i | 0.901553 | − | 0.432670i | \(-0.142428\pi\) |
0.0760733 | + | 0.997102i | \(0.475762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.46410 | + | 4.92820i | 0.696031 | + | 0.459557i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.00000 | − | 13.8564i | −0.733359 | − | 1.27021i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0000 | + | 2.00000i | 0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.00000i | − | 0.354943i | −0.984126 | − | 0.177471i | \(-0.943208\pi\) | ||
0.984126 | − | 0.177471i | \(-0.0567917\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | − | 10.3923i | 0.524222 | − | 0.907980i | −0.475380 | − | 0.879781i | \(-0.657689\pi\) |
0.999602 | − | 0.0281993i | \(-0.00897729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3923 | − | 6.00000i | 0.887875 | − | 0.512615i | 0.0146279 | − | 0.999893i | \(-0.495344\pi\) |
0.873247 | + | 0.487278i | \(0.162010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | − | 13.8564i | 0.678551 | − | 1.17529i | −0.296866 | − | 0.954919i | \(-0.595942\pi\) |
0.975417 | − | 0.220366i | \(-0.0707252\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.00000 | + | 12.0000i | 0.498273 | + | 0.996546i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.00000 | − | 1.73205i | 0.0819232 | − | 0.141895i | −0.822153 | − | 0.569267i | \(-0.807227\pi\) |
0.904076 | + | 0.427372i | \(0.140560\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000 | + | 17.3205i | 0.813788 | + | 1.40952i | 0.910195 | + | 0.414181i | \(0.135932\pi\) |
−0.0964061 | + | 0.995342i | \(0.530735\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.92820 | + | 7.46410i | −0.395843 | + | 0.599531i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.92820 | + | 4.00000i | 0.552931 | + | 0.319235i | 0.750303 | − | 0.661094i | \(-0.229907\pi\) |
−0.197372 | + | 0.980329i | \(0.563241\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.0000 | −1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.0000i | 1.56652i | 0.621694 | + | 0.783260i | \(0.286445\pi\) | ||||
−0.621694 | + | 0.783260i | \(0.713555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.3923 | − | 6.00000i | −0.804181 | − | 0.464294i | 0.0407502 | − | 0.999169i | \(-0.487025\pi\) |
−0.844931 | + | 0.534875i | \(0.820359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.50000 | − | 11.2583i | −0.500000 | − | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.46410 | − | 2.00000i | 0.263371 | − | 0.152057i | −0.362500 | − | 0.931984i | \(-0.618077\pi\) |
0.625871 | + | 0.779926i | \(0.284744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.3923 | + | 7.85641i | −1.39033 | + | 0.593889i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.07180 | + | 17.8564i | −0.0788001 | + | 1.31283i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.8564 | − | 8.00000i | 1.01328 | − | 0.585018i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000 | + | 20.7846i | 0.868290 | + | 1.50392i | 0.863743 | + | 0.503932i | \(0.168114\pi\) |
0.00454614 | + | 0.999990i | \(0.498553\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.8564 | − | 8.00000i | −0.997406 | − | 0.575853i | −0.0899262 | − | 0.995948i | \(-0.528663\pi\) |
−0.907480 | + | 0.420096i | \(0.861996\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.00000i | − | 0.284988i | −0.989796 | − | 0.142494i | \(-0.954488\pi\) | ||
0.989796 | − | 0.142494i | \(-0.0455122\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0000 | 0.850657 | 0.425329 | − | 0.905039i | \(-0.360158\pi\) | ||||
0.425329 | + | 0.905039i | \(0.360158\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.7846 | − | 12.0000i | −1.45879 | − | 0.842235i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.3205 | + | 18.6603i | −0.860502 | + | 1.30329i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | − | 4.00000i | 0.545595 | − | 0.272798i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.0000i | − | 1.08615i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.3205 | + | 10.0000i | −1.15987 | + | 0.669650i | −0.951272 | − | 0.308353i | \(-0.900222\pi\) |
−0.208595 | + | 0.978002i | \(0.566889\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.3205 | + | 10.0000i | −1.14960 | + | 0.663723i | −0.948790 | − | 0.315906i | \(-0.897691\pi\) |
−0.200812 | + | 0.979630i | \(0.564358\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0000 | − | 22.5167i | 0.859064 | − | 1.48794i | −0.0137585 | − | 0.999905i | \(-0.504380\pi\) |
0.872823 | − | 0.488037i | \(-0.162287\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 20.0000i | − | 1.31024i | −0.755523 | − | 0.655122i | \(-0.772617\pi\) | ||
0.755523 | − | 0.655122i | \(-0.227383\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | + | 4.00000i | −0.521862 | + | 0.260931i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.00000 | + | 6.92820i | −0.258738 | + | 0.448148i | −0.965904 | − | 0.258900i | \(-0.916640\pi\) |
0.707166 | + | 0.707048i | \(0.249973\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | + | 1.73205i | 0.0644157 | + | 0.111571i | 0.896435 | − | 0.443176i | \(-0.146148\pi\) |
−0.832019 | + | 0.554747i | \(0.812815\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.0885 | − | 16.7942i | 0.708416 | − | 1.07294i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 16.0000i | − | 1.00591i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.3923 | − | 6.00000i | −0.648254 | − | 0.374270i | 0.139533 | − | 0.990217i | \(-0.455440\pi\) |
−0.787787 | + | 0.615948i | \(0.788773\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0000 | − | 27.7128i | −0.994192 | − | 1.72199i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.46410 | + | 2.00000i | −0.213606 | + | 0.123325i | −0.602986 | − | 0.797752i | \(-0.706023\pi\) |
0.389380 | + | 0.921077i | \(0.372689\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.60770 | + | 26.7846i | −0.0987599 | + | 1.64537i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.00000 | 0.242983 | 0.121491 | − | 0.992592i | \(-0.461232\pi\) | ||||
0.121491 | + | 0.992592i | \(0.461232\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.85641 | − | 18.3923i | −0.473759 | − | 1.10910i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.7128 | − | 16.0000i | 1.66510 | − | 0.961347i | 0.694881 | − | 0.719125i | \(-0.255457\pi\) |
0.970221 | − | 0.242222i | \(-0.0778761\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | + | 5.19615i | 0.178965 | + | 0.309976i | 0.941526 | − | 0.336939i | \(-0.109392\pi\) |
−0.762561 | + | 0.646916i | \(0.776058\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.2487 | + | 14.0000i | 1.44144 | + | 0.832214i | 0.997946 | − | 0.0640654i | \(-0.0204066\pi\) |
0.443491 | + | 0.896279i | \(0.353740\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 40.0000i | − | 2.36113i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.3923 | + | 6.00000i | 0.607125 | + | 0.350524i | 0.771839 | − | 0.635818i | \(-0.219337\pi\) |
−0.164714 | + | 0.986341i | \(0.552670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.92820 | + | 7.46410i | −0.286931 | + | 0.434577i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | + | 13.8564i | −0.461112 | + | 0.798670i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.00000 | − | 4.00000i | −0.114520 | − | 0.229039i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.0000i | − | 0.684876i | −0.939540 | − | 0.342438i | \(-0.888747\pi\) | ||
0.939540 | − | 0.342438i | \(-0.111253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.8564 | − | 8.00000i | 0.783210 | − | 0.452187i | −0.0543564 | − | 0.998522i | \(-0.517311\pi\) |
0.837567 | + | 0.546335i | \(0.183977\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.46410 | − | 2.00000i | 0.194563 | − | 0.112331i | −0.399554 | − | 0.916710i | \(-0.630835\pi\) |
0.594117 | + | 0.804379i | \(0.297502\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | − | 20.7846i | 0.671871 | − | 1.16371i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000 | − | 13.8564i | 0.441054 | − | 0.763928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | + | 6.92820i | 0.219860 | + | 0.380808i | 0.954765 | − | 0.297361i | \(-0.0961066\pi\) |
−0.734905 | + | 0.678170i | \(0.762773\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.46410 | − | 4.92820i | −0.407807 | − | 0.269257i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.92820 | − | 4.00000i | −0.377403 | − | 0.217894i | 0.299285 | − | 0.954164i | \(-0.403252\pi\) |
−0.676688 | + | 0.736270i | \(0.736585\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000 | 0.866449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.3923 | − | 6.00000i | −0.557888 | − | 0.322097i | 0.194409 | − | 0.980921i | \(-0.437721\pi\) |
−0.752297 | + | 0.658824i | \(0.771054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.00000 | − | 12.1244i | −0.374701 | − | 0.649002i | 0.615581 | − | 0.788074i | \(-0.288921\pi\) |
−0.990282 | + | 0.139072i | \(0.955588\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.2487 | − | 14.0000i | 1.29063 | − | 0.745145i | 0.311863 | − | 0.950127i | \(-0.399047\pi\) |
0.978766 | + | 0.204982i | \(0.0657137\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.07180 | − | 17.8564i | 0.0561004 | − | 0.934647i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.46410 | + | 2.00000i | −0.180825 | + | 0.104399i | −0.587680 | − | 0.809093i | \(-0.699959\pi\) |
0.406855 | + | 0.913493i | \(0.366625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.0000 | − | 41.5692i | −1.24602 | − | 2.15817i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.7846 | − | 12.0000i | −1.07619 | − | 0.621336i | −0.146321 | − | 0.989237i | \(-0.546743\pi\) |
−0.929865 | + | 0.367901i | \(0.880077\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.00000 | −0.410932 | −0.205466 | − | 0.978664i | \(-0.565871\pi\) | ||||
−0.205466 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.2487 | − | 14.0000i | −1.23905 | − | 0.715367i | −0.270151 | − | 0.962818i | \(-0.587074\pi\) |
−0.968900 | + | 0.247451i | \(0.920407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 29.8564 | + | 19.7128i | 1.52162 | + | 1.00466i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.0000 | + | 29.4449i | 0.861934 | + | 1.49291i | 0.870059 | + | 0.492947i | \(0.164080\pi\) |
−0.00812520 | + | 0.999967i | \(0.502586\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | + | 13.8564i | −0.404577 | + | 0.700749i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.0000 | − | 24.0000i | −0.603786 | − | 1.20757i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.00000i | 0.401508i | 0.979642 | + | 0.200754i | \(0.0643393\pi\) | ||||
−0.979642 | + | 0.200754i | \(0.935661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.00000 | + | 12.1244i | −0.349563 | + | 0.605461i | −0.986172 | − | 0.165726i | \(-0.947003\pi\) |
0.636609 | + | 0.771187i | \(0.280337\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.7128 | − | 16.0000i | 1.37367 | − | 0.793091i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.0000 | − | 22.5167i | 0.642809 | − | 1.11338i | −0.341994 | − | 0.939702i | \(-0.611102\pi\) |
0.984803 | − | 0.173675i | \(-0.0555643\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 16.0000i | − | 0.787309i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.00000 | + | 4.00000i | −0.392705 | + | 0.196352i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.0000 | − | 24.2487i | 0.683945 | − | 1.18463i | −0.289822 | − | 0.957080i | \(-0.593596\pi\) |
0.973767 | − | 0.227547i | \(-0.0730704\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.00000 | − | 8.66025i | −0.243685 | − | 0.422075i | 0.718076 | − | 0.695965i | \(-0.245023\pi\) |
−0.961761 | + | 0.273890i | \(0.911690\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.39230 | + | 19.8564i | −0.116044 | + | 0.963177i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.92820 | + | 4.00000i | 0.335279 | + | 0.193574i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.00000 | −0.385346 | −0.192673 | − | 0.981263i | \(-0.561716\pi\) | ||||
−0.192673 | + | 0.981263i | \(0.561716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.0000i | 0.768911i | 0.923144 | + | 0.384455i | \(0.125611\pi\) | ||||
−0.923144 | + | 0.384455i | \(0.874389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.00000 | − | 10.3923i | −0.286364 | − | 0.495998i | 0.686575 | − | 0.727059i | \(-0.259113\pi\) |
−0.972939 | + | 0.231062i | \(0.925780\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.1769 | + | 18.0000i | −1.48126 | + | 0.855206i | −0.999774 | − | 0.0212481i | \(-0.993236\pi\) |
−0.481486 | + | 0.876454i | \(0.659903\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.3205 | − | 1.33975i | −1.05809 | − | 0.0635100i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.0000 | 1.88353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.6410 | + | 20.0000i | −1.62044 | + | 0.935561i | −0.633636 | + | 0.773631i | \(0.718438\pi\) |
−0.986802 | + | 0.161929i | \(0.948228\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.00000 | + | 5.19615i | 0.139724 | + | 0.242009i | 0.927392 | − | 0.374091i | \(-0.122045\pi\) |
−0.787668 | + | 0.616100i | \(0.788712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.3923 | − | 6.00000i | −0.482971 | − | 0.278844i | 0.238683 | − | 0.971098i | \(-0.423284\pi\) |
−0.721654 | + | 0.692254i | \(0.756618\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0000i | 0.555294i | 0.960683 | + | 0.277647i | \(0.0895545\pi\) | ||||
−0.960683 | + | 0.277647i | \(0.910445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.8564 | − | 8.00000i | −0.637118 | − | 0.367840i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.00000 | + | 13.8564i | 0.365529 | + | 0.633115i | 0.988861 | − | 0.148842i | \(-0.0475547\pi\) |
−0.623332 | + | 0.781958i | \(0.714221\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.0000 | + | 8.00000i | −0.726523 | + | 0.363261i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0000i | 0.543772i | 0.962329 | + | 0.271886i | \(0.0876473\pi\) | ||||
−0.962329 | + | 0.271886i | \(0.912353\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.0000 | + | 31.1769i | −0.812329 | + | 1.40699i | 0.0989017 | + | 0.995097i | \(0.468467\pi\) |
−0.911230 | + | 0.411897i | \(0.864866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.7846 | + | 12.0000i | −0.936092 | + | 0.540453i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0000 | − | 20.7846i | 0.537194 | − | 0.930447i | −0.461860 | − | 0.886953i | \(-0.652818\pi\) |
0.999054 | − | 0.0434940i | \(-0.0138489\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 36.0000i | − | 1.60516i | −0.596544 | − | 0.802580i | \(-0.703460\pi\) | ||
0.596544 | − | 0.802580i | \(-0.296540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.00000 | − | 4.00000i | −0.0889988 | − | 0.177998i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.0000 | + | 36.3731i | −0.930809 | + | 1.61221i | −0.148866 | + | 0.988857i | \(0.547562\pi\) |
−0.781943 | + | 0.623350i | \(0.785771\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0000 | + | 27.7128i | 0.707798 | + | 1.22594i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.46410 | + | 4.92820i | 0.328908 | + | 0.217163i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.8564 | + | 8.00000i | 0.609404 | + | 0.351840i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.0000 | 1.66481 | 0.832405 | − | 0.554168i | \(-0.186963\pi\) | ||||
0.832405 | + | 0.554168i | \(0.186963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 28.0000i | − | 1.22435i | −0.790721 | − | 0.612177i | \(-0.790294\pi\) | ||
0.790721 | − | 0.612177i | \(-0.209706\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.8564 | − | 8.00000i | −0.603595 | − | 0.348485i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.50000 | − | 6.06218i | −0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.60770 | + | 26.7846i | −0.0695067 | + | 1.15800i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −36.0000 | −1.55063 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.46410 | + | 0.267949i | 0.191221 | + | 0.0114777i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.2487 | + | 14.0000i | −1.03680 | + | 0.598597i | −0.918925 | − | 0.394432i | \(-0.870941\pi\) |
−0.117875 | + | 0.993028i | \(0.537608\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 41.5692 | + | 24.0000i | 1.76770 | + | 1.02058i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 12.0000i | − | 0.508456i | −0.967144 | − | 0.254228i | \(-0.918179\pi\) | ||
0.967144 | − | 0.254228i | \(-0.0818214\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.3205 | + | 10.0000i | 0.729972 | + | 0.421450i | 0.818412 | − | 0.574632i | \(-0.194855\pi\) |
−0.0884397 | + | 0.996082i | \(0.528188\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.3923 | + | 14.7846i | 0.942051 | + | 0.621993i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.0000 | − | 22.5167i | −0.544988 | − | 0.943948i | −0.998608 | − | 0.0527519i | \(-0.983201\pi\) |
0.453619 | − | 0.891196i | \(-0.350133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | + | 34.6410i | −0.836974 | + | 1.44968i | 0.0554391 | + | 0.998462i | \(0.482344\pi\) |
−0.892413 | + | 0.451219i | \(0.850989\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.0000 | + | 12.0000i | 0.667246 | + | 0.500435i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.0000i | 1.33218i | 0.745873 | + | 0.666089i | \(0.232033\pi\) | ||||
−0.745873 | + | 0.666089i | \(0.767967\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.00000 | − | 13.8564i | 0.331896 | − | 0.574861i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 41.5692 | − | 24.0000i | 1.72162 | − | 0.993978i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.1769 | + | 18.0000i | −1.28681 | + | 0.742940i | −0.978084 | − | 0.208212i | \(-0.933236\pi\) |
−0.308725 | + | 0.951151i | \(0.599902\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.0000i | 1.47834i | 0.673517 | + | 0.739171i | \(0.264783\pi\) | ||||
−0.673517 | + | 0.739171i | \(0.735217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.0000 | − | 32.0000i | −0.655936 | − | 1.31187i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | − | 20.7846i | 0.490307 | − | 0.849236i | −0.509631 | − | 0.860393i | \(-0.670218\pi\) |
0.999938 | + | 0.0111569i | \(0.00355143\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.0000 | − | 32.9090i | −0.775026 | − | 1.34238i | −0.934780 | − | 0.355228i | \(-0.884403\pi\) |
0.159754 | − | 0.987157i | \(-0.448930\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.16025 | + | 9.33013i | −0.250450 | + | 0.379324i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.2487 | − | 14.0000i | −0.984225 | − | 0.568242i | −0.0806818 | − | 0.996740i | \(-0.525710\pi\) |
−0.903543 | + | 0.428497i | \(0.859043\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8.00000i | − | 0.323117i | −0.986863 | − | 0.161558i | \(-0.948348\pi\) | ||
0.986863 | − | 0.161558i | \(-0.0516520\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.1051 | + | 22.0000i | 1.53405 | + | 0.885687i | 0.999169 | + | 0.0407620i | \(0.0129786\pi\) |
0.534885 | + | 0.844925i | \(0.320355\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.00000 | − | 13.8564i | −0.321547 | − | 0.556936i | 0.659260 | − | 0.751915i | \(-0.270870\pi\) |
−0.980807 | + | 0.194979i | \(0.937536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 34.6410 | − | 20.0000i | 1.38786 | − | 0.801283i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2846 | + | 5.93782i | 0.971384 | + | 0.237513i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −32.0000 | −1.27592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.0000 | −1.11466 | −0.557331 | − | 0.830290i | \(-0.688175\pi\) | ||||
−0.557331 | + | 0.830290i | \(0.688175\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.535898 | − | 8.92820i | 0.0212665 | − | 0.354305i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.00000 | + | 12.1244i | 0.276483 | + | 0.478883i | 0.970508 | − | 0.241068i | \(-0.0774976\pi\) |
−0.694025 | + | 0.719951i | \(0.744164\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.1769 | − | 18.0000i | −1.22950 | − | 0.709851i | −0.262573 | − | 0.964912i | \(-0.584571\pi\) |
−0.966925 | + | 0.255062i | \(0.917904\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000i | 0.471769i | 0.971781 | + | 0.235884i | \(0.0757987\pi\) | ||||
−0.971781 | + | 0.235884i | \(0.924201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.0000 | 0.628055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.46410 | + | 2.00000i | 0.135561 | + | 0.0782660i | 0.566247 | − | 0.824236i | \(-0.308395\pi\) |
−0.430686 | + | 0.902502i | \(0.641728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.7846 | − | 22.3923i | 0.577683 | − | 0.874940i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.0000 | − | 24.2487i | −0.545363 | − | 0.944596i | −0.998584 | − | 0.0531977i | \(-0.983059\pi\) |
0.453221 | − | 0.891398i | \(-0.350275\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.0000 | − | 19.0526i | 0.427850 | − | 0.741059i | −0.568831 | − | 0.822454i | \(-0.692604\pi\) |
0.996682 | + | 0.0813955i | \(0.0259377\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.0000i | 0.929284i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.00000 | + | 6.92820i | −0.154418 | + | 0.267460i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.46410 | − | 2.00000i | 0.133136 | − | 0.0768662i | −0.431953 | − | 0.901896i | \(-0.642175\pi\) |
0.565089 | + | 0.825030i | \(0.308842\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.0000 | − | 27.7128i | 0.614024 | − | 1.06352i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.0000i | 1.68361i | 0.539779 | + | 0.841807i | \(0.318508\pi\) | ||||
−0.539779 | + | 0.841807i | \(0.681492\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.0000 | − | 12.0000i | 0.916993 | − | 0.458496i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.0000 | + | 27.7128i | 0.608669 | + | 1.05425i | 0.991460 | + | 0.130410i | \(0.0416295\pi\) |
−0.382791 | + | 0.923835i | \(0.625037\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.7128 | − | 29.8564i | 0.747750 | − | 1.13252i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34.6410 | − | 20.0000i | −1.31212 | − | 0.757554i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.0000 | −0.982006 | −0.491003 | − | 0.871158i | \(-0.663370\pi\) | ||||
−0.491003 | + | 0.871158i | \(0.663370\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.92820 | + | 4.00000i | 0.260562 | + | 0.150435i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.00000 | − | 5.19615i | −0.112667 | − | 0.195146i | 0.804178 | − | 0.594389i | \(-0.202606\pi\) |
−0.916845 | + | 0.399244i | \(0.869273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.8564 | + | 8.00000i | −0.518927 | + | 0.299602i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.00000 | 0.298350 | 0.149175 | − | 0.988811i | \(-0.452338\pi\) | ||||
0.149175 | + | 0.988811i | \(0.452338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0000 | −0.595871 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.7846 | + | 27.5885i | 0.437669 | + | 1.02461i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.3923 | − | 6.00000i | 0.385429 | − | 0.222528i | −0.294749 | − | 0.955575i | \(-0.595236\pi\) |
0.680178 | + | 0.733047i | \(0.261903\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.00000 | + | 13.8564i | 0.295891 | + | 0.512498i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.8564 | + | 8.00000i | 0.511798 | + | 0.295487i | 0.733572 | − | 0.679611i | \(-0.237852\pi\) |
−0.221774 | + | 0.975098i | \(0.571185\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0000i | 0.589368i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.0000 | −1.47142 | −0.735712 | − | 0.677295i | \(-0.763152\pi\) | ||||
−0.735712 | + | 0.677295i | \(0.763152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.1769 | + | 18.0000i | 1.14377 | + | 0.660356i | 0.947361 | − | 0.320166i | \(-0.103739\pi\) |
0.196409 | + | 0.980522i | \(0.437072\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.46410 | − | 3.73205i | 0.0902777 | − | 0.136732i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.0000 | − | 41.5692i | −0.876941 | − | 1.51891i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0000 | − | 24.2487i | 0.510867 | − | 0.884848i | −0.489053 | − | 0.872254i | \(-0.662658\pi\) |
0.999921 | − | 0.0125942i | \(-0.00400897\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.0000 | + | 40.0000i | 0.727875 | + | 1.45575i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 16.0000i | − | 0.581530i | −0.956795 | − | 0.290765i | \(-0.906090\pi\) | ||
0.956795 | − | 0.290765i | \(-0.0939098\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0000 | − | 36.3731i | 0.761249 | − | 1.31852i | −0.180957 | − | 0.983491i | \(-0.557920\pi\) |
0.942207 | − | 0.335032i | \(-0.108747\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.92820 | + | 4.00000i | −0.250818 | + | 0.144810i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.00000 | + | 15.5885i | −0.324548 | + | 0.562134i | −0.981421 | − | 0.191867i | \(-0.938546\pi\) |
0.656873 | + | 0.754002i | \(0.271879\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.0000i | 0.431610i | 0.976436 | + | 0.215805i | \(0.0692376\pi\) | ||||
−0.976436 | + | 0.215805i | \(0.930762\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.0000 | + | 16.0000i | −0.431053 | + | 0.574737i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.9282 | + | 9.85641i | 0.532810 | + | 0.351790i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.2487 | + | 14.0000i | 0.864373 | + | 0.499046i | 0.865474 | − | 0.500953i | \(-0.167017\pi\) |
−0.00110111 | + | 0.999999i | \(0.500350\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −48.0000 | −1.70668 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.2487 | − | 14.0000i | −0.858933 | − | 0.495905i | 0.00472155 | − | 0.999989i | \(-0.498497\pi\) |
−0.863655 | + | 0.504083i | \(0.831830\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | − | 13.8564i | −0.283020 | − | 0.490204i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.7128 | + | 16.0000i | −0.977964 | + | 0.564628i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −35.7128 | − | 2.14359i | −1.25871 | − | 0.0755517i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.00000 | 0.210949 | 0.105474 | − | 0.994422i | \(-0.466364\pi\) | ||||
0.105474 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.0000 | 1.40459 | 0.702295 | − | 0.711886i | \(-0.252159\pi\) | ||||
0.702295 | + | 0.711886i | \(0.252159\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.67949 | + | 44.6410i | −0.0938585 | + | 1.56371i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.00000 | − | 12.1244i | −0.244302 | − | 0.423143i | 0.717633 | − | 0.696421i | \(-0.245225\pi\) |
−0.961935 | + | 0.273278i | \(0.911892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.3923 | − | 6.00000i | −0.362253 | − | 0.209147i | 0.307816 | − | 0.951446i | \(-0.400402\pi\) |
−0.670069 | + | 0.742299i | \(0.733735\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.0000i | 0.973655i | 0.873498 | + | 0.486828i | \(0.161846\pi\) | ||||
−0.873498 | + | 0.486828i | \(0.838154\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.0000 | 0.625166 | 0.312583 | − | 0.949890i | \(-0.398806\pi\) | ||||
0.312583 | + | 0.949890i | \(0.398806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.1769 | + | 18.0000i | 1.08022 | + | 0.623663i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.3923 | − | 14.7846i | −0.774918 | − | 0.511643i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.0000 | + | 48.4974i | 0.966667 | + | 1.67432i | 0.705067 | + | 0.709141i | \(0.250917\pi\) |
0.261600 | + | 0.965176i | \(0.415750\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.0000 | − | 26.0000i | −0.447214 | − | 0.894427i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 20.0000i | − | 0.687208i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.0000 | + | 27.7128i | −0.548473 | + | 0.949983i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.92820 | − | 4.00000i | 0.237217 | − | 0.136957i | −0.376680 | − | 0.926343i | \(-0.622934\pi\) |
0.613897 | + | 0.789386i | \(0.289601\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.3923 | + | 6.00000i | −0.354994 | + | 0.204956i | −0.666883 | − | 0.745163i | \(-0.732372\pi\) |
0.311888 | + | 0.950119i | \(0.399038\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.0000 | + | 34.6410i | −0.682391 | + | 1.18194i | 0.291858 | + | 0.956462i | \(0.405727\pi\) |
−0.974249 | + | 0.225475i | \(0.927607\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.0000i | 0.408485i | 0.978920 | + | 0.204242i | \(0.0654731\pi\) | ||||
−0.978920 | + | 0.204242i | \(0.934527\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.00000 | − | 4.00000i | 0.272008 | − | 0.136004i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.0000 | + | 41.5692i | −0.814144 | + | 1.41014i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −42.1051 | + | 15.0718i | −1.42341 | + | 0.509520i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.4974 | + | 28.0000i | 1.63764 | + | 0.945493i | 0.981642 | + | 0.190731i | \(0.0610859\pi\) |
0.655999 | + | 0.754761i | \(0.272247\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 12.0000i | − | 0.403832i | −0.979403 | − | 0.201916i | \(-0.935283\pi\) | ||
0.979403 | − | 0.201916i | \(-0.0647168\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.1769 | + | 18.0000i | 1.04682 | + | 0.604381i | 0.921757 | − | 0.387768i | \(-0.126754\pi\) |
0.125061 | + | 0.992149i | \(0.460087\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000 | + | 13.8564i | 0.268311 | + | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.92820 | + | 0.535898i | 0.298437 | + | 0.0179131i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.0000 | −0.800445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.0000 | −1.59911 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.3205 | − | 1.33975i | −0.741959 | − | 0.0445347i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.3923 | + | 6.00000i | −0.345071 | + | 0.199227i | −0.662512 | − | 0.749051i | \(-0.730510\pi\) |
0.317441 | + | 0.948278i | \(0.397176\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.0000 | + | 41.5692i | 0.795155 | + | 1.37725i | 0.922740 | + | 0.385422i | \(0.125944\pi\) |
−0.127585 | + | 0.991828i | \(0.540723\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.8564 | + | 8.00000i | 0.458580 | + | 0.264761i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 48.0000i | 1.58510i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.0000 | 0.395843 | 0.197922 | − | 0.980218i | \(-0.436581\pi\) | ||||
0.197922 | + | 0.980218i | \(0.436581\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.78461 | + | 39.7128i | −0.157317 | + | 1.30575i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.00000 | − | 15.5885i | −0.295280 | − | 0.511441i | 0.679770 | − | 0.733426i | \(-0.262080\pi\) |
−0.975050 | + | 0.221985i | \(0.928746\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 32.0000 | − | 16.0000i | 1.04651 | − | 0.523256i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 32.0000i | − | 1.04539i | −0.852518 | − | 0.522697i | \(-0.824926\pi\) | ||
0.852518 | − | 0.522697i | \(-0.175074\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.00000 | + | 8.66025i | −0.162995 | + | 0.282316i | −0.935942 | − | 0.352155i | \(-0.885449\pi\) |
0.772946 | + | 0.634472i | \(0.218782\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.6410 | + | 20.0000i | −1.12807 | + | 0.651290i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.3923 | − | 6.00000i | 0.337705 | − | 0.194974i | −0.321552 | − | 0.946892i | \(-0.604204\pi\) |
0.659256 | + | 0.751918i | \(0.270871\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.00000i | 0.129573i | 0.997899 | + | 0.0647864i | \(0.0206366\pi\) | ||||
−0.997899 | + | 0.0647864i | \(0.979363\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.0000 | + | 48.0000i | 0.776622 | + | 1.55324i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.0000 | + | 41.5692i | −0.775000 | + | 1.34234i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29.8564 | − | 19.7128i | −0.961112 | − | 0.634578i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.3205 | + | 10.0000i | 0.556990 | + | 0.321578i | 0.751936 | − | 0.659236i | \(-0.229120\pi\) |
−0.194946 | + | 0.980814i | \(0.562453\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | 0.385098 | 0.192549 | − | 0.981287i | \(-0.438325\pi\) | ||||
0.192549 | + | 0.981287i | \(0.438325\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 64.0000i | 2.05175i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.3923 | + | 6.00000i | 0.332479 | + | 0.191957i | 0.656941 | − | 0.753942i | \(-0.271850\pi\) |
−0.324462 | + | 0.945899i | \(0.605183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0000 | + | 34.6410i | 0.639203 | + | 1.10713i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.2487 | − | 14.0000i | 0.773414 | − | 0.446531i | −0.0606773 | − | 0.998157i | \(-0.519326\pi\) |
0.834091 | + | 0.551627i | \(0.185993\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.535898 | − | 8.92820i | 0.0170751 | − | 0.284476i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.0000 | 0.508770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.0000 | 0.889449 | 0.444725 | − | 0.895667i | \(-0.353302\pi\) | ||||
0.444725 | + | 0.895667i | \(0.353302\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.7846 | + | 1.60770i | 0.849129 | + | 0.0509674i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.7846 | − | 12.0000i | 0.658255 | − | 0.380044i | −0.133357 | − | 0.991068i | \(-0.542576\pi\) |
0.791612 | + | 0.611024i | \(0.209242\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))