Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(17,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bc (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: | \(2.68297350792\) |
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: | \( 3 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.17 |
Dual form | 336.2.bc.e.257.2 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.866025 | − | 1.50000i | 0.500000 | − | 0.866025i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.866025 | − | 1.50000i | −0.387298 | − | 0.670820i | 0.604787 | − | 0.796387i | \(-0.293258\pi\) |
−0.992085 | + | 0.125567i | \(0.959925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | − | 0.866025i | 0.944911 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.50000 | − | 2.59808i | −0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.59808 | − | 1.50000i | −0.783349 | − | 0.452267i | 0.0542666 | − | 0.998526i | \(-0.482718\pi\) |
−0.837616 | + | 0.546259i | \(0.816051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00000 | −0.774597 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.73205 | − | 3.00000i | 0.420084 | − | 0.727607i | −0.575863 | − | 0.817546i | \(-0.695334\pi\) |
0.995947 | + | 0.0899392i | \(0.0286673\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | + | 1.73205i | −0.688247 | + | 0.397360i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.866025 | − | 4.50000i | 0.188982 | − | 0.981981i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.19615 | − | 3.00000i | 1.08347 | − | 0.625543i | 0.151642 | − | 0.988436i | \(-0.451544\pi\) |
0.931831 | + | 0.362892i | \(0.118211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | − | 1.73205i | 0.200000 | − | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000i | 0.557086i | 0.960424 | + | 0.278543i | \(0.0898515\pi\) | ||||
−0.960424 | + | 0.278543i | \(0.910149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50000 | + | 0.866025i | 0.269408 | + | 0.155543i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.50000 | + | 2.59808i | −0.783349 | + | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.46410 | − | 3.00000i | −0.585540 | − | 0.507093i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | + | 1.73205i | 0.164399 | + | 0.284747i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.19615 | + | 3.00000i | 0.832050 | + | 0.480384i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.92820 | −1.08200 | −0.541002 | − | 0.841021i | \(-0.681955\pi\) | ||||
−0.541002 | + | 0.841021i | \(0.681955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.59808 | + | 4.50000i | −0.387298 | + | 0.670820i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.46410 | + | 6.00000i | 0.505291 | + | 0.875190i | 0.999981 | + | 0.00612051i | \(0.00194823\pi\) |
−0.494690 | + | 0.869069i | \(0.664718\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | − | 5.19615i | −0.420084 | − | 0.727607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.79423 | + | 4.50000i | 1.07062 | + | 0.618123i | 0.928351 | − | 0.371706i | \(-0.121227\pi\) |
0.142269 | + | 0.989828i | \(0.454560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.19615i | 0.700649i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.866025 | + | 1.50000i | −0.112747 | + | 0.195283i | −0.916877 | − | 0.399170i | \(-0.869298\pi\) |
0.804130 | + | 0.594454i | \(0.202632\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.00000 | − | 5.19615i | −0.755929 | − | 0.654654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.19615 | − | 3.00000i | 0.644503 | − | 0.372104i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | − | 1.73205i | 0.122169 | − | 0.211604i | −0.798454 | − | 0.602056i | \(-0.794348\pi\) |
0.920623 | + | 0.390453i | \(0.127682\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 10.3923i | − | 1.25109i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000i | 1.42414i | 0.702109 | + | 0.712069i | \(0.252242\pi\) | ||||
−0.702109 | + | 0.712069i | \(0.747758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | + | 3.46410i | 0.702247 | + | 0.405442i | 0.808184 | − | 0.588930i | \(-0.200451\pi\) |
−0.105937 | + | 0.994373i | \(0.533784\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.73205 | − | 3.00000i | −0.200000 | − | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.79423 | − | 1.50000i | −0.888235 | − | 0.170941i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.500000 | − | 0.866025i | −0.0562544 | − | 0.0974355i | 0.836527 | − | 0.547926i | \(-0.184582\pi\) |
−0.892781 | + | 0.450490i | \(0.851249\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.66025 | −0.950586 | −0.475293 | − | 0.879827i | \(-0.657658\pi\) | ||||
−0.475293 | + | 0.879827i | \(0.657658\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.50000 | + | 2.59808i | 0.482451 | + | 0.278543i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.19615 | + | 9.00000i | 0.550791 | + | 0.953998i | 0.998218 | + | 0.0596775i | \(0.0190072\pi\) |
−0.447427 | + | 0.894321i | \(0.647659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.00000 | + | 8.66025i | 0.314485 | + | 0.907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.59808 | − | 1.50000i | 0.269408 | − | 0.155543i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.19615 | + | 3.00000i | 0.533114 | + | 0.307794i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.19615i | 0.527589i | 0.964579 | + | 0.263795i | \(0.0849741\pi\) | ||||
−0.964579 | + | 0.263795i | \(0.915026\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.00000i | 0.904534i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.00000 | − | 1.73205i | 0.295599 | − | 0.170664i | −0.344865 | − | 0.938652i | \(-0.612075\pi\) |
0.640464 | + | 0.767988i | \(0.278742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.50000 | + | 2.59808i | −0.731925 | + | 0.253546i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.59808 | − | 1.50000i | 0.251166 | − | 0.145010i | −0.369132 | − | 0.929377i | \(-0.620345\pi\) |
0.620298 | + | 0.784366i | \(0.287012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | − | 1.73205i | 0.0957826 | − | 0.165900i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.46410 | 0.328798 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0000i | 1.12887i | 0.825479 | + | 0.564433i | \(0.190905\pi\) | ||||
−0.825479 | + | 0.564433i | \(0.809095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.00000 | − | 5.19615i | −0.839254 | − | 0.484544i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.00000 | − | 5.19615i | 0.832050 | − | 0.480384i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.73205 | − | 9.00000i | 0.158777 | − | 0.825029i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | − | 1.73205i | −0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.00000 | + | 10.3923i | −0.541002 | + | 0.937043i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1244 | −1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0000 | −0.976092 | −0.488046 | − | 0.872818i | \(-0.662290\pi\) | ||||
−0.488046 | + | 0.872818i | \(0.662290\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.92820 | − | 12.0000i | 0.609994 | − | 1.05654i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.59808 | − | 4.50000i | −0.226995 | − | 0.393167i | 0.729921 | − | 0.683531i | \(-0.239557\pi\) |
−0.956916 | + | 0.290365i | \(0.906223\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 6.92820i | −0.520266 | + | 0.600751i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.50000 | + | 7.79423i | 0.387298 | + | 0.670820i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.5885 | − | 9.00000i | −1.33181 | − | 0.768922i | −0.346235 | − | 0.938148i | \(-0.612540\pi\) |
−0.985577 | + | 0.169226i | \(0.945873\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.3205i | − | 1.46911i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||
0.678551 | − | 0.734553i | \(-0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000 | 1.01058 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.19615 | − | 9.00000i | 0.434524 | − | 0.752618i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.50000 | − | 2.59808i | 0.373705 | − | 0.215758i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.73205 | − | 12.0000i | −0.142857 | − | 0.989743i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.5885 | − | 9.00000i | 1.27706 | − | 0.737309i | 0.300750 | − | 0.953703i | \(-0.402763\pi\) |
0.976306 | + | 0.216394i | \(0.0694297\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.50000 | − | 6.06218i | 0.284826 | − | 0.493333i | −0.687741 | − | 0.725956i | \(-0.741398\pi\) |
0.972567 | + | 0.232623i | \(0.0747309\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.3923 | −0.840168 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3.00000i | − | 0.240966i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.0000 | − | 10.3923i | −1.43656 | − | 0.829396i | −0.438948 | − | 0.898513i | \(-0.644649\pi\) |
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.5000 | − | 7.79423i | 1.07062 | − | 0.618123i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3923 | − | 12.0000i | 0.819028 | − | 0.945732i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.00000 | + | 12.1244i | 0.548282 | + | 0.949653i | 0.998392 | + | 0.0566798i | \(0.0180514\pi\) |
−0.450110 | + | 0.892973i | \(0.648615\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.79423 | + | 4.50000i | 0.606780 | + | 0.350325i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.3205 | −1.34030 | −0.670151 | − | 0.742225i | \(-0.733770\pi\) | ||||
−0.670151 | + | 0.742225i | \(0.733770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.00000 | + | 5.19615i | 0.688247 | + | 0.397360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | − | 5.19615i | 0.0755929 | − | 0.392792i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.50000 | + | 2.59808i | 0.112747 | + | 0.195283i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.3923 | + | 6.00000i | 0.776757 | + | 0.448461i | 0.835280 | − | 0.549825i | \(-0.185306\pi\) |
−0.0585225 | + | 0.998286i | \(0.518639\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.92820i | 0.514969i | 0.966282 | + | 0.257485i | \(0.0828937\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.73205 | − | 3.00000i | 0.127343 | − | 0.220564i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | + | 5.19615i | −0.658145 | + | 0.379980i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.9904 | + | 4.50000i | −0.944911 | + | 0.327327i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.5000 | − | 19.9186i | 0.827788 | − | 1.43377i | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) |
0.899770 | − | 0.436365i | \(-0.143734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 10.3923i | − | 0.744208i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.00000 | − | 5.19615i | −0.637993 | − | 0.368345i | 0.145848 | − | 0.989307i | \(-0.453409\pi\) |
−0.783841 | + | 0.620962i | \(0.786742\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.73205 | − | 3.00000i | −0.122169 | − | 0.211604i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.59808 | + | 7.50000i | 0.182349 | + | 0.526397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | + | 10.3923i | 0.419058 | + | 0.725830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.5885 | − | 9.00000i | −1.08347 | − | 0.625543i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.3923 | 0.718851 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.0000 | + | 10.3923i | 1.23334 | + | 0.712069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.92820 | − | 12.0000i | −0.472500 | − | 0.818393i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.50000 | + | 0.866025i | 0.305480 | + | 0.0587896i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.3923 | − | 6.00000i | 0.702247 | − | 0.405442i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.3923 | + | 6.00000i | 0.699062 | + | 0.403604i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.9808i | 1.73980i | 0.493228 | + | 0.869900i | \(0.335817\pi\) | ||||
−0.493228 | + | 0.869900i | \(0.664183\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.00000 | −0.400000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.59808 | − | 4.50000i | 0.172440 | − | 0.298675i | −0.766832 | − | 0.641848i | \(-0.778168\pi\) |
0.939272 | + | 0.343172i | \(0.111501\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | + | 6.92820i | −0.792982 | + | 0.457829i | −0.841011 | − | 0.541017i | \(-0.818039\pi\) |
0.0480291 | + | 0.998846i | \(0.484706\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.00000 | + | 10.3923i | −0.592157 | + | 0.683763i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.5885 | + | 9.00000i | −1.02123 | + | 0.589610i | −0.914461 | − | 0.404674i | \(-0.867385\pi\) |
−0.106773 | + | 0.994283i | \(0.534052\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.00000 | − | 10.3923i | 0.391397 | − | 0.677919i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.73205 | −0.112509 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6.00000i | − | 0.388108i | −0.980991 | − | 0.194054i | \(-0.937836\pi\) | ||
0.980991 | − | 0.194054i | \(-0.0621637\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.5000 | − | 12.9904i | −1.44935 | − | 0.836784i | −0.450910 | − | 0.892570i | \(-0.648900\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.79423 | + | 13.5000i | 0.500000 | + | 0.866025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.2583 | − | 4.50000i | −0.719268 | − | 0.287494i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | − | 10.3923i | −0.381771 | − | 0.661247i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.50000 | + | 12.9904i | −0.475293 | + | 0.823232i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.0526 | 1.20259 | 0.601293 | − | 0.799028i | \(-0.294652\pi\) | ||||
0.601293 | + | 0.799028i | \(0.294652\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.0000 | −1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.19615 | + | 9.00000i | −0.325396 | + | 0.563602i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.19615 | − | 9.00000i | −0.324127 | − | 0.561405i | 0.657208 | − | 0.753709i | \(-0.271737\pi\) |
−0.981335 | + | 0.192304i | \(0.938404\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | + | 3.46410i | 0.248548 | + | 0.215249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.79423 | − | 4.50000i | 0.482451 | − | 0.278543i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 15.5885i | − | 0.957591i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.0000 | 1.10158 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.7224 | + | 25.5000i | −0.897643 | + | 1.55476i | −0.0671428 | + | 0.997743i | \(0.521388\pi\) |
−0.830500 | + | 0.557019i | \(0.811945\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.50000 | + | 2.59808i | −0.273356 | + | 0.157822i | −0.630412 | − | 0.776261i | \(-0.717114\pi\) |
0.357056 | + | 0.934083i | \(0.383781\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.5885 | + | 3.00000i | 0.943456 | + | 0.181568i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.19615 | + | 3.00000i | −0.313340 | + | 0.180907i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.00000 | + | 6.92820i | −0.240337 | + | 0.416275i | −0.960810 | − | 0.277207i | \(-0.910591\pi\) |
0.720473 | + | 0.693482i | \(0.243925\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 5.19615i | − | 0.311086i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.0000i | 1.78965i | 0.446417 | + | 0.894825i | \(0.352700\pi\) | ||||
−0.446417 | + | 0.894825i | \(0.647300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.0000 | − | 13.8564i | −1.42665 | − | 0.823678i | −0.429797 | − | 0.902926i | \(-0.641415\pi\) |
−0.996855 | + | 0.0792477i | \(0.974748\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.00000 | − | 5.19615i | 0.533114 | − | 0.307794i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.3205 | + | 6.00000i | −1.02240 | + | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.50000 | + | 4.33013i | 0.147059 | + | 0.254713i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.79423 | + | 4.50000i | 0.456906 | + | 0.263795i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.0526 | 1.11306 | 0.556531 | − | 0.830827i | \(-0.312132\pi\) | ||||
0.556531 | + | 0.830827i | \(0.312132\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00000 | 0.174667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.5000 | + | 7.79423i | 0.783349 | + | 0.452267i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.3923 | + | 18.0000i | 0.601003 | + | 1.04097i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0000 | − | 6.92820i | 1.15278 | − | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.2487i | 1.38395i | 0.721923 | + | 0.691974i | \(0.243259\pi\) | ||||
−0.721923 | + | 0.691974i | \(0.756741\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 6.00000i | − | 0.341328i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.92820 | + | 12.0000i | −0.392862 | + | 0.680458i | −0.992826 | − | 0.119570i | \(-0.961848\pi\) |
0.599963 | + | 0.800027i | \(0.295182\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.50000 | − | 0.866025i | 0.0847850 | − | 0.0489506i | −0.457008 | − | 0.889463i | \(-0.651079\pi\) |
0.541793 | + | 0.840512i | \(0.317746\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.59808 | + | 13.5000i | −0.146385 | + | 0.760639i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.9904 | + | 7.50000i | −0.729612 | + | 0.421242i | −0.818280 | − | 0.574819i | \(-0.805072\pi\) |
0.0886679 | + | 0.996061i | \(0.471739\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.50000 | − | 7.79423i | 0.251952 | − | 0.436393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 5.19615i | − | 0.290021i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000 | + | 3.46410i | 0.332820 | + | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.73205 | − | 3.00000i | −0.0957826 | − | 0.165900i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.8564 | + | 12.0000i | 0.763928 | + | 0.661581i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | − | 6.92820i | −0.219860 | − | 0.380808i | 0.734905 | − | 0.678170i | \(-0.237227\pi\) |
−0.954765 | + | 0.297361i | \(0.903893\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.00000 | − | 5.19615i | 0.164399 | − | 0.284747i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.46410 | −0.189264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.0000 | 0.708155 | 0.354078 | − | 0.935216i | \(-0.384795\pi\) | ||||
0.354078 | + | 0.935216i | \(0.384795\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.0000 | + | 10.3923i | 0.977626 | + | 0.564433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.59808 | − | 4.50000i | −0.140694 | − | 0.243689i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.5885 | + | 9.00000i | −0.839254 | + | 0.484544i | ||||
\(346\) | 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 | ||||||||
\(349\) | 10.3923i | 0.556287i | 0.960539 | + | 0.278144i | \(0.0897191\pi\) | ||||
−0.960539 | + | 0.278144i | \(0.910281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 18.0000i | − | 0.960769i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.3205 | − | 30.0000i | 0.921878 | − | 1.59674i | 0.125370 | − | 0.992110i | \(-0.459988\pi\) |
0.796507 | − | 0.604629i | \(-0.206679\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.0000 | − | 10.3923i | 0.955341 | − | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.0000 | − | 10.3923i | −0.635107 | − | 0.550019i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.19615 | + | 3.00000i | −0.274242 | + | 0.158334i | −0.630814 | − | 0.775934i | \(-0.717279\pi\) |
0.356572 | + | 0.934268i | \(0.383946\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.50000 | + | 6.06218i | −0.184211 | + | 0.319062i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.46410 | −0.181818 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 12.0000i | − | 0.628109i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.5000 | + | 11.2583i | 1.01789 | + | 0.587680i | 0.913493 | − | 0.406855i | \(-0.133375\pi\) |
0.104399 | + | 0.994535i | \(0.466708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.3923 | + | 18.0000i | 0.541002 | + | 0.937043i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.3827 | + | 4.50000i | 1.21397 | + | 0.233628i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.0000 | − | 27.7128i | −0.828449 | − | 1.43492i | −0.899255 | − | 0.437425i | \(-0.855891\pi\) |
0.0708063 | − | 0.997490i | \(-0.477443\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.5000 | + | 18.1865i | −0.542218 | + | 0.939149i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.3923 | −0.535231 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.52628 | + | 16.5000i | −0.488046 | + | 0.845321i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.73205 | + | 3.00000i | 0.0885037 | + | 0.153293i | 0.906879 | − | 0.421392i | \(-0.138458\pi\) |
−0.818375 | + | 0.574684i | \(0.805125\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.50000 | + | 12.9904i | 0.229341 | + | 0.662051i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.0000 | − | 20.7846i | −0.609994 | − | 1.05654i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.5885 | + | 9.00000i | 0.790366 | + | 0.456318i | 0.840091 | − | 0.542445i | \(-0.182501\pi\) |
−0.0497253 | + | 0.998763i | \(0.515835\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 20.7846i | − | 1.05112i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.00000 | −0.453990 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.866025 | + | 1.50000i | −0.0435745 | + | 0.0754732i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.0000 | + | 13.8564i | −1.20453 | + | 0.695433i | −0.961558 | − | 0.274601i | \(-0.911454\pi\) |
−0.242967 | + | 0.970034i | \(0.578121\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.19615 | + | 15.0000i | 0.260133 | + | 0.750939i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.3923 | + | 6.00000i | −0.518967 | + | 0.299626i | −0.736512 | − | 0.676425i | \(-0.763528\pi\) |
0.217545 | + | 0.976050i | \(0.430195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.00000 | + | 5.19615i | −0.149441 | + | 0.258839i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.5885 | 0.774597 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6.00000i | − | 0.297409i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.50000 | + | 4.33013i | 0.370851 | + | 0.214111i | 0.673830 | − | 0.738886i | \(-0.264648\pi\) |
−0.302979 | + | 0.952997i | \(0.597981\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −27.0000 | + | 15.5885i | −1.33181 | + | 0.768922i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.866025 | + | 4.50000i | −0.0426143 | + | 0.221431i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.50000 | + | 12.9904i | 0.368161 | + | 0.637673i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.9808 | − | 15.0000i | −1.27228 | − | 0.734553i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.2487 | 1.18463 | 0.592314 | − | 0.805708i | \(-0.298215\pi\) | ||||
0.592314 | + | 0.805708i | \(0.298215\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.0000 | 1.55958 | 0.779792 | − | 0.626038i | \(-0.215325\pi\) | ||||
0.779792 | + | 0.626038i | \(0.215325\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.3923 | − | 18.0000i | 0.505291 | − | 0.875190i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.46410 | − | 6.00000i | −0.168034 | − | 0.291043i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.00000 | − | 15.5885i | −0.434524 | − | 0.752618i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.7846 | − | 12.0000i | −1.00116 | − | 0.578020i | −0.0925683 | − | 0.995706i | \(-0.529508\pi\) |
−0.908591 | + | 0.417687i | \(0.862841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.6410i | 1.66474i | 0.554220 | + | 0.832370i | \(0.313017\pi\) | ||||
−0.554220 | + | 0.832370i | \(0.686983\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 9.00000i | − | 0.431517i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.3923 | + | 18.0000i | −0.497131 | + | 0.861057i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.5000 | + | 18.1865i | −1.50341 | + | 0.867996i | −0.503421 | + | 0.864041i | \(0.667925\pi\) |
−0.999992 | + | 0.00395451i | \(0.998741\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.5000 | − | 7.79423i | −0.928571 | − | 0.371154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.79423 | + | 4.50000i | −0.370315 | + | 0.213801i | −0.673596 | − | 0.739100i | \(-0.735251\pi\) |
0.303281 | + | 0.952901i | \(0.401918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.00000 | − | 15.5885i | 0.426641 | − | 0.738964i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 31.1769i | − | 1.47462i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 30.0000i | − | 1.41579i | −0.706319 | − | 0.707894i | \(-0.749646\pi\) | ||
0.706319 | − | 0.707894i | \(-0.250354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.0000 | + | 10.3923i | 0.847587 | + | 0.489355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.06218 | − | 10.5000i | −0.284826 | − | 0.493333i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.3923 | − | 12.0000i | 0.487199 | − | 0.562569i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.50000 | + | 4.33013i | 0.116945 | + | 0.202555i | 0.918556 | − | 0.395292i | \(-0.129357\pi\) |
−0.801611 | + | 0.597847i | \(0.796023\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.00000 | + | 15.5885i | −0.420084 | + | 0.727607i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8564 | 0.645357 | 0.322679 | − | 0.946509i | \(-0.395417\pi\) | ||||
0.322679 | + | 0.946509i | \(0.395417\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | 0.185896 | 0.0929479 | − | 0.995671i | \(-0.470371\pi\) | ||||
0.0929479 | + | 0.995671i | \(0.470371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.50000 | − | 2.59808i | −0.208683 | − | 0.120483i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.5885 | − | 27.0000i | −0.721348 | − | 1.24941i | −0.960460 | − | 0.278419i | \(-0.910190\pi\) |
0.239112 | − | 0.970992i | \(-0.423144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.00000 | − | 5.19615i | 0.0461757 | − | 0.239936i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −31.1769 | + | 18.0000i | −1.43656 | + | 0.829396i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.7846 | − | 12.0000i | −0.955677 | − | 0.551761i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.92820i | 0.317888i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 27.0000i | − | 1.23625i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.46410 | + | 6.00000i | −0.158279 | + | 0.274147i | −0.934248 | − | 0.356624i | \(-0.883928\pi\) |
0.775969 | + | 0.630771i | \(0.217261\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | + | 3.46410i | −0.273576 | + | 0.157949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.00000 | − | 25.9808i | −0.409514 | − | 1.18217i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.79423 | − | 4.50000i | 0.353918 | − | 0.204334i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.500000 | − | 0.866025i | 0.0226572 | − | 0.0392434i | −0.854475 | − | 0.519493i | \(-0.826121\pi\) |
0.877132 | + | 0.480250i | \(0.159454\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.2487 | 1.09656 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 33.0000i | − | 1.48927i | −0.667472 | − | 0.744635i | \(-0.732624\pi\) | ||
0.667472 | − | 0.744635i | \(-0.267376\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | + | 5.19615i | 0.405340 | + | 0.234023i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.5000 | − | 7.79423i | 0.606780 | − | 0.350325i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.3923 | + | 30.0000i | 0.466159 | + | 1.34568i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.0000 | + | 19.0526i | 0.492428 | + | 0.852910i | 0.999962 | − | 0.00872186i | \(-0.00277629\pi\) |
−0.507534 | + | 0.861632i | \(0.669443\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.0000 | + | 25.9808i | −0.670151 | + | 1.16073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.1051 | 1.69902 | 0.849512 | − | 0.527570i | \(-0.176897\pi\) | ||||
0.849512 | + | 0.527570i | \(0.176897\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.866025 | − | 1.50000i | 0.0384615 | − | 0.0666173i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.52628 | − | 16.5000i | −0.422245 | − | 0.731350i | 0.573914 | − | 0.818916i | \(-0.305424\pi\) |
−0.996159 | + | 0.0875661i | \(0.972091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0000 | + | 3.46410i | 0.796273 | + | 0.153243i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.5885 | − | 9.00000i | 0.688247 | − | 0.397360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.19615 | − | 3.00000i | −0.228970 | − | 0.132196i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 20.7846i | − | 0.914106i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.8564 | − | 24.0000i | 0.607060 | − | 1.05146i | −0.384662 | − | 0.923057i | \(-0.625682\pi\) |
0.991722 | − | 0.128402i | \(-0.0409847\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.0000 | − | 19.0526i | 1.44299 | − | 0.833110i | 0.444941 | − | 0.895560i | \(-0.353225\pi\) |
0.998048 | + | 0.0624496i | \(0.0198913\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.92820 | − | 6.00000i | −0.302372 | − | 0.261861i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.19615 | − | 3.00000i | 0.226348 | − | 0.130682i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | − | 11.2583i | 0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.19615 | 0.225494 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 24.0000i | − | 1.03956i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.50000 | − | 2.59808i | −0.194552 | − | 0.112325i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.0000 | − | 10.3923i | 0.776757 | − | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.7846 | + | 3.00000i | −0.895257 | + | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | + | 13.8564i | 0.343947 | + | 0.595733i | 0.985162 | − | 0.171628i | \(-0.0549027\pi\) |
−0.641215 | + | 0.767361i | \(0.721569\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3923 | + | 6.00000i | 0.445976 | + | 0.257485i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.46410 | −0.148386 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.00000 | −0.0855138 | −0.0427569 | − | 0.999086i | \(-0.513614\pi\) | ||||
−0.0427569 | + | 0.999086i | \(0.513614\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.19615 | − | 9.00000i | −0.221364 | − | 0.383413i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.00000 | − | 1.73205i | −0.0850487 | − | 0.0736543i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.00000 | − | 5.19615i | −0.127343 | − | 0.220564i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.59808 | + | 1.50000i | 0.110084 | + | 0.0635570i | 0.554031 | − | 0.832496i | \(-0.313089\pi\) |
−0.443947 | + | 0.896053i | \(0.646422\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.7128i | 1.17213i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.0000i | 0.759961i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.9904 | + | 22.5000i | −0.547479 | + | 0.948262i | 0.450967 | + | 0.892541i | \(0.351079\pi\) |
−0.998446 | + | 0.0557214i | \(0.982254\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.0000 | − | 10.3923i | 0.757266 | − | 0.437208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.50000 | + | 23.3827i | −0.188982 | + | 0.981981i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.19615 | + | 3.00000i | −0.217834 | + | 0.125767i | −0.604947 | − | 0.796266i | \(-0.706806\pi\) |
0.387113 | + | 0.922032i | \(0.373472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0000 | − | 27.7128i | 0.669579 | − | 1.15975i | −0.308443 | − | 0.951243i | \(-0.599808\pi\) |
0.978022 | − | 0.208502i | \(-0.0668588\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 12.0000i | − | 0.500435i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.50000 | − | 0.866025i | −0.0624458 | − | 0.0360531i | 0.468452 | − | 0.883489i | \(-0.344812\pi\) |
−0.530898 | + | 0.847436i | \(0.678145\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.9186 | − | 34.5000i | −0.827788 | − | 1.43377i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.6506 | + | 7.50000i | −0.898220 | + | 0.311152i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.5000 | − | 23.3827i | −0.559113 | − | 0.968412i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.5885 | − | 9.00000i | −0.644503 | − | 0.372104i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.5885 | −0.643404 | −0.321702 | − | 0.946841i | \(-0.604255\pi\) | ||||
−0.321702 | + | 0.946841i | \(0.604255\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.00000 | −0.247226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.0000 | − | 15.5885i | −1.11063 | − | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.0526 | + | 33.0000i | 0.782395 | + | 1.35515i | 0.930543 | + | 0.366182i | \(0.119335\pi\) |
−0.148148 | + | 0.988965i | \(0.547331\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.0000 | + | 5.19615i | −0.614940 | + | 0.213021i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.5885 | + | 9.00000i | −0.637993 | + | 0.368345i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.9808 | + | 15.0000i | 1.06155 | + | 0.612883i | 0.925859 | − | 0.377869i | \(-0.123343\pi\) |
0.135686 | + | 0.990752i | \(0.456676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 29.4449i | − | 1.20108i | −0.799594 | − | 0.600541i | \(-0.794952\pi\) | ||
0.799594 | − | 0.600541i | \(-0.205048\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.00000 | −0.244339 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.73205 | + | 3.00000i | −0.0704179 | + | 0.121967i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.5000 | + | 11.2583i | −0.791481 | + | 0.456962i | −0.840484 | − | 0.541837i | \(-0.817729\pi\) |
0.0490029 | + | 0.998799i | \(0.484396\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.5000 | + | 2.59808i | 0.547048 | + | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.7846 | + | 12.0000i | −0.840855 | + | 0.485468i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00000 | + | 1.73205i | −0.0403896 | + | 0.0699569i | −0.885514 | − | 0.464614i | \(-0.846193\pi\) |
0.845124 | + | 0.534570i | \(0.179527\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20.7846 | 0.838116 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.0000i | − | 0.483102i | −0.970388 | − | 0.241551i | \(-0.922344\pi\) | ||
0.970388 | − | 0.241551i | \(-0.0776561\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.00000 | − | 3.46410i | −0.241160 | − | 0.139234i | 0.374550 | − | 0.927207i | \(-0.377797\pi\) |
−0.615710 | + | 0.787973i | \(0.711131\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.0000 | + | 15.5885i | −1.08347 | + | 0.625543i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.7846 | + | 18.0000i | 0.832718 | + | 0.721155i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.00000 | − | 15.5885i | 0.359425 | − | 0.622543i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.92820 | 0.276246 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.0000 | 1.23409 | 0.617045 | − | 0.786928i | \(-0.288330\pi\) | ||||
0.617045 | + | 0.786928i | \(0.288330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.46410 | + | 6.00000i | −0.137686 | + | 0.238479i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.52628 | + | 16.5000i | 0.378039 | + | 0.654783i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.0000 | + | 19.0526i | 0.594322 | + | 0.754890i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 31.1769 | − | 18.0000i | 1.23334 | − | 0.712069i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.7846 | − | 12.0000i | −0.820943 | − | 0.473972i | 0.0297987 | − | 0.999556i | \(-0.490513\pi\) |
−0.850741 | + | 0.525584i | \(0.823847\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.3205i | 0.683054i | 0.939872 | + | 0.341527i | \(0.110944\pi\) | ||||
−0.939872 | + | 0.341527i | \(0.889056\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.0000 | −0.944999 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.50000 | − | 2.59808i | 0.176640 | − | 0.101983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.19615 | − | 6.00000i | 0.203653 | − | 0.235159i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.59808 | + | 1.50000i | −0.101671 | + | 0.0586995i | −0.549973 | − | 0.835182i | \(-0.685362\pi\) |
0.448303 | + | 0.893882i | \(0.352029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.50000 | + | 7.79423i | −0.175830 | + | 0.304546i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 20.7846i | − | 0.810885i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 12.0000i | − | 0.467454i | −0.972302 | − | 0.233727i | \(-0.924908\pi\) | ||
0.972302 | − | 0.233727i | \(-0.0750921\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.00000 | − | 3.46410i | −0.233373 | − | 0.134738i | 0.378754 | − | 0.925497i | \(-0.376353\pi\) |
−0.612127 | + | 0.790759i | \(0.709686\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.0000 | − | 10.3923i | 0.699062 | − | 0.403604i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.5885 | + | 3.00000i | 0.604494 | + | 0.116335i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | + | 15.5885i | 0.348481 | + | 0.603587i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 38.9711 | + | 22.5000i | 1.50671 | + | 0.869900i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.0000 | −1.58043 | −0.790217 | − | 0.612827i | \(-0.790032\pi\) | ||||
−0.790217 | + | 0.612827i | \(0.790032\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.19615 | + | 9.00000i | −0.200000 | + | 0.346410i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.59808 | + | 4.50000i | 0.0998522 | + | 0.172949i | 0.911623 | − | 0.411027i | \(-0.134830\pi\) |
−0.811771 | + | 0.583976i | \(0.801496\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.50000 | + | 12.9904i | 0.172694 | + | 0.498525i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.50000 | − | 7.79423i | −0.172440 | − | 0.298675i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.1865 | − | 10.5000i | −0.695888 | − | 0.401771i | 0.109926 | − | 0.993940i | \(-0.464939\pi\) |
−0.805814 | + | 0.592168i | \(0.798272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.1769i | 1.19121i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.0000i | 0.915657i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.5885 | + | 27.0000i | −0.593873 | + | 1.02862i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.00000 | − | 3.46410i | 0.228251 | − | 0.131781i | −0.381514 | − | 0.924363i | \(-0.624597\pi\) |
0.609765 | + | 0.792582i | \(0.291264\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.79423 | + | 22.5000i | 0.296078 | + | 0.854704i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.9808 | + | 15.0000i | −0.985506 | + | 0.568982i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.0000 | + | 20.7846i | −0.454532 | + | 0.787273i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.1769i | 1.17922i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 3.00000i | − | 0.113308i | −0.998394 | − | 0.0566542i | \(-0.981957\pi\) | ||
0.998394 | − | 0.0566542i | \(-0.0180433\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00000 | − | 3.46410i | −0.226294 | − | 0.130651i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.3923 | − | 18.0000i | −0.391397 | − | 0.677919i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.0000 | + | 32.9090i | 0.713560 | + | 1.23592i | 0.963512 | + | 0.267664i | \(0.0862517\pi\) |
−0.249952 | + | 0.968258i | \(0.580415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.50000 | + | 2.59808i | −0.0562544 | + | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.3923 | 0.389195 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0000 | −0.673162 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.00000 | − | 5.19615i | −0.336111 | − | 0.194054i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.5167 | + | 39.0000i | 0.839730 | + | 1.45445i | 0.890121 | + | 0.455725i | \(0.150620\pi\) |
−0.0503909 | + | 0.998730i | \(0.516047\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | − | 6.92820i | 0.223452 | − | 0.258020i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −38.9711 | + | 22.5000i | −1.44935 | + | 0.836784i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.19615 | + | 3.00000i | 0.192980 | + | 0.111417i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 29.4449i | − | 1.09205i | −0.837769 | − | 0.546025i | \(-0.816140\pi\) | ||
0.837769 | − | 0.546025i | \(-0.183860\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.8564 | − | 24.0000i | 0.512498 | − | 0.887672i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.0000 | − | 17.3205i | 1.10808 | − | 0.639748i | 0.169745 | − | 0.985488i | \(-0.445706\pi\) |
0.938330 | + | 0.345740i | \(0.112372\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.5000 | + | 12.9904i | −0.608612 | + | 0.479157i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.19615 | + | 3.00000i | −0.191403 | + | 0.110506i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.00000 | + | 8.66025i | −0.183928 | + | 0.318573i | −0.943215 | − | 0.332184i | \(-0.892215\pi\) |
0.759287 | + | 0.650756i | \(0.225548\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.7846 | −0.763542 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.0000i | 0.660356i | 0.943919 | + | 0.330178i | \(0.107109\pi\) | ||||
−0.943919 | + | 0.330178i | \(0.892891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.0000 | − | 15.5885i | −0.989203 | − | 0.571117i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.9904 | + | 22.5000i | 0.475293 | + | 0.823232i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.19615 | − | 6.00000i | 0.189863 | − | 0.219235i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.50000 | − | 9.52628i | −0.200698 | − | 0.347619i | 0.748056 | − | 0.663636i | \(-0.230988\pi\) |
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.5000 | − | 28.5788i | 0.601293 | − | 1.04147i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.1244 | −0.441250 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.00000 | 0.145382 | 0.0726912 | − | 0.997354i | \(-0.476841\pi\) | ||||
0.0726912 | + | 0.997354i | \(0.476841\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.5885 | + | 27.0000i | −0.565825 | + | 0.980038i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.66025 | + | 15.0000i | 0.313934 | + | 0.543750i | 0.979210 | − | 0.202848i | \(-0.0650196\pi\) |
−0.665276 | + | 0.746597i | \(0.731686\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.00000 | − | 5.19615i | 0.0362024 | − | 0.188113i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.00000 | + | 15.5885i | 0.325396 | + | 0.563602i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.19615 | − | 3.00000i | −0.187622 | − | 0.108324i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.0526i | 0.687053i | 0.939143 | + | 0.343526i | \(0.111621\pi\) | ||||
−0.939143 | + | 0.343526i | \(0.888379\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.8564 | + | 24.0000i | −0.498380 | + | 0.863220i | −0.999998 | − | 0.00186926i | \(-0.999405\pi\) |
0.501618 | + | 0.865089i | \(0.332738\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.00000 | − | 1.73205i | 0.107763 | − | 0.0622171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.66025 | − | 3.00000i | 0.310685 | − | 0.107624i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.7846 | − | 12.0000i | 0.744686 | − | 0.429945i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | − | 31.1769i | 0.644091 | − | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 15.5885i | − | 0.557086i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.0000i | 1.28490i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.0000 | − | 20.7846i | −1.28326 | − | 0.740891i | −0.305818 | − | 0.952090i | \(-0.598930\pi\) |
−0.977443 | + | 0.211199i | \(0.932263\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.3923 | + | 30.0000i | 0.369508 | + | 1.06668i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −23.3827 | − | 13.5000i | −0.829298 | − | 0.478796i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.9808 | 0.920286 | 0.460143 | − | 0.887845i | \(-0.347798\pi\) | ||||
0.460143 | + | 0.887845i | \(0.347798\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.5885 | − | 27.0000i | 0.550791 | − | 0.953998i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.3923 | − | 18.0000i | −0.366736 | − | 0.635206i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.0000 | − | 5.19615i | −0.951625 | − | 0.183140i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.5000 | + | 44.1673i | 0.897643 | + | 1.55476i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.1769i | − | 1.09477i | −0.836881 | − | 0.547385i | \(-0.815623\pi\) | ||
0.836881 | − | 0.547385i | \(-0.184377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.00000i | 0.315644i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.1244 | − | 21.0000i | 0.424698 | − | 0.735598i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.0000 | + | 13.8564i | −0.839654 | + | 0.484774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.0000 | − | 20.7846i | 0.628971 | − | 0.726273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.59808 | − | 1.50000i | 0.0906735 | − | 0.0523504i | −0.453978 | − | 0.891013i | \(-0.649995\pi\) |
0.544651 | + | 0.838663i | \(0.316662\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.00000 | − | 6.92820i | 0.139431 | − | 0.241502i | −0.787850 | − | 0.615867i | \(-0.788806\pi\) |
0.927281 | + | 0.374365i | \(0.122139\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.3923i | 0.361814i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.00000i | 0.312961i | 0.987681 | + | 0.156480i | \(0.0500148\pi\) | ||||
−0.987681 | + | 0.156480i | \(0.949985\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.0000 | − | 8.66025i | −0.520972 | − | 0.300783i | 0.216361 | − | 0.976314i | \(-0.430581\pi\) |
−0.737332 | + | 0.675530i | \(0.763915\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.92820 | + | 12.0000i | 0.240337 | + | 0.416275i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.46410 | − | 24.0000i | −0.120024 | − | 0.831551i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.0000 | + | 25.9808i | 0.519096 | + | 0.899101i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.79423 | − | 4.50000i | −0.269408 | − | 0.155543i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.46410 | 0.119594 | 0.0597970 | − | 0.998211i | \(-0.480955\pi\) | ||||
0.0597970 | + | 0.998211i | \(0.480955\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 45.0000 | + | 25.9808i | 1.54988 | + | 0.894825i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.866025 | − | 1.50000i | −0.0297922 | − | 0.0516016i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.00000 | − | 3.46410i | −0.137442 | − | 0.119028i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −41.5692 | + | 24.0000i | −1.42665 | + | 0.823678i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.3923 | + | 6.00000i | 0.356244 | + | 0.205677i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 24.2487i | − | 0.830260i | −0.909762 | − | 0.415130i | \(-0.863736\pi\) | ||
0.909762 | − | 0.415130i | \(-0.136264\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 18.0000i | − | 0.615587i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.92820 | − | 12.0000i | 0.236663 | − | 0.409912i | −0.723092 | − | 0.690752i | \(-0.757280\pi\) |
0.959755 | + | 0.280840i | \(0.0906130\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.0000 | − | 10.3923i | 0.614152 | − | 0.354581i | −0.160437 | − | 0.987046i | \(-0.551290\pi\) |
0.774589 | + | 0.632465i | \(0.217957\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.00000 | + | 31.1769i | −0.204479 | + | 1.06251i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.7654 | − | 27.0000i | 1.59191 | − | 0.919091i | 0.598933 | − | 0.800799i | \(-0.295592\pi\) |
0.992979 | − | 0.118291i | \(-0.0377417\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.66025 | 0.294118 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.00000i | 0.101768i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.00000 | + | 3.46410i | 0.203302 | + | 0.117377i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.5000 | − | 7.79423i | 0.456906 | − | 0.263795i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.3109 | + | 10.5000i | −1.02470 | + | 0.354965i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.0000 | − | 38.1051i | −0.742887 | − | 1.28672i | −0.951175 | − | 0.308651i | \(-0.900123\pi\) |
0.208288 | − | 0.978068i | \(-0.433211\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.5000 | − | 28.5788i | 0.556531 | − | 0.963940i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.3923 | −0.350126 | −0.175063 | − | 0.984557i | \(-0.556013\pi\) | ||||
−0.175063 | + | 0.984557i | \(0.556013\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.0000 | −1.74994 | −0.874970 | − | 0.484178i | \(-0.839119\pi\) | ||||
−0.874970 | + | 0.484178i | \(0.839119\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.59808 | − | 4.50000i | 0.0873334 | − | 0.151266i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.1244 | − | 21.0000i | −0.407096 | − | 0.705111i | 0.587467 | − | 0.809248i | \(-0.300125\pi\) |
−0.994563 | + | 0.104137i | \(0.966792\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.5000 | + | 9.52628i | −0.922320 | + | 0.319501i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.3827 | − | 13.5000i | 0.783349 | − | 0.452267i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.7846 | − | 12.0000i | −0.695530 | − | 0.401565i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 20.7846i | − | 0.694753i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 36.0000 | 1.20201 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.59808 | + | 4.50000i | −0.0866507 | + | 0.150083i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.0000 | − | 15.5885i | 0.899500 | − | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.92820 | − | 36.0000i | 0.230556 | − | 1.19800i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.3923 | − | 6.00000i | 0.345452 | − | 0.199447i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.0000 | + | 22.5167i | −0.431658 | + | 0.747653i | −0.997016 | − | 0.0771920i | \(-0.975405\pi\) |
0.565358 | + | 0.824845i | \(0.308738\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.5000 | + | 12.9904i | 0.744641 | + | 0.429919i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.3923 | − | 9.00000i | −0.343184 | − | 0.297206i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.0000 | − | 17.3205i | −0.329870 | − | 0.571351i | 0.652616 | − | 0.757689i | \(-0.273671\pi\) |
−0.982486 | + | 0.186338i | \(0.940338\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 36.3731 | + | 21.0000i | 1.19853 | + | 0.691974i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −41.5692 | −1.36827 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | 0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.00000 | − | 5.19615i | −0.295599 | − | 0.170664i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.2487 | − | 42.0000i | −0.795574 | − | 1.37798i | −0.922474 | − | 0.386060i | \(-0.873836\pi\) |
0.126899 | − | 0.991916i | \(-0.459497\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.00000 | + | 22.5167i | −0.294963 | + | 0.737954i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.0000 | + | 20.7846i | 0.392862 | + | 0.680458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.5885 | + | 9.00000i | 0.509797 | + | 0.294331i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.5167i | 0.735587i | 0.929907 | + | 0.367794i | \(0.119887\pi\) | ||||
−0.929907 | + | 0.367794i | \(0.880113\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 3.00000i | − | 0.0979013i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.4545 | − | 28.5000i | 0.536401 | − | 0.929073i | −0.462693 | − | 0.886518i | \(-0.653117\pi\) |
0.999094 | − | 0.0425550i | \(-0.0135498\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.0000 | + | 20.7846i | −1.17232 | + | 0.676840i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.0000 | + | 15.5885i | 0.585540 | + | 0.507093i | ||||
\(946\) | 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 | ||||||||
\(949\) | −12.0000 | + | 20.7846i | −0.389536 | + | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.9808i | 0.842484i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.79423 | − | 13.5000i | −0.251952 | − | 0.436393i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46.7654 | − | 9.00000i | −1.51013 | − | 0.290625i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.79423 | − | 4.50000i | −0.251166 | − | 0.145010i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −39.8372 | −1.28240 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.00000 | 0.225105 | 0.112552 | − | 0.993646i | \(-0.464097\pi\) | ||||
0.112552 | + | 0.993646i | \(0.464097\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.0000 | + | 10.3923i | 0.578243 | + | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.33013 | + | 7.50000i | 0.138960 | + | 0.240686i | 0.927103 | − | 0.374806i | \(-0.122291\pi\) |
−0.788143 | + | 0.615492i | \(0.788957\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.0000 | − | 43.3013i | −0.480878 | − | 1.38817i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.3923 | − | 6.00000i | 0.332820 | − | 0.192154i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.7846 | + | 12.0000i | 0.664959 | + | 0.383914i | 0.794164 | − | 0.607704i | \(-0.207909\pi\) |
−0.129205 | + | 0.991618i | \(0.541243\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 31.1769i | − | 0.996419i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.00000 | −0.191565 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.92820 | − | 12.0000i | 0.220975 | − | 0.382741i | −0.734129 | − | 0.679010i | \(-0.762409\pi\) |
0.955104 | + | 0.296269i | \(0.0957426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.0000 | + | 15.5885i | −0.860292 | + | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 30.0000 | − | 10.3923i | 0.954911 | − | 0.330791i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 41.5692 | − | 24.0000i | 1.32182 | − | 0.763156i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.5000 | + | 40.7032i | −0.746502 | + | 1.29298i | 0.202988 | + | 0.979181i | \(0.434935\pi\) |
−0.949490 | + | 0.313798i | \(0.898398\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.8564 | −0.439720 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.0000i | 0.570638i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.0000 | + | 8.66025i | 0.475055 | + | 0.274273i | 0.718353 | − | 0.695678i | \(-0.244896\pi\) |
−0.243299 | + | 0.969951i | \(0.578229\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.19615 | − | 9.00000i | −0.164399 | − | 0.284747i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))