Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(109,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("405.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.j (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: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 379.2 | ||
Root | \(1.93649 + 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.379 |
Dual form | 405.2.j.c.109.2 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.93649 | + | 1.11803i | 1.36931 | + | 0.790569i | 0.990839 | − | 0.135045i | \(-0.0431180\pi\) |
0.378467 | + | 0.925615i | \(0.376451\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.50000 | + | 2.59808i | 0.750000 | + | 1.29904i | ||||
\(5\) | 1.93649 | − | 1.11803i | 0.866025 | − | 0.500000i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(8\) | 2.23607i | 0.790569i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.00000 | 1.58114 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 4.47214i | 1.08465i | 0.840168 | + | 0.542326i | \(0.182456\pi\) | ||||
−0.840168 | + | 0.542326i | \(0.817544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 5.80948 | + | 3.35410i | 1.29904 | + | 0.750000i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.74597 | + | 4.47214i | −1.61515 | + | 0.932505i | −0.626994 | + | 0.779024i | \(0.715715\pi\) |
−0.988152 | + | 0.153481i | \(0.950952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | − | 6.92820i | −0.718421 | − | 1.24434i | −0.961625 | − | 0.274367i | \(-0.911532\pi\) |
0.243204 | − | 0.969975i | \(-0.421802\pi\) | |||||||
\(32\) | 5.80948 | − | 3.35410i | 1.02698 | − | 0.592927i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.00000 | + | 8.66025i | −0.857493 | + | 1.48522i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | −7.74597 | − | 4.47214i | −1.25656 | − | 0.725476i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.50000 | + | 4.33013i | 0.395285 | + | 0.684653i | ||||
\(41\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −20.0000 | −2.94884 | ||||||||
\(47\) | 7.74597 | + | 4.47214i | 1.12987 | + | 0.652328i | 0.943901 | − | 0.330228i | \(-0.107126\pi\) |
0.185964 | + | 0.982556i | \(0.440459\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.50000 | − | 6.06218i | −0.500000 | − | 0.866025i | ||||
\(50\) | 9.68246 | − | 5.59017i | 1.36931 | − | 0.790569i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.47214i | 0.614295i | 0.951662 | + | 0.307148i | \(0.0993745\pi\) | ||||
−0.951662 | + | 0.307148i | \(0.900625\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | + | 1.73205i | −0.128037 | + | 0.221766i | −0.922916 | − | 0.385002i | \(-0.874201\pi\) |
0.794879 | + | 0.606768i | \(0.207534\pi\) | |||||||
\(62\) | − | 17.8885i | − | 2.27185i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000 | 1.62500 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | −11.6190 | + | 6.70820i | −1.40900 | + | 0.813489i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.00000 | − | 10.3923i | −0.688247 | − | 1.19208i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | − | 13.8564i | 0.900070 | − | 1.55897i | 0.0726692 | − | 0.997356i | \(-0.476848\pi\) |
0.827401 | − | 0.561611i | \(-0.189818\pi\) | |||||||
\(80\) | − | 2.23607i | − | 0.250000i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.4919 | − | 8.94427i | −1.70046 | − | 0.981761i | −0.945289 | − | 0.326234i | \(-0.894220\pi\) |
−0.755172 | − | 0.655527i | \(-0.772447\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.00000 | + | 8.66025i | 0.542326 | + | 0.939336i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −23.2379 | − | 13.4164i | −2.42272 | − | 1.39876i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.0000 | + | 17.3205i | 1.03142 | + | 1.78647i | ||||
\(95\) | −7.74597 | + | 4.47214i | −0.794719 | + | 0.458831i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(98\) | − | 15.6525i | − | 1.58114i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 15.0000 | 1.50000 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.00000 | + | 8.66025i | −0.485643 | + | 0.841158i | ||||
\(107\) | 17.8885i | 1.72935i | 0.502331 | + | 0.864675i | \(0.332476\pi\) | ||||
−0.502331 | + | 0.864675i | \(0.667524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.87298 | − | 2.23607i | 0.364340 | − | 0.210352i | −0.306643 | − | 0.951825i | \(-0.599206\pi\) |
0.670983 | + | 0.741473i | \(0.265872\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.0000 | + | 17.3205i | −0.932505 | + | 1.61515i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | −3.87298 | + | 2.23607i | −0.350643 | + | 0.202444i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.0000 | − | 20.7846i | 1.07763 | − | 1.86651i | ||||
\(125\) | − | 11.1803i | − | 1.00000i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 13.5554 | + | 7.82624i | 1.19814 | + | 0.691748i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.0000 | −0.857493 | ||||||||
\(137\) | 19.3649 | + | 11.1803i | 1.65446 | + | 0.955201i | 0.975207 | + | 0.221293i | \(0.0710278\pi\) |
0.679249 | + | 0.733908i | \(0.262306\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | + | 3.46410i | 0.169638 | + | 0.293821i | 0.938293 | − | 0.345843i | \(-0.112407\pi\) |
−0.768655 | + | 0.639664i | \(0.779074\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | + | 6.92820i | −0.325515 | + | 0.563809i | −0.981617 | − | 0.190864i | \(-0.938871\pi\) |
0.656101 | + | 0.754673i | \(0.272204\pi\) | |||||||
\(152\) | − | 8.94427i | − | 0.725476i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.4919 | − | 8.94427i | −1.24434 | − | 0.718421i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(158\) | 30.9839 | − | 17.8885i | 2.46494 | − | 1.42314i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.50000 | − | 12.9904i | 0.592927 | − | 1.02698i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −20.0000 | − | 34.6410i | −1.55230 | − | 2.68866i | ||||
\(167\) | −7.74597 | + | 4.47214i | −0.599401 | + | 0.346064i | −0.768806 | − | 0.639482i | \(-0.779149\pi\) |
0.169405 | + | 0.985547i | \(0.445815\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.50000 | + | 11.2583i | −0.500000 | + | 0.866025i | ||||
\(170\) | 22.3607i | 1.71499i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.3649 | + | 11.1803i | 1.47229 | + | 0.850026i | 0.999514 | − | 0.0311588i | \(-0.00991976\pi\) |
0.472773 | + | 0.881184i | \(0.343253\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.0000 | − | 17.3205i | −0.737210 | − | 1.27688i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 26.8328i | 1.95698i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20.0000 | −1.45095 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.5000 | − | 18.1865i | 0.750000 | − | 1.29904i | ||||
\(197\) | 4.47214i | 0.318626i | 0.987228 | + | 0.159313i | \(0.0509280\pi\) | ||||
−0.987228 | + | 0.159313i | \(0.949072\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 9.68246 | + | 5.59017i | 0.684653 | + | 0.395285i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0000 | + | 24.2487i | 0.963800 | + | 1.66935i | 0.712806 | + | 0.701361i | \(0.247424\pi\) |
0.250994 | + | 0.967989i | \(0.419243\pi\) | |||||||
\(212\) | −11.6190 | + | 6.70820i | −0.797993 | + | 0.460721i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −20.0000 | + | 34.6410i | −1.36717 | + | 2.36801i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 27.1109 | + | 15.6525i | 1.83618 | + | 1.06012i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.0000 | 0.665190 | ||||||||
\(227\) | −15.4919 | − | 8.94427i | −1.02824 | − | 0.593652i | −0.111757 | − | 0.993736i | \(-0.535648\pi\) |
−0.916479 | + | 0.400083i | \(0.868981\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.0000 | − | 22.5167i | −0.859064 | − | 1.48794i | −0.872823 | − | 0.488037i | \(-0.837713\pi\) |
0.0137585 | − | 0.999905i | \(-0.495620\pi\) | |||||||
\(230\) | −38.7298 | + | 22.3607i | −2.55377 | + | 1.47442i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 22.3607i | − | 1.46490i | −0.680823 | − | 0.732448i | \(-0.738378\pi\) | ||
0.680823 | − | 0.732448i | \(-0.261622\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.0000 | 1.30466 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | + | 1.73205i | −0.0644157 | + | 0.111571i | −0.896435 | − | 0.443176i | \(-0.853852\pi\) |
0.832019 | + | 0.554747i | \(0.187185\pi\) | |||||||
\(242\) | 24.5967i | 1.58114i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | −13.5554 | − | 7.82624i | −0.866025 | − | 0.500000i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 15.4919 | − | 8.94427i | 0.983739 | − | 0.567962i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.5000 | − | 21.6506i | 0.790569 | − | 1.36931i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.50000 | + | 7.79423i | 0.281250 | + | 0.487139i | ||||
\(257\) | 27.1109 | − | 15.6525i | 1.69113 | − | 0.976375i | 0.737523 | − | 0.675322i | \(-0.235995\pi\) |
0.953608 | − | 0.301052i | \(-0.0973379\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.74597 | + | 4.47214i | 0.477637 | + | 0.275764i | 0.719431 | − | 0.694564i | \(-0.244403\pi\) |
−0.241794 | + | 0.970328i | \(0.577736\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.00000 | + | 8.66025i | 0.307148 | + | 0.531995i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.0000 | 1.94386 | 0.971931 | − | 0.235267i | \(-0.0755965\pi\) | ||||
0.971931 | + | 0.235267i | \(0.0755965\pi\) | |||||||
\(272\) | 3.87298 | + | 2.23607i | 0.234834 | + | 0.135582i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.0000 | + | 43.3013i | 1.51031 | + | 2.61593i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(278\) | 8.94427i | 0.536442i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.00000 | −0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.1109 | − | 15.6525i | 1.58383 | − | 0.914427i | 0.589542 | − | 0.807737i | \(-0.299308\pi\) |
0.994292 | − | 0.106690i | \(-0.0340252\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −15.4919 | + | 8.94427i | −0.891461 | + | 0.514685i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.00000 | + | 3.46410i | −0.114708 | + | 0.198680i | ||||
\(305\) | 4.47214i | 0.256074i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −20.0000 | − | 34.6410i | −1.13592 | − | 1.96748i | ||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 48.0000 | 2.70021 | ||||||||
\(317\) | 19.3649 | + | 11.1803i | 1.08764 | + | 0.627950i | 0.932948 | − | 0.360012i | \(-0.117227\pi\) |
0.154694 | + | 0.987962i | \(0.450561\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 25.1744 | − | 14.5344i | 1.40729 | − | 0.812500i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 17.8885i | − | 0.995345i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | − | 24.2487i | 0.769510 | − | 1.33283i | −0.168320 | − | 0.985732i | \(-0.553834\pi\) |
0.937829 | − | 0.347097i | \(-0.112833\pi\) | |||||||
\(332\) | − | 53.6656i | − | 2.94528i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −20.0000 | −1.09435 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(338\) | −25.1744 | + | 14.5344i | −1.36931 | + | 0.790569i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −15.0000 | + | 25.9808i | −0.813489 | + | 1.40900i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.0000 | + | 43.3013i | 1.34401 | + | 2.32789i | ||||
\(347\) | −30.9839 | + | 17.8885i | −1.66330 | + | 0.960307i | −0.692179 | + | 0.721726i | \(0.743349\pi\) |
−0.971123 | + | 0.238581i | \(0.923318\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.0000 | − | 29.4449i | 0.909989 | − | 1.57615i | 0.0959126 | − | 0.995390i | \(-0.469423\pi\) |
0.814076 | − | 0.580758i | \(-0.197244\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.1109 | − | 15.6525i | −1.44297 | − | 0.833097i | −0.444920 | − | 0.895570i | \(-0.646768\pi\) |
−0.998047 | + | 0.0624731i | \(0.980101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | −42.6028 | − | 24.5967i | −2.23915 | − | 1.29278i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(368\) | 8.94427i | 0.466252i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.0000 | + | 17.3205i | −0.515711 | + | 0.893237i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | −23.2379 | − | 13.4164i | −1.19208 | − | 0.688247i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.74597 | + | 4.47214i | −0.395800 | + | 0.228515i | −0.684670 | − | 0.728853i | \(-0.740054\pi\) |
0.288870 | + | 0.957368i | \(0.406720\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.0000 | − | 34.6410i | −1.01144 | − | 1.75187i | ||||
\(392\) | 13.5554 | − | 7.82624i | 0.684653 | − | 0.395285i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.00000 | + | 8.66025i | −0.251896 | + | 0.436297i | ||||
\(395\) | − | 35.7771i | − | 1.80014i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | −30.9839 | − | 17.8885i | −1.55308 | − | 0.896672i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.50000 | − | 4.33013i | −0.125000 | − | 0.216506i | ||||
\(401\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.0000 | − | 22.5167i | −0.642809 | − | 1.11338i | −0.984803 | − | 0.173675i | \(-0.944436\pi\) |
0.341994 | − | 0.939702i | \(-0.388898\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −40.0000 | −1.96352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0000 | + | 32.9090i | −0.926003 | + | 1.60388i | −0.136064 | + | 0.990700i | \(0.543445\pi\) |
−0.789940 | + | 0.613185i | \(0.789888\pi\) | |||||||
\(422\) | 62.6099i | 3.04780i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.0000 | −0.485643 | ||||||||
\(425\) | 19.3649 | + | 11.1803i | 0.939336 | + | 0.542326i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −46.4758 | + | 26.8328i | −2.24649 | + | 1.29701i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.0000 | + | 36.3731i | 1.00572 | + | 1.74195i | ||||
\(437\) | 30.9839 | − | 17.8885i | 1.48216 | − | 0.855725i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | − | 13.8564i | 0.381819 | − | 0.661330i | −0.609503 | − | 0.792784i | \(-0.708631\pi\) |
0.991322 | + | 0.131453i | \(0.0419644\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.4919 | − | 8.94427i | −0.736044 | − | 0.424955i | 0.0845852 | − | 0.996416i | \(-0.473043\pi\) |
−0.820629 | + | 0.571461i | \(0.806377\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 11.6190 | + | 6.70820i | 0.546509 | + | 0.315527i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20.0000 | − | 34.6410i | −0.938647 | − | 1.62578i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(458\) | − | 58.1378i | − | 2.71660i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −60.0000 | −2.79751 | ||||||||
\(461\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.0000 | − | 43.3013i | 1.15810 | − | 2.00589i | ||||
\(467\) | − | 35.7771i | − | 1.65557i | −0.561048 | − | 0.827783i | \(-0.689602\pi\) | ||
0.561048 | − | 0.827783i | \(-0.310398\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 38.7298 | + | 22.3607i | 1.78647 | + | 1.03142i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.0000 | + | 17.3205i | −0.458831 | + | 0.794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −3.87298 | + | 2.23607i | −0.176410 | + | 0.101850i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.5000 | + | 28.5788i | −0.750000 | + | 1.29904i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | −3.87298 | − | 2.23607i | −0.175322 | − | 0.101222i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −17.5000 | − | 30.3109i | −0.790569 | − | 1.36931i | ||||
\(491\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.00000 | −0.359211 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.0000 | − | 38.1051i | −0.984855 | − | 1.70582i | −0.642578 | − | 0.766220i | \(-0.722135\pi\) |
−0.342277 | − | 0.939599i | \(-0.611198\pi\) | |||||||
\(500\) | 29.0474 | − | 16.7705i | 1.29904 | − | 0.750000i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 44.7214i | 1.99403i | 0.0772283 | + | 0.997013i | \(0.475393\pi\) | ||||
−0.0772283 | + | 0.997013i | \(0.524607\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 11.1803i | − | 0.494106i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 70.0000 | 3.08757 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.0000 | + | 17.3205i | 0.436021 | + | 0.755210i | ||||
\(527\) | 30.9839 | − | 17.8885i | 1.34968 | − | 0.779237i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.5000 | − | 49.3634i | 1.23913 | − | 2.14624i | ||||
\(530\) | 22.3607i | 0.971286i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.0000 | + | 34.6410i | 0.864675 | + | 1.49766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 61.9677 | + | 35.7771i | 2.66174 | + | 1.53676i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15.0000 | + | 25.9808i | 0.643120 | + | 1.11392i | ||||
\(545\) | 27.1109 | − | 15.6525i | 1.16130 | − | 0.670478i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(548\) | 67.0820i | 2.86560i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.00000 | + | 10.3923i | −0.254457 | + | 0.440732i | ||||
\(557\) | − | 22.3607i | − | 0.947452i | −0.880672 | − | 0.473726i | \(-0.842909\pi\) | ||
0.880672 | − | 0.473726i | \(-0.157091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.9839 | + | 17.8885i | −1.30581 | + | 0.753912i | −0.981395 | − | 0.192001i | \(-0.938502\pi\) |
−0.324420 | + | 0.945913i | \(0.605169\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.00000 | − | 8.66025i | 0.210352 | − | 0.364340i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.0000 | + | 24.2487i | 0.585882 | + | 1.01478i | 0.994765 | + | 0.102190i | \(0.0325850\pi\) |
−0.408883 | + | 0.912587i | \(0.634082\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 44.7214i | 1.86501i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | −5.80948 | − | 3.35410i | −0.241642 | − | 0.139512i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 70.0000 | 2.89167 | ||||||||
\(587\) | −15.4919 | − | 8.94427i | −0.639421 | − | 0.369170i | 0.144971 | − | 0.989436i | \(-0.453691\pi\) |
−0.784391 | + | 0.620266i | \(0.787025\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | + | 27.7128i | 0.659269 | + | 1.14189i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.47214i | 0.183649i | 0.995775 | + | 0.0918243i | \(0.0292698\pi\) | ||||
−0.995775 | + | 0.0918243i | \(0.970730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.0000 | + | 32.9090i | −0.775026 | + | 1.34238i | 0.159754 | + | 0.987157i | \(0.448930\pi\) |
−0.934780 | + | 0.355228i | \(0.884403\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −24.0000 | −0.976546 | ||||||||
\(605\) | 21.3014 | + | 12.2984i | 0.866025 | + | 0.500000i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(608\) | −23.2379 | + | 13.4164i | −0.942421 | + | 0.544107i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.00000 | + | 8.66025i | −0.202444 | + | 0.350643i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.6028 | + | 24.5967i | −1.71512 | + | 0.990228i | −0.787833 | + | 0.615889i | \(0.788797\pi\) |
−0.927292 | + | 0.374338i | \(0.877870\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.0000 | + | 38.1051i | −0.884255 | + | 1.53157i | −0.0376891 | + | 0.999290i | \(0.512000\pi\) |
−0.846566 | + | 0.532284i | \(0.821334\pi\) | |||||||
\(620\) | − | 53.6656i | − | 2.15526i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | 30.9839 | + | 17.8885i | 1.23247 | + | 0.711568i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25.0000 | + | 43.3013i | 0.992877 | + | 1.71971i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 35.0000 | 1.38350 | ||||||||
\(641\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.0000 | − | 34.6410i | 0.786889 | − | 1.36293i | ||||
\(647\) | 44.7214i | 1.75818i | 0.476658 | + | 0.879089i | \(0.341848\pi\) | ||||
−0.476658 | + | 0.879089i | \(0.658152\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.6028 | + | 24.5967i | −1.66718 | + | 0.962545i | −0.698028 | + | 0.716071i | \(0.745939\pi\) |
−0.969149 | + | 0.246474i | \(0.920728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.0000 | + | 19.0526i | 0.427850 | + | 0.741059i | 0.996682 | − | 0.0813955i | \(-0.0259377\pi\) |
−0.568831 | + | 0.822454i | \(0.692604\pi\) | |||||||
\(662\) | 54.2218 | − | 31.3050i | 2.10739 | − | 1.21670i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.0000 | − | 34.6410i | 0.776151 | − | 1.34433i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −23.2379 | − | 13.4164i | −0.899101 | − | 0.519096i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −39.0000 | −1.50000 | ||||||||
\(677\) | −27.1109 | − | 15.6525i | −1.04196 | − | 0.601574i | −0.121569 | − | 0.992583i | \(-0.538793\pi\) |
−0.920387 | + | 0.391009i | \(0.872126\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −19.3649 | + | 11.1803i | −0.742611 | + | 0.428746i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 35.7771i | − | 1.36897i | −0.729026 | − | 0.684486i | \(-0.760027\pi\) | ||
0.729026 | − | 0.684486i | \(-0.239973\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 50.0000 | 1.91040 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.0000 | − | 45.0333i | 0.989087 | − | 1.71315i | 0.366947 | − | 0.930242i | \(-0.380403\pi\) |
0.622139 | − | 0.782907i | \(-0.286264\pi\) | |||||||
\(692\) | 67.0820i | 2.55008i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −80.0000 | −3.03676 | ||||||||
\(695\) | 7.74597 | + | 4.47214i | 0.293821 | + | 0.169638i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 65.8407 | − | 38.0132i | 2.49211 | − | 1.43882i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −35.0000 | − | 60.6218i | −1.31724 | − | 2.28153i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0000 | + | 22.5167i | −0.488225 | + | 0.845631i | −0.999908 | − | 0.0135434i | \(-0.995689\pi\) |
0.511683 | + | 0.859174i | \(0.329022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 61.9677 | + | 35.7771i | 2.32071 | + | 1.33986i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.80948 | − | 3.35410i | −0.216206 | − | 0.124827i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −33.0000 | − | 57.1577i | −1.22644 | − | 2.12425i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −30.0000 | + | 51.9615i | −1.10581 | + | 1.91533i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.00000 | −0.147142 | −0.0735712 | − | 0.997290i | \(-0.523440\pi\) | ||||
−0.0735712 | + | 0.997290i | \(0.523440\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.7298 | − | 22.3607i | 1.42086 | − | 0.820334i | 0.424487 | − | 0.905434i | \(-0.360454\pi\) |
0.996372 | + | 0.0851001i | \(0.0271210\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | − | 6.92820i | −0.145962 | − | 0.252814i | 0.783769 | − | 0.621052i | \(-0.213294\pi\) |
−0.929731 | + | 0.368238i | \(0.879961\pi\) | |||||||
\(752\) | 7.74597 | − | 4.47214i | 0.282466 | − | 0.163082i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.8885i | 0.651031i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | −7.74597 | − | 4.47214i | −0.281346 | − | 0.162435i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10.0000 | − | 17.3205i | −0.362738 | − | 0.628281i | ||||
\(761\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.0000 | −0.722629 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.0000 | + | 39.8372i | 0.829401 | + | 1.43657i | 0.898509 | + | 0.438956i | \(0.144652\pi\) |
−0.0691074 | + | 0.997609i | \(0.522015\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.47214i | 0.160852i | 0.996761 | + | 0.0804258i | \(0.0256280\pi\) | ||||
−0.996761 | + | 0.0804258i | \(0.974372\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.0000 | −1.43684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 89.4427i | − | 3.19847i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.00000 | −0.250000 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(788\) | −11.6190 | + | 6.70820i | −0.413908 | + | 0.238970i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 40.0000 | − | 69.2820i | 1.42314 | − | 2.46494i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −24.0000 | − | 41.5692i | −0.850657 | − | 1.47338i | ||||
\(797\) | −42.6028 | + | 24.5967i | −1.50907 | + | 0.871262i | −0.509125 | + | 0.860693i | \(0.670031\pi\) |
−0.999944 | + | 0.0105689i | \(0.996636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.0000 | + | 34.6410i | −0.707549 | + | 1.22551i | ||||
\(800\) | − | 33.5410i | − | 1.18585i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −52.0000 | −1.82597 | −0.912983 | − | 0.407997i | \(-0.866228\pi\) | ||||
−0.912983 | + | 0.407997i | \(0.866228\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 58.1378i | − | 2.03274i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 35.7771i | − | 1.24409i | −0.782981 | − | 0.622046i | \(-0.786302\pi\) | ||
0.782981 | − | 0.622046i | \(-0.213698\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.0000 | −1.18087 | −0.590434 | − | 0.807086i | \(-0.701044\pi\) | ||||
−0.590434 | + | 0.807086i | \(0.701044\pi\) | |||||||
\(830\) | −77.4597 | − | 44.7214i | −2.68866 | − | 1.55230i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.1109 | − | 15.6525i | 0.939336 | − | 0.542326i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.0000 | + | 17.3205i | −0.346064 | + | 0.599401i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.5000 | + | 25.1147i | 0.500000 | + | 0.866025i | ||||
\(842\) | −73.5867 | + | 42.4853i | −2.53596 | + | 1.46414i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −42.0000 | + | 72.7461i | −1.44570 | + | 2.50403i | ||||
\(845\) | 29.0689i | 1.00000i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.87298 | + | 2.23607i | 0.132999 | + | 0.0767869i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 25.0000 | + | 43.3013i | 0.857493 | + | 1.48522i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −40.0000 | −1.36717 | ||||||||
\(857\) | −50.3488 | − | 29.0689i | −1.71988 | − | 0.992974i | −0.919107 | − | 0.394009i | \(-0.871088\pi\) |
−0.800775 | − | 0.598965i | \(-0.795579\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.0000 | − | 38.1051i | −0.750630 | − | 1.30013i | −0.947518 | − | 0.319704i | \(-0.896417\pi\) |
0.196887 | − | 0.980426i | \(-0.436917\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.7214i | 1.52233i | 0.648557 | + | 0.761166i | \(0.275373\pi\) | ||||
−0.648557 | + | 0.761166i | \(0.724627\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 50.0000 | 1.70005 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 31.3050i | 1.06012i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 80.0000 | 2.70604 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(878\) | 30.9839 | − | 17.8885i | 1.04565 | − | 0.603709i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.0000 | − | 34.6410i | −0.671913 | − | 1.16379i | ||||
\(887\) | −7.74597 | + | 4.47214i | −0.260084 | + | 0.150160i | −0.624373 | − | 0.781126i | \(-0.714645\pi\) |
0.364289 | + | 0.931286i | \(0.381312\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30.9839 | − | 17.8885i | −1.03684 | − | 0.598617i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.0000 | −0.666297 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.00000 | + | 8.66025i | 0.166298 | + | 0.288036i | ||||
\(905\) | −42.6028 | + | 24.5967i | −1.41617 | + | 0.817624i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(908\) | − | 53.6656i | − | 1.78096i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 39.0000 | − | 67.5500i | 1.28860 | − | 2.23191i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.0000 | 1.84727 | 0.923635 | − | 0.383274i | \(-0.125203\pi\) | ||||
0.923635 | + | 0.383274i | \(0.125203\pi\) | |||||||
\(920\) | −38.7298 | − | 22.3607i | −1.27688 | − | 0.737210i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.0000 | + | 24.2487i | 0.458831 | + | 0.794719i | ||||
\(932\) | 58.0948 | − | 33.5410i | 1.90296 | − | 1.09867i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 40.0000 | − | 69.2820i | 1.30884 | − | 2.26698i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 30.0000 | + | 51.9615i | 0.978492 | + | 1.69480i | ||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.4919 | − | 8.94427i | −0.503420 | − | 0.290650i | 0.226705 | − | 0.973964i | \(-0.427205\pi\) |
−0.730125 | + | 0.683314i | \(0.760538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −38.7298 | + | 22.3607i | −1.25656 | + | 0.725476i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 58.1378i | 1.88327i | 0.336640 | + | 0.941634i | \(0.390710\pi\) | ||||
−0.336640 | + | 0.941634i | \(0.609290\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | + | 28.5788i | −0.532258 | + | 0.921898i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.00000 | −0.193247 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(968\) | −21.3014 | + | 12.2984i | −0.684653 | + | 0.395285i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.00000 | + | 1.73205i | 0.0320092 | + | 0.0554416i | ||||
\(977\) | 3.87298 | − | 2.23607i | 0.123908 | − | 0.0715382i | −0.436765 | − | 0.899576i | \(-0.643876\pi\) |
0.560673 | + | 0.828037i | \(0.310543\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 46.9574i | − | 1.50000i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 54.2218 | + | 31.3050i | 1.72941 | + | 0.998473i | 0.892325 | + | 0.451394i | \(0.149073\pi\) |
0.837081 | + | 0.547079i | \(0.184260\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.00000 | + | 8.66025i | 0.159313 | + | 0.275939i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0000 | 1.01651 | 0.508257 | − | 0.861206i | \(-0.330290\pi\) | ||||
0.508257 | + | 0.861206i | \(0.330290\pi\) | |||||||
\(992\) | −46.4758 | − | 26.8328i | −1.47561 | − | 0.851943i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.9839 | + | 17.8885i | −0.982255 | + | 0.567105i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(998\) | − | 98.3870i | − | 3.11439i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))