Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(305,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.cn (of order \(12\), degree \(4\), 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: | \(4.98266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{U}(1)[D_{12}]$ |
Embedding invariants
Embedding label | 353.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.353 |
Dual form | 624.2.cn.b.449.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(-1\) | \(1\) |
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 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.23205 | − | 1.13397i | 1.59956 | − | 0.428602i | 0.654654 | − | 0.755929i | \(-0.272814\pi\) |
0.944911 | + | 0.327327i | \(0.106148\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.59808 | − | 2.50000i | 0.720577 | − | 0.693375i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.830127 | + | 3.09808i | 0.190444 | + | 0.710747i | 0.993399 | + | 0.114708i | \(0.0365932\pi\) |
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.36603 | + | 5.36603i | 1.17096 | + | 1.17096i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 5.00000i | − | 1.00000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.830127 | + | 0.830127i | −0.149095 | + | 0.149095i | −0.777714 | − | 0.628619i | \(-0.783621\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.09808 | + | 11.5622i | −0.509321 | + | 1.90081i | −0.0821995 | + | 0.996616i | \(0.526194\pi\) |
−0.427121 | + | 0.904194i | \(0.640472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.00000 | + | 1.73205i | 0.960769 | + | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.50000 | + | 0.866025i | 0.228748 | + | 0.132068i | 0.609994 | − | 0.792406i | \(-0.291172\pi\) |
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.5622 | − | 6.09808i | 1.50888 | − | 0.871154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.92820 | + | 3.92820i | −0.520303 | + | 0.520303i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.33013 | + | 7.50000i | −0.554416 | + | 0.960277i | 0.443533 | + | 0.896258i | \(0.353725\pi\) |
−0.997949 | + | 0.0640184i | \(0.979608\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.40192 | + | 12.6962i | −0.428602 | + | 1.59956i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.7942 | − | 4.23205i | −1.92957 | − | 0.517027i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) |
−0.952217 | − | 0.305424i | \(-0.901202\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.63397 | − | 7.63397i | −0.893489 | − | 0.893489i | 0.101361 | − | 0.994850i | \(-0.467680\pi\) |
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.50000 | − | 4.33013i | 0.866025 | − | 0.500000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.1244 | 1.36410 | 0.682048 | − | 0.731307i | \(-0.261089\pi\) | ||||
0.682048 | + | 0.731307i | \(0.261089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.16025 | − | 13.5263i | 0.855427 | − | 1.41794i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.96410 | − | 0.526279i | −0.203668 | − | 0.0545726i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.57180 | − | 9.59808i | −0.261126 | − | 0.974537i | −0.964579 | − | 0.263795i | \(-0.915026\pi\) |
0.703452 | − | 0.710742i | \(-0.251641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 15.5885i | − | 1.53598i | −0.640464 | − | 0.767988i | \(-0.721258\pi\) | ||
0.640464 | − | 0.767988i | \(-0.278742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.8301 | − | 13.8301i | 1.32469 | − | 1.32469i | 0.414751 | − | 0.909935i | \(-0.363869\pi\) |
0.909935 | − | 0.414751i | \(-0.136131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.0263 | + | 5.36603i | −1.90081 | + | 0.509321i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.59808 | + | 10.5000i | 0.240192 | + | 0.970725i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.52628 | − | 5.50000i | −0.866025 | − | 0.500000i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.866025 | + | 0.500000i | −0.0768473 | + | 0.0443678i | −0.537931 | − | 0.842989i | \(-0.680794\pi\) |
0.461084 | + | 0.887357i | \(0.347461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.00000i | 0.264135i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.02628 | + | 12.1699i | 0.609256 | + | 1.05526i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.50000 | + | 6.06218i | −0.296866 | + | 0.514187i | −0.975417 | − | 0.220366i | \(-0.929275\pi\) |
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 18.2942 | + | 10.5622i | 1.50888 | + | 0.871154i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.1244 | − | 10.1244i | −0.823908 | − | 0.823908i | 0.162758 | − | 0.986666i | \(-0.447961\pi\) |
−0.986666 | + | 0.162758i | \(0.947961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.0000 | −0.877896 | −0.438948 | − | 0.898513i | \(-0.644649\pi\) | ||||
−0.438948 | + | 0.898513i | \(0.644649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.5263 | + | 3.62436i | −1.05946 | + | 0.283881i | −0.746156 | − | 0.665771i | \(-0.768103\pi\) |
−0.313304 | + | 0.949653i | \(0.601436\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.500000 | − | 12.9904i | 0.0384615 | − | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.29423 | − | 2.49038i | −0.710747 | − | 0.190444i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.66987 | − | 21.1603i | −0.428602 | − | 1.59956i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.92820i | − | 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.0000 | −1.10883 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −21.9904 | + | 5.89230i | −1.59956 | + | 0.428602i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.35641 | + | 5.06218i | −0.0976363 | + | 0.364384i | −0.997406 | − | 0.0719816i | \(-0.977068\pi\) |
0.899770 | + | 0.436365i | \(0.143734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.7224 | − | 8.50000i | −1.04365 | − | 0.602549i | −0.122782 | − | 0.992434i | \(-0.539182\pi\) |
−0.920864 | + | 0.389885i | \(0.872515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.33013 | − | 27.3564i | −0.517027 | − | 1.92957i | ||||
\(202\) | 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 | ||||||||
\(211\) | 12.9904 | + | 22.5000i | 0.894295 | + | 1.54896i | 0.834675 | + | 0.550743i | \(0.185655\pi\) |
0.0596196 | + | 0.998221i | \(0.481011\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.57180 | + | 4.45448i | −0.174585 | + | 0.302390i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.83975 | − | 18.0622i | 0.327040 | − | 1.22053i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.2224 | + | 7.02628i | 1.75598 | + | 0.470514i | 0.985887 | − | 0.167412i | \(-0.0535411\pi\) |
0.770097 | + | 0.637927i | \(0.220208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.9904 | + | 7.50000i | 0.866025 | + | 0.500000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.607695 | + | 0.607695i | 0.0401576 | + | 0.0401576i | 0.726900 | − | 0.686743i | \(-0.240960\pi\) |
−0.686743 | + | 0.726900i | \(0.740960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.5000 | + | 18.1865i | 0.682048 | + | 1.18134i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.4904 | + | 7.63397i | −1.83523 | + | 0.491748i | −0.998443 | − | 0.0557856i | \(-0.982234\pi\) |
−0.836784 | + | 0.547533i | \(0.815567\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.79423 | − | 13.5000i | 0.500000 | − | 0.866025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.90192 | + | 5.97372i | 0.630044 | + | 0.380099i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 52.4449i | 3.25877i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.16025 | + | 30.4545i | −0.495700 | + | 1.84998i | 0.0303728 | + | 0.999539i | \(0.490331\pi\) |
−0.526073 | + | 0.850439i | \(0.676336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 27.3564 | + | 0.526279i | 1.65569 | + | 0.0318519i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.0000 | + | 10.3923i | 1.08152 | + | 0.624413i | 0.931305 | − | 0.364241i | \(-0.118672\pi\) |
0.150210 | + | 0.988654i | \(0.452005\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.911543 | − | 3.40192i | −0.0545726 | − | 0.203668i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.6506 | − | 12.5000i | 1.28700 | − | 0.743048i | 0.308879 | − | 0.951101i | \(-0.400046\pi\) |
0.978117 | + | 0.208053i | \(0.0667128\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.1699 | − | 12.1699i | 0.713411 | − | 0.713411i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.33013 | + | 1.96410i | 0.422501 | + | 0.113209i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.3660 | − | 18.3660i | −1.04820 | − | 1.04820i | −0.998778 | − | 0.0494267i | \(-0.984261\pi\) |
−0.0494267 | − | 0.998778i | \(-0.515739\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.3827 | − | 13.5000i | 1.33019 | − | 0.767988i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.9090 | 1.86012 | 0.930062 | − | 0.367402i | \(-0.119753\pi\) | ||||
0.930062 | + | 0.367402i | \(0.119753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.5000 | − | 12.9904i | −0.693375 | − | 0.720577i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 32.7224 | + | 8.76795i | 1.80955 | + | 0.484869i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.18653 | − | 8.16025i | −0.120183 | − | 0.448528i | 0.879440 | − | 0.476011i | \(-0.157918\pi\) |
−0.999622 | + | 0.0274825i | \(0.991251\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −25.3923 | − | 25.3923i | −1.39149 | − | 1.39149i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.0000i | 1.57973i | 0.613280 | + | 0.789865i | \(0.289850\pi\) | ||||
−0.613280 | + | 0.789865i | \(0.710150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.0981 | − | 16.0981i | 0.869214 | − | 0.869214i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.59808 | + | 35.8205i | −0.513773 | + | 1.91743i | −0.139072 | + | 0.990282i | \(0.544412\pi\) |
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.5000 | + | 12.9904i | −0.720577 | + | 0.693375i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.54552 | − | 4.35641i | 0.397132 | − | 0.229285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 19.0526i | − | 1.00000i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.5000 | + | 26.8468i | 0.809093 | + | 1.40139i | 0.913493 | + | 0.406855i | \(0.133375\pi\) |
−0.104399 | + | 0.994535i | \(0.533292\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.1865 | − | 31.5000i | 0.941663 | − | 1.63101i | 0.179364 | − | 0.983783i | \(-0.442596\pi\) |
0.762299 | − | 0.647225i | \(-0.224071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.5526 | − | 8.99038i | −1.72348 | − | 0.461805i | −0.744815 | − | 0.667271i | \(-0.767462\pi\) |
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.50000 | − | 0.866025i | −0.0768473 | − | 0.0443678i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.50000 | + | 2.59808i | −0.228748 | + | 0.132068i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.5263 | − | 7.10770i | 1.33132 | − | 0.356725i | 0.478110 | − | 0.878300i | \(-0.341322\pi\) |
0.853206 | + | 0.521575i | \(0.174655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.1699 | + | 21.0788i | −0.609256 | + | 1.05526i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0814157 | + | 4.23205i | −0.00405561 | + | 0.210813i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.4282 | + | 38.9186i | 0.515641 | + | 1.92440i | 0.342578 | + | 0.939490i | \(0.388700\pi\) |
0.173064 | + | 0.984911i | \(0.444633\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.1244 | −0.593732 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.68653 | + | 8.68653i | −0.423356 | + | 0.423356i | −0.886357 | − | 0.463002i | \(-0.846772\pi\) |
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.82051 | + | 36.6506i | −0.475248 | + | 1.77365i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.3109 | − | 17.5000i | −1.45665 | − | 0.840996i | −0.457804 | − | 0.889053i | \(-0.651364\pi\) |
−0.998845 | + | 0.0480569i | \(0.984697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.5000 | − | 19.9186i | 1.64660 | − | 0.950662i | 0.668184 | − | 0.743996i | \(-0.267072\pi\) |
0.978412 | − | 0.206666i | \(-0.0662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 36.5885i | 1.74231i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.41858 | − | 23.9545i | 0.301571 | − | 1.12548i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.7224 | − | 5.28461i | −0.922576 | − | 0.247204i | −0.233890 | − | 0.972263i | \(-0.575146\pi\) |
−0.688686 | + | 0.725059i | \(0.741812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.6340 | + | 20.6340i | 0.958942 | + | 0.958942i | 0.999190 | − | 0.0402476i | \(-0.0128147\pi\) |
−0.0402476 | + | 0.999190i | \(0.512815\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −71.6410 | −3.30807 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.52628 | − | 16.5000i | −0.438948 | − | 0.760280i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.4904 | − | 4.15064i | 0.710747 | − | 0.190444i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.8564 | + | 37.7846i | 0.950970 | + | 1.72283i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.68653 | − | 32.4186i | −0.393624 | − | 1.46903i | −0.824110 | − | 0.566429i | \(-0.808325\pi\) |
0.430486 | − | 0.902597i | \(-0.358342\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.1506 | − | 17.1506i | −0.775579 | − | 0.775579i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 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 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.5885 | + | 31.5885i | −1.41409 | + | 1.41409i | −0.697835 | + | 0.716258i | \(0.745853\pi\) |
−0.716258 | + | 0.697835i | \(0.754147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.9186 | − | 10.5000i | 0.884615 | − | 0.466321i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.9641 | − | 23.6506i | −1.81215 | − | 1.04624i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.31347 | − | 16.0981i | −0.190444 | − | 0.710747i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.00000 | − | 6.92820i | −0.174908 | − | 0.302949i | 0.765222 | − | 0.643767i | \(-0.222629\pi\) |
−0.940129 | + | 0.340818i | \(0.889296\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 26.8301 | − | 26.8301i | 1.17096 | − | 1.17096i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.1506 | − | 30.1506i | −1.29628 | − | 1.29628i | −0.930834 | − | 0.365444i | \(-0.880917\pi\) |
−0.365444 | − | 0.930834i | \(-0.619083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3923 | − | 6.00000i | 0.445976 | − | 0.257485i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.0000 | −1.75303 | −0.876517 | − | 0.481371i | \(-0.840139\pi\) | ||||
−0.876517 | + | 0.481371i | \(0.840139\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.9904 | − | 22.5000i | −0.554416 | − | 0.960277i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 51.3109 | − | 13.7487i | 2.18196 | − | 0.584655i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.06218 | − | 1.50000i | 0.256403 | − | 0.0634432i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −27.8827 | − | 27.8827i | −1.17096 | − | 1.17096i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 16.0000i | − | 0.669579i | −0.942293 | − | 0.334790i | \(-0.891335\pi\) | ||
0.942293 | − | 0.334790i | \(-0.108665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.9282 | + | 29.9282i | −1.24593 | + | 1.24593i | −0.288425 | + | 0.957503i | \(0.593132\pi\) |
−0.957503 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.76795 | + | 2.34936i | −0.364384 | + | 0.0976363i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.26091 | − | 1.88269i | −0.134363 | − | 0.0775747i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 29.4449i | − | 1.20510i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.7846 | + | 36.0000i | 0.847822 | + | 1.46847i | 0.883148 | + | 0.469095i | \(0.155420\pi\) |
−0.0353259 | + | 0.999376i | \(0.511247\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 34.6865 | − | 34.6865i | 1.41254 | − | 1.41254i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.0000 | + | 17.3205i | −0.405887 | + | 0.703018i | −0.994424 | − | 0.105453i | \(-0.966371\pi\) |
0.588537 | + | 0.808470i | \(0.299704\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.79423 | + | 0.748711i | 0.112858 | + | 0.0302402i | 0.314806 | − | 0.949156i | \(-0.398061\pi\) |
−0.201948 | + | 0.979396i | \(0.564727\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.8827 | − | 14.8827i | −0.598186 | − | 0.598186i | 0.341644 | − | 0.939829i | \(-0.389016\pi\) |
−0.939829 | + | 0.341644i | \(0.889016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.9904 | − | 9.37564i | 1.39295 | − | 0.373239i | 0.517139 | − | 0.855901i | \(-0.326997\pi\) |
0.875806 | + | 0.482663i | \(0.160330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.5000 | + | 38.9711i | −0.894295 | + | 1.54896i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.1962 | − | 42.2487i | 0.483229 | − | 1.67395i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0885 | + | 45.1147i | 0.476722 | + | 1.77915i | 0.614749 | + | 0.788723i | \(0.289257\pi\) |
−0.138027 | + | 0.990429i | \(0.544076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.90897 | −0.349170 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.2846 | − | 8.38269i | 1.22053 | − | 0.327040i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.11474 | + | 22.8205i | −0.237836 | + | 0.887615i | 0.739014 | + | 0.673690i | \(0.235292\pi\) |
−0.976850 | + | 0.213925i | \(0.931375\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.1699 | + | 45.4186i | 0.470514 | + | 1.75598i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.5000 | − | 25.1147i | 1.67680 | − | 0.968102i | 0.713123 | − | 0.701039i | \(-0.247280\pi\) |
0.963679 | − | 0.267063i | \(-0.0860531\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.9808i | 1.00000i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.7679 | − | 37.7032i | −0.835377 | − | 1.44692i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.385263 | + | 1.43782i | −0.0146987 | + | 0.0548563i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 50.4808 | + | 13.5263i | 1.92038 | + | 0.514564i | 0.988355 | + | 0.152167i | \(0.0486252\pi\) |
0.932024 | + | 0.362397i | \(0.118041\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −38.3923 | −1.44799 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.7487 | + | 10.6506i | −1.49279 | + | 0.399993i | −0.910679 | − | 0.413114i | \(-0.864441\pi\) |
−0.582115 | + | 0.813107i | \(0.697775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.1865 | + | 31.5000i | −0.682048 | + | 1.18134i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.6769 | − | 65.9711i | −0.658323 | − | 2.45689i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −36.1244 | − | 36.1244i | −1.34348 | − | 1.34348i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.0000i | 1.81731i | 0.417548 | + | 0.908655i | \(0.362889\pi\) | ||||
−0.417548 | + | 0.908655i | \(0.637111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.3468 | − | 23.3468i | 0.862333 | − | 0.862333i | −0.129275 | − | 0.991609i | \(-0.541265\pi\) |
0.991609 | + | 0.129275i | \(0.0412651\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.58142 | − | 24.5622i | 0.242101 | − | 0.903534i | −0.732717 | − | 0.680534i | \(-0.761748\pi\) |
0.974818 | − | 0.223001i | \(-0.0715853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.385263 | + | 20.0263i | −0.0141530 | + | 0.735684i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.0000 | − | 8.66025i | 0.547358 | − | 0.316017i | −0.200698 | − | 0.979653i | \(-0.564321\pi\) |
0.748056 | + | 0.663636i | \(0.230988\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.2487 | − | 42.0000i | −0.881334 | − | 1.52652i | −0.849858 | − | 0.527011i | \(-0.823312\pi\) |
−0.0314762 | − | 0.999505i | \(-0.510021\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.8468 | − | 74.2128i | 1.55116 | − | 2.68668i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.2224 | − | 10.5096i | −1.41440 | − | 0.378987i | −0.530904 | − | 0.847432i | \(-0.678148\pi\) |
−0.883493 | + | 0.468445i | \(0.844814\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.15064 | + | 4.15064i | 0.149095 | + | 0.149095i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −78.6673 | + | 45.4186i | −2.82217 | + | 1.62938i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.2321 | − | 4.61731i | 0.614256 | − | 0.164589i | 0.0617409 | − | 0.998092i | \(-0.480335\pi\) |
0.552515 | + | 0.833503i | \(0.313668\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.50000 | + | 30.3109i | 0.266333 | + | 1.07637i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 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 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.3468 | + | 36.3468i | −1.27631 | + | 1.27631i | −0.333590 | + | 0.942718i | \(0.608260\pi\) |
−0.942718 | + | 0.333590i | \(0.891740\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −52.7487 | + | 14.1340i | −1.84998 | + | 0.495700i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.43782 | + | 5.36603i | −0.0503030 | + | 0.187733i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 22.9019 | + | 41.4904i | 0.800258 | + | 1.44979i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.0000 | + | 12.1244i | 0.732014 | + | 0.422628i | 0.819159 | − | 0.573567i | \(-0.194441\pi\) |
−0.0871445 | + | 0.996196i | \(0.527774\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.8993 | − | 26.5000i | 1.59415 | − | 0.920383i | 0.601566 | − | 0.798823i | \(-0.294544\pi\) |
0.992584 | − | 0.121560i | \(-0.0387897\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.0000i | 1.24883i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.31347 | − | 4.31347i | 0.149095 | − | 0.149095i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5000 | + | 25.1147i | −0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −46.5526 | − | 12.4737i | −1.59956 | − | 0.428602i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 37.5000 | + | 21.6506i | 1.28700 | + | 0.743048i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.8827 | + | 40.8827i | 1.39980 | + | 1.39980i | 0.800608 | + | 0.599189i | \(0.204510\pi\) |
0.599189 | + | 0.800608i | \(0.295490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 57.1577 | 1.95019 | 0.975097 | − | 0.221777i | \(-0.0711857\pi\) | ||||
0.975097 | + | 0.221777i | \(0.0711857\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.7224 | + | 25.5000i | −0.500000 | + | 0.866025i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −51.6147 | + | 28.4904i | −1.74890 | + | 0.965360i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 28.7942 | + | 7.71539i | 0.974537 | + | 0.261126i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.65321 | + | 9.90192i | 0.0895926 | + | 0.334364i | 0.996144 | − | 0.0877308i | \(-0.0279615\pi\) |
−0.906552 | + | 0.422095i | \(0.861295\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 55.0000i | − | 1.85090i | −0.378873 | − | 0.925449i | \(-0.623688\pi\) | ||
0.378873 | − | 0.925449i | \(-0.376312\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.09808 | + | 3.09808i | −0.103906 | + | 0.103906i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.40192 | + | 12.6962i | 0.113209 | + | 0.422501i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.6410 | + | 20.0000i | −1.15024 | + | 0.664089i | −0.948945 | − | 0.315442i | \(-0.897847\pi\) |
−0.201291 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.5885 | − | 27.0000i | 0.514216 | − | 0.890648i | −0.485648 | − | 0.874154i | \(-0.661416\pi\) |
0.999864 | − | 0.0164935i | \(-0.00525028\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.6436 | − | 43.4545i | 0.383669 | − | 1.43187i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 57.8109 | + | 15.4904i | 1.90081 | + | 0.509321i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 40.5000 | + | 23.3827i | 1.33019 | + | 0.767988i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.6603 | + | 27.6603i | 0.906528 | + | 0.906528i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55.4256 | 1.81068 | 0.905338 | − | 0.424691i | \(-0.139617\pi\) | ||||
0.905338 | + | 0.424691i | \(0.139617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.5000 | + | 49.3634i | 0.930062 | + | 1.61092i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.9186 | − | 0.748711i | −1.26335 | − | 0.0243042i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.6218i | 0.955541i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.4449 | − | 39.4449i | 1.26846 | − | 1.26846i | 0.321578 | − | 0.946883i | \(-0.395787\pi\) |
0.946883 | − | 0.321578i | \(-0.104213\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.93782 | + | 29.6244i | −0.254475 | + | 0.949713i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.66025 | − | 30.0000i | 0.277350 | − | 0.960769i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.1865 | + | 56.6769i | 0.484869 | + | 1.80955i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.0000 | + | 38.1051i | 0.698853 | + | 1.21045i | 0.968864 | + | 0.247592i | \(0.0796392\pi\) |
−0.270011 | + | 0.962857i | \(0.587027\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.3468 | − | 10.3468i | 0.328345 | − | 0.328345i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.5000 | − | 51.0955i | 0.934274 | − | 1.61821i | 0.158352 | − | 0.987383i | \(-0.449382\pi\) |
0.775923 | − | 0.630828i | \(-0.217285\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.0981 | − | 60.0788i | 0.509321 | − | 1.90081i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))