Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(19,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.s (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: | \(7.82533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 19.3 | ||
Root | \(-1.01575 + 1.40294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.19 |
Dual form | 980.2.s.a.619.3 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 1.22474i | 0.500000 | − | 0.866025i | ||||
\(3\) | −0.308646 | + | 0.178197i | −0.178197 | + | 0.102882i | −0.586445 | − | 0.809989i | \(-0.699473\pi\) |
0.408248 | + | 0.912871i | \(0.366140\pi\) | |||||||
\(4\) | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||||
\(5\) | −1.93649 | − | 1.11803i | −0.866025 | − | 0.500000i | ||||
\(6\) | 0.504017i | 0.205764i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.82843 | −1.00000 | ||||||||
\(9\) | −1.43649 | + | 2.48808i | −0.478831 | + | 0.829359i | ||||
\(10\) | −2.73861 | + | 1.58114i | −0.866025 | + | 0.500000i | ||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 0.617292 | + | 0.356394i | 0.178197 | + | 0.102882i | ||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.796921 | 0.205764 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 2.03151 | + | 3.51867i | 0.478831 | + | 0.829359i | ||||
\(19\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(20\) | 4.47214i | 1.00000i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.75437 | + | 6.50275i | −0.782839 | + | 1.35592i | 0.147442 | + | 0.989071i | \(0.452896\pi\) |
−0.930281 | + | 0.366847i | \(0.880437\pi\) | |||||||
\(24\) | 0.872983 | − | 0.504017i | 0.178197 | − | 0.102882i | ||||
\(25\) | 2.50000 | + | 4.33013i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.09310i | − | 0.402816i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.74597 | 0.881304 | 0.440652 | − | 0.897678i | \(-0.354747\pi\) | ||||
0.440652 | + | 0.897678i | \(0.354747\pi\) | |||||||
\(30\) | 0.563508 | − | 0.976025i | 0.102882 | − | 0.178197i | ||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | 2.82843 | + | 4.89898i | 0.500000 | + | 0.866025i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.74597 | 0.957661 | ||||||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.47723 | + | 3.16228i | 0.866025 | + | 0.500000i | ||||
\(41\) | 12.6284i | 1.97222i | 0.166092 | + | 0.986110i | \(0.446885\pi\) | ||||
−0.166092 | + | 0.986110i | \(0.553115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.10257 | −1.38813 | −0.694065 | − | 0.719913i | \(-0.744182\pi\) | ||||
−0.694065 | + | 0.719913i | \(0.744182\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.56351 | − | 3.21209i | 0.829359 | − | 0.478831i | ||||
\(46\) | 5.30948 | + | 9.19628i | 0.782839 | + | 1.35592i | ||||
\(47\) | −8.21584 | − | 4.74342i | −1.19840 | − | 0.691898i | −0.238204 | − | 0.971215i | \(-0.576559\pi\) |
−0.960199 | + | 0.279317i | \(0.909892\pi\) | |||||||
\(48\) | − | 1.42558i | − | 0.205764i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.07107 | 1.00000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | −2.56351 | − | 1.48004i | −0.348849 | − | 0.201408i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.35591 | − | 5.81260i | 0.440652 | − | 0.763232i | ||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | −0.796921 | − | 1.38031i | −0.102882 | − | 0.178197i | ||||
\(61\) | 11.8095 | + | 6.81820i | 1.51205 | + | 0.872982i | 0.999901 | + | 0.0140840i | \(0.00448323\pi\) |
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.90719 | − | 13.6957i | −0.966017 | − | 1.67319i | −0.706857 | − | 0.707357i | \(-0.749887\pi\) |
−0.259161 | − | 0.965834i | \(-0.583446\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 2.67607i | − | 0.322161i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 4.06301 | − | 7.03734i | 0.478831 | − | 0.829359i | ||||
\(73\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.54323 | − | 0.890985i | −0.178197 | − | 0.102882i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(80\) | 7.74597 | − | 4.47214i | 0.866025 | − | 0.500000i | ||||
\(81\) | −3.93649 | − | 6.81820i | −0.437388 | − | 0.757578i | ||||
\(82\) | 15.4665 | + | 8.92961i | 1.70799 | + | 0.986110i | ||||
\(83\) | 18.2156i | 1.99942i | 0.0240199 | + | 0.999711i | \(0.492353\pi\) | ||||
−0.0240199 | + | 0.999711i | \(0.507647\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.43649 | + | 11.1483i | −0.694065 | + | 1.20216i | ||||
\(87\) | −1.46482 | + | 0.845717i | −0.157046 | + | 0.0906704i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.2460 | − | 7.07021i | −1.29807 | − | 0.749441i | −0.317999 | − | 0.948091i | \(-0.603011\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | − | 9.08517i | − | 0.957661i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 15.0175 | 1.56568 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −11.6190 | + | 6.70820i | −1.19840 | + | 0.691898i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.74597 | − | 1.00803i | −0.178197 | − | 0.102882i | ||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.00000 | − | 8.66025i | 0.500000 | − | 0.866025i | ||||
\(101\) | −9.62702 | + | 5.55816i | −0.957924 | + | 0.553058i | −0.895533 | − | 0.444994i | \(-0.853206\pi\) |
−0.0623905 | + | 0.998052i | \(0.519872\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.3925 | − | 9.46420i | −1.61520 | − | 0.932535i | −0.988139 | − | 0.153564i | \(-0.950925\pi\) |
−0.627060 | − | 0.778971i | \(-0.715742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.70411 | + | 15.0760i | −0.841458 | + | 1.45745i | 0.0472033 | + | 0.998885i | \(0.484969\pi\) |
−0.888662 | + | 0.458563i | \(0.848364\pi\) | |||||||
\(108\) | −3.62535 | + | 2.09310i | −0.348849 | + | 0.201408i | ||||
\(109\) | 1.80948 | + | 3.13410i | 0.173316 | + | 0.300193i | 0.939577 | − | 0.342337i | \(-0.111218\pi\) |
−0.766261 | + | 0.642529i | \(0.777885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.5406 | − | 8.39502i | 1.35592 | − | 0.782839i | ||||
\(116\) | −4.74597 | − | 8.22026i | −0.440652 | − | 0.763232i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.25403 | −0.205764 | ||||||||
\(121\) | −5.50000 | + | 9.52628i | −0.500000 | + | 0.866025i | ||||
\(122\) | 16.7011 | − | 9.64240i | 1.51205 | − | 0.872982i | ||||
\(123\) | −2.25034 | − | 3.89770i | −0.202906 | − | 0.351444i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 1.00000i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.24264 | 0.376473 | 0.188237 | − | 0.982124i | \(-0.439723\pi\) | ||||
0.188237 | + | 0.982124i | \(0.439723\pi\) | |||||||
\(128\) | 5.65685 | − | 9.79796i | 0.500000 | − | 0.866025i | ||||
\(129\) | 2.80948 | − | 1.62205i | 0.247360 | − | 0.142814i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −22.3649 | −1.93203 | ||||||||
\(135\) | −2.34015 | + | 4.05326i | −0.201408 | + | 0.348849i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | −3.27750 | − | 1.89226i | −0.278999 | − | 0.161080i | ||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.38105 | 0.284736 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.74597 | − | 9.95231i | −0.478831 | − | 0.829359i | ||||
\(145\) | −9.19052 | − | 5.30615i | −0.763232 | − | 0.440652i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.06351 | − | 7.03820i | 0.332896 | − | 0.576592i | −0.650183 | − | 0.759778i | \(-0.725308\pi\) |
0.983078 | + | 0.183186i | \(0.0586410\pi\) | |||||||
\(150\) | −2.18246 | + | 1.26004i | −0.178197 | + | 0.102882i | ||||
\(151\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 12.6491i | − | 1.00000i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −11.1341 | −0.874776 | ||||||||
\(163\) | 6.36396 | − | 11.0227i | 0.498464 | − | 0.863365i | −0.501535 | − | 0.865138i | \(-0.667231\pi\) |
0.999998 | + | 0.00177283i | \(0.000564310\pi\) | |||||||
\(164\) | 21.8730 | − | 12.6284i | 1.70799 | − | 0.986110i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 22.3095 | + | 12.8804i | 1.73155 | + | 0.999711i | ||||
\(167\) | − | 16.0772i | − | 1.24409i | −0.782980 | − | 0.622047i | \(-0.786301\pi\) | ||
0.782980 | − | 0.622047i | \(-0.213699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.10257 | + | 15.7661i | 0.694065 | + | 1.20216i | ||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 2.39205i | 0.181341i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −17.3184 | + | 9.99879i | −1.29807 | + | 0.749441i | ||||
\(179\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(180\) | −11.1270 | − | 6.42419i | −0.829359 | − | 0.478831i | ||||
\(181\) | − | 15.1485i | − | 1.12598i | −0.826465 | − | 0.562988i | \(-0.809652\pi\) | ||
0.826465 | − | 0.562988i | \(-0.190348\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.85993 | −0.359257 | ||||||||
\(184\) | 10.6190 | − | 18.3926i | 0.782839 | − | 1.35592i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 18.9737i | 1.38380i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | −2.46917 | + | 1.42558i | −0.178197 | + | 0.102882i | ||||
\(193\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(200\) | −7.07107 | − | 12.2474i | −0.500000 | − | 0.866025i | ||||
\(201\) | 4.88105 | + | 2.81808i | 0.344283 | + | 0.198772i | ||||
\(202\) | 15.7209i | 1.10612i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.1190 | − | 24.4547i | 0.986110 | − | 1.70799i | ||||
\(206\) | −23.1825 | + | 13.3844i | −1.61520 | + | 0.932535i | ||||
\(207\) | −10.7862 | − | 18.6823i | −0.749695 | − | 1.29851i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.3095 | + | 21.3206i | 0.841458 | + | 1.45745i | ||||
\(215\) | 17.6271 | + | 10.1770i | 1.20216 | + | 0.694065i | ||||
\(216\) | 5.92017i | 0.402816i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.11797 | 0.346633 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3.16228i | − | 0.211762i | −0.994379 | − | 0.105881i | \(-0.966234\pi\) | ||
0.994379 | − | 0.105881i | \(-0.0337662\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.3649 | −0.957661 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.6475 | + | 14.2302i | −1.63591 | + | 0.944495i | −0.653693 | + | 0.756760i | \(0.726781\pi\) |
−0.982220 | + | 0.187735i | \(0.939885\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.2379 | + | 13.4164i | 1.53560 | + | 0.886581i | 0.999088 | + | 0.0426906i | \(0.0135930\pi\) |
0.536515 | + | 0.843891i | \(0.319740\pi\) | |||||||
\(230\) | − | 23.7447i | − | 1.56568i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.4236 | −0.881304 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.6066 | + | 18.3712i | 0.691898 | + | 1.19840i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | −1.59384 | + | 2.76062i | −0.102882 | + | 0.178197i | ||||
\(241\) | −11.6190 | + | 6.70820i | −0.748442 | + | 0.432113i | −0.825131 | − | 0.564942i | \(-0.808899\pi\) |
0.0766885 | + | 0.997055i | \(0.475565\pi\) | |||||||
\(242\) | 7.77817 | + | 13.4722i | 0.500000 | + | 0.866025i | ||||
\(243\) | 7.86799 | + | 4.54259i | 0.504732 | + | 0.291407i | ||||
\(244\) | − | 27.2728i | − | 1.74596i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.36492 | −0.405812 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.24597 | − | 5.62218i | −0.205705 | − | 0.356291i | ||||
\(250\) | −13.6931 | − | 7.90569i | −0.866025 | − | 0.500000i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.00000 | − | 5.19615i | 0.188237 | − | 0.326036i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | − | 4.58785i | − | 0.285627i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.81754 | + | 11.8083i | −0.421995 | + | 0.730917i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.2128 | + | 28.0815i | 0.999727 | + | 1.73158i | 0.520104 | + | 0.854103i | \(0.325893\pi\) |
0.479623 | + | 0.877475i | \(0.340774\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.03956 | 0.308416 | ||||||||
\(268\) | −15.8144 | + | 27.3913i | −0.966017 | + | 1.67319i | ||||
\(269\) | 8.31754 | − | 4.80213i | 0.507129 | − | 0.292791i | −0.224523 | − | 0.974469i | \(-0.572083\pi\) |
0.731653 | + | 0.681677i | \(0.238749\pi\) | |||||||
\(270\) | 3.30948 | + | 5.73218i | 0.201408 | + | 0.348849i | ||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.63508 | + | 2.67607i | −0.278999 | + | 0.161080i | ||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | 2.39076 | − | 4.14092i | 0.142368 | − | 0.246588i | ||||
\(283\) | 13.6931 | − | 7.90569i | 0.813968 | − | 0.469945i | −0.0343638 | − | 0.999409i | \(-0.510941\pi\) |
0.848332 | + | 0.529465i | \(0.177607\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −16.2520 | −0.957661 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | −12.9974 | + | 7.50403i | −0.763232 | + | 0.440652i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.74667 | − | 9.95352i | −0.332896 | − | 0.576592i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 3.56394i | 0.205764i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.98089 | − | 3.43101i | 0.113799 | − | 0.197106i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.2460 | − | 26.4068i | −0.872982 | − | 1.51205i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.0668i | − | 1.20234i | −0.799120 | − | 0.601172i | \(-0.794701\pi\) | ||
0.799120 | − | 0.601172i | \(-0.205299\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.74597 | 0.383765 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −15.4919 | − | 8.94427i | −0.866025 | − | 0.500000i | ||||
\(321\) | − | 6.20419i | − | 0.346284i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −7.87298 | + | 13.6364i | −0.437388 | + | 0.757578i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.00000 | − | 15.5885i | −0.498464 | − | 0.863365i | ||||
\(327\) | −1.11698 | − | 0.644886i | −0.0617689 | − | 0.0356623i | ||||
\(328\) | − | 35.7184i | − | 1.97222i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(332\) | 31.5504 | − | 18.2156i | 1.73155 | − | 0.999711i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.6905 | − | 11.3683i | −1.07742 | − | 0.622047i | ||||
\(335\) | 35.3620i | 1.93203i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | −9.19239 | + | 15.9217i | −0.500000 | + | 0.866025i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 25.7460 | 1.38813 | ||||||||
\(345\) | −2.99193 | + | 5.18218i | −0.161080 | + | 0.278999i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.31335 | + | 10.9350i | 0.338918 | + | 0.587024i | 0.984230 | − | 0.176896i | \(-0.0566056\pi\) |
−0.645311 | + | 0.763920i | \(0.723272\pi\) | |||||||
\(348\) | 2.92965 | + | 1.69143i | 0.157046 | + | 0.0906704i | ||||
\(349\) | 9.10025i | 0.487125i | 0.969885 | + | 0.243563i | \(0.0783162\pi\) | ||||
−0.969885 | + | 0.243563i | \(0.921684\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 28.2808i | 1.49888i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | −15.7360 | + | 9.08517i | −0.829359 | + | 0.478831i | ||||
\(361\) | 9.50000 | + | 16.4545i | 0.500000 | + | 0.866025i | ||||
\(362\) | −18.5530 | − | 10.7116i | −0.975124 | − | 0.562988i | ||||
\(363\) | − | 3.92033i | − | 0.205764i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.43649 | + | 5.95218i | −0.179628 | + | 0.311125i | ||||
\(367\) | −30.0071 | + | 17.3246i | −1.56636 | + | 0.904338i | −0.569771 | + | 0.821803i | \(0.692968\pi\) |
−0.996588 | + | 0.0825348i | \(0.973698\pi\) | |||||||
\(368\) | −15.0175 | − | 26.0110i | −0.782839 | − | 1.35592i | ||||
\(369\) | −31.4204 | − | 18.1406i | −1.63568 | − | 0.944359i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.99230 | + | 3.45077i | 0.102882 | + | 0.178197i | ||||
\(376\) | 23.2379 | + | 13.4164i | 1.19840 | + | 0.691898i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.30948 | + | 0.756026i | −0.0670864 | + | 0.0387324i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.4763 | + | 18.7502i | 1.65946 | + | 0.958091i | 0.972964 | + | 0.230959i | \(0.0741862\pi\) |
0.686498 | + | 0.727132i | \(0.259147\pi\) | |||||||
\(384\) | 4.03214i | 0.205764i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.0758 | − | 22.6479i | 0.664679 | − | 1.15126i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.0000 | + | 20.7846i | 0.608424 | + | 1.05382i | 0.991500 | + | 0.130105i | \(0.0415314\pi\) |
−0.383076 | + | 0.923717i | \(0.625135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.0000 | −1.00000 | ||||||||
\(401\) | −19.9919 | + | 34.6270i | −0.998350 | + | 1.72919i | −0.449439 | + | 0.893311i | \(0.648376\pi\) |
−0.548911 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(402\) | 6.90285 | − | 3.98536i | 0.344283 | − | 0.198772i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 19.2540 | + | 11.1163i | 0.957924 | + | 0.553058i | ||||
\(405\) | 17.6045i | 0.874776i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.4284 | − | 8.33026i | 0.713440 | − | 0.411905i | −0.0988936 | − | 0.995098i | \(-0.531530\pi\) |
0.812333 | + | 0.583193i | \(0.198197\pi\) | |||||||
\(410\) | −19.9672 | − | 34.5842i | −0.986110 | − | 1.70799i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 37.8568i | 1.86507i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −30.5081 | −1.49939 | ||||||||
\(415\) | 20.3657 | − | 35.2744i | 0.999711 | − | 1.73155i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.8569 | 1.89377 | 0.946883 | − | 0.321577i | \(-0.104213\pi\) | ||||
0.946883 | + | 0.321577i | \(0.104213\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 23.6040 | − | 13.6278i | 1.14766 | − | 0.662604i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 34.8165 | 1.68292 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 24.9284 | − | 14.3924i | 1.20216 | − | 0.694065i | ||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 7.25070 | + | 4.18619i | 0.348849 | + | 0.201408i | ||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.78216 | 0.181341 | ||||||||
\(436\) | 3.61895 | − | 6.26821i | 0.173316 | − | 0.300193i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.14513 | − | 10.6437i | 0.291964 | − | 0.505696i | −0.682310 | − | 0.731063i | \(-0.739025\pi\) |
0.974274 | + | 0.225367i | \(0.0723580\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.8095 | + | 27.3828i | 0.749441 | + | 1.29807i | ||||
\(446\) | −3.87298 | − | 2.23607i | −0.183391 | − | 0.105881i | ||||
\(447\) | 2.89642i | 0.136996i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.36492 | −0.0644144 | −0.0322072 | − | 0.999481i | \(-0.510254\pi\) | ||||
−0.0322072 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(450\) | −10.1575 | + | 17.5934i | −0.478831 | + | 0.829359i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 40.2492i | 1.88899i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(458\) | 32.8634 | − | 18.9737i | 1.53560 | − | 0.886581i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −29.0812 | − | 16.7900i | −1.35592 | − | 0.782839i | ||||
\(461\) | 8.94427i | 0.416576i | 0.978068 | + | 0.208288i | \(0.0667892\pi\) | ||||
−0.978068 | + | 0.208288i | \(0.933211\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.2380 | 1.35881 | 0.679403 | − | 0.733766i | \(-0.262239\pi\) | ||||
0.679403 | + | 0.733766i | \(0.262239\pi\) | |||||||
\(464\) | −9.49193 | + | 16.4405i | −0.440652 | + | 0.763232i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.0714 | − | 6.96944i | −0.558599 | − | 0.322507i | 0.193984 | − | 0.981005i | \(-0.437859\pi\) |
−0.752583 | + | 0.658497i | \(0.771192\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 30.0000 | 1.38380 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 2.25403 | + | 3.90410i | 0.102882 | + | 0.178197i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 18.9737i | 0.864227i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.0000 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 11.1270 | − | 6.42419i | 0.504732 | − | 0.291407i | ||||
\(487\) | −19.0919 | − | 33.0681i | −0.865136 | − | 1.49846i | −0.866912 | − | 0.498461i | \(-0.833899\pi\) |
0.00177647 | − | 0.999998i | \(-0.499435\pi\) | |||||||
\(488\) | −33.4022 | − | 19.2848i | −1.51205 | − | 0.872982i | ||||
\(489\) | 4.53615i | 0.205132i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | −4.50068 | + | 7.79540i | −0.202906 | + | 0.351444i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −9.18098 | −0.411410 | ||||||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | −19.3649 | + | 11.1803i | −0.866025 | + | 0.500000i | ||||
\(501\) | 2.86492 | + | 4.96218i | 0.127995 | + | 0.221694i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 33.2237i | − | 1.48137i | −0.671852 | − | 0.740685i | \(-0.734501\pi\) | ||
0.671852 | − | 0.740685i | \(-0.265499\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.8569 | 1.10612 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.01240 | − | 2.31656i | 0.178197 | − | 0.102882i | ||||
\(508\) | −4.24264 | − | 7.34847i | −0.188237 | − | 0.326036i | ||||
\(509\) | 14.8649 | + | 8.58226i | 0.658876 | + | 0.380402i | 0.791849 | − | 0.610718i | \(-0.209119\pi\) |
−0.132973 | + | 0.991120i | \(0.542452\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6274 | −1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.1626 | + | 36.6547i | 0.932535 | + | 1.61520i | ||||
\(516\) | −5.61895 | − | 3.24410i | −0.247360 | − | 0.142814i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.4919 | − | 8.94427i | 0.678714 | − | 0.391856i | −0.120656 | − | 0.992694i | \(-0.538500\pi\) |
0.799370 | + | 0.600839i | \(0.205167\pi\) | |||||||
\(522\) | 9.64146 | + | 16.6995i | 0.421995 | + | 0.730917i | ||||
\(523\) | 30.1247 | + | 17.3925i | 1.31726 | + | 0.760522i | 0.983287 | − | 0.182060i | \(-0.0582764\pi\) |
0.333975 | + | 0.942582i | \(0.391610\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 45.8569 | 1.99945 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6905 | − | 28.9088i | −0.725675 | − | 1.25691i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.56351 | − | 6.17218i | 0.154208 | − | 0.267096i | ||||
\(535\) | 33.7109 | − | 19.4630i | 1.45745 | − | 0.841458i | ||||
\(536\) | 22.3649 | + | 38.7372i | 0.966017 | + | 1.67319i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 13.5825i | − | 0.585583i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.36061 | 0.402816 | ||||||||
\(541\) | 21.1190 | − | 36.5791i | 0.907975 | − | 1.57266i | 0.0911008 | − | 0.995842i | \(-0.470961\pi\) |
0.816874 | − | 0.576816i | \(-0.195705\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.69941 | + | 4.67551i | 0.115843 | + | 0.200646i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 8.09222i | − | 0.346633i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.5959 | 0.880618 | 0.440309 | − | 0.897846i | \(-0.354869\pi\) | ||||
0.440309 | + | 0.897846i | \(0.354869\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −33.9284 | + | 19.5886i | −1.44803 | + | 0.836020i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 7.56906i | 0.322161i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.48528 | + | 14.6969i | −0.357930 | + | 0.619953i | ||||
\(563\) | −19.4789 | + | 11.2462i | −0.820939 | + | 0.473970i | −0.850740 | − | 0.525586i | \(-0.823846\pi\) |
0.0298010 | + | 0.999556i | \(0.490513\pi\) | |||||||
\(564\) | −3.38105 | − | 5.85615i | −0.142368 | − | 0.246588i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 22.3607i | − | 0.939889i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.0000 | + | 31.1769i | −0.754599 | + | 1.30700i | 0.190974 | + | 0.981595i | \(0.438835\pi\) |
−0.945573 | + | 0.325409i | \(0.894498\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −37.5437 | −1.56568 | ||||||||
\(576\) | −11.4919 | + | 19.9046i | −0.478831 | + | 0.829359i | ||||
\(577\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(578\) | −12.0208 | − | 20.8207i | −0.500000 | − | 0.866025i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 21.2246i | 0.881304i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 47.4342i | − | 1.95782i | −0.204298 | − | 0.978909i | \(-0.565491\pi\) | ||
0.204298 | − | 0.978909i | \(-0.434509\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.2540 | −0.665791 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 4.36492 | + | 2.52009i | 0.178197 | + | 0.102882i | ||||
\(601\) | 40.2492i | 1.64180i | 0.571072 | + | 0.820900i | \(0.306528\pi\) | ||||
−0.571072 | + | 0.820900i | \(0.693472\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 45.4345 | 1.85023 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.3014 | − | 12.2984i | 0.866025 | − | 0.500000i | ||||
\(606\) | −2.80141 | − | 4.85218i | −0.113799 | − | 0.197106i | ||||
\(607\) | 28.1553 | + | 16.2554i | 1.14279 | + | 0.659788i | 0.947119 | − | 0.320882i | \(-0.103979\pi\) |
0.195667 | + | 0.980670i | \(0.437313\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −43.1221 | −1.74596 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(614\) | −25.8014 | − | 14.8965i | −1.04126 | − | 0.601172i | ||||
\(615\) | 10.0638i | 0.405812i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 4.77012 | − | 8.26209i | 0.191882 | − | 0.332350i | ||||
\(619\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.6109 | + | 7.85825i | 0.546186 | + | 0.315341i | ||||
\(622\) | 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 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.21584 | − | 4.74342i | −0.326036 | − | 0.188237i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.9089 | + | 12.6491i | −0.866025 | + | 0.500000i | ||||
\(641\) | −18.3014 | − | 31.6990i | −0.722862 | − | 1.25203i | −0.959848 | − | 0.280521i | \(-0.909493\pi\) |
0.236986 | − | 0.971513i | \(-0.423841\pi\) | |||||||
\(642\) | −7.59855 | − | 4.38702i | −0.299891 | − | 0.173142i | ||||
\(643\) | 41.1096i | 1.62120i | 0.585597 | + | 0.810602i | \(0.300860\pi\) | ||||
−0.585597 | + | 0.810602i | \(0.699140\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.25403 | −0.285627 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.3282 | + | 19.8194i | −1.34958 | + | 0.779180i | −0.988190 | − | 0.153234i | \(-0.951031\pi\) |
−0.361390 | + | 0.932415i | \(0.617698\pi\) | |||||||
\(648\) | 11.1341 | + | 19.2848i | 0.437388 | + | 0.757578i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −25.4558 | −0.996928 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | −1.57964 | + | 0.912006i | −0.0617689 | + | 0.0356623i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −43.7460 | − | 25.2567i | −1.70799 | − | 0.986110i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.57157 | + | 3.79410i | −0.255605 | + | 0.147573i | −0.622328 | − | 0.782757i | \(-0.713813\pi\) |
0.366723 | + | 0.930330i | \(0.380480\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 51.5215i | − | 1.99942i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.8181 | + | 30.8618i | −0.689919 | + | 1.19498i | ||||
\(668\) | −27.8466 | + | 16.0772i | −1.07742 | + | 0.622047i | ||||
\(669\) | 0.563508 | + | 0.976025i | 0.0217865 | + | 0.0377353i | ||||
\(670\) | 43.3095 | + | 25.0047i | 1.67319 | + | 0.966017i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.06337 | − | 5.23274i | 0.348849 | − | 0.201408i | ||||
\(676\) | 13.0000 | + | 22.5167i | 0.500000 | + | 0.866025i | ||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.07157 | − | 8.78423i | 0.194343 | − | 0.336612i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.36360 | + | 2.36183i | 0.0521768 | + | 0.0903729i | 0.890934 | − | 0.454132i | \(-0.150051\pi\) |
−0.838757 | + | 0.544505i | \(0.816717\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.56305 | −0.364853 | ||||||||
\(688\) | 18.2051 | − | 31.5322i | 0.694065 | − | 1.20216i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.23123 | + | 7.32871i | 0.161080 | + | 0.278999i | ||||
\(691\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.8569 | 0.677837 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.14315 | − | 2.39205i | 0.157046 | − | 0.0906704i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 11.1455 | + | 6.43485i | 0.421863 | + | 0.243563i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.3649 | −1.63787 | −0.818935 | − | 0.573886i | \(-0.805435\pi\) | ||||
−0.818935 | + | 0.573886i | \(0.805435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.54738 | − | 3.78013i | −0.246588 | − | 0.142368i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.118950 | − | 0.206028i | 0.00446726 | − | 0.00773753i | −0.863783 | − | 0.503864i | \(-0.831911\pi\) |
0.868250 | + | 0.496126i | \(0.165245\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 34.6368 | + | 19.9976i | 1.29807 | + | 0.749441i | ||||
\(713\) | 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 | \(0.166667\pi\) | |||||||
\(720\) | 25.6967i | 0.957661i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 26.8701 | 1.00000 | ||||||||
\(723\) | 2.39076 | − | 4.14092i | 0.0889134 | − | 0.154003i | ||||
\(724\) | −26.2379 | + | 15.1485i | −0.975124 | + | 0.562988i | ||||
\(725\) | 11.8649 | + | 20.5506i | 0.440652 | + | 0.763232i | ||||
\(726\) | −4.80141 | − | 2.77209i | −0.178197 | − | 0.102882i | ||||
\(727\) | 23.2051i | 0.860630i | 0.902679 | + | 0.430315i | \(0.141598\pi\) | ||||
−0.902679 | + | 0.430315i | \(0.858402\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.3810 | 0.754854 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 4.85993 | + | 8.41765i | 0.179628 | + | 0.311125i | ||||
\(733\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(734\) | 49.0014i | 1.80868i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −42.4758 | −1.56568 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −44.4351 | + | 25.6546i | −1.63568 | + | 0.944359i | ||||
\(739\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.6442 | −1.01417 | −0.507083 | − | 0.861897i | \(-0.669276\pi\) | ||||
−0.507083 | + | 0.861897i | \(0.669276\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.7379 | + | 9.08628i | −0.576592 | + | 0.332896i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −45.3218 | − | 26.1666i | −1.65824 | − | 0.957385i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.63508 | 0.205764 | ||||||||
\(751\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(752\) | 32.8634 | − | 18.9737i | 1.19840 | − | 0.691898i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.9839 | − | 17.8885i | −1.12316 | − | 0.648459i | −0.180957 | − | 0.983491i | \(-0.557920\pi\) |
−0.942207 | + | 0.335032i | \(0.891253\pi\) | |||||||
\(762\) | 2.13836i | 0.0774647i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 45.9284 | − | 26.5168i | 1.65946 | − | 0.958091i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 4.93834 | + | 2.85115i | 0.178197 | + | 0.102882i | ||||
\(769\) | − | 53.6656i | − | 1.93523i | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||
0.252426 | − | 0.967616i | \(-0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(774\) | −18.4919 | − | 32.0290i | −0.664679 | − | 1.15126i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.9411 | 1.21685 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 9.93376i | − | 0.355004i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.8368 | + | 6.25665i | −0.386292 | + | 0.223026i | −0.680552 | − | 0.732700i | \(-0.738260\pi\) |
0.294260 | + | 0.955725i | \(0.404927\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.0081 | − | 5.77816i | −0.356297 | − | 0.205708i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −14.1421 | + | 24.4949i | −0.500000 | + | 0.866025i | ||||
\(801\) | 35.1825 | − | 20.3126i | 1.24311 | − | 0.717710i | ||||
\(802\) | 28.2729 | + | 48.9700i | 0.998350 | + | 1.72919i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 11.2723i | − | 0.397543i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.71145 | + | 2.96432i | −0.0602460 | + | 0.104349i | ||||
\(808\) | 27.2293 | − | 15.7209i | 0.957924 | − | 0.553058i | ||||
\(809\) | 5.75403 | + | 9.96628i | 0.202301 | + | 0.350396i | 0.949269 | − | 0.314464i | \(-0.101825\pi\) |
−0.746968 | + | 0.664860i | \(0.768491\pi\) | |||||||
\(810\) | 21.5611 | + | 12.4483i | 0.757578 | + | 0.437388i | ||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.6475 | + | 14.2302i | −0.863365 | + | 0.498464i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 23.5615i | − | 0.823809i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −56.4758 | −1.97222 | ||||||||
\(821\) | 24.0000 | − | 41.5692i | 0.837606 | − | 1.45078i | −0.0542853 | − | 0.998525i | \(-0.517288\pi\) |
0.891891 | − | 0.452250i | \(-0.149379\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.94205 | + | 12.0240i | 0.241985 | + | 0.419130i | 0.961280 | − | 0.275575i | \(-0.0888683\pi\) |
−0.719295 | + | 0.694705i | \(0.755535\pi\) | |||||||
\(824\) | 46.3649 | + | 26.7688i | 1.61520 | + | 0.932535i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −57.3426 | −1.99400 | −0.997000 | − | 0.0774065i | \(-0.975336\pi\) | ||||
−0.997000 | + | 0.0774065i | \(0.975336\pi\) | |||||||
\(828\) | −21.5725 | + | 37.3646i | −0.749695 | + | 1.29851i | ||||
\(829\) | −11.6190 | + | 6.70820i | −0.403543 | + | 0.232986i | −0.688012 | − | 0.725700i | \(-0.741516\pi\) |
0.284469 | + | 0.958685i | \(0.408183\pi\) | |||||||
\(830\) | −28.8014 | − | 49.8855i | −0.999711 | − | 1.73155i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.9749 | + | 31.1335i | −0.622047 | + | 1.07742i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.47580 | −0.223303 | ||||||||
\(842\) | 27.4759 | − | 47.5897i | 0.946883 | − | 1.64005i | ||||
\(843\) | 3.70375 | − | 2.13836i | 0.127564 | − | 0.0736492i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.1744 | + | 14.5344i | 0.866025 | + | 0.500000i | ||||
\(846\) | − | 38.5451i | − | 1.32521i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.81754 | + | 4.88013i | −0.0966978 | + | 0.167485i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24.6190 | − | 42.6413i | 0.841458 | − | 1.45745i | ||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(860\) | − | 40.7079i | − | 1.38813i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.6036 | + | 32.2224i | −0.633274 | + | 1.09686i | 0.353604 | + | 0.935395i | \(0.384956\pi\) |
−0.986878 | + | 0.161468i | \(0.948377\pi\) | |||||||
\(864\) | 10.2540 | − | 5.92017i | 0.348849 | − | 0.201408i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.05870i | 0.205764i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 2.67439 | − | 4.63218i | 0.0906704 | − | 0.157046i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −5.11797 | − | 8.86458i | −0.173316 | − | 0.300193i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 18.6766i | − | 0.629230i | −0.949219 | − | 0.314615i | \(-0.898125\pi\) | ||
0.949219 | − | 0.314615i | \(-0.101875\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.1543 | −1.85609 | −0.928045 | − | 0.372467i | \(-0.878512\pi\) | ||||
−0.928045 | + | 0.372467i | \(0.878512\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.69052 | − | 15.0524i | −0.291964 | − | 0.505696i | ||||
\(887\) | −26.9207 | − | 15.5427i | −0.903908 | − | 0.521871i | −0.0254417 | − | 0.999676i | \(-0.508099\pi\) |
−0.878466 | + | 0.477805i | \(0.841433\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 44.7159 | 1.49888 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.47723 | + | 3.16228i | −0.183391 | + | 0.105881i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 3.54738 | + | 2.04808i | 0.118642 | + | 0.0684980i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.965142 | + | 1.67167i | −0.0322072 | + | 0.0557845i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 14.3649 | + | 24.8808i | 0.478831 | + | 0.829359i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.9365 | + | 29.3349i | −0.562988 | + | 0.975124i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.0775 | − | 46.8996i | −0.899093 | − | 1.55727i | −0.828656 | − | 0.559759i | \(-0.810894\pi\) |
−0.0704373 | − | 0.997516i | \(-0.522439\pi\) | |||||||
\(908\) | 49.2950 | + | 28.4605i | 1.63591 | + | 0.944495i | ||||
\(909\) | − | 31.9370i | − | 1.05928i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.41122 | + | 5.43357i | 0.311125 | + | 0.179628i | ||||
\(916\) | − | 53.6656i | − | 1.77316i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(920\) | −41.1270 | + | 23.7447i | −1.35592 | + | 0.782839i | ||||
\(921\) | 3.75403 | + | 6.50218i | 0.123700 | + | 0.214254i | ||||
\(922\) | 10.9545 | + | 6.32456i | 0.360766 | + | 0.208288i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 20.6744 | − | 35.8091i | 0.679403 | − | 1.17676i | ||||
\(927\) | 47.0953 | − | 27.1905i | 1.54681 | − | 0.893053i | ||||
\(928\) | 13.4236 | + | 23.2504i | 0.440652 | + | 0.763232i | ||||
\(929\) | 5.69859 | + | 3.29008i | 0.186965 | + | 0.107944i | 0.590561 | − | 0.806993i | \(-0.298907\pi\) |
−0.403596 | + | 0.914937i | \(0.632240\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.0716 | + | 9.85628i | −0.558599 | + | 0.322507i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 21.2132 | − | 36.7423i | 0.691898 | − | 1.19840i | ||||
\(941\) | −38.7298 | + | 22.3607i | −1.26256 | + | 0.728937i | −0.973568 | − | 0.228395i | \(-0.926652\pi\) |
−0.288988 | + | 0.957333i | \(0.593319\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −82.1192 | − | 47.4115i | −2.67417 | − | 1.54393i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.0949 | − | 19.2169i | 0.360535 | − | 0.624465i | −0.627514 | − | 0.778605i | \(-0.715927\pi\) |
0.988049 | + | 0.154140i | \(0.0492608\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6.37537 | 0.205764 | ||||||||
\(961\) | 15.5000 | − | 26.8468i | 0.500000 | − | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.0068 | − | 43.3130i | −0.805832 | − | 1.39574i | ||||
\(964\) | 23.2379 | + | 13.4164i | 0.748442 | + | 0.432113i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.9365 | 1.89527 | 0.947635 | − | 0.319356i | \(-0.103467\pi\) | ||||
0.947635 | + | 0.319356i | \(0.103467\pi\) | |||||||
\(968\) | 15.5563 | − | 26.9444i | 0.500000 | − | 0.866025i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(972\) | − | 18.1703i | − | 0.582814i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −54.0000 | −1.73027 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −47.2379 | + | 27.2728i | −1.51205 | + | 0.872982i | ||||
\(977\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 5.55563 | + | 3.20755i | 0.177650 | + | 0.102566i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.3972 | −0.331957 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.2195 | − | 5.90026i | 0.325953 | − | 0.188189i | −0.328090 | − | 0.944646i | \(-0.606405\pi\) |
0.654043 | + | 0.756457i | \(0.273072\pi\) | |||||||
\(984\) | 6.36492 | + | 11.0244i | 0.202906 | + | 0.351444i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.1744 | − | 59.1918i | 1.08668 | − | 1.88219i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.49193 | + | 11.2444i | −0.205705 | + | 0.356291i | ||||
\(997\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))