Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2028,2,Mod(529,2028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2028, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2028.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2028.i (of order \(3\), 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: | \(16.1936615299\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 156) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2028.529 |
Dual form | 2028.2.i.a.2005.1 |
$q$-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 \(\left(\mathbb{Z}/2028\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(1015\) | \(1861\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 3.46410i | −0.755929 | − | 1.30931i | −0.944911 | − | 0.327327i | \(-0.893852\pi\) |
0.188982 | − | 0.981981i | \(-0.439481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | − | 5.19615i | 0.904534 | − | 1.56670i | 0.0829925 | − | 0.996550i | \(-0.473552\pi\) |
0.821541 | − | 0.570149i | \(-0.193114\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | − | 1.73205i | 0.258199 | − | 0.447214i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | − | 1.73205i | −0.242536 | − | 0.420084i | 0.718900 | − | 0.695113i | \(-0.244646\pi\) |
−0.961436 | + | 0.275029i | \(0.911312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | + | 6.92820i | −0.834058 | + | 1.44463i | 0.0607377 | + | 0.998154i | \(0.480655\pi\) |
−0.894795 | + | 0.446476i | \(0.852679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | + | 1.73205i | −0.185695 | + | 0.321634i | −0.943811 | − | 0.330487i | \(-0.892787\pi\) |
0.758115 | + | 0.652121i | \(0.226120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.00000 | + | 5.19615i | 0.522233 | + | 0.904534i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.00000 | + | 6.92820i | 0.676123 | + | 1.17108i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | + | 6.92820i | −0.657596 | + | 1.13899i | 0.323640 | + | 0.946180i | \(0.395093\pi\) |
−0.981236 | + | 0.192809i | \(0.938240\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | + | 1.73205i | −0.156174 | + | 0.270501i | −0.933486 | − | 0.358614i | \(-0.883249\pi\) |
0.777312 | + | 0.629115i | \(0.216583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | − | 6.92820i | −0.609994 | − | 1.05654i | −0.991241 | − | 0.132068i | \(-0.957838\pi\) |
0.381246 | − | 0.924473i | \(-0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | + | 1.73205i | 0.149071 | + | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.50000 | + | 7.79423i | −0.642857 | + | 1.11346i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | + | 10.3923i | −0.809040 | + | 1.40130i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | + | 1.73205i | 0.130189 | + | 0.225494i | 0.923749 | − | 0.382998i | \(-0.125108\pi\) |
−0.793560 | + | 0.608492i | \(0.791775\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | − | 1.73205i | −0.128037 | − | 0.221766i | 0.794879 | − | 0.606768i | \(-0.207534\pi\) |
−0.922916 | + | 0.385002i | \(0.874201\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.00000 | + | 3.46410i | −0.251976 | + | 0.436436i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.00000 | − | 6.92820i | −0.481543 | − | 0.834058i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | + | 5.19615i | 0.356034 | + | 0.616670i | 0.987294 | − | 0.158901i | \(-0.0507952\pi\) |
−0.631260 | + | 0.775571i | \(0.717462\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −24.0000 | −2.73505 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.0000 | −1.53670 | −0.768350 | − | 0.640030i | \(-0.778922\pi\) | ||||
−0.768350 | + | 0.640030i | \(0.778922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | + | 3.46410i | 0.216930 | + | 0.375735i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | − | 1.73205i | −0.107211 | − | 0.185695i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.00000 | + | 6.92820i | −0.414781 | + | 0.718421i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | − | 10.3923i | −0.609208 | − | 1.05518i | −0.991371 | − | 0.131084i | \(-0.958154\pi\) |
0.382164 | − | 0.924095i | \(-0.375179\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.00000 | + | 8.66025i | −0.497519 | + | 0.861727i | −0.999996 | − | 0.00286291i | \(-0.999089\pi\) |
0.502477 | + | 0.864590i | \(0.332422\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.00000 | −0.780720 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.0000 | + | 17.3205i | −0.966736 | + | 1.67444i | −0.261861 | + | 0.965106i | \(0.584336\pi\) |
−0.704875 | + | 0.709331i | \(0.748997\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | − | 6.92820i | −0.379663 | − | 0.657596i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.00000 | + | 8.66025i | 0.470360 | + | 0.814688i | 0.999425 | − | 0.0338931i | \(-0.0107906\pi\) |
−0.529065 | + | 0.848581i | \(0.677457\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | − | 13.8564i | 0.746004 | − | 1.29212i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.00000 | + | 6.92820i | −0.366679 | + | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | − | 21.6506i | −1.13636 | − | 1.96824i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.00000 | − | 1.73205i | −0.0901670 | − | 0.156174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | − | 6.92820i | 0.354943 | − | 0.614779i | −0.632166 | − | 0.774833i | \(-0.717834\pi\) |
0.987108 | + | 0.160055i | \(0.0511671\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.00000 | −0.172133 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.00000 | − | 8.66025i | −0.427179 | − | 0.739895i | 0.569442 | − | 0.822031i | \(-0.307159\pi\) |
−0.996621 | + | 0.0821359i | \(0.973826\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | + | 6.92820i | 0.339276 | + | 0.587643i | 0.984297 | − | 0.176522i | \(-0.0564848\pi\) |
−0.645021 | + | 0.764165i | \(0.723151\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | − | 5.19615i | 0.252646 | − | 0.437595i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | − | 3.46410i | 0.166091 | − | 0.287678i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.50000 | − | 7.79423i | −0.371154 | − | 0.642857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.00000 | − | 8.66025i | −0.409616 | − | 0.709476i | 0.585231 | − | 0.810867i | \(-0.301004\pi\) |
−0.994847 | + | 0.101391i | \(0.967671\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.00000 | + | 1.73205i | −0.0808452 | + | 0.140028i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.0000 | −1.28515 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.00000 | + | 5.19615i | −0.237915 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 32.0000 | 2.52195 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | + | 6.92820i | 0.313304 | + | 0.542659i | 0.979076 | − | 0.203497i | \(-0.0652307\pi\) |
−0.665771 | + | 0.746156i | \(0.731897\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.00000 | − | 10.3923i | −0.467099 | − | 0.809040i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.00000 | + | 15.5885i | −0.696441 | + | 1.20627i | 0.273252 | + | 0.961943i | \(0.411901\pi\) |
−0.969693 | + | 0.244328i | \(0.921432\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | \(-0.0934200\pi\) |
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | + | 3.46410i | 0.151186 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.00000 | −0.150329 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.00000 | + | 10.3923i | −0.448461 | + | 0.776757i | −0.998286 | − | 0.0585225i | \(-0.981361\pi\) |
0.549825 | + | 0.835280i | \(0.314694\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.00000 | − | 13.8564i | 0.588172 | − | 1.01874i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | −0.877527 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.00000 | − | 3.46410i | −0.145479 | − | 0.251976i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000 | + | 20.7846i | 0.868290 | + | 1.50392i | 0.863743 | + | 0.503932i | \(0.168114\pi\) |
0.00454614 | + | 0.999990i | \(0.498553\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.00000 | − | 6.92820i | 0.287926 | − | 0.498703i | −0.685388 | − | 0.728178i | \(-0.740368\pi\) |
0.973315 | + | 0.229475i | \(0.0737008\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.0000 | − | 22.5167i | 0.926212 | − | 1.60425i | 0.136611 | − | 0.990625i | \(-0.456379\pi\) |
0.789601 | − | 0.613621i | \(-0.210288\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | + | 3.46410i | 0.141069 | + | 0.244339i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.00000 | 0.561490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | − | 3.46410i | 0.139686 | − | 0.241943i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.00000 | 0.556038 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.00000 | + | 10.3923i | −0.413057 | + | 0.715436i | −0.995222 | − | 0.0976347i | \(-0.968872\pi\) |
0.582165 | + | 0.813070i | \(0.302206\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.00000 | −0.411113 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | + | 13.8564i | 0.545595 | + | 0.944999i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.0000 | − | 27.7128i | −1.08615 | − | 1.88127i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.00000 | − | 3.46410i | 0.135147 | − | 0.234082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | + | 6.92820i | −0.267860 | + | 0.463947i | −0.968309 | − | 0.249756i | \(-0.919650\pi\) |
0.700449 | + | 0.713702i | \(0.252983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.500000 | + | 0.866025i | 0.0333333 | + | 0.0577350i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.00000 | + | 1.73205i | 0.0663723 | + | 0.114960i | 0.897302 | − | 0.441417i | \(-0.145524\pi\) |
−0.830930 | + | 0.556378i | \(0.812191\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.0000 | −1.32164 | −0.660819 | − | 0.750546i | \(-0.729791\pi\) | ||||
−0.660819 | + | 0.750546i | \(0.729791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | − | 20.7846i | 0.789542 | − | 1.36753i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000 | 0.782794 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.0000 | 0.646846 | 0.323423 | − | 0.946254i | \(-0.395166\pi\) | ||||
0.323423 | + | 0.946254i | \(0.395166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | − | 17.3205i | −0.644157 | − | 1.11571i | −0.984496 | − | 0.175409i | \(-0.943875\pi\) |
0.340339 | − | 0.940303i | \(-0.389458\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.00000 | − | 15.5885i | 0.574989 | − | 0.995910i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.00000 | − | 12.1244i | 0.443607 | − | 0.768350i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.0000 | + | 17.3205i | 0.631194 | + | 1.09326i | 0.987308 | + | 0.158818i | \(0.0507683\pi\) |
−0.356113 | + | 0.934443i | \(0.615898\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.0000 | + | 41.5692i | 1.50887 | + | 2.61343i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.00000 | + | 5.19615i | −0.187135 | + | 0.324127i | −0.944294 | − | 0.329104i | \(-0.893253\pi\) |
0.757159 | + | 0.653231i | \(0.226587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 32.0000 | 1.98838 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | −0.737154 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.00000 | − | 5.19615i | −0.183597 | − | 0.317999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.0000 | + | 19.0526i | 0.670682 | + | 1.16166i | 0.977711 | + | 0.209955i | \(0.0673317\pi\) |
−0.307029 | + | 0.951700i | \(0.599335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0000 | + | 17.3205i | −0.607457 | + | 1.05215i | 0.384201 | + | 0.923249i | \(0.374477\pi\) |
−0.991658 | + | 0.128897i | \(0.958856\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.00000 | + | 5.19615i | −0.180907 | + | 0.313340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | + | 19.0526i | 0.660926 | + | 1.14476i | 0.980373 | + | 0.197153i | \(0.0631696\pi\) |
−0.319447 | + | 0.947604i | \(0.603497\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | − | 6.92820i | −0.239474 | − | 0.414781i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.0000 | −1.31241 | −0.656205 | − | 0.754583i | \(-0.727839\pi\) | ||||
−0.656205 | + | 0.754583i | \(0.727839\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.00000 | − | 3.46410i | 0.118888 | − | 0.205919i | −0.800439 | − | 0.599414i | \(-0.795400\pi\) |
0.919327 | + | 0.393494i | \(0.128734\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.00000 | 0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0000 | 0.703452 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.00000 | + | 12.1244i | 0.408944 | + | 0.708312i | 0.994772 | − | 0.102123i | \(-0.0325637\pi\) |
−0.585827 | + | 0.810436i | \(0.699230\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.00000 | − | 3.46410i | −0.116445 | − | 0.201688i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.00000 | − | 5.19615i | 0.174078 | − | 0.301511i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | + | 27.7128i | −0.922225 | + | 1.59734i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.00000 | − | 8.66025i | −0.287242 | − | 0.497519i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.00000 | + | 3.46410i | 0.114520 | + | 0.198354i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.0000 | −1.14146 | −0.570730 | − | 0.821138i | \(-0.693340\pi\) | ||||
−0.570730 | + | 0.821138i | \(0.693340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.00000 | + | 3.46410i | −0.113776 | + | 0.197066i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.0000 | 0.907277 | 0.453638 | − | 0.891186i | \(-0.350126\pi\) | ||||
0.453638 | + | 0.891186i | \(0.350126\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.0000 | −0.791327 | −0.395663 | − | 0.918396i | \(-0.629485\pi\) | ||||
−0.395663 | + | 0.918396i | \(0.629485\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.00000 | − | 6.92820i | 0.225374 | − | 0.390360i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.00000 | + | 10.3923i | 0.335936 | + | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.0000 | − | 17.3205i | −0.558146 | − | 0.966736i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.00000 | − | 3.46410i | 0.110600 | − | 0.191565i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | + | 20.7846i | 0.661581 | + | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.0000 | − | 24.2487i | −0.769510 | − | 1.33283i | −0.937829 | − | 0.347097i | \(-0.887167\pi\) |
0.168320 | − | 0.985732i | \(-0.446166\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.00000 | 0.438397 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | + | 6.92820i | −0.218543 | + | 0.378528i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.0000 | −0.543125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.0000 | − | 41.5692i | 1.29967 | − | 2.25110i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.00000 | + | 13.8564i | 0.430706 | + | 0.746004i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.00000 | − | 10.3923i | −0.322097 | − | 0.557888i | 0.658824 | − | 0.752297i | \(-0.271054\pi\) |
−0.980921 | + | 0.194409i | \(0.937721\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.00000 | + | 6.92820i | −0.214115 | + | 0.370858i | −0.952998 | − | 0.302975i | \(-0.902020\pi\) |
0.738883 | + | 0.673833i | \(0.235353\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.00000 | + | 8.66025i | −0.266123 | + | 0.460939i | −0.967857 | − | 0.251500i | \(-0.919076\pi\) |
0.701734 | + | 0.712439i | \(0.252409\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | − | 10.3923i | −0.318447 | − | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.00000 | − | 6.92820i | −0.211702 | − | 0.366679i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.0000 | 0.527780 | 0.263890 | − | 0.964553i | \(-0.414994\pi\) | ||||
0.263890 | + | 0.964553i | \(0.414994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.50000 | − | 16.4545i | 0.500000 | − | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.0000 | 1.31216 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.00000 | 0.418739 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.0000 | − | 24.2487i | 0.730794 | − | 1.26577i | −0.225750 | − | 0.974185i | \(-0.572483\pi\) |
0.956544 | − | 0.291587i | \(-0.0941834\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | − | 20.7846i | −0.623009 | − | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.00000 | − | 5.19615i | −0.155334 | − | 0.269047i | 0.777847 | − | 0.628454i | \(-0.216312\pi\) |
−0.933181 | + | 0.359408i | \(0.882979\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.00000 | + | 10.3923i | −0.309839 | + | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000 | − | 13.8564i | 0.410932 | − | 0.711756i | −0.584060 | − | 0.811711i | \(-0.698537\pi\) |
0.994992 | + | 0.0999550i | \(0.0318699\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.00000 | + | 6.92820i | 0.204926 | + | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.0000 | − | 19.0526i | −0.562074 | − | 0.973540i | −0.997315 | − | 0.0732266i | \(-0.976670\pi\) |
0.435242 | − | 0.900314i | \(-0.356663\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 48.0000 | 2.44631 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.00000 | + | 6.92820i | −0.203331 | + | 0.352180i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.00000 | + | 3.46410i | −0.100887 | + | 0.174741i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.00000 | + | 13.8564i | 0.401508 | + | 0.695433i | 0.993908 | − | 0.110211i | \(-0.0351527\pi\) |
−0.592400 | + | 0.805644i | \(0.701819\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.00000 | + | 5.19615i | −0.149813 | + | 0.259483i | −0.931158 | − | 0.364615i | \(-0.881200\pi\) |
0.781345 | + | 0.624099i | \(0.214534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | − | 1.73205i | 0.0496904 | − | 0.0860663i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000 | + | 41.5692i | 1.18964 | + | 2.06051i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0000 | − | 17.3205i | −0.494468 | − | 0.856444i | 0.505511 | − | 0.862820i | \(-0.331304\pi\) |
−0.999980 | + | 0.00637586i | \(0.997970\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.0000 | 0.493264 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.00000 | − | 6.92820i | 0.196827 | − | 0.340915i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.0000 | 1.37447 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.00000 | −0.391762 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.0000 | + | 24.2487i | −0.683945 | + | 1.18463i | 0.289822 | + | 0.957080i | \(0.406404\pi\) |
−0.973767 | + | 0.227547i | \(0.926930\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.00000 | 0.194948 | 0.0974740 | − | 0.995238i | \(-0.468924\pi\) | ||||
0.0974740 | + | 0.995238i | \(0.468924\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.00000 | + | 5.19615i | 0.145865 | + | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00000 | + | 1.73205i | 0.0485071 | + | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.00000 | + | 6.92820i | −0.193574 | + | 0.335279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.00000 | − | 8.66025i | 0.240842 | − | 0.417150i | −0.720113 | − | 0.693857i | \(-0.755910\pi\) |
0.960954 | + | 0.276707i | \(0.0892433\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.0000 | + | 19.0526i | 0.528626 | + | 0.915608i | 0.999443 | + | 0.0333764i | \(0.0106260\pi\) |
−0.470817 | + | 0.882231i | \(0.656041\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.00000 | + | 3.46410i | 0.0958927 | + | 0.166091i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.0000 | − | 31.1769i | 0.859093 | − | 1.48799i | −0.0137020 | − | 0.999906i | \(-0.504362\pi\) |
0.872795 | − | 0.488087i | \(-0.162305\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.0000 | 0.950229 | 0.475114 | − | 0.879924i | \(-0.342407\pi\) | ||||
0.475114 | + | 0.879924i | \(0.342407\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | − | 10.3923i | 0.284427 | − | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.0000 | 0.472984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.0000 | − | 25.9808i | −0.707894 | − | 1.22611i | −0.965637 | − | 0.259895i | \(-0.916312\pi\) |
0.257743 | − | 0.966213i | \(-0.417021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.00000 | + | 10.3923i | 0.282529 | + | 0.489355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.00000 | + | 13.8564i | −0.375873 | + | 0.651031i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.00000 | − | 3.46410i | 0.0935561 | − | 0.162044i | −0.815449 | − | 0.578829i | \(-0.803510\pi\) |
0.909005 | + | 0.416785i | \(0.136843\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00000 | − | 1.73205i | −0.0466760 | − | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.00000 | − | 5.19615i | −0.139724 | − | 0.242009i | 0.787668 | − | 0.616100i | \(-0.211288\pi\) |
−0.927392 | + | 0.374091i | \(0.877955\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.0000 | 0.557687 | 0.278844 | − | 0.960337i | \(-0.410049\pi\) | ||||
0.278844 | + | 0.960337i | \(0.410049\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.00000 | − | 13.8564i | 0.370991 | − | 0.642575i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.00000 | − | 12.1244i | 0.322543 | − | 0.558661i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −48.0000 | −2.20704 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.00000 | − | 5.19615i | −0.137361 | − | 0.237915i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.00000 | − | 15.5885i | 0.411220 | − | 0.712255i | −0.583803 | − | 0.811895i | \(-0.698436\pi\) |
0.995023 | + | 0.0996406i | \(0.0317693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.0000 | + | 27.7128i | −0.728025 | + | 1.26098i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.0000 | + | 20.7846i | 0.544892 | + | 0.943781i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.00000 | −0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.0000 | − | 17.3205i | 0.451294 | − | 0.781664i | −0.547173 | − | 0.837020i | \(-0.684296\pi\) |
0.998467 | + | 0.0553560i | \(0.0176294\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00000 | 0.180151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.0000 | 0.539360 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000 | − | 20.7846i | 0.538274 | − | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.00000 | − | 15.5885i | −0.402090 | − | 0.696441i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0000 | − | 20.7846i | −0.535054 | − | 0.926740i | −0.999161 | − | 0.0409609i | \(-0.986958\pi\) |
0.464107 | − | 0.885779i | \(-0.346375\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | − | 17.3205i | 0.444994 | − | 0.770752i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.0000 | + | 25.9808i | −0.664863 | + | 1.15158i | 0.314459 | + | 0.949271i | \(0.398177\pi\) |
−0.979322 | + | 0.202306i | \(0.935156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.00000 | + | 13.8564i | 0.353899 | + | 0.612971i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.00000 | −0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.0000 | + | 31.1769i | −0.791639 | + | 1.37116i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000 | − | 6.92820i | 0.174908 | − | 0.302949i | −0.765222 | − | 0.643767i | \(-0.777371\pi\) |
0.940129 | + | 0.340818i | \(0.110704\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.00000 | −0.174574 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.00000 | − | 13.8564i | −0.348485 | − | 0.603595i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5000 | − | 35.5070i | −0.891304 | − | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.00000 | − | 1.73205i | 0.0433963 | − | 0.0751646i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.0000 | − | 34.6410i | 0.864675 | − | 1.49766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.00000 | − | 10.3923i | −0.258919 | − | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.0000 | + | 46.7654i | 1.16297 | + | 2.01433i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.0000 | −0.859867 | −0.429934 | − | 0.902861i | \(-0.641463\pi\) | ||||
−0.429934 | + | 0.902861i | \(0.641463\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.00000 | − | 8.66025i | 0.214571 | − | 0.371647i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.00000 | 0.342682 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.00000 | + | 1.73205i | −0.0426790 | + | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.00000 | + | 13.8564i | 0.339581 | + | 0.588172i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.0000 | − | 25.9808i | 0.635570 | − | 1.10084i | −0.350824 | − | 0.936442i | \(-0.614098\pi\) |
0.986394 | − | 0.164399i | \(-0.0525683\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.00000 | − | 10.3923i | 0.253320 | − | 0.438763i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.00000 | − | 3.46410i | −0.0842900 | − | 0.145994i | 0.820798 | − | 0.571218i | \(-0.193529\pi\) |
−0.905088 | + | 0.425223i | \(0.860196\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0000 | − | 17.3205i | −0.420703 | − | 0.728679i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.00000 | 0.167984 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.0000 | − | 29.4449i | 0.712677 | − | 1.23439i | −0.251172 | − | 0.967943i | \(-0.580816\pi\) |
0.963849 | − | 0.266450i | \(-0.0858508\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.0000 | −1.00261 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | − | 6.92820i | 0.166812 | − | 0.288926i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.0000 | 1.66522 | 0.832611 | − | 0.553858i | \(-0.186845\pi\) | ||||
0.832611 | + | 0.553858i | \(0.186845\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.00000 | + | 6.92820i | 0.166234 | + | 0.287926i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.0000 | + | 48.4974i | 1.16164 | + | 2.01201i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0000 | − | 31.1769i | 0.745484 | − | 1.29122i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.00000 | + | 1.73205i | −0.0412744 | + | 0.0714894i | −0.885925 | − | 0.463829i | \(-0.846475\pi\) |
0.844650 | + | 0.535319i | \(0.179808\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.0000 | + | 22.5167i | 0.534749 | + | 0.926212i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.0000 | −1.39621 | −0.698106 | − | 0.715994i | \(-0.745974\pi\) | ||||
−0.698106 | + | 0.715994i | \(0.745974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.00000 | − | 13.8564i | 0.327968 | − | 0.568057i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.00000 | − | 12.1244i | 0.285536 | − | 0.494563i | −0.687203 | − | 0.726465i | \(-0.741162\pi\) |
0.972739 | + | 0.231903i | \(0.0744951\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.0000 | + | 43.3013i | 1.01639 | + | 1.76045i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.00000 | − | 3.46410i | −0.0811775 | − | 0.140604i | 0.822578 | − | 0.568652i | \(-0.192535\pi\) |
−0.903756 | + | 0.428048i | \(0.859201\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.00000 | + | 6.92820i | −0.162088 | + | 0.280745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.00000 | − | 13.8564i | 0.323117 | − | 0.559655i | −0.658012 | − | 0.753007i | \(-0.728603\pi\) |
0.981129 | + | 0.193352i | \(0.0619359\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.00000 | + | 3.46410i | 0.0806478 | + | 0.139686i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.00000 | + | 12.1244i | 0.281809 | + | 0.488108i | 0.971830 | − | 0.235681i | \(-0.0757321\pi\) |
−0.690021 | + | 0.723789i | \(0.742399\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.0000 | −0.803868 | −0.401934 | − | 0.915669i | \(-0.631662\pi\) | ||||
−0.401934 | + | 0.915669i | \(0.631662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | + | 6.92820i | −0.160514 | + | 0.278019i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.0000 | 0.961540 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.0000 | 0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.00000 | + | 6.92820i | 0.159237 | + | 0.275807i | 0.934594 | − | 0.355716i | \(-0.115763\pi\) |
−0.775356 | + | 0.631524i | \(0.782430\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.00000 | − | 10.3923i | −0.238479 | − | 0.413057i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.00000 | + | 13.8564i | −0.317470 | + | 0.549875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.00000 | − | 5.19615i | 0.118678 | − | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.0000 | − | 36.3731i | −0.829450 | − | 1.43665i | −0.898470 | − | 0.439034i | \(-0.855321\pi\) |
0.0690201 | − | 0.997615i | \(-0.478013\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0000 | + | 31.1769i | 0.709851 | + | 1.22950i | 0.964912 | + | 0.262573i | \(0.0845709\pi\) |
−0.255062 | + | 0.966925i | \(0.582096\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.0000 | −0.629999 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.0000 | + | 27.7128i | −0.629025 | + | 1.08950i | 0.358723 | + | 0.933444i | \(0.383212\pi\) |
−0.987748 | + | 0.156059i | \(0.950121\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.0000 | 0.471041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.0000 | 1.25418 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.00000 | − | 12.1244i | 0.273931 | − | 0.474463i | −0.695934 | − | 0.718106i | \(-0.745009\pi\) |
0.969865 | + | 0.243643i | \(0.0783426\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.00000 | −0.312586 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | + | 3.46410i | 0.0780274 | + | 0.135147i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.0000 | − | 17.3205i | −0.389545 | − | 0.674711i | 0.602844 | − | 0.797859i | \(-0.294034\pi\) |
−0.992388 | + | 0.123148i | \(0.960701\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0000 | + | 27.7128i | −0.622328 | + | 1.07790i | 0.366723 | + | 0.930330i | \(0.380480\pi\) |
−0.989051 | + | 0.147573i | \(0.952854\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.00000 | − | 13.8564i | −0.309761 | − | 0.536522i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.00000 | − | 6.92820i | −0.154649 | − | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.0000 | − | 25.9808i | 0.578208 | − | 1.00148i | −0.417477 | − | 0.908687i | \(-0.637086\pi\) |
0.995685 | − | 0.0927975i | \(-0.0295809\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.0000 | −0.691796 | −0.345898 | − | 0.938272i | \(-0.612426\pi\) | ||||
−0.345898 | + | 0.938272i | \(0.612426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.0000 | + | 41.5692i | −0.921035 | + | 1.59528i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.00000 | −0.0766402 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.00000 | + | 5.19615i | 0.114792 | + | 0.198825i | 0.917697 | − | 0.397282i | \(-0.130047\pi\) |
−0.802905 | + | 0.596107i | \(0.796713\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.0000 | + | 17.3205i | 0.382080 | + | 0.661783i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.0000 | − | 17.3205i | 0.381524 | − | 0.660819i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.00000 | + | 3.46410i | −0.0760836 | + | 0.131781i | −0.901557 | − | 0.432660i | \(-0.857575\pi\) |
0.825473 | + | 0.564441i | \(0.190908\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.0000 | + | 20.7846i | 0.455842 | + | 0.789542i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.00000 | − | 13.8564i | −0.303457 | − | 0.525603i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.00000 | − | 15.5885i | 0.340411 | − | 0.589610i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.0000 | −0.377695 | −0.188847 | − | 0.982006i | \(-0.560475\pi\) | ||||
−0.188847 | + | 0.982006i | \(0.560475\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.00000 | + | 10.3923i | −0.225973 | + | 0.391397i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 40.0000 | 1.50435 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.0000 | − | 31.1769i | −0.676004 | − | 1.17087i | −0.976174 | − | 0.216988i | \(-0.930377\pi\) |
0.300170 | − | 0.953886i | \(-0.402957\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −32.0000 | + | 55.4256i | −1.19841 | + | 2.07571i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.00000 | + | 8.66025i | −0.186728 | + | 0.323423i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.00000 | − | 13.8564i | −0.298350 | − | 0.516757i | 0.677409 | − | 0.735607i | \(-0.263103\pi\) |
−0.975759 | + | 0.218850i | \(0.929769\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | − | 13.8564i | −0.297936 | − | 0.516040i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.0000 | 0.743808 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.00000 | − | 1.73205i | 0.0371391 | − | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | + | 13.8564i | −0.295891 | + | 0.512498i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.0000 | 0.738717 | 0.369358 | − | 0.929287i | \(-0.379577\pi\) | ||||
0.369358 | + | 0.929287i | \(0.379577\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.00000 | + | 15.5885i | 0.331970 | + | 0.574989i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.0000 | − | 20.7846i | −0.442026 | − | 0.765611i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.0000 | + | 24.2487i | −0.514998 | + | 0.892003i | 0.484850 | + | 0.874597i | \(0.338874\pi\) |
−0.999849 | + | 0.0174060i | \(0.994459\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.0000 | − | 19.0526i | 0.403551 | − | 0.698971i | −0.590601 | − | 0.806964i | \(-0.701109\pi\) |
0.994152 | + | 0.107993i | \(0.0344425\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0000 | + | 17.3205i | 0.366372 | + | 0.634574i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.00000 | + | 12.1244i | 0.256117 | + | 0.443607i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 80.0000 | 2.92314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0000 | − | 17.3205i | 0.364905 | − | 0.632034i | −0.623856 | − | 0.781540i | \(-0.714435\pi\) |
0.988761 | + | 0.149505i | \(0.0477681\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.0000 | −0.728841 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32.0000 | −1.16460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.00000 | + | 1.73205i | −0.0363456 | + | 0.0629525i | −0.883626 | − | 0.468193i | \(-0.844905\pi\) |
0.847280 | + | 0.531146i | \(0.178238\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −48.0000 | −1.74229 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0000 | + | 25.9808i | 0.543750 | + | 0.941802i | 0.998684 | + | 0.0512772i | \(0.0163292\pi\) |
−0.454935 | + | 0.890525i | \(0.650337\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000 | + | 13.8564i | 0.289619 | + | 0.501636i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.00000 | − | 3.46410i | 0.0723102 | − | 0.125245i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.00000 | − | 5.19615i | −0.108042 | − | 0.187135i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.00000 | − | 15.5885i | −0.323708 | − | 0.560678i | 0.657542 | − | 0.753418i | \(-0.271596\pi\) |
−0.981250 | + | 0.192740i | \(0.938263\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.00000 | −0.287368 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.0000 | + | 27.7128i | −0.573997 | + | 0.994192i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | + | 1.73205i | −0.0357371 | + | 0.0618984i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.0000 | 0.999363 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.0000 | − | 38.1051i | −0.784215 | − | 1.35830i | −0.929467 | − | 0.368906i | \(-0.879732\pi\) |
0.145251 | − | 0.989395i | \(-0.453601\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.0000 | − | 34.6410i | 0.711118 | − | 1.23169i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.00000 | − | 10.3923i | 0.212798 | − | 0.368577i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.00000 | + | 8.66025i | 0.177109 | + | 0.306762i | 0.940889 | − | 0.338715i | \(-0.109992\pi\) |
−0.763780 | + | 0.645477i | \(0.776659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.00000 | + | 10.3923i | 0.212265 | + | 0.367653i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.0000 | + | 20.7846i | −0.423471 | + | 0.733473i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −64.0000 | −2.25570 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.0000 | −0.774437 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.0000 | + | 19.0526i | −0.386739 | + | 0.669852i | −0.992009 | − | 0.126168i | \(-0.959732\pi\) |
0.605269 | + | 0.796021i | \(0.293065\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.0000 | −1.40459 | −0.702295 | − | 0.711886i | \(-0.747841\pi\) | ||||
−0.702295 | + | 0.711886i | \(0.747841\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.0000 | − | 17.3205i | −0.350715 | − | 0.607457i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.00000 | − | 13.8564i | −0.280228 | − | 0.485369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.0000 | − | 25.9808i | 0.523504 | − | 0.906735i | −0.476122 | − | 0.879379i | \(-0.657958\pi\) |
0.999626 | − | 0.0273557i | \(-0.00870868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.0000 | − | 31.1769i | −0.627441 | − | 1.08676i | −0.988063 | − | 0.154047i | \(-0.950769\pi\) |
0.360623 | − | 0.932712i | \(-0.382564\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.00000 | − | 5.19615i | −0.104447 | − | 0.180907i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.0000 | 0.625921 | 0.312961 | − | 0.949766i | \(-0.398679\pi\) | ||||
0.312961 | + | 0.949766i | \(0.398679\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.0000 | + | 46.7654i | −0.937749 | + | 1.62423i | −0.168091 | + | 0.985771i | \(0.553760\pi\) |
−0.769657 | + | 0.638457i | \(0.779573\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.0000 | −0.763172 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000 | 0.623663 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0000 | − | 31.1769i | 0.622916 | − | 1.07892i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.00000 | + | 8.66025i | 0.172619 | + | 0.298985i | 0.939335 | − | 0.343002i | \(-0.111444\pi\) |
−0.766716 | + | 0.641987i | \(0.778110\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5000 | + | 21.6506i | 0.431034 | + | 0.746574i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.0000 | − | 19.0526i | 0.378860 | − | 0.656205i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −50.0000 | + | 86.6025i | −1.71802 | + | 2.97570i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.00000 | + | 3.46410i | 0.0686398 | + | 0.118888i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.0000 | − | 55.4256i | −1.09695 | − | 1.89997i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.0000 | −0.547830 | −0.273915 | − | 0.961754i | \(-0.588319\pi\) | ||||
−0.273915 | + | 0.961754i | \(0.588319\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.0000 | 0.751506 | 0.375753 | − | 0.926720i | \(-0.377384\pi\) | ||||
0.375753 | + | 0.926720i | \(0.377384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 52.0000 | 1.77422 | 0.887109 | − | 0.461561i | \(-0.152710\pi\) | ||||
0.887109 | + | 0.461561i | \(0.152710\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00000 | + | 6.92820i | −0.136320 | + | 0.236113i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34.0000 | −1.15737 | −0.578687 | − | 0.815550i | \(-0.696435\pi\) | ||||
−0.578687 | + | 0.815550i | \(0.696435\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | − | 10.3923i | −0.204006 | − | 0.353349i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.50000 | + | 11.2583i | 0.220752 | + | 0.382353i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.00000 | + | 10.3923i | −0.203069 | + | 0.351726i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.0000 | − | 41.5692i | −0.811348 | − | 1.40530i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.00000 | − | 13.8564i | −0.270141 | − | 0.467898i | 0.698757 | − | 0.715359i | \(-0.253737\pi\) |
−0.968898 | + | 0.247462i | \(0.920404\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.0000 | −0.472208 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.0000 | − | 36.3731i | 0.707508 | − | 1.22544i | −0.258271 | − | 0.966073i | \(-0.583153\pi\) |
0.965779 | − | 0.259367i | \(-0.0835140\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0000 | 0.403832 | 0.201916 | − | 0.979403i | \(-0.435283\pi\) | ||||
0.201916 | + | 0.979403i | \(0.435283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.00000 | 0.134459 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.0000 | + | 20.7846i | −0.402921 | + | 0.697879i | −0.994077 | − | 0.108678i | \(-0.965338\pi\) |
0.591156 | + | 0.806557i | \(0.298672\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.0000 | −1.07325 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.00000 | + | 5.19615i | 0.100504 | + | 0.174078i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0000 | − | 20.7846i | 0.401116 | − | 0.694753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.00000 | + | 13.8564i | −0.266815 | + | 0.462137i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.00000 | − | 10.3923i | −0.199889 | − | 0.346218i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.0000 | − | 27.7128i | −0.532447 | − | 0.922225i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.0000 | 0.664822 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.0000 | + | 38.1051i | −0.730498 | + | 1.26526i | 0.226173 | + | 0.974087i | \(0.427379\pi\) |
−0.956671 | + | 0.291172i | \(0.905955\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.0000 | 0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.0000 | + | 72.7461i | −1.39000 | + | 2.40755i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.00000 | −0.132236 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.00000 | − | 13.8564i | −0.264183 | − | 0.457579i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.0000 | + | 20.7846i | 0.395843 | + | 0.685621i | 0.993208 | − | 0.116348i | \(-0.0371189\pi\) |
−0.597365 | + | 0.801970i | \(0.703786\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0000 | − | 17.3205i | 0.329511 | − | 0.570730i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | − | 6.92820i | 0.131519 | − | 0.227798i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.00000 | − | 3.46410i | −0.0656886 | − | 0.113776i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.0000 | + | 25.9808i | 0.492134 | + | 0.852401i | 0.999959 | − | 0.00905914i | \(-0.00288365\pi\) |
−0.507825 | + | 0.861460i | \(0.669550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.00000 | + | 13.8564i | −0.261908 | + | 0.453638i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.0000 | 0.784884 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.0000 | −1.63343 | −0.816714 | − | 0.577042i | \(-0.804207\pi\) | ||||
−0.816714 | + | 0.577042i | \(0.804207\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.00000 | − | 12.1244i | 0.228436 | − | 0.395663i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.0000 | −1.23876 | −0.619382 | − | 0.785090i | \(-0.712617\pi\) | ||||
−0.619382 | + | 0.785090i | \(0.712617\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.00000 | − | 13.8564i | −0.260516 | − | 0.451227i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.00000 | + | 6.92820i | 0.130120 | + | 0.225374i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.0000 | + | 32.9090i | −0.617417 | + | 1.06940i | 0.372538 | + | 0.928017i | \(0.378488\pi\) |
−0.989955 | + | 0.141381i | \(0.954846\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.00000 | − | 15.5885i | 0.291845 | − | 0.505490i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.0000 | − | 46.7654i | −0.874616 | − | 1.51488i | −0.857171 | − | 0.515031i | \(-0.827780\pi\) |
−0.0174443 | − | 0.999848i | \(-0.505553\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.0000 | − | 41.5692i | −0.776622 | − | 1.34515i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.0000 | −0.387905 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.0000 | + | 34.6410i | −0.645834 | + | 1.11862i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.0000 | 0.644491 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.00000 | + | 13.8564i | −0.257529 | + | 0.446054i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.00000 | + | 10.3923i | 0.192549 | + | 0.333505i | 0.946094 | − | 0.323891i | \(-0.104991\pi\) |
−0.753545 | + | 0.657396i | \(0.771658\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.0000 | − | 27.7128i | 0.512936 | − | 0.888432i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.0000 | + | 25.9808i | −0.479893 | + | 0.831198i | −0.999734 | − | 0.0230645i | \(-0.992658\pi\) |
0.519841 | + | 0.854263i | \(0.325991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0000 | + | 31.1769i | 0.575282 | + | 0.996419i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | + | 3.46410i | 0.0638551 | + | 0.110600i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.0000 | −0.574111 | −0.287055 | − | 0.957914i | \(-0.592676\pi\) | ||||
−0.287055 | + | 0.957914i | \(0.592676\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.0000 | + | 45.0333i | −0.828429 | + | 1.43488i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.0000 | −0.763928 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 64.0000 | 2.03508 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.0000 | − | 38.1051i | 0.698853 | − | 1.21045i | −0.270011 | − | 0.962857i | \(-0.587027\pi\) |
0.968864 | − | 0.247592i | \(-0.0796392\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.0000 | 0.888553 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.00000 | − | 5.19615i | −0.0950110 | − | 0.164564i | 0.814602 | − | 0.580020i | \(-0.196955\pi\) |
−0.909613 | + | 0.415456i | \(0.863622\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.00000 | + | 6.92820i | −0.126554 | + | 0.219199i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))