Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(109,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.g (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: | \(4.52751779461\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 541.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.541 |
Dual form | 567.2.g.a.109.1 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.73205i | −0.707107 | − | 1.22474i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | + | 3.46410i | 0.632456 | + | 1.09545i | ||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | 0.788320 | − | 0.615265i | \(-0.210951\pi\) |
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | −5.00000 | + | 1.73205i | −1.33631 | + | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 2.00000 | − | 3.46410i | 0.447214 | − | 0.774597i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | + | 3.46410i | 0.426401 | + | 0.738549i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −1.00000 | + | 1.73205i | −0.196116 | + | 0.339683i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.00000 | + | 3.46410i | 0.755929 | + | 0.654654i | ||||
\(29\) | −2.00000 | + | 3.46410i | −0.371391 | + | 0.643268i | −0.989780 | − | 0.142605i | \(-0.954452\pi\) |
0.618389 | + | 0.785872i | \(0.287786\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.50000 | + | 7.79423i | −0.808224 | + | 1.39988i | 0.105869 | + | 0.994380i | \(0.466238\pi\) |
−0.914093 | + | 0.405505i | \(0.867096\pi\) | |||||||
\(32\) | 4.00000 | − | 6.92820i | 0.707107 | − | 1.22474i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | + | 5.19615i | −0.169031 | + | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50000 | + | 2.59808i | −0.246598 | + | 0.427121i | −0.962580 | − | 0.270998i | \(-0.912646\pi\) |
0.715981 | + | 0.698119i | \(0.245980\pi\) | |||||||
\(38\) | 2.00000 | 0.324443 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.00000 | + | 8.66025i | 0.780869 | + | 1.35250i | 0.931436 | + | 0.363905i | \(0.118557\pi\) |
−0.150567 | + | 0.988600i | \(0.548110\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.50000 | + | 4.33013i | −0.381246 | + | 0.660338i | −0.991241 | − | 0.132068i | \(-0.957838\pi\) |
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 2.00000 | − | 3.46410i | 0.301511 | − | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000 | + | 5.19615i | 0.437595 | + | 0.757937i | 0.997503 | − | 0.0706177i | \(-0.0224970\pi\) |
−0.559908 | + | 0.828554i | \(0.689164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 1.00000 | + | 1.73205i | 0.141421 | + | 0.244949i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | −6.00000 | − | 10.3923i | −0.824163 | − | 1.42749i | −0.902557 | − | 0.430570i | \(-0.858312\pi\) |
0.0783936 | − | 0.996922i | \(-0.475021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.00000 | 1.05045 | ||||||||
\(59\) | 6.00000 | − | 10.3923i | 0.781133 | − | 1.35296i | −0.150148 | − | 0.988663i | \(-0.547975\pi\) |
0.931282 | − | 0.364299i | \(-0.118692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | − | 8.66025i | −0.640184 | − | 1.10883i | −0.985391 | − | 0.170305i | \(-0.945525\pi\) |
0.345207 | − | 0.938527i | \(-0.387809\pi\) | |||||||
\(62\) | 18.0000 | 2.28600 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 1.00000 | + | 1.73205i | 0.124035 | + | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.50000 | − | 4.33013i | 0.305424 | − | 0.529009i | −0.671932 | − | 0.740613i | \(-0.734535\pi\) |
0.977356 | + | 0.211604i | \(0.0678686\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 10.0000 | − | 3.46410i | 1.19523 | − | 0.414039i | ||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.50000 | + | 2.59808i | 0.175562 | + | 0.304082i | 0.940356 | − | 0.340193i | \(-0.110493\pi\) |
−0.764794 | + | 0.644275i | \(0.777159\pi\) | |||||||
\(74\) | 6.00000 | 0.697486 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | − | 1.73205i | −0.114708 | − | 0.198680i | ||||
\(77\) | −1.00000 | + | 5.19615i | −0.113961 | + | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | −4.00000 | − | 6.92820i | −0.447214 | − | 0.774597i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.0000 | − | 17.3205i | 1.10432 | − | 1.91273i | ||||
\(83\) | −3.00000 | + | 5.19615i | −0.329293 | + | 0.570352i | −0.982372 | − | 0.186938i | \(-0.940144\pi\) |
0.653079 | + | 0.757290i | \(0.273477\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.0000 | 1.07833 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.00000 | + | 13.8564i | −0.847998 | + | 1.46878i | 0.0349934 | + | 0.999388i | \(0.488859\pi\) |
−0.882992 | + | 0.469389i | \(0.844474\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.50000 | + | 0.866025i | −0.262071 | + | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.00000 | − | 10.3923i | 0.618853 | − | 1.07188i | ||||
\(95\) | 1.00000 | − | 1.73205i | 0.102598 | − | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00000 | − | 5.19615i | 0.304604 | − | 0.527589i | −0.672569 | − | 0.740034i | \(-0.734809\pi\) |
0.977173 | + | 0.212445i | \(0.0681426\pi\) | |||||||
\(98\) | 2.00000 | + | 13.8564i | 0.202031 | + | 1.39971i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | − | 1.73205i | 0.100000 | − | 0.173205i | ||||
\(101\) | 2.00000 | 0.199007 | 0.0995037 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995037 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.00000 | −0.689730 | −0.344865 | − | 0.938652i | \(-0.612075\pi\) | ||||
−0.344865 | + | 0.938652i | \(0.612075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | + | 20.7846i | −1.16554 | + | 2.01878i | ||||
\(107\) | 4.00000 | − | 6.92820i | 0.386695 | − | 0.669775i | −0.605308 | − | 0.795991i | \(-0.706950\pi\) |
0.992003 | + | 0.126217i | \(0.0402834\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.50000 | − | 7.79423i | −0.431022 | − | 0.746552i | 0.565940 | − | 0.824447i | \(-0.308513\pi\) |
−0.996962 | + | 0.0778949i | \(0.975180\pi\) | |||||||
\(110\) | −4.00000 | − | 6.92820i | −0.381385 | − | 0.660578i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.0000 | − | 3.46410i | 0.944911 | − | 0.327327i | ||||
\(113\) | −5.00000 | − | 8.66025i | −0.470360 | − | 0.814688i | 0.529065 | − | 0.848581i | \(-0.322543\pi\) |
−0.999425 | + | 0.0338931i | \(0.989209\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.00000 | − | 6.92820i | −0.371391 | − | 0.643268i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −24.0000 | −2.20938 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −10.0000 | + | 17.3205i | −0.905357 | + | 1.56813i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.00000 | − | 15.5885i | −0.808224 | − | 1.39988i | ||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.0000 | −1.33103 | −0.665517 | − | 0.746382i | \(-0.731789\pi\) | ||||
−0.665517 | + | 0.746382i | \(0.731789\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | − | 3.46410i | 0.175412 | − | 0.303822i | ||||
\(131\) | −14.0000 | −1.22319 | −0.611593 | − | 0.791173i | \(-0.709471\pi\) | ||||
−0.611593 | + | 0.791173i | \(0.709471\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000 | + | 1.73205i | 0.173422 | + | 0.150188i | ||||
\(134\) | −10.0000 | −0.863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.0000 | −1.02523 | −0.512615 | − | 0.858619i | \(-0.671323\pi\) | ||||
−0.512615 | + | 0.858619i | \(0.671323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.50000 | + | 2.59808i | 0.127228 | + | 0.220366i | 0.922602 | − | 0.385754i | \(-0.126059\pi\) |
−0.795373 | + | 0.606120i | \(0.792725\pi\) | |||||||
\(140\) | −8.00000 | − | 6.92820i | −0.676123 | − | 0.585540i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | + | 10.3923i | 0.503509 | + | 0.872103i | ||||
\(143\) | 1.00000 | + | 1.73205i | 0.0836242 | + | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.00000 | − | 6.92820i | 0.332182 | − | 0.575356i | ||||
\(146\) | 3.00000 | − | 5.19615i | 0.248282 | − | 0.430037i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.00000 | − | 5.19615i | −0.246598 | − | 0.427121i | ||||
\(149\) | −12.0000 | −0.983078 | −0.491539 | − | 0.870855i | \(-0.663566\pi\) | ||||
−0.491539 | + | 0.870855i | \(0.663566\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.0000 | − | 3.46410i | 0.805823 | − | 0.279145i | ||||
\(155\) | 9.00000 | − | 15.5885i | 0.722897 | − | 1.25210i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.00000 | − | 12.1244i | 0.558661 | − | 0.967629i | −0.438948 | − | 0.898513i | \(-0.644649\pi\) |
0.997609 | − | 0.0691164i | \(-0.0220180\pi\) | |||||||
\(158\) | 1.00000 | − | 1.73205i | 0.0795557 | − | 0.137795i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.00000 | + | 13.8564i | −0.632456 | + | 1.09545i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | + | 3.46410i | −0.156652 | + | 0.271329i | −0.933659 | − | 0.358162i | \(-0.883403\pi\) |
0.777007 | + | 0.629492i | \(0.216737\pi\) | |||||||
\(164\) | −20.0000 | −1.56174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.0000 | 0.931381 | ||||||||
\(167\) | 7.00000 | + | 12.1244i | 0.541676 | + | 0.938211i | 0.998808 | + | 0.0488118i | \(0.0155435\pi\) |
−0.457132 | + | 0.889399i | \(0.651123\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.00000 | − | 8.66025i | −0.381246 | − | 0.660338i | ||||
\(173\) | −4.00000 | − | 6.92820i | −0.304114 | − | 0.526742i | 0.672949 | − | 0.739689i | \(-0.265027\pi\) |
−0.977064 | + | 0.212947i | \(0.931694\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.500000 | + | 2.59808i | −0.0377964 | + | 0.196396i | ||||
\(176\) | −4.00000 | − | 6.92820i | −0.301511 | − | 0.522233i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 32.0000 | 2.39850 | ||||||||
\(179\) | −1.00000 | − | 1.73205i | −0.0747435 | − | 0.129460i | 0.826231 | − | 0.563331i | \(-0.190480\pi\) |
−0.900975 | + | 0.433872i | \(0.857147\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0000 | 0.966282 | 0.483141 | − | 0.875542i | \(-0.339496\pi\) | ||||
0.483141 | + | 0.875542i | \(0.339496\pi\) | |||||||
\(182\) | 4.00000 | + | 3.46410i | 0.296500 | + | 0.256776i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | − | 5.19615i | 0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −12.0000 | −0.875190 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | −5.00000 | − | 8.66025i | −0.361787 | − | 0.626634i | 0.626468 | − | 0.779447i | \(-0.284500\pi\) |
−0.988255 | + | 0.152813i | \(0.951167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.50000 | + | 9.52628i | −0.395899 | + | 0.685717i | −0.993215 | − | 0.116289i | \(-0.962900\pi\) |
0.597317 | + | 0.802005i | \(0.296234\pi\) | |||||||
\(194\) | −12.0000 | −0.861550 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.0000 | − | 8.66025i | 0.785714 | − | 0.618590i | ||||
\(197\) | 16.0000 | 1.13995 | 0.569976 | − | 0.821661i | \(-0.306952\pi\) | ||||
0.569976 | + | 0.821661i | \(0.306952\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.00000 | − | 3.46410i | −0.140720 | − | 0.243733i | ||||
\(203\) | 8.00000 | + | 6.92820i | 0.561490 | + | 0.486265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.0000 | − | 17.3205i | −0.698430 | − | 1.20972i | ||||
\(206\) | 7.00000 | + | 12.1244i | 0.487713 | + | 0.844744i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000 | − | 3.46410i | 0.138675 | − | 0.240192i | ||||
\(209\) | 1.00000 | − | 1.73205i | 0.0691714 | − | 0.119808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.00000 | − | 3.46410i | −0.137686 | − | 0.238479i | 0.788935 | − | 0.614477i | \(-0.210633\pi\) |
−0.926620 | + | 0.375999i | \(0.877300\pi\) | |||||||
\(212\) | 24.0000 | 1.64833 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.0000 | −1.09374 | ||||||||
\(215\) | 5.00000 | − | 8.66025i | 0.340997 | − | 0.590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0000 | + | 15.5885i | 1.22192 | + | 1.05821i | ||||
\(218\) | −9.00000 | + | 15.5885i | −0.609557 | + | 1.05578i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.00000 | + | 6.92820i | −0.269680 | + | 0.467099i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.00000 | + | 13.8564i | −0.535720 | + | 0.927894i | 0.463409 | + | 0.886145i | \(0.346626\pi\) |
−0.999128 | + | 0.0417488i | \(0.986707\pi\) | |||||||
\(224\) | −16.0000 | − | 13.8564i | −1.06904 | − | 0.925820i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.0000 | + | 17.3205i | −0.665190 | + | 1.15214i | ||||
\(227\) | 18.0000 | 1.19470 | 0.597351 | − | 0.801980i | \(-0.296220\pi\) | ||||
0.597351 | + | 0.801980i | \(0.296220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.0000 | −1.25556 | −0.627778 | − | 0.778393i | \(-0.716035\pi\) | ||||
−0.627778 | + | 0.778393i | \(0.716035\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00000 | + | 5.19615i | −0.196537 | + | 0.340411i | −0.947403 | − | 0.320043i | \(-0.896303\pi\) |
0.750867 | + | 0.660454i | \(0.229636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | − | 10.3923i | −0.391397 | − | 0.677919i | ||||
\(236\) | 12.0000 | + | 20.7846i | 0.781133 | + | 1.35296i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.00000 | − | 5.19615i | −0.194054 | − | 0.336111i | 0.752536 | − | 0.658551i | \(-0.228830\pi\) |
−0.946590 | + | 0.322440i | \(0.895497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 7.00000 | + | 12.1244i | 0.449977 | + | 0.779383i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.0000 | 1.28037 | ||||||||
\(245\) | 13.0000 | + | 5.19615i | 0.830540 | + | 0.331970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.00000 | 0.0636285 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.0000 | − | 20.7846i | −0.758947 | − | 1.31453i | ||||
\(251\) | −8.00000 | −0.504956 | −0.252478 | − | 0.967603i | \(-0.581245\pi\) | ||||
−0.252478 | + | 0.967603i | \(0.581245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 15.0000 | + | 25.9808i | 0.941184 | + | 1.63018i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 26.0000 | 1.62184 | 0.810918 | − | 0.585160i | \(-0.198968\pi\) | ||||
0.810918 | + | 0.585160i | \(0.198968\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000 | + | 5.19615i | 0.372822 | + | 0.322873i | ||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.0000 | + | 24.2487i | 0.864923 | + | 1.49809i | ||||
\(263\) | 4.00000 | 0.246651 | 0.123325 | − | 0.992366i | \(-0.460644\pi\) | ||||
0.123325 | + | 0.992366i | \(0.460644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.0000 | + | 20.7846i | 0.737154 | + | 1.27679i | ||||
\(266\) | 1.00000 | − | 5.19615i | 0.0613139 | − | 0.318597i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.00000 | + | 8.66025i | 0.305424 | + | 0.529009i | ||||
\(269\) | −3.00000 | − | 5.19615i | −0.182913 | − | 0.316815i | 0.759958 | − | 0.649972i | \(-0.225219\pi\) |
−0.942871 | + | 0.333157i | \(0.891886\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | + | 13.8564i | −0.485965 | + | 0.841717i | −0.999870 | − | 0.0161307i | \(-0.994865\pi\) |
0.513905 | + | 0.857847i | \(0.328199\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.0000 | + | 20.7846i | 0.724947 | + | 1.25564i | ||||
\(275\) | 2.00000 | 0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0000 | 0.781094 | 0.390547 | − | 0.920583i | \(-0.372286\pi\) | ||||
0.390547 | + | 0.920583i | \(0.372286\pi\) | |||||||
\(278\) | 3.00000 | − | 5.19615i | 0.179928 | − | 0.311645i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | − | 3.46410i | 0.119310 | − | 0.206651i | −0.800184 | − | 0.599754i | \(-0.795265\pi\) |
0.919494 | + | 0.393103i | \(0.128598\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.50000 | − | 9.52628i | 0.326941 | − | 0.566279i | −0.654962 | − | 0.755662i | \(-0.727315\pi\) |
0.981903 | + | 0.189383i | \(0.0606488\pi\) | |||||||
\(284\) | 6.00000 | − | 10.3923i | 0.356034 | − | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.00000 | − | 3.46410i | 0.118262 | − | 0.204837i | ||||
\(287\) | 25.0000 | − | 8.66025i | 1.47570 | − | 0.511199i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | −16.0000 | −0.939552 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.00000 | −0.351123 | ||||||||
\(293\) | −4.00000 | − | 6.92820i | −0.233682 | − | 0.404750i | 0.725206 | − | 0.688531i | \(-0.241744\pi\) |
−0.958889 | + | 0.283782i | \(0.908411\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.0000 | + | 20.7846i | −0.698667 | + | 1.21013i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.0000 | + | 20.7846i | 0.695141 | + | 1.20402i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0000 | + | 8.66025i | 0.576390 | + | 0.499169i | ||||
\(302\) | 16.0000 | + | 27.7128i | 0.920697 | + | 1.59469i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | 10.0000 | + | 17.3205i | 0.572598 | + | 0.991769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.0000 | −0.970241 | −0.485121 | − | 0.874447i | \(-0.661224\pi\) | ||||
−0.485121 | + | 0.874447i | \(0.661224\pi\) | |||||||
\(308\) | −8.00000 | − | 6.92820i | −0.455842 | − | 0.394771i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −36.0000 | −2.04466 | ||||||||
\(311\) | 3.00000 | − | 5.19615i | 0.170114 | − | 0.294647i | −0.768345 | − | 0.640036i | \(-0.778920\pi\) |
0.938460 | + | 0.345389i | \(0.112253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.500000 | + | 0.866025i | 0.0282617 | + | 0.0489506i | 0.879810 | − | 0.475325i | \(-0.157669\pi\) |
−0.851549 | + | 0.524276i | \(0.824336\pi\) | |||||||
\(314\) | −28.0000 | −1.58013 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.00000 | −0.112509 | ||||||||
\(317\) | −12.0000 | − | 20.7846i | −0.673987 | − | 1.16738i | −0.976764 | − | 0.214318i | \(-0.931247\pi\) |
0.302777 | − | 0.953062i | \(-0.402086\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | − | 6.92820i | 0.223957 | − | 0.387905i | ||||
\(320\) | 16.0000 | 0.894427 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.500000 | + | 0.866025i | 0.0277350 | + | 0.0480384i | ||||
\(326\) | 8.00000 | 0.443079 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.0000 | − | 5.19615i | 0.826977 | − | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5000 | + | 21.6506i | 0.687062 | + | 1.19003i | 0.972784 | + | 0.231714i | \(0.0744333\pi\) |
−0.285722 | + | 0.958313i | \(0.592233\pi\) | |||||||
\(332\) | −6.00000 | − | 10.3923i | −0.329293 | − | 0.570352i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.0000 | − | 24.2487i | 0.766046 | − | 1.32683i | ||||
\(335\) | −5.00000 | + | 8.66025i | −0.273179 | + | 0.473160i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.50000 | − | 11.2583i | −0.354078 | − | 0.613280i | 0.632882 | − | 0.774248i | \(-0.281872\pi\) |
−0.986960 | + | 0.160968i | \(0.948538\pi\) | |||||||
\(338\) | −24.0000 | −1.30543 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.00000 | − | 15.5885i | 0.487377 | − | 0.844162i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.00000 | + | 13.8564i | −0.430083 | + | 0.744925i | ||||
\(347\) | −16.0000 | + | 27.7128i | −0.858925 | + | 1.48770i | 0.0140303 | + | 0.999902i | \(0.495534\pi\) |
−0.872955 | + | 0.487800i | \(0.837799\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.00000 | − | 12.1244i | 0.374701 | − | 0.649002i | −0.615581 | − | 0.788074i | \(-0.711079\pi\) |
0.990282 | + | 0.139072i | \(0.0444119\pi\) | |||||||
\(350\) | 5.00000 | − | 1.73205i | 0.267261 | − | 0.0925820i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.00000 | + | 13.8564i | −0.426401 | + | 0.738549i | ||||
\(353\) | 34.0000 | 1.80964 | 0.904819 | − | 0.425797i | \(-0.140006\pi\) | ||||
0.904819 | + | 0.425797i | \(0.140006\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.0000 | 0.636894 | ||||||||
\(356\) | −16.0000 | − | 27.7128i | −0.847998 | − | 1.46878i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.00000 | + | 3.46410i | −0.105703 | + | 0.183083i | ||||
\(359\) | −10.0000 | + | 17.3205i | −0.527780 | + | 0.914141i | 0.471696 | + | 0.881761i | \(0.343642\pi\) |
−0.999476 | + | 0.0323801i | \(0.989691\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | −13.0000 | − | 22.5167i | −0.683265 | − | 1.18345i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.00000 | − | 5.19615i | 0.0524142 | − | 0.272352i | ||||
\(365\) | −3.00000 | − | 5.19615i | −0.157027 | − | 0.271979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.00000 | −0.469796 | −0.234898 | − | 0.972020i | \(-0.575476\pi\) | ||||
−0.234898 | + | 0.972020i | \(0.575476\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.0000 | −0.623850 | ||||||||
\(371\) | −30.0000 | + | 10.3923i | −1.55752 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.0000 | 1.19089 | 0.595447 | − | 0.803394i | \(-0.296975\pi\) | ||||
0.595447 | + | 0.803394i | \(0.296975\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000 | 0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.00000 | 0.154100 | 0.0770498 | − | 0.997027i | \(-0.475450\pi\) | ||||
0.0770498 | + | 0.997027i | \(0.475450\pi\) | |||||||
\(380\) | 2.00000 | + | 3.46410i | 0.102598 | + | 0.177705i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.0000 | + | 17.3205i | −0.511645 | + | 0.886194i | ||||
\(383\) | −12.0000 | −0.613171 | −0.306586 | − | 0.951843i | \(-0.599187\pi\) | ||||
−0.306586 | + | 0.951843i | \(0.599187\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | − | 10.3923i | 0.101929 | − | 0.529641i | ||||
\(386\) | 22.0000 | 1.11977 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.00000 | + | 10.3923i | 0.304604 | + | 0.527589i | ||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −16.0000 | − | 27.7128i | −0.806068 | − | 1.39615i | ||||
\(395\) | −1.00000 | − | 1.73205i | −0.0503155 | − | 0.0871489i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.50000 | − | 7.79423i | 0.225849 | − | 0.391181i | −0.730725 | − | 0.682672i | \(-0.760818\pi\) |
0.956574 | + | 0.291491i | \(0.0941512\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | −36.0000 | −1.79775 | −0.898877 | − | 0.438201i | \(-0.855616\pi\) | ||||
−0.898877 | + | 0.438201i | \(0.855616\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.00000 | 0.448322 | ||||||||
\(404\) | −2.00000 | + | 3.46410i | −0.0995037 | + | 0.172345i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.00000 | − | 20.7846i | 0.198517 | − | 1.03152i | ||||
\(407\) | 3.00000 | − | 5.19615i | 0.148704 | − | 0.257564i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.50000 | + | 4.33013i | −0.123617 | + | 0.214111i | −0.921192 | − | 0.389109i | \(-0.872783\pi\) |
0.797574 | + | 0.603220i | \(0.206116\pi\) | |||||||
\(410\) | −20.0000 | + | 34.6410i | −0.987730 | + | 1.71080i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.00000 | − | 12.1244i | 0.344865 | − | 0.597324i | ||||
\(413\) | −24.0000 | − | 20.7846i | −1.18096 | − | 1.02274i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | − | 10.3923i | 0.294528 | − | 0.510138i | ||||
\(416\) | −8.00000 | −0.392232 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.00000 | −0.195646 | ||||||||
\(419\) | −15.0000 | − | 25.9808i | −0.732798 | − | 1.26924i | −0.955683 | − | 0.294398i | \(-0.904881\pi\) |
0.222885 | − | 0.974845i | \(-0.428453\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.50000 | − | 6.06218i | 0.170580 | − | 0.295452i | −0.768043 | − | 0.640398i | \(-0.778769\pi\) |
0.938623 | + | 0.344946i | \(0.112103\pi\) | |||||||
\(422\) | −4.00000 | + | 6.92820i | −0.194717 | + | 0.337260i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.0000 | + | 8.66025i | −1.20983 | + | 0.419099i | ||||
\(428\) | 8.00000 | + | 13.8564i | 0.386695 | + | 0.669775i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −20.0000 | −0.964486 | ||||||||
\(431\) | 9.00000 | + | 15.5885i | 0.433515 | + | 0.750870i | 0.997173 | − | 0.0751385i | \(-0.0239399\pi\) |
−0.563658 | + | 0.826008i | \(0.690607\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.0000 | 1.48976 | 0.744882 | − | 0.667196i | \(-0.232506\pi\) | ||||
0.744882 | + | 0.667196i | \(0.232506\pi\) | |||||||
\(434\) | 9.00000 | − | 46.7654i | 0.432014 | − | 2.24481i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.0000 | 0.862044 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.00000 | − | 10.3923i | −0.285069 | − | 0.493753i | 0.687557 | − | 0.726130i | \(-0.258683\pi\) |
−0.972626 | + | 0.232377i | \(0.925350\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.0000 | − | 27.7128i | 0.758473 | − | 1.31371i | ||||
\(446\) | 32.0000 | 1.51524 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.00000 | + | 20.7846i | −0.188982 | + | 0.981981i | ||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.0000 | − | 17.3205i | −0.470882 | − | 0.815591i | ||||
\(452\) | 20.0000 | 0.940721 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18.0000 | − | 31.1769i | −0.844782 | − | 1.46321i | ||||
\(455\) | 5.00000 | − | 1.73205i | 0.234404 | − | 0.0811998i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.50000 | + | 9.52628i | 0.257279 | + | 0.445621i | 0.965512 | − | 0.260358i | \(-0.0838407\pi\) |
−0.708233 | + | 0.705979i | \(0.750507\pi\) | |||||||
\(458\) | 19.0000 | + | 32.9090i | 0.887812 | + | 1.53773i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0000 | + | 17.3205i | −0.465746 | + | 0.806696i | −0.999235 | − | 0.0391109i | \(-0.987547\pi\) |
0.533488 | + | 0.845807i | \(0.320881\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.50000 | + | 14.7224i | 0.395029 | + | 0.684209i | 0.993105 | − | 0.117230i | \(-0.0374014\pi\) |
−0.598076 | + | 0.801439i | \(0.704068\pi\) | |||||||
\(464\) | −16.0000 | −0.742781 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.0000 | 0.555889 | ||||||||
\(467\) | −3.00000 | + | 5.19615i | −0.138823 | + | 0.240449i | −0.927052 | − | 0.374934i | \(-0.877665\pi\) |
0.788228 | + | 0.615383i | \(0.210999\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.0000 | − | 8.66025i | −0.461757 | − | 0.399893i | ||||
\(470\) | −12.0000 | + | 20.7846i | −0.553519 | + | 0.958723i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.00000 | − | 8.66025i | 0.229900 | − | 0.398199i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.500000 | − | 0.866025i | 0.0229416 | − | 0.0397360i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.00000 | + | 10.3923i | −0.274434 | + | 0.475333i | ||||
\(479\) | −28.0000 | −1.27935 | −0.639676 | − | 0.768644i | \(-0.720932\pi\) | ||||
−0.639676 | + | 0.768644i | \(0.720932\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.00000 | 0.136788 | ||||||||
\(482\) | −14.0000 | − | 24.2487i | −0.637683 | − | 1.10450i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | − | 12.1244i | 0.318182 | − | 0.551107i | ||||
\(485\) | −6.00000 | + | 10.3923i | −0.272446 | + | 0.471890i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.5000 | − | 26.8468i | −0.702372 | − | 1.21654i | −0.967632 | − | 0.252367i | \(-0.918791\pi\) |
0.265260 | − | 0.964177i | \(-0.414542\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.00000 | − | 27.7128i | −0.180702 | − | 1.25194i | ||||
\(491\) | 14.0000 | + | 24.2487i | 0.631811 | + | 1.09433i | 0.987181 | + | 0.159603i | \(0.0510215\pi\) |
−0.355370 | + | 0.934726i | \(0.615645\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −1.00000 | − | 1.73205i | −0.0449921 | − | 0.0779287i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −36.0000 | −1.61645 | ||||||||
\(497\) | −3.00000 | + | 15.5885i | −0.134568 | + | 0.699238i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.0000 | 1.65635 | 0.828174 | − | 0.560471i | \(-0.189380\pi\) | ||||
0.828174 | + | 0.560471i | \(0.189380\pi\) | |||||||
\(500\) | −12.0000 | + | 20.7846i | −0.536656 | + | 0.929516i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.00000 | + | 13.8564i | 0.357057 | + | 0.618442i | ||||
\(503\) | −42.0000 | −1.87269 | −0.936344 | − | 0.351085i | \(-0.885813\pi\) | ||||
−0.936344 | + | 0.351085i | \(0.885813\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.00000 | −0.177998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.0000 | − | 25.9808i | 0.665517 | − | 1.15271i | ||||
\(509\) | 2.00000 | 0.0886484 | 0.0443242 | − | 0.999017i | \(-0.485887\pi\) | ||||
0.0443242 | + | 0.999017i | \(0.485887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.50000 | − | 2.59808i | 0.331780 | − | 0.114932i | ||||
\(512\) | 32.0000 | 1.41421 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.0000 | − | 45.0333i | −1.14681 | − | 1.98633i | ||||
\(515\) | 14.0000 | 0.616914 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.00000 | − | 10.3923i | −0.263880 | − | 0.457053i | ||||
\(518\) | 3.00000 | − | 15.5885i | 0.131812 | − | 0.684917i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | − | 10.3923i | −0.262865 | − | 0.455295i | 0.704137 | − | 0.710064i | \(-0.251334\pi\) |
−0.967002 | + | 0.254769i | \(0.918001\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5000 | + | 26.8468i | −0.677768 | + | 1.17393i | 0.297884 | + | 0.954602i | \(0.403719\pi\) |
−0.975652 | + | 0.219326i | \(0.929614\pi\) | |||||||
\(524\) | 14.0000 | − | 24.2487i | 0.611593 | − | 1.05931i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.00000 | − | 6.92820i | −0.174408 | − | 0.302084i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 24.0000 | − | 41.5692i | 1.04249 | − | 1.80565i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.00000 | + | 1.73205i | −0.216777 | + | 0.0750939i | ||||
\(533\) | 5.00000 | − | 8.66025i | 0.216574 | − | 0.375117i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.00000 | + | 13.8564i | −0.345870 | + | 0.599065i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.00000 | + | 10.3923i | −0.258678 | + | 0.448044i | ||||
\(539\) | 13.0000 | + | 5.19615i | 0.559950 | + | 0.223814i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.50000 | − | 16.4545i | 0.408437 | − | 0.707433i | −0.586278 | − | 0.810110i | \(-0.699407\pi\) |
0.994715 | + | 0.102677i | \(0.0327407\pi\) | |||||||
\(542\) | 32.0000 | 1.37452 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.00000 | + | 15.5885i | 0.385518 | + | 0.667736i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.0000 | + | 24.2487i | −0.598597 | + | 1.03680i | 0.394432 | + | 0.918925i | \(0.370941\pi\) |
−0.993028 | + | 0.117875i | \(0.962392\pi\) | |||||||
\(548\) | 12.0000 | − | 20.7846i | 0.512615 | − | 0.887875i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00000 | − | 3.46410i | −0.0852803 | − | 0.147710i | ||||
\(551\) | −2.00000 | − | 3.46410i | −0.0852029 | − | 0.147576i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.50000 | − | 0.866025i | 0.106311 | − | 0.0368271i | ||||
\(554\) | −13.0000 | − | 22.5167i | −0.552317 | − | 0.956641i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.00000 | −0.254457 | ||||||||
\(557\) | 1.00000 | + | 1.73205i | 0.0423714 | + | 0.0733893i | 0.886433 | − | 0.462856i | \(-0.153175\pi\) |
−0.844062 | + | 0.536246i | \(0.819842\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.00000 | 0.211477 | ||||||||
\(560\) | −20.0000 | + | 6.92820i | −0.845154 | + | 0.292770i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.00000 | −0.337460 | ||||||||
\(563\) | 13.0000 | − | 22.5167i | 0.547885 | − | 0.948964i | −0.450535 | − | 0.892759i | \(-0.648767\pi\) |
0.998419 | − | 0.0562051i | \(-0.0179001\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0000 | + | 17.3205i | 0.420703 | + | 0.728679i | ||||
\(566\) | −22.0000 | −0.924729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.0000 | + | 22.5167i | 0.544988 | + | 0.943948i | 0.998608 | + | 0.0527519i | \(0.0167993\pi\) |
−0.453619 | + | 0.891196i | \(0.649867\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.50000 | − | 16.4545i | 0.397563 | − | 0.688599i | −0.595862 | − | 0.803087i | \(-0.703189\pi\) |
0.993425 | + | 0.114488i | \(0.0365228\pi\) | |||||||
\(572\) | −4.00000 | −0.167248 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −40.0000 | − | 34.6410i | −1.66957 | − | 1.44589i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.50000 | + | 14.7224i | 0.353860 | + | 0.612903i | 0.986922 | − | 0.161198i | \(-0.0515357\pi\) |
−0.633062 | + | 0.774101i | \(0.718202\pi\) | |||||||
\(578\) | −34.0000 | −1.41421 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.00000 | + | 13.8564i | 0.332182 | + | 0.575356i | ||||
\(581\) | 12.0000 | + | 10.3923i | 0.497844 | + | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0000 | + | 20.7846i | 0.496989 | + | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.00000 | + | 13.8564i | −0.330477 | + | 0.572403i | ||||
\(587\) | −8.00000 | + | 13.8564i | −0.330195 | + | 0.571915i | −0.982550 | − | 0.185999i | \(-0.940448\pi\) |
0.652355 | + | 0.757914i | \(0.273781\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.50000 | − | 7.79423i | −0.185419 | − | 0.321156i | ||||
\(590\) | 48.0000 | 1.97613 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.0000 | −0.493197 | ||||||||
\(593\) | 3.00000 | − | 5.19615i | 0.123195 | − | 0.213380i | −0.797831 | − | 0.602881i | \(-0.794019\pi\) |
0.921026 | + | 0.389501i | \(0.127353\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.0000 | − | 20.7846i | 0.491539 | − | 0.851371i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.00000 | + | 10.3923i | −0.245153 | + | 0.424618i | −0.962175 | − | 0.272433i | \(-0.912172\pi\) |
0.717021 | + | 0.697051i | \(0.245505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.50000 | − | 7.79423i | 0.183559 | − | 0.317933i | −0.759531 | − | 0.650471i | \(-0.774572\pi\) |
0.943090 | + | 0.332538i | \(0.107905\pi\) | |||||||
\(602\) | 5.00000 | − | 25.9808i | 0.203785 | − | 1.05890i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.0000 | − | 27.7128i | 0.651031 | − | 1.12762i | ||||
\(605\) | 14.0000 | 0.569181 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.0000 | 0.933541 | 0.466771 | − | 0.884378i | \(-0.345417\pi\) | ||||
0.466771 | + | 0.884378i | \(0.345417\pi\) | |||||||
\(608\) | 4.00000 | + | 6.92820i | 0.162221 | + | 0.280976i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.0000 | − | 34.6410i | 0.809776 | − | 1.40257i | ||||
\(611\) | 3.00000 | − | 5.19615i | 0.121367 | − | 0.210214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.0000 | − | 29.4449i | −0.686624 | − | 1.18927i | −0.972924 | − | 0.231127i | \(-0.925759\pi\) |
0.286300 | − | 0.958140i | \(-0.407575\pi\) | |||||||
\(614\) | 17.0000 | + | 29.4449i | 0.686064 | + | 1.18830i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.00000 | + | 5.19615i | 0.120775 | + | 0.209189i | 0.920074 | − | 0.391745i | \(-0.128129\pi\) |
−0.799298 | + | 0.600935i | \(0.794795\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.0000 | −1.16561 | −0.582804 | − | 0.812613i | \(-0.698045\pi\) | ||||
−0.582804 | + | 0.812613i | \(0.698045\pi\) | |||||||
\(620\) | 18.0000 | + | 31.1769i | 0.722897 | + | 1.25210i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.0000 | −0.481156 | ||||||||
\(623\) | 32.0000 | + | 27.7128i | 1.28205 | + | 1.11029i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 1.00000 | − | 1.73205i | 0.0399680 | − | 0.0692267i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.0000 | + | 24.2487i | 0.558661 | + | 0.967629i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −24.0000 | + | 41.5692i | −0.953162 | + | 1.65092i | ||||
\(635\) | 30.0000 | 1.19051 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | + | 6.92820i | 0.0396214 | + | 0.274505i | ||||
\(638\) | −16.0000 | −0.633446 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.50000 | + | 16.4545i | 0.374643 | + | 0.648901i | 0.990274 | − | 0.139134i | \(-0.0444318\pi\) |
−0.615630 | + | 0.788035i | \(0.711098\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.00000 | − | 1.73205i | −0.0393141 | − | 0.0680939i | 0.845699 | − | 0.533660i | \(-0.179184\pi\) |
−0.885013 | + | 0.465566i | \(0.845851\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.0000 | + | 20.7846i | −0.471041 | + | 0.815867i | ||||
\(650\) | 1.00000 | − | 1.73205i | 0.0392232 | − | 0.0679366i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | − | 6.92820i | −0.156652 | − | 0.271329i | ||||
\(653\) | 18.0000 | 0.704394 | 0.352197 | − | 0.935926i | \(-0.385435\pi\) | ||||
0.352197 | + | 0.935926i | \(0.385435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.0000 | 1.09405 | ||||||||
\(656\) | −20.0000 | + | 34.6410i | −0.780869 | + | 1.35250i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.0000 | − | 20.7846i | −0.935617 | − | 0.810268i | ||||
\(659\) | −18.0000 | + | 31.1769i | −0.701180 | + | 1.21448i | 0.266872 | + | 0.963732i | \(0.414010\pi\) |
−0.968052 | + | 0.250748i | \(0.919323\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.5000 | − | 35.5070i | 0.797358 | − | 1.38106i | −0.123974 | − | 0.992286i | \(-0.539564\pi\) |
0.921331 | − | 0.388778i | \(-0.127103\pi\) | |||||||
\(662\) | 25.0000 | − | 43.3013i | 0.971653 | − | 1.68295i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.00000 | − | 3.46410i | −0.155113 | − | 0.134332i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −28.0000 | −1.08335 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.0000 | 0.772667 | ||||||||
\(671\) | 10.0000 | + | 17.3205i | 0.386046 | + | 0.668651i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.5000 | − | 35.5070i | 0.790217 | − | 1.36870i | −0.135615 | − | 0.990762i | \(-0.543301\pi\) |
0.925832 | − | 0.377934i | \(-0.123365\pi\) | |||||||
\(674\) | −13.0000 | + | 22.5167i | −0.500741 | + | 0.867309i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.0000 | + | 20.7846i | 0.461538 | + | 0.799408i | ||||
\(677\) | −6.00000 | − | 10.3923i | −0.230599 | − | 0.399409i | 0.727386 | − | 0.686229i | \(-0.240735\pi\) |
−0.957984 | + | 0.286820i | \(0.907402\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0000 | − | 10.3923i | −0.460518 | − | 0.398820i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −36.0000 | −1.37851 | ||||||||
\(683\) | 6.00000 | + | 10.3923i | 0.229584 | + | 0.397650i | 0.957685 | − | 0.287819i | \(-0.0929302\pi\) |
−0.728101 | + | 0.685470i | \(0.759597\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.0000 | 0.916993 | ||||||||
\(686\) | 37.0000 | + | 1.73205i | 1.41267 | + | 0.0661300i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.0000 | −0.762493 | ||||||||
\(689\) | −6.00000 | + | 10.3923i | −0.228582 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.5000 | + | 32.0429i | 0.703773 | + | 1.21897i | 0.967132 | + | 0.254273i | \(0.0818362\pi\) |
−0.263359 | + | 0.964698i | \(0.584830\pi\) | |||||||
\(692\) | 16.0000 | 0.608229 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 64.0000 | 2.42941 | ||||||||
\(695\) | −3.00000 | − | 5.19615i | −0.113796 | − | 0.197101i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −28.0000 | −1.05982 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.00000 | − | 3.46410i | −0.151186 | − | 0.130931i | ||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.50000 | − | 2.59808i | −0.0565736 | − | 0.0979883i | ||||
\(704\) | 16.0000 | 0.603023 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −34.0000 | − | 58.8897i | −1.27961 | − | 2.21634i | ||||
\(707\) | 1.00000 | − | 5.19615i | 0.0376089 | − | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.0000 | − | 25.9808i | −0.563337 | − | 0.975728i | −0.997202 | − | 0.0747503i | \(-0.976184\pi\) |
0.433865 | − | 0.900978i | \(-0.357149\pi\) | |||||||
\(710\) | −12.0000 | − | 20.7846i | −0.450352 | − | 0.780033i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.00000 | − | 3.46410i | −0.0747958 | − | 0.129550i | ||||
\(716\) | 4.00000 | 0.149487 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 40.0000 | 1.49279 | ||||||||
\(719\) | 9.00000 | − | 15.5885i | 0.335643 | − | 0.581351i | −0.647965 | − | 0.761670i | \(-0.724380\pi\) |
0.983608 | + | 0.180319i | \(0.0577130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.50000 | + | 18.1865i | −0.130347 | + | 0.677302i | ||||
\(722\) | 18.0000 | − | 31.1769i | 0.669891 | − | 1.16028i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.0000 | + | 22.5167i | −0.483141 | + | 0.836825i | ||||
\(725\) | 2.00000 | − | 3.46410i | 0.0742781 | − | 0.128654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.50000 | − | 11.2583i | 0.241072 | − | 0.417548i | −0.719948 | − | 0.694028i | \(-0.755834\pi\) |
0.961020 | + | 0.276479i | \(0.0891678\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.00000 | + | 10.3923i | −0.222070 | + | 0.384636i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.0000 | −0.554038 | −0.277019 | − | 0.960864i | \(-0.589346\pi\) | ||||
−0.277019 | + | 0.960864i | \(0.589346\pi\) | |||||||
\(734\) | 9.00000 | + | 15.5885i | 0.332196 | + | 0.575380i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.00000 | + | 8.66025i | −0.184177 | + | 0.319005i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.50000 | + | 12.9904i | 0.275892 | + | 0.477859i | 0.970360 | − | 0.241665i | \(-0.0776935\pi\) |
−0.694468 | + | 0.719524i | \(0.744360\pi\) | |||||||
\(740\) | 6.00000 | + | 10.3923i | 0.220564 | + | 0.382029i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 48.0000 | + | 41.5692i | 1.76214 | + | 1.52605i | ||||
\(743\) | −21.0000 | − | 36.3731i | −0.770415 | − | 1.33440i | −0.937336 | − | 0.348428i | \(-0.886716\pi\) |
0.166920 | − | 0.985970i | \(-0.446618\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.0000 | 0.879292 | ||||||||
\(746\) | −23.0000 | − | 39.8372i | −0.842090 | − | 1.45854i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.0000 | − | 13.8564i | −0.584627 | − | 0.506302i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0000 | 0.474377 | 0.237188 | − | 0.971464i | \(-0.423774\pi\) | ||||
0.237188 | + | 0.971464i | \(0.423774\pi\) | |||||||
\(752\) | −12.0000 | + | 20.7846i | −0.437595 | + | 0.757937i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.00000 | − | 6.92820i | −0.145671 | − | 0.252310i | ||||
\(755\) | 32.0000 | 1.16460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | −3.00000 | − | 5.19615i | −0.108965 | − | 0.188733i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.0000 | −1.74000 | −0.869999 | − | 0.493053i | \(-0.835881\pi\) | ||||
−0.869999 | + | 0.493053i | \(0.835881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.5000 | + | 7.79423i | −0.814555 | + | 0.282170i | ||||
\(764\) | 20.0000 | 0.723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000 | + | 20.7846i | 0.433578 | + | 0.750978i | ||||
\(767\) | −12.0000 | −0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.5000 | + | 42.4352i | 0.883493 | + | 1.53025i | 0.847432 | + | 0.530904i | \(0.178148\pi\) |
0.0360609 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(770\) | −20.0000 | + | 6.92820i | −0.720750 | + | 0.249675i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.0000 | − | 19.0526i | −0.395899 | − | 0.685717i | ||||
\(773\) | 17.0000 | + | 29.4449i | 0.611448 | + | 1.05906i | 0.990997 | + | 0.133887i | \(0.0427458\pi\) |
−0.379549 | + | 0.925172i | \(0.623921\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.50000 | − | 7.79423i | 0.161645 | − | 0.279977i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.00000 | + | 10.3923i | 0.215110 | + | 0.372582i | ||||
\(779\) | −10.0000 | −0.358287 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.0000 | 0.429394 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.00000 | − | 27.7128i | −0.142857 | − | 0.989743i | ||||
\(785\) | −14.0000 | + | 24.2487i | −0.499681 | + | 0.865474i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.0000 | + | 34.6410i | −0.712923 | + | 1.23482i | 0.250832 | + | 0.968031i | \(0.419296\pi\) |
−0.963755 | + | 0.266788i | \(0.914038\pi\) | |||||||
\(788\) | −16.0000 | + | 27.7128i | −0.569976 | + | 0.987228i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.00000 | + | 3.46410i | −0.0711568 | + | 0.123247i | ||||
\(791\) | −25.0000 | + | 8.66025i | −0.888898 | + | 0.307923i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.00000 | + | 8.66025i | −0.177555 | + | 0.307535i | ||||
\(794\) | −18.0000 | −0.638796 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.00000 | + | 6.92820i | 0.141687 | + | 0.245410i | 0.928132 | − | 0.372251i | \(-0.121414\pi\) |
−0.786445 | + | 0.617661i | \(0.788081\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −4.00000 | + | 6.92820i | −0.141421 | + | 0.244949i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 36.0000 | + | 62.3538i | 1.27120 | + | 2.20179i | ||||
\(803\) | −3.00000 | − | 5.19615i | −0.105868 | − | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.00000 | − | 15.5885i | −0.317011 | − | 0.549080i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.0000 | − | 25.9808i | −0.527372 | − | 0.913435i | −0.999491 | − | 0.0319002i | \(-0.989844\pi\) |
0.472119 | − | 0.881535i | \(-0.343489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.0000 | 1.12367 | 0.561836 | − | 0.827249i | \(-0.310095\pi\) | ||||
0.561836 | + | 0.827249i | \(0.310095\pi\) | |||||||
\(812\) | −20.0000 | + | 6.92820i | −0.701862 | + | 0.243132i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12.0000 | −0.420600 | ||||||||
\(815\) | 4.00000 | − | 6.92820i | 0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.50000 | − | 4.33013i | −0.0874639 | − | 0.151492i | ||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 40.0000 | 1.39686 | ||||||||
\(821\) | −1.00000 | − | 1.73205i | −0.0349002 | − | 0.0604490i | 0.848048 | − | 0.529920i | \(-0.177778\pi\) |
−0.882948 | + | 0.469471i | \(0.844445\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.0000 | + | 62.3538i | −0.417533 | + | 2.16957i | ||||
\(827\) | −30.0000 | −1.04320 | −0.521601 | − | 0.853189i | \(-0.674665\pi\) | ||||
−0.521601 | + | 0.853189i | \(0.674665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.5000 | − | 35.5070i | −0.711994 | − | 1.23321i | −0.964107 | − | 0.265513i | \(-0.914459\pi\) |
0.252113 | − | 0.967698i | \(-0.418875\pi\) | |||||||
\(830\) | −24.0000 | −0.833052 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.00000 | + | 6.92820i | 0.138675 | + | 0.240192i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.0000 | − | 24.2487i | −0.484490 | − | 0.839161i | ||||
\(836\) | 2.00000 | + | 3.46410i | 0.0691714 | + | 0.119808i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −30.0000 | + | 51.9615i | −1.03633 | + | 1.79498i | ||||
\(839\) | 22.0000 | − | 38.1051i | 0.759524 | − | 1.31553i | −0.183569 | − | 0.983007i | \(-0.558765\pi\) |
0.943093 | − | 0.332528i | \(-0.107902\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | + | 11.2583i | 0.224138 | + | 0.388218i | ||||
\(842\) | −14.0000 | −0.482472 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | −12.0000 | + | 20.7846i | −0.412813 | + | 0.715012i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.50000 | + | 18.1865i | −0.120261 | + | 0.624897i | ||||
\(848\) | 24.0000 | − | 41.5692i | 0.824163 | − | 1.42749i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.5000 | + | 30.3109i | −0.599189 | + | 1.03783i | 0.393753 | + | 0.919216i | \(0.371177\pi\) |
−0.992941 | + | 0.118609i | \(0.962157\pi\) | |||||||
\(854\) | 40.0000 | + | 34.6410i | 1.36877 | + | 1.18539i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.0000 | −1.09310 | −0.546550 | − | 0.837427i | \(-0.684059\pi\) | ||||
−0.546550 | + | 0.837427i | \(0.684059\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.0000 | −1.36478 | −0.682391 | − | 0.730987i | \(-0.739060\pi\) | ||||
−0.682391 | + | 0.730987i | \(0.739060\pi\) | |||||||
\(860\) | 10.0000 | + | 17.3205i | 0.340997 | + | 0.590624i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.0000 | − | 31.1769i | 0.613082 | − | 1.06189i | ||||
\(863\) | 27.0000 | − | 46.7654i | 0.919091 | − | 1.59191i | 0.118291 | − | 0.992979i | \(-0.462258\pi\) |
0.800799 | − | 0.598933i | \(-0.204408\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.00000 | + | 13.8564i | 0.272008 | + | 0.471132i | ||||
\(866\) | −31.0000 | − | 53.6936i | −1.05342 | − | 1.82458i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −45.0000 | + | 15.5885i | −1.52740 | + | 0.529107i | ||||
\(869\) | −1.00000 | − | 1.73205i | −0.0339227 | − | 0.0587558i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.00000 | −0.169419 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.00000 | − | 31.1769i | 0.202837 | − | 1.05397i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.0000 | −1.28317 | −0.641584 | − | 0.767052i | \(-0.721723\pi\) | ||||
−0.641584 | + | 0.767052i | \(0.721723\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.00000 | + | 13.8564i | 0.269680 | + | 0.467099i | ||||
\(881\) | 24.0000 | 0.808581 | 0.404290 | − | 0.914631i | \(-0.367519\pi\) | ||||
0.404290 | + | 0.914631i | \(0.367519\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.0000 | −0.437485 | −0.218742 | − | 0.975783i | \(-0.570195\pi\) | ||||
−0.218742 | + | 0.975783i | \(0.570195\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.0000 | + | 20.7846i | −0.403148 | + | 0.698273i | ||||
\(887\) | −34.0000 | −1.14161 | −0.570804 | − | 0.821086i | \(-0.693368\pi\) | ||||
−0.570804 | + | 0.821086i | \(0.693368\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.50000 | + | 38.9711i | −0.251542 | + | 1.30705i | ||||
\(890\) | −64.0000 | −2.14528 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.0000 | − | 27.7128i | −0.535720 | − | 0.927894i | ||||
\(893\) | −6.00000 | −0.200782 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.00000 | + | 3.46410i | 0.0668526 | + | 0.115792i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.0000 | + | 31.1769i | 0.600668 | + | 1.04039i | ||||
\(899\) | −18.0000 | − | 31.1769i | −0.600334 | − | 1.03981i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −20.0000 | + | 34.6410i | −0.665927 | + | 1.15342i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.0000 | −0.864269 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.0000 | −1.22856 | −0.614282 | − | 0.789086i | \(-0.710554\pi\) | ||||
−0.614282 | + | 0.789086i | \(0.710554\pi\) | |||||||
\(908\) | −18.0000 | + | 31.1769i | −0.597351 | + | 1.03464i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.00000 | − | 6.92820i | −0.265197 | − | 0.229668i | ||||
\(911\) | 12.0000 | − | 20.7846i | 0.397578 | − | 0.688625i | −0.595849 | − | 0.803097i | \(-0.703184\pi\) |
0.993426 | + | 0.114472i | \(0.0365176\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000 | − | 10.3923i | 0.198571 | − | 0.343935i | ||||
\(914\) | 11.0000 | − | 19.0526i | 0.363848 | − | 0.630203i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.0000 | − | 32.9090i | 0.627778 | − | 1.08734i | ||||
\(917\) | −7.00000 | + | 36.3731i | −0.231160 | + | 1.20114i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.5000 | + | 19.9186i | −0.379350 | + | 0.657053i | −0.990968 | − | 0.134100i | \(-0.957186\pi\) |
0.611618 | + | 0.791153i | \(0.290519\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 40.0000 | 1.31733 | ||||||||
\(923\) | 3.00000 | + | 5.19615i | 0.0987462 | + | 0.171033i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.50000 | − | 2.59808i | 0.0493197 | − | 0.0854242i | ||||
\(926\) | 17.0000 | − | 29.4449i | 0.558655 | − | 0.967618i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.0000 | + | 27.7128i | 0.525226 | + | 0.909718i | ||||
\(929\) | −7.00000 | − | 12.1244i | −0.229663 | − | 0.397787i | 0.728046 | − | 0.685529i | \(-0.240429\pi\) |
−0.957708 | + | 0.287742i | \(0.907096\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.50000 | − | 4.33013i | 0.180255 | − | 0.141914i | ||||
\(932\) | −6.00000 | − | 10.3923i | −0.196537 | − | 0.340411i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12.0000 | 0.392652 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.0000 | 0.490029 | 0.245014 | − | 0.969519i | \(-0.421207\pi\) | ||||
0.245014 | + | 0.969519i | \(0.421207\pi\) | |||||||
\(938\) | −5.00000 | + | 25.9808i | −0.163256 | + | 0.848302i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 24.0000 | 0.782794 | ||||||||
\(941\) | 2.00000 | − | 3.46410i | 0.0651981 | − | 0.112926i | −0.831584 | − | 0.555399i | \(-0.812565\pi\) |
0.896782 | + | 0.442473i | \(0.145899\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 48.0000 | 1.56227 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.0000 | −0.650256 | ||||||||
\(947\) | 5.00000 | + | 8.66025i | 0.162478 | + | 0.281420i | 0.935757 | − | 0.352646i | \(-0.114718\pi\) |
−0.773279 | + | 0.634066i | \(0.781385\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.50000 | − | 2.59808i | 0.0486921 | − | 0.0843371i | ||||
\(950\) | −2.00000 | −0.0648886 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.0000 | 1.42530 | 0.712650 | − | 0.701520i | \(-0.247495\pi\) | ||||
0.712650 | + | 0.701520i | \(0.247495\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.0000 | + | 17.3205i | 0.323592 | + | 0.560478i | ||||
\(956\) | 12.0000 | 0.388108 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.0000 | + | 48.4974i | 0.904639 | + | 1.56688i | ||||
\(959\) | −6.00000 | + | 31.1769i | −0.193750 | + | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0000 | − | 43.3013i | −0.806452 | − | 1.39682i | ||||
\(962\) | −3.00000 | − | 5.19615i | −0.0967239 | − | 0.167531i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.0000 | + | 24.2487i | −0.450910 | + | 0.780998i | ||||
\(965\) | 11.0000 | − | 19.0526i | 0.354103 | − | 0.613324i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.50000 | − | 16.4545i | −0.305499 | − | 0.529140i | 0.671873 | − | 0.740666i | \(-0.265490\pi\) |
−0.977372 | + | 0.211526i | \(0.932157\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 24.0000 | 0.770594 | ||||||||
\(971\) | −18.0000 | + | 31.1769i | −0.577647 | + | 1.00051i | 0.418101 | + | 0.908401i | \(0.362696\pi\) |
−0.995748 | + | 0.0921142i | \(0.970638\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.50000 | − | 2.59808i | 0.240439 | − | 0.0832905i | ||||
\(974\) | −31.0000 | + | 53.6936i | −0.993304 | + | 1.72045i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.0000 | − | 34.6410i | 0.640184 | − | 1.10883i | ||||
\(977\) | 9.00000 | − | 15.5885i | 0.287936 | − | 0.498719i | −0.685381 | − | 0.728184i | \(-0.740364\pi\) |
0.973317 | + | 0.229465i | \(0.0736978\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.0000 | − | 27.7128i | 0.511362 | − | 0.885705i | ||||
\(980\) | −22.0000 | + | 17.3205i | −0.702764 | + | 0.553283i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 28.0000 | − | 48.4974i | 0.893516 | − | 1.54761i | ||||
\(983\) | 36.0000 | 1.14822 | 0.574111 | − | 0.818778i | \(-0.305348\pi\) | ||||
0.574111 | + | 0.818778i | \(0.305348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32.0000 | −1.01960 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.00000 | + | 1.73205i | −0.0318142 | + | 0.0551039i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.50000 | − | 14.7224i | −0.270011 | − | 0.467673i | 0.698853 | − | 0.715265i | \(-0.253694\pi\) |
−0.968864 | + | 0.247592i | \(0.920361\pi\) | |||||||
\(992\) | 36.0000 | + | 62.3538i | 1.14300 | + | 1.97974i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 30.0000 | − | 10.3923i | 0.951542 | − | 0.329624i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0000 | 0.601736 | 0.300868 | − | 0.953666i | \(-0.402724\pi\) | ||||
0.300868 | + | 0.953666i | \(0.402724\pi\) | |||||||
\(998\) | −37.0000 | − | 64.0859i | −1.17121 | − | 2.02860i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))