Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(298,567)]
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([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.298");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.h (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: | \(0\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 298.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.298 |
Dual form | 567.2.h.f.352.1 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 1.00000 | ||||||||
\(5\) | 1.00000 | − | 1.73205i | 0.447214 | − | 0.774597i | −0.550990 | − | 0.834512i | \(-0.685750\pi\) |
0.998203 | + | 0.0599153i | \(0.0190830\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | − | 3.46410i | 0.632456 | − | 1.09545i | ||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | 0.788320 | − | 0.615265i | \(-0.210951\pi\) |
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 4.00000 | − | 3.46410i | 1.06904 | − | 0.925820i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | − | 0.866025i | −0.114708 | − | 0.198680i | 0.802955 | − | 0.596040i | \(-0.203260\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 2.00000 | − | 3.46410i | 0.447214 | − | 0.774597i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | + | 3.46410i | 0.426401 | + | 0.738549i | ||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | −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 | ||||||||
\(31\) | 9.00000 | 1.61645 | 0.808224 | − | 0.588875i | \(-0.200429\pi\) | ||||
0.808224 | + | 0.588875i | \(0.200429\pi\) | |||||||
\(32\) | −8.00000 | −1.41421 | ||||||||
\(33\) | 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 | 0.715981 | − | 0.698119i | \(-0.245980\pi\) |
−0.962580 | + | 0.270998i | \(0.912646\pi\) | |||||||
\(38\) | −1.00000 | − | 1.73205i | −0.162221 | − | 0.280976i | ||||
\(39\) | 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 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 1.00000 | + | 1.73205i | 0.141421 | + | 0.244949i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | − | 1.73205i | −0.138675 | − | 0.240192i | ||||
\(53\) | −6.00000 | + | 10.3923i | −0.824163 | + | 1.42749i | 0.0783936 | + | 0.996922i | \(0.475021\pi\) |
−0.902557 | + | 0.430570i | \(0.858312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.00000 | + | 6.92820i | −0.525226 | + | 0.909718i | ||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | 18.0000 | 2.28600 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | −0.610847 | −0.305424 | − | 0.952217i | \(-0.598798\pi\) | ||||
−0.305424 | + | 0.952217i | \(0.598798\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | − | 10.3923i | −0.239046 | − | 1.24212i | ||||
\(71\) | −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 | −0.764794 | − | 0.644275i | \(-0.777159\pi\) |
0.940356 | + | 0.340193i | \(0.110493\pi\) | |||||||
\(74\) | −3.00000 | − | 5.19615i | −0.348743 | − | 0.604040i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | − | 1.73205i | −0.114708 | − | 0.198680i | ||||
\(77\) | 5.00000 | + | 1.73205i | 0.569803 | + | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | −0.0562544 | − | 0.998416i | \(-0.517916\pi\) | ||||
−0.0562544 | + | 0.998416i | \(0.517916\pi\) | |||||||
\(80\) | −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 | ||||||||
\(86\) | −5.00000 | + | 8.66025i | −0.539164 | + | 0.933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.00000 | − | 13.8564i | −0.847998 | − | 1.46878i | −0.882992 | − | 0.469389i | \(-0.844474\pi\) |
0.0349934 | − | 0.999388i | \(-0.488859\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.50000 | − | 0.866025i | −0.262071 | − | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.0000 | −1.23771 | ||||||||
\(95\) | −2.00000 | −0.205196 | ||||||||
\(96\) | 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 | ||||
\(101\) | −1.00000 | − | 1.73205i | −0.0995037 | − | 0.172345i | 0.811976 | − | 0.583691i | \(-0.198392\pi\) |
−0.911479 | + | 0.411346i | \(0.865059\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.50000 | − | 6.06218i | 0.344865 | − | 0.597324i | −0.640464 | − | 0.767988i | \(-0.721258\pi\) |
0.985329 | + | 0.170664i | \(0.0545913\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | + | 20.7846i | −1.16554 | + | 2.01878i | ||||
\(107\) | 4.00000 | + | 6.92820i | 0.386695 | + | 0.669775i | 0.992003 | − | 0.126217i | \(-0.0402834\pi\) |
−0.605308 | + | 0.795991i | \(0.706950\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.50000 | + | 7.79423i | −0.431022 | + | 0.746552i | −0.996962 | − | 0.0778949i | \(-0.975180\pi\) |
0.565940 | + | 0.824447i | \(0.308513\pi\) | |||||||
\(110\) | 8.00000 | 0.762770 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.00000 | + | 6.92820i | −0.755929 | + | 0.654654i | ||||
\(113\) | −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 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 20.0000 | 1.81071 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18.0000 | 1.61645 | ||||||||
\(125\) | 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 | ||||||||
\(130\) | −4.00000 | −0.350823 | ||||||||
\(131\) | 7.00000 | − | 12.1244i | 0.611593 | − | 1.05931i | −0.379379 | − | 0.925241i | \(-0.623862\pi\) |
0.990972 | − | 0.134069i | \(-0.0428042\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.50000 | − | 0.866025i | −0.216777 | − | 0.0750939i | ||||
\(134\) | −10.0000 | −0.863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.50000 | + | 2.59808i | 0.127228 | + | 0.220366i | 0.922602 | − | 0.385754i | \(-0.126059\pi\) |
−0.795373 | + | 0.606120i | \(0.792725\pi\) | |||||||
\(140\) | −2.00000 | − | 10.3923i | −0.169031 | − | 0.878310i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.0000 | −1.00702 | ||||||||
\(143\) | 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 | ||||
\(149\) | 6.00000 | − | 10.3923i | 0.491539 | − | 0.851371i | −0.508413 | − | 0.861113i | \(-0.669768\pi\) |
0.999953 | + | 0.00974235i | \(0.00310113\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | + | 13.8564i | 0.651031 | + | 1.12762i | 0.982873 | + | 0.184284i | \(0.0589965\pi\) |
−0.331842 | + | 0.943335i | \(0.607670\pi\) | |||||||
\(152\) | 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 | ||||||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | −2.00000 | −0.159111 | ||||||||
\(159\) | 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 | 0.777007 | − | 0.629492i | \(-0.216737\pi\) |
−0.933659 | + | 0.358162i | \(0.883403\pi\) | |||||||
\(164\) | 10.0000 | + | 17.3205i | 0.780869 | + | 1.35250i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | + | 10.3923i | −0.465690 | + | 0.806599i | ||||
\(167\) | 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 | ||||
\(173\) | 8.00000 | 0.608229 | 0.304114 | − | 0.952636i | \(-0.401639\pi\) | ||||
0.304114 | + | 0.952636i | \(0.401639\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.50000 | + | 0.866025i | 0.188982 | + | 0.0654654i | ||||
\(176\) | −4.00000 | − | 6.92820i | −0.301511 | − | 0.522233i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.0000 | − | 27.7128i | −1.19925 | − | 2.07716i | ||||
\(179\) | −1.00000 | + | 1.73205i | −0.0747435 | + | 0.129460i | −0.900975 | − | 0.433872i | \(-0.857147\pi\) |
0.826231 | + | 0.563331i | \(0.190480\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0000 | 0.966282 | 0.483141 | − | 0.875542i | \(-0.339496\pi\) | ||||
0.483141 | + | 0.875542i | \(0.339496\pi\) | |||||||
\(182\) | −5.00000 | − | 1.73205i | −0.370625 | − | 0.128388i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | −0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −12.0000 | −0.875190 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 10.0000 | 0.723575 | 0.361787 | − | 0.932261i | \(-0.382167\pi\) | ||||
0.361787 | + | 0.932261i | \(0.382167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0000 | 0.791797 | 0.395899 | − | 0.918294i | \(-0.370433\pi\) | ||||
0.395899 | + | 0.918294i | \(0.370433\pi\) | |||||||
\(194\) | 6.00000 | − | 10.3923i | 0.430775 | − | 0.746124i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | − | 13.8564i | 0.142857 | − | 0.989743i | ||||
\(197\) | 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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.00000 | − | 3.46410i | −0.140720 | − | 0.243733i | ||||
\(203\) | 2.00000 | + | 10.3923i | 0.140372 | + | 0.729397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.0000 | 1.39686 | ||||||||
\(206\) | 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 | \(0.877300\pi\) | |||||||
\(212\) | −12.0000 | + | 20.7846i | −0.824163 | + | 1.42749i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.00000 | + | 13.8564i | 0.546869 | + | 0.947204i | ||||
\(215\) | 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 | ||||||||
\(220\) | 8.00000 | 0.539360 | ||||||||
\(221\) | 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 | ||||
\(227\) | −9.00000 | − | 15.5885i | −0.597351 | − | 1.03464i | −0.993210 | − | 0.116331i | \(-0.962887\pi\) |
0.395860 | − | 0.918311i | \(-0.370447\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.50000 | − | 16.4545i | 0.627778 | − | 1.08734i | −0.360219 | − | 0.932868i | \(-0.617298\pi\) |
0.987997 | − | 0.154475i | \(-0.0493686\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00000 | − | 5.19615i | −0.196537 | − | 0.340411i | 0.750867 | − | 0.660454i | \(-0.229636\pi\) |
−0.947403 | + | 0.320043i | \(0.896303\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | + | 10.3923i | −0.391397 | + | 0.677919i | ||||
\(236\) | −24.0000 | −1.56227 | ||||||||
\(237\) | 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 | ||||||||
\(241\) | −7.00000 | − | 12.1244i | −0.450910 | − | 0.780998i | 0.547533 | − | 0.836784i | \(-0.315567\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 7.00000 | − | 12.1244i | 0.449977 | − | 0.779383i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.0000 | 1.28037 | ||||||||
\(245\) | −11.0000 | − | 8.66025i | −0.702764 | − | 0.553283i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.500000 | + | 0.866025i | −0.0318142 | + | 0.0551039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 24.0000 | 1.51789 | ||||||||
\(251\) | −8.00000 | −0.504956 | −0.252478 | − | 0.967603i | \(-0.581245\pi\) | ||||
−0.252478 | + | 0.967603i | \(0.581245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −30.0000 | −1.88237 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | −13.0000 | + | 22.5167i | −0.810918 | + | 1.40455i | 0.101305 | + | 0.994855i | \(0.467698\pi\) |
−0.912222 | + | 0.409695i | \(0.865635\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.50000 | − | 2.59808i | −0.466027 | − | 0.161437i | ||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.0000 | − | 24.2487i | 0.864923 | − | 1.49809i | ||||
\(263\) | −2.00000 | − | 3.46410i | −0.123325 | − | 0.213606i | 0.797752 | − | 0.602986i | \(-0.206023\pi\) |
−0.921077 | + | 0.389380i | \(0.872689\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.0000 | + | 20.7846i | 0.737154 | + | 1.27679i | ||||
\(266\) | −5.00000 | − | 1.73205i | −0.306570 | − | 0.106199i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.0000 | −0.610847 | ||||||||
\(269\) | −3.00000 | + | 5.19615i | −0.182913 | + | 0.316815i | −0.942871 | − | 0.333157i | \(-0.891886\pi\) |
0.759958 | + | 0.649972i | \(0.225219\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | − | 13.8564i | −0.485965 | − | 0.841717i | 0.513905 | − | 0.857847i | \(-0.328199\pi\) |
−0.999870 | + | 0.0161307i | \(0.994865\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.0000 | + | 20.7846i | 0.724947 | + | 1.25564i | ||||
\(275\) | −1.00000 | + | 1.73205i | −0.0603023 | + | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.50000 | − | 11.2583i | −0.390547 | − | 0.676448i | 0.601975 | − | 0.798515i | \(-0.294381\pi\) |
−0.992522 | + | 0.122068i | \(0.961047\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −11.0000 | −0.653882 | −0.326941 | − | 0.945045i | \(-0.606018\pi\) | ||||
−0.326941 | + | 0.945045i | \(0.606018\pi\) | |||||||
\(284\) | −12.0000 | −0.712069 | ||||||||
\(285\) | 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 | ||||
\(290\) | 8.00000 | + | 13.8564i | 0.469776 | + | 0.813676i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.00000 | − | 5.19615i | 0.175562 | − | 0.304082i | ||||
\(293\) | −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 | ||||||||
\(301\) | 2.50000 | + | 12.9904i | 0.144098 | + | 0.748753i | ||||
\(302\) | 16.0000 | + | 27.7128i | 0.920697 | + | 1.59469i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | + | 3.46410i | 0.114708 | + | 0.198680i | ||||
\(305\) | 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 | \(0.661224\pi\) | |||||||
\(308\) | 10.0000 | + | 3.46410i | 0.569803 | + | 0.197386i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 18.0000 | − | 31.1769i | 1.02233 | − | 1.77073i | ||||
\(311\) | −6.00000 | −0.340229 | −0.170114 | − | 0.985424i | \(-0.554414\pi\) | ||||
−0.170114 | + | 0.985424i | \(0.554414\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.00000 | −0.0565233 | −0.0282617 | − | 0.999601i | \(-0.508997\pi\) | ||||
−0.0282617 | + | 0.999601i | \(0.508997\pi\) | |||||||
\(314\) | −28.0000 | −1.58013 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.00000 | −0.112509 | ||||||||
\(317\) | 24.0000 | 1.34797 | 0.673987 | − | 0.738743i | \(-0.264580\pi\) | ||||
0.673987 | + | 0.738743i | \(0.264580\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.00000 | −0.447914 | ||||||||
\(320\) | −8.00000 | + | 13.8564i | −0.447214 | + | 0.774597i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.500000 | − | 0.866025i | 0.0277350 | − | 0.0480384i | ||||
\(326\) | −4.00000 | − | 6.92820i | −0.221540 | − | 0.383718i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0000 | + | 10.3923i | −0.661581 | + | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.0000 | −1.37412 | −0.687062 | − | 0.726599i | \(-0.741100\pi\) | ||||
−0.687062 | + | 0.726599i | \(0.741100\pi\) | |||||||
\(332\) | −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 | \(0.948538\pi\) | |||||||
\(338\) | 12.0000 | − | 20.7846i | 0.652714 | − | 1.13053i | ||||
\(339\) | 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 | ||||||||
\(346\) | 16.0000 | 0.860165 | ||||||||
\(347\) | 32.0000 | 1.71785 | 0.858925 | − | 0.512101i | \(-0.171133\pi\) | ||||
0.858925 | + | 0.512101i | \(0.171133\pi\) | |||||||
\(348\) | 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 | ||||
\(353\) | −17.0000 | − | 29.4449i | −0.904819 | − | 1.56719i | −0.821160 | − | 0.570697i | \(-0.806673\pi\) |
−0.0836583 | − | 0.996495i | \(-0.526660\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | + | 10.3923i | −0.318447 | + | 0.551566i | ||||
\(356\) | −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 | −0.999476 | − | 0.0323801i | \(-0.989691\pi\) |
0.471696 | − | 0.881761i | \(-0.343642\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | − | 15.5885i | 0.473684 | − | 0.820445i | ||||
\(362\) | 26.0000 | 1.36653 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.00000 | − | 1.73205i | −0.262071 | − | 0.0907841i | ||||
\(365\) | −3.00000 | − | 5.19615i | −0.157027 | − | 0.271979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.50000 | + | 7.79423i | 0.234898 | + | 0.406855i | 0.959243 | − | 0.282582i | \(-0.0911910\pi\) |
−0.724345 | + | 0.689438i | \(0.757858\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.0000 | −0.623850 | ||||||||
\(371\) | 6.00000 | + | 31.1769i | 0.311504 | + | 1.61862i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.5000 | + | 19.9186i | −0.595447 | + | 1.03135i | 0.398036 | + | 0.917370i | \(0.369692\pi\) |
−0.993484 | + | 0.113975i | \(0.963641\pi\) | |||||||
\(374\) | 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 | \(0.475450\pi\) | |||||||
\(380\) | −4.00000 | −0.205196 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.0000 | 1.02329 | ||||||||
\(383\) | 6.00000 | − | 10.3923i | 0.306586 | − | 0.531022i | −0.671027 | − | 0.741433i | \(-0.734147\pi\) |
0.977613 | + | 0.210411i | \(0.0674801\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.00000 | − | 6.92820i | 0.407718 | − | 0.353094i | ||||
\(386\) | 22.0000 | 1.11977 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.00000 | − | 10.3923i | 0.304604 | − | 0.527589i | ||||
\(389\) | 3.00000 | + | 5.19615i | 0.152106 | + | 0.263455i | 0.932002 | − | 0.362454i | \(-0.118061\pi\) |
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 32.0000 | 1.61214 | ||||||||
\(395\) | −1.00000 | + | 1.73205i | −0.0503155 | + | 0.0871489i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.50000 | + | 7.79423i | 0.225849 | + | 0.391181i | 0.956574 | − | 0.291491i | \(-0.0941512\pi\) |
−0.730725 | + | 0.682672i | \(0.760818\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | 18.0000 | − | 31.1769i | 0.898877 | − | 1.55690i | 0.0699455 | − | 0.997551i | \(-0.477717\pi\) |
0.828932 | − | 0.559350i | \(-0.188949\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.50000 | − | 7.79423i | −0.224161 | − | 0.388258i | ||||
\(404\) | −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 | ||||||||
\(409\) | 5.00000 | 0.247234 | 0.123617 | − | 0.992330i | \(-0.460551\pi\) | ||||
0.123617 | + | 0.992330i | \(0.460551\pi\) | |||||||
\(410\) | 40.0000 | 1.97546 | ||||||||
\(411\) | 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 | ||||
\(416\) | 4.00000 | + | 6.92820i | 0.196116 | + | 0.339683i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.00000 | − | 3.46410i | 0.0978232 | − | 0.169435i | ||||
\(419\) | −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 | ||||||||
\(427\) | 20.0000 | − | 17.3205i | 0.967868 | − | 0.838198i | ||||
\(428\) | 8.00000 | + | 13.8564i | 0.386695 | + | 0.669775i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.0000 | + | 17.3205i | 0.482243 | + | 0.835269i | ||||
\(431\) | 9.00000 | − | 15.5885i | 0.433515 | − | 0.750870i | −0.563658 | − | 0.826008i | \(-0.690607\pi\) |
0.997173 | + | 0.0751385i | \(0.0239399\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.0000 | 1.48976 | 0.744882 | − | 0.667196i | \(-0.232506\pi\) | ||||
0.744882 | + | 0.667196i | \(0.232506\pi\) | |||||||
\(434\) | 36.0000 | − | 31.1769i | 1.72806 | − | 1.49654i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.00000 | + | 15.5885i | −0.431022 | + | 0.746552i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0000 | 0.570137 | 0.285069 | − | 0.958507i | \(-0.407984\pi\) | ||||
0.285069 | + | 0.958507i | \(0.407984\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.0000 | −1.51695 | ||||||||
\(446\) | −16.0000 | + | 27.7128i | −0.757622 | + | 1.31224i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −16.0000 | + | 13.8564i | −0.755929 | + | 0.654654i | ||||
\(449\) | −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 | ||||
\(452\) | −10.0000 | − | 17.3205i | −0.470360 | − | 0.814688i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18.0000 | − | 31.1769i | −0.844782 | − | 1.46321i | ||||
\(455\) | −4.00000 | + | 3.46410i | −0.187523 | + | 0.162400i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0000 | −0.514558 | −0.257279 | − | 0.966337i | \(-0.582826\pi\) | ||||
−0.257279 | + | 0.966337i | \(0.582826\pi\) | |||||||
\(458\) | 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 | \(0.704068\pi\) | |||||||
\(464\) | 8.00000 | − | 13.8564i | 0.371391 | − | 0.643268i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.00000 | − | 10.3923i | −0.277945 | − | 0.481414i | ||||
\(467\) | −3.00000 | − | 5.19615i | −0.138823 | − | 0.240449i | 0.788228 | − | 0.615383i | \(-0.210999\pi\) |
−0.927052 | + | 0.374934i | \(0.877665\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | −10.0000 | −0.459800 | ||||||||
\(474\) | 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 | ||||
\(479\) | 14.0000 | + | 24.2487i | 0.639676 | + | 1.10795i | 0.985504 | + | 0.169654i | \(0.0542649\pi\) |
−0.345827 | + | 0.938298i | \(0.612402\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.50000 | + | 2.59808i | −0.0683941 | + | 0.118462i | ||||
\(482\) | −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 | 0.265260 | + | 0.964177i | \(0.414542\pi\) |
−0.967632 | + | 0.252367i | \(0.918791\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −22.0000 | − | 17.3205i | −0.993859 | − | 0.782461i | ||||
\(491\) | 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 | ||||||||
\(497\) | −12.0000 | + | 10.3923i | −0.538274 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.5000 | + | 32.0429i | −0.828174 | + | 1.43444i | 0.0712957 | + | 0.997455i | \(0.477287\pi\) |
−0.899469 | + | 0.436984i | \(0.856047\pi\) | |||||||
\(500\) | 24.0000 | 1.07331 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.0000 | −0.714115 | ||||||||
\(503\) | −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 | ||||||||
\(508\) | −30.0000 | −1.33103 | ||||||||
\(509\) | −1.00000 | + | 1.73205i | −0.0443242 | + | 0.0767718i | −0.887336 | − | 0.461123i | \(-0.847447\pi\) |
0.843012 | + | 0.537895i | \(0.180780\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.50000 | − | 7.79423i | −0.0663561 | − | 0.344796i | ||||
\(512\) | 32.0000 | 1.41421 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.0000 | + | 45.0333i | −1.14681 | + | 1.98633i | ||||
\(515\) | −7.00000 | − | 12.1244i | −0.308457 | − | 0.534263i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.00000 | − | 10.3923i | −0.263880 | − | 0.457053i | ||||
\(518\) | −15.0000 | − | 5.19615i | −0.659062 | − | 0.228306i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | + | 10.3923i | −0.262865 | + | 0.455295i | −0.967002 | − | 0.254769i | \(-0.918001\pi\) |
0.704137 | + | 0.710064i | \(0.251334\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5000 | − | 26.8468i | −0.677768 | − | 1.17393i | −0.975652 | − | 0.219326i | \(-0.929614\pi\) |
0.297884 | − | 0.954602i | \(-0.403719\pi\) | |||||||
\(524\) | 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 | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 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 | ||||||||
\(535\) | 16.0000 | 0.691740 | ||||||||
\(536\) | 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 | 0.994715 | − | 0.102677i | \(-0.0327407\pi\) |
−0.586278 | + | 0.810110i | \(0.699407\pi\) | |||||||
\(542\) | −16.0000 | − | 27.7128i | −0.687259 | − | 1.19037i | ||||
\(543\) | 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 | ||||
\(551\) | 4.00000 | 0.170406 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.00000 | + | 1.73205i | −0.0850487 | + | 0.0736543i | ||||
\(554\) | −13.0000 | − | 22.5167i | −0.552317 | − | 0.956641i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.00000 | + | 5.19615i | 0.127228 | + | 0.220366i | ||||
\(557\) | 1.00000 | − | 1.73205i | 0.0423714 | − | 0.0733893i | −0.844062 | − | 0.536246i | \(-0.819842\pi\) |
0.886433 | + | 0.462856i | \(0.153175\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.00000 | 0.211477 | ||||||||
\(560\) | 4.00000 | + | 20.7846i | 0.169031 | + | 0.878310i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.00000 | − | 6.92820i | 0.168730 | − | 0.292249i | ||||
\(563\) | −26.0000 | −1.09577 | −0.547885 | − | 0.836554i | \(-0.684567\pi\) | ||||
−0.547885 | + | 0.836554i | \(0.684567\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.0000 | −0.841406 | ||||||||
\(566\) | −22.0000 | −0.924729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.0000 | −1.08998 | −0.544988 | − | 0.838444i | \(-0.683466\pi\) | ||||
−0.544988 | + | 0.838444i | \(0.683466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.0000 | −0.795125 | −0.397563 | − | 0.917575i | \(-0.630144\pi\) | ||||
−0.397563 | + | 0.917575i | \(0.630144\pi\) | |||||||
\(572\) | 2.00000 | − | 3.46410i | 0.0836242 | − | 0.144841i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 50.0000 | + | 17.3205i | 2.08696 | + | 0.722944i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.50000 | − | 14.7224i | 0.353860 | − | 0.612903i | −0.633062 | − | 0.774101i | \(-0.718202\pi\) |
0.986922 | + | 0.161198i | \(0.0515357\pi\) | |||||||
\(578\) | 17.0000 | + | 29.4449i | 0.707107 | + | 1.22474i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.00000 | + | 13.8564i | 0.332182 | + | 0.575356i | ||||
\(581\) | 3.00000 | + | 15.5885i | 0.124461 | + | 0.646718i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.0000 | −0.993978 | ||||||||
\(584\) | 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 | ||||
\(590\) | −24.0000 | + | 41.5692i | −0.988064 | + | 1.71138i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.00000 | + | 10.3923i | 0.246598 | + | 0.427121i | ||||
\(593\) | 3.00000 | + | 5.19615i | 0.123195 | + | 0.213380i | 0.921026 | − | 0.389501i | \(-0.127353\pi\) |
−0.797831 | + | 0.602881i | \(0.794019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.0000 | − | 20.7846i | 0.491539 | − | 0.851371i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 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 | ||||
\(605\) | −7.00000 | − | 12.1244i | −0.284590 | − | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.5000 | + | 19.9186i | −0.466771 | + | 0.808470i | −0.999279 | − | 0.0379540i | \(-0.987916\pi\) |
0.532509 | + | 0.846424i | \(0.321249\pi\) | |||||||
\(608\) | 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 | 0.286300 | + | 0.958140i | \(0.407575\pi\) |
−0.972924 | + | 0.231127i | \(0.925759\pi\) | |||||||
\(614\) | −34.0000 | −1.37213 | ||||||||
\(615\) | 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 | ||||||||
\(619\) | 14.5000 | + | 25.1147i | 0.582804 | + | 1.00945i | 0.995145 | + | 0.0984169i | \(0.0313779\pi\) |
−0.412341 | + | 0.911030i | \(0.635289\pi\) | |||||||
\(620\) | 18.0000 | − | 31.1769i | 0.722897 | − | 1.25210i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.0000 | −0.481156 | ||||||||
\(623\) | −40.0000 | − | 13.8564i | −1.60257 | − | 0.555145i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | −2.00000 | −0.0799361 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.0000 | −1.11732 | ||||||||
\(629\) | 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 | ||||||||
\(634\) | 48.0000 | 1.90632 | ||||||||
\(635\) | −15.0000 | + | 25.9808i | −0.595257 | + | 1.03102i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.50000 | + | 2.59808i | −0.257539 | + | 0.102940i | ||||
\(638\) | −16.0000 | −0.633446 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 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 | −0.885013 | − | 0.465566i | \(-0.845851\pi\) |
0.845699 | + | 0.533660i | \(0.179184\pi\) | |||||||
\(648\) | 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 | ||||
\(653\) | −9.00000 | + | 15.5885i | −0.352197 | + | 0.610023i | −0.986634 | − | 0.162951i | \(-0.947899\pi\) |
0.634437 | + | 0.772975i | \(0.281232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.0000 | − | 24.2487i | −0.547025 | − | 0.947476i | ||||
\(656\) | −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 | ||||||||
\(661\) | −41.0000 | −1.59472 | −0.797358 | − | 0.603507i | \(-0.793769\pi\) | ||||
−0.797358 | + | 0.603507i | \(0.793769\pi\) | |||||||
\(662\) | −50.0000 | −1.94331 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.00000 | + | 3.46410i | −0.155113 | + | 0.134332i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 14.0000 | + | 24.2487i | 0.541676 | + | 0.938211i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.0000 | + | 17.3205i | −0.386334 | + | 0.669150i | ||||
\(671\) | 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 | ||||
\(677\) | 12.0000 | 0.461197 | 0.230599 | − | 0.973049i | \(-0.425932\pi\) | ||||
0.230599 | + | 0.973049i | \(0.425932\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.00000 | − | 15.5885i | −0.115129 | − | 0.598230i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 18.0000 | + | 31.1769i | 0.689256 | + | 1.19383i | ||||
\(683\) | 6.00000 | − | 10.3923i | 0.229584 | − | 0.397650i | −0.728101 | − | 0.685470i | \(-0.759597\pi\) |
0.957685 | + | 0.287819i | \(0.0929302\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.0000 | 0.916993 | ||||||||
\(686\) | −20.0000 | − | 31.1769i | −0.763604 | − | 1.19034i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.0000 | − | 17.3205i | 0.381246 | − | 0.660338i | ||||
\(689\) | 12.0000 | 0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.0000 | −1.40755 | −0.703773 | − | 0.710425i | \(-0.748503\pi\) | ||||
−0.703773 | + | 0.710425i | \(0.748503\pi\) | |||||||
\(692\) | 16.0000 | 0.608229 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 64.0000 | 2.42941 | ||||||||
\(695\) | 6.00000 | 0.227593 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 14.0000 | − | 24.2487i | 0.529908 | − | 0.917827i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.00000 | + | 1.73205i | 0.188982 | + | 0.0654654i | ||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.50000 | + | 2.59808i | −0.0565736 | + | 0.0979883i | ||||
\(704\) | −8.00000 | − | 13.8564i | −0.301511 | − | 0.522233i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −34.0000 | − | 58.8897i | −1.27961 | − | 2.21634i | ||||
\(707\) | −5.00000 | − | 1.73205i | −0.188044 | − | 0.0651405i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.0000 | 1.12667 | 0.563337 | − | 0.826227i | \(-0.309517\pi\) | ||||
0.563337 | + | 0.826227i | \(0.309517\pi\) | |||||||
\(710\) | −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 | ||||
\(716\) | −2.00000 | + | 3.46410i | −0.0747435 | + | 0.129460i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20.0000 | − | 34.6410i | −0.746393 | − | 1.29279i | ||||
\(719\) | 9.00000 | + | 15.5885i | 0.335643 | + | 0.581351i | 0.983608 | − | 0.180319i | \(-0.0577130\pi\) |
−0.647965 | + | 0.761670i | \(0.724380\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.50000 | − | 18.1865i | −0.130347 | − | 0.677302i | ||||
\(722\) | 18.0000 | − | 31.1769i | 0.669891 | − | 1.16028i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 26.0000 | 0.966282 | ||||||||
\(725\) | −4.00000 | −0.148556 | ||||||||
\(726\) | 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 | ||||||||
\(733\) | 7.50000 | − | 12.9904i | 0.277019 | − | 0.479811i | −0.693624 | − | 0.720338i | \(-0.743987\pi\) |
0.970642 | + | 0.240527i | \(0.0773202\pi\) | |||||||
\(734\) | 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 | −0.694468 | − | 0.719524i | \(-0.744360\pi\) |
0.970360 | + | 0.241665i | \(0.0776935\pi\) | |||||||
\(740\) | −12.0000 | −0.441129 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.0000 | + | 62.3538i | 0.440534 | + | 2.28908i | ||||
\(743\) | −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 | ||||||||
\(745\) | −12.0000 | − | 20.7846i | −0.439646 | − | 0.761489i | ||||
\(746\) | −23.0000 | + | 39.8372i | −0.842090 | + | 1.45854i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.0000 | + | 6.92820i | 0.730784 | + | 0.253151i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.50000 | + | 11.2583i | −0.237188 | + | 0.410822i | −0.959906 | − | 0.280321i | \(-0.909559\pi\) |
0.722718 | + | 0.691143i | \(0.242893\pi\) | |||||||
\(752\) | 24.0000 | 0.875190 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.00000 | 0.291343 | ||||||||
\(755\) | 32.0000 | 1.16460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 6.00000 | 0.217930 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.0000 | − | 41.5692i | 0.869999 | − | 1.50688i | 0.00800331 | − | 0.999968i | \(-0.497452\pi\) |
0.861996 | − | 0.506915i | \(-0.169214\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.50000 | + | 23.3827i | 0.162911 | + | 0.846510i | ||||
\(764\) | 20.0000 | 0.723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000 | − | 20.7846i | 0.433578 | − | 0.750978i | ||||
\(767\) | 6.00000 | + | 10.3923i | 0.216647 | + | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.5000 | + | 42.4352i | 0.883493 | + | 1.53025i | 0.847432 | + | 0.530904i | \(0.178148\pi\) |
0.0360609 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(770\) | 16.0000 | − | 13.8564i | 0.576600 | − | 0.499350i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.0000 | 0.791797 | ||||||||
\(773\) | 17.0000 | − | 29.4449i | 0.611448 | − | 1.05906i | −0.379549 | − | 0.925172i | \(-0.623921\pi\) |
0.990997 | − | 0.133887i | \(-0.0427458\pi\) | |||||||
\(774\) | 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 | ||||
\(779\) | 5.00000 | − | 8.66025i | 0.179144 | − | 0.310286i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.00000 | − | 10.3923i | −0.214697 | − | 0.371866i | ||||
\(782\) | 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 | ||||||||
\(787\) | 40.0000 | 1.42585 | 0.712923 | − | 0.701242i | \(-0.247371\pi\) | ||||
0.712923 | + | 0.701242i | \(0.247371\pi\) | |||||||
\(788\) | 32.0000 | 1.13995 | ||||||||
\(789\) | 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 | ||||
\(794\) | 9.00000 | + | 15.5885i | 0.319398 | + | 0.553214i | ||||
\(795\) | 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 | ||||
\(803\) | 6.00000 | 0.211735 | ||||||||
\(804\) | 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 | 0.472119 | + | 0.881535i | \(0.343489\pi\) |
−0.999491 | + | 0.0319002i | \(0.989844\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.0000 | 1.12367 | 0.561836 | − | 0.827249i | \(-0.310095\pi\) | ||||
0.561836 | + | 0.827249i | \(0.310095\pi\) | |||||||
\(812\) | 4.00000 | + | 20.7846i | 0.140372 | + | 0.729397i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.00000 | − | 10.3923i | 0.210300 | − | 0.364250i | ||||
\(815\) | −8.00000 | −0.280228 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.00000 | 0.174928 | ||||||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 40.0000 | 1.39686 | ||||||||
\(821\) | 2.00000 | 0.0698005 | 0.0349002 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0349002 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −48.0000 | + | 41.5692i | −1.67013 | + | 1.44638i | ||||
\(827\) | −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 | 0.252113 | + | 0.967698i | \(0.418875\pi\) |
−0.964107 | + | 0.265513i | \(0.914459\pi\) | |||||||
\(830\) | 12.0000 | + | 20.7846i | 0.416526 | + | 0.721444i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.00000 | + | 6.92820i | 0.138675 | + | 0.240192i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.0000 | 0.968980 | ||||||||
\(836\) | 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 | ||||
\(842\) | 7.00000 | − | 12.1244i | 0.241236 | − | 0.417833i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.00000 | − | 6.92820i | −0.137686 | − | 0.238479i | ||||
\(845\) | −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 | ||||||||
\(857\) | 16.0000 | + | 27.7128i | 0.546550 | + | 0.946652i | 0.998508 | + | 0.0546125i | \(0.0173923\pi\) |
−0.451958 | + | 0.892039i | \(0.649274\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | − | 34.6410i | 0.682391 | − | 1.18194i | −0.291858 | − | 0.956462i | \(-0.594273\pi\) |
0.974249 | − | 0.225475i | \(-0.0723932\pi\) | |||||||
\(860\) | 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 | 0.800799 | + | 0.598933i | \(0.204408\pi\) |
0.118291 | + | 0.992979i | \(0.462258\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.00000 | − | 13.8564i | 0.272008 | − | 0.471132i | ||||
\(866\) | 62.0000 | 2.10685 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 36.0000 | − | 31.1769i | 1.22192 | − | 1.05821i | ||||
\(869\) | −1.00000 | − | 1.73205i | −0.0339227 | − | 0.0587558i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.50000 | + | 4.33013i | 0.0847093 | + | 0.146721i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.0000 | − | 20.7846i | 0.811348 | − | 0.702648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.0000 | − | 32.9090i | 0.641584 | − | 1.11126i | −0.343495 | − | 0.939155i | \(-0.611611\pi\) |
0.985079 | − | 0.172102i | \(-0.0550559\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −16.0000 | −0.539360 | ||||||||
\(881\) | 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 | ||||||||
\(886\) | 24.0000 | 0.806296 | ||||||||
\(887\) | 17.0000 | − | 29.4449i | 0.570804 | − | 0.988662i | −0.425679 | − | 0.904874i | \(-0.639965\pi\) |
0.996484 | − | 0.0837878i | \(-0.0267018\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.0000 | + | 25.9808i | −1.00617 | + | 0.871367i | ||||
\(890\) | −64.0000 | −2.14528 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.0000 | + | 27.7128i | −0.535720 | + | 0.927894i | ||||
\(893\) | 3.00000 | + | 5.19615i | 0.100391 | + | 0.173883i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.00000 | + | 3.46410i | 0.0668526 | + | 0.115792i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −36.0000 | −1.20134 | ||||||||
\(899\) | −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 | ||||||||
\(905\) | 13.0000 | − | 22.5167i | 0.432135 | − | 0.748479i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5000 | + | 32.0429i | 0.614282 | + | 1.06397i | 0.990510 | + | 0.137441i | \(0.0438878\pi\) |
−0.376228 | + | 0.926527i | \(0.622779\pi\) | |||||||
\(908\) | −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 | ||||||||
\(913\) | −12.0000 | −0.397142 | ||||||||
\(914\) | −22.0000 | −0.727695 | ||||||||
\(915\) | 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 | 0.611618 | − | 0.791153i | \(-0.290519\pi\) |
−0.990968 | + | 0.134100i | \(0.957186\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.0000 | + | 34.6410i | −0.658665 | + | 1.14084i | ||||
\(923\) | 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 | ||||
\(929\) | 14.0000 | 0.459325 | 0.229663 | − | 0.973270i | \(-0.426238\pi\) | ||||
0.229663 | + | 0.973270i | \(0.426238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.50000 | + | 2.59808i | −0.213029 | + | 0.0851485i | ||||
\(932\) | −6.00000 | − | 10.3923i | −0.196537 | − | 0.340411i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.00000 | − | 10.3923i | −0.196326 | − | 0.340047i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.0000 | 0.490029 | 0.245014 | − | 0.969519i | \(-0.421207\pi\) | ||||
0.245014 | + | 0.969519i | \(0.421207\pi\) | |||||||
\(938\) | −20.0000 | + | 17.3205i | −0.653023 | + | 0.565535i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.0000 | + | 20.7846i | −0.391397 | + | 0.677919i | ||||
\(941\) | −4.00000 | −0.130396 | −0.0651981 | − | 0.997872i | \(-0.520768\pi\) | ||||
−0.0651981 | + | 0.997872i | \(0.520768\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 48.0000 | 1.56227 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.0000 | −0.650256 | ||||||||
\(947\) | −10.0000 | −0.324956 | −0.162478 | − | 0.986712i | \(-0.551949\pi\) | ||||
−0.162478 | + | 0.986712i | \(0.551949\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.00000 | −0.0973841 | ||||||||
\(950\) | 1.00000 | − | 1.73205i | 0.0324443 | − | 0.0561951i | ||||
\(951\) | 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 | ||||
\(956\) | −6.00000 | − | 10.3923i | −0.194054 | − | 0.336111i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.0000 | + | 48.4974i | 0.904639 | + | 1.56688i | ||||
\(959\) | 30.0000 | + | 10.3923i | 0.968751 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 50.0000 | 1.61290 | ||||||||
\(962\) | −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 | ||||||||
\(970\) | −12.0000 | − | 20.7846i | −0.385297 | − | 0.667354i | ||||
\(971\) | −18.0000 | − | 31.1769i | −0.577647 | − | 1.00051i | −0.995748 | − | 0.0921142i | \(-0.970638\pi\) |
0.418101 | − | 0.908401i | \(-0.362696\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.50000 | + | 2.59808i | 0.240439 | + | 0.0832905i | ||||
\(974\) | −31.0000 | + | 53.6936i | −0.993304 | + | 1.72045i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −40.0000 | −1.28037 | ||||||||
\(977\) | −18.0000 | −0.575871 | −0.287936 | − | 0.957650i | \(-0.592969\pi\) | ||||
−0.287936 | + | 0.957650i | \(0.592969\pi\) | |||||||
\(978\) | 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 | ||||
\(983\) | −18.0000 | − | 31.1769i | −0.574111 | − | 0.994389i | −0.996138 | − | 0.0878058i | \(-0.972015\pi\) |
0.422027 | − | 0.906583i | \(-0.361319\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0000 | − | 27.7128i | 0.509802 | − | 0.883004i | ||||
\(986\) | 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 | −0.968864 | − | 0.247592i | \(-0.920361\pi\) |
0.698853 | + | 0.715265i | \(0.253694\pi\) | |||||||
\(992\) | −72.0000 | −2.28600 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −24.0000 | + | 20.7846i | −0.761234 | + | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.50000 | − | 16.4545i | −0.300868 | − | 0.521119i | 0.675465 | − | 0.737392i | \(-0.263943\pi\) |
−0.976333 | + | 0.216274i | \(0.930610\pi\) | |||||||
\(998\) | −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 \(a_p\))