Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3240,2,Mod(1081,3240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3240, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3240.1081");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3240.q (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: | \(25.8715302549\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1081.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3240.1081 |
Dual form | 3240.2.q.x.2161.1 |
$q$-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 \(\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times\).
\(n\) | \(1297\) | \(1621\) | \(2431\) | \(3161\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 3.46410i | 0.755929 | + | 1.30931i | 0.944911 | + | 0.327327i | \(0.106148\pi\) |
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | + | 3.46410i | 0.603023 | + | 1.04447i | 0.992361 | + | 0.123371i | \(0.0393705\pi\) |
−0.389338 | + | 0.921095i | \(0.627296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | − | 1.73205i | 0.277350 | − | 0.480384i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | − | 3.46410i | 0.417029 | − | 0.722315i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.995639 | + | 0.0932891i | \(0.0297381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | − | 1.73205i | −0.185695 | − | 0.321634i | 0.758115 | − | 0.652121i | \(-0.226120\pi\) |
−0.943811 | + | 0.330487i | \(0.892787\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | − | 6.92820i | 0.718421 | − | 1.24434i | −0.243204 | − | 0.969975i | \(-0.578198\pi\) |
0.961625 | − | 0.274367i | \(-0.0884683\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.00000 | 0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | + | 5.19615i | −0.468521 | + | 0.811503i | −0.999353 | − | 0.0359748i | \(-0.988546\pi\) |
0.530831 | + | 0.847477i | \(0.321880\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | + | 6.92820i | 0.609994 | + | 1.05654i | 0.991241 | + | 0.132068i | \(0.0421616\pi\) |
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.00000 | + | 3.46410i | 0.291730 | + | 0.505291i | 0.974219 | − | 0.225605i | \(-0.0724358\pi\) |
−0.682489 | + | 0.730896i | \(0.739102\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.50000 | + | 7.79423i | −0.642857 | + | 1.11346i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | + | 1.73205i | 0.128037 | + | 0.221766i | 0.922916 | − | 0.385002i | \(-0.125799\pi\) |
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | − | 1.73205i | −0.124035 | − | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | + | 6.92820i | −0.488678 | + | 0.846415i | −0.999915 | − | 0.0130248i | \(-0.995854\pi\) |
0.511237 | + | 0.859440i | \(0.329187\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.00000 | + | 13.8564i | −0.911685 | + | 1.57908i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.00000 | − | 13.8564i | −0.878114 | − | 1.52094i | −0.853408 | − | 0.521243i | \(-0.825468\pi\) |
−0.0247060 | − | 0.999695i | \(-0.507865\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | + | 1.73205i | −0.108465 | + | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000 | 0.838628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | − | 3.46410i | 0.205196 | − | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000 | + | 12.1244i | 0.710742 | + | 1.23104i | 0.964579 | + | 0.263795i | \(0.0849741\pi\) |
−0.253837 | + | 0.967247i | \(0.581693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | + | 5.19615i | 0.298511 | + | 0.517036i | 0.975796 | − | 0.218685i | \(-0.0701767\pi\) |
−0.677284 | + | 0.735721i | \(0.736843\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00000 | + | 3.46410i | −0.197066 | + | 0.341328i | −0.947576 | − | 0.319531i | \(-0.896475\pi\) |
0.750510 | + | 0.660859i | \(0.229808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.00000 | − | 15.5885i | 0.846649 | − | 1.46644i | −0.0375328 | − | 0.999295i | \(-0.511950\pi\) |
0.884182 | − | 0.467143i | \(-0.154717\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.00000 | − | 3.46410i | −0.186501 | − | 0.323029i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.00000 | − | 6.92820i | −0.366679 | − | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | − | 10.3923i | 0.524222 | − | 0.907980i | −0.475380 | − | 0.879781i | \(-0.657689\pi\) |
0.999602 | − | 0.0281993i | \(-0.00897729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000 | + | 13.8564i | 0.693688 | + | 1.20150i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.00000 | + | 8.66025i | 0.427179 | + | 0.739895i | 0.996621 | − | 0.0821359i | \(-0.0261741\pi\) |
−0.569442 | + | 0.822031i | \(0.692841\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00000 | + | 10.3923i | −0.508913 | + | 0.881464i | 0.491033 | + | 0.871141i | \(0.336619\pi\) |
−0.999947 | + | 0.0103230i | \(0.996714\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.00000 | 0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.00000 | + | 8.66025i | −0.409616 | + | 0.709476i | −0.994847 | − | 0.101391i | \(-0.967671\pi\) |
0.585231 | + | 0.810867i | \(0.301004\pi\) | |||||||
\(150\) | 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 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | − | 6.92820i | −0.321288 | − | 0.556487i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.00000 | − | 1.73205i | 0.0798087 | − | 0.138233i | −0.823359 | − | 0.567521i | \(-0.807902\pi\) |
0.903167 | + | 0.429289i | \(0.141236\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.0000 | 1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0000 | 1.25322 | 0.626608 | − | 0.779334i | \(-0.284443\pi\) | ||||
0.626608 | + | 0.779334i | \(0.284443\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | − | 10.3923i | 0.464294 | − | 0.804181i | −0.534875 | − | 0.844931i | \(-0.679641\pi\) |
0.999169 | + | 0.0407502i | \(0.0129748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.00000 | + | 12.1244i | 0.532200 | + | 0.921798i | 0.999293 | + | 0.0375896i | \(0.0119679\pi\) |
−0.467093 | + | 0.884208i | \(0.654699\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | − | 3.46410i | 0.151186 | − | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.0000 | −1.49487 | −0.747435 | − | 0.664335i | \(-0.768715\pi\) | ||||
−0.747435 | + | 0.664335i | \(0.768715\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | − | 5.19615i | 0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | − | 6.92820i | −0.292509 | − | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.00000 | + | 6.92820i | 0.289430 | + | 0.501307i | 0.973674 | − | 0.227946i | \(-0.0732010\pi\) |
−0.684244 | + | 0.729253i | \(0.739868\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.00000 | − | 12.1244i | 0.503871 | − | 0.872730i | −0.496119 | − | 0.868255i | \(-0.665242\pi\) |
0.999990 | − | 0.00447566i | \(-0.00142465\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.0000 | −1.56744 | −0.783718 | − | 0.621117i | \(-0.786679\pi\) | ||||
−0.783718 | + | 0.621117i | \(0.786679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.00000 | − | 6.92820i | 0.280745 | − | 0.486265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | + | 5.19615i | 0.209529 | + | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | + | 13.8564i | 0.553372 | + | 0.958468i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | − | 3.46410i | 0.137686 | − | 0.238479i | −0.788935 | − | 0.614477i | \(-0.789367\pi\) |
0.926620 | + | 0.375999i | \(0.122700\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 32.0000 | 2.17230 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.00000 | + | 3.46410i | −0.134535 | + | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.00000 | + | 3.46410i | 0.133930 | + | 0.231973i | 0.925188 | − | 0.379509i | \(-0.123907\pi\) |
−0.791258 | + | 0.611482i | \(0.790574\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.0000 | − | 20.7846i | −0.796468 | − | 1.37952i | −0.921903 | − | 0.387421i | \(-0.873366\pi\) |
0.125435 | − | 0.992102i | \(-0.459967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0000 | − | 22.5167i | 0.859064 | − | 1.48794i | −0.0137585 | − | 0.999905i | \(-0.504380\pi\) |
0.872823 | − | 0.488037i | \(-0.162287\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | 0.260931 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | − | 1.73205i | −0.0644157 | − | 0.111571i | 0.832019 | − | 0.554747i | \(-0.187185\pi\) |
−0.896435 | + | 0.443176i | \(0.853852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.50000 | + | 7.79423i | 0.287494 | + | 0.497955i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | − | 6.92820i | 0.254514 | − | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | 1.00591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.0000 | + | 25.9808i | −0.935674 | + | 1.62064i | −0.162247 | + | 0.986750i | \(0.551874\pi\) |
−0.773427 | + | 0.633885i | \(0.781459\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.0000 | + | 20.7846i | 0.745644 | + | 1.29149i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.00000 | − | 10.3923i | −0.369976 | − | 0.640817i | 0.619586 | − | 0.784929i | \(-0.287301\pi\) |
−0.989561 | + | 0.144112i | \(0.953967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.00000 | + | 5.19615i | −0.184289 | + | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.0000 | −0.853595 | −0.426798 | − | 0.904347i | \(-0.640358\pi\) | ||||
−0.426798 | + | 0.904347i | \(0.640358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.0000 | 1.45790 | 0.728948 | − | 0.684569i | \(-0.240010\pi\) | ||||
0.728948 | + | 0.684569i | \(0.240010\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000 | − | 3.46410i | 0.120605 | − | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | + | 8.66025i | 0.300421 | + | 0.520344i | 0.976231 | − | 0.216731i | \(-0.0695395\pi\) |
−0.675810 | + | 0.737075i | \(0.736206\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.00000 | + | 8.66025i | 0.298275 | + | 0.516627i | 0.975741 | − | 0.218926i | \(-0.0702554\pi\) |
−0.677466 | + | 0.735554i | \(0.736922\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | + | 6.92820i | −0.237775 | + | 0.411839i | −0.960076 | − | 0.279741i | \(-0.909752\pi\) |
0.722300 | + | 0.691580i | \(0.243085\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.0000 | −1.41668 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.0000 | + | 22.5167i | −0.759468 | + | 1.31544i | 0.183654 | + | 0.982991i | \(0.441207\pi\) |
−0.943122 | + | 0.332446i | \(0.892126\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.00000 | + | 3.46410i | 0.116445 | + | 0.201688i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.00000 | − | 6.92820i | −0.231326 | − | 0.400668i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | + | 27.7128i | −0.922225 | + | 1.59734i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.00000 | −0.456584 | −0.228292 | − | 0.973593i | \(-0.573314\pi\) | ||||
−0.228292 | + | 0.973593i | \(0.573314\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.0000 | − | 27.7128i | 0.907277 | − | 1.57145i | 0.0894452 | − | 0.995992i | \(-0.471491\pi\) |
0.817832 | − | 0.575458i | \(-0.195176\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.0000 | − | 22.5167i | −0.734803 | − | 1.27272i | −0.954810 | − | 0.297218i | \(-0.903941\pi\) |
0.220006 | − | 0.975499i | \(-0.429392\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.00000 | − | 15.5885i | −0.505490 | − | 0.875535i | −0.999980 | − | 0.00635137i | \(-0.997978\pi\) |
0.494489 | − | 0.869184i | \(-0.335355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | − | 6.92820i | 0.223957 | − | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.00000 | + | 13.8564i | −0.441054 | + | 0.763928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.00000 | + | 10.3923i | 0.329790 | + | 0.571213i | 0.982470 | − | 0.186421i | \(-0.0596888\pi\) |
−0.652680 | + | 0.757634i | \(0.726355\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.00000 | + | 6.92820i | 0.218543 | + | 0.378528i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.00000 | − | 12.1244i | 0.381314 | − | 0.660456i | −0.609936 | − | 0.792451i | \(-0.708805\pi\) |
0.991250 | + | 0.131995i | \(0.0421382\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.0000 | 1.73290 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.00000 | + | 13.8564i | −0.429463 | + | 0.743851i | −0.996826 | − | 0.0796169i | \(-0.974630\pi\) |
0.567363 | + | 0.823468i | \(0.307964\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.0000 | − | 25.9808i | −0.802932 | − | 1.39072i | −0.917679 | − | 0.397324i | \(-0.869939\pi\) |
0.114747 | − | 0.993395i | \(-0.463394\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.00000 | + | 1.73205i | 0.0532246 | + | 0.0921878i | 0.891410 | − | 0.453197i | \(-0.149717\pi\) |
−0.838186 | + | 0.545385i | \(0.816383\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.00000 | + | 5.19615i | −0.157027 | + | 0.271979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0000 | − | 17.3205i | −0.521996 | − | 0.904123i | −0.999673 | − | 0.0255875i | \(-0.991854\pi\) |
0.477677 | − | 0.878536i | \(-0.341479\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | − | 20.7846i | −0.623009 | − | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0000 | + | 19.0526i | −0.569558 | + | 0.986504i | 0.427051 | + | 0.904227i | \(0.359552\pi\) |
−0.996610 | + | 0.0822766i | \(0.973781\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.00000 | −0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.0000 | + | 31.1769i | −0.919757 | + | 1.59307i | −0.119974 | + | 0.992777i | \(0.538281\pi\) |
−0.799783 | + | 0.600289i | \(0.795052\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.00000 | + | 13.8564i | 0.407718 | + | 0.706188i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 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 | ||||||||
\(391\) | −4.00000 | + | 6.92820i | −0.202289 | + | 0.350374i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.00000 | −0.100377 | −0.0501886 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.00000 | − | 15.5885i | 0.449439 | − | 0.778450i | −0.548911 | − | 0.835881i | \(-0.684957\pi\) |
0.998350 | + | 0.0574304i | \(0.0182907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | − | 13.8564i | −0.398508 | − | 0.690237i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000 | + | 20.7846i | 0.594818 | + | 1.03025i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.00000 | + | 8.66025i | −0.247234 | + | 0.428222i | −0.962757 | − | 0.270367i | \(-0.912855\pi\) |
0.715523 | + | 0.698589i | \(0.246188\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.0000 | −0.787309 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.0000 | −0.785409 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0000 | − | 31.1769i | 0.879358 | − | 1.52309i | 0.0273103 | − | 0.999627i | \(-0.491306\pi\) |
0.852047 | − | 0.523465i | \(-0.175361\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.00000 | − | 5.19615i | −0.146211 | − | 0.253245i | 0.783613 | − | 0.621249i | \(-0.213375\pi\) |
−0.929824 | + | 0.368004i | \(0.880041\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00000 | + | 1.73205i | 0.0485071 | + | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.00000 | + | 6.92820i | −0.193574 | + | 0.335279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 40.0000 | 1.92673 | 0.963366 | − | 0.268190i | \(-0.0864254\pi\) | ||||
0.963366 | + | 0.268190i | \(0.0864254\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.00000 | − | 13.8564i | 0.382692 | − | 0.662842i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | + | 6.92820i | 0.190910 | + | 0.330665i | 0.945552 | − | 0.325471i | \(-0.105523\pi\) |
−0.754642 | + | 0.656136i | \(0.772190\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0000 | + | 20.7846i | 0.570137 | + | 0.987507i | 0.996551 | + | 0.0829786i | \(0.0264433\pi\) |
−0.426414 | + | 0.904528i | \(0.640223\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.00000 | − | 5.19615i | 0.142214 | − | 0.246321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.0000 | −1.13012 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.00000 | − | 6.92820i | 0.187523 | − | 0.324799i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.00000 | − | 8.66025i | −0.233890 | − | 0.405110i | 0.725059 | − | 0.688686i | \(-0.241812\pi\) |
−0.958950 | + | 0.283577i | \(0.908479\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.00000 | − | 15.5885i | −0.419172 | − | 0.726027i | 0.576685 | − | 0.816967i | \(-0.304346\pi\) |
−0.995856 | + | 0.0909401i | \(0.971013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.00000 | + | 10.3923i | −0.278844 | + | 0.482971i | −0.971098 | − | 0.238683i | \(-0.923284\pi\) |
0.692254 | + | 0.721654i | \(0.256618\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.00000 | −0.370196 | −0.185098 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185098 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.0000 | −1.47762 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.0000 | + | 27.7128i | −0.735681 | + | 1.27424i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.00000 | − | 3.46410i | −0.0917663 | − | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.00000 | + | 13.8564i | 0.365529 | + | 0.633115i | 0.988861 | − | 0.148842i | \(-0.0475547\pi\) |
−0.623332 | + | 0.781958i | \(0.714221\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.00000 | − | 10.3923i | 0.273576 | − | 0.473848i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.0000 | 0.635707 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.0000 | −0.906287 | −0.453143 | − | 0.891438i | \(-0.649697\pi\) | ||||
−0.453143 | + | 0.891438i | \(0.649697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.0000 | − | 31.1769i | 0.812329 | − | 1.40699i | −0.0989017 | − | 0.995097i | \(-0.531533\pi\) |
0.911230 | − | 0.411897i | \(-0.135134\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.00000 | + | 3.46410i | 0.0900755 | + | 0.156015i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0000 | − | 24.2487i | 0.626726 | − | 1.08552i | −0.361478 | − | 0.932381i | \(-0.617728\pi\) |
0.988204 | − | 0.153141i | \(-0.0489388\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −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 | ||||||||
\(511\) | −12.0000 | − | 20.7846i | −0.530849 | − | 0.919457i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.00000 | + | 3.46410i | 0.0881305 | + | 0.152647i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.00000 | + | 13.8564i | −0.351840 | + | 0.609404i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0000 | −0.438108 | −0.219054 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219054 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.00000 | −0.349816 | −0.174908 | − | 0.984585i | \(-0.555963\pi\) | ||||
−0.174908 | + | 0.984585i | \(0.555963\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.00000 | + | 13.8564i | −0.348485 | + | 0.603595i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000 | + | 10.3923i | 0.259889 | + | 0.450141i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −36.0000 | −1.55063 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.00000 | − | 12.1244i | 0.299847 | − | 0.519350i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.00000 | − | 6.92820i | −0.171028 | − | 0.296229i | 0.767752 | − | 0.640747i | \(-0.221375\pi\) |
−0.938779 | + | 0.344519i | \(0.888042\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.00000 | − | 6.92820i | −0.170406 | − | 0.295151i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.0000 | −0.593199 | −0.296600 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296600 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.00000 | − | 13.8564i | 0.337160 | − | 0.583978i | −0.646737 | − | 0.762713i | \(-0.723867\pi\) |
0.983897 | + | 0.178735i | \(0.0572004\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.00000 | − | 15.5885i | −0.378633 | − | 0.655811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.0000 | − | 19.0526i | −0.461144 | − | 0.798725i | 0.537874 | − | 0.843025i | \(-0.319228\pi\) |
−0.999018 | + | 0.0443003i | \(0.985894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.00000 | + | 3.46410i | −0.0836974 | + | 0.144968i | −0.904835 | − | 0.425762i | \(-0.860006\pi\) |
0.821138 | + | 0.570730i | \(0.193340\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 32.0000 | − | 55.4256i | 1.32758 | − | 2.29944i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | − | 20.7846i | −0.496989 | − | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.0000 | − | 41.5692i | −0.990586 | − | 1.71575i | −0.613845 | − | 0.789427i | \(-0.710378\pi\) |
−0.376741 | − | 0.926319i | \(-0.622955\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | − | 27.7128i | 0.659269 | − | 1.14189i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.0000 | −0.739171 | −0.369586 | − | 0.929197i | \(-0.620500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.00000 | −0.327968 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.0000 | + | 20.7846i | −0.490307 | + | 0.849236i | −0.999938 | − | 0.0111569i | \(-0.996449\pi\) |
0.509631 | + | 0.860393i | \(0.329782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.00000 | − | 8.66025i | −0.203954 | − | 0.353259i | 0.745845 | − | 0.666120i | \(-0.232046\pi\) |
−0.949799 | + | 0.312861i | \(0.898713\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.50000 | + | 4.33013i | 0.101639 | + | 0.176045i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.00000 | − | 10.3923i | 0.243532 | − | 0.421811i | −0.718186 | − | 0.695852i | \(-0.755027\pi\) |
0.961718 | + | 0.274041i | \(0.0883604\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.0000 | −1.69636 | −0.848182 | − | 0.529705i | \(-0.822303\pi\) | ||||
−0.848182 | + | 0.529705i | \(0.822303\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.00000 | + | 5.19615i | −0.120775 | + | 0.209189i | −0.920074 | − | 0.391745i | \(-0.871871\pi\) |
0.799298 | + | 0.600935i | \(0.205205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.00000 | + | 3.46410i | 0.0803868 | + | 0.139234i | 0.903416 | − | 0.428765i | \(-0.141051\pi\) |
−0.823029 | + | 0.567999i | \(0.807718\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0000 | + | 20.7846i | 0.480770 | + | 0.832718i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.00000 | + | 10.3923i | −0.238103 | + | 0.412406i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.00000 | + | 15.5885i | 0.356593 | + | 0.617637i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.00000 | + | 15.5885i | 0.355479 | + | 0.615707i | 0.987200 | − | 0.159489i | \(-0.0509845\pi\) |
−0.631721 | + | 0.775196i | \(0.717651\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.0000 | − | 41.5692i | 0.946468 | − | 1.63933i | 0.193682 | − | 0.981064i | \(-0.437957\pi\) |
0.752786 | − | 0.658266i | \(-0.228710\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.0000 | −0.628055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.0000 | + | 29.4449i | −0.665261 | + | 1.15227i | 0.313953 | + | 0.949439i | \(0.398347\pi\) |
−0.979214 | + | 0.202828i | \(0.934987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.00000 | − | 10.3923i | −0.234439 | − | 0.406061i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.00000 | − | 10.3923i | −0.233727 | − | 0.404827i | 0.725175 | − | 0.688565i | \(-0.241759\pi\) |
−0.958902 | + | 0.283738i | \(0.908425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.0000 | − | 36.3731i | 0.816805 | − | 1.41475i | −0.0912190 | − | 0.995831i | \(-0.529076\pi\) |
0.908024 | − | 0.418917i | \(-0.137590\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.0000 | 0.620453 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.00000 | −0.309761 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.00000 | + | 6.92820i | −0.154418 | + | 0.267460i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.00000 | − | 15.5885i | −0.346925 | − | 0.600891i | 0.638777 | − | 0.769392i | \(-0.279441\pi\) |
−0.985701 | + | 0.168501i | \(0.946107\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.0000 | + | 19.0526i | 0.422764 | + | 0.732249i | 0.996209 | − | 0.0869952i | \(-0.0277265\pi\) |
−0.573444 | + | 0.819244i | \(0.694393\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.0000 | + | 48.4974i | −1.07454 | + | 1.86116i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0000 | −0.918334 | −0.459167 | − | 0.888350i | \(-0.651852\pi\) | ||||
−0.459167 | + | 0.888350i | \(0.651852\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.0000 | 0.382080 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.00000 | + | 10.3923i | −0.228582 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.0000 | − | 38.1051i | −0.836919 | − | 1.44959i | −0.892458 | − | 0.451130i | \(-0.851021\pi\) |
0.0555386 | − | 0.998457i | \(-0.482312\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.00000 | + | 10.3923i | 0.227593 | + | 0.394203i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.00000 | − | 10.3923i | 0.227266 | − | 0.393637i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.0000 | 1.28416 | 0.642081 | − | 0.766637i | \(-0.278071\pi\) | ||||
0.642081 | + | 0.766637i | \(0.278071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000 | 0.905177 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.0000 | + | 20.7846i | −0.451306 | + | 0.781686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.0000 | − | 32.9090i | −0.713560 | − | 1.23592i | −0.963512 | − | 0.267664i | \(-0.913748\pi\) |
0.249952 | − | 0.968258i | \(-0.419585\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.0000 | − | 27.7128i | −0.599205 | − | 1.03785i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | − | 6.92820i | 0.149592 | − | 0.259100i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.0000 | 1.19340 | 0.596699 | − | 0.802465i | \(-0.296479\pi\) | ||||
0.596699 | + | 0.802465i | \(0.296479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0000 | −0.595871 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.00000 | + | 1.73205i | −0.0371391 | + | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.0000 | − | 38.1051i | −0.815935 | − | 1.41324i | −0.908655 | − | 0.417548i | \(-0.862889\pi\) |
0.0927199 | − | 0.995692i | \(-0.470444\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | − | 13.8564i | −0.295891 | − | 0.512498i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.0000 | + | 25.9808i | −0.554038 | + | 0.959621i | 0.443940 | + | 0.896056i | \(0.353580\pi\) |
−0.997978 | + | 0.0635649i | \(0.979753\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32.0000 | −1.17874 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.0000 | 1.32428 | 0.662141 | − | 0.749380i | \(-0.269648\pi\) | ||||
0.662141 | + | 0.749380i | \(0.269648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.0000 | − | 31.1769i | 0.660356 | − | 1.14377i | −0.320166 | − | 0.947361i | \(-0.603739\pi\) |
0.980522 | − | 0.196409i | \(-0.0629279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.00000 | + | 8.66025i | 0.183186 | + | 0.317287i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0000 | − | 20.7846i | 0.437886 | − | 0.758441i | −0.559640 | − | 0.828736i | \(-0.689061\pi\) |
0.997526 | + | 0.0702946i | \(0.0223939\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.00000 | + | 5.19615i | −0.108750 | + | 0.188360i | −0.915264 | − | 0.402854i | \(-0.868018\pi\) |
0.806514 | + | 0.591215i | \(0.201351\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.0000 | + | 48.4974i | 1.01367 | + | 1.75572i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.00000 | + | 6.92820i | 0.144432 | + | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.0000 | + | 29.4449i | −0.613036 | + | 1.06181i | 0.377690 | + | 0.925932i | \(0.376718\pi\) |
−0.990726 | + | 0.135877i | \(0.956615\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.0000 | 1.51064 | 0.755318 | − | 0.655359i | \(-0.227483\pi\) | ||||
0.755318 | + | 0.655359i | \(0.227483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.00000 | −0.287368 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.0000 | + | 20.7846i | −0.429945 | + | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.00000 | − | 1.73205i | −0.0356915 | − | 0.0618195i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.00000 | + | 6.92820i | −0.142585 | + | 0.246964i | −0.928469 | − | 0.371409i | \(-0.878875\pi\) |
0.785885 | + | 0.618373i | \(0.212208\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 72.0000 | 2.56003 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.00000 | 0.142044 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.00000 | + | 15.5885i | −0.318796 | + | 0.552171i | −0.980237 | − | 0.197826i | \(-0.936612\pi\) |
0.661441 | + | 0.749997i | \(0.269945\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.00000 | − | 6.92820i | −0.141510 | − | 0.245102i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.0000 | − | 20.7846i | −0.423471 | − | 0.733473i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.00000 | − | 13.8564i | 0.281963 | − | 0.488374i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.0000 | −1.47664 | −0.738321 | − | 0.674450i | \(-0.764381\pi\) | ||||
−0.738321 | + | 0.674450i | \(0.764381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.00000 | − | 13.8564i | 0.280228 | − | 0.485369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000 | + | 27.7128i | 0.559769 | + | 0.969549i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.0000 | + | 19.0526i | 0.383903 | + | 0.664939i | 0.991616 | − | 0.129217i | \(-0.0412465\pi\) |
−0.607714 | + | 0.794156i | \(0.707913\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.00000 | + | 3.46410i | −0.0697156 | + | 0.120751i | −0.898776 | − | 0.438408i | \(-0.855543\pi\) |
0.829060 | + | 0.559159i | \(0.188876\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.0000 | −1.66912 | −0.834562 | − | 0.550914i | \(-0.814279\pi\) | ||||
−0.834562 | + | 0.550914i | \(0.814279\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.00000 | −0.0694629 | −0.0347314 | − | 0.999397i | \(-0.511058\pi\) | ||||
−0.0347314 | + | 0.999397i | \(0.511058\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.00000 | − | 15.5885i | 0.311832 | − | 0.540108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.00000 | − | 10.3923i | −0.207639 | − | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.0000 | − | 34.6410i | −0.690477 | − | 1.19594i | −0.971682 | − | 0.236293i | \(-0.924067\pi\) |
0.281205 | − | 0.959648i | \(-0.409266\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.00000 | 0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.0000 | −0.687208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0000 | − | 20.7846i | 0.411355 | − | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.0000 | − | 32.9090i | −0.650548 | − | 1.12678i | −0.982990 | − | 0.183658i | \(-0.941206\pi\) |
0.332443 | − | 0.943123i | \(-0.392127\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.00000 | − | 5.19615i | −0.102478 | − | 0.177497i | 0.810227 | − | 0.586116i | \(-0.199344\pi\) |
−0.912705 | + | 0.408619i | \(0.866010\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000 | − | 3.46410i | 0.0682391 | − | 0.118194i | −0.829887 | − | 0.557931i | \(-0.811595\pi\) |
0.898126 | + | 0.439738i | \(0.144929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.0000 | −0.408485 | −0.204242 | − | 0.978920i | \(-0.565473\pi\) | ||||
−0.204242 | + | 0.978920i | \(0.565473\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.0000 | 0.476014 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.00000 | + | 13.8564i | 0.271070 | + | 0.469506i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.00000 | − | 3.46410i | −0.0676123 | − | 0.117108i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.0000 | + | 39.8372i | −0.776655 | + | 1.34521i | 0.157205 | + | 0.987566i | \(0.449752\pi\) |
−0.933860 | + | 0.357640i | \(0.883582\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.0000 | −0.538443 | −0.269221 | − | 0.963078i | \(-0.586766\pi\) | ||||
−0.269221 | + | 0.963078i | \(0.586766\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.0000 | + | 17.3205i | −0.335767 | + | 0.581566i | −0.983632 | − | 0.180190i | \(-0.942329\pi\) |
0.647865 | + | 0.761755i | \(0.275662\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.0000 | − | 41.5692i | −0.804934 | − | 1.39419i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.00000 | + | 13.8564i | 0.267710 | + | 0.463687i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.0000 | + | 17.3205i | −0.334263 | + | 0.578961i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.0000 | −0.533630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.00000 | + | 8.66025i | −0.166206 | + | 0.287877i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.0000 | − | 41.5692i | −0.796907 | − | 1.38028i | −0.921621 | − | 0.388091i | \(-0.873135\pi\) |
0.124714 | − | 0.992193i | \(-0.460199\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.0000 | + | 34.6410i | 0.662630 | + | 1.14771i | 0.979922 | + | 0.199380i | \(0.0638929\pi\) |
−0.317293 | + | 0.948328i | \(0.602774\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.0000 | − | 55.4256i | 1.05905 | − | 1.83432i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 48.0000 | 1.58510 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.00000 | 0.263896 | 0.131948 | − | 0.991257i | \(-0.457877\pi\) | ||||
0.131948 | + | 0.991257i | \(0.457877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.00000 | − | 5.19615i | −0.0986394 | − | 0.170848i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −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 | ||||||||
\(931\) | −18.0000 | + | 31.1769i | −0.589926 | + | 1.02178i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.00000 | −0.261628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.0000 | −1.24141 | −0.620703 | − | 0.784046i | \(-0.713153\pi\) | ||||
−0.620703 | + | 0.784046i | \(0.713153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.0000 | − | 39.8372i | 0.749779 | − | 1.29865i | −0.198150 | − | 0.980172i | \(-0.563493\pi\) |
0.947929 | − | 0.318483i | \(-0.103173\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.0000 | + | 20.7846i | 0.390774 | + | 0.676840i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.00000 | − | 6.92820i | −0.129983 | − | 0.225136i | 0.793687 | − | 0.608326i | \(-0.208159\pi\) |
−0.923670 | + | 0.383190i | \(0.874825\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | + | 10.3923i | −0.194768 | + | 0.337348i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000 | 0.258874 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.0000 | + | 34.6410i | −0.645834 | + | 1.11862i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.00000 | − | 12.1244i | −0.225338 | − | 0.390297i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.0000 | − | 31.1769i | 0.578841 | − | 1.00258i | −0.416772 | − | 0.909011i | \(-0.636839\pi\) |
0.995613 | − | 0.0935708i | \(-0.0298281\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.0000 | −0.641831 | −0.320915 | − | 0.947108i | \(-0.603990\pi\) | ||||
−0.320915 | + | 0.947108i | \(0.603990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −48.0000 | −1.53881 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.00000 | − | 1.73205i | 0.0319928 | − | 0.0554132i | −0.849586 | − | 0.527451i | \(-0.823148\pi\) |
0.881579 | + | 0.472037i | \(0.156481\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000 | + | 20.7846i | 0.383522 | + | 0.664279i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.0000 | + | 31.1769i | 0.574111 | + | 0.994389i | 0.996138 | + | 0.0878058i | \(0.0279855\pi\) |
−0.422027 | + | 0.906583i | \(0.638681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.0000 | + | 19.0526i | −0.350489 | + | 0.607065i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.0000 | 1.01754 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.0000 | −1.27064 | −0.635321 | − | 0.772248i | \(-0.719132\pi\) | ||||
−0.635321 | + | 0.772248i | \(0.719132\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.00000 | − | 6.92820i | 0.126809 | − | 0.219639i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.0000 | + | 36.3731i | 0.665077 | + | 1.15195i | 0.979265 | + | 0.202586i | \(0.0649345\pi\) |
−0.314188 | + | 0.949361i | \(0.601732\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))