Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2106,2,Mod(703,2106)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2106, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2106.703");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2106 = 2 \cdot 3^{4} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2106.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.8164946657\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 26) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 703.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2106.703 |
Dual form | 2106.2.e.b.1405.1 |
$q$-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 \(\left(\mathbb{Z}/2106\mathbb{Z}\right)^\times\).
\(n\) | \(1379\) | \(1783\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.50000 | − | 2.59808i | −0.670820 | − | 1.16190i | −0.977672 | − | 0.210138i | \(-0.932609\pi\) |
0.306851 | − | 0.951757i | \(-0.400725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | −0.755929 | − | 0.654654i | \(-0.772814\pi\) |
0.944911 | + | 0.327327i | \(0.106148\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.00000 | 0.948683 | ||||||||
\(11\) | 3.00000 | − | 5.19615i | 0.904534 | − | 1.56670i | 0.0829925 | − | 0.996550i | \(-0.473552\pi\) |
0.821541 | − | 0.570149i | \(-0.193114\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | ||||
\(14\) | 0.500000 | + | 0.866025i | 0.133631 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | −1.50000 | + | 2.59808i | −0.335410 | + | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000 | + | 5.19615i | 0.639602 | + | 1.10782i | ||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 3.00000 | − | 5.19615i | 0.557086 | − | 0.964901i | −0.440652 | − | 0.897678i | \(-0.645253\pi\) |
0.997738 | − | 0.0672232i | \(-0.0214140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | + | 3.46410i | 0.359211 | + | 0.622171i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.50000 | + | 2.59808i | −0.257248 | + | 0.445566i | ||||
\(35\) | −3.00000 | −0.507093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.00000 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(38\) | −1.00000 | + | 1.73205i | −0.162221 | + | 0.280976i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.50000 | − | 2.59808i | −0.237171 | − | 0.410792i | ||||
\(41\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.500000 | − | 0.866025i | 0.0762493 | − | 0.132068i | −0.825380 | − | 0.564578i | \(-0.809039\pi\) |
0.901629 | + | 0.432511i | \(0.142372\pi\) | |||||||
\(44\) | −6.00000 | −0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.50000 | − | 2.59808i | 0.218797 | − | 0.378968i | −0.735643 | − | 0.677369i | \(-0.763120\pi\) |
0.954441 | + | 0.298401i | \(0.0964533\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | + | 5.19615i | 0.428571 | + | 0.742307i | ||||
\(50\) | −2.00000 | − | 3.46410i | −0.282843 | − | 0.489898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.500000 | + | 0.866025i | −0.0693375 | + | 0.120096i | ||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.0000 | −2.42712 | ||||||||
\(56\) | 0.500000 | − | 0.866025i | 0.0668153 | − | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | + | 5.19615i | 0.393919 | + | 0.682288i | ||||
\(59\) | −3.00000 | − | 5.19615i | −0.390567 | − | 0.676481i | 0.601958 | − | 0.798528i | \(-0.294388\pi\) |
−0.992524 | + | 0.122047i | \(0.961054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | + | 6.92820i | −0.512148 | + | 0.887066i | 0.487753 | + | 0.872982i | \(0.337817\pi\) |
−0.999901 | + | 0.0140840i | \(0.995517\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.50000 | + | 2.59808i | −0.186052 | + | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | − | 12.1244i | −0.855186 | − | 1.48123i | −0.876472 | − | 0.481452i | \(-0.840109\pi\) |
0.0212861 | − | 0.999773i | \(-0.493224\pi\) | |||||||
\(68\) | −1.50000 | − | 2.59808i | −0.181902 | − | 0.315063i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.50000 | − | 2.59808i | 0.179284 | − | 0.310530i | ||||
\(71\) | 3.00000 | 0.356034 | 0.178017 | − | 0.984027i | \(-0.443032\pi\) | ||||
0.178017 | + | 0.984027i | \(0.443032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 3.50000 | − | 6.06218i | 0.406867 | − | 0.704714i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | − | 1.73205i | −0.114708 | − | 0.198680i | ||||
\(77\) | −3.00000 | − | 5.19615i | −0.341882 | − | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | + | 6.92820i | −0.450035 | + | 0.779484i | −0.998388 | − | 0.0567635i | \(-0.981922\pi\) |
0.548352 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | − | 10.3923i | 0.658586 | − | 1.14070i | −0.322396 | − | 0.946605i | \(-0.604488\pi\) |
0.980982 | − | 0.194099i | \(-0.0621783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.50000 | − | 7.79423i | −0.488094 | − | 0.845403i | ||||
\(86\) | 0.500000 | + | 0.866025i | 0.0539164 | + | 0.0933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.00000 | − | 5.19615i | 0.319801 | − | 0.553912i | ||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.50000 | + | 2.59808i | 0.154713 | + | 0.267971i | ||||
\(95\) | −3.00000 | − | 5.19615i | −0.307794 | − | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00000 | − | 8.66025i | 0.507673 | − | 0.879316i | −0.492287 | − | 0.870433i | \(-0.663839\pi\) |
0.999961 | − | 0.00888289i | \(-0.00282755\pi\) | |||||||
\(98\) | −6.00000 | −0.606092 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | −6.00000 | + | 10.3923i | −0.597022 | + | 1.03407i | 0.396236 | + | 0.918149i | \(0.370316\pi\) |
−0.993258 | + | 0.115924i | \(0.963017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | + | 3.46410i | 0.197066 | + | 0.341328i | 0.947576 | − | 0.319531i | \(-0.103525\pi\) |
−0.750510 | + | 0.660859i | \(0.770192\pi\) | |||||||
\(104\) | −0.500000 | − | 0.866025i | −0.0490290 | − | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | −0.670478 | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
−0.335239 | + | 0.942133i | \(0.608817\pi\) | |||||||
\(110\) | 9.00000 | − | 15.5885i | 0.858116 | − | 1.48630i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | + | 0.866025i | 0.0472456 | + | 0.0818317i | ||||
\(113\) | −3.00000 | − | 5.19615i | −0.282216 | − | 0.488813i | 0.689714 | − | 0.724082i | \(-0.257736\pi\) |
−0.971930 | + | 0.235269i | \(0.924403\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | 1.50000 | − | 2.59808i | 0.137505 | − | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | − | 21.6506i | −1.13636 | − | 1.96824i | ||||
\(122\) | −4.00000 | − | 6.92820i | −0.362143 | − | 0.627250i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.0000 | 1.77471 | 0.887357 | − | 0.461084i | \(-0.152539\pi\) | ||||
0.887357 | + | 0.461084i | \(0.152539\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.50000 | − | 2.59808i | −0.131559 | − | 0.227866i | ||||
\(131\) | −10.5000 | − | 18.1865i | −0.917389 | − | 1.58896i | −0.803365 | − | 0.595487i | \(-0.796959\pi\) |
−0.114024 | − | 0.993478i | \(-0.536374\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | − | 1.73205i | 0.0867110 | − | 0.150188i | ||||
\(134\) | 14.0000 | 1.20942 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | 0.257248 | ||||||||
\(137\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50000 | + | 11.2583i | 0.551323 | + | 0.954919i | 0.998179 | + | 0.0603135i | \(0.0192101\pi\) |
−0.446857 | + | 0.894606i | \(0.647457\pi\) | |||||||
\(140\) | 1.50000 | + | 2.59808i | 0.126773 | + | 0.219578i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.50000 | + | 2.59808i | −0.125877 | + | 0.218026i | ||||
\(143\) | −6.00000 | −0.501745 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.0000 | −1.49482 | ||||||||
\(146\) | −1.00000 | + | 1.73205i | −0.0827606 | + | 0.143346i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.50000 | + | 6.06218i | 0.287698 | + | 0.498308i | ||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.50000 | + | 14.7224i | −0.691720 | + | 1.19809i | 0.279554 | + | 0.960130i | \(0.409814\pi\) |
−0.971274 | + | 0.237964i | \(0.923520\pi\) | |||||||
\(152\) | 2.00000 | 0.162221 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.00000 | 0.483494 | ||||||||
\(155\) | 6.00000 | − | 10.3923i | 0.481932 | − | 0.834730i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | − | 12.1244i | −0.558661 | − | 0.967629i | −0.997609 | − | 0.0691164i | \(-0.977982\pi\) |
0.438948 | − | 0.898513i | \(-0.355351\pi\) | |||||||
\(158\) | −4.00000 | − | 6.92820i | −0.318223 | − | 0.551178i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.50000 | + | 2.59808i | −0.118585 | + | 0.205396i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0000 | −1.25322 | −0.626608 | − | 0.779334i | \(-0.715557\pi\) | ||||
−0.626608 | + | 0.779334i | \(0.715557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | + | 10.3923i | 0.465690 | + | 0.806599i | ||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | 9.00000 | 0.690268 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.00000 | −0.0762493 | ||||||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | + | 3.46410i | 0.151186 | + | 0.261861i | ||||
\(176\) | 3.00000 | + | 5.19615i | 0.226134 | + | 0.391675i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.00000 | + | 5.19615i | −0.224860 | + | 0.389468i | ||||
\(179\) | −3.00000 | −0.224231 | −0.112115 | − | 0.993695i | \(-0.535763\pi\) | ||||
−0.112115 | + | 0.993695i | \(0.535763\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | 0.500000 | − | 0.866025i | 0.0370625 | − | 0.0641941i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.5000 | + | 18.1865i | 0.771975 | + | 1.33710i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00000 | − | 15.5885i | 0.658145 | − | 1.13994i | ||||
\(188\) | −3.00000 | −0.218797 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | 0.435286 | ||||||||
\(191\) | −9.00000 | + | 15.5885i | −0.651217 | + | 1.12794i | 0.331611 | + | 0.943416i | \(0.392408\pi\) |
−0.982828 | + | 0.184525i | \(0.940925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000 | + | 3.46410i | 0.143963 | + | 0.249351i | 0.928986 | − | 0.370116i | \(-0.120682\pi\) |
−0.785022 | + | 0.619467i | \(0.787349\pi\) | |||||||
\(194\) | 5.00000 | + | 8.66025i | 0.358979 | + | 0.621770i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | − | 5.19615i | 0.214286 | − | 0.371154i | ||||
\(197\) | −3.00000 | −0.213741 | −0.106871 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | −2.00000 | + | 3.46410i | −0.141421 | + | 0.244949i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.00000 | − | 10.3923i | −0.422159 | − | 0.731200i | ||||
\(203\) | −3.00000 | − | 5.19615i | −0.210559 | − | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.00000 | −0.278693 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 6.00000 | − | 10.3923i | 0.415029 | − | 0.718851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.50000 | + | 11.2583i | 0.447478 | + | 0.775055i | 0.998221 | − | 0.0596196i | \(-0.0189888\pi\) |
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | − | 10.3923i | 0.410152 | − | 0.710403i | ||||
\(215\) | −3.00000 | −0.204598 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | 3.50000 | − | 6.06218i | 0.237050 | − | 0.410582i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.00000 | + | 15.5885i | 0.606780 | + | 1.05097i | ||||
\(221\) | −1.50000 | − | 2.59808i | −0.100901 | − | 0.174766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.50000 | − | 16.4545i | 0.636167 | − | 1.10187i | −0.350100 | − | 0.936713i | \(-0.613852\pi\) |
0.986267 | − | 0.165161i | \(-0.0528144\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.50000 | + | 11.2583i | 0.429532 | + | 0.743971i | 0.996832 | − | 0.0795401i | \(-0.0253452\pi\) |
−0.567300 | + | 0.823511i | \(0.692012\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | − | 5.19615i | 0.196960 | − | 0.341144i | ||||
\(233\) | 27.0000 | 1.76883 | 0.884414 | − | 0.466702i | \(-0.154558\pi\) | ||||
0.884414 | + | 0.466702i | \(0.154558\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.00000 | −0.587095 | ||||||||
\(236\) | −3.00000 | + | 5.19615i | −0.195283 | + | 0.338241i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.50000 | + | 2.59808i | 0.0972306 | + | 0.168408i | ||||
\(239\) | 7.50000 | + | 12.9904i | 0.485135 | + | 0.840278i | 0.999854 | − | 0.0170808i | \(-0.00543724\pi\) |
−0.514719 | + | 0.857359i | \(0.672104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | − | 8.66025i | 0.322078 | − | 0.557856i | −0.658838 | − | 0.752285i | \(-0.728952\pi\) |
0.980917 | + | 0.194429i | \(0.0622852\pi\) | |||||||
\(242\) | 25.0000 | 1.60706 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.00000 | 0.512148 | ||||||||
\(245\) | 9.00000 | − | 15.5885i | 0.574989 | − | 0.995910i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.00000 | − | 1.73205i | −0.0636285 | − | 0.110208i | ||||
\(248\) | 2.00000 | + | 3.46410i | 0.127000 | + | 0.219971i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.50000 | − | 2.59808i | 0.0948683 | − | 0.164317i | ||||
\(251\) | −24.0000 | −1.51487 | −0.757433 | − | 0.652913i | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −10.0000 | + | 17.3205i | −0.627456 | + | 1.08679i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 4.50000 | + | 7.79423i | 0.280702 | + | 0.486191i | 0.971558 | − | 0.236802i | \(-0.0760993\pi\) |
−0.690856 | + | 0.722993i | \(0.742766\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.50000 | + | 6.06218i | −0.217479 | + | 0.376685i | ||||
\(260\) | 3.00000 | 0.186052 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 21.0000 | 1.29738 | ||||||||
\(263\) | −6.00000 | + | 10.3923i | −0.369976 | + | 0.640817i | −0.989561 | − | 0.144112i | \(-0.953967\pi\) |
0.619586 | + | 0.784929i | \(0.287301\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.00000 | + | 1.73205i | 0.0613139 | + | 0.106199i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.00000 | + | 12.1244i | −0.427593 | + | 0.740613i | ||||
\(269\) | −24.0000 | −1.46331 | −0.731653 | − | 0.681677i | \(-0.761251\pi\) | ||||
−0.731653 | + | 0.681677i | \(0.761251\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0000 | 0.668202 | 0.334101 | − | 0.942537i | \(-0.391567\pi\) | ||||
0.334101 | + | 0.942537i | \(0.391567\pi\) | |||||||
\(272\) | −1.50000 | + | 2.59808i | −0.0909509 | + | 0.157532i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.0000 | + | 20.7846i | 0.723627 | + | 1.25336i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0000 | − | 24.2487i | 0.841178 | − | 1.45696i | −0.0477206 | − | 0.998861i | \(-0.515196\pi\) |
0.888899 | − | 0.458103i | \(-0.151471\pi\) | |||||||
\(278\) | −13.0000 | −0.779688 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.00000 | −0.179284 | ||||||||
\(281\) | −3.00000 | + | 5.19615i | −0.178965 | + | 0.309976i | −0.941526 | − | 0.336939i | \(-0.890608\pi\) |
0.762561 | + | 0.646916i | \(0.223942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.00000 | + | 3.46410i | 0.118888 | + | 0.205919i | 0.919327 | − | 0.393494i | \(-0.128734\pi\) |
−0.800439 | + | 0.599414i | \(0.795400\pi\) | |||||||
\(284\) | −1.50000 | − | 2.59808i | −0.0890086 | − | 0.154167i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.00000 | − | 5.19615i | 0.177394 | − | 0.307255i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 9.00000 | − | 15.5885i | 0.528498 | − | 0.915386i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.00000 | − | 1.73205i | −0.0585206 | − | 0.101361i | ||||
\(293\) | 10.5000 | + | 18.1865i | 0.613417 | + | 1.06247i | 0.990660 | + | 0.136355i | \(0.0435386\pi\) |
−0.377244 | + | 0.926114i | \(0.623128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.00000 | + | 15.5885i | −0.524000 | + | 0.907595i | ||||
\(296\) | −7.00000 | −0.406867 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.500000 | − | 0.866025i | −0.0288195 | − | 0.0499169i | ||||
\(302\) | −8.50000 | − | 14.7224i | −0.489120 | − | 0.847181i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | + | 1.73205i | −0.0573539 | + | 0.0993399i | ||||
\(305\) | 24.0000 | 1.37424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.00000 | 0.114146 | 0.0570730 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570730 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(308\) | −3.00000 | + | 5.19615i | −0.170941 | + | 0.296078i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.00000 | + | 10.3923i | 0.340777 | + | 0.590243i | ||||
\(311\) | −15.0000 | − | 25.9808i | −0.850572 | − | 1.47323i | −0.880693 | − | 0.473688i | \(-0.842923\pi\) |
0.0301210 | − | 0.999546i | \(-0.490411\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.500000 | − | 0.866025i | 0.0282617 | − | 0.0489506i | −0.851549 | − | 0.524276i | \(-0.824336\pi\) |
0.879810 | + | 0.475325i | \(0.157669\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | −3.00000 | + | 5.19615i | −0.168497 | + | 0.291845i | −0.937892 | − | 0.346929i | \(-0.887225\pi\) |
0.769395 | + | 0.638774i | \(0.220558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | − | 31.1769i | −1.00781 | − | 1.74557i | ||||
\(320\) | −1.50000 | − | 2.59808i | −0.0838525 | − | 0.145237i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | 0.221880 | ||||||||
\(326\) | 8.00000 | − | 13.8564i | 0.443079 | − | 0.767435i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.50000 | − | 2.59808i | −0.0826977 | − | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | + | 6.92820i | −0.219860 | + | 0.380808i | −0.954765 | − | 0.297361i | \(-0.903893\pi\) |
0.734905 | + | 0.678170i | \(0.237227\pi\) | |||||||
\(332\) | −12.0000 | −0.658586 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.0000 | + | 36.3731i | −1.14735 | + | 1.98727i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.5000 | − | 19.9186i | −0.626445 | − | 1.08503i | −0.988260 | − | 0.152784i | \(-0.951176\pi\) |
0.361815 | − | 0.932250i | \(-0.382157\pi\) | |||||||
\(338\) | −0.500000 | − | 0.866025i | −0.0271964 | − | 0.0471056i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.50000 | + | 7.79423i | −0.244047 | + | 0.422701i | ||||
\(341\) | 24.0000 | 1.29967 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 0.500000 | − | 0.866025i | 0.0269582 | − | 0.0466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.50000 | + | 2.59808i | 0.0805242 | + | 0.139472i | 0.903475 | − | 0.428640i | \(-0.141007\pi\) |
−0.822951 | + | 0.568112i | \(0.807674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.50000 | − | 16.4545i | 0.508523 | − | 0.880788i | −0.491428 | − | 0.870918i | \(-0.663525\pi\) |
0.999951 | − | 0.00987003i | \(-0.00314178\pi\) | |||||||
\(350\) | −4.00000 | −0.213809 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.00000 | −0.319801 | ||||||||
\(353\) | 12.0000 | − | 20.7846i | 0.638696 | − | 1.10625i | −0.347024 | − | 0.937856i | \(-0.612808\pi\) |
0.985719 | − | 0.168397i | \(-0.0538590\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.50000 | − | 7.79423i | −0.238835 | − | 0.413675i | ||||
\(356\) | −3.00000 | − | 5.19615i | −0.159000 | − | 0.275396i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.50000 | − | 2.59808i | 0.0792775 | − | 0.137313i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | −10.0000 | + | 17.3205i | −0.525588 | + | 0.910346i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.500000 | + | 0.866025i | 0.0262071 | + | 0.0453921i | ||||
\(365\) | −3.00000 | − | 5.19615i | −0.157027 | − | 0.271979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.0000 | + | 22.5167i | −0.678594 | + | 1.17536i | 0.296810 | + | 0.954937i | \(0.404077\pi\) |
−0.975404 | + | 0.220423i | \(0.929256\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −21.0000 | −1.09174 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.00000 | + | 3.46410i | 0.103556 | + | 0.179364i | 0.913147 | − | 0.407630i | \(-0.133645\pi\) |
−0.809591 | + | 0.586994i | \(0.800311\pi\) | |||||||
\(374\) | 9.00000 | + | 15.5885i | 0.465379 | + | 0.806060i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.50000 | − | 2.59808i | 0.0773566 | − | 0.133986i | ||||
\(377\) | −6.00000 | −0.309016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | −3.00000 | + | 5.19615i | −0.153897 | + | 0.266557i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.00000 | − | 15.5885i | −0.460480 | − | 0.797575i | ||||
\(383\) | 10.5000 | + | 18.1865i | 0.536525 | + | 0.929288i | 0.999088 | + | 0.0427020i | \(0.0135966\pi\) |
−0.462563 | + | 0.886586i | \(0.653070\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.00000 | + | 15.5885i | −0.458682 | + | 0.794461i | ||||
\(386\) | −4.00000 | −0.203595 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.0000 | −0.507673 | ||||||||
\(389\) | −3.00000 | + | 5.19615i | −0.152106 | + | 0.263455i | −0.932002 | − | 0.362454i | \(-0.881939\pi\) |
0.779895 | + | 0.625910i | \(0.215272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.00000 | + | 5.19615i | 0.151523 | + | 0.262445i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.50000 | − | 2.59808i | 0.0755689 | − | 0.130889i | ||||
\(395\) | 24.0000 | 1.20757 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.0000 | −1.70641 | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | −1.00000 | + | 1.73205i | −0.0501255 | + | 0.0868199i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | 18.0000 | + | 31.1769i | 0.898877 | + | 1.55690i | 0.828932 | + | 0.559350i | \(0.188949\pi\) |
0.0699455 | + | 0.997551i | \(0.477717\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.00000 | − | 3.46410i | 0.0996271 | − | 0.172559i | ||||
\(404\) | 12.0000 | 0.597022 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00000 | 0.297775 | ||||||||
\(407\) | −21.0000 | + | 36.3731i | −1.04093 | + | 1.80295i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0000 | − | 27.7128i | −0.791149 | − | 1.37031i | −0.925256 | − | 0.379344i | \(-0.876150\pi\) |
0.134107 | − | 0.990967i | \(-0.457183\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.00000 | − | 3.46410i | 0.0985329 | − | 0.170664i | ||||
\(413\) | −6.00000 | −0.295241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −36.0000 | −1.76717 | ||||||||
\(416\) | −0.500000 | + | 0.866025i | −0.0245145 | + | 0.0424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.00000 | + | 10.3923i | 0.293470 | + | 0.508304i | ||||
\(419\) | 4.50000 | + | 7.79423i | 0.219839 | + | 0.380773i | 0.954759 | − | 0.297382i | \(-0.0961133\pi\) |
−0.734919 | + | 0.678155i | \(0.762780\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.50000 | + | 14.7224i | −0.414265 | + | 0.717527i | −0.995351 | − | 0.0963145i | \(-0.969295\pi\) |
0.581086 | + | 0.813842i | \(0.302628\pi\) | |||||||
\(422\) | −13.0000 | −0.632830 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | + | 10.3923i | −0.291043 | + | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.00000 | + | 6.92820i | 0.193574 | + | 0.335279i | ||||
\(428\) | 6.00000 | + | 10.3923i | 0.290021 | + | 0.502331i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.50000 | − | 2.59808i | 0.0723364 | − | 0.125290i | ||||
\(431\) | 33.0000 | 1.58955 | 0.794777 | − | 0.606902i | \(-0.207588\pi\) | ||||
0.794777 | + | 0.606902i | \(0.207588\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.0000 | −1.20142 | −0.600712 | − | 0.799466i | \(-0.705116\pi\) | ||||
−0.600712 | + | 0.799466i | \(0.705116\pi\) | |||||||
\(434\) | −2.00000 | + | 3.46410i | −0.0960031 | + | 0.166282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.50000 | + | 6.06218i | 0.167620 | + | 0.290326i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.0000 | + | 22.5167i | −0.620456 | + | 1.07466i | 0.368945 | + | 0.929451i | \(0.379719\pi\) |
−0.989401 | + | 0.145210i | \(0.953614\pi\) | |||||||
\(440\) | −18.0000 | −0.858116 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.00000 | 0.142695 | ||||||||
\(443\) | 10.5000 | − | 18.1865i | 0.498870 | − | 0.864068i | −0.501129 | − | 0.865373i | \(-0.667082\pi\) |
0.999999 | + | 0.00130426i | \(0.000415158\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | − | 15.5885i | −0.426641 | − | 0.738964i | ||||
\(446\) | 9.50000 | + | 16.4545i | 0.449838 | + | 0.779142i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.500000 | − | 0.866025i | 0.0236228 | − | 0.0409159i | ||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −3.00000 | + | 5.19615i | −0.141108 | + | 0.244406i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.50000 | + | 2.59808i | 0.0703211 | + | 0.121800i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.00000 | − | 8.66025i | 0.233890 | − | 0.405110i | −0.725059 | − | 0.688686i | \(-0.758188\pi\) |
0.958950 | + | 0.283577i | \(0.0915211\pi\) | |||||||
\(458\) | −13.0000 | −0.607450 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.50000 | − | 7.79423i | 0.209586 | − | 0.363013i | −0.741998 | − | 0.670402i | \(-0.766122\pi\) |
0.951584 | + | 0.307388i | \(0.0994551\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.0000 | + | 34.6410i | 0.929479 | + | 1.60990i | 0.784195 | + | 0.620515i | \(0.213076\pi\) |
0.145284 | + | 0.989390i | \(0.453590\pi\) | |||||||
\(464\) | 3.00000 | + | 5.19615i | 0.139272 | + | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.5000 | + | 23.3827i | −0.625375 | + | 1.08318i | ||||
\(467\) | −36.0000 | −1.66588 | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0000 | −0.646460 | ||||||||
\(470\) | 4.50000 | − | 7.79423i | 0.207570 | − | 0.359521i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.00000 | − | 5.19615i | −0.138086 | − | 0.239172i | ||||
\(473\) | −3.00000 | − | 5.19615i | −0.137940 | − | 0.238919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | + | 6.92820i | −0.183533 | + | 0.317888i | ||||
\(476\) | −3.00000 | −0.137505 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.0000 | −0.686084 | ||||||||
\(479\) | −10.5000 | + | 18.1865i | −0.479757 | + | 0.830964i | −0.999730 | − | 0.0232187i | \(-0.992609\pi\) |
0.519973 | + | 0.854183i | \(0.325942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.50000 | + | 6.06218i | 0.159586 | + | 0.276412i | ||||
\(482\) | 5.00000 | + | 8.66025i | 0.227744 | + | 0.394464i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.5000 | + | 21.6506i | −0.568182 | + | 0.984120i | ||||
\(485\) | −30.0000 | −1.36223 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.0000 | −0.725029 | −0.362515 | − | 0.931978i | \(-0.618082\pi\) | ||||
−0.362515 | + | 0.931978i | \(0.618082\pi\) | |||||||
\(488\) | −4.00000 | + | 6.92820i | −0.181071 | + | 0.313625i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.00000 | + | 15.5885i | 0.406579 | + | 0.704215i | ||||
\(491\) | −4.50000 | − | 7.79423i | −0.203082 | − | 0.351749i | 0.746438 | − | 0.665455i | \(-0.231763\pi\) |
−0.949520 | + | 0.313707i | \(0.898429\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | − | 15.5885i | 0.405340 | − | 0.702069i | ||||
\(494\) | 2.00000 | 0.0899843 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 1.50000 | − | 2.59808i | 0.0672842 | − | 0.116540i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000 | + | 34.6410i | 0.895323 | + | 1.55074i | 0.833404 | + | 0.552664i | \(0.186389\pi\) |
0.0619186 | + | 0.998081i | \(0.480278\pi\) | |||||||
\(500\) | 1.50000 | + | 2.59808i | 0.0670820 | + | 0.116190i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0000 | − | 20.7846i | 0.535586 | − | 0.927663i | ||||
\(503\) | 30.0000 | 1.33763 | 0.668817 | − | 0.743427i | \(-0.266801\pi\) | ||||
0.668817 | + | 0.743427i | \(0.266801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0000 | 1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.0000 | − | 17.3205i | −0.443678 | − | 0.768473i | ||||
\(509\) | −9.00000 | − | 15.5885i | −0.398918 | − | 0.690946i | 0.594675 | − | 0.803966i | \(-0.297281\pi\) |
−0.993593 | + | 0.113020i | \(0.963948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.00000 | − | 1.73205i | 0.0442374 | − | 0.0766214i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.00000 | −0.396973 | ||||||||
\(515\) | 6.00000 | − | 10.3923i | 0.264392 | − | 0.457940i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.00000 | − | 15.5885i | −0.395820 | − | 0.685580i | ||||
\(518\) | −3.50000 | − | 6.06218i | −0.153781 | − | 0.266357i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.50000 | + | 2.59808i | −0.0657794 | + | 0.113933i | ||||
\(521\) | 9.00000 | 0.394297 | 0.197149 | − | 0.980374i | \(-0.436832\pi\) | ||||
0.197149 | + | 0.980374i | \(0.436832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | −10.5000 | + | 18.1865i | −0.458695 | + | 0.794482i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.00000 | − | 10.3923i | −0.261612 | − | 0.453126i | ||||
\(527\) | 6.00000 | + | 10.3923i | 0.261364 | + | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.00000 | −0.0867110 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.0000 | + | 31.1769i | 0.778208 | + | 1.34790i | ||||
\(536\) | −7.00000 | − | 12.1244i | −0.302354 | − | 0.523692i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.0000 | − | 20.7846i | 0.517357 | − | 0.896088i | ||||
\(539\) | 36.0000 | 1.55063 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0000 | 0.472927 | 0.236463 | − | 0.971640i | \(-0.424012\pi\) | ||||
0.236463 | + | 0.971640i | \(0.424012\pi\) | |||||||
\(542\) | −5.50000 | + | 9.52628i | −0.236245 | + | 0.409189i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.50000 | − | 2.59808i | −0.0643120 | − | 0.111392i | ||||
\(545\) | 10.5000 | + | 18.1865i | 0.449771 | + | 0.779026i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.50000 | + | 14.7224i | −0.363434 | + | 0.629486i | −0.988524 | − | 0.151067i | \(-0.951729\pi\) |
0.625090 | + | 0.780553i | \(0.285062\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −24.0000 | −1.02336 | ||||||||
\(551\) | 6.00000 | − | 10.3923i | 0.255609 | − | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | + | 6.92820i | 0.170097 | + | 0.294617i | ||||
\(554\) | 14.0000 | + | 24.2487i | 0.594803 | + | 1.03023i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.50000 | − | 11.2583i | 0.275661 | − | 0.477460i | ||||
\(557\) | −3.00000 | −0.127114 | −0.0635570 | − | 0.997978i | \(-0.520244\pi\) | ||||
−0.0635570 | + | 0.997978i | \(0.520244\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.00000 | −0.0422955 | ||||||||
\(560\) | 1.50000 | − | 2.59808i | 0.0633866 | − | 0.109789i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.00000 | − | 5.19615i | −0.126547 | − | 0.219186i | ||||
\(563\) | 19.5000 | + | 33.7750i | 0.821827 | + | 1.42345i | 0.904320 | + | 0.426855i | \(0.140378\pi\) |
−0.0824933 | + | 0.996592i | \(0.526288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.00000 | + | 15.5885i | −0.378633 | + | 0.655811i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.00000 | 0.125877 | ||||||||
\(569\) | 7.50000 | − | 12.9904i | 0.314416 | − | 0.544585i | −0.664897 | − | 0.746935i | \(-0.731525\pi\) |
0.979313 | + | 0.202350i | \(0.0648579\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.50000 | − | 4.33013i | −0.104622 | − | 0.181210i | 0.808962 | − | 0.587861i | \(-0.200030\pi\) |
−0.913584 | + | 0.406651i | \(0.866697\pi\) | |||||||
\(572\) | 3.00000 | + | 5.19615i | 0.125436 | + | 0.217262i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.0000 | 1.58196 | 0.790980 | − | 0.611842i | \(-0.209571\pi\) | ||||
0.790980 | + | 0.611842i | \(0.209571\pi\) | |||||||
\(578\) | 4.00000 | − | 6.92820i | 0.166378 | − | 0.288175i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.00000 | + | 15.5885i | 0.373705 | + | 0.647275i | ||||
\(581\) | −6.00000 | − | 10.3923i | −0.248922 | − | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.0000 | −0.867502 | ||||||||
\(587\) | 12.0000 | − | 20.7846i | 0.495293 | − | 0.857873i | −0.504692 | − | 0.863299i | \(-0.668394\pi\) |
0.999985 | + | 0.00542667i | \(0.00172737\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00000 | + | 6.92820i | 0.164817 | + | 0.285472i | ||||
\(590\) | −9.00000 | − | 15.5885i | −0.370524 | − | 0.641767i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.50000 | − | 6.06218i | 0.143849 | − | 0.249154i | ||||
\(593\) | −18.0000 | −0.739171 | −0.369586 | − | 0.929197i | \(-0.620500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.00000 | −0.368964 | ||||||||
\(596\) | −3.00000 | + | 5.19615i | −0.122885 | + | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.00000 | + | 5.19615i | 0.122577 | + | 0.212309i | 0.920783 | − | 0.390075i | \(-0.127551\pi\) |
−0.798206 | + | 0.602384i | \(0.794218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.50000 | − | 16.4545i | 0.387513 | − | 0.671192i | −0.604601 | − | 0.796528i | \(-0.706668\pi\) |
0.992114 | + | 0.125336i | \(0.0400009\pi\) | |||||||
\(602\) | 1.00000 | 0.0407570 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.0000 | 0.691720 | ||||||||
\(605\) | −37.5000 | + | 64.9519i | −1.52459 | + | 2.64067i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.00000 | − | 12.1244i | −0.284121 | − | 0.492112i | 0.688274 | − | 0.725450i | \(-0.258368\pi\) |
−0.972396 | + | 0.233338i | \(0.925035\pi\) | |||||||
\(608\) | −1.00000 | − | 1.73205i | −0.0405554 | − | 0.0702439i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.0000 | + | 20.7846i | −0.485866 | + | 0.841544i | ||||
\(611\) | −3.00000 | −0.121367 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.0000 | 1.53481 | 0.767403 | − | 0.641165i | \(-0.221549\pi\) | ||||
0.767403 | + | 0.641165i | \(0.221549\pi\) | |||||||
\(614\) | −1.00000 | + | 1.73205i | −0.0403567 | + | 0.0698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.00000 | − | 5.19615i | −0.120873 | − | 0.209359i | ||||
\(617\) | −12.0000 | − | 20.7846i | −0.483102 | − | 0.836757i | 0.516710 | − | 0.856161i | \(-0.327157\pi\) |
−0.999812 | + | 0.0194037i | \(0.993823\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0000 | − | 24.2487i | 0.562708 | − | 0.974638i | −0.434551 | − | 0.900647i | \(-0.643093\pi\) |
0.997259 | − | 0.0739910i | \(-0.0235736\pi\) | |||||||
\(620\) | −12.0000 | −0.481932 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30.0000 | 1.20289 | ||||||||
\(623\) | 3.00000 | − | 5.19615i | 0.120192 | − | 0.208179i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 0.500000 | + | 0.866025i | 0.0199840 | + | 0.0346133i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.00000 | + | 12.1244i | −0.279330 | + | 0.483814i | ||||
\(629\) | −21.0000 | −0.837325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.0000 | 1.15447 | 0.577236 | − | 0.816577i | \(-0.304131\pi\) | ||||
0.577236 | + | 0.816577i | \(0.304131\pi\) | |||||||
\(632\) | −4.00000 | + | 6.92820i | −0.159111 | + | 0.275589i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.00000 | − | 5.19615i | −0.119145 | − | 0.206366i | ||||
\(635\) | −30.0000 | − | 51.9615i | −1.19051 | − | 2.06203i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | − | 5.19615i | 0.118864 | − | 0.205879i | ||||
\(638\) | 36.0000 | 1.42525 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.00000 | 0.118585 | ||||||||
\(641\) | −9.00000 | + | 15.5885i | −0.355479 | + | 0.615707i | −0.987200 | − | 0.159489i | \(-0.949015\pi\) |
0.631721 | + | 0.775196i | \(0.282349\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.00000 | − | 12.1244i | −0.276053 | − | 0.478138i | 0.694347 | − | 0.719640i | \(-0.255693\pi\) |
−0.970400 | + | 0.241502i | \(0.922360\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.00000 | + | 5.19615i | −0.118033 | + | 0.204440i | ||||
\(647\) | 6.00000 | 0.235884 | 0.117942 | − | 0.993020i | \(-0.462370\pi\) | ||||
0.117942 | + | 0.993020i | \(0.462370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.0000 | −1.41312 | ||||||||
\(650\) | −2.00000 | + | 3.46410i | −0.0784465 | + | 0.135873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.00000 | + | 13.8564i | 0.313304 | + | 0.542659i | ||||
\(653\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31.5000 | + | 54.5596i | −1.23081 | + | 2.13182i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.00000 | 0.116952 | ||||||||
\(659\) | −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 | ||||||||
\(661\) | 11.0000 | + | 19.0526i | 0.427850 | + | 0.741059i | 0.996682 | − | 0.0813955i | \(-0.0259377\pi\) |
−0.568831 | + | 0.822454i | \(0.692604\pi\) | |||||||
\(662\) | −4.00000 | − | 6.92820i | −0.155464 | − | 0.269272i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | − | 10.3923i | 0.232845 | − | 0.403300i | ||||
\(665\) | −6.00000 | −0.232670 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −21.0000 | − | 36.3731i | −0.811301 | − | 1.40521i | ||||
\(671\) | 24.0000 | + | 41.5692i | 0.926510 | + | 1.60476i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.50000 | − | 16.4545i | 0.366198 | − | 0.634274i | −0.622770 | − | 0.782405i | \(-0.713993\pi\) |
0.988968 | + | 0.148132i | \(0.0473259\pi\) | |||||||
\(674\) | 23.0000 | 0.885927 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 24.0000 | − | 41.5692i | 0.922395 | − | 1.59763i | 0.126697 | − | 0.991941i | \(-0.459562\pi\) |
0.795698 | − | 0.605693i | \(-0.207104\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.00000 | − | 8.66025i | −0.191882 | − | 0.332350i | ||||
\(680\) | −4.50000 | − | 7.79423i | −0.172567 | − | 0.298895i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.0000 | + | 20.7846i | −0.459504 | + | 0.795884i | ||||
\(683\) | −24.0000 | −0.918334 | −0.459167 | − | 0.888350i | \(-0.651852\pi\) | ||||
−0.459167 | + | 0.888350i | \(0.651852\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.50000 | + | 11.2583i | −0.248171 | + | 0.429845i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.500000 | + | 0.866025i | 0.0190623 | + | 0.0330169i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | + | 6.92820i | −0.152167 | + | 0.263561i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
0.779857 | + | 0.625958i | \(0.215292\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.00000 | −0.113878 | ||||||||
\(695\) | 19.5000 | − | 33.7750i | 0.739677 | − | 1.28116i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 9.50000 | + | 16.4545i | 0.359580 | + | 0.622811i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.00000 | − | 3.46410i | 0.0755929 | − | 0.130931i | ||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0000 | −0.528020 | ||||||||
\(704\) | 3.00000 | − | 5.19615i | 0.113067 | − | 0.195837i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.0000 | + | 20.7846i | 0.451626 | + | 0.782239i | ||||
\(707\) | 6.00000 | + | 10.3923i | 0.225653 | + | 0.390843i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0000 | + | 22.5167i | −0.488225 | + | 0.845631i | −0.999908 | − | 0.0135434i | \(-0.995689\pi\) |
0.511683 | + | 0.859174i | \(0.329022\pi\) | |||||||
\(710\) | 9.00000 | 0.337764 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.00000 | 0.224860 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.00000 | + | 15.5885i | 0.336581 | + | 0.582975i | ||||
\(716\) | 1.50000 | + | 2.59808i | 0.0560576 | + | 0.0970947i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.00000 | −0.223762 | −0.111881 | − | 0.993722i | \(-0.535688\pi\) | ||||
−0.111881 | + | 0.993722i | \(0.535688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00000 | 0.148968 | ||||||||
\(722\) | 7.50000 | − | 12.9904i | 0.279121 | − | 0.483452i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.0000 | − | 17.3205i | −0.371647 | − | 0.643712i | ||||
\(725\) | 12.0000 | + | 20.7846i | 0.445669 | + | 0.771921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.00000 | − | 8.66025i | 0.185440 | − | 0.321191i | −0.758285 | − | 0.651923i | \(-0.773962\pi\) |
0.943725 | + | 0.330732i | \(0.107296\pi\) | |||||||
\(728\) | −1.00000 | −0.0370625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.00000 | 0.222070 | ||||||||
\(731\) | 1.50000 | − | 2.59808i | 0.0554795 | − | 0.0960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.5000 | − | 19.9186i | −0.424762 | − | 0.735710i | 0.571636 | − | 0.820507i | \(-0.306309\pi\) |
−0.996398 | + | 0.0847976i | \(0.972976\pi\) | |||||||
\(734\) | −13.0000 | − | 22.5167i | −0.479839 | − | 0.831105i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −84.0000 | −3.09418 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 10.5000 | − | 18.1865i | 0.385988 | − | 0.668550i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.50000 | − | 7.79423i | −0.165089 | − | 0.285943i | 0.771598 | − | 0.636111i | \(-0.219458\pi\) |
−0.936687 | + | 0.350168i | \(0.886124\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.00000 | + | 15.5885i | −0.329734 | + | 0.571117i | ||||
\(746\) | −4.00000 | −0.146450 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −18.0000 | −0.658145 | ||||||||
\(749\) | −6.00000 | + | 10.3923i | −0.219235 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0000 | + | 34.6410i | 0.729810 | + | 1.26407i | 0.956963 | + | 0.290209i | \(0.0937250\pi\) |
−0.227153 | + | 0.973859i | \(0.572942\pi\) | |||||||
\(752\) | 1.50000 | + | 2.59808i | 0.0546994 | + | 0.0947421i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.00000 | − | 5.19615i | 0.109254 | − | 0.189233i | ||||
\(755\) | 51.0000 | 1.85608 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.0000 | −0.581530 | −0.290765 | − | 0.956795i | \(-0.593910\pi\) | ||||
−0.290765 | + | 0.956795i | \(0.593910\pi\) | |||||||
\(758\) | −10.0000 | + | 17.3205i | −0.363216 | + | 0.629109i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.00000 | − | 5.19615i | −0.108821 | − | 0.188484i | ||||
\(761\) | −3.00000 | − | 5.19615i | −0.108750 | − | 0.188360i | 0.806514 | − | 0.591215i | \(-0.201351\pi\) |
−0.915264 | + | 0.402854i | \(0.868018\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.50000 | + | 6.06218i | −0.126709 | + | 0.219466i | ||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.0000 | −0.758761 | ||||||||
\(767\) | −3.00000 | + | 5.19615i | −0.108324 | + | 0.187622i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.0000 | − | 27.7128i | −0.576975 | − | 0.999350i | −0.995824 | − | 0.0912938i | \(-0.970900\pi\) |
0.418849 | − | 0.908056i | \(-0.362434\pi\) | |||||||
\(770\) | −9.00000 | − | 15.5885i | −0.324337 | − | 0.561769i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.00000 | − | 3.46410i | 0.0719816 | − | 0.124676i | ||||
\(773\) | 39.0000 | 1.40273 | 0.701366 | − | 0.712801i | \(-0.252574\pi\) | ||||
0.701366 | + | 0.712801i | \(0.252574\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.0000 | −0.574737 | ||||||||
\(776\) | 5.00000 | − | 8.66025i | 0.179490 | − | 0.310885i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.00000 | − | 5.19615i | −0.107555 | − | 0.186291i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | − | 15.5885i | 0.322045 | − | 0.557799i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.00000 | −0.214286 | ||||||||
\(785\) | −21.0000 | + | 36.3731i | −0.749522 | + | 1.29821i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0000 | + | 34.6410i | 0.712923 | + | 1.23482i | 0.963755 | + | 0.266788i | \(0.0859624\pi\) |
−0.250832 | + | 0.968031i | \(0.580704\pi\) | |||||||
\(788\) | 1.50000 | + | 2.59808i | 0.0534353 | + | 0.0925526i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.0000 | + | 20.7846i | −0.426941 | + | 0.739483i | ||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.00000 | 0.284088 | ||||||||
\(794\) | 17.0000 | − | 29.4449i | 0.603307 | − | 1.04496i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.00000 | − | 1.73205i | −0.0354441 | − | 0.0613909i | ||||
\(797\) | −21.0000 | − | 36.3731i | −0.743858 | − | 1.28840i | −0.950726 | − | 0.310031i | \(-0.899660\pi\) |
0.206868 | − | 0.978369i | \(-0.433673\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.50000 | − | 7.79423i | 0.159199 | − | 0.275740i | ||||
\(800\) | 4.00000 | 0.141421 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −36.0000 | −1.27120 | ||||||||
\(803\) | 6.00000 | − | 10.3923i | 0.211735 | − | 0.366736i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.00000 | + | 3.46410i | 0.0704470 | + | 0.122018i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.00000 | + | 10.3923i | −0.211079 | + | 0.365600i | ||||
\(809\) | 33.0000 | 1.16022 | 0.580109 | − | 0.814539i | \(-0.303010\pi\) | ||||
0.580109 | + | 0.814539i | \(0.303010\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | −3.00000 | + | 5.19615i | −0.105279 | + | 0.182349i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −21.0000 | − | 36.3731i | −0.736050 | − | 1.27488i | ||||
\(815\) | 24.0000 | + | 41.5692i | 0.840683 | + | 1.45611i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.00000 | − | 1.73205i | 0.0349856 | − | 0.0605968i | ||||
\(818\) | 32.0000 | 1.11885 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.50000 | + | 2.59808i | −0.0523504 | + | 0.0906735i | −0.891013 | − | 0.453978i | \(-0.850005\pi\) |
0.838663 | + | 0.544651i | \(0.183338\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.00000 | − | 12.1244i | −0.244005 | − | 0.422628i | 0.717847 | − | 0.696201i | \(-0.245128\pi\) |
−0.961851 | + | 0.273573i | \(0.911795\pi\) | |||||||
\(824\) | 2.00000 | + | 3.46410i | 0.0696733 | + | 0.120678i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.00000 | − | 5.19615i | 0.104383 | − | 0.180797i | ||||
\(827\) | −18.0000 | −0.625921 | −0.312961 | − | 0.949766i | \(-0.601321\pi\) | ||||
−0.312961 | + | 0.949766i | \(0.601321\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.0000 | 1.31979 | 0.659897 | − | 0.751356i | \(-0.270600\pi\) | ||||
0.659897 | + | 0.751356i | \(0.270600\pi\) | |||||||
\(830\) | 18.0000 | − | 31.1769i | 0.624789 | − | 1.08217i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.500000 | − | 0.866025i | −0.0173344 | − | 0.0300240i | ||||
\(833\) | 9.00000 | + | 15.5885i | 0.311832 | + | 0.540108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.0000 | −0.415029 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.00000 | −0.310900 | ||||||||
\(839\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | −8.50000 | − | 14.7224i | −0.292929 | − | 0.507369i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.50000 | − | 11.2583i | 0.223739 | − | 0.387528i | ||||
\(845\) | 3.00000 | 0.103203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.0000 | −0.859010 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.00000 | − | 10.3923i | −0.205798 | − | 0.356453i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.5000 | − | 32.0429i | 0.633428 | − | 1.09713i | −0.353418 | − | 0.935466i | \(-0.614981\pi\) |
0.986846 | − | 0.161664i | \(-0.0516860\pi\) | |||||||
\(854\) | −8.00000 | −0.273754 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | −21.0000 | + | 36.3731i | −0.717346 | + | 1.24248i | 0.244701 | + | 0.969599i | \(0.421310\pi\) |
−0.962048 | + | 0.272882i | \(0.912023\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000 | + | 3.46410i | 0.0682391 | + | 0.118194i | 0.898126 | − | 0.439738i | \(-0.144929\pi\) |
−0.829887 | + | 0.557931i | \(0.811595\pi\) | |||||||
\(860\) | 1.50000 | + | 2.59808i | 0.0511496 | + | 0.0885937i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.5000 | + | 28.5788i | −0.561992 | + | 0.973399i | ||||
\(863\) | 45.0000 | 1.53182 | 0.765909 | − | 0.642949i | \(-0.222289\pi\) | ||||
0.765909 | + | 0.642949i | \(0.222289\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.5000 | − | 21.6506i | 0.424767 | − | 0.735719i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.00000 | − | 3.46410i | −0.0678844 | − | 0.117579i | ||||
\(869\) | 24.0000 | + | 41.5692i | 0.814144 | + | 1.41014i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.00000 | + | 12.1244i | −0.237186 | + | 0.410818i | ||||
\(872\) | −7.00000 | −0.237050 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.50000 | + | 2.59808i | −0.0507093 | + | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.50000 | + | 11.2583i | 0.219489 | + | 0.380167i | 0.954652 | − | 0.297724i | \(-0.0962275\pi\) |
−0.735163 | + | 0.677891i | \(0.762894\pi\) | |||||||
\(878\) | −13.0000 | − | 22.5167i | −0.438729 | − | 0.759900i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.00000 | − | 15.5885i | 0.303390 | − | 0.525487i | ||||
\(881\) | −21.0000 | −0.707508 | −0.353754 | − | 0.935339i | \(-0.615095\pi\) | ||||
−0.353754 | + | 0.935339i | \(0.615095\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0000 | 0.975928 | 0.487964 | − | 0.872864i | \(-0.337740\pi\) | ||||
0.487964 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(884\) | −1.50000 | + | 2.59808i | −0.0504505 | + | 0.0873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.5000 | + | 18.1865i | 0.352754 | + | 0.610989i | ||||
\(887\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.0000 | − | 17.3205i | 0.335389 | − | 0.580911i | ||||
\(890\) | 18.0000 | 0.603361 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.0000 | −0.636167 | ||||||||
\(893\) | 3.00000 | − | 5.19615i | 0.100391 | − | 0.173883i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.50000 | + | 7.79423i | 0.150418 | + | 0.260532i | ||||
\(896\) | 0.500000 | + | 0.866025i | 0.0167038 | + | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.00000 | − | 5.19615i | 0.100111 | − | 0.173398i | ||||
\(899\) | 24.0000 | 0.800445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.00000 | − | 5.19615i | −0.0997785 | − | 0.172821i | ||||
\(905\) | −30.0000 | − | 51.9615i | −0.997234 | − | 1.72726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5000 | − | 32.0429i | 0.614282 | − | 1.06397i | −0.376228 | − | 0.926527i | \(-0.622779\pi\) |
0.990510 | − | 0.137441i | \(-0.0438878\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.00000 | −0.0994490 | ||||||||
\(911\) | 15.0000 | − | 25.9808i | 0.496972 | − | 0.860781i | −0.503022 | − | 0.864274i | \(-0.667778\pi\) |
0.999994 | + | 0.00349271i | \(0.00111177\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.0000 | − | 62.3538i | −1.19143 | − | 2.06361i | ||||
\(914\) | 5.00000 | + | 8.66025i | 0.165385 | + | 0.286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.50000 | − | 11.2583i | 0.214766 | − | 0.371986i | ||||
\(917\) | −21.0000 | −0.693481 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.50000 | + | 7.79423i | 0.148200 | + | 0.256689i | ||||
\(923\) | −1.50000 | − | 2.59808i | −0.0493731 | − | 0.0855167i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000 | − | 24.2487i | 0.460317 | − | 0.797293i | ||||
\(926\) | −40.0000 | −1.31448 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.00000 | −0.196960 | ||||||||
\(929\) | 18.0000 | − | 31.1769i | 0.590561 | − | 1.02288i | −0.403596 | − | 0.914937i | \(-0.632240\pi\) |
0.994157 | − | 0.107944i | \(-0.0344268\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | + | 10.3923i | 0.196642 | + | 0.340594i | ||||
\(932\) | −13.5000 | − | 23.3827i | −0.442207 | − | 0.765925i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.0000 | − | 31.1769i | 0.588978 | − | 1.02014i | ||||
\(935\) | −54.0000 | −1.76599 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 7.00000 | − | 12.1244i | 0.228558 | − | 0.395874i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.50000 | + | 7.79423i | 0.146774 | + | 0.254220i | ||||
\(941\) | −10.5000 | − | 18.1865i | −0.342290 | − | 0.592864i | 0.642567 | − | 0.766229i | \(-0.277869\pi\) |
−0.984858 | + | 0.173365i | \(0.944536\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.00000 | 0.195077 | ||||||||
\(947\) | 3.00000 | − | 5.19615i | 0.0974869 | − | 0.168852i | −0.813157 | − | 0.582045i | \(-0.802253\pi\) |
0.910644 | + | 0.413192i | \(0.135586\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.00000 | − | 1.73205i | −0.0324614 | − | 0.0562247i | ||||
\(950\) | −4.00000 | − | 6.92820i | −0.129777 | − | 0.224781i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.50000 | − | 2.59808i | 0.0486153 | − | 0.0842041i | ||||
\(953\) | −15.0000 | −0.485898 | −0.242949 | − | 0.970039i | \(-0.578115\pi\) | ||||
−0.242949 | + | 0.970039i | \(0.578115\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 54.0000 | 1.74740 | ||||||||
\(956\) | 7.50000 | − | 12.9904i | 0.242567 | − | 0.420139i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.5000 | − | 18.1865i | −0.339240 | − | 0.587580i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | −7.00000 | −0.225689 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.0000 | −0.322078 | ||||||||
\(965\) | 6.00000 | − | 10.3923i | 0.193147 | − | 0.334540i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5000 | + | 26.8468i | 0.498446 | + | 0.863334i | 0.999998 | − | 0.00179302i | \(-0.000570736\pi\) |
−0.501552 | + | 0.865128i | \(0.667237\pi\) | |||||||
\(968\) | −12.5000 | − | 21.6506i | −0.401765 | − | 0.695878i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15.0000 | − | 25.9808i | 0.481621 | − | 0.834192i | ||||
\(971\) | 3.00000 | 0.0962746 | 0.0481373 | − | 0.998841i | \(-0.484672\pi\) | ||||
0.0481373 | + | 0.998841i | \(0.484672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.0000 | 0.416761 | ||||||||
\(974\) | 8.00000 | − | 13.8564i | 0.256337 | − | 0.443988i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | − | 6.92820i | −0.128037 | − | 0.221766i | ||||
\(977\) | −27.0000 | − | 46.7654i | −0.863807 | − | 1.49616i | −0.868227 | − | 0.496167i | \(-0.834741\pi\) |
0.00442082 | − | 0.999990i | \(-0.498593\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0000 | − | 31.1769i | 0.575282 | − | 0.996419i | ||||
\(980\) | −18.0000 | −0.574989 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.00000 | 0.287202 | ||||||||
\(983\) | 19.5000 | − | 33.7750i | 0.621953 | − | 1.07725i | −0.367168 | − | 0.930155i | \(-0.619673\pi\) |
0.989122 | − | 0.147100i | \(-0.0469940\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.50000 | + | 7.79423i | 0.143382 | + | 0.248345i | ||||
\(986\) | 9.00000 | + | 15.5885i | 0.286618 | + | 0.496438i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.00000 | + | 1.73205i | −0.0318142 | + | 0.0551039i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.00000 | 0.0635321 | 0.0317660 | − | 0.999495i | \(-0.489887\pi\) | ||||
0.0317660 | + | 0.999495i | \(0.489887\pi\) | |||||||
\(992\) | 2.00000 | − | 3.46410i | 0.0635001 | − | 0.109985i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.50000 | + | 2.59808i | 0.0475771 | + | 0.0824060i | ||||
\(995\) | −3.00000 | − | 5.19615i | −0.0951064 | − | 0.164729i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.0000 | − | 39.8372i | 0.728417 | − | 1.26166i | −0.229135 | − | 0.973395i | \(-0.573590\pi\) |
0.957552 | − | 0.288261i | \(-0.0930771\pi\) | |||||||
\(998\) | −40.0000 | −1.26618 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))