Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(226,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.226");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.h (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.991381711347.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.2 | ||
Root | \(-0.335166 + 0.580525i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.226 |
Dual form | 1323.2.h.f.802.2 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.670333 | −0.473997 | −0.236998 | − | 0.971510i | \(-0.576164\pi\) | ||||
−0.236998 | + | 0.971510i | \(0.576164\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.55065 | −0.775327 | ||||||||
\(5\) | −0.712469 | − | 1.23403i | −0.318626 | − | 0.551876i | 0.661576 | − | 0.749878i | \(-0.269888\pi\) |
−0.980202 | + | 0.198002i | \(0.936555\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.38012 | 0.841499 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.477591 | + | 0.827212i | 0.151028 | + | 0.261587i | ||||
\(11\) | −2.46539 | + | 4.27018i | −0.743342 | + | 1.28751i | 0.207623 | + | 0.978209i | \(0.433427\pi\) |
−0.950965 | + | 0.309297i | \(0.899906\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.37730 | − | 2.38556i | 0.381995 | − | 0.661635i | −0.609352 | − | 0.792900i | \(-0.708571\pi\) |
0.991347 | + | 0.131265i | \(0.0419038\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.50584 | 0.376459 | ||||||||
\(17\) | 0.559839 | + | 0.969670i | 0.135781 | + | 0.235180i | 0.925896 | − | 0.377780i | \(-0.123312\pi\) |
−0.790115 | + | 0.612959i | \(0.789979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00752 | − | 3.47713i | 0.460557 | − | 0.797709i | −0.538431 | − | 0.842669i | \(-0.680983\pi\) |
0.998989 | + | 0.0449606i | \(0.0143162\pi\) | |||||||
\(20\) | 1.10479 | + | 1.91356i | 0.247039 | + | 0.427884i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.65263 | − | 2.86244i | 0.352342 | − | 0.610274i | ||||
\(23\) | 2.71830 | + | 4.70824i | 0.566806 | + | 0.981736i | 0.996879 | + | 0.0789424i | \(0.0251543\pi\) |
−0.430073 | + | 0.902794i | \(0.641512\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.48478 | − | 2.57171i | 0.296955 | − | 0.514342i | ||||
\(26\) | −0.923251 | + | 1.59912i | −0.181064 | + | 0.313613i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.40555 | − | 5.89858i | −0.632394 | − | 1.09534i | −0.987061 | − | 0.160346i | \(-0.948739\pi\) |
0.354667 | − | 0.934993i | \(-0.384594\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50584 | −0.450061 | −0.225031 | − | 0.974352i | \(-0.572248\pi\) | ||||
−0.225031 | + | 0.974352i | \(0.572248\pi\) | |||||||
\(32\) | −5.76965 | −1.01994 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.375279 | − | 0.650002i | −0.0643597 | − | 0.111474i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.709787 | − | 1.22939i | 0.116688 | − | 0.202110i | −0.801765 | − | 0.597639i | \(-0.796106\pi\) |
0.918453 | + | 0.395529i | \(0.129439\pi\) | |||||||
\(38\) | −1.34571 | + | 2.33083i | −0.218303 | + | 0.378111i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.69576 | − | 2.93714i | −0.268123 | − | 0.464403i | ||||
\(41\) | 0.124384 | − | 0.215440i | 0.0194256 | − | 0.0336460i | −0.856149 | − | 0.516729i | \(-0.827150\pi\) |
0.875575 | + | 0.483083i | \(0.160483\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.498313 | − | 0.863104i | −0.0759921 | − | 0.131622i | 0.825525 | − | 0.564365i | \(-0.190879\pi\) |
−0.901517 | + | 0.432743i | \(0.857546\pi\) | |||||||
\(44\) | 3.82296 | − | 6.62156i | 0.576333 | − | 0.998238i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.82217 | − | 3.15609i | −0.268664 | − | 0.465340i | ||||
\(47\) | −9.47579 | −1.38219 | −0.691093 | − | 0.722766i | \(-0.742871\pi\) | ||||
−0.691093 | + | 0.722766i | \(0.742871\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.995294 | + | 1.72390i | −0.140756 | + | 0.243796i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.13572 | + | 3.69917i | −0.296171 | + | 0.512983i | ||||
\(53\) | 0.410229 | + | 0.710537i | 0.0563493 | + | 0.0975998i | 0.892824 | − | 0.450406i | \(-0.148721\pi\) |
−0.836475 | + | 0.548005i | \(0.815387\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.02604 | 0.947392 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.28285 | + | 3.95401i | 0.299753 | + | 0.519187i | ||||
\(59\) | −6.58407 | −0.857173 | −0.428586 | − | 0.903501i | \(-0.640988\pi\) | ||||
−0.428586 | + | 0.903501i | \(0.640988\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0752645 | −0.00963663 | −0.00481831 | − | 0.999988i | \(-0.501534\pi\) | ||||
−0.00481831 | + | 0.999988i | \(0.501534\pi\) | |||||||
\(62\) | 1.67974 | 0.213328 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.855913 | 0.106989 | ||||||||
\(65\) | −3.92514 | −0.486854 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.5877 | −1.53783 | −0.768916 | − | 0.639350i | \(-0.779204\pi\) | ||||
−0.768916 | + | 0.639350i | \(0.779204\pi\) | |||||||
\(68\) | −0.868117 | − | 1.50362i | −0.105275 | − | 0.182341i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0804951 | −0.00955301 | −0.00477651 | − | 0.999989i | \(-0.501520\pi\) | ||||
−0.00477651 | + | 0.999989i | \(0.501520\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.34551 | − | 9.25869i | −0.625644 | − | 1.08365i | −0.988416 | − | 0.151769i | \(-0.951503\pi\) |
0.362772 | − | 0.931878i | \(-0.381830\pi\) | |||||||
\(74\) | −0.475793 | + | 0.824098i | −0.0553098 | + | 0.0957995i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.11297 | + | 5.39183i | −0.357083 | + | 0.618485i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.84491 | −0.207569 | −0.103785 | − | 0.994600i | \(-0.533095\pi\) | ||||
−0.103785 | + | 0.994600i | \(0.533095\pi\) | |||||||
\(80\) | −1.07286 | − | 1.85825i | −0.119950 | − | 0.207759i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.0833788 | + | 0.144416i | −0.00920765 | + | 0.0159481i | ||||
\(83\) | −7.23583 | − | 12.5328i | −0.794236 | − | 1.37566i | −0.923323 | − | 0.384023i | \(-0.874538\pi\) |
0.129088 | − | 0.991633i | \(-0.458795\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.797736 | − | 1.38172i | 0.0865266 | − | 0.149868i | ||||
\(86\) | 0.334036 | + | 0.578567i | 0.0360200 | + | 0.0623885i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.86792 | + | 10.1635i | −0.625522 | + | 1.08344i | ||||
\(89\) | 6.76292 | − | 11.7137i | 0.716868 | − | 1.24165i | −0.245366 | − | 0.969430i | \(-0.578908\pi\) |
0.962235 | − | 0.272222i | \(-0.0877584\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.21515 | − | 7.30085i | −0.439460 | − | 0.761167i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.35193 | 0.655152 | ||||||||
\(95\) | −5.72119 | −0.586982 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.70160 | − | 4.67930i | −0.274306 | − | 0.475111i | 0.695654 | − | 0.718377i | \(-0.255115\pi\) |
−0.969960 | + | 0.243266i | \(0.921781\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.30238 | + | 3.98783i | −0.230238 | + | 0.398783i | ||||
\(101\) | 2.56770 | − | 4.44739i | 0.255496 | − | 0.442531i | −0.709534 | − | 0.704671i | \(-0.751095\pi\) |
0.965030 | + | 0.262139i | \(0.0844280\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.10561 | − | 12.3073i | −0.700137 | − | 1.21267i | −0.968418 | − | 0.249332i | \(-0.919789\pi\) |
0.268282 | − | 0.963341i | \(-0.413544\pi\) | |||||||
\(104\) | 3.27814 | − | 5.67791i | 0.321448 | − | 0.556765i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.274990 | − | 0.476296i | −0.0267094 | − | 0.0462620i | ||||
\(107\) | −3.83015 | + | 6.63401i | −0.370274 | + | 0.641334i | −0.989608 | − | 0.143794i | \(-0.954070\pi\) |
0.619333 | + | 0.785128i | \(0.287403\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.849394 | − | 1.47119i | −0.0813572 | − | 0.140915i | 0.822476 | − | 0.568800i | \(-0.192592\pi\) |
−0.903833 | + | 0.427885i | \(0.859259\pi\) | |||||||
\(110\) | −4.70979 | −0.449061 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.300351 | − | 0.520224i | 0.0282547 | − | 0.0489385i | −0.851552 | − | 0.524270i | \(-0.824338\pi\) |
0.879807 | + | 0.475331i | \(0.157672\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.87341 | − | 6.70895i | 0.361198 | − | 0.625613i | ||||
\(116\) | 5.28083 | + | 9.14666i | 0.490312 | + | 0.849246i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.41352 | 0.406297 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.65626 | − | 11.5290i | −0.605115 | − | 1.04809i | ||||
\(122\) | 0.0504522 | 0.00456773 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.88569 | 0.348945 | ||||||||
\(125\) | −11.3561 | −1.01572 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.25977 | 0.644200 | 0.322100 | − | 0.946706i | \(-0.395611\pi\) | ||||
0.322100 | + | 0.946706i | \(0.395611\pi\) | |||||||
\(128\) | 10.9656 | 0.969227 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.63115 | 0.230767 | ||||||||
\(131\) | 10.2265 | + | 17.7128i | 0.893492 | + | 1.54757i | 0.835660 | + | 0.549248i | \(0.185086\pi\) |
0.0578326 | + | 0.998326i | \(0.481581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.43794 | 0.728927 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.33248 | + | 2.30793i | 0.114260 | + | 0.197903i | ||||
\(137\) | 6.10581 | − | 10.5756i | 0.521655 | − | 0.903532i | −0.478028 | − | 0.878345i | \(-0.658648\pi\) |
0.999683 | − | 0.0251879i | \(-0.00801840\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.24092 | − | 2.14933i | 0.105253 | − | 0.182304i | −0.808588 | − | 0.588375i | \(-0.799768\pi\) |
0.913842 | + | 0.406071i | \(0.133101\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.0539585 | 0.00452810 | ||||||||
\(143\) | 6.79117 | + | 11.7626i | 0.567906 | + | 0.983642i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.85269 | + | 8.40511i | −0.402994 | + | 0.698006i | ||||
\(146\) | 3.58327 | + | 6.20640i | 0.296553 | + | 0.513645i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.10063 | + | 1.90635i | −0.0904715 | + | 0.156701i | ||||
\(149\) | −4.27797 | − | 7.40966i | −0.350465 | − | 0.607023i | 0.635866 | − | 0.771799i | \(-0.280643\pi\) |
−0.986331 | + | 0.164777i | \(0.947310\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.82962 | − | 15.2933i | 0.718544 | − | 1.24455i | −0.243033 | − | 0.970018i | \(-0.578142\pi\) |
0.961577 | − | 0.274537i | \(-0.0885244\pi\) | |||||||
\(152\) | 4.77814 | − | 8.27599i | 0.387559 | − | 0.671271i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.78533 | + | 3.09228i | 0.143401 | + | 0.248378i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.32149 | −0.504510 | −0.252255 | − | 0.967661i | \(-0.581172\pi\) | ||||
−0.252255 | + | 0.967661i | \(0.581172\pi\) | |||||||
\(158\) | 1.23671 | 0.0983871 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.11070 | + | 7.11993i | 0.324979 | + | 0.562880i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.01134 | + | 6.94784i | −0.314192 | + | 0.544197i | −0.979265 | − | 0.202581i | \(-0.935067\pi\) |
0.665073 | + | 0.746778i | \(0.268400\pi\) | |||||||
\(164\) | −0.192877 | + | 0.334073i | −0.0150612 | + | 0.0260867i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.85041 | + | 8.40116i | 0.376465 | + | 0.652057i | ||||
\(167\) | 1.06038 | − | 1.83663i | 0.0820545 | − | 0.142123i | −0.822078 | − | 0.569375i | \(-0.807185\pi\) |
0.904132 | + | 0.427253i | \(0.140518\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.70608 | + | 4.68706i | 0.208160 | + | 0.360543i | ||||
\(170\) | −0.534749 | + | 0.926212i | −0.0410133 | + | 0.0710372i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.772712 | + | 1.33838i | 0.0589187 | + | 0.102050i | ||||
\(173\) | −18.2881 | −1.39042 | −0.695208 | − | 0.718808i | \(-0.744688\pi\) | ||||
−0.695208 | + | 0.718808i | \(0.744688\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.71247 | + | 6.43018i | −0.279838 | + | 0.484693i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.53341 | + | 7.85209i | −0.339793 | + | 0.588539i | ||||
\(179\) | −3.81276 | − | 6.60389i | −0.284979 | − | 0.493598i | 0.687625 | − | 0.726066i | \(-0.258653\pi\) |
−0.972604 | + | 0.232468i | \(0.925320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.5305 | −1.15438 | −0.577188 | − | 0.816611i | \(-0.695850\pi\) | ||||
−0.577188 | + | 0.816611i | \(0.695850\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.46989 | + | 11.2062i | 0.476967 | + | 0.826130i | ||||
\(185\) | −2.02280 | −0.148719 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.52088 | −0.403727 | ||||||||
\(188\) | 14.6937 | 1.07165 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.83510 | 0.278227 | ||||||||
\(191\) | −14.8325 | −1.07324 | −0.536620 | − | 0.843824i | \(-0.680299\pi\) | ||||
−0.536620 | + | 0.843824i | \(0.680299\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.5677 | 1.19257 | 0.596286 | − | 0.802772i | \(-0.296642\pi\) | ||||
0.596286 | + | 0.802772i | \(0.296642\pi\) | |||||||
\(194\) | 1.81097 | + | 3.13669i | 0.130020 | + | 0.225201i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.03740 | 0.287653 | 0.143826 | − | 0.989603i | \(-0.454059\pi\) | ||||
0.143826 | + | 0.989603i | \(0.454059\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.6407 | + | 21.8943i | 0.896076 | + | 1.55205i | 0.832468 | + | 0.554074i | \(0.186927\pi\) |
0.0636081 | + | 0.997975i | \(0.479739\pi\) | |||||||
\(200\) | 3.53395 | − | 6.12097i | 0.249888 | − | 0.432818i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.72121 | + | 2.98123i | −0.121104 | + | 0.209758i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.354480 | −0.0247579 | ||||||||
\(206\) | 4.76312 | + | 8.24997i | 0.331862 | + | 0.574803i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.07399 | − | 3.59226i | 0.143805 | − | 0.249078i | ||||
\(209\) | 9.89864 | + | 17.1449i | 0.684703 | + | 1.18594i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.76246 | + | 6.51678i | −0.259019 | + | 0.448634i | −0.965979 | − | 0.258619i | \(-0.916732\pi\) |
0.706961 | + | 0.707253i | \(0.250066\pi\) | |||||||
\(212\) | −0.636123 | − | 1.10180i | −0.0436891 | − | 0.0756718i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.56747 | − | 4.44699i | 0.175509 | − | 0.303990i | ||||
\(215\) | −0.710065 | + | 1.22987i | −0.0484261 | + | 0.0838764i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.569377 | + | 0.986190i | 0.0385631 | + | 0.0667932i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.8950 | −0.734538 | ||||||||
\(221\) | 3.08427 | 0.207471 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.49230 | − | 11.2450i | −0.434757 | − | 0.753020i | 0.562519 | − | 0.826784i | \(-0.309832\pi\) |
−0.997276 | + | 0.0737638i | \(0.976499\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.201335 | + | 0.348723i | −0.0133926 | + | 0.0231967i | ||||
\(227\) | 14.4832 | − | 25.0857i | 0.961286 | − | 1.66500i | 0.242009 | − | 0.970274i | \(-0.422194\pi\) |
0.719277 | − | 0.694723i | \(-0.244473\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.71790 | + | 13.3678i | 0.510013 | + | 0.883369i | 0.999933 | + | 0.0116012i | \(0.00369285\pi\) |
−0.489919 | + | 0.871768i | \(0.662974\pi\) | |||||||
\(230\) | −2.59648 | + | 4.49723i | −0.171207 | + | 0.296538i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.10561 | − | 14.0393i | −0.532159 | − | 0.921727i | ||||
\(233\) | 2.47324 | − | 4.28378i | 0.162027 | − | 0.280640i | −0.773568 | − | 0.633713i | \(-0.781530\pi\) |
0.935596 | + | 0.353073i | \(0.114863\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.75121 | + | 11.6934i | 0.440400 | + | 0.762795i | ||||
\(236\) | 10.2096 | 0.664589 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.51732 | + | 11.2883i | −0.421571 | + | 0.730182i | −0.996093 | − | 0.0883069i | \(-0.971854\pi\) |
0.574523 | + | 0.818489i | \(0.305188\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.29123 | − | 12.6288i | 0.469670 | − | 0.813492i | −0.529729 | − | 0.848167i | \(-0.677706\pi\) |
0.999399 | + | 0.0346754i | \(0.0110397\pi\) | |||||||
\(242\) | 4.46191 | + | 7.72826i | 0.286823 | + | 0.496791i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.116709 | 0.00747154 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.52993 | − | 9.57812i | −0.351861 | − | 0.609441i | ||||
\(248\) | −5.96419 | −0.378726 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.61238 | 0.481449 | ||||||||
\(251\) | −14.0715 | −0.888187 | −0.444094 | − | 0.895980i | \(-0.646474\pi\) | ||||
−0.444094 | + | 0.895980i | \(0.646474\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.8067 | −1.68532 | ||||||||
\(254\) | −4.86646 | −0.305349 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.06240 | −0.566400 | ||||||||
\(257\) | 4.18108 | + | 7.24184i | 0.260808 | + | 0.451733i | 0.966457 | − | 0.256829i | \(-0.0826776\pi\) |
−0.705649 | + | 0.708562i | \(0.749344\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.08653 | 0.377471 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.85515 | − | 11.8735i | −0.423512 | − | 0.733545i | ||||
\(263\) | 1.63533 | − | 2.83247i | 0.100839 | − | 0.174658i | −0.811192 | − | 0.584780i | \(-0.801181\pi\) |
0.912030 | + | 0.410122i | \(0.134514\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.584551 | − | 1.01247i | 0.0359087 | − | 0.0621956i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 19.5192 | 1.19232 | ||||||||
\(269\) | −7.69349 | − | 13.3255i | −0.469081 | − | 0.812471i | 0.530295 | − | 0.847813i | \(-0.322081\pi\) |
−0.999375 | + | 0.0353420i | \(0.988748\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.06308 | + | 7.03747i | −0.246815 | + | 0.427496i | −0.962640 | − | 0.270783i | \(-0.912717\pi\) |
0.715825 | + | 0.698279i | \(0.246051\pi\) | |||||||
\(272\) | 0.843026 | + | 1.46016i | 0.0511160 | + | 0.0885355i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.09293 | + | 7.08915i | −0.247263 | + | 0.428271i | ||||
\(275\) | 7.32110 | + | 12.6805i | 0.441479 | + | 0.764664i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.42287 | + | 11.1247i | −0.385913 | + | 0.668421i | −0.991895 | − | 0.127057i | \(-0.959447\pi\) |
0.605982 | + | 0.795478i | \(0.292780\pi\) | |||||||
\(278\) | −0.831826 | + | 1.44077i | −0.0498896 | + | 0.0864114i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.724081 | + | 1.25415i | 0.0431951 | + | 0.0748161i | 0.886815 | − | 0.462125i | \(-0.152913\pi\) |
−0.843620 | + | 0.536941i | \(0.819580\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.4385 | 1.03661 | 0.518306 | − | 0.855195i | \(-0.326563\pi\) | ||||
0.518306 | + | 0.855195i | \(0.326563\pi\) | |||||||
\(284\) | 0.124820 | 0.00740671 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.55234 | − | 7.88489i | −0.269186 | − | 0.466243i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.87316 | − | 13.6367i | 0.463127 | − | 0.802160i | ||||
\(290\) | 3.25292 | − | 5.63422i | 0.191018 | − | 0.330853i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.28903 | + | 14.3570i | 0.485079 | + | 0.840181i | ||||
\(293\) | −0.900048 | + | 1.55893i | −0.0525814 | + | 0.0910736i | −0.891118 | − | 0.453772i | \(-0.850078\pi\) |
0.838537 | + | 0.544845i | \(0.183412\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.69094 | + | 8.12495i | 0.273117 | + | 0.473053i | ||||
\(296\) | 1.68938 | − | 2.92609i | 0.0981931 | − | 0.170075i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.86766 | + | 4.96693i | 0.166119 | + | 0.287727i | ||||
\(299\) | 14.9757 | 0.866068 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.91878 | + | 10.2516i | −0.340588 | + | 0.589915i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.02300 | − | 5.23599i | 0.173381 | − | 0.300305i | ||||
\(305\) | 0.0536236 | + | 0.0928787i | 0.00307048 | + | 0.00531822i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.06478 | −0.0607699 | −0.0303850 | − | 0.999538i | \(-0.509673\pi\) | ||||
−0.0303850 | + | 0.999538i | \(0.509673\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.19676 | − | 2.07286i | −0.0679717 | − | 0.117730i | ||||
\(311\) | −16.9293 | −0.959970 | −0.479985 | − | 0.877277i | \(-0.659358\pi\) | ||||
−0.479985 | + | 0.877277i | \(0.659358\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.27856 | 0.467932 | 0.233966 | − | 0.972245i | \(-0.424830\pi\) | ||||
0.233966 | + | 0.972245i | \(0.424830\pi\) | |||||||
\(314\) | 4.23750 | 0.239136 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.86082 | 0.160934 | ||||||||
\(317\) | −6.54741 | −0.367739 | −0.183870 | − | 0.982951i | \(-0.558862\pi\) | ||||
−0.183870 | + | 0.982951i | \(0.558862\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 33.5840 | 1.88034 | ||||||||
\(320\) | −0.609811 | − | 1.05622i | −0.0340895 | − | 0.0590447i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.49556 | 0.250140 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.08997 | − | 7.08404i | −0.226871 | − | 0.392952i | ||||
\(326\) | 2.68893 | − | 4.65736i | 0.148926 | − | 0.257947i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.296049 | − | 0.512773i | 0.0163466 | − | 0.0283131i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.7258 | −1.46899 | −0.734493 | − | 0.678617i | \(-0.762580\pi\) | ||||
−0.734493 | + | 0.678617i | \(0.762580\pi\) | |||||||
\(332\) | 11.2203 | + | 19.4341i | 0.615792 | + | 1.06658i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.710806 | + | 1.23115i | −0.0388936 | + | 0.0673657i | ||||
\(335\) | 8.96834 | + | 15.5336i | 0.489993 | + | 0.848692i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.76164 | + | 8.24740i | −0.259383 | + | 0.449264i | −0.966077 | − | 0.258255i | \(-0.916853\pi\) |
0.706694 | + | 0.707520i | \(0.250186\pi\) | |||||||
\(338\) | −1.81397 | − | 3.14189i | −0.0986670 | − | 0.170896i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.23701 | + | 2.14257i | −0.0670864 | + | 0.116197i | ||||
\(341\) | 6.17786 | − | 10.7004i | 0.334550 | − | 0.579457i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.18605 | − | 2.05429i | −0.0639473 | − | 0.110760i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.2591 | 0.659053 | ||||||||
\(347\) | 18.7031 | 1.00404 | 0.502018 | − | 0.864857i | \(-0.332591\pi\) | ||||
0.502018 | + | 0.864857i | \(0.332591\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.0542 | + | 26.0747i | 0.805834 | + | 1.39574i | 0.915727 | + | 0.401801i | \(0.131616\pi\) |
−0.109893 | + | 0.993943i | \(0.535051\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14.2244 | − | 24.6374i | 0.758164 | − | 1.31318i | ||||
\(353\) | −3.12966 | + | 5.42074i | −0.166575 | + | 0.288517i | −0.937214 | − | 0.348756i | \(-0.886604\pi\) |
0.770638 | + | 0.637273i | \(0.219938\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0573502 | + | 0.0993335i | 0.00304383 | + | 0.00527208i | ||||
\(356\) | −10.4870 | + | 18.1639i | −0.555807 | + | 0.962686i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.55582 | + | 4.42680i | 0.135079 | + | 0.233964i | ||||
\(359\) | 5.09755 | − | 8.82921i | 0.269038 | − | 0.465988i | −0.699575 | − | 0.714559i | \(-0.746628\pi\) |
0.968614 | + | 0.248571i | \(0.0799608\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.43970 | + | 2.49364i | 0.0757739 | + | 0.131244i | ||||
\(362\) | 10.4106 | 0.547171 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.61701 | + | 13.1931i | −0.398693 | + | 0.690556i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.3278 | + | 24.8165i | −0.747906 | + | 1.29541i | 0.200918 | + | 0.979608i | \(0.435608\pi\) |
−0.948824 | + | 0.315804i | \(0.897726\pi\) | |||||||
\(368\) | 4.09332 | + | 7.08984i | 0.213379 | + | 0.369584i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.35595 | 0.0704926 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.03670 | + | 13.9200i | 0.416124 | + | 0.720749i | 0.995546 | − | 0.0942796i | \(-0.0300548\pi\) |
−0.579421 | + | 0.815028i | \(0.696721\pi\) | |||||||
\(374\) | 3.70083 | 0.191365 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −22.5535 | −1.16311 | ||||||||
\(377\) | −18.7619 | −0.966286 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.01893 | −0.0523388 | −0.0261694 | − | 0.999658i | \(-0.508331\pi\) | ||||
−0.0261694 | + | 0.999658i | \(0.508331\pi\) | |||||||
\(380\) | 8.87158 | 0.455103 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.94270 | 0.508713 | ||||||||
\(383\) | 5.79327 | + | 10.0342i | 0.296022 | + | 0.512725i | 0.975222 | − | 0.221228i | \(-0.0710065\pi\) |
−0.679200 | + | 0.733953i | \(0.737673\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.1059 | −0.565275 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.18924 | + | 7.25598i | 0.212677 | + | 0.368367i | ||||
\(389\) | 8.90675 | − | 15.4270i | 0.451590 | − | 0.782178i | −0.546895 | − | 0.837201i | \(-0.684190\pi\) |
0.998485 | + | 0.0550239i | \(0.0175235\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.04363 | + | 5.27172i | −0.153923 | + | 0.266602i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.70640 | −0.136346 | ||||||||
\(395\) | 1.31444 | + | 2.27668i | 0.0661369 | + | 0.114552i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.54229 | − | 11.3316i | 0.328348 | − | 0.568715i | −0.653836 | − | 0.756636i | \(-0.726841\pi\) |
0.982184 | + | 0.187921i | \(0.0601748\pi\) | |||||||
\(398\) | −8.47348 | − | 14.6765i | −0.424737 | − | 0.735666i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.23583 | − | 3.87257i | 0.111792 | − | 0.193629i | ||||
\(401\) | 7.05165 | + | 12.2138i | 0.352143 | + | 0.609929i | 0.986625 | − | 0.163009i | \(-0.0521199\pi\) |
−0.634482 | + | 0.772938i | \(0.718787\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.45129 | + | 5.97782i | −0.171921 | + | 0.297776i | ||||
\(404\) | −3.98161 | + | 6.89636i | −0.198093 | + | 0.343107i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.49980 | + | 6.06183i | 0.173479 | + | 0.300474i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.64599 | 0.130836 | 0.0654179 | − | 0.997858i | \(-0.479162\pi\) | ||||
0.0654179 | + | 0.997858i | \(0.479162\pi\) | |||||||
\(410\) | 0.237619 | 0.0117352 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.0183 | + | 19.0843i | 0.542835 | + | 0.940217i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.3106 | + | 17.8585i | −0.506128 | + | 0.876639i | ||||
\(416\) | −7.94655 | + | 13.7638i | −0.389612 | + | 0.674827i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.63538 | − | 11.4928i | −0.324547 | − | 0.562132i | ||||
\(419\) | 16.7567 | − | 29.0235i | 0.818619 | − | 1.41789i | −0.0880816 | − | 0.996113i | \(-0.528074\pi\) |
0.906700 | − | 0.421776i | \(-0.138593\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.41950 | − | 4.19071i | −0.117919 | − | 0.204242i | 0.801024 | − | 0.598633i | \(-0.204289\pi\) |
−0.918943 | + | 0.394390i | \(0.870956\pi\) | |||||||
\(422\) | 2.52210 | − | 4.36841i | 0.122774 | − | 0.212651i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.976394 | + | 1.69116i | 0.0474179 | + | 0.0821302i | ||||
\(425\) | 3.32495 | 0.161284 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.93923 | − | 10.2871i | 0.287084 | − | 0.497244i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.475980 | − | 0.824422i | 0.0229538 | − | 0.0397571i | ||||
\(431\) | −17.6643 | − | 30.5954i | −0.850858 | − | 1.47373i | −0.880435 | − | 0.474166i | \(-0.842749\pi\) |
0.0295774 | − | 0.999562i | \(-0.490584\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.47404 | −0.263066 | −0.131533 | − | 0.991312i | \(-0.541990\pi\) | ||||
−0.131533 | + | 0.991312i | \(0.541990\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.31712 | + | 2.28131i | 0.0630785 | + | 0.109255i | ||||
\(437\) | 21.8282 | 1.04419 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.39812 | −0.305365 | −0.152683 | − | 0.988275i | \(-0.548791\pi\) | ||||
−0.152683 | + | 0.988275i | \(0.548791\pi\) | |||||||
\(440\) | 16.7228 | 0.797229 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.06749 | −0.0983404 | ||||||||
\(443\) | 6.38682 | 0.303447 | 0.151723 | − | 0.988423i | \(-0.451518\pi\) | ||||
0.151723 | + | 0.988423i | \(0.451518\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.2735 | −0.913650 | ||||||||
\(446\) | 4.35200 | + | 7.53789i | 0.206073 | + | 0.356929i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.7460 | 0.554327 | 0.277163 | − | 0.960823i | \(-0.410606\pi\) | ||||
0.277163 | + | 0.960823i | \(0.410606\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.613311 | + | 1.06229i | 0.0288797 | + | 0.0500210i | ||||
\(452\) | −0.465741 | + | 0.806687i | −0.0219066 | + | 0.0379434i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.70859 | + | 16.8158i | −0.455647 | + | 0.789203i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.5224 | 0.492217 | 0.246108 | − | 0.969242i | \(-0.420848\pi\) | ||||
0.246108 | + | 0.969242i | \(0.420848\pi\) | |||||||
\(458\) | −5.17356 | − | 8.96087i | −0.241745 | − | 0.418714i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.00633 | + | 10.4033i | −0.280046 | + | 0.485055i | ||||
\(461\) | −3.54278 | − | 6.13627i | −0.165004 | − | 0.285794i | 0.771653 | − | 0.636044i | \(-0.219430\pi\) |
−0.936657 | + | 0.350249i | \(0.886097\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.3760 | − | 28.3641i | 0.761059 | − | 1.31819i | −0.181246 | − | 0.983438i | \(-0.558013\pi\) |
0.942305 | − | 0.334755i | \(-0.108654\pi\) | |||||||
\(464\) | −5.12820 | − | 8.88230i | −0.238071 | − | 0.412350i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.65789 | + | 2.87156i | −0.0768004 | + | 0.133022i | ||||
\(467\) | 1.96216 | − | 3.39856i | 0.0907978 | − | 0.157266i | −0.817049 | − | 0.576568i | \(-0.804392\pi\) |
0.907847 | + | 0.419301i | \(0.137725\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.52555 | − | 7.83849i | −0.208748 | − | 0.361563i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.6709 | −0.721310 | ||||||||
\(473\) | 4.91414 | 0.225952 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.96145 | − | 10.3255i | −0.273530 | − | 0.473768i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.36878 | − | 7.56694i | 0.199823 | − | 0.346104i | ||||
\(479\) | −8.04324 | + | 13.9313i | −0.367505 | + | 0.636537i | −0.989175 | − | 0.146742i | \(-0.953121\pi\) |
0.621670 | + | 0.783279i | \(0.286455\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.95518 | − | 3.38647i | −0.0891486 | − | 0.154410i | ||||
\(482\) | −4.88755 | + | 8.46549i | −0.222622 | + | 0.385592i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.3216 | + | 17.8775i | 0.469162 | + | 0.812612i | ||||
\(485\) | −3.84961 | + | 6.66771i | −0.174802 | + | 0.302765i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.75172 | − | 3.03407i | −0.0793781 | − | 0.137487i | 0.823604 | − | 0.567166i | \(-0.191960\pi\) |
−0.902982 | + | 0.429679i | \(0.858627\pi\) | |||||||
\(488\) | −0.179138 | −0.00810921 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.5546 | − | 35.6017i | 0.927618 | − | 1.60668i | 0.140321 | − | 0.990106i | \(-0.455186\pi\) |
0.787296 | − | 0.616575i | \(-0.211480\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.81312 | − | 6.60452i | 0.171734 | − | 0.297452i | ||||
\(494\) | 3.70689 | + | 6.42053i | 0.166781 | + | 0.288873i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.77338 | −0.169430 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.91486 | − | 10.2448i | −0.264785 | − | 0.458622i | 0.702722 | − | 0.711465i | \(-0.251968\pi\) |
−0.967507 | + | 0.252843i | \(0.918634\pi\) | |||||||
\(500\) | 17.6094 | 0.787517 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.43261 | 0.420998 | ||||||||
\(503\) | 21.8595 | 0.974665 | 0.487332 | − | 0.873217i | \(-0.337970\pi\) | ||||
0.487332 | + | 0.873217i | \(0.337970\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.31762 | −0.325630 | ||||||||
\(506\) | 17.9694 | 0.798837 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.2574 | −0.499466 | ||||||||
\(509\) | −8.44831 | − | 14.6329i | −0.374465 | − | 0.648592i | 0.615782 | − | 0.787917i | \(-0.288840\pi\) |
−0.990247 | + | 0.139324i | \(0.955507\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −15.8563 | −0.700756 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.80271 | − | 4.85444i | −0.123622 | − | 0.214120i | ||||
\(515\) | −10.1250 | + | 17.5371i | −0.446163 | + | 0.772777i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.3615 | − | 40.4633i | 1.02744 | − | 1.77957i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.34230 | −0.409687 | ||||||||
\(521\) | −17.2466 | − | 29.8720i | −0.755587 | − | 1.30872i | −0.945082 | − | 0.326834i | \(-0.894018\pi\) |
0.189495 | − | 0.981882i | \(-0.439315\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.995615 | + | 1.72445i | −0.0435352 | + | 0.0754051i | −0.886972 | − | 0.461823i | \(-0.847195\pi\) |
0.843437 | + | 0.537229i | \(0.180529\pi\) | |||||||
\(524\) | −15.8577 | − | 27.4664i | −0.692749 | − | 1.19988i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.09622 | + | 1.89870i | −0.0477972 | + | 0.0827873i | ||||
\(527\) | −1.40287 | − | 2.42983i | −0.0611098 | − | 0.105845i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.27836 | + | 5.67829i | −0.142538 | + | 0.246882i | ||||
\(530\) | −0.391843 | + | 0.678693i | −0.0170206 | + | 0.0294805i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.342629 | − | 0.593452i | −0.0148409 | − | 0.0257052i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.9154 | 0.471916 | ||||||||
\(536\) | −29.9602 | −1.29408 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.15720 | + | 8.93253i | 0.222343 | + | 0.385109i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0681 | + | 26.0988i | −0.647830 | + | 1.12207i | 0.335810 | + | 0.941930i | \(0.390990\pi\) |
−0.983640 | + | 0.180145i | \(0.942343\pi\) | |||||||
\(542\) | 2.72362 | − | 4.71745i | 0.116989 | − | 0.202632i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.23008 | − | 5.59466i | −0.138488 | − | 0.239869i | ||||
\(545\) | −1.21033 | + | 2.09636i | −0.0518450 | + | 0.0897982i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.68070 | + | 13.3034i | 0.328403 | + | 0.568810i | 0.982195 | − | 0.187864i | \(-0.0601563\pi\) |
−0.653792 | + | 0.756674i | \(0.726823\pi\) | |||||||
\(548\) | −9.46800 | + | 16.3991i | −0.404453 | + | 0.700533i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.90757 | − | 8.50016i | −0.209260 | − | 0.362448i | ||||
\(551\) | −27.3469 | −1.16502 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.30546 | − | 7.45728i | 0.182921 | − | 0.316829i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.92423 | + | 3.33287i | −0.0816056 | + | 0.141345i | ||||
\(557\) | 11.6412 | + | 20.1631i | 0.493252 | + | 0.854338i | 0.999970 | − | 0.00777438i | \(-0.00247469\pi\) |
−0.506718 | + | 0.862112i | \(0.669141\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.74531 | −0.116114 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.485375 | − | 0.840695i | −0.0204743 | − | 0.0354626i | ||||
\(563\) | 4.55885 | 0.192133 | 0.0960663 | − | 0.995375i | \(-0.469374\pi\) | ||||
0.0960663 | + | 0.995375i | \(0.469374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.855964 | −0.0360107 | ||||||||
\(566\) | −11.6896 | −0.491351 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.191588 | −0.00803885 | ||||||||
\(569\) | −18.1995 | −0.762963 | −0.381482 | − | 0.924376i | \(-0.624586\pi\) | ||||
−0.381482 | + | 0.924376i | \(0.624586\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.0455 | −0.713332 | −0.356666 | − | 0.934232i | \(-0.616087\pi\) | ||||
−0.356666 | + | 0.934232i | \(0.616087\pi\) | |||||||
\(572\) | −10.5307 | − | 18.2398i | −0.440313 | − | 0.762644i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.1443 | 0.673264 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.70473 | + | 9.88088i | 0.237491 | + | 0.411346i | 0.959994 | − | 0.280022i | \(-0.0903417\pi\) |
−0.722503 | + | 0.691368i | \(0.757008\pi\) | |||||||
\(578\) | −5.27764 | + | 9.14113i | −0.219521 | + | 0.380221i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.52485 | − | 13.0334i | 0.312452 | − | 0.541183i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.04549 | −0.167547 | ||||||||
\(584\) | −12.7229 | − | 22.0368i | −0.526479 | − | 0.911889i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.603332 | − | 1.04500i | 0.0249234 | − | 0.0431686i | ||||
\(587\) | 2.52544 | + | 4.37420i | 0.104236 | + | 0.180543i | 0.913426 | − | 0.407005i | \(-0.133427\pi\) |
−0.809190 | + | 0.587548i | \(0.800094\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.03052 | + | 8.71312i | −0.207279 | + | 0.359018i | ||||
\(590\) | −3.14449 | − | 5.44642i | −0.129457 | − | 0.224226i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.06882 | − | 1.85126i | 0.0439283 | − | 0.0760861i | ||||
\(593\) | −9.98892 | + | 17.3013i | −0.410196 | + | 0.710480i | −0.994911 | − | 0.100759i | \(-0.967873\pi\) |
0.584715 | + | 0.811239i | \(0.301206\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.63365 | + | 11.4898i | 0.271725 | + | 0.470641i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.0387 | −0.410513 | ||||||||
\(599\) | −4.39321 | −0.179502 | −0.0897508 | − | 0.995964i | \(-0.528607\pi\) | ||||
−0.0897508 | + | 0.995964i | \(0.528607\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1778 | − | 21.0926i | −0.496743 | − | 0.860385i | 0.503250 | − | 0.864141i | \(-0.332138\pi\) |
−0.999993 | + | 0.00375637i | \(0.998804\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.6917 | + | 23.7147i | −0.557107 | + | 0.964937i | ||||
\(605\) | −9.48476 | + | 16.4281i | −0.385610 | + | 0.667897i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.56281 | + | 11.3671i | 0.266376 | + | 0.461377i | 0.967923 | − | 0.251246i | \(-0.0808403\pi\) |
−0.701547 | + | 0.712623i | \(0.747507\pi\) | |||||||
\(608\) | −11.5827 | + | 20.0618i | −0.469741 | + | 0.813615i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.0359456 | − | 0.0622597i | −0.00145540 | − | 0.00252082i | ||||
\(611\) | −13.0510 | + | 22.6051i | −0.527988 | + | 0.914502i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.2403 | − | 40.2534i | −0.938667 | − | 1.62582i | −0.767960 | − | 0.640497i | \(-0.778728\pi\) |
−0.170707 | − | 0.985322i | \(-0.554605\pi\) | |||||||
\(614\) | 0.713754 | 0.0288048 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.1948 | + | 24.5862i | −0.571463 | + | 0.989803i | 0.424953 | + | 0.905215i | \(0.360291\pi\) |
−0.996416 | + | 0.0845873i | \(0.973043\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.9606 | − | 27.6446i | 0.641511 | − | 1.11113i | −0.343585 | − | 0.939122i | \(-0.611641\pi\) |
0.985096 | − | 0.172008i | \(-0.0550254\pi\) | |||||||
\(620\) | −2.76843 | − | 4.79506i | −0.111183 | − | 0.192574i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.3482 | 0.455023 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.666993 | + | 1.15527i | 0.0266797 | + | 0.0462106i | ||||
\(626\) | −5.54939 | −0.221798 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.80244 | 0.391160 | ||||||||
\(629\) | 1.58947 | 0.0633762 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.7184 | 1.54135 | 0.770677 | − | 0.637226i | \(-0.219918\pi\) | ||||
0.770677 | + | 0.637226i | \(0.219918\pi\) | |||||||
\(632\) | −4.39112 | −0.174669 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.38895 | 0.174307 | ||||||||
\(635\) | −5.17236 | − | 8.95878i | −0.205259 | − | 0.355519i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −22.5124 | −0.891276 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.81261 | − | 13.5318i | −0.308821 | − | 0.534893i | ||||
\(641\) | −20.2001 | + | 34.9875i | −0.797854 | + | 1.38192i | 0.123157 | + | 0.992387i | \(0.460698\pi\) |
−0.921011 | + | 0.389537i | \(0.872635\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.27355 | + | 10.8661i | −0.247405 | + | 0.428517i | −0.962805 | − | 0.270198i | \(-0.912911\pi\) |
0.715400 | + | 0.698715i | \(0.246244\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.01352 | −0.118565 | ||||||||
\(647\) | 17.2774 | + | 29.9253i | 0.679245 | + | 1.17649i | 0.975209 | + | 0.221287i | \(0.0710258\pi\) |
−0.295964 | + | 0.955199i | \(0.595641\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.2323 | − | 28.1151i | 0.637173 | − | 1.10362i | ||||
\(650\) | 2.74164 | + | 4.74866i | 0.107536 | + | 0.186258i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.22019 | − | 10.7737i | 0.243602 | − | 0.421930i | ||||
\(653\) | −11.1472 | − | 19.3075i | −0.436223 | − | 0.755560i | 0.561172 | − | 0.827699i | \(-0.310351\pi\) |
−0.997395 | + | 0.0721392i | \(0.977017\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.5721 | − | 25.2396i | 0.569379 | − | 0.986194i | ||||
\(656\) | 0.187302 | − | 0.324417i | 0.00731293 | − | 0.0126664i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.57493 | − | 6.19196i | −0.139259 | − | 0.241204i | 0.787957 | − | 0.615730i | \(-0.211139\pi\) |
−0.927217 | + | 0.374526i | \(0.877806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.9060 | −1.66885 | −0.834425 | − | 0.551122i | \(-0.814200\pi\) | ||||
−0.834425 | + | 0.551122i | \(0.814200\pi\) | |||||||
\(662\) | 17.9152 | 0.696294 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17.2221 | − | 29.8296i | −0.668349 | − | 1.15761i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.5146 | − | 32.0683i | 0.716889 | − | 1.24169i | ||||
\(668\) | −1.64428 | + | 2.84798i | −0.0636191 | + | 0.110192i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.01177 | − | 10.4127i | −0.232255 | − | 0.402277i | ||||
\(671\) | 0.185556 | − | 0.321392i | 0.00716331 | − | 0.0124072i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.8270 | − | 32.6094i | −0.725729 | − | 1.25700i | −0.958673 | − | 0.284510i | \(-0.908169\pi\) |
0.232944 | − | 0.972490i | \(-0.425164\pi\) | |||||||
\(674\) | 3.19188 | − | 5.52850i | 0.122947 | − | 0.212950i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.19619 | − | 7.26801i | −0.161392 | − | 0.279539i | ||||
\(677\) | −26.3616 | −1.01316 | −0.506580 | − | 0.862193i | \(-0.669090\pi\) | ||||
−0.506580 | + | 0.862193i | \(0.669090\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.89871 | − | 3.28866i | 0.0728121 | − | 0.126114i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.14122 | + | 7.17280i | −0.158575 | + | 0.274661i | ||||
\(683\) | −1.96588 | − | 3.40500i | −0.0752222 | − | 0.130289i | 0.825961 | − | 0.563728i | \(-0.190633\pi\) |
−0.901183 | + | 0.433439i | \(0.857300\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.4008 | −0.664850 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.750378 | − | 1.29969i | −0.0286079 | − | 0.0495503i | ||||
\(689\) | 2.26004 | 0.0861006 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.9010 | −0.757072 | −0.378536 | − | 0.925587i | \(-0.623572\pi\) | ||||
−0.378536 | + | 0.925587i | \(0.623572\pi\) | |||||||
\(692\) | 28.3585 | 1.07803 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.5373 | −0.475910 | ||||||||
\(695\) | −3.53645 | −0.134145 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.278541 | 0.0105505 | ||||||||
\(698\) | −10.0913 | − | 17.4787i | −0.381963 | − | 0.661579i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.7908 | −1.65396 | −0.826979 | − | 0.562234i | \(-0.809942\pi\) | ||||
−0.826979 | + | 0.562234i | \(0.809942\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.84983 | − | 4.93604i | −0.107483 | − | 0.186166i | ||||
\(704\) | −2.11016 | + | 3.65490i | −0.0795295 | + | 0.137749i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.09792 | − | 3.63370i | 0.0789561 | − | 0.136756i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.6344 | 1.67628 | 0.838139 | − | 0.545457i | \(-0.183644\pi\) | ||||
0.838139 | + | 0.545457i | \(0.183644\pi\) | |||||||
\(710\) | −0.0384437 | − | 0.0665865i | −0.00144277 | − | 0.00249895i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.0966 | − | 27.8801i | 0.603244 | − | 1.04485i | ||||
\(713\) | −6.81163 | − | 11.7981i | −0.255097 | − | 0.441842i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.67699 | − | 16.7610i | 0.361899 | − | 0.626827i | ||||
\(716\) | 5.91227 | + | 10.2403i | 0.220952 | + | 0.382700i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.41705 | + | 5.91851i | −0.127523 | + | 0.220877i | ||||
\(719\) | −19.5096 | + | 33.7917i | −0.727586 | + | 1.26022i | 0.230315 | + | 0.973116i | \(0.426024\pi\) |
−0.957901 | + | 0.287100i | \(0.907309\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.965081 | − | 1.67157i | −0.0359166 | − | 0.0622094i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 24.0825 | 0.895019 | ||||||||
\(725\) | −20.2259 | −0.751171 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.2554 | + | 19.4949i | 0.417439 | + | 0.723025i | 0.995681 | − | 0.0928402i | \(-0.0295946\pi\) |
−0.578242 | + | 0.815865i | \(0.696261\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.10593 | − | 8.84373i | 0.188979 | − | 0.327321i | ||||
\(731\) | 0.557951 | − | 0.966399i | 0.0206366 | − | 0.0357436i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.448519 | − | 0.776858i | −0.0165664 | − | 0.0286939i | 0.857623 | − | 0.514278i | \(-0.171940\pi\) |
−0.874190 | + | 0.485584i | \(0.838607\pi\) | |||||||
\(734\) | 9.60441 | − | 16.6353i | 0.354505 | − | 0.614021i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.6837 | − | 27.1649i | −0.578108 | − | 1.00131i | ||||
\(737\) | 31.0335 | − | 53.7517i | 1.14314 | − | 1.97997i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.79032 | + | 3.10092i | 0.0658578 | + | 0.114069i | 0.897074 | − | 0.441880i | \(-0.145688\pi\) |
−0.831216 | + | 0.555949i | \(0.812355\pi\) | |||||||
\(740\) | 3.13667 | 0.115306 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.7964 | − | 42.9486i | 0.909691 | − | 1.57563i | 0.0951977 | − | 0.995458i | \(-0.469652\pi\) |
0.814493 | − | 0.580173i | \(-0.197015\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.09583 | + | 10.5583i | −0.223334 | + | 0.386826i | ||||
\(746\) | −5.38726 | − | 9.33101i | −0.197242 | − | 0.341633i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.56098 | 0.313020 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.4515 | + | 37.1551i | 0.782776 | + | 1.35581i | 0.930319 | + | 0.366752i | \(0.119530\pi\) |
−0.147543 | + | 0.989056i | \(0.547136\pi\) | |||||||
\(752\) | −14.2690 | −0.520337 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.5767 | 0.458016 | ||||||||
\(755\) | −25.1633 | −0.915786 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.8029 | 0.501677 | 0.250838 | − | 0.968029i | \(-0.419294\pi\) | ||||
0.250838 | + | 0.968029i | \(0.419294\pi\) | |||||||
\(758\) | 0.683021 | 0.0248084 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.6171 | −0.493945 | ||||||||
\(761\) | −20.3599 | − | 35.2643i | −0.738044 | − | 1.27833i | −0.953375 | − | 0.301789i | \(-0.902416\pi\) |
0.215330 | − | 0.976541i | \(-0.430917\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 23.0001 | 0.832113 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.88342 | − | 6.72627i | −0.140313 | − | 0.243030i | ||||
\(767\) | −9.06826 | + | 15.7067i | −0.327436 | + | 0.567135i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.57381 | + | 9.65413i | −0.200997 | + | 0.348137i | −0.948850 | − | 0.315728i | \(-0.897751\pi\) |
0.747853 | + | 0.663864i | \(0.231085\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −25.6908 | −0.924633 | ||||||||
\(773\) | −0.462831 | − | 0.801647i | −0.0166469 | − | 0.0288332i | 0.857582 | − | 0.514347i | \(-0.171966\pi\) |
−0.874229 | + | 0.485514i | \(0.838632\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.72061 | + | 6.44428i | −0.133648 | + | 0.231485i | ||||
\(776\) | −6.43012 | − | 11.1373i | −0.230828 | − | 0.399806i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.97049 | + | 10.3412i | −0.214052 | + | 0.370750i | ||||
\(779\) | −0.499408 | − | 0.865001i | −0.0178932 | − | 0.0309919i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.198452 | − | 0.343728i | 0.00710116 | − | 0.0122996i | ||||
\(782\) | 2.04024 | − | 3.53381i | 0.0729590 | − | 0.126369i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.50386 | + | 7.80092i | 0.160750 | + | 0.278427i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.0240 | −0.820716 | −0.410358 | − | 0.911925i | \(-0.634596\pi\) | ||||
−0.410358 | + | 0.911925i | \(0.634596\pi\) | |||||||
\(788\) | −6.26061 | −0.223025 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.881115 | − | 1.52614i | −0.0313487 | − | 0.0542975i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.103662 | + | 0.179548i | −0.00368114 | + | 0.00637593i | ||||
\(794\) | −4.38551 | + | 7.59592i | −0.155636 | + | 0.269569i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19.6014 | − | 33.9505i | −0.694752 | − | 1.20335i | ||||
\(797\) | 11.3925 | − | 19.7325i | 0.403544 | − | 0.698960i | −0.590606 | − | 0.806960i | \(-0.701111\pi\) |
0.994151 | + | 0.108000i | \(0.0344447\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.30492 | − | 9.18839i | −0.187675 | − | 0.325062i | ||||
\(800\) | −8.56664 | + | 14.8379i | −0.302877 | + | 0.524598i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.72695 | − | 8.18732i | −0.166914 | − | 0.289104i | ||||
\(803\) | 52.7150 | 1.86027 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.31352 | − | 4.00713i | 0.0814901 | − | 0.141145i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.11143 | − | 10.5853i | 0.214999 | − | 0.372390i | ||||
\(809\) | −6.73753 | − | 11.6697i | −0.236879 | − | 0.410286i | 0.722938 | − | 0.690913i | \(-0.242791\pi\) |
−0.959817 | + | 0.280627i | \(0.909458\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.7348 | 1.07924 | 0.539622 | − | 0.841907i | \(-0.318567\pi\) | ||||
0.539622 | + | 0.841907i | \(0.318567\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.34603 | − | 4.06344i | −0.0822283 | − | 0.142424i | ||||
\(815\) | 11.4318 | 0.400439 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.00150 | −0.139995 | ||||||||
\(818\) | −1.77369 | −0.0620158 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.549675 | 0.0191955 | ||||||||
\(821\) | 16.9864 | 0.592829 | 0.296414 | − | 0.955059i | \(-0.404209\pi\) | ||||
0.296414 | + | 0.955059i | \(0.404209\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.5831 | −0.647768 | −0.323884 | − | 0.946097i | \(-0.604989\pi\) | ||||
−0.323884 | + | 0.946097i | \(0.604989\pi\) | |||||||
\(824\) | −16.9122 | − | 29.2928i | −0.589164 | − | 1.02046i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.5419 | −0.505670 | −0.252835 | − | 0.967509i | \(-0.581363\pi\) | ||||
−0.252835 | + | 0.967509i | \(0.581363\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.78717 | − | 8.29161i | −0.166265 | − | 0.287980i | 0.770839 | − | 0.637030i | \(-0.219837\pi\) |
−0.937104 | + | 0.349051i | \(0.886504\pi\) | |||||||
\(830\) | 6.91154 | − | 11.9711i | 0.239903 | − | 0.415524i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.17885 | − | 2.04183i | 0.0408693 | − | 0.0707877i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.02195 | −0.104579 | ||||||||
\(836\) | −15.3494 | − | 26.5859i | −0.530869 | − | 0.919492i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.2326 | + | 19.4554i | −0.388023 | + | 0.672075i | ||||
\(839\) | 21.2303 | + | 36.7720i | 0.732952 | + | 1.26951i | 0.955616 | + | 0.294615i | \(0.0951913\pi\) |
−0.222664 | + | 0.974895i | \(0.571475\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.69551 | + | 15.0611i | −0.299845 | + | 0.519347i | ||||
\(842\) | 1.62187 | + | 2.80917i | 0.0558934 | + | 0.0968103i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.83428 | − | 10.1053i | 0.200824 | − | 0.347838i | ||||
\(845\) | 3.85599 | − | 6.67877i | 0.132650 | − | 0.229757i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.617738 | + | 1.06995i | 0.0212132 | + | 0.0367423i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.22882 | −0.0764479 | ||||||||
\(851\) | 7.71767 | 0.264558 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.14039 | − | 12.3675i | −0.244482 | − | 0.423456i | 0.717504 | − | 0.696555i | \(-0.245285\pi\) |
−0.961986 | + | 0.273099i | \(0.911951\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.11621 | + | 15.7897i | −0.311586 | + | 0.539682i | ||||
\(857\) | −17.3895 | + | 30.1195i | −0.594013 | + | 1.02886i | 0.399672 | + | 0.916658i | \(0.369124\pi\) |
−0.993685 | + | 0.112203i | \(0.964209\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.32429 | − | 10.9540i | −0.215782 | − | 0.373745i | 0.737732 | − | 0.675093i | \(-0.235897\pi\) |
−0.953514 | + | 0.301348i | \(0.902563\pi\) | |||||||
\(860\) | 1.10107 | − | 1.90710i | 0.0375460 | − | 0.0650316i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.8409 | + | 20.5091i | 0.403304 | + | 0.698543i | ||||
\(863\) | −13.2398 | + | 22.9321i | −0.450690 | + | 0.780617i | −0.998429 | − | 0.0560318i | \(-0.982155\pi\) |
0.547739 | + | 0.836649i | \(0.315489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.0297 | + | 22.5681i | 0.443022 | + | 0.767337i | ||||
\(866\) | 3.66943 | 0.124692 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.54843 | − | 7.87811i | 0.154295 | − | 0.267247i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.3371 | + | 30.0287i | −0.587444 | + | 1.01748i | ||||
\(872\) | −2.02166 | − | 3.50162i | −0.0684621 | − | 0.118580i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.6322 | −0.494941 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.2267 | − | 24.6414i | −0.480402 | − | 0.832081i | 0.519345 | − | 0.854565i | \(-0.326176\pi\) |
−0.999747 | + | 0.0224835i | \(0.992843\pi\) | |||||||
\(878\) | 4.28887 | 0.144742 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.5801 | 0.356654 | ||||||||
\(881\) | −20.3637 | −0.686071 | −0.343036 | − | 0.939322i | \(-0.611455\pi\) | ||||
−0.343036 | + | 0.939322i | \(0.611455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.1950 | 1.65554 | 0.827772 | − | 0.561065i | \(-0.189608\pi\) | ||||
0.827772 | + | 0.561065i | \(0.189608\pi\) | |||||||
\(884\) | −4.78264 | −0.160858 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.28129 | −0.143833 | ||||||||
\(887\) | 2.10846 | + | 3.65196i | 0.0707952 | + | 0.122621i | 0.899250 | − | 0.437435i | \(-0.144113\pi\) |
−0.828455 | + | 0.560056i | \(0.810780\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 12.9196 | 0.433067 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.0673 | + | 17.4371i | 0.337078 | + | 0.583837i | ||||
\(893\) | −19.0229 | + | 32.9486i | −0.636576 | + | 1.10258i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.43294 | + | 9.41013i | −0.181603 | + | 0.314546i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.87371 | −0.262749 | ||||||||
\(899\) | 8.53374 | + | 14.7809i | 0.284616 | + | 0.492970i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.459325 | + | 0.795574i | −0.0153023 | + | 0.0265044i | ||||
\(902\) | −0.411122 | − | 0.712084i | −0.0136889 | − | 0.0237098i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.714872 | − | 1.23819i | 0.0237763 | − | 0.0411817i | ||||
\(905\) | 11.0650 | + | 19.1652i | 0.367814 | + | 0.637072i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.9925 | + | 41.5563i | −0.796659 | + | 1.37985i | 0.125121 | + | 0.992142i | \(0.460068\pi\) |
−0.921780 | + | 0.387713i | \(0.873265\pi\) | |||||||
\(908\) | −22.4585 | + | 38.8993i | −0.745311 | + | 1.29092i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.8667 | + | 22.2858i | 0.426294 | + | 0.738362i | 0.996540 | − | 0.0831113i | \(-0.0264857\pi\) |
−0.570247 | + | 0.821474i | \(0.693152\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 71.3565 | 2.36155 | ||||||||
\(914\) | −7.05351 | −0.233309 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.9678 | − | 20.7288i | −0.395427 | − | 0.684900i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.13478 | − | 1.96550i | 0.0374330 | − | 0.0648359i | −0.846702 | − | 0.532068i | \(-0.821415\pi\) |
0.884135 | + | 0.467232i | \(0.154749\pi\) | |||||||
\(920\) | 9.21919 | − | 15.9681i | 0.303948 | − | 0.526453i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.37484 | + | 4.11334i | 0.0782111 | + | 0.135466i | ||||
\(923\) | −0.110866 | + | 0.192026i | −0.00364920 | + | 0.00632060i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.10775 | − | 3.65073i | −0.0693024 | − | 0.120035i | ||||
\(926\) | −10.9774 | + | 19.0134i | −0.360740 | + | 0.624819i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 19.6488 | + | 34.0328i | 0.645004 | + | 1.11718i | ||||
\(929\) | 45.8496 | 1.50428 | 0.752138 | − | 0.659006i | \(-0.229023\pi\) | ||||
0.752138 | + | 0.659006i | \(0.229023\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.83514 | + | 6.64266i | −0.125624 | + | 0.217587i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.31530 | + | 2.27816i | −0.0430379 | + | 0.0745438i | ||||
\(935\) | 3.93346 | + | 6.81294i | 0.128638 | + | 0.222807i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.2075 | 1.83622 | 0.918110 | − | 0.396325i | \(-0.129715\pi\) | ||||
0.918110 | + | 0.396325i | \(0.129715\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.4688 | − | 18.1325i | −0.341454 | − | 0.591416i | ||||
\(941\) | −35.2803 | −1.15011 | −0.575053 | − | 0.818116i | \(-0.695018\pi\) | ||||
−0.575053 | + | 0.818116i | \(0.695018\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.35246 | 0.0440421 | ||||||||
\(944\) | −9.91453 | −0.322691 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.29411 | −0.107101 | ||||||||
\(947\) | 50.7130 | 1.64795 | 0.823976 | − | 0.566625i | \(-0.191751\pi\) | ||||
0.823976 | + | 0.566625i | \(0.191751\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −29.4495 | −0.955972 | ||||||||
\(950\) | 3.99615 | + | 6.92154i | 0.129652 | + | 0.224564i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.9988 | −0.842184 | −0.421092 | − | 0.907018i | \(-0.638353\pi\) | ||||
−0.421092 | + | 0.907018i | \(0.638353\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.5677 | + | 18.3038i | 0.341962 | + | 0.592296i | ||||
\(956\) | 10.1061 | − | 17.5043i | 0.326855 | − | 0.566130i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.39165 | − | 9.33861i | 0.174196 | − | 0.301717i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.7208 | −0.797445 | ||||||||
\(962\) | 1.31062 | + | 2.27006i | 0.0422562 | + | 0.0731898i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.3062 | + | 19.5829i | −0.364148 | + | 0.630722i | ||||
\(965\) | −11.8040 | − | 20.4451i | −0.379984 | − | 0.658152i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.9810 | + | 22.4838i | −0.417442 | + | 0.723031i | −0.995681 | − | 0.0928360i | \(-0.970407\pi\) |
0.578239 | + | 0.815867i | \(0.303740\pi\) | |||||||
\(968\) | −15.8427 | − | 27.4404i | −0.509204 | − | 0.881967i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.58052 | − | 4.46959i | 0.0828554 | − | 0.143510i | ||||
\(971\) | −3.97206 | + | 6.87981i | −0.127469 | + | 0.220783i | −0.922696 | − | 0.385530i | \(-0.874019\pi\) |
0.795226 | + | 0.606313i | \(0.207352\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.17424 | + | 2.03384i | 0.0376249 | + | 0.0651683i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.113336 | −0.00362779 | ||||||||
\(977\) | 52.2548 | 1.67178 | 0.835889 | − | 0.548898i | \(-0.184952\pi\) | ||||
0.835889 | + | 0.548898i | \(0.184952\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.3464 | + | 57.7577i | 1.06576 | + | 1.84594i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.7784 | + | 23.8650i | −0.439688 | + | 0.761562i | ||||
\(983\) | 19.4190 | − | 33.6346i | 0.619369 | − | 1.07278i | −0.370232 | − | 0.928939i | \(-0.620722\pi\) |
0.989601 | − | 0.143839i | \(-0.0459448\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.87652 | − | 4.98228i | −0.0916535 | − | 0.158749i | ||||
\(986\) | −2.55606 | + | 4.42722i | −0.0814015 | + | 0.140991i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.57501 | + | 14.8524i | 0.272807 | + | 0.472516i | ||||
\(989\) | 2.70914 | − | 4.69236i | 0.0861455 | − | 0.149208i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.4689 | − | 26.7929i | −0.491385 | − | 0.851104i | 0.508565 | − | 0.861023i | \(-0.330176\pi\) |
−0.999951 | + | 0.00991892i | \(0.996843\pi\) | |||||||
\(992\) | 14.4578 | 0.459036 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.0122 | − | 31.1981i | 0.571025 | − | 0.989045i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.5335 | − | 40.7612i | 0.745313 | − | 1.29092i | −0.204735 | − | 0.978817i | \(-0.565633\pi\) |
0.950048 | − | 0.312103i | \(-0.101033\pi\) | |||||||
\(998\) | 3.96492 | + | 6.86745i | 0.125507 | + | 0.217385i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))