Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(1979,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.1979");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.t (of order \(6\), 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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 2285.1 | ||
Root | \(-1.62181 - 0.608059i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.2285 |
Dual form | 2646.2.t.a.1979.1 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −3.89111 | −1.74016 | −0.870080 | − | 0.492911i | \(-0.835933\pi\) | ||||
−0.870080 | + | 0.492911i | \(0.835933\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.36980 | + | 1.94556i | 1.06563 | + | 0.615239i | ||||
\(11\) | − | 3.94462i | − | 1.18935i | −0.803967 | − | 0.594674i | \(-0.797281\pi\) | ||
0.803967 | − | 0.594674i | \(-0.202719\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.46687 | − | 1.42425i | −0.684186 | − | 0.395015i | 0.117244 | − | 0.993103i | \(-0.462594\pi\) |
−0.801430 | + | 0.598088i | \(0.795927\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.371058 | + | 0.642692i | −0.0899949 | + | 0.155876i | −0.907509 | − | 0.420033i | \(-0.862018\pi\) |
0.817514 | + | 0.575909i | \(0.195352\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.54563 | − | 0.892369i | 0.354591 | − | 0.204723i | −0.312114 | − | 0.950045i | \(-0.601037\pi\) |
0.666706 | + | 0.745321i | \(0.267704\pi\) | |||||||
\(20\) | −1.94556 | − | 3.36980i | −0.435040 | − | 0.753511i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.97231 | + | 3.41614i | −0.420498 | + | 0.728324i | ||||
\(23\) | − | 6.25311i | − | 1.30386i | −0.758278 | − | 0.651932i | \(-0.773959\pi\) | ||
0.758278 | − | 0.651932i | \(-0.226041\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.1408 | 2.02815 | ||||||||
\(26\) | 1.42425 | + | 2.46687i | 0.279318 | + | 0.483793i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.50079 | − | 1.44383i | 0.464385 | − | 0.268113i | −0.249501 | − | 0.968374i | \(-0.580267\pi\) |
0.713886 | + | 0.700262i | \(0.246933\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.04125 | − | 1.75587i | 0.546225 | − | 0.315363i | −0.201373 | − | 0.979515i | \(-0.564540\pi\) |
0.747598 | + | 0.664152i | \(0.231207\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.642692 | − | 0.371058i | 0.110221 | − | 0.0636360i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50079 | − | 2.59944i | −0.246728 | − | 0.427346i | 0.715888 | − | 0.698215i | \(-0.246022\pi\) |
−0.962616 | + | 0.270870i | \(0.912689\pi\) | |||||||
\(38\) | −1.78474 | −0.289523 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.89111i | 0.615239i | ||||||||
\(41\) | −5.24705 | + | 9.08816i | −0.819452 | + | 1.41933i | 0.0866345 | + | 0.996240i | \(0.472389\pi\) |
−0.906087 | + | 0.423092i | \(0.860945\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.471521 | + | 0.816699i | 0.0719063 | + | 0.124545i | 0.899737 | − | 0.436433i | \(-0.143758\pi\) |
−0.827830 | + | 0.560978i | \(0.810425\pi\) | |||||||
\(44\) | 3.41614 | − | 1.97231i | 0.515003 | − | 0.297337i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.12656 | + | 5.41535i | −0.460985 | + | 0.798450i | ||||
\(47\) | 1.09263 | − | 1.89248i | 0.159376 | − | 0.276047i | −0.775268 | − | 0.631633i | \(-0.782385\pi\) |
0.934644 | + | 0.355585i | \(0.115718\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.78217 | − | 5.07039i | −1.24199 | − | 0.717061i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 2.84849i | − | 0.395015i | ||||||
\(53\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.3490i | 2.06965i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.88766 | −0.379169 | ||||||||
\(59\) | 0.0105673 | + | 0.0183031i | 0.00137575 | + | 0.00238286i | 0.866712 | − | 0.498808i | \(-0.166229\pi\) |
−0.865337 | + | 0.501191i | \(0.832895\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.13832 | − | 1.23456i | −0.273783 | − | 0.158069i | 0.356822 | − | 0.934172i | \(-0.383860\pi\) |
−0.630606 | + | 0.776103i | \(0.717193\pi\) | |||||||
\(62\) | −3.51174 | −0.445991 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 9.59886 | + | 5.54191i | 1.19059 | + | 0.687389i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.72463 | − | 11.6474i | −0.821544 | − | 1.42296i | −0.904532 | − | 0.426406i | \(-0.859779\pi\) |
0.0829874 | − | 0.996551i | \(-0.473554\pi\) | |||||||
\(68\) | −0.742117 | −0.0899949 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.94304i | 0.230597i | 0.993331 | + | 0.115298i | \(0.0367824\pi\) | ||||
−0.993331 | + | 0.115298i | \(0.963218\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.20443 | + | 2.42743i | 0.492092 | + | 0.284109i | 0.725442 | − | 0.688284i | \(-0.241636\pi\) |
−0.233350 | + | 0.972393i | \(0.574969\pi\) | |||||||
\(74\) | 3.00158i | 0.348926i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.54563 | + | 0.892369i | 0.177296 | + | 0.102362i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.81806 | + | 3.14898i | −0.204548 | + | 0.354288i | −0.949989 | − | 0.312284i | \(-0.898906\pi\) |
0.745440 | + | 0.666572i | \(0.232239\pi\) | |||||||
\(80\) | 1.94556 | − | 3.36980i | 0.217520 | − | 0.376756i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.08816 | − | 5.24705i | 1.00362 | − | 0.579440i | ||||
\(83\) | −4.02998 | − | 6.98012i | −0.442347 | − | 0.766168i | 0.555516 | − | 0.831506i | \(-0.312521\pi\) |
−0.997863 | + | 0.0653378i | \(0.979188\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.44383 | − | 2.50079i | 0.156605 | − | 0.271249i | ||||
\(86\) | − | 0.943042i | − | 0.101691i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.94462 | −0.420498 | ||||||||
\(89\) | 4.63323 | + | 8.02499i | 0.491122 | + | 0.850647i | 0.999948 | − | 0.0102218i | \(-0.00325375\pi\) |
−0.508826 | + | 0.860869i | \(0.669920\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.41535 | − | 3.12656i | 0.564589 | − | 0.325966i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.89248 | + | 1.09263i | −0.195195 | + | 0.112696i | ||||
\(95\) | −6.01422 | + | 3.47231i | −0.617046 | + | 0.356251i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.2983 | + | 9.40980i | −1.65484 | + | 0.955421i | −0.679794 | + | 0.733403i | \(0.737931\pi\) |
−0.975043 | + | 0.222018i | \(0.928736\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.07039 | + | 8.78217i | 0.507039 | + | 0.878217i | ||||
\(101\) | −8.28158 | −0.824048 | −0.412024 | − | 0.911173i | \(-0.635178\pi\) | ||||
−0.412024 | + | 0.911173i | \(0.635178\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 17.0487i | − | 1.67986i | −0.542697 | − | 0.839929i | \(-0.682597\pi\) | ||
0.542697 | − | 0.839929i | \(-0.317403\pi\) | |||||||
\(104\) | −1.42425 | + | 2.46687i | −0.139659 | + | 0.241896i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.4161 | + | 7.16846i | −1.20031 | + | 0.693001i | −0.960625 | − | 0.277848i | \(-0.910379\pi\) |
−0.239689 | + | 0.970850i | \(0.577045\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.63998 | + | 9.76874i | −0.540212 | + | 0.935675i | 0.458679 | + | 0.888602i | \(0.348323\pi\) |
−0.998891 | + | 0.0470733i | \(0.985011\pi\) | |||||||
\(110\) | 7.67448 | − | 13.2926i | 0.731733 | − | 1.26740i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.51501 | + | 4.91614i | 0.801024 | + | 0.462472i | 0.843829 | − | 0.536612i | \(-0.180296\pi\) |
−0.0428049 | + | 0.999083i | \(0.513629\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.3316i | 2.26893i | ||||||||
\(116\) | 2.50079 | + | 1.44383i | 0.232192 | + | 0.134056i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 0.0211346i | − | 0.00194560i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.56002 | −0.414548 | ||||||||
\(122\) | 1.23456 | + | 2.13832i | 0.111772 | + | 0.193594i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.04125 | + | 1.75587i | 0.273112 | + | 0.157682i | ||||
\(125\) | −20.0033 | −1.78915 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.94462 | 0.261293 | 0.130646 | − | 0.991429i | \(-0.458295\pi\) | ||||
0.130646 | + | 0.991429i | \(0.458295\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.54191 | − | 9.59886i | −0.486057 | − | 0.841876i | ||||
\(131\) | −15.0651 | −1.31624 | −0.658122 | − | 0.752911i | \(-0.728649\pi\) | ||||
−0.658122 | + | 0.752911i | \(0.728649\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.4493i | 1.16184i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.642692 | + | 0.371058i | 0.0551104 | + | 0.0318180i | ||||
\(137\) | 15.7199i | 1.34305i | 0.740984 | + | 0.671523i | \(0.234359\pi\) | ||||
−0.740984 | + | 0.671523i | \(0.765641\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.86373 | − | 1.65337i | −0.242898 | − | 0.140237i | 0.373610 | − | 0.927586i | \(-0.378120\pi\) |
−0.616508 | + | 0.787349i | \(0.711453\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.971521 | − | 1.68272i | 0.0815282 | − | 0.141211i | ||||
\(143\) | −5.61811 | + | 9.73085i | −0.469810 | + | 0.813735i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.73085 | + | 5.61811i | −0.808103 | + | 0.466559i | ||||
\(146\) | −2.42743 | − | 4.20443i | −0.200896 | − | 0.347961i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.50079 | − | 2.59944i | 0.123364 | − | 0.213673i | ||||
\(149\) | 11.0016i | 0.901284i | 0.892705 | + | 0.450642i | \(0.148805\pi\) | ||||
−0.892705 | + | 0.450642i | \(0.851195\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.43998 | −0.117184 | −0.0585918 | − | 0.998282i | \(-0.518661\pi\) | ||||
−0.0585918 | + | 0.998282i | \(0.518661\pi\) | |||||||
\(152\) | −0.892369 | − | 1.54563i | −0.0723807 | − | 0.125367i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.8339 | + | 6.83228i | −0.950518 | + | 0.548782i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.3822 | − | 8.30354i | 1.14782 | − | 0.662695i | 0.199465 | − | 0.979905i | \(-0.436079\pi\) |
0.948355 | + | 0.317210i | \(0.102746\pi\) | |||||||
\(158\) | 3.14898 | − | 1.81806i | 0.250519 | − | 0.144637i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.36980 | + | 1.94556i | −0.266406 | + | 0.153810i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.19773 | + | 10.7348i | 0.485444 | + | 0.840813i | 0.999860 | − | 0.0167274i | \(-0.00532476\pi\) |
−0.514416 | + | 0.857541i | \(0.671991\pi\) | |||||||
\(164\) | −10.4941 | −0.819452 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.05995i | 0.625574i | ||||||||
\(167\) | −5.86087 | + | 10.1513i | −0.453528 | + | 0.785534i | −0.998602 | − | 0.0528541i | \(-0.983168\pi\) |
0.545074 | + | 0.838388i | \(0.316502\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.44304 | − | 4.23147i | −0.187926 | − | 0.325498i | ||||
\(170\) | −2.50079 | + | 1.44383i | −0.191802 | + | 0.110737i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.471521 | + | 0.816699i | −0.0359532 | + | 0.0622727i | ||||
\(173\) | −8.38548 | + | 14.5241i | −0.637536 | + | 1.10425i | 0.348435 | + | 0.937333i | \(0.386713\pi\) |
−0.985972 | + | 0.166913i | \(0.946620\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.41614 | + | 1.97231i | 0.257501 | + | 0.148668i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 9.26646i | − | 0.694551i | ||||||
\(179\) | −5.00158 | − | 2.88766i | −0.373835 | − | 0.215834i | 0.301297 | − | 0.953530i | \(-0.402580\pi\) |
−0.675133 | + | 0.737696i | \(0.735914\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.53310i | − | 0.411272i | −0.978629 | − | 0.205636i | \(-0.934074\pi\) | ||
0.978629 | − | 0.205636i | \(-0.0659263\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.25311 | −0.460985 | ||||||||
\(185\) | 5.83974 | + | 10.1147i | 0.429346 | + | 0.743649i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.53518 | + | 1.46368i | 0.185390 | + | 0.107035i | ||||
\(188\) | 2.18525 | 0.159376 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.94462 | 0.503816 | ||||||||
\(191\) | −5.38124 | − | 3.10686i | −0.389373 | − | 0.224805i | 0.292515 | − | 0.956261i | \(-0.405508\pi\) |
−0.681888 | + | 0.731456i | \(0.738841\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.90271 | + | 6.75970i | 0.280923 | + | 0.486574i | 0.971612 | − | 0.236578i | \(-0.0760260\pi\) |
−0.690689 | + | 0.723152i | \(0.742693\pi\) | |||||||
\(194\) | 18.8196 | 1.35117 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 12.7737i | − | 0.910092i | −0.890468 | − | 0.455046i | \(-0.849623\pi\) | ||
0.890468 | − | 0.455046i | \(-0.150377\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.56925 | + | 0.906005i | 0.111241 | + | 0.0642250i | 0.554588 | − | 0.832125i | \(-0.312876\pi\) |
−0.443347 | + | 0.896350i | \(0.646209\pi\) | |||||||
\(200\) | − | 10.1408i | − | 0.717061i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.17206 | + | 4.14079i | 0.504624 | + | 0.291345i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.4169 | − | 35.3631i | 1.42598 | − | 2.46986i | ||||
\(206\) | −8.52435 | + | 14.7646i | −0.593919 | + | 1.02870i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.46687 | − | 1.42425i | 0.171047 | − | 0.0987537i | ||||
\(209\) | −3.52006 | − | 6.09692i | −0.243487 | − | 0.421732i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.88766 | + | 3.26953i | −0.129952 | + | 0.225083i | −0.923658 | − | 0.383218i | \(-0.874816\pi\) |
0.793706 | + | 0.608302i | \(0.208149\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.3369 | 0.980052 | ||||||||
\(215\) | −1.83474 | − | 3.17787i | −0.125128 | − | 0.216729i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.76874 | − | 5.63998i | 0.661622 | − | 0.381988i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13.2926 | + | 7.67448i | −0.896187 | + | 0.517414i | ||||
\(221\) | 1.83070 | − | 1.05696i | 0.123146 | − | 0.0710987i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.0662 | + | 6.38910i | −0.741051 | + | 0.427846i | −0.822451 | − | 0.568836i | \(-0.807394\pi\) |
0.0814006 | + | 0.996681i | \(0.474061\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.91614 | − | 8.51501i | −0.327017 | − | 0.566410i | ||||
\(227\) | 19.9822 | 1.32627 | 0.663133 | − | 0.748502i | \(-0.269227\pi\) | ||||
0.663133 | + | 0.748502i | \(0.269227\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.1314i | 0.669500i | 0.942307 | + | 0.334750i | \(0.108652\pi\) | ||||
−0.942307 | + | 0.334750i | \(0.891348\pi\) | |||||||
\(230\) | 12.1658 | − | 21.0718i | 0.802188 | − | 1.38943i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.44383 | − | 2.50079i | −0.0947921 | − | 0.164185i | ||||
\(233\) | −6.33070 | + | 3.65503i | −0.414738 | + | 0.239449i | −0.692824 | − | 0.721107i | \(-0.743634\pi\) |
0.278085 | + | 0.960556i | \(0.410300\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.25153 | + | 7.36387i | −0.277339 | + | 0.480366i | ||||
\(236\) | −0.0105673 | + | 0.0183031i | −0.000687873 | + | 0.00119143i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.28317 | − | 4.20494i | −0.471109 | − | 0.271995i | 0.245595 | − | 0.969373i | \(-0.421017\pi\) |
−0.716704 | + | 0.697378i | \(0.754350\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.95213i | 0.576657i | 0.957531 | + | 0.288329i | \(0.0930996\pi\) | ||||
−0.957531 | + | 0.288329i | \(0.906900\pi\) | |||||||
\(242\) | 3.94910 | + | 2.28001i | 0.253858 | + | 0.146565i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 2.46911i | − | 0.158069i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.08381 | −0.323475 | ||||||||
\(248\) | −1.75587 | − | 3.04125i | −0.111498 | − | 0.193120i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 17.3234 | + | 10.0017i | 1.09563 | + | 0.632561i | ||||
\(251\) | 12.6432 | 0.798033 | 0.399017 | − | 0.916944i | \(-0.369352\pi\) | ||||
0.399017 | + | 0.916944i | \(0.369352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.6661 | −1.55075 | ||||||||
\(254\) | −2.55012 | − | 1.47231i | −0.160008 | − | 0.0923809i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 16.3066 | 1.01718 | 0.508588 | − | 0.861010i | \(-0.330168\pi\) | ||||
0.508588 | + | 0.861010i | \(0.330168\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 11.0838i | 0.687389i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.0468 | + | 7.53255i | 0.806032 | + | 0.465363i | ||||
\(263\) | − | 23.7215i | − | 1.46273i | −0.681985 | − | 0.731366i | \(-0.738883\pi\) | ||
0.681985 | − | 0.731366i | \(-0.261117\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.72463 | − | 11.6474i | 0.410772 | − | 0.711478i | ||||
\(269\) | −3.64144 | + | 6.30716i | −0.222022 | + | 0.384554i | −0.955422 | − | 0.295244i | \(-0.904599\pi\) |
0.733400 | + | 0.679798i | \(0.237932\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.6483 | + | 11.3440i | −1.19355 | + | 0.689097i | −0.959110 | − | 0.283033i | \(-0.908659\pi\) |
−0.234441 | + | 0.972130i | \(0.575326\pi\) | |||||||
\(272\) | −0.371058 | − | 0.642692i | −0.0224987 | − | 0.0389689i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.85997 | − | 13.6139i | 0.474838 | − | 0.822444i | ||||
\(275\) | − | 40.0015i | − | 2.41218i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.1676 | 1.45209 | 0.726046 | − | 0.687646i | \(-0.241356\pi\) | ||||
0.726046 | + | 0.687646i | \(0.241356\pi\) | |||||||
\(278\) | 1.65337 | + | 2.86373i | 0.0991628 | + | 0.171755i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.11229 | − | 2.37423i | 0.245319 | − | 0.141635i | −0.372300 | − | 0.928112i | \(-0.621431\pi\) |
0.617619 | + | 0.786478i | \(0.288097\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.4484 | + | 14.6926i | −1.51275 | + | 0.873387i | −0.512861 | + | 0.858471i | \(0.671415\pi\) |
−0.999889 | + | 0.0149153i | \(0.995252\pi\) | |||||||
\(284\) | −1.68272 | + | 0.971521i | −0.0998513 | + | 0.0576492i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.73085 | − | 5.61811i | 0.575398 | − | 0.332206i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.22463 | + | 14.2455i | 0.483802 | + | 0.837969i | ||||
\(290\) | 11.2362 | 0.659814 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.85486i | 0.284109i | ||||||||
\(293\) | 3.31206 | − | 5.73666i | 0.193493 | − | 0.335139i | −0.752913 | − | 0.658121i | \(-0.771352\pi\) |
0.946405 | + | 0.322981i | \(0.104685\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0411186 | − | 0.0712195i | −0.00239402 | − | 0.00414656i | ||||
\(296\) | −2.59944 | + | 1.50079i | −0.151090 | + | 0.0872316i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.50079 | − | 9.52765i | 0.318652 | − | 0.551922i | ||||
\(299\) | −8.90597 | + | 15.4256i | −0.515046 | + | 0.892085i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.24706 | + | 0.719988i | 0.0717600 | + | 0.0414307i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.78474i | 0.102362i | ||||||||
\(305\) | 8.32043 | + | 4.80380i | 0.476426 | + | 0.275065i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.7242i | 1.23987i | 0.784655 | + | 0.619933i | \(0.212840\pi\) | ||||
−0.784655 | + | 0.619933i | \(0.787160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.6646 | 0.776095 | ||||||||
\(311\) | 3.14900 | + | 5.45422i | 0.178563 | + | 0.309281i | 0.941389 | − | 0.337324i | \(-0.109522\pi\) |
−0.762825 | + | 0.646605i | \(0.776188\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.2423 | − | 11.1095i | −1.08764 | − | 0.627948i | −0.154691 | − | 0.987963i | \(-0.549438\pi\) |
−0.932946 | + | 0.360015i | \(0.882771\pi\) | |||||||
\(314\) | −16.6071 | −0.937192 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.63613 | −0.204548 | ||||||||
\(317\) | 13.5632 | + | 7.83070i | 0.761784 | + | 0.439816i | 0.829936 | − | 0.557859i | \(-0.188377\pi\) |
−0.0681519 | + | 0.997675i | \(0.521710\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.69536 | − | 9.86466i | −0.318879 | − | 0.552315i | ||||
\(320\) | 3.89111 | 0.217520 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.32448i | 0.0736963i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −25.0159 | − | 14.4430i | −1.38763 | − | 0.801151i | ||||
\(326\) | − | 12.3955i | − | 0.686521i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.08816 | + | 5.24705i | 0.501810 | + | 0.289720i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.636129 | + | 1.10181i | −0.0349648 | + | 0.0605608i | −0.882978 | − | 0.469414i | \(-0.844465\pi\) |
0.848013 | + | 0.529975i | \(0.177799\pi\) | |||||||
\(332\) | 4.02998 | − | 6.98012i | 0.221174 | − | 0.383084i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.1513 | − | 5.86087i | 0.555456 | − | 0.320693i | ||||
\(335\) | 26.1663 | + | 45.3214i | 1.42962 | + | 2.47617i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.78001 | + | 6.54717i | −0.205910 | + | 0.356647i | −0.950422 | − | 0.310962i | \(-0.899349\pi\) |
0.744512 | + | 0.667609i | \(0.232682\pi\) | |||||||
\(338\) | 4.88608i | 0.265768i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.88766 | 0.156605 | ||||||||
\(341\) | −6.92623 | − | 11.9966i | −0.375076 | − | 0.649651i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.816699 | − | 0.471521i | 0.0440334 | − | 0.0254227i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.5241 | − | 8.38548i | 0.780820 | − | 0.450806i | ||||
\(347\) | 19.1470 | − | 11.0545i | 1.02787 | − | 0.593439i | 0.111494 | − | 0.993765i | \(-0.464436\pi\) |
0.916373 | + | 0.400326i | \(0.131103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.7682 | − | 7.37173i | 0.683467 | − | 0.394600i | −0.117693 | − | 0.993050i | \(-0.537550\pi\) |
0.801160 | + | 0.598450i | \(0.204217\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.97231 | − | 3.41614i | −0.105124 | − | 0.182081i | ||||
\(353\) | −17.2776 | −0.919595 | −0.459798 | − | 0.888024i | \(-0.652078\pi\) | ||||
−0.459798 | + | 0.888024i | \(0.652078\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 7.56060i | − | 0.401275i | ||||||
\(356\) | −4.63323 | + | 8.02499i | −0.245561 | + | 0.425324i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.88766 | + | 5.00158i | 0.152618 | + | 0.264342i | ||||
\(359\) | −9.45088 | + | 5.45647i | −0.498799 | + | 0.287982i | −0.728217 | − | 0.685346i | \(-0.759651\pi\) |
0.229419 | + | 0.973328i | \(0.426318\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.90736 | + | 13.6959i | −0.416177 | + | 0.720839i | ||||
\(362\) | −2.76655 | + | 4.79180i | −0.145407 | + | 0.251852i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.3599 | − | 9.44541i | −0.856318 | − | 0.494395i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 35.7272i | − | 1.86494i | −0.361242 | − | 0.932472i | \(-0.617647\pi\) | ||
0.361242 | − | 0.932472i | \(-0.382353\pi\) | |||||||
\(368\) | 5.41535 | + | 3.12656i | 0.282295 | + | 0.162983i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 11.6795i | − | 0.607187i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.0600 | −1.66001 | −0.830003 | − | 0.557760i | \(-0.811661\pi\) | ||||
−0.830003 | + | 0.557760i | \(0.811661\pi\) | |||||||
\(374\) | −1.46368 | − | 2.53518i | −0.0756853 | − | 0.131091i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.89248 | − | 1.09263i | −0.0975974 | − | 0.0563479i | ||||
\(377\) | −8.22549 | −0.423634 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.8891 | 1.79214 | 0.896068 | − | 0.443918i | \(-0.146412\pi\) | ||||
0.896068 | + | 0.443918i | \(0.146412\pi\) | |||||||
\(380\) | −6.01422 | − | 3.47231i | −0.308523 | − | 0.178126i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.10686 | + | 5.38124i | 0.158961 | + | 0.275328i | ||||
\(383\) | 17.5342 | 0.895957 | 0.447978 | − | 0.894044i | \(-0.352144\pi\) | ||||
0.447978 | + | 0.894044i | \(0.352144\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 7.80542i | − | 0.397286i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.2983 | − | 9.40980i | −0.827418 | − | 0.477710i | ||||
\(389\) | 7.62171i | 0.386436i | 0.981156 | + | 0.193218i | \(0.0618925\pi\) | ||||
−0.981156 | + | 0.193218i | \(0.938108\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.01882 | + | 2.32027i | 0.203241 | + | 0.117341i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.38687 | + | 11.0624i | −0.321766 | + | 0.557315i | ||||
\(395\) | 7.07430 | − | 12.2530i | 0.355947 | − | 0.616517i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.6032 | − | 18.8234i | 1.63631 | − | 0.944722i | 0.654216 | − | 0.756307i | \(-0.272999\pi\) |
0.982090 | − | 0.188414i | \(-0.0603348\pi\) | |||||||
\(398\) | −0.906005 | − | 1.56925i | −0.0454139 | − | 0.0786592i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.07039 | + | 8.78217i | −0.253519 | + | 0.439108i | ||||
\(401\) | 21.4415i | 1.07074i | 0.844619 | + | 0.535368i | \(0.179827\pi\) | ||||
−0.844619 | + | 0.535368i | \(0.820173\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.0032 | −0.498293 | ||||||||
\(404\) | −4.14079 | − | 7.17206i | −0.206012 | − | 0.356823i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.2538 | + | 5.92004i | −0.508262 | + | 0.293445i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.6086 | + | 14.7851i | −1.26627 | + | 0.731079i | −0.974279 | − | 0.225344i | \(-0.927649\pi\) |
−0.291986 | + | 0.956423i | \(0.594316\pi\) | |||||||
\(410\) | −35.3631 | + | 20.4169i | −1.74646 | + | 1.00832i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.7646 | − | 8.52435i | 0.727400 | − | 0.419964i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.6811 | + | 27.1605i | 0.769755 | + | 1.33325i | ||||
\(416\) | −2.84849 | −0.139659 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.04011i | 0.344343i | ||||||||
\(419\) | 3.56481 | − | 6.17443i | 0.174152 | − | 0.301641i | −0.765715 | − | 0.643180i | \(-0.777615\pi\) |
0.939868 | + | 0.341539i | \(0.110948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.31007 | − | 4.00115i | −0.112586 | − | 0.195004i | 0.804226 | − | 0.594323i | \(-0.202580\pi\) |
−0.916812 | + | 0.399319i | \(0.869247\pi\) | |||||||
\(422\) | 3.26953 | − | 1.88766i | 0.159158 | − | 0.0918899i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.76282 | + | 6.51739i | −0.182524 | + | 0.316140i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.4161 | − | 7.16846i | −0.600157 | − | 0.346501i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.66949i | 0.176958i | ||||||||
\(431\) | −3.47078 | − | 2.00385i | −0.167181 | − | 0.0965223i | 0.414075 | − | 0.910243i | \(-0.364105\pi\) |
−0.581256 | + | 0.813721i | \(0.697439\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 29.4125i | − | 1.41348i | −0.707475 | − | 0.706738i | \(-0.750166\pi\) | ||
0.707475 | − | 0.706738i | \(-0.249834\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.2800 | −0.540212 | ||||||||
\(437\) | −5.58008 | − | 9.66498i | −0.266931 | − | 0.462339i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.5130 | + | 10.6885i | 0.883575 | + | 0.510133i | 0.871836 | − | 0.489799i | \(-0.162930\pi\) |
0.0117398 | + | 0.999931i | \(0.496263\pi\) | |||||||
\(440\) | 15.3490 | 0.731733 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.11392 | −0.100549 | ||||||||
\(443\) | 5.05227 | + | 2.91693i | 0.240041 | + | 0.138587i | 0.615195 | − | 0.788375i | \(-0.289077\pi\) |
−0.375155 | + | 0.926962i | \(0.622410\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.0284 | − | 31.2262i | −0.854630 | − | 1.48026i | ||||
\(446\) | 12.7782 | 0.605065 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.5823i | 1.06573i | 0.846202 | + | 0.532863i | \(0.178884\pi\) | ||||
−0.846202 | + | 0.532863i | \(0.821116\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.8493 | + | 20.6976i | 1.68808 | + | 0.974613i | ||||
\(452\) | 9.83228i | 0.462472i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.3051 | − | 9.99110i | −0.812168 | − | 0.468906i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.9311 | + | 34.5218i | −0.932340 | + | 1.61486i | −0.153029 | + | 0.988222i | \(0.548903\pi\) |
−0.779310 | + | 0.626638i | \(0.784430\pi\) | |||||||
\(458\) | 5.06568 | − | 8.77402i | 0.236704 | − | 0.409983i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −21.0718 | + | 12.1658i | −0.982476 | + | 0.567233i | ||||
\(461\) | 3.68254 | + | 6.37834i | 0.171513 | + | 0.297069i | 0.938949 | − | 0.344056i | \(-0.111801\pi\) |
−0.767436 | + | 0.641125i | \(0.778468\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.3457 | + | 24.8475i | −0.666702 | + | 1.15476i | 0.312119 | + | 0.950043i | \(0.398961\pi\) |
−0.978821 | + | 0.204718i | \(0.934372\pi\) | |||||||
\(464\) | 2.88766i | 0.134056i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.31007 | 0.338632 | ||||||||
\(467\) | −6.83519 | − | 11.8389i | −0.316295 | − | 0.547839i | 0.663417 | − | 0.748250i | \(-0.269106\pi\) |
−0.979712 | + | 0.200411i | \(0.935772\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.36387 | − | 4.25153i | 0.339670 | − | 0.196109i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.0183031 | − | 0.0105673i | 0.000842469 | − | 0.000486400i | ||||
\(473\) | 3.22157 | − | 1.85997i | 0.148128 | − | 0.0855216i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.6739 | − | 9.04931i | 0.719166 | − | 0.415211i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.20494 | + | 7.28317i | 0.192329 | + | 0.333124i | ||||
\(479\) | 10.4107 | 0.475679 | 0.237839 | − | 0.971304i | \(-0.423561\pi\) | ||||
0.237839 | + | 0.971304i | \(0.423561\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.54997i | 0.389845i | ||||||||
\(482\) | 4.47607 | − | 7.75277i | 0.203879 | − | 0.353129i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.28001 | − | 3.94910i | −0.103637 | − | 0.179504i | ||||
\(485\) | 63.4184 | − | 36.6146i | 2.87968 | − | 1.66258i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.16925 | + | 2.02520i | −0.0529838 | + | 0.0917707i | −0.891301 | − | 0.453412i | \(-0.850207\pi\) |
0.838317 | + | 0.545183i | \(0.183540\pi\) | |||||||
\(488\) | −1.23456 | + | 2.13832i | −0.0558858 | + | 0.0967970i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.3448 | + | 16.9422i | 1.32431 | + | 0.764591i | 0.984413 | − | 0.175871i | \(-0.0562742\pi\) |
0.339898 | + | 0.940462i | \(0.389608\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.14298i | 0.0965151i | ||||||||
\(494\) | 4.40271 | + | 2.54191i | 0.198087 | + | 0.114366i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.51174i | 0.157682i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.6045 | −0.743317 | −0.371659 | − | 0.928369i | \(-0.621211\pi\) | ||||
−0.371659 | + | 0.928369i | \(0.621211\pi\) | |||||||
\(500\) | −10.0017 | − | 17.3234i | −0.447288 | − | 0.774726i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.9494 | − | 6.32161i | −0.488694 | − | 0.282147i | ||||
\(503\) | 35.3661 | 1.57690 | 0.788449 | − | 0.615100i | \(-0.210885\pi\) | ||||
0.788449 | + | 0.615100i | \(0.210885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.2246 | 1.43398 | ||||||||
\(506\) | 21.3615 | + | 12.3331i | 0.949635 | + | 0.548272i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.47231 | + | 2.55012i | 0.0653232 | + | 0.113143i | ||||
\(509\) | −37.0582 | −1.64257 | −0.821287 | − | 0.570515i | \(-0.806744\pi\) | ||||
−0.821287 | + | 0.570515i | \(0.806744\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.1219 | − | 8.15329i | −0.622891 | − | 0.359626i | ||||
\(515\) | 66.3384i | 2.92322i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.46513 | − | 4.30999i | −0.328316 | − | 0.189553i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.54191 | − | 9.59886i | 0.243029 | − | 0.420938i | ||||
\(521\) | 0.891547 | − | 1.54420i | 0.0390594 | − | 0.0676528i | −0.845835 | − | 0.533445i | \(-0.820897\pi\) |
0.884894 | + | 0.465792i | \(0.154231\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.8312 | + | 12.0269i | −0.910886 | + | 0.525901i | −0.880716 | − | 0.473644i | \(-0.842938\pi\) |
−0.0301702 | + | 0.999545i | \(0.509605\pi\) | |||||||
\(524\) | −7.53255 | − | 13.0468i | −0.329061 | − | 0.569950i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.8608 | + | 20.5434i | −0.517154 | + | 0.895737i | ||||
\(527\) | 2.60612i | 0.113524i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.1014 | −0.700060 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.8876 | − | 14.9462i | 1.12132 | − | 0.647392i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 48.3126 | − | 27.8933i | 2.08874 | − | 1.20593i | ||||
\(536\) | −11.6474 | + | 6.72463i | −0.503091 | + | 0.290460i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.30716 | − | 3.64144i | 0.271921 | − | 0.156994i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0016 | − | 25.9835i | −0.644968 | − | 1.11712i | −0.984309 | − | 0.176454i | \(-0.943537\pi\) |
0.339341 | − | 0.940664i | \(-0.389796\pi\) | |||||||
\(542\) | 22.6879 | 0.974530 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.742117i | 0.0318180i | ||||||||
\(545\) | 21.9458 | − | 38.0113i | 0.940056 | − | 1.62822i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.7816 | − | 18.6743i | −0.460987 | − | 0.798454i | 0.538023 | − | 0.842930i | \(-0.319171\pi\) |
−0.999010 | + | 0.0444765i | \(0.985838\pi\) | |||||||
\(548\) | −13.6139 | + | 7.85997i | −0.581556 | + | 0.335761i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20.0007 | + | 34.6423i | −0.852835 | + | 1.47715i | ||||
\(551\) | 2.57686 | − | 4.46325i | 0.109778 | − | 0.190141i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −20.9298 | − | 12.0838i | −0.889221 | − | 0.513392i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 3.30675i | − | 0.140237i | ||||||
\(557\) | −31.9976 | − | 18.4738i | −1.35578 | − | 0.782762i | −0.366731 | − | 0.930327i | \(-0.619523\pi\) |
−0.989052 | + | 0.147565i | \(0.952856\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.68625i | − | 0.113616i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.74847 | −0.200302 | ||||||||
\(563\) | −7.58422 | − | 13.1363i | −0.319637 | − | 0.553627i | 0.660776 | − | 0.750584i | \(-0.270228\pi\) |
−0.980412 | + | 0.196957i | \(0.936894\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.1329 | − | 19.1293i | −1.39391 | − | 0.804774i | ||||
\(566\) | 29.3853 | 1.23516 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.94304 | 0.0815282 | ||||||||
\(569\) | −31.8084 | − | 18.3646i | −1.33348 | − | 0.769885i | −0.347648 | − | 0.937625i | \(-0.613020\pi\) |
−0.985831 | + | 0.167740i | \(0.946353\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.61387 | − | 9.72351i | −0.234933 | − | 0.406916i | 0.724320 | − | 0.689464i | \(-0.242154\pi\) |
−0.959253 | + | 0.282548i | \(0.908820\pi\) | |||||||
\(572\) | −11.2362 | −0.469810 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 63.4114i | − | 2.64444i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.6545 | − | 18.2757i | −1.31780 | − | 0.760829i | −0.334422 | − | 0.942424i | \(-0.608541\pi\) |
−0.983374 | + | 0.181594i | \(0.941874\pi\) | |||||||
\(578\) | − | 16.4493i | − | 0.684199i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.73085 | − | 5.61811i | −0.404052 | − | 0.233279i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2.42743 | − | 4.20443i | 0.100448 | − | 0.173981i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.73666 | + | 3.31206i | −0.236979 | + | 0.136820i | ||||
\(587\) | −4.99738 | − | 8.65571i | −0.206264 | − | 0.357259i | 0.744271 | − | 0.667878i | \(-0.232797\pi\) |
−0.950535 | + | 0.310619i | \(0.899464\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.13376 | − | 5.42784i | 0.129124 | − | 0.223650i | ||||
\(590\) | 0.0822372i | 0.00338565i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.00158 | 0.123364 | ||||||||
\(593\) | 3.89111 | + | 6.73961i | 0.159789 | + | 0.276763i | 0.934792 | − | 0.355194i | \(-0.115585\pi\) |
−0.775004 | + | 0.631957i | \(0.782252\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.52765 | + | 5.50079i | −0.390268 | + | 0.225321i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.4256 | − | 8.90597i | 0.630800 | − | 0.364192i | ||||
\(599\) | 21.6614 | − | 12.5062i | 0.885061 | − | 0.510990i | 0.0127373 | − | 0.999919i | \(-0.495945\pi\) |
0.872324 | + | 0.488929i | \(0.162612\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.9925 | − | 15.0068i | 1.06026 | − | 0.612139i | 0.134753 | − | 0.990879i | \(-0.456976\pi\) |
0.925503 | + | 0.378740i | \(0.123643\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.719988 | − | 1.24706i | −0.0292959 | − | 0.0507420i | ||||
\(605\) | 17.7436 | 0.721379 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 4.58280i | − | 0.186010i | −0.995666 | − | 0.0930050i | \(-0.970353\pi\) | ||
0.995666 | − | 0.0930050i | \(-0.0296473\pi\) | |||||||
\(608\) | 0.892369 | − | 1.54563i | 0.0361903 | − | 0.0626835i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.80380 | − | 8.32043i | −0.194500 | − | 0.336884i | ||||
\(611\) | −5.39073 | + | 3.11234i | −0.218085 | + | 0.125912i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.2761 | + | 26.4590i | −0.616996 | + | 1.06867i | 0.373034 | + | 0.927818i | \(0.378317\pi\) |
−0.990031 | + | 0.140852i | \(0.955016\pi\) | |||||||
\(614\) | 10.8621 | − | 18.8137i | 0.438359 | − | 0.759259i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.2484 | + | 16.3092i | 1.13724 | + | 0.656585i | 0.945745 | − | 0.324909i | \(-0.105334\pi\) |
0.191493 | + | 0.981494i | \(0.438667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 20.0045i | − | 0.804049i | −0.915629 | − | 0.402024i | \(-0.868307\pi\) | ||
0.915629 | − | 0.402024i | \(-0.131693\pi\) | |||||||
\(620\) | −11.8339 | − | 6.83228i | −0.475259 | − | 0.274391i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 6.29800i | − | 0.252527i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 27.1314 | 1.08526 | ||||||||
\(626\) | 11.1095 | + | 19.2423i | 0.444026 | + | 0.769076i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.3822 | + | 8.30354i | 0.573910 | + | 0.331347i | ||||
\(629\) | 2.22752 | 0.0888171 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.09634 | 0.242692 | 0.121346 | − | 0.992610i | \(-0.461279\pi\) | ||||
0.121346 | + | 0.992610i | \(0.461279\pi\) | |||||||
\(632\) | 3.14898 | + | 1.81806i | 0.125260 | + | 0.0723187i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.83070 | − | 13.5632i | −0.310997 | − | 0.538663i | ||||
\(635\) | −11.4579 | −0.454691 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 11.3907i | 0.450963i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.36980 | − | 1.94556i | −0.133203 | − | 0.0769049i | ||||
\(641\) | − | 33.4415i | − | 1.32086i | −0.750888 | − | 0.660429i | \(-0.770374\pi\) | ||
0.750888 | − | 0.660429i | \(-0.229626\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.6022 | − | 9.58527i | −0.654726 | − | 0.378006i | 0.135539 | − | 0.990772i | \(-0.456724\pi\) |
−0.790264 | + | 0.612766i | \(0.790057\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.662242 | − | 1.14704i | 0.0260556 | − | 0.0451296i | ||||
\(647\) | 22.3025 | − | 38.6290i | 0.876800 | − | 1.51866i | 0.0219681 | − | 0.999759i | \(-0.493007\pi\) |
0.854832 | − | 0.518904i | \(-0.173660\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.0721988 | − | 0.0416840i | 0.00283405 | − | 0.00163624i | ||||
\(650\) | 14.4430 | + | 25.0159i | 0.566500 | + | 0.981206i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.19773 | + | 10.7348i | −0.242722 | + | 0.420407i | ||||
\(653\) | − | 0.652123i | − | 0.0255195i | −0.999919 | − | 0.0127598i | \(-0.995938\pi\) | ||
0.999919 | − | 0.0127598i | \(-0.00406167\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 58.6200 | 2.29047 | ||||||||
\(656\) | −5.24705 | − | 9.08816i | −0.204863 | − | 0.354833i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.2738 | + | 15.1692i | −1.02348 | + | 0.590908i | −0.915111 | − | 0.403202i | \(-0.867897\pi\) |
−0.108372 | + | 0.994110i | \(0.534564\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.1004 | + | 6.40881i | −0.431755 | + | 0.249274i | −0.700094 | − | 0.714051i | \(-0.746859\pi\) |
0.268339 | + | 0.963325i | \(0.413525\pi\) | |||||||
\(662\) | 1.10181 | − | 0.636129i | 0.0428230 | − | 0.0247239i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.98012 | + | 4.02998i | −0.270881 | + | 0.156393i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.02843 | − | 15.6377i | −0.349582 | − | 0.605494i | ||||
\(668\) | −11.7217 | −0.453528 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 52.3326i | − | 2.02179i | ||||||
\(671\) | −4.86986 | + | 8.43484i | −0.187999 | + | 0.325623i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.2246 | + | 19.4416i | 0.432678 | + | 0.749420i | 0.997103 | − | 0.0760644i | \(-0.0242355\pi\) |
−0.564425 | + | 0.825484i | \(0.690902\pi\) | |||||||
\(674\) | 6.54717 | − | 3.78001i | 0.252188 | − | 0.145601i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.44304 | − | 4.23147i | 0.0939632 | − | 0.162749i | ||||
\(677\) | 25.5903 | − | 44.3237i | 0.983516 | − | 1.70350i | 0.335163 | − | 0.942160i | \(-0.391209\pi\) |
0.648353 | − | 0.761340i | \(-0.275458\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.50079 | − | 1.44383i | −0.0959009 | − | 0.0553684i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13.8525i | 0.530438i | ||||||||
\(683\) | −12.6107 | − | 7.28080i | −0.482536 | − | 0.278592i | 0.238937 | − | 0.971035i | \(-0.423201\pi\) |
−0.721473 | + | 0.692443i | \(0.756534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 61.1681i | − | 2.33711i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.943042 | −0.0359532 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.1757 | − | 12.2258i | −0.805560 | − | 0.465090i | 0.0398517 | − | 0.999206i | \(-0.487311\pi\) |
−0.845412 | + | 0.534115i | \(0.820645\pi\) | |||||||
\(692\) | −16.7710 | −0.637536 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.1091 | −0.839250 | ||||||||
\(695\) | 11.1431 | + | 6.43347i | 0.422682 | + | 0.244035i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.89393 | − | 6.74448i | −0.147493 | − | 0.255465i | ||||
\(698\) | −14.7435 | −0.558048 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.21697i | 0.0837337i | 0.999123 | + | 0.0418669i | \(0.0133305\pi\) | ||||
−0.999123 | + | 0.0418669i | \(0.986669\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.63932 | − | 2.67851i | −0.174975 | − | 0.101022i | ||||
\(704\) | 3.94462i | 0.148668i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.9629 | + | 8.63881i | 0.563135 | + | 0.325126i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.1962 | − | 21.1244i | 0.458036 | − | 0.793342i | −0.540821 | − | 0.841138i | \(-0.681886\pi\) |
0.998857 | + | 0.0477959i | \(0.0152197\pi\) | |||||||
\(710\) | −3.78030 | + | 6.54767i | −0.141872 | + | 0.245730i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.02499 | − | 4.63323i | 0.300749 | − | 0.173638i | ||||
\(713\) | −10.9796 | − | 19.0173i | −0.411190 | − | 0.712203i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.8607 | − | 37.8639i | 0.817544 | − | 1.41603i | ||||
\(716\) | − | 5.77532i | − | 0.215834i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.9129 | 0.407267 | ||||||||
\(719\) | 1.11376 | + | 1.92909i | 0.0415363 | + | 0.0719429i | 0.886046 | − | 0.463597i | \(-0.153441\pi\) |
−0.844510 | + | 0.535540i | \(0.820108\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.6959 | − | 7.90736i | 0.509710 | − | 0.294281i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.79180 | − | 2.76655i | 0.178086 | − | 0.102818i | ||||
\(725\) | 25.3599 | − | 14.6416i | 0.941844 | − | 0.543774i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.4880 | + | 6.05523i | −0.388977 | + | 0.224576i | −0.681717 | − | 0.731616i | \(-0.738766\pi\) |
0.292740 | + | 0.956192i | \(0.405433\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.44541 | + | 16.3599i | 0.349590 | + | 0.605508i | ||||
\(731\) | −0.699848 | −0.0258848 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.6661i | 0.578641i | 0.957232 | + | 0.289321i | \(0.0934293\pi\) | ||||
−0.957232 | + | 0.289321i | \(0.906571\pi\) | |||||||
\(734\) | −17.8636 | + | 30.9407i | −0.659357 | + | 1.14204i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.12656 | − | 5.41535i | −0.115246 | − | 0.199613i | ||||
\(737\) | −45.9446 | + | 26.5261i | −1.69239 | + | 0.977102i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.05227 | − | 7.01874i | 0.149065 | − | 0.258188i | −0.781817 | − | 0.623508i | \(-0.785707\pi\) |
0.930882 | + | 0.365319i | \(0.119040\pi\) | |||||||
\(740\) | −5.83974 | + | 10.1147i | −0.214673 | + | 0.371825i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.5429 | + | 6.08697i | 0.386783 | + | 0.223309i | 0.680765 | − | 0.732502i | \(-0.261647\pi\) |
−0.293982 | + | 0.955811i | \(0.594981\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 42.8084i | − | 1.56838i | ||||||
\(746\) | 27.7648 | + | 16.0300i | 1.01654 | + | 0.586900i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.92737i | 0.107035i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.6123 | 1.26302 | 0.631511 | − | 0.775367i | \(-0.282435\pi\) | ||||
0.631511 | + | 0.775367i | \(0.282435\pi\) | |||||||
\(752\) | 1.09263 | + | 1.89248i | 0.0398440 | + | 0.0690118i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.12348 | + | 4.11274i | 0.259422 | + | 0.149777i | ||||
\(755\) | 5.60311 | 0.203918 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.0553 | −1.41949 | −0.709744 | − | 0.704459i | \(-0.751190\pi\) | ||||
−0.709744 | + | 0.704459i | \(0.751190\pi\) | |||||||
\(758\) | −30.2149 | − | 17.4446i | −1.09745 | − | 0.633615i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.47231 | + | 6.01422i | 0.125954 | + | 0.218159i | ||||
\(761\) | −10.2252 | −0.370665 | −0.185332 | − | 0.982676i | \(-0.559336\pi\) | ||||
−0.185332 | + | 0.982676i | \(0.559336\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 6.21372i | − | 0.224805i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.1851 | − | 8.76711i | −0.548659 | − | 0.316769i | ||||
\(767\) | − | 0.0602018i | − | 0.00217376i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.6746 | + | 15.4006i | 0.961910 | + | 0.555359i | 0.896760 | − | 0.442517i | \(-0.145914\pi\) |
0.0651494 | + | 0.997876i | \(0.479248\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.90271 | + | 6.75970i | −0.140462 | + | 0.243287i | ||||
\(773\) | 17.8916 | − | 30.9892i | 0.643518 | − | 1.11461i | −0.341124 | − | 0.940018i | \(-0.610808\pi\) |
0.984642 | − | 0.174587i | \(-0.0558590\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.8406 | − | 17.8059i | 1.10783 | − | 0.639605i | ||||
\(776\) | 9.40980 | + | 16.2983i | 0.337792 | + | 0.585073i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.81086 | − | 6.60060i | 0.136626 | − | 0.236643i | ||||
\(779\) | 18.7292i | 0.671044i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.66456 | 0.274260 | ||||||||
\(782\) | −2.32027 | − | 4.01882i | −0.0829727 | − | 0.143713i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −55.9626 | + | 32.3100i | −1.99739 | + | 1.15319i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.2859 | − | 7.67064i | 0.473592 | − | 0.273429i | −0.244150 | − | 0.969737i | \(-0.578509\pi\) |
0.717742 | + | 0.696309i | \(0.245176\pi\) | |||||||
\(788\) | 11.0624 | − | 6.38687i | 0.394081 | − | 0.227523i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.2530 | + | 7.07430i | −0.435944 | + | 0.251692i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.51663 | + | 6.09098i | 0.124879 | + | 0.216297i | ||||
\(794\) | −37.6469 | −1.33604 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.81201i | 0.0642250i | ||||||||
\(797\) | −17.5200 | + | 30.3455i | −0.620590 | + | 1.07489i | 0.368786 | + | 0.929514i | \(0.379774\pi\) |
−0.989376 | + | 0.145379i | \(0.953560\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.810856 | + | 1.40444i | 0.0286860 | + | 0.0496857i | ||||
\(800\) | 8.78217 | − | 5.07039i | 0.310496 | − | 0.179265i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.7207 | − | 18.5689i | 0.378562 | − | 0.655689i | ||||
\(803\) | 9.57529 | − | 16.5849i | 0.337905 | − | 0.585268i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.66299 | + | 5.00158i | 0.305141 | + | 0.176173i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.28158i | 0.291345i | ||||||||
\(809\) | 23.6360 | + | 13.6462i | 0.830997 | + | 0.479777i | 0.854194 | − | 0.519954i | \(-0.174051\pi\) |
−0.0231967 | + | 0.999731i | \(0.507384\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.7628i | 0.974883i | 0.873156 | + | 0.487442i | \(0.162070\pi\) | ||||
−0.873156 | + | 0.487442i | \(0.837930\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.8401 | 0.414995 | ||||||||
\(815\) | −24.1161 | − | 41.7703i | −0.844749 | − | 1.46315i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.45759 | + | 0.841542i | 0.0509947 | + | 0.0294418i | ||||
\(818\) | 29.5703 | 1.03390 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 40.8338 | 1.42598 | ||||||||
\(821\) | −38.4968 | − | 22.2262i | −1.34355 | − | 0.775698i | −0.356223 | − | 0.934401i | \(-0.615936\pi\) |
−0.987326 | + | 0.158703i | \(0.949269\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.5577 | + | 44.2672i | 0.890884 | + | 1.54306i | 0.838818 | + | 0.544413i | \(0.183247\pi\) |
0.0520663 | + | 0.998644i | \(0.483419\pi\) | |||||||
\(824\) | −17.0487 | −0.593919 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.5414i | 0.505653i | 0.967512 | + | 0.252826i | \(0.0813601\pi\) | ||||
−0.967512 | + | 0.252826i | \(0.918640\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.2211 | + | 13.9841i | 0.841234 | + | 0.485686i | 0.857683 | − | 0.514178i | \(-0.171903\pi\) |
−0.0164497 | + | 0.999865i | \(0.505236\pi\) | |||||||
\(830\) | − | 31.3622i | − | 1.08860i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.46687 | + | 1.42425i | 0.0855233 | + | 0.0493769i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.8053 | − | 39.5000i | 0.789211 | − | 1.36695i | ||||
\(836\) | 3.52006 | − | 6.09692i | 0.121744 | − | 0.210866i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.17443 | + | 3.56481i | −0.213292 | + | 0.123144i | ||||
\(839\) | −0.499354 | − | 0.864906i | −0.0172396 | − | 0.0298599i | 0.857277 | − | 0.514856i | \(-0.172154\pi\) |
−0.874517 | + | 0.484996i | \(0.838821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.3307 | + | 17.8933i | −0.356231 | + | 0.617011i | ||||
\(842\) | 4.62014i | 0.159220i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.77532 | −0.129952 | ||||||||
\(845\) | 9.50616 | + | 16.4651i | 0.327022 | + | 0.566418i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.51739 | − | 3.76282i | 0.223545 | − | 0.129064i | ||||
\(851\) | −16.2546 | + | 9.38460i | −0.557200 | + | 0.321700i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.48739 | + | 4.90020i | −0.290603 | + | 0.167780i | −0.638214 | − | 0.769859i | \(-0.720326\pi\) |
0.347611 | + | 0.937639i | \(0.386993\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.16846 | + | 12.4161i | 0.245013 | + | 0.424375i | ||||
\(857\) | −7.70003 | −0.263028 | −0.131514 | − | 0.991314i | \(-0.541984\pi\) | ||||
−0.131514 | + | 0.991314i | \(0.541984\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 18.9396i | − | 0.646210i | −0.946363 | − | 0.323105i | \(-0.895273\pi\) | ||
0.946363 | − | 0.323105i | \(-0.104727\pi\) | |||||||
\(860\) | 1.83474 | − | 3.17787i | 0.0625642 | − | 0.108364i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.00385 | + | 3.47078i | 0.0682515 | + | 0.118215i | ||||
\(863\) | −15.1156 | + | 8.72700i | −0.514541 | + | 0.297070i | −0.734698 | − | 0.678394i | \(-0.762676\pi\) |
0.220157 | + | 0.975464i | \(0.429343\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.6289 | − | 56.5149i | 1.10942 | − | 1.92156i | ||||
\(866\) | −14.7063 | + | 25.4720i | −0.499740 | + | 0.865574i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.4215 | + | 7.17157i | 0.421371 | + | 0.243279i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.3101i | 1.29809i | ||||||||
\(872\) | 9.76874 | + | 5.63998i | 0.330811 | + | 0.190994i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.1602i | 0.377498i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.392305 | 0.0132472 | 0.00662360 | − | 0.999978i | \(-0.497892\pi\) | ||||
0.00662360 | + | 0.999978i | \(0.497892\pi\) | |||||||
\(878\) | −10.6885 | − | 18.5130i | −0.360718 | − | 0.624782i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.2926 | − | 7.67448i | −0.448093 | − | 0.258707i | ||||
\(881\) | 37.0259 | 1.24744 | 0.623718 | − | 0.781650i | \(-0.285622\pi\) | ||||
0.623718 | + | 0.781650i | \(0.285622\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.9586 | −1.00819 | −0.504094 | − | 0.863649i | \(-0.668174\pi\) | ||||
−0.504094 | + | 0.863649i | \(0.668174\pi\) | |||||||
\(884\) | 1.83070 | + | 1.05696i | 0.0615732 | + | 0.0355493i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.91693 | − | 5.05227i | −0.0979962 | − | 0.169734i | ||||
\(887\) | 28.9859 | 0.973252 | 0.486626 | − | 0.873610i | \(-0.338227\pi\) | ||||
0.486626 | + | 0.873610i | \(0.338227\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 36.0569i | 1.20863i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.0662 | − | 6.38910i | −0.370525 | − | 0.213923i | ||||
\(893\) | − | 3.90010i | − | 0.130512i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.4617 | + | 11.2362i | 0.650533 | + | 0.375586i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.2912 | − | 19.5569i | 0.376791 | − | 0.652621i | ||||
\(899\) | 5.07035 | − | 8.78211i | 0.169106 | − | 0.292900i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −20.6976 | − | 35.8493i | −0.689156 | − | 1.19365i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.91614 | − | 8.51501i | 0.163508 | − | 0.283205i | ||||
\(905\) | 21.5299i | 0.715679i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.89546 | −0.129347 | −0.0646733 | − | 0.997906i | \(-0.520601\pi\) | ||||
−0.0646733 | + | 0.997906i | \(0.520601\pi\) | |||||||
\(908\) | 9.99110 | + | 17.3051i | 0.331566 | + | 0.574290i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.32768 | + | 0.766538i | −0.0439881 | + | 0.0253966i | −0.521833 | − | 0.853048i | \(-0.674752\pi\) |
0.477845 | + | 0.878444i | \(0.341418\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.5339 | + | 15.8967i | −0.911240 | + | 0.526105i | ||||
\(914\) | 34.5218 | − | 19.9311i | 1.14188 | − | 0.659264i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.77402 | + | 5.06568i | −0.289902 | + | 0.167375i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.1266 | − | 24.4679i | −0.465992 | − | 0.807122i | 0.533254 | − | 0.845955i | \(-0.320969\pi\) |
−0.999246 | + | 0.0388335i | \(0.987636\pi\) | |||||||
\(920\) | 24.3316 | 0.802188 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 7.36507i | − | 0.242556i | ||||||
\(923\) | 2.76737 | − | 4.79323i | 0.0910892 | − | 0.157771i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.2192 | − | 26.3603i | −0.500403 | − | 0.866723i | ||||
\(926\) | 24.8475 | − | 14.3457i | 0.816539 | − | 0.471429i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.44383 | − | 2.50079i | 0.0473961 | − | 0.0820924i | ||||
\(929\) | 1.64363 | − | 2.84685i | 0.0539257 | − | 0.0934021i | −0.837802 | − | 0.545974i | \(-0.816160\pi\) |
0.891728 | + | 0.452571i | \(0.149493\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.33070 | − | 3.65503i | −0.207369 | − | 0.119725i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.6704i | 0.447308i | ||||||||
\(935\) | −9.86466 | − | 5.69536i | −0.322609 | − | 0.186258i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 35.5084i | − | 1.16001i | −0.814613 | − | 0.580005i | \(-0.803051\pi\) | ||
0.814613 | − | 0.580005i | \(-0.196949\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.50307 | −0.277339 | ||||||||
\(941\) | 6.24941 | + | 10.8243i | 0.203725 | + | 0.352862i | 0.949726 | − | 0.313083i | \(-0.101362\pi\) |
−0.746001 | + | 0.665945i | \(0.768028\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 56.8293 | + | 32.8104i | 1.85062 | + | 1.06845i | ||||
\(944\) | −0.0211346 | −0.000687873 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.71994 | −0.120946 | ||||||||
\(947\) | 31.2769 | + | 18.0577i | 1.01636 | + | 0.586796i | 0.913048 | − | 0.407852i | \(-0.133722\pi\) |
0.103313 | + | 0.994649i | \(0.467056\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.91452 | − | 11.9763i | −0.224455 | − | 0.388767i | ||||
\(950\) | −18.0986 | −0.587197 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 45.2925i | − | 1.46717i | −0.679599 | − | 0.733584i | \(-0.737846\pi\) | ||
0.679599 | − | 0.733584i | \(-0.262154\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.9390 | + | 12.0892i | 0.677571 | + | 0.391196i | ||||
\(956\) | − | 8.40988i | − | 0.271995i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.01596 | − | 5.20537i | −0.291293 | − | 0.168178i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.33386 | + | 16.1667i | −0.301092 | + | 0.521507i | ||||
\(962\) | 4.27499 | − | 7.40449i | 0.137831 | − | 0.238730i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.75277 | + | 4.47607i | −0.249700 | + | 0.144164i | ||||
\(965\) | −15.1859 | − | 26.3028i | −0.488851 | − | 0.846716i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.0000 | − | 20.7845i | 0.385893 | − | 0.668385i | −0.606000 | − | 0.795465i | \(-0.707227\pi\) |
0.991893 | + | 0.127079i | \(0.0405602\pi\) | |||||||
\(968\) | 4.56002i | 0.146565i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −73.2292 | −2.35125 | ||||||||
\(971\) | 16.6813 | + | 28.8928i | 0.535328 | + | 0.927215i | 0.999147 | + | 0.0412855i | \(0.0131453\pi\) |
−0.463819 | + | 0.885930i | \(0.653521\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.02520 | − | 1.16925i | 0.0648917 | − | 0.0374652i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.13832 | − | 1.23456i | 0.0684458 | − | 0.0395172i | ||||
\(977\) | −29.8846 | + | 17.2539i | −0.956091 | + | 0.552000i | −0.894968 | − | 0.446131i | \(-0.852802\pi\) |
−0.0611236 | + | 0.998130i | \(0.519468\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.6555 | − | 18.2763i | 1.01172 | − | 0.584114i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16.9422 | − | 29.3448i | −0.540648 | − | 0.936429i | ||||
\(983\) | 2.41302 | 0.0769633 | 0.0384817 | − | 0.999259i | \(-0.487748\pi\) | ||||
0.0384817 | + | 0.999259i | \(0.487748\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49.7041i | 1.58370i | ||||||||
\(986\) | 1.07149 | − | 1.85588i | 0.0341232 | − | 0.0591032i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.54191 | − | 4.40271i | −0.0808688 | − | 0.140069i | ||||
\(989\) | 5.10691 | − | 2.94847i | 0.162390 | − | 0.0937560i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.2991 | + | 42.0873i | −0.771887 | + | 1.33695i | 0.164641 | + | 0.986354i | \(0.447353\pi\) |
−0.936528 | + | 0.350594i | \(0.885980\pi\) | |||||||
\(992\) | 1.75587 | − | 3.04125i | 0.0557488 | − | 0.0965598i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.10612 | − | 3.52537i | −0.193577 | − | 0.111762i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 44.8542i | − | 1.42055i | −0.703926 | − | 0.710274i | \(-0.748571\pi\) | ||
0.703926 | − | 0.710274i | \(-0.251429\pi\) | |||||||
\(998\) | 14.3799 | + | 8.30223i | 0.455187 | + | 0.262802i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))