Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(241,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 481.2 | ||
Root | \(-1.18614 - 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.481 |
Dual form | 720.2.q.f.241.1 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | + | 1.65831i | −0.288675 | + | 0.957427i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.18614 | − | 2.05446i | −0.448319 | − | 0.776511i | 0.549958 | − | 0.835192i | \(-0.314644\pi\) |
−0.998277 | + | 0.0586811i | \(0.981310\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.50000 | − | 1.65831i | −0.833333 | − | 0.552771i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.686141 | + | 1.18843i | 0.206879 | + | 0.358325i | 0.950730 | − | 0.310021i | \(-0.100336\pi\) |
−0.743851 | + | 0.668346i | \(0.767003\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.37228 | + | 4.10891i | −0.657952 | + | 1.13961i | 0.323192 | + | 0.946333i | \(0.395244\pi\) |
−0.981145 | + | 0.193274i | \(0.938089\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.18614 | + | 1.26217i | 0.306260 | + | 0.325891i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.37228 | −1.78804 | −0.894020 | − | 0.448026i | \(-0.852127\pi\) | ||||
−0.894020 | + | 0.448026i | \(0.852127\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.37228 | −0.773654 | −0.386827 | − | 0.922152i | \(-0.626429\pi\) | ||||
−0.386827 | + | 0.922152i | \(0.626429\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | − | 0.939764i | 0.872872 | − | 0.205073i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.18614 | + | 3.78651i | −0.455842 | + | 0.789541i | −0.998736 | − | 0.0502598i | \(-0.983995\pi\) |
0.542894 | + | 0.839801i | \(0.317328\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | − | 3.31662i | 0.769800 | − | 0.638285i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.18614 | + | 3.78651i | 0.405956 | + | 0.703137i | 0.994432 | − | 0.105378i | \(-0.0336052\pi\) |
−0.588476 | + | 0.808515i | \(0.700272\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.37228 | + | 5.84096i | −0.605680 | + | 1.04907i | 0.386264 | + | 0.922388i | \(0.373765\pi\) |
−0.991944 | + | 0.126680i | \(0.959568\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.31386 | + | 0.543620i | −0.402791 | + | 0.0946322i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.37228 | −0.400989 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.62772 | − | 5.98844i | −0.901156 | − | 0.958918i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | − | 2.59808i | 0.234261 | − | 0.405751i | −0.724797 | − | 0.688963i | \(-0.758066\pi\) |
0.959058 | + | 0.283211i | \(0.0913998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.68614 | − | 9.84868i | −0.867128 | − | 1.50191i | −0.864918 | − | 0.501913i | \(-0.832630\pi\) |
−0.00221007 | − | 0.999998i | \(-0.500703\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.68614 | + | 1.33591i | −0.400426 | + | 0.199145i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.813859 | − | 1.40965i | −0.118714 | − | 0.205618i | 0.800545 | − | 0.599273i | \(-0.204544\pi\) |
−0.919258 | + | 0.393655i | \(0.871210\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.686141 | − | 1.18843i | 0.0980201 | − | 0.169776i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.68614 | − | 12.2255i | 0.516163 | − | 1.71192i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.4891 | 1.57815 | 0.789076 | − | 0.614295i | \(-0.210560\pi\) | ||||
0.789076 | + | 0.614295i | \(0.210560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.37228 | 0.185038 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.68614 | − | 5.59230i | 0.223335 | − | 0.740718i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.686141 | + | 1.18843i | −0.0893279 | + | 0.154720i | −0.907227 | − | 0.420641i | \(-0.861805\pi\) |
0.817899 | + | 0.575361i | \(0.195139\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.55842 | − | 7.89542i | −0.583646 | − | 1.01090i | −0.995043 | − | 0.0994483i | \(-0.968292\pi\) |
0.411397 | − | 0.911456i | \(-0.365041\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.441578 | + | 7.10313i | −0.0556336 | + | 0.894910i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.37228 | + | 4.10891i | 0.294245 | + | 0.509648i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.50000 | + | 6.06218i | −0.427593 | + | 0.740613i | −0.996659 | − | 0.0816792i | \(-0.973972\pi\) |
0.569066 | + | 0.822292i | \(0.307305\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.18614 | − | 5.51856i | −0.624338 | − | 0.664356i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.1168 | −1.65225 | −0.826126 | − | 0.563486i | \(-0.809460\pi\) | ||||
−0.826126 | + | 0.563486i | \(0.809460\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.68614 | − | 0.396143i | 0.194699 | − | 0.0457427i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.62772 | − | 2.81929i | 0.185496 | − | 0.321288i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | + | 1.73205i | 0.112509 | + | 0.194871i | 0.916781 | − | 0.399390i | \(-0.130778\pi\) |
−0.804272 | + | 0.594261i | \(0.797445\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.50000 | + | 8.29156i | 0.388889 | + | 0.921285i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.813859 | + | 1.40965i | 0.0893327 | + | 0.154729i | 0.907229 | − | 0.420637i | \(-0.138193\pi\) |
−0.817897 | + | 0.575365i | \(0.804860\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.68614 | + | 6.38458i | −0.399818 | + | 0.692505i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.37228 | + | 1.73205i | −0.790392 | + | 0.185695i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.11684 | −0.118385 | −0.0591926 | − | 0.998247i | \(-0.518853\pi\) | ||||
−0.0591926 | + | 0.998247i | \(0.518853\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.2554 | 1.17989 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.00000 | − | 8.51278i | −0.829561 | − | 0.882734i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.68614 | + | 2.92048i | −0.172994 | + | 0.299635i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.31386 | + | 2.27567i | 0.133402 | + | 0.231059i | 0.924986 | − | 0.380001i | \(-0.124076\pi\) |
−0.791584 | + | 0.611061i | \(0.790743\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.255437 | − | 4.10891i | 0.0256724 | − | 0.412961i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.37228 | + | 7.57301i | 0.435058 | + | 0.753543i | 0.997300 | − | 0.0734297i | \(-0.0233944\pi\) |
−0.562242 | + | 0.826973i | \(0.690061\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | + | 13.8564i | −0.788263 | + | 1.36531i | 0.138767 | + | 0.990325i | \(0.455686\pi\) |
−0.927030 | + | 0.374987i | \(0.877647\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.18614 | − | 3.93398i | 0.115755 | − | 0.383917i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.4891 | 1.40072 | 0.700358 | − | 0.713791i | \(-0.253024\pi\) | ||||
0.700358 | + | 0.713791i | \(0.253024\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.62772 | 0.922168 | 0.461084 | − | 0.887356i | \(-0.347461\pi\) | ||||
0.461084 | + | 0.887356i | \(0.347461\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | − | 6.63325i | 0.189832 | − | 0.629600i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.37228 | + | 12.7692i | −0.693526 | + | 1.20122i | 0.277149 | + | 0.960827i | \(0.410610\pi\) |
−0.970675 | + | 0.240395i | \(0.922723\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.18614 | + | 3.78651i | 0.203859 | + | 0.353094i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.7446 | − | 6.33830i | 1.17824 | − | 0.585976i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.74456 | + | 15.1460i | 0.801613 | + | 1.38843i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.55842 | − | 7.89542i | 0.414402 | − | 0.717765i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.55842 | + | 3.78651i | 0.320852 | + | 0.341418i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.11684 | −0.808989 | −0.404495 | − | 0.914540i | \(-0.632553\pi\) | ||||
−0.404495 | + | 0.914540i | \(0.632553\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19.1753 | − | 4.50506i | 1.68829 | − | 0.396648i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.37228 | − | 7.57301i | 0.382008 | − | 0.661657i | −0.609341 | − | 0.792908i | \(-0.708566\pi\) |
0.991349 | + | 0.131251i | \(0.0418993\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | + | 6.92820i | 0.346844 | + | 0.600751i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.872281 | − | 5.12241i | −0.0750740 | − | 0.440867i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.941578 | + | 1.63086i | 0.0804444 | + | 0.139334i | 0.903441 | − | 0.428713i | \(-0.141033\pi\) |
−0.822996 | + | 0.568046i | \(0.807699\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.05842 | − | 15.6896i | 0.768325 | − | 1.33078i | −0.170145 | − | 0.985419i | \(-0.554424\pi\) |
0.938470 | − | 0.345359i | \(-0.112243\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.74456 | − | 0.644810i | 0.231134 | − | 0.0543028i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.51087 | −0.544467 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.37228 | 0.363098 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.62772 | + | 1.73205i | 0.134252 | + | 0.142857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.55842 | + | 16.5557i | −0.783056 | + | 1.35629i | 0.147097 | + | 0.989122i | \(0.453007\pi\) |
−0.930153 | + | 0.367171i | \(0.880326\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | − | 8.66025i | −0.406894 | − | 0.704761i | 0.587646 | − | 0.809118i | \(-0.300055\pi\) |
−0.994540 | + | 0.104357i | \(0.966722\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.4307 | + | 12.2255i | 1.49003 | + | 0.988377i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.37228 | + | 5.84096i | 0.270868 | + | 0.469157i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.37228 | + | 4.10891i | −0.189329 | + | 0.327927i | −0.945027 | − | 0.326993i | \(-0.893964\pi\) |
0.755698 | + | 0.654920i | \(0.227298\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.74456 | + | 19.0526i | −0.455573 | + | 1.51097i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3723 | 0.817450 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.48913 | −0.116637 | −0.0583186 | − | 0.998298i | \(-0.518574\pi\) | ||||
−0.0583186 | + | 0.998298i | \(0.518574\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.686141 | + | 2.27567i | −0.0534160 | + | 0.177161i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.81386 | − | 6.60580i | 0.295125 | − | 0.511172i | −0.679889 | − | 0.733315i | \(-0.737972\pi\) |
0.975014 | + | 0.222143i | \(0.0713053\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.75544 | − | 8.23666i | −0.365803 | − | 0.633589i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.43070 | + | 5.59230i | 0.644712 | + | 0.427654i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.62772 | − | 8.01544i | −0.351839 | − | 0.609403i | 0.634733 | − | 0.772732i | \(-0.281110\pi\) |
−0.986572 | + | 0.163329i | \(0.947777\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.18614 | + | 2.05446i | −0.0896638 | + | 0.155302i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.62772 | − | 1.73205i | −0.122347 | − | 0.130189i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.25544 | 0.243323 | 0.121661 | − | 0.992572i | \(-0.461178\pi\) | ||||
0.121661 | + | 0.992572i | \(0.461178\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.86141 | −0.584334 | −0.292167 | − | 0.956367i | \(-0.594376\pi\) | ||||
−0.292167 | + | 0.956367i | \(0.594376\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.3723 | − | 3.61158i | 1.13635 | − | 0.266976i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00000 | + | 3.46410i | −0.147043 | + | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.05842 | − | 8.76144i | −0.369908 | − | 0.640700i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.5584 | − | 4.28384i | −0.840751 | − | 0.311604i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.74456 | − | 4.75372i | −0.198590 | − | 0.343967i | 0.749482 | − | 0.662025i | \(-0.230303\pi\) |
−0.948071 | + | 0.318058i | \(0.896969\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.94158 | + | 3.36291i | −0.139758 | + | 0.242068i | −0.927405 | − | 0.374059i | \(-0.877966\pi\) |
0.787647 | + | 0.616127i | \(0.211299\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.00000 | + | 1.87953i | −0.572892 | + | 0.134596i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.4891 | 1.24605 | 0.623024 | − | 0.782202i | \(-0.285904\pi\) | ||||
0.623024 | + | 0.782202i | \(0.285904\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.48913 | 0.672666 | 0.336333 | − | 0.941743i | \(-0.390813\pi\) | ||||
0.336333 | + | 0.941743i | \(0.390813\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.30298 | − | 8.83518i | −0.585647 | − | 0.623186i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.18614 | − | 8.98266i | 0.363996 | − | 0.630459i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.50000 | − | 2.59808i | −0.104765 | − | 0.181458i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.7446 | − | 5.84096i | 0.816304 | − | 0.405975i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.31386 | − | 4.00772i | −0.160053 | − | 0.277220i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.62772 | + | 6.28339i | −0.249742 | + | 0.432567i | −0.963454 | − | 0.267873i | \(-0.913679\pi\) |
0.713712 | + | 0.700439i | \(0.247013\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.00000 | + | 9.94987i | −0.205557 | + | 0.681754i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.3723 | −0.775583 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000 | 1.08615 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.05842 | − | 23.4101i | 0.476964 | − | 1.58191i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.4891 | − | 30.2921i | 1.17645 | − | 2.03766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.18614 | + | 10.7147i | 0.414255 | + | 0.717510i | 0.995350 | − | 0.0963255i | \(-0.0307090\pi\) |
−0.581095 | + | 0.813836i | \(0.697376\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.186141 | + | 2.99422i | −0.0124094 | + | 0.199615i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.941578 | + | 1.63086i | 0.0624947 | + | 0.108244i | 0.895580 | − | 0.444901i | \(-0.146761\pi\) |
−0.833085 | + | 0.553145i | \(0.813428\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.18614 | + | 15.9109i | −0.607037 | + | 1.05142i | 0.384689 | + | 0.923046i | \(0.374309\pi\) |
−0.991726 | + | 0.128373i | \(0.959025\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.86141 | + | 4.10891i | 0.254062 | + | 0.270347i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.1168 | −0.662776 | −0.331388 | − | 0.943494i | \(-0.607517\pi\) | ||||
−0.331388 | + | 0.943494i | \(0.607517\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.62772 | −0.106181 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.37228 | + | 0.792287i | −0.219053 | + | 0.0514646i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.37228 | + | 12.7692i | −0.476873 | + | 0.825969i | −0.999649 | − | 0.0265017i | \(-0.991563\pi\) |
0.522776 | + | 0.852470i | \(0.324897\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.24456 | − | 9.08385i | −0.337832 | − | 0.585142i | 0.646193 | − | 0.763174i | \(-0.276360\pi\) |
−0.984025 | + | 0.178032i | \(0.943027\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5000 | + | 1.65831i | −0.994325 | + | 0.106381i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.686141 | − | 1.18843i | −0.0438359 | − | 0.0759260i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.00000 | − | 13.8564i | 0.509028 | − | 0.881662i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.74456 | + | 0.644810i | −0.173930 | + | 0.0408632i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.6060 | −0.985040 | −0.492520 | − | 0.870301i | \(-0.663924\pi\) | ||||
−0.492520 | + | 0.870301i | \(0.663924\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.74456 | − | 9.30506i | −0.547606 | − | 0.582706i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.686141 | − | 1.18843i | 0.0428003 | − | 0.0741323i | −0.843832 | − | 0.536608i | \(-0.819705\pi\) |
0.886632 | + | 0.462476i | \(0.153039\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.74456 | + | 8.21782i | 0.294813 | + | 0.510631i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.813859 | − | 13.0916i | 0.0503766 | − | 0.810348i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.74456 | + | 4.75372i | 0.169237 | + | 0.293127i | 0.938152 | − | 0.346224i | \(-0.112536\pi\) |
−0.768915 | + | 0.639351i | \(0.779203\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.74456 | − | 9.94987i | 0.352886 | − | 0.611216i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.558422 | − | 1.85208i | 0.0341749 | − | 0.113345i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.37228 | 0.266583 | 0.133291 | − | 0.991077i | \(-0.457445\pi\) | ||||
0.133291 | + | 0.991077i | \(0.457445\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.62772 | + | 18.6650i | −0.340605 | + | 1.12966i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.686141 | − | 1.18843i | 0.0413758 | − | 0.0716651i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.62772 | − | 4.55134i | −0.157884 | − | 0.273464i | 0.776221 | − | 0.630461i | \(-0.217134\pi\) |
−0.934106 | + | 0.356997i | \(0.883801\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.1168 | − | 9.01011i | 1.08463 | − | 0.539421i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.18614 | − | 3.78651i | −0.130414 | − | 0.225884i | 0.793422 | − | 0.608672i | \(-0.208297\pi\) |
−0.923836 | + | 0.382788i | \(0.874964\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.9307 | + | 27.5928i | −0.946982 | + | 1.64022i | −0.195249 | + | 0.980754i | \(0.562551\pi\) |
−0.751733 | + | 0.659467i | \(0.770782\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.00000 | − | 4.25639i | −0.236940 | − | 0.252127i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.11684 | −0.420094 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.3505 | 2.19709 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.43070 | + | 1.04095i | −0.259732 | + | 0.0610218i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.11684 | − | 7.13058i | 0.240509 | − | 0.416573i | −0.720351 | − | 0.693610i | \(-0.756019\pi\) |
0.960859 | + | 0.277037i | \(0.0893524\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.686141 | + | 1.18843i | 0.0399487 | + | 0.0691931i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.68614 | + | 2.47805i | 0.387969 | + | 0.143791i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.3723 | − | 17.9653i | −0.599845 | − | 1.03896i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.4891 | + | 23.3639i | −0.777500 | + | 1.34667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.7446 | + | 3.46410i | −0.847053 | + | 0.199007i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.11684 | −0.522029 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.2337 | 1.89675 | 0.948373 | − | 0.317156i | \(-0.102728\pi\) | ||||
0.948373 | + | 0.317156i | \(0.102728\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.9783 | − | 20.1947i | −1.07963 | − | 1.14884i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.62772 | + | 8.01544i | −0.262414 | + | 0.454514i | −0.966883 | − | 0.255221i | \(-0.917852\pi\) |
0.704469 | + | 0.709735i | \(0.251185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.68614 | − | 8.11663i | −0.264876 | − | 0.458779i | 0.702655 | − | 0.711531i | \(-0.251998\pi\) |
−0.967531 | + | 0.252752i | \(0.918664\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.93070 | + | 3.93398i | 0.334157 | + | 0.221655i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.37228 | + | 7.57301i | 0.245572 | + | 0.425343i | 0.962292 | − | 0.272018i | \(-0.0876910\pi\) |
−0.716720 | + | 0.697361i | \(0.754358\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.00000 | + | 5.19615i | −0.167968 | + | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.24456 | + | 24.0275i | −0.404352 | + | 1.34108i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.8614 | 1.38333 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.74456 | 0.263181 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.81386 | + | 15.9658i | −0.266207 | + | 0.882909i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.93070 | + | 3.34408i | −0.106443 | + | 0.184365i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.11684 | − | 15.7908i | −0.501107 | − | 0.867943i | −0.999999 | − | 0.00127880i | \(-0.999593\pi\) |
0.498892 | − | 0.866664i | \(-0.333740\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.0000 | + | 6.63325i | 0.547997 | + | 0.363500i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.50000 | + | 6.06218i | 0.191225 | + | 0.331212i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.68614 | + | 2.92048i | −0.0918499 | + | 0.159089i | −0.908290 | − | 0.418342i | \(-0.862611\pi\) |
0.816440 | + | 0.577431i | \(0.195945\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.4891 | − | 18.6101i | −0.949879 | − | 1.01076i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.25544 | −0.501210 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.8614 | −1.07242 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.37228 | + | 1.73205i | −0.396910 | + | 0.0932505i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.0584 | + | 19.1537i | −0.593647 | + | 1.02823i | 0.400089 | + | 0.916476i | \(0.368979\pi\) |
−0.993736 | + | 0.111751i | \(0.964354\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.441578 | − | 0.764836i | −0.0236371 | − | 0.0409407i | 0.853965 | − | 0.520331i | \(-0.174191\pi\) |
−0.877602 | + | 0.479390i | \(0.840858\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.13859 | + | 24.3036i | 0.220902 | + | 1.29723i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.1753 | − | 26.2843i | −0.807698 | − | 1.39897i | −0.914455 | − | 0.404689i | \(-0.867380\pi\) |
0.106757 | − | 0.994285i | \(-0.465953\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.00000 | − | 5.19615i | 0.159223 | − | 0.275783i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −29.4891 | + | 6.92820i | −1.56073 | + | 0.366679i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.48913 | −0.289705 | −0.144852 | − | 0.989453i | \(-0.546271\pi\) | ||||
−0.144852 | + | 0.989453i | \(0.546271\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.62772 | −0.401459 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.8139 | + | 11.5070i | 0.567580 | + | 0.603961i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.05842 | + | 12.2255i | −0.369455 | + | 0.639914i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.00000 | − | 13.8564i | −0.417597 | − | 0.723299i | 0.578101 | − | 0.815966i | \(-0.303794\pi\) |
−0.995697 | + | 0.0926670i | \(0.970461\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.05842 | + | 4.00772i | −0.419505 | + | 0.208634i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.6277 | − | 23.6039i | −0.707516 | − | 1.22545i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.74456 | + | 6.48577i | −0.193886 | + | 0.335821i | −0.946535 | − | 0.322602i | \(-0.895443\pi\) |
0.752649 | + | 0.658422i | \(0.228776\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | − | 1.65831i | 0.0258199 | − | 0.0856349i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.7446 | −1.06840 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.8614 | 0.557913 | 0.278956 | − | 0.960304i | \(-0.410011\pi\) | ||||
0.278956 | + | 0.960304i | \(0.410011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.55842 | − | 15.1186i | 0.233535 | − | 0.774548i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.4891 | − | 19.8997i | 0.587067 | − | 1.01683i | −0.407547 | − | 0.913184i | \(-0.633616\pi\) |
0.994614 | − | 0.103646i | \(-0.0330508\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.62772 | − | 2.81929i | −0.0829562 | − | 0.143684i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.11684 | + | 34.0511i | −0.107605 | + | 1.73092i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.18614 | + | 8.98266i | 0.262948 | + | 0.455439i | 0.967024 | − | 0.254686i | \(-0.0819720\pi\) |
−0.704076 | + | 0.710124i | \(0.748639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.1168 | − | 27.9152i | 0.815064 | − | 1.41173i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.3723 | + | 11.0371i | 0.523212 | + | 0.556749i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.00000 | 0.100631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.2554 | 0.564894 | 0.282447 | − | 0.959283i | \(-0.408854\pi\) | ||||
0.282447 | + | 0.959283i | \(0.408854\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.4891 | + | 3.16915i | −0.675301 | + | 0.158656i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.05842 | + | 13.9576i | −0.402418 | + | 0.697009i | −0.994017 | − | 0.109223i | \(-0.965164\pi\) |
0.591599 | + | 0.806232i | \(0.298497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.0000 | − | 27.7128i | −0.797017 | − | 1.38047i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.93070 | + | 1.11469i | 0.443770 | + | 0.0553895i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.74456 | − | 4.75372i | −0.136043 | − | 0.235633i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.43070 | − | 9.40625i | 0.268531 | − | 0.465109i | −0.699952 | − | 0.714190i | \(-0.746795\pi\) |
0.968483 | + | 0.249081i | \(0.0801285\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.17527 | + | 0.746000i | −0.156624 | + | 0.0367975i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.25544 | 0.160190 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.62772 | 0.0799016 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.4891 | + | 22.8665i | 1.05233 | + | 1.11978i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.8614 | + | 27.4728i | −0.774880 | + | 1.34213i | 0.159981 | + | 0.987120i | \(0.448857\pi\) |
−0.934862 | + | 0.355012i | \(0.884477\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.2337 | + | 33.3137i | 0.937393 | + | 1.62361i | 0.770311 | + | 0.637669i | \(0.220101\pi\) |
0.167082 | + | 0.985943i | \(0.446566\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.302985 | + | 4.87375i | −0.0147316 | + | 0.236970i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.68614 | + | 6.38458i | 0.178804 | + | 0.309698i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.8139 | + | 18.7302i | −0.523319 | + | 0.906416i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.25544 | − | 10.7971i | 0.157174 | − | 0.521287i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.2337 | 1.26363 | 0.631816 | − | 0.775118i | \(-0.282310\pi\) | ||||
0.631816 | + | 0.775118i | \(0.282310\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.627719 | 0.0301662 | 0.0150831 | − | 0.999886i | \(-0.495199\pi\) | ||||
0.0150831 | + | 0.999886i | \(0.495199\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.18614 | + | 7.25061i | −0.104817 | + | 0.347640i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.37228 | − | 12.7692i | 0.352664 | − | 0.610832i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.11684 | + | 14.0588i | 0.387396 | + | 0.670989i | 0.992098 | − | 0.125462i | \(-0.0400414\pi\) |
−0.604703 | + | 0.796451i | \(0.706708\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.68614 | + | 1.83324i | −0.175531 | + | 0.0872972i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.2446 | − | 22.9403i | −0.629268 | − | 1.08992i | −0.987699 | − | 0.156368i | \(-0.950021\pi\) |
0.358431 | − | 0.933556i | \(-0.383312\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.558422 | + | 0.967215i | −0.0264717 | + | 0.0458504i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.6753 | − | 24.1287i | −1.07250 | − | 1.14125i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.8614 | −0.890125 | −0.445062 | − | 0.895500i | \(-0.646819\pi\) | ||||
−0.445062 | + | 0.895500i | \(0.646819\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.11684 | 0.193855 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.8614 | − | 3.96143i | 0.792218 | − | 0.186124i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.62772 | − | 9.74749i | 0.263832 | − | 0.456970i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0584 | − | 26.0820i | −0.704403 | − | 1.22006i | −0.966906 | − | 0.255131i | \(-0.917881\pi\) |
0.262503 | − | 0.964931i | \(-0.415452\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.4891 | + | 24.4511i | −1.37643 | + | 1.14128i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.55842 | − | 16.5557i | −0.445180 | − | 0.771075i | 0.552885 | − | 0.833258i | \(-0.313527\pi\) |
−0.998065 | + | 0.0621833i | \(0.980194\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.0000 | − | 17.3205i | 0.464739 | − | 0.804952i | −0.534450 | − | 0.845200i | \(-0.679481\pi\) |
0.999190 | + | 0.0402476i | \(0.0128147\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.3723 | + | 2.67181i | −0.527377 | + | 0.123902i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.8832 | −1.19773 | −0.598865 | − | 0.800850i | \(-0.704381\pi\) | ||||
−0.598865 | + | 0.800850i | \(0.704381\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.6060 | 0.766792 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.62772 | − | 5.98844i | −0.259312 | − | 0.275933i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.80298 | − | 13.5152i | 0.358782 | − | 0.621428i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.68614 | + | 2.92048i | 0.0773654 | + | 0.134001i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28.7228 | − | 19.0526i | −1.31513 | − | 0.872357i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.7446 | − | 20.3422i | −0.536623 | − | 0.929458i | −0.999083 | − | 0.0428178i | \(-0.986366\pi\) |
0.462460 | − | 0.886640i | \(-0.346967\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.48913 | − | 16.4356i | 0.432667 | − | 0.749401i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.18614 | + | 17.2005i | −0.235978 | + | 0.782649i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.62772 | 0.119319 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.25544 | 0.0568893 | 0.0284446 | − | 0.999595i | \(-0.490945\pi\) | ||||
0.0284446 | + | 0.999595i | \(0.490945\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.744563 | − | 2.46943i | 0.0336703 | − | 0.111672i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.80298 | − | 3.12286i | 0.0813676 | − | 0.140933i | −0.822470 | − | 0.568808i | \(-0.807405\pi\) |
0.903838 | + | 0.427876i | \(0.140738\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.1168 | − | 27.9152i | −0.725866 | − | 1.25724i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.43070 | − | 2.27567i | −0.154199 | − | 0.102284i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.11684 | − | 12.3267i | −0.319234 | − | 0.552930i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.05842 | + | 1.83324i | −0.0473815 | + | 0.0820671i | −0.888743 | − | 0.458405i | \(-0.848421\pi\) |
0.841362 | + | 0.540472i | \(0.181754\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.04755 | + | 9.62747i | 0.404215 | + | 0.430124i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.8614 | −0.974752 | −0.487376 | − | 0.873192i | \(-0.662046\pi\) | ||||
−0.487376 | + | 0.873192i | \(0.662046\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.74456 | 0.389128 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.0367 | − | 3.76767i | 0.712214 | − | 0.167328i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.67527 | + | 8.09780i | −0.207228 | + | 0.358929i | −0.950840 | − | 0.309682i | \(-0.899777\pi\) |
0.743613 | + | 0.668611i | \(0.233111\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.7446 | + | 29.0024i | 0.740736 | + | 1.28299i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.4891 | + | 11.1846i | −0.595559 | + | 0.493812i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | + | 13.8564i | 0.352522 | + | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.11684 | − | 1.93443i | 0.0491187 | − | 0.0850762i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.6060 | − | 3.66648i | 0.685026 | − | 0.160941i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.2337 | −1.80648 | −0.903240 | − | 0.429135i | \(-0.858818\pi\) | ||||
−0.903240 | + | 0.429135i | \(0.858818\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.1168 | 0.486106 | 0.243053 | − | 0.970013i | \(-0.421851\pi\) | ||||
0.243053 | + | 0.970013i | \(0.421851\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.81386 | − | 2.99422i | −0.122807 | − | 0.130678i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.8614 | − | 43.0612i | 1.08298 | − | 1.87578i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.94158 | + | 3.36291i | 0.0844164 | + | 0.146214i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.68614 | − | 1.83324i | 0.159965 | − | 0.0795559i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.11684 | + | 12.3267i | 0.308265 | + | 0.533930i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.24456 | − | 12.5480i | 0.313210 | − | 0.542495i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.62772 | + | 5.39853i | −0.0702412 | + | 0.232964i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.88316 | 0.0811133 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.6277 | 0.929848 | 0.464924 | − | 0.885351i | \(-0.346082\pi\) | ||||
0.464924 | + | 0.885351i | \(0.346082\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.93070 | − | 13.0367i | 0.168683 | − | 0.559457i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.81386 | − | 8.33785i | 0.206203 | − | 0.357154i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.7337 | + | 34.1798i | 0.843752 | + | 1.46142i | 0.886701 | + | 0.462343i | \(0.152991\pi\) |
−0.0429494 | + | 0.999077i | \(0.513675\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.69702 | + | 27.2978i | −0.0724269 | + | 1.16504i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.37228 | − | 12.7692i | −0.314070 | − | 0.543985i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.37228 | − | 4.10891i | 0.100880 | − | 0.174729i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.74456 | − | 5.04868i | −0.201395 | − | 0.214304i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.76631 | −0.413812 | −0.206906 | − | 0.978361i | \(-0.566339\pi\) | ||||
−0.206906 | + | 0.978361i | \(0.566339\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 53.9565 | 2.28212 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.0584 | − | 4.00772i | 0.720207 | − | 0.169206i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.36141 | − | 14.4824i | 0.352391 | − | 0.610360i | −0.634277 | − | 0.773106i | \(-0.718702\pi\) |
0.986668 | + | 0.162747i | \(0.0520353\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.37228 | + | 12.7692i | 0.310154 | + | 0.537203i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.8832 | − | 17.0256i | 0.541042 | − | 0.715006i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.80298 | − | 8.31901i | −0.201352 | − | 0.348751i | 0.747613 | − | 0.664135i | \(-0.231200\pi\) |
−0.948964 | + | 0.315384i | \(0.897867\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.8030 | + | 27.3716i | −0.661334 | + | 1.14546i | 0.318931 | + | 0.947778i | \(0.396676\pi\) |
−0.980265 | + | 0.197687i | \(0.936657\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.25544 | − | 2.17448i | 0.386651 | − | 0.0908403i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.37228 | 0.182337 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.8832 | −0.994269 | −0.497134 | − | 0.867674i | \(-0.665614\pi\) | ||||
−0.497134 | + | 0.867674i | \(0.665614\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.60597 | − | 4.90120i | −0.191418 | − | 0.203687i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.93070 | − | 3.34408i | 0.0800991 | − | 0.138736i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.88316 | + | 13.6540i | 0.326487 | + | 0.565492i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.883156 | − | 14.2063i | 0.0365140 | − | 0.587357i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.5000 | + | 23.3827i | 0.557205 | + | 0.965107i | 0.997728 | + | 0.0673658i | \(0.0214594\pi\) |
−0.440524 | + | 0.897741i | \(0.645207\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.3723 | − | 19.6974i | 0.468587 | − | 0.811616i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.74456 | + | 29.0024i | −0.359703 | + | 1.19300i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.7228 | 1.54909 | 0.774545 | − | 0.632519i | \(-0.217979\pi\) | ||||
0.774545 | + | 0.632519i | \(0.217979\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.4891 | 0.716984 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.74456 | + | 15.7359i | −0.194182 | + | 0.644029i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.1168 | + | 33.1113i | −0.781093 | + | 1.35289i | 0.150212 | + | 0.988654i | \(0.452004\pi\) |
−0.931305 | + | 0.364239i | \(0.881329\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.4307 | − | 23.2627i | −0.547850 | − | 0.948904i | −0.998422 | − | 0.0561635i | \(-0.982113\pi\) |
0.450572 | − | 0.892740i | \(-0.351220\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.8030 | − | 9.35135i | 0.765717 | − | 0.380816i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.55842 | − | 7.89542i | −0.185326 | − | 0.320994i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.441578 | − | 0.764836i | 0.0179231 | − | 0.0310437i | −0.856925 | − | 0.515442i | \(-0.827628\pi\) |
0.874848 | + | 0.484398i | \(0.160961\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.3030 | + | 13.0916i | 0.498542 | + | 0.530497i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.72281 | 0.312432 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.233688 | −0.00943857 | −0.00471928 | − | 0.999989i | \(-0.501502\pi\) | ||||
−0.00471928 | + | 0.999989i | \(0.501502\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.05842 | − | 1.18843i | 0.203975 | − | 0.0479221i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.0584 | − | 19.1537i | 0.445195 | − | 0.771101i | −0.552870 | − | 0.833267i | \(-0.686468\pi\) |
0.998066 | + | 0.0621663i | \(0.0198009\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.0584 | − | 33.0102i | −0.766023 | − | 1.32679i | −0.939704 | − | 0.341988i | \(-0.888900\pi\) |
0.173682 | − | 0.984802i | \(-0.444434\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.81386 | + | 22.3966i | 0.153045 | + | 0.898746i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.32473 | + | 2.29451i | 0.0530743 | + | 0.0919275i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.80298 | − | 1.83324i | 0.311621 | − | 0.0732126i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.4891 | 1.17581 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.7228 | −1.34248 | −0.671242 | − | 0.741238i | \(-0.734239\pi\) | ||||
−0.671242 | + | 0.741238i | \(0.734239\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.60597 | − | 9.15759i | −0.342057 | − | 0.363981i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.55842 | + | 7.89542i | −0.180895 | + | 0.313320i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.25544 | + | 5.63858i | 0.128985 | + | 0.223409i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.0000 | − | 9.94987i | −0.593391 | − | 0.393611i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.5000 | + | 33.7750i | 0.770204 | + | 1.33403i | 0.937451 | + | 0.348117i | \(0.113179\pi\) |
−0.167247 | + | 0.985915i | \(0.553488\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.50000 | − | 9.52628i | 0.216899 | − | 0.375680i | −0.736959 | − | 0.675937i | \(-0.763739\pi\) |
0.953858 | + | 0.300257i | \(0.0970725\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.68614 | − | 18.8588i | 0.223892 | − | 0.742564i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.0951 | −0.947276 | −0.473638 | − | 0.880720i | \(-0.657059\pi\) | ||||
−0.473638 | + | 0.880720i | \(0.657059\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.88316 | −0.0739203 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.00000 | + | 26.5330i | −0.313545 | + | 1.03991i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.8614 | − | 32.6689i | 0.738104 | − | 1.27843i | −0.215244 | − | 0.976560i | \(-0.569055\pi\) |
0.953348 | − | 0.301873i | \(-0.0976119\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.37228 | − | 7.57301i | −0.170839 | − | 0.295902i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 35.2921 | + | 23.4101i | 1.37688 | + | 0.913316i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.74456 | − | 4.75372i | −0.106913 | − | 0.185179i | 0.807605 | − | 0.589724i | \(-0.200763\pi\) |
−0.914518 | + | 0.404545i | \(0.867430\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.1168 | + | 19.2549i | −0.432395 | + | 0.748930i | −0.997079 | − | 0.0763770i | \(-0.975665\pi\) |
0.564684 | + | 0.825307i | \(0.308998\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 41.4891 | + | 44.1485i | 1.61130 | + | 1.71458i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.00000 | 0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.1168 | −0.740207 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.8614 | + | 4.90120i | −0.806549 | + | 0.189491i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.25544 | − | 10.8347i | 0.241488 | − | 0.418270i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.00000 | + | 8.66025i | 0.192736 | + | 0.333828i | 0.946156 | − | 0.323711i | \(-0.104931\pi\) |
−0.753420 | + | 0.657539i | \(0.771597\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.87228 | − | 1.80579i | −0.187534 | − | 0.0695049i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.8614 | + | 37.8651i | 0.840202 | + | 1.45527i | 0.889724 | + | 0.456500i | \(0.150897\pi\) |
−0.0495215 | + | 0.998773i | \(0.515770\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.11684 | − | 5.39853i | 0.119613 | − | 0.207177i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.17527 | + | 0.746000i | −0.121676 | + | 0.0285868i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.0951 | −1.26635 | −0.633174 | − | 0.774009i | \(-0.718248\pi\) | ||||
−0.633174 | + | 0.774009i | \(0.718248\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.88316 | 0.0719517 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.7921 | − | 23.1889i | −0.831421 | − | 0.884713i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.2554 | + | 47.2078i | −1.03835 | + | 1.79847i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.883156 | − | 1.52967i | −0.0335968 | − | 0.0581914i | 0.848738 | − | 0.528813i | \(-0.177363\pi\) |
−0.882335 | + | 0.470622i | \(0.844030\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.74456 | + | 4.34896i | −0.332178 | + | 0.165203i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.05842 | − | 15.6896i | −0.343606 | − | 0.595142i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.0584 | + | 19.1537i | −0.418868 | + | 0.725500i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.05842 | − | 16.7769i | 0.191327 | − | 0.634560i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.1386 | 0.534007 | 0.267004 | − | 0.963696i | \(-0.413966\pi\) | ||||
0.267004 | + | 0.963696i | \(0.413966\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.4891 | 0.508752 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.813859 | − | 2.69927i | 0.0306517 | − | 0.101660i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.3723 | − | 17.9653i | 0.390090 | − | 0.675655i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.9307 | + | 22.3966i | 0.485623 | + | 0.841123i | 0.999863 | − | 0.0165226i | \(-0.00525955\pi\) |
−0.514241 | + | 0.857646i | \(0.671926\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.372281 | − | 5.98844i | 0.0139616 | − | 0.224584i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.7446 | − | 25.5383i | −0.552188 | − | 0.956418i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.25544 | + | 5.63858i | −0.121746 | + | 0.210871i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.4891 | − | 18.6101i | −0.653143 | − | 0.695008i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.2337 | 1.42588 | 0.712938 | − | 0.701227i | \(-0.247364\pi\) | ||||
0.712938 | + | 0.701227i | \(0.247364\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.9565 | 1.41357 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.6861 | − | 4.15520i | 0.657755 | − | 0.154534i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.18614 | − | 3.78651i | 0.0811912 | − | 0.140627i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.441578 | + | 0.764836i | 0.0163772 | + | 0.0283662i | 0.874098 | − | 0.485750i | \(-0.161453\pi\) |
−0.857721 | + | 0.514116i | \(0.828120\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.00000 | − | 26.5330i | 0.185185 | − | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 41.9198 | + | 72.6073i | 1.55046 | + | 2.68548i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.1168 | + | 29.6472i | −0.632225 | + | 1.09505i | 0.354871 | + | 0.934915i | \(0.384525\pi\) |
−0.987096 | + | 0.160131i | \(0.948808\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.31386 | − | 0.543620i | 0.0853480 | − | 0.0200517i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.60597 | −0.353840 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.8832 | 0.878556 | 0.439278 | − | 0.898351i | \(-0.355234\pi\) | ||||
0.439278 | + | 0.898351i | \(0.355234\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.9783 | + | 20.1947i | 0.697183 | + | 0.741871i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.5584 | − | 21.7518i | 0.460724 | − | 0.797997i | −0.538273 | − | 0.842770i | \(-0.680923\pi\) |
0.998997 | + | 0.0447732i | \(0.0142565\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.55842 | + | 16.5557i | 0.350193 | + | 0.606553i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.302985 | − | 4.87375i | 0.0110856 | − | 0.178321i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.1861 | − | 29.7673i | −0.627968 | − | 1.08767i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.11684 | + | 15.7908i | −0.332678 | + | 0.576216i | −0.983036 | − | 0.183412i | \(-0.941286\pi\) |
0.650358 | + | 0.759628i | \(0.274619\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.80298 | − | 25.8796i | 0.284357 | − | 0.943104i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.0000 | −0.363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.00000 | − | 9.94987i | 0.108893 | − | 0.361158i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.04755 | + | 10.4747i | −0.219223 | + | 0.379706i | −0.954571 | − | 0.297984i | \(-0.903686\pi\) |
0.735347 | + | 0.677690i | \(0.237019\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.4198 | − | 19.7797i | −0.413426 | − | 0.716074i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19.8030 | − | 9.84868i | 0.715978 | − | 0.356080i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.25544 | − | 5.63858i | −0.117547 | − | 0.203597i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.06930 | − | 15.7085i | 0.327047 | − | 0.566462i | −0.654877 | − | 0.755735i | \(-0.727280\pi\) |
0.981925 | + | 0.189273i | \(0.0606131\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.62772 | + | 1.73205i | 0.0586209 | + | 0.0623783i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.7446 | 0.530325 | 0.265163 | − | 0.964204i | \(-0.414574\pi\) | ||||
0.265163 | + | 0.964204i | \(0.414574\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.74456 | 0.242272 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.0000 | + | 3.75906i | −0.573997 | + | 0.134855i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.05842 | + | 8.76144i | −0.181237 | + | 0.313911i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.11684 | + | 7.13058i | 0.147312 | + | 0.255152i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.3030 | + | 7.89542i | 0.761307 | + | 0.282159i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.37228 | + | 4.10891i | 0.0846704 | + | 0.146653i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.0000 | + | 24.2487i | −0.499046 | + | 0.864373i | −0.999999 | − | 0.00110111i | \(-0.999650\pi\) |
0.500953 | + | 0.865474i | \(0.332983\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.25544 | + | 2.17448i | −0.329502 | + | 0.0774136i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.9783 | 1.24368 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.2554 | 1.53605 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.6277 | + | 14.5012i | 0.483325 | + | 0.514305i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.62772 | + | 2.81929i | −0.0576568 | + | 0.0998644i | −0.893413 | − | 0.449236i | \(-0.851696\pi\) |
0.835756 | + | 0.549100i | \(0.185030\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.00000 | + | 10.3923i | 0.212265 | + | 0.367653i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.79211 | + | 1.85208i | 0.0986544 | + | 0.0654399i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.68614 | − | 16.7769i | −0.341816 | − | 0.592044i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.18614 | − | 8.98266i | 0.182787 | − | 0.316597i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.18614 | + | 7.25061i | −0.0769558 | + | 0.255234i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.3505 | −0.434222 | −0.217111 | − | 0.976147i | \(-0.569663\pi\) | ||||
−0.217111 | + | 0.976147i | \(0.569663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.37228 | −0.329105 | −0.164553 | − | 0.986368i | \(-0.552618\pi\) | ||||
−0.164553 | + | 0.986368i | \(0.552618\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.00000 | − | 13.2665i | 0.140286 | − | 0.465276i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.744563 | + | 1.28962i | −0.0260809 | + | 0.0451734i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.1753 | + | 33.2125i | 0.670858 | + | 1.16196i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −28.1386 | − | 18.6650i | −0.983242 | − | 0.652209i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.4198 | − | 44.0284i | −0.887158 | − | 1.53660i | −0.843220 | − | 0.537569i | \(-0.819343\pi\) |
−0.0439382 | − | 0.999034i | \(-0.513990\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.0475 | − | 32.9913i | 0.663956 | − | 1.15001i | −0.315612 | − | 0.948888i | \(-0.602210\pi\) |
0.979567 | − | 0.201117i | \(-0.0644570\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.62772 | + | 1.73205i | 0.0566699 | + | 0.0603023i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.13859 | −0.283007 | −0.141503 | − | 0.989938i | \(-0.545194\pi\) | ||||
−0.141503 | + | 0.989938i | \(0.545194\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.8832 | −1.14208 | −0.571040 | − | 0.820923i | \(-0.693460\pi\) | ||||
−0.571040 | + | 0.820923i | \(0.693460\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.86141 | − | 2.08191i | 0.307399 | − | 0.0722206i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.05842 | + | 8.76144i | −0.175264 | + | 0.303566i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.81386 | − | 6.60580i | −0.131984 | − | 0.228603i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.88316 | + | 34.5484i | 0.203352 | + | 1.19417i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.1168 | + | 38.3075i | 0.763558 | + | 1.32252i | 0.941005 | + | 0.338391i | \(0.109883\pi\) |
−0.177447 | + | 0.984130i | \(0.556784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.94158 | − | 8.55906i | 0.170399 | − | 0.295140i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.37228 | − | 1.73205i | 0.253915 | − | 0.0596550i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.51087 | −0.327184 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.6277 | −0.743137 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −37.7921 | − | 40.2145i | −1.29702 | − | 1.38016i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.74456 | − | 15.1460i | 0.299760 | − | 0.519199i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.883156 | + | 1.52967i | 0.0302387 | + | 0.0523749i | 0.880749 | − | 0.473584i | \(-0.157040\pi\) |
−0.850510 | + | 0.525959i | \(0.823707\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.05842 | − | 4.50506i | 0.309791 | − | 0.154070i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.7446 | − | 20.3422i | −0.401187 | − | 0.694876i | 0.592683 | − | 0.805436i | \(-0.298069\pi\) |
−0.993869 | + | 0.110560i | \(0.964735\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.0584220 | − | 0.101190i | 0.00199333 | − | 0.00345255i | −0.865027 | − | 0.501725i | \(-0.832699\pi\) |
0.867020 | + | 0.498273i | \(0.166032\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.55842 | − | 11.8020i | 0.121271 | − | 0.402209i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.6060 | 1.45032 | 0.725162 | − | 0.688578i | \(-0.241765\pi\) | ||||
0.725162 | + | 0.688578i | \(0.241765\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.25544 | −0.314694 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.6753 | + | 61.9389i | −0.634245 | + | 2.10355i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.37228 | + | 2.37686i | −0.0465515 | + | 0.0806295i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.6060 | − | 28.7624i | −0.562672 | − | 0.974576i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.489125 | − | 7.86797i | 0.0165544 | − | 0.266290i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.18614 | + | 2.05446i | 0.0400989 | + | 0.0694533i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.9783 | − | 48.4598i | 0.944758 | − | 1.63637i | 0.188524 | − | 0.982069i | \(-0.439630\pi\) |
0.756234 | − | 0.654301i | \(-0.227037\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.76631 | + | 10.3923i | 0.329410 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.3505 | 0.921463 | 0.460731 | − | 0.887540i | \(-0.347587\pi\) | ||||
0.460731 | + | 0.887540i | \(0.347587\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.7228 | −0.428157 | −0.214078 | − | 0.976816i | \(-0.568675\pi\) | ||||
−0.214078 | + | 0.976816i | \(0.568675\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.31386 | + | 0.543620i | −0.0777795 | + | 0.0182736i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.8614 | + | 32.6689i | −0.633304 | + | 1.09691i | 0.353568 | + | 0.935409i | \(0.384968\pi\) |
−0.986872 | + | 0.161506i | \(0.948365\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.8139 | + | 18.7302i | 0.362685 | + | 0.628189i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.45245 | + | 9.84868i | −0.249667 | + | 0.329943i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.74456 | + | 4.75372i | 0.0918433 | + | 0.159077i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.62772 | − | 2.81929i | 0.0544086 | − | 0.0942385i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 34.9783 | − | 8.21782i | 1.16789 | − | 0.274385i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.4891 | −0.983517 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −84.7011 | −2.82180 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −32.0000 | − | 34.0511i | −1.06489 | − | 1.13315i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.93070 | + | 6.80818i | −0.130661 | + | 0.226311i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.50000 | − | 6.06218i | −0.116216 | − | 0.201291i | 0.802049 | − | 0.597258i | \(-0.203743\pi\) |
−0.918265 | + | 0.395966i | \(0.870410\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.62772 | − | 26.1831i | 0.0539880 | − | 0.868440i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0000 | − | 36.3731i | −0.695761 | − | 1.20509i | −0.969923 | − | 0.243410i | \(-0.921734\pi\) |
0.274162 | − | 0.961683i | \(-0.411599\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.11684 | + | 1.93443i | −0.0369621 | + | 0.0640203i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.55842 | − | 15.1186i | 0.150697 | − | 0.499805i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.7446 | −0.685046 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.4674 | −1.40087 | −0.700435 | − | 0.713716i | \(-0.747011\pi\) | ||||
−0.700435 | + | 0.713716i | \(0.747011\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.6168 | + | 55.1118i | −0.547544 | + | 1.81600i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.2337 | + | 24.6535i | −0.468508 | + | 0.811479i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | + | 3.46410i | 0.0657596 | + | 0.113899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 42.9783 | − | 21.3745i | 1.41159 | − | 0.702031i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.9783 | + | 34.6033i | 0.655465 | + | 1.13530i | 0.981777 | + | 0.190037i | \(0.0608607\pi\) |
−0.326312 | + | 0.945262i | \(0.605806\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.31386 | + | 4.00772i | −0.0758337 | + | 0.131348i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.9783 | − | 11.6819i | −0.359412 | − | 0.382449i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.1168 | −0.330856 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.7228 | −0.578979 | −0.289490 | − | 0.957181i | \(-0.593486\pi\) | ||||
−0.289490 | + | 0.957181i | \(0.593486\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.8030 | − | 3.71277i | 0.515711 | − | 0.121162i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.8139 | + | 32.5866i | −0.613314 | + | 1.06229i | 0.377363 | + | 0.926065i | \(0.376831\pi\) |
−0.990678 | + | 0.136226i | \(0.956503\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.55842 | + | 11.3595i | 0.213572 | + | 0.369917i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.48913 | + | 7.86797i | −0.308681 | + | 0.255945i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.3614 | + | 19.6785i | 0.369196 | + | 0.639466i | 0.989440 | − | 0.144943i | \(-0.0462997\pi\) |
−0.620244 | + | 0.784409i | \(0.712966\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.4891 | − | 58.0049i | 1.08710 | − | 1.88292i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.7446 | + | 3.46410i | −0.478125 | + | 0.112331i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.8614 | 0.999699 | 0.499850 | − | 0.866112i | \(-0.333389\pi\) | ||||
0.499850 | + | 0.866112i | \(0.333389\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.48913 | −0.177624 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.11684 | − | 7.57301i | −0.230055 | − | 0.244801i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.23369 | − | 3.86886i | 0.0721295 | − | 0.124932i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.24456 | − | 12.5480i | −0.233696 | − | 0.404773i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36.2228 | − | 24.0275i | −1.16726 | − | 0.774275i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.94158 | + | 3.36291i | 0.0625016 | + | 0.108256i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.44158 | − | 16.3533i | 0.303621 | − | 0.525886i | −0.673333 | − | 0.739340i | \(-0.735138\pi\) |
0.976953 | + | 0.213453i | \(0.0684711\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.4307 | + | 41.2280i | −0.399332 | + | 1.32443i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.9783 | −0.737407 | −0.368704 | − | 0.929547i | \(-0.620198\pi\) | ||||
−0.368704 | + | 0.929547i | \(0.620198\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42.9783 | −1.37782 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.37228 | + | 7.86797i | −0.0759738 | + | 0.251977i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.0584 | − | 34.7422i | 0.641726 | − | 1.11150i | −0.343322 | − | 0.939218i | \(-0.611552\pi\) |
0.985047 | − | 0.172284i | \(-0.0551146\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.766312 | − | 1.32729i | −0.0244914 | − | 0.0424204i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.0693 | − | 15.9658i | −0.768474 | − | 0.509748i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.93070 | + | 13.7364i | 0.252950 | + | 0.438123i | 0.964337 | − | 0.264678i | \(-0.0852658\pi\) |
−0.711387 | + | 0.702801i | \(0.751932\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.74456 | − | 15.1460i | 0.278625 | − | 0.482593i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.58017 | − | 4.87375i | −0.145788 | − | 0.155133i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 49.7228 | 1.58109 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.2337 | 0.579212 | 0.289606 | − | 0.957146i | \(-0.406476\pi\) | ||||
0.289606 | + | 0.957146i | \(0.406476\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.7446 | − | 7.22316i | 0.975649 | − | 0.229220i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.74456 | − | 8.21782i | 0.150413 | − | 0.260523i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.00000 | − | 12.1244i | −0.221692 | − | 0.383982i | 0.733630 | − | 0.679549i | \(-0.237825\pi\) |
−0.955322 | + | 0.295567i | \(0.904491\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.0000 | + | 13.2665i | −0.506218 | + | 0.419733i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))