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 | 481.1 | ||
Root | \(1.68614 + 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.481 |
Dual form | 720.2.q.f.241.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(7\) | 1.68614 | + | 2.92048i | 0.637301 | + | 1.10384i | 0.986023 | + | 0.166612i | \(0.0532826\pi\) |
−0.348721 | + | 0.937226i | \(0.613384\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.50000 | + | 1.65831i | −0.833333 | + | 0.552771i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.18614 | − | 3.78651i | −0.659146 | − | 1.14167i | −0.980837 | − | 0.194830i | \(-0.937584\pi\) |
0.321691 | − | 0.946845i | \(-0.395749\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.37228 | − | 5.84096i | 0.935303 | − | 1.61999i | 0.161209 | − | 0.986920i | \(-0.448461\pi\) |
0.774094 | − | 0.633071i | \(-0.218206\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.68614 | − | 0.396143i | −0.435360 | − | 0.102284i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.62772 | −0.394780 | −0.197390 | − | 0.980325i | \(-0.563246\pi\) | ||||
−0.197390 | + | 0.980325i | \(0.563246\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.37228 | 0.544239 | 0.272119 | − | 0.962264i | \(-0.412275\pi\) | ||||
0.272119 | + | 0.962264i | \(0.412275\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | − | 4.25639i | 0.872872 | − | 0.928820i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.686141 | − | 1.18843i | 0.143070 | − | 0.247805i | −0.785581 | − | 0.618759i | \(-0.787636\pi\) |
0.928651 | + | 0.370954i | \(0.120969\pi\) | |||||||
\(24\) | 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 | ||||||||
\(29\) | −0.686141 | − | 1.18843i | −0.127413 | − | 0.220686i | 0.795261 | − | 0.606268i | \(-0.207334\pi\) |
−0.922674 | + | 0.385582i | \(0.874001\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.37228 | − | 4.10891i | 0.426074 | − | 0.737982i | −0.570446 | − | 0.821335i | \(-0.693230\pi\) |
0.996520 | + | 0.0833529i | \(0.0265629\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.18614 | + | 5.51856i | −0.902791 | + | 0.960658i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.37228 | 0.570020 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.3723 | − | 2.67181i | −1.82102 | − | 0.427833i | ||||
\(40\) | 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 | ||||||||
\(43\) | −2.81386 | − | 4.87375i | −0.429110 | − | 0.743240i | 0.567685 | − | 0.823246i | \(-0.307839\pi\) |
−0.996794 | + | 0.0800065i | \(0.974506\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.186141 | + | 2.99422i | 0.0277482 | + | 0.446352i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.68614 | − | 6.38458i | −0.537679 | − | 0.931287i | −0.999029 | − | 0.0440687i | \(-0.985968\pi\) |
0.461350 | − | 0.887218i | \(-0.347365\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.18614 | + | 3.78651i | −0.312306 | + | 0.540930i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.813859 | + | 2.69927i | 0.113963 | + | 0.377973i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.4891 | −1.57815 | −0.789076 | − | 0.614295i | \(-0.789440\pi\) | ||||
−0.789076 | + | 0.614295i | \(0.789440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.37228 | −0.589558 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.18614 | − | 3.93398i | −0.157108 | − | 0.521069i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.18614 | − | 3.78651i | 0.284611 | − | 0.492961i | −0.687904 | − | 0.725802i | \(-0.741469\pi\) |
0.972515 | + | 0.232841i | \(0.0748021\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.05842 | + | 7.02939i | 0.519628 | + | 0.900022i | 0.999740 | + | 0.0228144i | \(0.00726267\pi\) |
−0.480112 | + | 0.877207i | \(0.659404\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.05842 | − | 4.50506i | −1.14125 | − | 0.567584i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.37228 | − | 5.84096i | −0.418280 | − | 0.724482i | ||||
\(66\) | 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 | ||||||||
\(69\) | −2.31386 | − | 0.543620i | −0.278556 | − | 0.0654442i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.11684 | 0.364799 | 0.182399 | − | 0.983225i | \(-0.441614\pi\) | ||||
0.182399 | + | 0.983225i | \(0.441614\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.18614 | + | 1.26217i | −0.136964 | + | 0.145743i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.37228 | − | 12.7692i | 0.840149 | − | 1.45518i | ||||
\(78\) | 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 | ||||||||
\(83\) | 3.68614 | + | 6.38458i | 0.404607 | + | 0.700799i | 0.994276 | − | 0.106846i | \(-0.0340752\pi\) |
−0.589669 | + | 0.807645i | \(0.700742\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.813859 | + | 1.40965i | −0.0882754 | + | 0.152898i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.62772 | + | 1.73205i | −0.174510 | + | 0.185695i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.1168 | 1.70838 | 0.854191 | − | 0.519959i | \(-0.174053\pi\) | ||||
0.854191 | + | 0.519959i | \(0.174053\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 22.7446 | 2.38428 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.00000 | − | 1.87953i | −0.829561 | − | 0.194898i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.18614 | − | 2.05446i | 0.121695 | − | 0.210783i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.18614 | + | 7.25061i | 0.425038 | + | 0.736188i | 0.996424 | − | 0.0844938i | \(-0.0269273\pi\) |
−0.571386 | + | 0.820682i | \(0.693594\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.7446 | + | 5.84096i | 1.18037 | + | 0.587039i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.37228 | − | 2.37686i | −0.136547 | − | 0.236507i | 0.789640 | − | 0.613570i | \(-0.210267\pi\) |
−0.926187 | + | 0.377064i | \(0.876934\pi\) | |||||||
\(102\) | 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 | ||||||||
\(105\) | −1.68614 | − | 5.59230i | −0.164550 | − | 0.545752i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.48913 | −0.820675 | −0.410337 | − | 0.911934i | \(-0.634589\pi\) | ||||
−0.410337 | + | 0.911934i | \(0.634589\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.3723 | 1.47240 | 0.736199 | − | 0.676765i | \(-0.236619\pi\) | ||||
0.736199 | + | 0.676765i | \(0.236619\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | + | 6.63325i | 0.189832 | + | 0.629600i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.62772 | + | 2.81929i | −0.153123 | + | 0.265217i | −0.932374 | − | 0.361495i | \(-0.882266\pi\) |
0.779251 | + | 0.626712i | \(0.215600\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.686141 | − | 1.18843i | −0.0639829 | − | 0.110822i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.25544 | + | 20.1947i | 0.116065 | + | 1.86700i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.74456 | − | 4.75372i | −0.251594 | − | 0.435773i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.05842 | + | 7.02939i | −0.368947 | + | 0.639036i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.05842 | − | 1.18843i | −0.456103 | − | 0.107157i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.11684 | 0.720253 | 0.360127 | − | 0.932903i | \(-0.382733\pi\) | ||||
0.360127 | + | 0.932903i | \(0.382733\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.67527 | + | 7.10313i | −0.587724 | + | 0.625396i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.37228 | + | 2.37686i | −0.119897 | + | 0.207667i | −0.919727 | − | 0.392560i | \(-0.871590\pi\) |
0.799830 | + | 0.600227i | \(0.204923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | + | 6.92820i | 0.346844 | + | 0.600751i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.87228 | − | 1.80579i | 0.419339 | − | 0.155418i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.55842 | + | 16.5557i | 0.816631 | + | 1.41445i | 0.908151 | + | 0.418643i | \(0.137494\pi\) |
−0.0915197 | + | 0.995803i | \(0.529172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.441578 | − | 0.764836i | 0.0374542 | − | 0.0648725i | −0.846691 | − | 0.532085i | \(-0.821409\pi\) |
0.884145 | + | 0.467213i | \(0.154742\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.74456 | + | 9.30506i | −0.736425 | + | 0.783628i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −29.4891 | −2.46600 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.37228 | −0.113962 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.37228 | + | 1.73205i | 0.608056 | + | 0.142857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.941578 | + | 1.63086i | −0.0771371 | + | 0.133605i | −0.902014 | − | 0.431708i | \(-0.857911\pi\) |
0.824877 | + | 0.565313i | \(0.191245\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 4.06930 | − | 2.69927i | 0.328983 | − | 0.218223i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.37228 | − | 4.10891i | −0.190546 | − | 0.330036i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.37228 | − | 5.84096i | 0.269137 | − | 0.466160i | −0.699502 | − | 0.714631i | \(-0.746595\pi\) |
0.968639 | + | 0.248471i | \(0.0799281\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.74456 | + | 19.0526i | 0.455573 | + | 1.51097i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.62772 | 0.364715 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.4891 | 1.68316 | 0.841579 | − | 0.540134i | \(-0.181626\pi\) | ||||
0.841579 | + | 0.540134i | \(0.181626\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.18614 | + | 7.25061i | 0.170191 | + | 0.564459i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.68614 | − | 11.5807i | 0.517389 | − | 0.896144i | −0.482407 | − | 0.875947i | \(-0.660237\pi\) |
0.999796 | − | 0.0201970i | \(-0.00642933\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16.2446 | − | 28.1364i | −1.24958 | − | 2.16434i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.93070 | + | 3.93398i | −0.453532 | + | 0.300839i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.3723 | − | 17.9653i | −0.788590 | − | 1.36588i | −0.926831 | − | 0.375479i | \(-0.877478\pi\) |
0.138241 | − | 0.990399i | \(-0.455855\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.68614 | − | 2.92048i | 0.127460 | − | 0.220768i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.37228 | − | 1.73205i | −0.554135 | − | 0.130189i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.7446 | 1.10206 | 0.551030 | − | 0.834485i | \(-0.314235\pi\) | ||||
0.551030 | + | 0.834485i | \(0.314235\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.8614 | 1.55062 | 0.775308 | − | 0.631583i | \(-0.217595\pi\) | ||||
0.775308 | + | 0.631583i | \(0.217595\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.62772 | − | 10.2448i | 0.711701 | − | 0.757319i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00000 | + | 3.46410i | −0.147043 | + | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.55842 | + | 6.16337i | 0.260218 | + | 0.450710i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.94158 | + | 17.2742i | −0.213968 | + | 1.25651i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.74456 | + | 15.1460i | 0.632734 | + | 1.09593i | 0.986990 | + | 0.160780i | \(0.0514008\pi\) |
−0.354256 | + | 0.935148i | \(0.615266\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5584 | + | 18.2877i | −0.760012 | + | 1.31638i | 0.182832 | + | 0.983144i | \(0.441474\pi\) |
−0.942844 | + | 0.333235i | \(0.891860\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.00000 | + | 8.51278i | −0.572892 | + | 0.609613i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.48913 | −0.391084 | −0.195542 | − | 0.980695i | \(-0.562647\pi\) | ||||
−0.195542 | + | 0.980695i | \(0.562647\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.4891 | −0.956219 | −0.478109 | − | 0.878300i | \(-0.658678\pi\) | ||||
−0.478109 | + | 0.878300i | \(0.658678\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.8030 | + | 2.77300i | 0.832518 | + | 0.195593i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.31386 | − | 4.00772i | 0.162401 | − | 0.281287i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.50000 | − | 2.59808i | −0.104765 | − | 0.181458i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.255437 | + | 4.10891i | 0.0177541 | + | 0.285589i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.18614 | − | 8.98266i | −0.358733 | − | 0.621344i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.37228 | + | 16.2333i | −0.645214 | + | 1.11754i | 0.339037 | + | 0.940773i | \(0.389899\pi\) |
−0.984252 | + | 0.176771i | \(0.943435\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.00000 | − | 9.94987i | −0.205557 | − | 0.681754i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.62772 | −0.383807 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000 | 1.08615 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.55842 | − | 5.16870i | −0.105308 | − | 0.349268i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.48913 | + | 9.50744i | −0.369239 | + | 0.639540i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.31386 | + | 5.73977i | 0.221912 | + | 0.384364i | 0.955389 | − | 0.295351i | \(-0.0954368\pi\) |
−0.733476 | + | 0.679715i | \(0.762103\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.68614 | + | 1.33591i | 0.179076 | + | 0.0890605i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.55842 | + | 16.5557i | 0.634415 | + | 1.09884i | 0.986639 | + | 0.162923i | \(0.0520922\pi\) |
−0.352224 | + | 0.935916i | \(0.614574\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.31386 | + | 10.9359i | −0.417232 | + | 0.722666i | −0.995660 | − | 0.0930670i | \(-0.970333\pi\) |
0.578428 | + | 0.815733i | \(0.303666\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.8614 | − | 5.84096i | −1.63576 | − | 0.384307i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.11684 | 0.466240 | 0.233120 | − | 0.972448i | \(-0.425107\pi\) | ||||
0.233120 | + | 0.972448i | \(0.425107\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.37228 | −0.480915 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.37228 | − | 2.52434i | 0.154096 | − | 0.163973i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.62772 | + | 2.81929i | −0.105288 | + | 0.182365i | −0.913856 | − | 0.406038i | \(-0.866910\pi\) |
0.808568 | + | 0.588403i | \(0.200243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.24456 | + | 10.8159i | 0.402248 | + | 0.696713i | 0.993997 | − | 0.109409i | \(-0.0348958\pi\) |
−0.591749 | + | 0.806122i | \(0.701562\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5000 | − | 1.65831i | −0.994325 | − | 0.106381i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.18614 | + | 3.78651i | 0.139667 | + | 0.241911i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.00000 | − | 13.8564i | 0.509028 | − | 0.881662i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.74456 | − | 9.30506i | 0.554164 | − | 0.589684i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.6060 | 1.55312 | 0.776558 | − | 0.630046i | \(-0.216964\pi\) | ||||
0.776558 | + | 0.630046i | \(0.216964\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.74456 | + | 0.644810i | 0.171871 | + | 0.0403796i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.18614 | + | 3.78651i | −0.136368 | + | 0.236196i | −0.926119 | − | 0.377231i | \(-0.876876\pi\) |
0.789751 | + | 0.613427i | \(0.210210\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.74456 | − | 11.6819i | −0.419087 | − | 0.725880i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.68614 | + | 1.83324i | 0.228166 | + | 0.113475i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.74456 | − | 15.1460i | −0.539213 | − | 0.933944i | −0.998947 | − | 0.0458872i | \(-0.985389\pi\) |
0.459734 | − | 0.888057i | \(-0.347945\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.74456 | + | 9.94987i | −0.352886 | + | 0.611216i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.05842 | − | 26.7268i | −0.493167 | − | 1.63565i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.37228 | −0.0836695 | −0.0418347 | − | 0.999125i | \(-0.513320\pi\) | ||||
−0.0418347 | + | 0.999125i | \(0.513320\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.3723 | − | 37.7176i | −0.688282 | − | 2.28277i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.18614 | + | 3.78651i | −0.131829 | + | 0.228335i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.37228 | − | 14.5012i | −0.503042 | − | 0.871294i | −0.999994 | − | 0.00351574i | \(-0.998881\pi\) |
0.496952 | − | 0.867778i | \(-0.334452\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.883156 | + | 14.2063i | 0.0528732 | + | 0.850507i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.686141 | + | 1.18843i | 0.0409317 | + | 0.0708958i | 0.885765 | − | 0.464133i | \(-0.153634\pi\) |
−0.844834 | + | 0.535029i | \(0.820301\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.56930 | + | 2.71810i | −0.0932850 | + | 0.161574i | −0.908892 | − | 0.417033i | \(-0.863070\pi\) |
0.815607 | + | 0.578607i | \(0.196403\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.00000 | − | 0.939764i | −0.236940 | − | 0.0556668i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.1168 | 0.597178 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.3505 | −0.844149 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.93070 | − | 10.5672i | 0.582148 | − | 0.619462i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.1168 | + | 22.7190i | −0.766294 | + | 1.32726i | 0.173265 | + | 0.984875i | \(0.444568\pi\) |
−0.939560 | + | 0.342385i | \(0.888765\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.18614 | − | 3.78651i | −0.127282 | − | 0.220459i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.81386 | − | 22.3966i | 0.221303 | − | 1.29958i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.62772 | − | 8.01544i | −0.267628 | − | 0.463545i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.48913 | − | 16.4356i | 0.546944 | − | 0.947335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.25544 | + | 3.46410i | −0.187020 | + | 0.199007i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.11684 | 0.464769 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.23369 | −0.0704103 | −0.0352051 | − | 0.999380i | \(-0.511208\pi\) | ||||
−0.0352051 | + | 0.999380i | \(0.511208\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.9783 | + | 6.33830i | 1.53474 | + | 0.360573i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.3723 | + | 17.9653i | −0.588158 | + | 1.01872i | 0.406315 | + | 0.913733i | \(0.366813\pi\) |
−0.994474 | + | 0.104987i | \(0.966520\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.81386 | − | 3.14170i | −0.102525 | − | 0.177579i | 0.810199 | − | 0.586155i | \(-0.199359\pi\) |
−0.912724 | + | 0.408576i | \(0.866026\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.43070 | + | 5.59230i | −0.475016 | + | 0.315090i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.37228 | − | 2.37686i | −0.0770750 | − | 0.133498i | 0.824912 | − | 0.565262i | \(-0.191225\pi\) |
−0.901987 | + | 0.431764i | \(0.857891\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.00000 | + | 5.19615i | −0.167968 | + | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.24456 | + | 14.0776i | 0.236908 | + | 0.785736i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.86141 | −0.214854 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.74456 | −0.374121 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.68614 | − | 25.4920i | −0.425045 | − | 1.40971i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.4307 | − | 21.5306i | 0.685327 | − | 1.18702i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.11684 | + | 14.0588i | 0.446142 | + | 0.772741i | 0.998131 | − | 0.0611107i | \(-0.0194643\pi\) |
−0.551989 | + | 0.833851i | \(0.686131\pi\) | |||||||
\(332\) | 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 | ||||||||
\(337\) | 1.18614 | − | 2.05446i | 0.0646132 | − | 0.111913i | −0.831909 | − | 0.554912i | \(-0.812752\pi\) |
0.896522 | + | 0.442999i | \(0.146085\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.48913 | + | 1.28962i | 0.298128 | + | 0.0700426i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.7446 | −1.12338 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.86141 | 0.478471 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.62772 | + | 1.73205i | −0.0876334 | + | 0.0932505i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.44158 | + | 4.22894i | −0.131071 | + | 0.227021i | −0.924090 | − | 0.382176i | \(-0.875175\pi\) |
0.793019 | + | 0.609197i | \(0.208508\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.05842 | − | 15.6896i | −0.484886 | − | 0.839848i | 0.514963 | − | 0.857212i | \(-0.327806\pi\) |
−0.999849 | + | 0.0173648i | \(0.994472\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32.8614 | − | 12.1793i | 1.75401 | − | 0.650081i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.6753 | + | 18.4901i | 0.568187 | + | 0.984129i | 0.996745 | + | 0.0806147i | \(0.0256883\pi\) |
−0.428558 | + | 0.903514i | \(0.640978\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.00000 | − | 5.19615i | 0.159223 | − | 0.275783i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.51087 | + | 6.92820i | −0.344592 | + | 0.366679i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.4891 | 0.923041 | 0.461520 | − | 0.887130i | \(-0.347304\pi\) | ||||
0.461520 | + | 0.887130i | \(0.347304\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.3723 | −0.703804 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.6861 | + | 3.21543i | 0.718336 | + | 0.168767i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.55842 | − | 2.69927i | 0.0815715 | − | 0.141286i | ||||
\(366\) | 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 | ||||||||
\(369\) | 0.558422 | + | 8.98266i | 0.0290703 | + | 0.467619i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.3723 | − | 33.5538i | −1.00576 | − | 1.74203i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.74456 | − | 13.4140i | 0.400998 | − | 0.694549i | −0.592848 | − | 0.805314i | \(-0.701997\pi\) |
0.993847 | + | 0.110765i | \(0.0353300\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | + | 1.65831i | 0.0258199 | + | 0.0856349i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.25544 | −0.476679 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.8614 | −0.917479 | −0.458739 | − | 0.888571i | \(-0.651699\pi\) | ||||
−0.458739 | + | 0.888571i | \(0.651699\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.05842 | − | 13.4603i | −0.207919 | − | 0.689590i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.4891 | + | 19.8997i | −0.587067 | + | 1.01683i | 0.407547 | + | 0.913184i | \(0.366384\pi\) |
−0.994614 | + | 0.103646i | \(0.966949\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.37228 | − | 12.7692i | −0.375726 | − | 0.650777i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.1168 | + | 7.51811i | 0.768432 | + | 0.382167i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.31386 | + | 4.00772i | 0.117317 | + | 0.203200i | 0.918704 | − | 0.394947i | \(-0.129237\pi\) |
−0.801386 | + | 0.598147i | \(0.795904\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.11684 | + | 1.93443i | −0.0564812 | + | 0.0978284i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.62772 | + | 1.08724i | 0.233438 | + | 0.0548440i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.00000 | 0.100631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.7446 | 1.14152 | 0.570758 | − | 0.821118i | \(-0.306649\pi\) | ||||
0.570758 | + | 0.821118i | \(0.306649\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.48913 | − | 10.0974i | 0.475050 | − | 0.505500i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.558422 | − | 0.967215i | 0.0278863 | − | 0.0483004i | −0.851745 | − | 0.523956i | \(-0.824456\pi\) |
0.879632 | + | 0.475655i | \(0.157789\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.0000 | − | 27.7128i | −0.797017 | − | 1.38047i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.43070 | − | 7.17687i | −0.269854 | − | 0.356622i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.74456 | + | 15.1460i | 0.433452 | + | 0.750761i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.93070 | + | 15.4684i | −0.441595 | + | 0.764865i | −0.997808 | − | 0.0661749i | \(-0.978920\pi\) |
0.556213 | + | 0.831040i | \(0.312254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.6753 | − | 24.1287i | 1.11849 | − | 1.19018i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.7446 | 0.725532 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.37228 | 0.361891 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.48913 | − | 0.349857i | −0.0729228 | − | 0.0171325i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.8614 | − | 22.2766i | 0.628321 | − | 1.08828i | −0.359568 | − | 0.933119i | \(-0.617076\pi\) |
0.987889 | − | 0.155165i | \(-0.0495908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.2337 | − | 26.3855i | −0.742445 | − | 1.28595i | −0.951379 | − | 0.308022i | \(-0.900333\pi\) |
0.208935 | − | 0.977930i | \(-0.433000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.8030 | + | 9.84868i | 0.962854 | + | 0.478859i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.813859 | + | 1.40965i | 0.0394780 | + | 0.0683779i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.6861 | + | 23.7051i | −0.662319 | + | 1.14717i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.7446 | + | 48.9022i | 0.711874 | + | 2.36102i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.23369 | −0.396603 | −0.198301 | − | 0.980141i | \(-0.563542\pi\) | ||||
−0.198301 | + | 0.980141i | \(0.563542\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.37228 | 0.306232 | 0.153116 | − | 0.988208i | \(-0.451069\pi\) | ||||
0.153116 | + | 0.988208i | \(0.451069\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.686141 | + | 2.27567i | 0.0328979 | + | 0.109110i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.62772 | − | 2.81929i | 0.0778643 | − | 0.134865i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.11684 | − | 15.7908i | −0.435123 | − | 0.753656i | 0.562182 | − | 0.827013i | \(-0.309962\pi\) |
−0.997306 | + | 0.0733577i | \(0.976629\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.813859 | − | 13.0916i | −0.0387552 | − | 0.623408i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.75544 | − | 3.04051i | −0.0834033 | − | 0.144459i | 0.821306 | − | 0.570487i | \(-0.193246\pi\) |
−0.904710 | + | 0.426029i | \(0.859912\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.05842 | − | 13.9576i | 0.382006 | − | 0.661654i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.17527 | + | 0.746000i | 0.150185 | + | 0.0352846i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.86141 | 0.465389 | 0.232694 | − | 0.972550i | \(-0.425246\pi\) | ||||
0.232694 | + | 0.972550i | \(0.425246\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.1168 | −0.617648 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.8614 | + | 12.6217i | −0.557297 | + | 0.593019i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.3723 | − | 19.6974i | 0.533141 | − | 0.923427i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.44158 | − | 11.1571i | −0.301324 | − | 0.521909i | 0.675112 | − | 0.737715i | \(-0.264095\pi\) |
−0.976436 | + | 0.215806i | \(0.930762\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.51087 | − | 5.39853i | −0.303902 | − | 0.251982i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.941578 | − | 1.63086i | −0.0438537 | − | 0.0759568i | 0.843265 | − | 0.537497i | \(-0.180630\pi\) |
−0.887119 | + | 0.461541i | \(0.847297\pi\) | |||||||
\(462\) | 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 | ||||||||
\(465\) | −5.62772 | + | 5.98844i | −0.260979 | + | 0.277707i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −43.1168 | −1.99521 | −0.997605 | − | 0.0691713i | \(-0.977964\pi\) | ||||
−0.997605 | + | 0.0691713i | \(0.977964\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.6060 | −1.09002 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.3723 | − | 2.67181i | −0.524007 | − | 0.123111i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.3030 | + | 21.3094i | −0.565692 | + | 0.979807i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.18614 | − | 2.05446i | −0.0544239 | − | 0.0942649i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.7228 | − | 19.0526i | 1.31513 | − | 0.872357i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.255437 | − | 0.442430i | −0.0116712 | − | 0.0202152i | 0.860131 | − | 0.510074i | \(-0.170382\pi\) |
−0.871802 | + | 0.489858i | \(0.837048\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.4891 | + | 23.3639i | −0.615051 | + | 1.06530i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.31386 | − | 7.67420i | −0.105284 | − | 0.349188i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.37228 | 0.380166 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.7446 | 0.577511 | 0.288756 | − | 0.957403i | \(-0.406758\pi\) | ||||
0.288756 | + | 0.957403i | \(0.406758\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.7446 | − | 35.6357i | −0.485886 | − | 1.61150i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.3030 | + | 31.7017i | −0.826002 | + | 1.43068i | 0.0751489 | + | 0.997172i | \(0.476057\pi\) |
−0.901151 | + | 0.433505i | \(0.857277\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.11684 | + | 1.93443i | 0.0503001 | + | 0.0871224i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.9307 | − | 7.25061i | 0.491299 | − | 0.325891i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.1168 | + | 17.5229i | 0.453802 | + | 0.786009i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.55842 | − | 13.0916i | 0.338361 | − | 0.586059i | −0.645763 | − | 0.763538i | \(-0.723461\pi\) |
0.984125 | + | 0.177479i | \(0.0567940\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.5475 | − | 5.29734i | −1.00735 | − | 0.236668i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.86141 | 0.305935 | 0.152967 | − | 0.988231i | \(-0.451117\pi\) | ||||
0.152967 | + | 0.988231i | \(0.451117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.74456 | −0.122131 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −38.5367 | + | 41.0068i | −1.71147 | + | 1.82117i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.1753 | − | 36.6766i | 0.938577 | − | 1.62566i | 0.170450 | − | 0.985366i | \(-0.445478\pi\) |
0.768127 | − | 0.640297i | \(-0.221189\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.25544 | + | 9.10268i | 0.232487 | + | 0.402679i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.48913 | + | 7.86797i | 0.418955 | + | 0.347379i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | + | 13.8564i | 0.352522 | + | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.1168 | + | 27.9152i | −0.708818 | + | 1.22771i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.6060 | + | 26.1831i | −1.08008 | + | 1.14931i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.76631 | −0.296438 | −0.148219 | − | 0.988955i | \(-0.547354\pi\) | ||||
−0.148219 | + | 0.988955i | \(0.547354\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.11684 | −0.267471 | −0.133735 | − | 0.991017i | \(-0.542697\pi\) | ||||
−0.133735 | + | 0.991017i | \(0.542697\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.68614 | − | 1.33591i | −0.248164 | − | 0.0583038i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.86141 | + | 6.68815i | −0.168206 | + | 0.291340i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.5584 | + | 18.2877i | 0.459062 | + | 0.795118i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.813859 | + | 13.0916i | 0.0353185 | + | 0.568126i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.1168 | − | 17.5229i | −0.438209 | − | 0.759001i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.24456 | + | 7.35180i | −0.183508 | + | 0.317846i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.37228 | − | 24.4511i | −0.318137 | − | 1.05514i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.1168 | 0.823421 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.3723 | 1.17683 | 0.588413 | − | 0.808560i | \(-0.299753\pi\) | ||||
0.588413 | + | 0.808560i | \(0.299753\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.4307 | − | 34.5947i | −0.447624 | − | 1.48460i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.68614 | − | 13.3128i | 0.329238 | − | 0.570257i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.7337 | − | 25.5195i | −0.629967 | − | 1.09113i | −0.987558 | − | 0.157256i | \(-0.949735\pi\) |
0.357591 | − | 0.933878i | \(-0.383598\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.8030 | − | 10.8434i | −0.930529 | − | 0.462783i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.62772 | − | 2.81929i | −0.0693431 | − | 0.120106i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.37228 | + | 5.84096i | −0.143404 | + | 0.248383i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.74456 | + | 1.58457i | 0.286291 | + | 0.0672614i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44.2337 | −1.87424 | −0.937121 | − | 0.349005i | \(-0.886520\pi\) | ||||
−0.937121 | + | 0.349005i | \(0.886520\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.9565 | −1.60539 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.44158 | − | 8.98266i | 0.356404 | − | 0.379248i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.3614 | + | 35.2670i | −0.858131 | + | 1.48633i | 0.0155787 | + | 0.999879i | \(0.495041\pi\) |
−0.873710 | + | 0.486448i | \(0.838292\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.62772 | + | 2.81929i | 0.0684786 | + | 0.118608i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 30.1168 | − | 3.75906i | 1.26479 | − | 0.157865i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.3030 | + | 26.5055i | 0.641534 | + | 1.11117i | 0.985090 | + | 0.172038i | \(0.0550352\pi\) |
−0.343556 | + | 0.939132i | \(0.611631\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.30298 | − | 7.45299i | 0.180074 | − | 0.311898i | −0.761831 | − | 0.647775i | \(-0.775700\pi\) |
0.941906 | + | 0.335878i | \(0.109033\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.7446 | − | 22.0742i | 0.866617 | − | 0.922164i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.37228 | −0.0572281 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.1168 | −1.71172 | −0.855858 | − | 0.517210i | \(-0.826970\pi\) | ||||
−0.855858 | + | 0.517210i | \(0.826970\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 35.6060 | + | 8.36530i | 1.47973 | + | 0.347650i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.4307 | + | 21.5306i | −0.515712 | + | 0.893240i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.1168 | + | 43.5036i | 1.04023 | + | 1.80174i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.1168 | + | 9.01011i | 0.749039 | + | 0.372522i | ||||
\(586\) | 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 | ||||||||
\(589\) | 5.62772 | − | 9.74749i | 0.231886 | − | 0.401639i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.74456 | + | 9.10268i | 0.112896 | + | 0.374434i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.7228 | −0.809919 | −0.404959 | − | 0.914335i | \(-0.632714\pi\) | ||||
−0.404959 | + | 0.914335i | \(0.632714\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.48913 | −0.225032 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.74456 | + | 22.3692i | 0.276037 | + | 0.915510i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.88316 | + | 3.26172i | −0.0769437 | + | 0.133270i | −0.901930 | − | 0.431883i | \(-0.857849\pi\) |
0.824986 | + | 0.565153i | \(0.191183\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.930703 | + | 1.61203i | 0.0379642 | + | 0.0657559i | 0.884383 | − | 0.466762i | \(-0.154579\pi\) |
−0.846419 | + | 0.532517i | \(0.821246\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.30298 | − | 20.9595i | −0.0530616 | − | 0.853538i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.05842 | + | 7.02939i | 0.164998 | + | 0.285785i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.05842 | − | 15.6896i | 0.367670 | − | 0.636823i | −0.621531 | − | 0.783390i | \(-0.713489\pi\) |
0.989201 | + | 0.146567i | \(0.0468223\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.80298 | − | 1.83324i | −0.316193 | − | 0.0742867i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −49.7228 | −2.01157 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.2337 | 1.38269 | 0.691343 | − | 0.722527i | \(-0.257019\pi\) | ||||
0.691343 | + | 0.722527i | \(0.257019\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.55842 | + | 3.78651i | −0.143489 | + | 0.152687i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.44158 | − | 4.22894i | 0.0982942 | − | 0.170251i | −0.812684 | − | 0.582704i | \(-0.801995\pi\) |
0.910979 | + | 0.412453i | \(0.135328\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.4416 | − | 18.0853i | −0.419682 | − | 0.726911i | 0.576225 | − | 0.817291i | \(-0.304525\pi\) |
−0.995907 | + | 0.0903798i | \(0.971192\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.68614 | − | 2.47805i | 0.268306 | − | 0.0994408i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.1753 | + | 47.0689i | 1.08875 | + | 1.88578i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.3030 | + | 13.0916i | −0.491334 | + | 0.522827i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.51087 | 0.259606 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.7228 | 0.944390 | 0.472195 | − | 0.881494i | \(-0.343462\pi\) | ||||
0.472195 | + | 0.881494i | \(0.343462\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 31.6060 | + | 7.42554i | 1.25622 | + | 0.295139i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.05842 | − | 7.02939i | 0.161054 | − | 0.278953i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.7446 | + | 25.5383i | 0.584201 | + | 1.01187i | ||||
\(638\) | 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 | ||||||||
\(645\) | 2.81386 | + | 9.33252i | 0.110796 | + | 0.367467i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.0951 | 1.53699 | 0.768493 | − | 0.639858i | \(-0.221007\pi\) | ||||
0.768493 | + | 0.639858i | \(0.221007\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.1168 | −0.750402 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.00000 | − | 26.5330i | −0.313545 | − | 1.03991i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.86141 | + | 17.0805i | −0.385907 | + | 0.668410i | −0.991895 | − | 0.127064i | \(-0.959445\pi\) |
0.605988 | + | 0.795474i | \(0.292778\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.37228 | + | 2.37686i | 0.0536195 | + | 0.0928716i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.79211 | + | 5.16870i | −0.303999 | + | 0.201650i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.74456 | + | 15.1460i | 0.340640 | + | 0.590005i | 0.984552 | − | 0.175094i | \(-0.0560230\pi\) |
−0.643912 | + | 0.765100i | \(0.722690\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.11684 | − | 10.5947i | 0.237918 | − | 0.412085i | −0.722199 | − | 0.691685i | \(-0.756868\pi\) |
0.960117 | + | 0.279600i | \(0.0902018\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.5109 | + | 4.34896i | 0.718903 | + | 0.168900i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.00000 | 0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.88316 | −0.0729161 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.86141 | − | 8.36530i | 0.303940 | − | 0.323421i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.7446 | − | 30.7345i | 0.685021 | − | 1.18649i | ||||
\(672\) | 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 | ||||||||
\(675\) | 0.872281 | − | 5.12241i | 0.0335741 | − | 0.197162i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.86141 | − | 11.8843i | −0.263705 | − | 0.456751i | 0.703518 | − | 0.710677i | \(-0.251611\pi\) |
−0.967224 | + | 0.253926i | \(0.918278\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.1168 | + | 24.4511i | −0.541755 | + | 0.938347i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.6753 | − | 24.1287i | 0.868918 | − | 0.924613i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.0951 | 1.15156 | 0.575778 | − | 0.817606i | \(-0.304699\pi\) | ||||
0.575778 | + | 0.817606i | \(0.304699\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.1168 | 0.730417 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.2921 | + | 5.00239i | 0.812345 | + | 0.190853i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38.7446 | + | 67.1076i | −1.47605 | + | 2.55659i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.1168 | − | 31.3793i | −0.689197 | − | 1.19372i | −0.972098 | − | 0.234575i | \(-0.924630\pi\) |
0.282901 | − | 0.959149i | \(-0.408703\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.74456 | + | 44.1485i | 0.104257 | + | 1.67706i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.441578 | − | 0.764836i | −0.0167500 | − | 0.0290119i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.44158 | + | 4.22894i | −0.0924814 | + | 0.160182i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.55842 | − | 11.8020i | −0.134592 | − | 0.446391i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.8614 | 1.61885 | 0.809426 | − | 0.587221i | \(-0.199778\pi\) | ||||
0.809426 | + | 0.587221i | \(0.199778\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.48913 | −0.357889 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.68614 | + | 12.2255i | 0.138828 | + | 0.460441i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.62772 | − | 8.01544i | 0.174043 | − | 0.301452i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.43070 | − | 2.47805i | −0.0537312 | − | 0.0930652i | 0.837909 | − | 0.545810i | \(-0.183778\pi\) |
−0.891640 | + | 0.452745i | \(0.850445\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.37228 | − | 2.67181i | −0.201476 | − | 0.100201i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.25544 | − | 5.63858i | −0.121917 | − | 0.211167i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.7446 | + | 25.5383i | −0.551415 | + | 0.955079i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.48913 | + | 1.28962i | 0.204995 | + | 0.0481618i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.76631 | 0.140460 | 0.0702299 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702299 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −53.9565 | −2.00945 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.8139 | − | 15.7634i | 0.550933 | − | 0.586247i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.686141 | + | 1.18843i | −0.0254826 | + | 0.0441372i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.05842 | + | 15.6896i | 0.335958 | + | 0.581897i | 0.983668 | − | 0.179990i | \(-0.0576066\pi\) |
−0.647710 | + | 0.761887i | \(0.724273\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.00000 | + | 26.5330i | 0.185185 | + | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.58017 | + | 7.93309i | 0.169404 | + | 0.293416i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.116844 | − | 0.202380i | 0.00431573 | − | 0.00747506i | −0.863859 | − | 0.503733i | \(-0.831960\pi\) |
0.868175 | + | 0.496258i | \(0.165293\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.18614 | − | 5.51856i | 0.191294 | − | 0.203555i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.6060 | 1.12739 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.1168 | 1.51251 | 0.756254 | − | 0.654278i | \(-0.227028\pi\) | ||||
0.756254 | + | 0.654278i | \(0.227028\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.9783 | − | 6.33830i | −0.991071 | − | 0.232843i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.94158 | − | 6.82701i | 0.144602 | − | 0.250459i | −0.784622 | − | 0.619974i | \(-0.787143\pi\) |
0.929225 | + | 0.369516i | \(0.120476\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.941578 | + | 1.63086i | 0.0344967 | + | 0.0597501i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.8030 | − | 9.84868i | −0.724553 | − | 0.360345i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.3139 | − | 24.7923i | −0.523017 | − | 0.905892i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.11684 | − | 14.0588i | 0.296188 | − | 0.513012i | −0.679073 | − | 0.734071i | \(-0.737618\pi\) |
0.975261 | + | 0.221059i | \(0.0709512\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.3030 | − | 40.8044i | −0.448346 | − | 1.48699i | ||||
\(754\) | 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 | ||||||||
\(761\) | 25.5475 | − | 44.2496i | 0.926098 | − | 1.60405i | 0.136312 | − | 0.990666i | \(-0.456475\pi\) |
0.789786 | − | 0.613383i | \(-0.210192\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.9198 | + | 44.8945i | 0.938361 | + | 1.62529i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.302985 | − | 4.87375i | −0.0109544 | − | 0.176211i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.7446 | − | 25.5383i | −0.532395 | − | 0.922136i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.4307 | − | 40.5832i | 0.844933 | − | 1.46347i | −0.0407468 | − | 0.999170i | \(-0.512974\pi\) |
0.885680 | − | 0.464297i | \(-0.153693\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.37228 | + | 1.73205i | 0.265506 | + | 0.0623783i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.25544 | 0.117090 | 0.0585450 | − | 0.998285i | \(-0.481354\pi\) | ||||
0.0585450 | + | 0.998285i | \(0.481354\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.74456 | −0.170430 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.0000 | + | 17.0256i | −0.573997 | + | 0.610788i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.55842 | − | 6.16337i | 0.127494 | − | 0.220826i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.1168 | − | 22.7190i | −0.469358 | − | 0.812951i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.19702 | − | 7.02939i | 0.0427778 | − | 0.251210i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.37228 | − | 5.84096i | −0.120362 | − | 0.208473i | ||||
\(786\) | 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 | ||||||||
\(789\) | −20.7446 | + | 22.0742i | −0.738526 | + | 0.785863i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9783 | −0.390342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.7446 | 1.94404 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.3723 | + | 4.55134i | 0.687064 | + | 0.161419i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.37228 | + | 12.7692i | −0.261140 | + | 0.452307i | −0.966545 | − | 0.256497i | \(-0.917432\pi\) |
0.705405 | + | 0.708804i | \(0.250765\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.00000 | + | 10.3923i | 0.212265 | + | 0.367653i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −40.2921 | + | 26.7268i | −1.42365 | + | 0.944344i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.81386 | − | 11.8020i | −0.240456 | − | 0.416482i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.31386 | − | 4.00772i | 0.0815528 | − | 0.141254i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.686141 | + | 2.27567i | 0.0241533 | + | 0.0801074i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.3505 | 1.38349 | 0.691746 | − | 0.722141i | \(-0.256842\pi\) | ||||
0.691746 | + | 0.722141i | \(0.256842\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.62772 | −0.127386 | −0.0636932 | − | 0.997970i | \(-0.520288\pi\) | ||||
−0.0636932 | + | 0.997970i | \(0.520288\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.00000 | + | 13.2665i | 0.140286 | + | 0.465276i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.7446 | − | 18.6101i | 0.376366 | − | 0.651884i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.67527 | − | 11.5619i | −0.233538 | − | 0.404500i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −56.8614 | + | 37.7176i | −1.98690 | + | 1.31796i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.9198 | + | 20.6457i | 0.416005 | + | 0.720542i | 0.995533 | − | 0.0944104i | \(-0.0300966\pi\) |
−0.579528 | + | 0.814952i | \(0.696763\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.5475 | + | 21.7330i | −0.437380 | + | 0.757564i | −0.997487 | − | 0.0708562i | \(-0.977427\pi\) |
0.560107 | + | 0.828421i | \(0.310760\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.37228 | + | 1.73205i | 0.256670 | + | 0.0603023i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.8614 | −1.28180 | −0.640898 | − | 0.767626i | \(-0.721438\pi\) | ||||
−0.640898 | + | 0.767626i | \(0.721438\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.1168 | −1.74063 | −0.870315 | − | 0.492496i | \(-0.836085\pi\) | ||||
−0.870315 | + | 0.492496i | \(0.836085\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.8614 | + | 21.1345i | −0.688985 | + | 0.733147i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.55842 | − | 6.16337i | 0.123292 | − | 0.213548i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.68614 | − | 11.5807i | −0.231383 | − | 0.400768i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23.1168 | − | 8.56768i | 0.799035 | − | 0.296142i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.88316 | + | 8.45787i | 0.168585 | + | 0.291998i | 0.937923 | − | 0.346844i | \(-0.112747\pi\) |
−0.769337 | + | 0.638843i | \(0.779413\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5584 | − | 23.4839i | 0.467532 | − | 0.809789i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.62772 | − | 1.73205i | 0.0560616 | − | 0.0596550i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −32.4891 | −1.11766 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.3723 | −0.940523 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.29211 | + | 1.24333i | 0.181625 | + | 0.0426711i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.74456 | + | 4.75372i | −0.0940824 | + | 0.162955i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.1168 | + | 31.3793i | 0.620309 | + | 1.07441i | 0.989428 | + | 0.145024i | \(0.0463261\pi\) |
−0.369119 | + | 0.929382i | \(0.620341\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.441578 | + | 7.10313i | 0.0151016 | + | 0.242922i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.255437 | − | 0.442430i | −0.00872557 | − | 0.0151131i | 0.861630 | − | 0.507538i | \(-0.169444\pi\) |
−0.870355 | + | 0.492424i | \(0.836111\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.55842 | + | 14.8236i | −0.292010 | + | 0.505775i | −0.974285 | − | 0.225320i | \(-0.927657\pi\) |
0.682275 | + | 0.731095i | \(0.260991\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.05842 | − | 16.7769i | −0.172391 | − | 0.571755i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.39403 | 0.0814938 | 0.0407469 | − | 0.999170i | \(-0.487026\pi\) | ||||
0.0407469 | + | 0.999170i | \(0.487026\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.7446 | −0.705336 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.17527 | + | 23.7977i | 0.243685 | + | 0.808211i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.37228 | − | 7.57301i | 0.148319 | − | 0.256897i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.6060 | + | 40.8867i | 0.799858 | + | 1.38539i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.4891 | − | 11.1846i | −0.761142 | − | 0.378541i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.68614 | − | 2.92048i | −0.0570020 | − | 0.0987303i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.9783 | + | 31.1392i | −0.607082 | + | 1.05150i | 0.384636 | + | 0.923068i | \(0.374327\pi\) |
−0.991719 | + | 0.128429i | \(0.959006\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 44.2337 | + | 10.3923i | 1.49197 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.3505 | −0.820390 | −0.410195 | − | 0.911998i | \(-0.634539\pi\) | ||||
−0.410195 | + | 0.911998i | \(0.634539\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.7228 | 1.50504 | 0.752521 | − | 0.658568i | \(-0.228837\pi\) | ||||
0.752521 | + | 0.658568i | \(0.228837\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.18614 | + | 5.51856i | −0.174330 | + | 0.185504i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.86141 | − | 17.0805i | 0.331114 | − | 0.573506i | −0.651617 | − | 0.758548i | \(-0.725909\pi\) |
0.982730 | + | 0.185043i | \(0.0592423\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.6861 | + | 23.7051i | 0.459018 | + | 0.795043i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −39.0475 | + | 4.87375i | −1.30814 | + | 0.163277i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.74456 | − | 15.1460i | −0.292626 | − | 0.506842i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.37228 | − | 12.7692i | 0.246428 | − | 0.426826i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.9783 | + | 11.6819i | −0.366553 | + | 0.390048i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.51087 | −0.217150 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.7011 | 0.623023 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −32.0000 | − | 7.51811i | −1.06489 | − | 0.250187i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.4307 | − | 18.0665i | 0.346728 | − | 0.600551i | ||||
\(906\) | 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 | ||||||||
\(909\) | 7.37228 | + | 3.66648i | 0.244523 | + | 0.121610i | ||||
\(910\) | 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 | ||||||||
\(913\) | 16.1168 | − | 27.9152i | 0.533390 | − | 0.923858i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.05842 | − | 13.4603i | −0.134167 | − | 0.444983i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.25544 | −0.305641 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.4674 | 0.873078 | 0.436539 | − | 0.899685i | \(-0.356204\pi\) | ||||
0.436539 | + | 0.899685i | \(0.356204\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.616844 | + | 2.04584i | 0.0203257 | + | 0.0674127i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.2337 | − | 35.0458i | 0.666000 | − | 1.15355i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | + | 3.46410i | 0.0657596 | + | 0.113899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.97825 | − | 47.9075i | −0.0978186 | − | 1.57349i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.9783 | − | 44.9956i | −0.852319 | − | 1.47626i | −0.879110 | − | 0.476618i | \(-0.841862\pi\) |
0.0267916 | − | 0.999641i | \(-0.491471\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.18614 | + | 8.98266i | −0.169969 | + | 0.294395i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.9783 | + | 8.21782i | 1.14514 | + | 0.269039i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.11684 | 0.232746 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.7228 | 1.29769 | 0.648844 | − | 0.760922i | \(-0.275253\pi\) | ||||
0.648844 | + | 0.760922i | \(0.275253\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.30298 | + | 4.57879i | −0.140423 | + | 0.149423i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.6861 | + | 37.5615i | −0.706948 | + | 1.22447i | 0.259036 | + | 0.965868i | \(0.416595\pi\) |
−0.965984 | + | 0.258602i | \(0.916738\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.05842 | − | 3.56529i | −0.0670314 | − | 0.116102i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.4891 | + | 11.1846i | 0.438801 | + | 0.363835i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.3614 | − | 30.0708i | −0.564170 | − | 0.977171i | −0.997126 | − | 0.0757561i | \(-0.975863\pi\) |
0.432956 | − | 0.901415i | \(-0.357470\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.5109 | − | 18.2054i | 0.341197 | − | 0.590971i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.25544 | + | 3.46410i | −0.105565 | + | 0.112331i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.13859 | 0.0692758 | 0.0346379 | − | 0.999400i | \(-0.488972\pi\) | ||||
0.0346379 | + | 0.999400i | \(0.488972\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.4891 | 0.565935 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.1168 | + | 2.37686i | 0.327031 | + | 0.0768330i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.2337 | + | 55.8304i | −1.04088 | + | 1.80286i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.24456 | + | 7.35180i | 0.136921 | + | 0.237155i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.2228 | − | 14.0776i | 0.683896 | − | 0.453645i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.5584 | + | 18.2877i | 0.339888 | + | 0.588703i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.0584 | − | 31.2781i | 0.580720 | − | 1.00584i | −0.414675 | − | 0.909970i | \(-0.636105\pi\) |
0.995394 | − | 0.0958662i | \(-0.0305621\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.93070 | + | 6.40342i | 0.0620231 | + | 0.205707i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.9783 | 0.737407 | 0.368704 | − | 0.929547i | \(-0.379802\pi\) | ||||
0.368704 | + | 0.929547i | \(0.379802\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.97825 | 0.0954783 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.37228 | + | 11.1846i | 0.107999 | + | 0.358194i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.4416 | − | 19.8174i | 0.366049 | − | 0.634015i | −0.622895 | − | 0.782305i | \(-0.714044\pi\) |
0.988944 | + | 0.148291i | \(0.0473771\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.2337 | − | 61.0265i | −1.12607 | − | 1.95042i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −38.4307 | + | 25.4920i | −1.22700 | + | 0.813898i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.43070 | − | 11.1383i | −0.205108 | − | 0.355257i | 0.745059 | − | 0.666998i | \(-0.232421\pi\) |
−0.950167 | + | 0.311741i | \(0.899088\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.74456 | + | 4.75372i | −0.0874490 | + | 0.151466i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −41.9198 | − | 9.84868i | −1.33432 | − | 0.313487i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.72281 | −0.245571 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.2337 | −0.515680 | −0.257840 | − | 0.966188i | \(-0.583011\pi\) | ||||
−0.257840 | + | 0.966188i | \(0.583011\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.2554 | − | 20.4897i | 0.611053 | − | 0.650220i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.74456 | + | 11.6819i | −0.213817 | + | 0.370342i | ||||
\(996\) | 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 \(a_p\))