Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(85,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.85");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.j (of order \(3\), degree \(2\), 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: | \(2.01223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 169.3 | ||
Root | \(0.500000 + 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.169 |
Dual form | 252.2.j.b.85.3 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.29418 | + | 1.15113i | 0.747196 | + | 0.664603i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.555632 | + | 0.962383i | 0.248486 | + | 0.430391i | 0.963106 | − | 0.269122i | \(-0.0867336\pi\) |
−0.714620 | + | 0.699513i | \(0.753400\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.349814 | + | 2.97954i | 0.116605 | + | 0.993178i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.944368 | − | 1.63569i | 0.284738 | − | 0.493180i | −0.687808 | − | 0.725893i | \(-0.741427\pi\) |
0.972546 | + | 0.232713i | \(0.0747602\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | 0.926995 | − | 0.375073i | \(-0.122382\pi\) |
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.388736 | + | 1.88510i | −0.100371 | + | 0.486731i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.87636 | −1.42523 | −0.712613 | − | 0.701557i | \(-0.752488\pi\) | ||||
−0.712613 | + | 0.701557i | \(0.752488\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.09888 | 1.62860 | 0.814298 | − | 0.580447i | \(-0.197122\pi\) | ||||
0.814298 | + | 0.580447i | \(0.197122\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.64400 | + | 0.545231i | −0.358749 | + | 0.118979i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.99381 | − | 3.45338i | −0.415738 | − | 0.720080i | 0.579767 | − | 0.814782i | \(-0.303143\pi\) |
−0.995506 | + | 0.0947024i | \(0.969810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.88255 | − | 3.26067i | 0.376509 | − | 0.652133i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.97710 | + | 4.25874i | −0.572943 | + | 0.819595i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.493810 | + | 0.855304i | −0.0916982 | + | 0.158826i | −0.908226 | − | 0.418480i | \(-0.862563\pi\) |
0.816528 | + | 0.577306i | \(0.195896\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.333104 | + | 0.576953i | 0.0598272 | + | 0.103624i | 0.894388 | − | 0.447292i | \(-0.147612\pi\) |
−0.834561 | + | 0.550916i | \(0.814278\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.10507 | − | 1.02980i | 0.540524 | − | 0.179265i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.11126 | −0.187838 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.33379 | −0.219274 | −0.109637 | − | 0.993972i | \(-0.534969\pi\) | ||||
−0.109637 | + | 0.993972i | \(0.534969\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.349814 | + | 1.69636i | −0.0560151 | + | 0.271635i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.944368 | + | 1.63569i | 0.147485 | + | 0.255452i | 0.930297 | − | 0.366806i | \(-0.119549\pi\) |
−0.782812 | + | 0.622258i | \(0.786215\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.43199 | − | 9.40848i | 0.828370 | − | 1.43478i | −0.0709455 | − | 0.997480i | \(-0.522602\pi\) |
0.899316 | − | 0.437299i | \(-0.144065\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.67309 | + | 1.99218i | −0.398480 | + | 0.296977i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.54944 | − | 9.61192i | 0.809469 | − | 1.40204i | −0.103763 | − | 0.994602i | \(-0.533088\pi\) |
0.913232 | − | 0.407440i | \(-0.133578\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.60507 | − | 6.76443i | −1.06492 | − | 0.947210i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.2101 | −1.67719 | −0.838596 | − | 0.544753i | \(-0.816623\pi\) | ||||
−0.838596 | + | 0.544753i | \(0.816623\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.09888 | 0.283014 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.18725 | + | 8.17172i | 1.21688 | + | 1.08237i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.38255 | − | 4.12669i | −0.310181 | − | 0.537249i | 0.668220 | − | 0.743963i | \(-0.267056\pi\) |
−0.978401 | + | 0.206714i | \(0.933723\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.88255 | + | 3.26067i | −0.241035 | + | 0.417485i | −0.961009 | − | 0.276515i | \(-0.910820\pi\) |
0.719974 | + | 0.694001i | \(0.244154\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.75526 | − | 1.18682i | −0.347130 | − | 0.149525i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.555632 | + | 0.962383i | −0.0689177 | + | 0.119369i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.04944 | − | 3.54974i | −0.250379 | − | 0.433670i | 0.713251 | − | 0.700909i | \(-0.247222\pi\) |
−0.963630 | + | 0.267239i | \(0.913889\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.39493 | − | 6.76443i | 0.167929 | − | 0.814342i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7651 | −1.27758 | −0.638791 | − | 0.769381i | \(-0.720565\pi\) | ||||
−0.638791 | + | 0.769381i | \(0.720565\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.09888 | −0.362697 | −0.181348 | − | 0.983419i | \(-0.558046\pi\) | ||||
−0.181348 | + | 0.983419i | \(0.558046\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.18980 | − | 2.05285i | 0.714736 | − | 0.237042i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.944368 | + | 1.63569i | 0.107621 | + | 0.186405i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.21565 | + | 5.56967i | −0.361789 | + | 0.626637i | −0.988255 | − | 0.152812i | \(-0.951167\pi\) |
0.626466 | + | 0.779448i | \(0.284501\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.75526 | + | 2.08457i | −0.972807 | + | 0.231619i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.93818 | − | 10.2852i | 0.651800 | − | 1.12895i | −0.330886 | − | 0.943671i | \(-0.607348\pi\) |
0.982686 | − | 0.185280i | \(-0.0593191\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.26509 | − | 5.65531i | −0.354149 | − | 0.613404i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.62364 | + | 0.538481i | −0.174073 | + | 0.0577313i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.3090 | 1.51675 | 0.758377 | − | 0.651816i | \(-0.225993\pi\) | ||||
0.758377 | + | 0.651816i | \(0.225993\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.233049 | + | 1.13013i | −0.0241660 | + | 0.117189i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.94437 | + | 6.83185i | 0.404684 | + | 0.700933i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.382546 | + | 0.662589i | −0.0388417 | + | 0.0672757i | −0.884793 | − | 0.465985i | \(-0.845700\pi\) |
0.845951 | + | 0.533261i | \(0.179033\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.20396 | + | 2.24159i | 0.523018 | + | 0.225288i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.43818 | + | 7.68715i | −0.441615 | + | 0.764900i | −0.997810 | − | 0.0661523i | \(-0.978928\pi\) |
0.556194 | + | 0.831052i | \(0.312261\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.98143 | + | 8.62809i | 0.490835 | + | 0.850151i | 0.999944 | − | 0.0105508i | \(-0.00335848\pi\) |
−0.509109 | + | 0.860702i | \(0.670025\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.43818 | − | 1.27921i | −0.140352 | − | 0.124838i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.22253 | −0.504881 | −0.252440 | − | 0.967612i | \(-0.581233\pi\) | ||||
−0.252440 | + | 0.967612i | \(0.581233\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.09888 | −0.871515 | −0.435758 | − | 0.900064i | \(-0.643519\pi\) | ||||
−0.435758 | + | 0.900064i | \(0.643519\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.72617 | − | 1.53536i | −0.163841 | − | 0.145730i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.21015 | + | 10.7563i | 0.584202 | + | 1.01187i | 0.994974 | + | 0.100129i | \(0.0319256\pi\) |
−0.410773 | + | 0.911738i | \(0.634741\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.21565 | − | 3.83762i | 0.206610 | − | 0.357860i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.40545 | + | 1.79272i | −0.222384 | + | 0.165737i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.93818 | − | 5.08907i | 0.269342 | − | 0.466515i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.71634 | + | 6.43689i | 0.337849 | + | 0.585172i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.660706 | + | 3.20397i | −0.0595739 | + | 0.288892i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.74033 | 0.871202 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.66621 | 0.680266 | 0.340133 | − | 0.940377i | \(-0.389528\pi\) | ||||
0.340133 | + | 0.940377i | \(0.389528\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.8603 | − | 5.92338i | 1.57251 | − | 0.521524i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.27128 | + | 12.5942i | 0.635295 | + | 1.10036i | 0.986453 | + | 0.164047i | \(0.0524548\pi\) |
−0.351158 | + | 0.936316i | \(0.614212\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.54944 | + | 6.14781i | −0.307776 | + | 0.533083i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.75271 | − | 0.498817i | −0.495115 | − | 0.0429313i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.32072 | + | 4.01961i | −0.198273 | + | 0.343419i | −0.947969 | − | 0.318364i | \(-0.896867\pi\) |
0.749696 | + | 0.661783i | \(0.230200\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.64833 | + | 16.7114i | 0.818360 | + | 1.41744i | 0.906890 | + | 0.421368i | \(0.138450\pi\) |
−0.0885293 | + | 0.996074i | \(0.528217\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.2465 | − | 6.05146i | 1.53663 | − | 0.509625i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.88874 | 0.157944 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.09751 | −0.0911430 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.349814 | − | 1.69636i | 0.0288522 | − | 0.139913i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.82072 | + | 11.8138i | 0.558775 | + | 0.967828i | 0.997599 | + | 0.0692543i | \(0.0220620\pi\) |
−0.438824 | + | 0.898573i | \(0.644605\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.48143 | + | 14.6903i | −0.690209 | + | 1.19548i | 0.281560 | + | 0.959544i | \(0.409148\pi\) |
−0.971769 | + | 0.235934i | \(0.924185\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.05563 | − | 17.5088i | −0.166188 | − | 1.41550i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.370166 | + | 0.641147i | −0.0297325 | + | 0.0514981i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.3145 | − | 19.5973i | −0.902998 | − | 1.56404i | −0.823582 | − | 0.567197i | \(-0.808028\pi\) |
−0.0794160 | − | 0.996842i | \(-0.525306\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.8022 | − | 14.0554i | −1.25319 | − | 1.11467i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.98762 | 0.314269 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.0989 | −1.41761 | −0.708807 | − | 0.705402i | \(-0.750766\pi\) | ||||
−0.708807 | + | 0.705402i | \(0.750766\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.71634 | + | 2.41608i | 0.211467 | + | 0.188092i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.61126 | + | 14.9151i | 0.666360 | + | 1.15417i | 0.978915 | + | 0.204269i | \(0.0654818\pi\) |
−0.312555 | + | 0.949900i | \(0.601185\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.48329 | + | 21.1514i | 0.189902 | + | 1.61749i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.431988 | − | 0.748226i | 0.0328435 | − | 0.0568865i | −0.849136 | − | 0.528174i | \(-0.822877\pi\) |
0.881980 | + | 0.471287i | \(0.156210\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.88255 | + | 3.26067i | 0.142307 | + | 0.246483i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.66690 | − | 8.08330i | 0.125292 | − | 0.607578i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.67859 | −0.349694 | −0.174847 | − | 0.984596i | \(-0.555943\pi\) | ||||
−0.174847 | + | 0.984596i | \(0.555943\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.8640 | −1.25349 | −0.626745 | − | 0.779225i | \(-0.715613\pi\) | ||||
−0.626745 | + | 0.779225i | \(0.715613\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.18980 | + | 2.05285i | −0.457563 | + | 0.151751i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.741098 | − | 1.28362i | −0.0544866 | − | 0.0943736i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.54944 | + | 9.61192i | −0.405815 | + | 0.702893i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.19963 | − | 4.70761i | −0.159999 | − | 0.342429i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.53087 | − | 14.7759i | 0.617272 | − | 1.06915i | −0.372709 | − | 0.927948i | \(-0.621571\pi\) |
0.989981 | − | 0.141199i | \(-0.0450956\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.71634 | − | 6.43689i | −0.267508 | − | 0.463337i | 0.700710 | − | 0.713446i | \(-0.252867\pi\) |
−0.968218 | + | 0.250109i | \(0.919533\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.82691 | + | 0.605896i | −0.130828 | + | 0.0433891i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.2953 | −1.87346 | −0.936730 | − | 0.350052i | \(-0.886164\pi\) | ||||
−0.936730 | + | 0.350052i | \(0.886164\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.4327 | 0.739553 | 0.369776 | − | 0.929121i | \(-0.379434\pi\) | ||||
0.369776 | + | 0.929121i | \(0.379434\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.43385 | − | 6.95317i | 0.101136 | − | 0.490439i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.493810 | − | 0.855304i | −0.0346587 | − | 0.0600306i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.04944 | + | 1.81769i | −0.0732962 | + | 0.126953i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.59201 | − | 7.14867i | 0.666690 | − | 0.496867i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.70396 | − | 11.6116i | 0.463723 | − | 0.803191i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.6978 | − | 21.9932i | −0.874150 | − | 1.51407i | −0.857665 | − | 0.514209i | \(-0.828086\pi\) |
−0.0164855 | − | 0.999864i | \(-0.505248\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.9320 | − | 12.3920i | −0.954604 | − | 0.849085i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.0727 | 0.823355 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.666208 | −0.0452251 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.01052 | − | 3.56721i | −0.271006 | − | 0.241050i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.93818 | − | 5.08907i | −0.197643 | − | 0.342328i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.26509 | + | 12.5835i | −0.486507 | + | 0.842654i | −0.999880 | − | 0.0155114i | \(-0.995062\pi\) |
0.513373 | + | 0.858165i | \(0.328396\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.3738 | + | 4.46849i | 0.691587 | + | 0.297899i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.70396 | + | 16.8077i | −0.644074 | + | 1.11557i | 0.340440 | + | 0.940266i | \(0.389424\pi\) |
−0.984514 | + | 0.175303i | \(0.943909\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.26509 | + | 9.11941i | 0.347927 | + | 0.602627i | 0.985881 | − | 0.167447i | \(-0.0535523\pi\) |
−0.637954 | + | 0.770074i | \(0.720219\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.660706 | + | 3.20397i | −0.0434713 | + | 0.210806i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.6414 | 1.48329 | 0.741645 | − | 0.670792i | \(-0.234046\pi\) | ||||
0.741645 | + | 0.670792i | \(0.234046\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.3338 | 0.804568 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.5730 | + | 3.50654i | −0.686792 | + | 0.227775i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.48762 | − | 4.30868i | −0.160911 | − | 0.278706i | 0.774285 | − | 0.632837i | \(-0.218110\pi\) |
−0.935196 | + | 0.354132i | \(0.884776\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.117454 | + | 0.203436i | −0.00756588 | + | 0.0131045i | −0.869784 | − | 0.493433i | \(-0.835742\pi\) |
0.862218 | + | 0.506538i | \(0.169075\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.7305 | − | 7.38061i | −0.880812 | − | 0.473466i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.555632 | − | 0.962383i | 0.0354980 | − | 0.0614844i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.54944 | + | 6.14781i | 0.225846 | + | 0.391176i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.5247 | − | 6.47536i | 1.23733 | − | 0.410359i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.09888 | −0.511197 | −0.255599 | − | 0.966783i | \(-0.582273\pi\) | ||||
−0.255599 | + | 0.966783i | \(0.582273\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.53156 | −0.473505 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.28435 | − | 11.0775i | 0.143052 | − | 0.693702i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.8764 | − | 20.5705i | −0.740827 | − | 1.28315i | −0.952119 | − | 0.305727i | \(-0.901101\pi\) |
0.211293 | − | 0.977423i | \(-0.432233\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.666896 | − | 1.15510i | 0.0414389 | − | 0.0717743i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.72115 | − | 1.17213i | −0.168435 | − | 0.0725529i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.32691 | − | 5.76238i | 0.205146 | − | 0.355324i | −0.745033 | − | 0.667028i | \(-0.767566\pi\) |
0.950179 | + | 0.311704i | \(0.100900\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.78435 | − | 11.7508i | −0.416759 | − | 0.721848i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.5185 | + | 16.4715i | 1.13331 | + | 1.00804i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.9876 | 1.15770 | 0.578848 | − | 0.815436i | \(-0.303503\pi\) | ||||
0.578848 | + | 0.815436i | \(0.303503\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.3338 | −1.35668 | −0.678341 | − | 0.734748i | \(-0.737301\pi\) | ||||
−0.678341 | + | 0.734748i | \(0.737301\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.29418 | − | 1.15113i | −0.0783275 | − | 0.0696694i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.55563 | − | 6.15854i | −0.214413 | − | 0.371374i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.9134 | − | 27.5628i | 0.956145 | − | 1.65609i | 0.224418 | − | 0.974493i | \(-0.427952\pi\) |
0.731727 | − | 0.681598i | \(-0.238715\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.60253 | + | 1.19432i | −0.0959407 | + | 0.0715021i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.92580 | + | 17.1920i | −0.592123 | + | 1.02559i | 0.401822 | + | 0.915718i | \(0.368377\pi\) |
−0.993946 | + | 0.109870i | \(0.964956\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.56801 | + | 2.71588i | 0.0932086 | + | 0.161442i | 0.908860 | − | 0.417102i | \(-0.136954\pi\) |
−0.815651 | + | 0.578544i | \(0.803621\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.75959 | + | 13.3821i | −0.163464 | + | 0.792688i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.88874 | −0.111489 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.5316 | 1.03127 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.25781 | + | 0.417152i | −0.0737340 | + | 0.0244539i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.93887 | − | 8.55437i | −0.288532 | − | 0.499752i | 0.684928 | − | 0.728611i | \(-0.259834\pi\) |
−0.973459 | + | 0.228859i | \(0.926500\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.64764 | − | 4.58584i | 0.154151 | − | 0.266998i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.15452 | + | 8.89144i | 0.241069 | + | 0.515934i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.99381 | − | 3.45338i | 0.115305 | − | 0.199714i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.43199 | + | 9.40848i | 0.313095 | + | 0.542296i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.5927 | + | 4.83967i | −0.838328 | + | 0.278032i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.18401 | −0.239576 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.4313 | 0.880711 | 0.440355 | − | 0.897824i | \(-0.354852\pi\) | ||||
0.440355 | + | 0.897824i | \(0.354852\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.48515 | + | 16.9006i | −0.198263 | + | 0.961440i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.83310 | − | 15.2994i | −0.500879 | − | 0.867549i | −0.999999 | − | 0.00101570i | \(-0.999677\pi\) |
0.499120 | − | 0.866533i | \(-0.333657\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.71634 | + | 11.6330i | −0.379630 | + | 0.657538i | −0.991008 | − | 0.133800i | \(-0.957282\pi\) |
0.611378 | + | 0.791338i | \(0.290615\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.388736 | − | 3.31105i | −0.0219028 | − | 0.186557i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.93199 | + | 13.7386i | −0.445505 | + | 0.771637i | −0.998087 | − | 0.0618213i | \(-0.980309\pi\) |
0.552582 | + | 0.833458i | \(0.313642\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.932677 | + | 1.61544i | 0.0522199 | + | 0.0904475i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.75890 | − | 6.01179i | −0.377245 | − | 0.335546i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −41.7156 | −2.32112 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.76509 | 0.208850 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.7756 | − | 10.4740i | −0.651193 | − | 0.579212i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.54944 | + | 9.61192i | 0.305951 | + | 0.529922i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.04944 | − | 15.6741i | 0.497402 | − | 0.861526i | −0.502593 | − | 0.864523i | \(-0.667621\pi\) |
0.999996 | + | 0.00299694i | \(0.000953957\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.466579 | − | 3.97408i | −0.0255684 | − | 0.217778i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.27747 | − | 3.94470i | 0.124432 | − | 0.215522i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.518570 | + | 0.898189i | 0.0282483 | + | 0.0489275i | 0.879804 | − | 0.475337i | \(-0.157674\pi\) |
−0.851556 | + | 0.524264i | \(0.824340\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.34479 | + | 21.0693i | −0.235977 | + | 1.14433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.25829 | 0.0681402 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.28504 | − | 2.41608i | 0.392213 | − | 0.130077i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.9821 | + | 19.0216i | 0.589551 | + | 1.02113i | 0.994291 | + | 0.106701i | \(0.0340286\pi\) |
−0.404740 | + | 0.914432i | \(0.632638\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.7651 | + | 20.3777i | −0.629771 | + | 1.09080i | 0.357827 | + | 0.933788i | \(0.383518\pi\) |
−0.987597 | + | 0.157007i | \(0.949815\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.17673 | − | 0.448873i | −0.276313 | − | 0.0239591i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.7713 | + | 25.5846i | −0.786196 | + | 1.36173i | 0.142086 | + | 0.989854i | \(0.454619\pi\) |
−0.928282 | + | 0.371877i | \(0.878714\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.98143 | − | 10.3601i | −0.317461 | − | 0.549859i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.66071 | − | 3.20397i | 0.511299 | − | 0.169572i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 34.0741 | 1.79836 | 0.899182 | − | 0.437575i | \(-0.144163\pi\) | ||||
0.899182 | + | 0.437575i | \(0.144163\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.3942 | 1.65232 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.60005 | + | 12.6085i | −0.136467 | + | 0.661774i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.72184 | − | 2.98231i | −0.0901252 | − | 0.156101i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.5309 | − | 23.4362i | 0.706306 | − | 1.22336i | −0.259912 | − | 0.965632i | \(-0.583694\pi\) |
0.966218 | − | 0.257725i | \(-0.0829730\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.54325 | + | 3.38597i | −0.236512 | + | 0.176266i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.10507 | − | 10.5743i | 0.316960 | − | 0.548990i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.43199 | + | 9.40848i | 0.281258 | + | 0.487153i | 0.971695 | − | 0.236240i | \(-0.0759151\pi\) |
−0.690437 | + | 0.723392i | \(0.742582\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.6058 | + | 11.2124i | 0.650959 | + | 0.579004i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.987620 | −0.0508650 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.765092 | 0.0393001 | 0.0196501 | − | 0.999807i | \(-0.493745\pi\) | ||||
0.0196501 | + | 0.999807i | \(0.493745\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.92147 | + | 8.82478i | 0.508292 | + | 0.452107i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.87704 | − | 8.44729i | −0.249205 | − | 0.431636i | 0.714100 | − | 0.700043i | \(-0.246836\pi\) |
−0.963306 | + | 0.268407i | \(0.913503\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.04944 | + | 1.81769i | −0.0534845 | + | 0.0926379i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 29.9331 | + | 12.8936i | 1.52158 | + | 0.655418i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.3269 | − | 21.3508i | 0.624999 | − | 1.08253i | −0.363542 | − | 0.931578i | \(-0.618433\pi\) |
0.988541 | − | 0.150953i | \(-0.0482341\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.7163 | + | 20.2933i | 0.592521 | + | 1.02628i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.08719 | + | 24.6694i | −0.256615 | + | 1.24441i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.14687 | −0.359598 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.1964 | 0.712496 | 0.356248 | − | 0.934391i | \(-0.384056\pi\) | ||||
0.356248 | + | 0.934391i | \(0.384056\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.6705 | + | 3.87053i | −0.584258 | + | 0.193769i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.4746 | − | 33.7309i | −0.972513 | − | 1.68444i | −0.687910 | − | 0.725796i | \(-0.741472\pi\) |
−0.284603 | − | 0.958646i | \(-0.591862\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.333104 | + | 0.576953i | −0.0165931 | + | 0.0287401i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.87085 | − | 7.26766i | −0.341416 | − | 0.361133i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.25959 | + | 2.18168i | −0.0624356 | + | 0.108142i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.09888 | + | 7.09948i | 0.202677 | + | 0.351047i | 0.949390 | − | 0.314100i | \(-0.101703\pi\) |
−0.746713 | + | 0.665146i | \(0.768369\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.63052 | + | 2.53066i | −0.376386 | + | 0.124828i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.76509 | 0.234475 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.1978 | 0.647853 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.75024 | + | 32.7340i | −0.330561 | + | 1.60299i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.228718 | + | 0.396151i | 0.0111736 | + | 0.0193533i | 0.871558 | − | 0.490292i | \(-0.163110\pi\) |
−0.860385 | + | 0.509645i | \(0.829777\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.31453 | − | 16.1332i | 0.453963 | − | 0.786286i | −0.544665 | − | 0.838654i | \(-0.683343\pi\) |
0.998628 | + | 0.0523672i | \(0.0166766\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 30.5803 | + | 13.1724i | 1.48687 | + | 0.640463i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.0625 | + | 19.1608i | −0.536611 | + | 0.929437i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.88255 | − | 3.26067i | −0.0911028 | − | 0.157795i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.44437 | + | 2.17417i | 0.118015 | + | 0.104970i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.5178 | 0.506625 | 0.253312 | − | 0.967385i | \(-0.418480\pi\) | ||||
0.253312 | + | 0.967385i | \(0.418480\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.80223 | −0.134667 | −0.0673333 | − | 0.997731i | \(-0.521449\pi\) | ||||
−0.0673333 | + | 0.997731i | \(0.521449\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.42037 | − | 1.26337i | −0.0681017 | − | 0.0605739i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.1538 | − | 24.5151i | −0.677069 | − | 1.17272i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.14764 | + | 3.71982i | −0.102501 | + | 0.177537i | −0.912715 | − | 0.408598i | \(-0.866018\pi\) |
0.810213 | + | 0.586135i | \(0.199351\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.40545 | − | 1.79272i | 0.114545 | − | 0.0853674i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.0989 | + | 19.2238i | −0.527324 | + | 0.913352i | 0.472169 | + | 0.881508i | \(0.343471\pi\) |
−0.999493 | + | 0.0318437i | \(0.989862\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.95056 | + | 13.7708i | 0.376893 | + | 0.652797i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.77197 | + | 23.1408i | −0.225706 | + | 1.09452i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.4313 | 0.633862 | 0.316931 | − | 0.948449i | \(-0.397348\pi\) | ||||
0.316931 | + | 0.948449i | \(0.397348\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.56732 | 0.167979 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −27.8869 | + | 9.24868i | −1.31024 | + | 0.434541i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.555632 | − | 0.962383i | −0.0260484 | − | 0.0451172i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.45056 | + | 12.9047i | −0.348522 | + | 0.603658i | −0.985987 | − | 0.166821i | \(-0.946650\pi\) |
0.637465 | + | 0.770479i | \(0.279983\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.4945 | − | 25.0259i | 0.816573 | − | 1.16811i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.39561 | + | 5.88138i | −0.158150 | + | 0.273923i | −0.934201 | − | 0.356746i | \(-0.883886\pi\) |
0.776052 | + | 0.630669i | \(0.217219\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.21634 | − | 3.83881i | −0.103002 | − | 0.178405i | 0.809918 | − | 0.586543i | \(-0.199511\pi\) |
−0.912920 | + | 0.408138i | \(0.866178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.21710 | + | 0.403652i | −0.0564418 | + | 0.0187189i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.4189 | −1.22252 | −0.611261 | − | 0.791429i | \(-0.709337\pi\) | ||||
−0.611261 | + | 0.791429i | \(0.709337\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.09888 | 0.189269 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.91597 | − | 38.3870i | 0.364748 | − | 1.76878i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.2596 | − | 17.7701i | −0.471736 | − | 0.817072i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.3640 | − | 23.1471i | 0.613181 | − | 1.06206i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.27128 | − | 36.3806i | −0.195569 | − | 1.66575i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.75959 | − | 4.77975i | 0.126089 | − | 0.218392i | −0.796069 | − | 0.605206i | \(-0.793091\pi\) |
0.922158 | + | 0.386813i | \(0.126424\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.666896 | − | 1.15510i | −0.0304079 | − | 0.0526679i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.16071 | + | 4.59026i | 0.234820 | + | 0.208864i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.850219 | −0.0386065 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −40.4930 | −1.83492 | −0.917458 | − | 0.397834i | \(-0.869762\pi\) | ||||
−0.917458 | + | 0.397834i | \(0.869762\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.4233 | − | 20.8341i | −1.05924 | − | 0.942151i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.555632 | − | 0.962383i | −0.0250753 | − | 0.0434317i | 0.853215 | − | 0.521559i | \(-0.174649\pi\) |
−0.878291 | + | 0.478127i | \(0.841316\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.90180 | − | 5.02607i | 0.130691 | − | 0.226363i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.734219 | + | 6.25370i | 0.0330007 | + | 0.281083i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.38255 | − | 9.32284i | 0.241440 | − | 0.418187i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.33379 | − | 2.31020i | −0.0597088 | − | 0.103419i | 0.834626 | − | 0.550817i | \(-0.185684\pi\) |
−0.894335 | + | 0.447399i | \(0.852351\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.02468 | + | 29.2156i | −0.269163 | + | 1.30526i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.86398 | 0.439813 | 0.219906 | − | 0.975521i | \(-0.429425\pi\) | ||||
0.219906 | + | 0.975521i | \(0.429425\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.86398 | −0.438941 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.7280 | − | 6.54277i | 0.876149 | − | 0.290575i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.99381 | − | 8.64953i | −0.221347 | − | 0.383384i | 0.733870 | − | 0.679289i | \(-0.237712\pi\) |
−0.955217 | + | 0.295906i | \(0.904379\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.54944 | − | 2.68371i | 0.0685433 | − | 0.118720i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −21.1341 | + | 30.2323i | −0.933093 | + | 1.33479i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.53569 | + | 9.58809i | −0.243931 | + | 0.422502i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.4814 | − | 18.1544i | −0.460973 | − | 0.798428i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.42037 | − | 0.471067i | 0.0623475 | − | 0.0206775i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.7527 | 1.69779 | 0.848894 | − | 0.528564i | \(-0.177269\pi\) | ||||
0.848894 | + | 0.528564i | \(0.177269\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.6304 | −0.858379 | −0.429190 | − | 0.903214i | \(-0.641201\pi\) | ||||
−0.429190 | + | 0.903214i | \(0.641201\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.31708 | + | 6.38694i | −0.0574822 | + | 0.278749i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.95744 | − | 3.39038i | −0.0852673 | − | 0.147687i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.54944 | − | 6.14781i | 0.154324 | − | 0.267296i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.4622 | − | 8.54245i | 0.497416 | − | 0.370711i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.944368 | + | 1.63569i | −0.0409051 | + | 0.0708497i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.90180 | − | 5.02607i | −0.125456 | − | 0.217296i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.05494 | − | 5.38565i | −0.261290 | − | 0.232408i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.88874 | −0.0813536 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.332415 | −0.0142916 | −0.00714582 | − | 0.999974i | \(-0.502275\pi\) | ||||
−0.00714582 | + | 0.999974i | \(0.502275\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.8251 | − | 19.4126i | −0.936603 | − | 0.833073i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.05563 | − | 8.75661i | −0.216559 | − | 0.375092i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.6476 | − | 23.6384i | 0.583531 | − | 1.01071i | −0.411526 | − | 0.911398i | \(-0.635004\pi\) |
0.995057 | − | 0.0993071i | \(-0.0316626\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.3738 | − | 4.46849i | −0.442743 | − | 0.190710i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.50550 | + | 6.07171i | −0.149339 | + | 0.258663i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.21565 | − | 5.56967i | −0.136743 | − | 0.236846i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.518493 | − | 2.51433i | 0.0220088 | − | 0.106728i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.4079 | −1.33080 | −0.665398 | − | 0.746489i | \(-0.731738\pi\) | ||||
−0.665398 | + | 0.746489i | \(0.731738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.8640 | 0.459497 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.2465 | + | 6.05146i | −0.770369 | + | 0.255493i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.8331 | − | 20.4955i | −0.498706 | − | 0.863784i | 0.501293 | − | 0.865278i | \(-0.332858\pi\) |
−0.999999 | + | 0.00149369i | \(0.999525\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.90112 | + | 11.9531i | −0.290332 | + | 0.502870i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.57234 | − | 8.62456i | 0.108028 | − | 0.362198i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.36398 | − | 4.09453i | 0.0991030 | − | 0.171652i | −0.812211 | − | 0.583364i | \(-0.801736\pi\) |
0.911314 | + | 0.411713i | \(0.135069\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.38255 | − | 11.0549i | −0.267101 | − | 0.462633i | 0.701011 | − | 0.713151i | \(-0.252732\pi\) |
−0.968112 | + | 0.250518i | \(0.919399\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 28.0494 | − | 9.30259i | 1.17178 | − | 0.388621i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.0138 | −0.626117 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.6304 | −0.442551 | −0.221276 | − | 0.975211i | \(-0.571022\pi\) | ||||
−0.221276 | + | 0.975211i | \(0.571022\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.60005 | − | 12.6085i | 0.108055 | − | 0.523991i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.93818 | + | 10.2852i | 0.246357 | + | 0.426703i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.5309 | + | 19.9721i | −0.477560 | + | 0.827158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.06182 | − | 1.31887i | −0.126591 | − | 0.0545286i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.80834 | + | 3.13214i | −0.0746384 | + | 0.129277i | −0.900929 | − | 0.433967i | \(-0.857114\pi\) |
0.826291 | + | 0.563244i | \(0.190447\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.36467 | + | 4.09572i | 0.0974343 | + | 0.168761i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −34.0309 | − | 30.2692i | −1.39984 | − | 1.24511i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.6786 | 0.931298 | 0.465649 | − | 0.884970i | \(-0.345821\pi\) | ||||
0.465649 | + | 0.884970i | \(0.345821\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.53018 | 0.267711 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.5018 | + | 12.0093i | 0.552591 | + | 0.491509i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.2953 | + | 35.1524i | 0.829242 | + | 1.43629i | 0.898633 | + | 0.438701i | \(0.144561\pi\) |
−0.0693908 | + | 0.997590i | \(0.522106\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.59957 | + | 11.4308i | −0.269202 | + | 0.466272i | −0.968656 | − | 0.248406i | \(-0.920093\pi\) |
0.699454 | + | 0.714678i | \(0.253427\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.85965 | − | 7.34813i | 0.401516 | − | 0.299239i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.12983 | + | 7.15308i | −0.167902 | + | 0.290814i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.833792 | + | 1.44417i | 0.0338426 | + | 0.0586171i | 0.882451 | − | 0.470405i | \(-0.155892\pi\) |
−0.848608 | + | 0.529022i | \(0.822559\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.345483 | − | 1.67536i | 0.0139997 | − | 0.0678889i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.0989 | 0.449013 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.9257 | 0.925961 | 0.462981 | − | 0.886368i | \(-0.346780\pi\) | ||||
0.462981 | + | 0.886368i | \(0.346780\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.45056 | + | 1.14438i | −0.139140 | + | 0.0461457i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.37567 | + | 9.31093i | 0.216416 | + | 0.374844i | 0.953710 | − | 0.300729i | \(-0.0972298\pi\) |
−0.737294 | + | 0.675573i | \(0.763897\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.9814 | + | 22.4845i | −0.521768 | + | 0.903728i | 0.477912 | + | 0.878408i | \(0.341394\pi\) |
−0.999679 | + | 0.0253203i | \(0.991939\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.6428 | + | 1.78994i | 0.828368 | + | 0.0718277i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.15452 | + | 12.3920i | −0.286640 | + | 0.496474i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.00069 | − | 6.92940i | −0.160028 | − | 0.277176i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 22.0426 | − | 7.31041i | 0.880295 | − | 0.291950i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.83784 | 0.312515 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.00138 | 0.119483 | 0.0597415 | − | 0.998214i | \(-0.480972\pi\) | ||||
0.0597415 | + | 0.998214i | \(0.480972\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.88372 | − | 43.0799i | 0.353096 | − | 1.71227i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.25959 | + | 7.37783i | 0.169037 | + | 0.292780i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.500000 | − | 0.866025i | 0.0198107 | − | 0.0343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.76578 | − | 32.0750i | −0.148972 | − | 1.26887i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.77266 | + | 11.7306i | −0.267504 | + | 0.463330i | −0.968217 | − | 0.250113i | \(-0.919532\pi\) |
0.700713 | + | 0.713444i | \(0.252866\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.4814 | − | 30.2787i | −0.689400 | − | 1.19408i | −0.972032 | − | 0.234848i | \(-0.924541\pi\) |
0.282632 | − | 0.959228i | \(-0.408793\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.6243 | + | 13.8973i | 0.615207 | + | 0.547204i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.9890 | 1.02173 | 0.510866 | − | 0.859660i | \(-0.329325\pi\) | ||||
0.510866 | + | 0.859660i | \(0.329325\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | −0.353281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.862194 | − | 0.766889i | −0.0337920 | − | 0.0300568i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.93818 | + | 5.08907i | 0.114980 | + | 0.199151i | 0.917772 | − | 0.397108i | \(-0.129986\pi\) |
−0.802792 | + | 0.596259i | \(0.796653\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.08031 | + | 13.9955i | −0.315724 | + | 0.546850i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.08403 | − | 9.23324i | −0.0422922 | − | 0.360223i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.6359 | − | 35.7425i | 0.803862 | − | 1.39233i | −0.113194 | − | 0.993573i | \(-0.536108\pi\) |
0.917056 | − | 0.398758i | \(-0.130559\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.4814 | + | 32.0108i | 0.718844 | + | 1.24507i | 0.961458 | + | 0.274952i | \(0.0886619\pi\) |
−0.242614 | + | 0.970123i | \(0.578005\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.05563 | − | 9.96840i | 0.0798341 | − | 0.387141i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.88874 | −0.305912 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.93825 | 0.152490 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.8876 | + | 7.92231i | −0.923547 | + | 0.306294i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.55563 | + | 6.15854i | 0.137264 | + | 0.237748i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.6971 | + | 39.3125i | −0.874908 | + | 1.51539i | −0.0180476 | + | 0.999837i | \(0.505745\pi\) |
−0.856861 | + | 0.515548i | \(0.827588\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.28180 | + | 17.7246i | 0.318767 | + | 0.682220i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.14764 | + | 1.98777i | −0.0441073 | + | 0.0763961i | −0.887236 | − | 0.461315i | \(-0.847378\pi\) |
0.843129 | + | 0.537711i | \(0.180711\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.382546 | − | 0.662589i | −0.0146808 | − | 0.0254278i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −31.9065 | + | 10.5818i | −1.22266 | + | 0.405495i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.1483 | 1.23012 | 0.615059 | − | 0.788481i | \(-0.289132\pi\) | ||||
0.615059 | + | 0.788481i | \(0.289132\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.15787 | −0.197072 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.68361 | + | 17.8630i | −0.140538 | + | 0.681514i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.10507 | − | 10.5743i | −0.232585 | − | 0.402849i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.40180 | − | 5.89210i | 0.129411 | − | 0.224146i | −0.794038 | − | 0.607869i | \(-0.792025\pi\) |
0.923448 | + | 0.383723i | \(0.125358\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.54325 | + | 3.38597i | −0.172584 | + | 0.128622i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.7218 | + | 18.5708i | −0.406703 | + | 0.704429i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.54944 | − | 9.61192i | −0.210200 | − | 0.364077i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.3022 | + | 26.0632i | 1.10831 | + | 0.985800i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.5933 | 1.60873 | 0.804363 | − | 0.594137i | \(-0.202507\pi\) | ||||
0.804363 | + | 0.594137i | \(0.202507\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.46844 | −0.357109 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.9622 | + | 14.1978i | 0.601170 | + | 0.534719i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.43818 | − | 7.68715i | −0.166915 | − | 0.289105i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.56732 | − | 4.44673i | 0.0964178 | − | 0.167001i | −0.813782 | − | 0.581171i | \(-0.802595\pi\) |
0.910199 | + | 0.414170i | \(0.135928\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.7199 | − | 7.63279i | −0.664548 | − | 0.286252i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.32829 | − | 2.30067i | 0.0497449 | − | 0.0861607i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.04944 | + | 1.81769i | 0.0392469 | + | 0.0679776i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.74041 | − | 8.43979i | 0.0649968 | − | 0.315190i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.6057 | 0.880344 | 0.440172 | − | 0.897914i | \(-0.354918\pi\) | ||||
0.440172 | + | 0.897914i | \(0.354918\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.96286 | −0.371036 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.386188 | + | 0.128079i | −0.0143625 | + | 0.00476332i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.85924 | + | 3.22030i | 0.0690505 | + | 0.119599i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.000688709 | 0.00119288i | −2.55428e−5 | 4.42414e-5i | −0.866038 | − | 0.499978i | \(-0.833341\pi\) | ||
0.866013 | + | 0.500022i | \(0.166675\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.27375 | − | 25.3574i | −0.343472 | − | 0.939163i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.9203 | + | 55.2876i | −1.18061 | + | 2.04488i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.6978 | + | 18.5291i | 0.395131 | + | 0.684387i | 0.993118 | − | 0.117119i | \(-0.0373658\pi\) |
−0.597987 | + | 0.801506i | \(0.704032\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.82691 | − | 0.605896i | 0.0673867 | − | 0.0223488i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.74171 | −0.285170 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.0232 | −1.17799 | −0.588997 | − | 0.808135i | \(-0.700477\pi\) | ||||
−0.588997 | + | 0.808135i | \(0.700477\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.48329 | + | 12.0422i | −0.0912259 | + | 0.442383i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.2596 | + | 43.7509i | 0.926685 | + | 1.60506i | 0.788829 | + | 0.614612i | \(0.210688\pi\) |
0.137855 | + | 0.990452i | \(0.455979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.57963 | + | 13.1283i | −0.277696 | + | 0.480984i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 32.7225 | + | 14.0951i | 1.19725 | + | 0.515713i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.61126 | − | 4.52284i | 0.0954135 | − | 0.165261i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.3145 | − | 35.1858i | −0.741288 | − | 1.28395i | −0.951909 | − | 0.306381i | \(-0.900882\pi\) |
0.210621 | − | 0.977568i | \(-0.432451\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.4814 | − | 9.32284i | −0.381965 | − | 0.339743i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.8502 | −0.686030 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.90112 | −0.287171 | −0.143585 | − | 0.989638i | \(-0.545863\pi\) | ||||
−0.143585 | + | 0.989638i | \(0.545863\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.74721 | − | 8.66978i | −0.353801 | − | 0.314693i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.0124 | − | 19.0740i | −0.399198 | − | 0.691432i | 0.594429 | − | 0.804148i | \(-0.297378\pi\) |
−0.993627 | + | 0.112716i | \(0.964045\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.54944 | − | 7.87987i | 0.164701 | − | 0.285270i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.7080 | − | 11.7068i | 0.567924 | − | 0.423259i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.38255 | − | 4.12669i | 0.0860287 | − | 0.149006i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.4127 | + | 42.2841i | 0.880346 | + | 1.52480i | 0.850957 | + | 0.525235i | \(0.176023\pi\) |
0.0293884 | + | 0.999568i | \(0.490644\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.30903 | − | 40.2931i | 0.299243 | − | 1.45112i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.4807 | 1.24018 | 0.620092 | − | 0.784529i | \(-0.287095\pi\) | ||||
0.620092 | + | 0.784529i | \(0.287095\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.50833 | 0.0901020 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.19275 | − | 0.727225i | 0.0786645 | − | 0.0260891i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.70396 | + | 11.6116i | 0.240194 | + | 0.416029i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.1662 | + | 17.6084i | −0.363776 | + | 0.630078i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.17240 | − | 4.64934i | −0.0776351 | − | 0.166154i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.5734 | − | 21.7778i | 0.448765 | − | 0.777284i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.86329 | − | 10.1555i | −0.209004 | − | 0.362005i | 0.742397 | − | 0.669960i | \(-0.233689\pi\) |
−0.951401 | + | 0.307955i | \(0.900355\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.9389 | − | 3.62787i | 0.389434 | − | 0.129156i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.4203 | −0.441615 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.76509 | −0.133702 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.74652 | − | 23.0174i | 0.168342 | − | 0.816342i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.1236 | + | 45.2473i | 0.925344 | + | 1.60274i | 0.791007 | + | 0.611808i | \(0.209557\pi\) |
0.134338 | + | 0.990936i | \(0.457109\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.6105 | + | 56.4830i | −1.15368 | + | 1.99823i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.00550 | + | 42.6343i | 0.176861 | + | 1.50641i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.92649 | + | 5.06882i | −0.103273 | + | 0.178875i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.21565 | + | 3.83762i | 0.0780914 | + | 0.135258i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.5734 | + | 21.8572i | 0.865026 | + | 0.769408i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.5439 | −1.07387 | −0.536934 | − | 0.843624i | \(-0.680418\pi\) | ||||
−0.536934 | + | 0.843624i | \(0.680418\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.9629 | −0.981909 | −0.490954 | − | 0.871185i | \(-0.663352\pi\) | ||||
−0.490954 | + | 0.871185i | \(0.663352\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.9040 | − | 25.7090i | −1.01371 | − | 0.901655i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.0563 | − | 17.4181i | −0.352258 | − | 0.610128i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.5611 | − | 66.7897i | 1.34908 | − | 2.33668i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.349814 | − | 2.97954i | −0.0122235 | − | 0.104113i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.78435 | − | 6.55469i | 0.132075 | − | 0.228760i | −0.792401 | − | 0.610000i | \(-0.791169\pi\) |
0.924476 | + | 0.381240i | \(0.124503\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.1978 | + | 31.5195i | 0.634334 | + | 1.09870i | 0.986656 | + | 0.162820i | \(0.0520591\pi\) |
−0.352321 | + | 0.935879i | \(0.614608\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.48762 | − | 12.0632i | 0.0866078 | − | 0.419988i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.36955 | −0.0823975 | −0.0411987 | − | 0.999151i | \(-0.513118\pi\) | ||||
−0.0411987 | + | 0.999151i | \(0.513118\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.2335 | −0.772202 | −0.386101 | − | 0.922456i | \(-0.626178\pi\) | ||||
−0.386101 | + | 0.922456i | \(0.626178\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 52.3232 | − | 17.3530i | 1.81507 | − | 0.601968i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.93818 | + | 5.08907i | 0.101802 | + | 0.176326i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.56939 | + | 16.5747i | −0.331162 | + | 0.573590i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.44878 | − | 0.299043i | −0.119207 | − | 0.0103364i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.05494 | − | 10.4875i | 0.209040 | − | 0.362068i | −0.742372 | − | 0.669987i | \(-0.766299\pi\) |
0.951412 | + | 0.307920i | \(0.0996328\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0123 | + | 24.2700i | 0.483183 | + | 0.836897i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.6359 | + | 10.8237i | −1.12404 | + | 0.372788i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.3352 | 0.458744 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.43268 | −0.255390 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.09703 | + | 5.31982i | −0.0376498 | + | 0.182576i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.65933 | + | 4.60609i | 0.0911606 | + | 0.157895i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.5494 | − | 28.6645i | 0.566642 | − | 0.981453i | −0.430253 | − | 0.902708i | \(-0.641576\pi\) |
0.996895 | − | 0.0787444i | \(-0.0250911\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.9759 | + | 14.1423i | −0.648963 | + | 0.483655i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.77128 | + | 15.1923i | −0.299621 | + | 0.518959i | −0.976049 | − | 0.217549i | \(-0.930194\pi\) |
0.676428 | + | 0.736509i | \(0.263527\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.93130 | − | 12.0054i | −0.236493 | − | 0.409618i | 0.723213 | − | 0.690625i | \(-0.242665\pi\) |
−0.959705 | + | 0.281008i | \(0.909331\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.44437 | − | 2.17417i | −0.0833038 | − | 0.0740957i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.9890 | −0.374070 | −0.187035 | − | 0.982353i | \(-0.559888\pi\) | ||||
−0.187035 | + | 0.982353i | \(0.559888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.960106 | 0.0326446 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.6890 | + | 20.1811i | 0.770560 | + | 0.685384i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.07351 | + | 10.5196i | 0.206030 | + | 0.356854i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.04944 | − | 3.54974i | 0.0694427 | − | 0.120278i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.10803 | − | 0.908026i | −0.0713459 | − | 0.0307320i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.87017 | + | 8.43538i | −0.164642 | + | 0.285168i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.2472 | − | 21.2128i | −0.413559 | − | 0.716305i | 0.581717 | − | 0.813391i | \(-0.302381\pi\) |
−0.995276 | + | 0.0970861i | \(0.969048\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.45537 | − | 16.7562i | 0.116547 | − | 0.565172i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.9243 | −0.671268 | −0.335634 | − | 0.941992i | \(-0.608951\pi\) | ||||
−0.335634 | + | 0.941992i | \(0.608951\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.5316 | 1.33034 | 0.665171 | − | 0.746691i | \(-0.268358\pi\) | ||||
0.665171 | + | 0.746691i | \(0.268358\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.70541 | − | 2.88715i | 0.292629 | − | 0.0970505i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.5378 | + | 35.5724i | 0.689590 | + | 1.19441i | 0.971971 | + | 0.235103i | \(0.0755427\pi\) |
−0.282380 | + | 0.959303i | \(0.591124\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.83310 | + | 6.63913i | −0.128558 | + | 0.222669i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.85848 | + | 16.2895i | −0.162765 | + | 0.545719i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39.3948 | − | 68.2339i | 1.31830 | − | 2.28336i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.59957 | − | 4.50259i | −0.0868941 | − | 0.150505i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.55563 | − | 2.17417i | 0.218886 | − | 0.0725936i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.657960 | −0.0219442 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 71.7512 | 2.39038 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.80037 | + | 18.4292i | −0.126468 | + | 0.613285i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.37017 | − | 16.2296i | −0.311475 | − | 0.539490i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.83242 | − | 10.1020i | 0.193662 | − | 0.335433i | −0.752799 | − | 0.658250i | \(-0.771297\pi\) |
0.946461 | + | 0.322818i | \(0.104630\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.4567 | − | 10.5346i | −0.811177 | − | 0.349412i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.8028 | − | 36.0316i | 0.689229 | − | 1.19378i | −0.282859 | − | 0.959162i | \(-0.591283\pi\) |
0.972088 | − | 0.234618i | \(-0.0753839\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.2156 | − | 19.4261i | −0.371184 | − | 0.642909i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.41487 | − | 4.81633i | −0.179010 | − | 0.159223i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.5426 | −0.480238 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.3338 | −0.934646 | −0.467323 | − | 0.884087i | \(-0.654781\pi\) | ||||
−0.467323 | + | 0.884087i | \(0.654781\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.9709 | + | 17.7634i | 0.658064 | + | 0.585323i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.38255 | − | 9.32284i | −0.177169 | − | 0.306865i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.51093 | + | 4.34905i | −0.0825587 | + | 0.142996i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.9651 | + | 17.8606i | −0.787118 | + | 0.586618i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.9127 | + | 25.8296i | −0.489271 | + | 0.847442i | −0.999924 | − | 0.0123450i | \(-0.996070\pi\) |
0.510653 | + | 0.859787i | \(0.329404\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.54944 | − | 6.14781i | −0.116328 | − | 0.201486i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.17989 | − | 29.9682i | 0.202320 | − | 0.981115i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.3338 | −0.403358 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.56870 | −0.0839158 | −0.0419579 | − | 0.999119i | \(-0.513360\pi\) | ||||
−0.0419579 | + | 0.999119i | \(0.513360\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.0833 | + | 7.32391i | −0.720660 | + | 0.239007i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.33448 | − | 4.04344i | −0.0761019 | − | 0.131812i | 0.825463 | − | 0.564456i | \(-0.190914\pi\) |
−0.901565 | + | 0.432644i | \(0.857581\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.76578 | − | 6.52252i | 0.122631 | − | 0.212403i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.30834 | − | 4.73259i | 0.107620 | − | 0.153951i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.8454 | + | 27.4450i | −0.514907 | + | 0.891844i | 0.484944 | + | 0.874545i | \(0.338840\pi\) |
−0.999850 | + | 0.0172990i | \(0.994493\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.54944 | − | 2.68371i | −0.0502970 | − | 0.0871170i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.0803 | + | 8.64953i | −0.845712 | + | 0.280480i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.0604 | 0.423067 | 0.211533 | − | 0.977371i | \(-0.432154\pi\) | ||||
0.211533 | + | 0.977371i | \(0.432154\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.9601 | 0.613535 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.652527 | + | 3.16431i | −0.0210932 | + | 0.102288i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.32072 | − | 4.01961i | −0.0749401 | − | 0.129800i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.2781 | − | 26.4624i | 0.492841 | − | 0.853626i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.82691 | − | 15.5607i | −0.0588715 | − | 0.501437i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.12983 | − | 7.15308i | 0.132944 | − | 0.230266i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.48074 | + | 7.76087i | 0.144091 | + | 0.249573i | 0.929033 | − | 0.369996i | \(-0.120641\pi\) |
−0.784942 | + | 0.619569i | \(0.787308\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −53.9875 | − | 48.0199i | −1.73433 | − | 1.54262i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.543941 | 0.0174559 | 0.00872795 | − | 0.999962i | \(-0.497222\pi\) | ||||
0.00872795 | + | 0.999962i | \(0.497222\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.2967 | −0.618622 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.87271 | + | 4.33410i | 0.156052 | + | 0.138802i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.2280 | − | 31.5717i | −0.583164 | − | 1.01007i | −0.995102 | − | 0.0988575i | \(-0.968481\pi\) |
0.411938 | − | 0.911212i | \(-0.364852\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.5130 | − | 23.4052i | 0.431877 | − | 0.748033i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.18292 | − | 27.1104i | −0.101623 | − | 0.865570i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.1916 | − | 31.5087i | 0.580221 | − | 1.00497i | −0.415231 | − | 0.909716i | \(-0.636299\pi\) |
0.995453 | − | 0.0952569i | \(-0.0303673\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.6105 | − | 25.3061i | −0.465529 | − | 0.806320i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.88255 | + | 18.8277i | −0.123583 | + | 0.599292i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −43.3214 | −1.37754 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.9642 | −1.01538 | −0.507689 | − | 0.861541i | \(-0.669500\pi\) | ||||
−0.507689 | + | 0.861541i | \(0.669500\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.7545 | − | 9.86807i | 0.944230 | − | 0.313154i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.79673 | + | 10.0402i | 0.183769 | + | 0.318297i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.0000 | + | 22.5167i | −0.411714 | + | 0.713110i | −0.995077 | − | 0.0991016i | \(-0.968403\pi\) |
0.583363 | + | 0.812211i | \(0.301736\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.97083 | − | 5.68028i | 0.125632 | − | 0.179716i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))