Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (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: | \(8.04892052375\) |
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: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 673.1 | ||
Root | \(0.500000 - 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.673 |
Dual form | 1008.2.r.g.337.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −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 | −0.972546 | − | 0.232713i | \(-0.925240\pi\) |
0.687808 | + | 0.725893i | \(0.258573\pi\) | |||||||
\(12\) | 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 | \(-0.802878\pi\) | ||||
−0.814298 | + | 0.580447i | \(0.802878\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.64400 | + | 0.545231i | −0.358749 | + | 0.118979i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.99381 | + | 3.45338i | 0.415738 | + | 0.720080i | 0.995506 | − | 0.0947024i | \(-0.0301899\pi\) |
−0.579767 | + | 0.814782i | \(0.696857\pi\) | |||||||
\(24\) | 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 | 0.834561 | − | 0.550916i | \(-0.185722\pi\) |
−0.894388 | + | 0.447292i | \(0.852388\pi\) | |||||||
\(32\) | 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 | \(0.477398\pi\) |
−0.899316 | + | 0.437299i | \(0.855935\pi\) | |||||||
\(44\) | 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 | \(0.466912\pi\) |
−0.913232 | + | 0.407440i | \(0.866422\pi\) | |||||||
\(48\) | 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 | 0.978401 | − | 0.206714i | \(-0.0662770\pi\) |
−0.668220 | + | 0.743963i | \(0.732944\pi\) | |||||||
\(60\) | 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 | 0.963630 | − | 0.267239i | \(-0.0861114\pi\) |
−0.713251 | + | 0.700909i | \(0.752778\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.39493 | − | 6.76443i | 0.167929 | − | 0.814342i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7651 | 1.27758 | 0.638791 | − | 0.769381i | \(-0.279435\pi\) | ||||
0.638791 | + | 0.769381i | \(0.279435\pi\) | |||||||
\(72\) | 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 | −0.626466 | − | 0.779448i | \(-0.715499\pi\) |
0.988255 | + | 0.152812i | \(0.0488328\pi\) | |||||||
\(80\) | 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 | \(0.392652\pi\) |
−0.982686 | + | 0.185280i | \(0.940681\pi\) | |||||||
\(84\) | 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 | 0.509109 | − | 0.860702i | \(-0.329975\pi\) |
−0.999944 | + | 0.0105508i | \(0.996642\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.43818 | − | 1.27921i | −0.140352 | − | 0.124838i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.22253 | 0.504881 | 0.252440 | − | 0.967612i | \(-0.418767\pi\) | ||||
0.252440 | + | 0.967612i | \(0.418767\pi\) | |||||||
\(108\) | 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 | \(-0.610472\pi\) | ||||
−0.340133 | + | 0.940377i | \(0.610472\pi\) | |||||||
\(128\) | 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 | \(-0.947545\pi\) |
0.351158 | − | 0.936316i | \(-0.385788\pi\) | |||||||
\(132\) | 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 | \(-0.861550\pi\) |
0.0885293 | − | 0.996074i | \(-0.471783\pi\) | |||||||
\(140\) | 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 | \(-0.590852\pi\) |
0.971769 | − | 0.235934i | \(-0.0758148\pi\) | |||||||
\(152\) | 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 | \(-0.249234\pi\) | ||||
0.708807 | + | 0.705402i | \(0.249234\pi\) | |||||||
\(164\) | 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 | \(-0.934518\pi\) |
0.312555 | − | 0.949900i | \(-0.398815\pi\) | |||||||
\(168\) | 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 | \(-0.444057\pi\) | ||||
0.174847 | + | 0.984596i | \(0.444057\pi\) | |||||||
\(180\) | 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 | \(0.378429\pi\) |
−0.989981 | + | 0.141199i | \(0.954904\pi\) | |||||||
\(192\) | 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 | \(-0.620566\pi\) | ||||
−0.369776 | + | 0.929121i | \(0.620566\pi\) | |||||||
\(200\) | 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 | \(0.171914\pi\) |
0.0164855 | + | 0.999864i | \(0.494752\pi\) | |||||||
\(212\) | 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 | −0.513373 | − | 0.858165i | \(-0.671604\pi\) |
0.999880 | + | 0.0155114i | \(0.00493764\pi\) | |||||||
\(224\) | 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 | \(-0.610576\pi\) |
0.984514 | − | 0.175303i | \(-0.0560906\pi\) | |||||||
\(228\) | 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 | 0.935196 | − | 0.354132i | \(-0.115224\pi\) |
−0.774285 | + | 0.632837i | \(0.781890\pi\) | |||||||
\(240\) | 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 | \(-0.417727\pi\) | ||||
0.255599 | + | 0.966783i | \(0.417727\pi\) | |||||||
\(252\) | 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 | −0.950179 | − | 0.311704i | \(-0.899100\pi\) |
0.745033 | + | 0.667028i | \(0.232434\pi\) | |||||||
\(264\) | 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 | \(-0.262699\pi\) | ||||
0.678341 | + | 0.734748i | \(0.262699\pi\) | |||||||
\(272\) | 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 | 0.815651 | − | 0.578544i | \(-0.196379\pi\) |
−0.908860 | + | 0.417102i | \(0.863046\pi\) | |||||||
\(284\) | 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 | \(-0.645148\pi\) | ||||
−0.440355 | + | 0.897824i | \(0.645148\pi\) | |||||||
\(308\) | 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 | \(0.000323307\pi\) |
−0.499120 | + | 0.866533i | \(0.666343\pi\) | |||||||
\(312\) | 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 | −0.999996 | − | 0.00299694i | \(-0.999046\pi\) |
0.502593 | + | 0.864523i | \(0.332379\pi\) | |||||||
\(332\) | 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 | \(-0.965971\pi\) |
0.404740 | − | 0.914432i | \(-0.367362\pi\) | |||||||
\(348\) | 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 | \(-0.855837\pi\) | ||||
−0.899182 | + | 0.437575i | \(0.855837\pi\) | |||||||
\(360\) | 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 | \(0.416306\pi\) |
−0.966218 | + | 0.257725i | \(0.917027\pi\) | |||||||
\(368\) | 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 | \(-0.506255\pi\) | ||||
−0.0196501 | + | 0.999807i | \(0.506255\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.92147 | + | 8.82478i | 0.508292 | + | 0.452107i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.87704 | + | 8.44729i | 0.249205 | + | 0.431636i | 0.963306 | − | 0.268407i | \(-0.0864973\pi\) |
−0.714100 | + | 0.700043i | \(0.753164\pi\) | |||||||
\(384\) | 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 | 0.860385 | − | 0.509645i | \(-0.170223\pi\) |
−0.871558 | + | 0.490292i | \(0.836890\pi\) | |||||||
\(420\) | 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 | \(-0.581520\pi\) | ||||
−0.253312 | + | 0.967385i | \(0.581520\pi\) | |||||||
\(432\) | 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 | −0.810213 | − | 0.586135i | \(-0.800649\pi\) |
0.912715 | + | 0.408598i | \(0.133982\pi\) | |||||||
\(440\) | 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 | \(-0.656529\pi\) |
0.999493 | − | 0.0318437i | \(-0.0101379\pi\) | |||||||
\(444\) | 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 | 0.912920 | − | 0.408138i | \(-0.133822\pi\) |
−0.809918 | + | 0.586543i | \(0.800489\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.21710 | + | 0.403652i | −0.0564418 | + | 0.0187189i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.4189 | 1.22252 | 0.611261 | − | 0.791429i | \(-0.290663\pi\) | ||||
0.611261 | + | 0.791429i | \(0.290663\pi\) | |||||||
\(468\) | 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 | −0.922158 | − | 0.386813i | \(-0.873576\pi\) |
0.796069 | + | 0.605206i | \(0.206909\pi\) | |||||||
\(480\) | 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 | \(-0.130238\pi\) | ||||
0.917458 | + | 0.397834i | \(0.130238\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.4233 | − | 20.8341i | −1.05924 | − | 0.942151i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.555632 | + | 0.962383i | 0.0250753 | + | 0.0434317i | 0.878291 | − | 0.478127i | \(-0.158684\pi\) |
−0.853215 | + | 0.521559i | \(0.825351\pi\) | |||||||
\(492\) | 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 | 0.894335 | − | 0.447399i | \(-0.147649\pi\) |
−0.834626 | + | 0.550817i | \(0.814316\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.02468 | + | 29.2156i | −0.269163 | + | 1.30526i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.86398 | −0.439813 | −0.219906 | − | 0.975521i | \(-0.570575\pi\) | ||||
−0.219906 | + | 0.975521i | \(0.570575\pi\) | |||||||
\(504\) | 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 | \(-0.358799\pi\) | ||||
0.429190 | + | 0.903214i | \(0.358799\pi\) | |||||||
\(524\) | 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 | \(0.364996\pi\) |
−0.995057 | + | 0.0993071i | \(0.968337\pi\) | |||||||
\(548\) | 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 | 0.999999 | − | 0.00149369i | \(-0.000475458\pi\) |
−0.501293 | + | 0.865278i | \(0.667142\pi\) | |||||||
\(564\) | 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 | 0.968112 | − | 0.250518i | \(-0.0806009\pi\) |
−0.701011 | + | 0.713151i | \(0.747268\pi\) | |||||||
\(572\) | 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 | −0.826291 | − | 0.563244i | \(-0.809553\pi\) |
0.900929 | + | 0.433967i | \(0.142886\pi\) | |||||||
\(588\) | 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 | \(-0.855439\pi\) |
0.0693908 | − | 0.997590i | \(-0.477894\pi\) | |||||||
\(600\) | 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 | 0.848608 | − | 0.529022i | \(-0.177441\pi\) |
−0.882451 | + | 0.470405i | \(0.844108\pi\) | |||||||
\(608\) | 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 | \(-0.658606\pi\) |
0.999679 | − | 0.0253203i | \(-0.00806057\pi\) | |||||||
\(620\) | 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 | \(-0.519028\pi\) | ||||
−0.0597415 | + | 0.998214i | \(0.519028\pi\) | |||||||
\(632\) | 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 | \(0.0754592\pi\) |
−0.282632 | + | 0.959228i | \(0.591207\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.6243 | + | 13.8973i | 0.615207 | + | 0.547204i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.9890 | −1.02173 | −0.510866 | − | 0.859660i | \(-0.670675\pi\) | ||||
−0.510866 | + | 0.859660i | \(0.670675\pi\) | |||||||
\(648\) | 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 | \(0.463892\pi\) |
−0.917056 | + | 0.398758i | \(0.869441\pi\) | |||||||
\(660\) | 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 | \(-0.710868\pi\) | ||||
−0.615059 | + | 0.788481i | \(0.710868\pi\) | |||||||
\(684\) | 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 | −0.923448 | − | 0.383723i | \(-0.874642\pi\) |
0.794038 | + | 0.607869i | \(0.207975\pi\) | |||||||
\(692\) | 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 | \(-0.645082\pi\) | ||||
−0.440172 | + | 0.897914i | \(0.645082\pi\) | |||||||
\(720\) | 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 | −0.866013 | − | 0.500022i | \(-0.833325\pi\) |
0.866038 | + | 0.499978i | \(0.166659\pi\) | |||||||
\(728\) | 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 | \(-0.299523\pi\) | ||||
0.588997 | + | 0.808135i | \(0.299523\pi\) | |||||||
\(740\) | 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 | \(-0.789312\pi\) |
−0.137855 | − | 0.990452i | \(-0.544021\pi\) | |||||||
\(744\) | 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 | \(0.0991180\pi\) |
−0.210621 | + | 0.977568i | \(0.567549\pi\) | |||||||
\(752\) | 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 | 0.951401 | − | 0.307955i | \(-0.0996446\pi\) |
−0.742397 | + | 0.669960i | \(0.766311\pi\) | |||||||
\(788\) | 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 | \(-0.336648\pi\) | ||||
0.490954 | + | 0.871185i | \(0.336648\pi\) | |||||||
\(812\) | 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 | \(-0.947941\pi\) |
0.352321 | − | 0.935879i | \(-0.385392\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.48762 | − | 12.0632i | 0.0866078 | − | 0.419988i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.36955 | 0.0823975 | 0.0411987 | − | 0.999151i | \(-0.486882\pi\) | ||||
0.0411987 | + | 0.999151i | \(0.486882\pi\) | |||||||
\(828\) | 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 | −0.951412 | − | 0.307920i | \(-0.900367\pi\) |
0.742372 | + | 0.669987i | \(0.233701\pi\) | |||||||
\(840\) | 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 | 0.959705 | − | 0.281008i | \(-0.0906687\pi\) |
−0.723213 | + | 0.690625i | \(0.757335\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.44437 | − | 2.17417i | −0.0833038 | − | 0.0740957i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.9890 | 0.374070 | 0.187035 | − | 0.982353i | \(-0.440112\pi\) | ||||
0.187035 | + | 0.982353i | \(0.440112\pi\) | |||||||
\(864\) | 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 | \(-0.731642\pi\) | ||||
−0.665171 | + | 0.746691i | \(0.731642\pi\) | |||||||
\(884\) | 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 | \(-0.924457\pi\) |
0.282380 | − | 0.959303i | \(-0.408876\pi\) | |||||||
\(888\) | 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 | −0.946461 | − | 0.322818i | \(-0.895370\pi\) |
0.752799 | + | 0.658250i | \(0.228703\pi\) | |||||||
\(908\) | 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 | \(0.408717\pi\) |
−0.972088 | + | 0.234618i | \(0.924616\pi\) | |||||||
\(912\) | 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 | \(-0.345219\pi\) | ||||
0.467323 | + | 0.884087i | \(0.345219\pi\) | |||||||
\(920\) | 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 | \(-0.661160\pi\) |
0.999850 | − | 0.0172990i | \(-0.00550671\pi\) | |||||||
\(948\) | 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 | 0.784942 | − | 0.619569i | \(-0.212692\pi\) |
−0.929033 | + | 0.369996i | \(0.879359\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −53.9875 | − | 48.0199i | −1.73433 | − | 1.54262i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.543941 | −0.0174559 | −0.00872795 | − | 0.999962i | \(-0.502778\pi\) | ||||
−0.00872795 | + | 0.999962i | \(0.502778\pi\) | |||||||
\(972\) | 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 | \(0.363701\pi\) |
−0.995453 | + | 0.0952569i | \(0.969633\pi\) | |||||||
\(984\) | 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 | \(-0.330500\pi\) | ||||
0.507689 | + | 0.861541i | \(0.330500\pi\) | |||||||
\(992\) | 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 \(a_p\))