Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(751,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.751");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.bc (of order \(6\), 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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 751.5 | ||
Root | \(-1.44229 - 0.433312i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.751 |
Dual form | 1950.2.bc.i.901.5 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.866025 | − | 0.500000i | −0.353553 | − | 0.204124i | ||||
\(7\) | 0.749482 | + | 0.432713i | 0.283277 | + | 0.163550i | 0.634906 | − | 0.772589i | \(-0.281039\pi\) |
−0.351629 | + | 0.936140i | \(0.614372\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.151430 | − | 0.0874279i | 0.0456577 | − | 0.0263605i | −0.476997 | − | 0.878905i | \(-0.658275\pi\) |
0.522655 | + | 0.852544i | \(0.324942\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.34131 | − | 1.35486i | −0.926713 | − | 0.375770i | ||||
\(14\) | 0.865427 | 0.231295 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −4.08960 | + | 7.08339i | −0.991873 | + | 1.71797i | −0.385748 | + | 0.922604i | \(0.626057\pi\) |
−0.606125 | + | 0.795370i | \(0.707277\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −5.20843 | − | 3.00709i | −1.19490 | − | 0.689873i | −0.235483 | − | 0.971879i | \(-0.575667\pi\) |
−0.959413 | + | 0.282005i | \(0.909000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.865427i | − | 0.188852i | ||||||
\(22\) | 0.0874279 | − | 0.151430i | 0.0186397 | − | 0.0322849i | ||||
\(23\) | −1.45614 | − | 2.52211i | −0.303626 | − | 0.525896i | 0.673328 | − | 0.739344i | \(-0.264864\pi\) |
−0.976954 | + | 0.213448i | \(0.931531\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.57109 | + | 0.497314i | −0.700348 | + | 0.0975312i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.749482 | − | 0.432713i | 0.141639 | − | 0.0817752i | ||||
\(29\) | −3.24491 | − | 5.62035i | −0.602564 | − | 1.04367i | −0.992431 | − | 0.122801i | \(-0.960812\pi\) |
0.389867 | − | 0.920871i | \(-0.372521\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.95057i | − | 1.24836i | −0.781281 | − | 0.624180i | \(-0.785433\pi\) | ||
0.781281 | − | 0.624180i | \(-0.214567\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −0.151430 | − | 0.0874279i | −0.0263605 | − | 0.0152192i | ||||
\(34\) | 8.17919i | 1.40272i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 1.52347 | − | 0.879573i | 0.250456 | − | 0.144601i | −0.369517 | − | 0.929224i | \(-0.620477\pi\) |
0.619973 | + | 0.784623i | \(0.287144\pi\) | |||||||
\(38\) | −6.01418 | −0.975628 | ||||||||
\(39\) | 0.497314 | + | 3.57109i | 0.0796339 | + | 0.571832i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.08339 | + | 4.08960i | −1.10624 | + | 0.638688i | −0.937853 | − | 0.347034i | \(-0.887189\pi\) |
−0.168387 | + | 0.985721i | \(0.553856\pi\) | |||||||
\(42\) | −0.432713 | − | 0.749482i | −0.0667691 | − | 0.115648i | ||||
\(43\) | −4.58691 | + | 7.94476i | −0.699497 | + | 1.21156i | 0.269144 | + | 0.963100i | \(0.413259\pi\) |
−0.968641 | + | 0.248465i | \(0.920074\pi\) | |||||||
\(44\) | − | 0.174856i | − | 0.0263605i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.52211 | − | 1.45614i | −0.371865 | − | 0.214696i | ||||
\(47\) | − | 11.9021i | − | 1.73610i | −0.496478 | − | 0.868050i | \(-0.665373\pi\) | ||
0.496478 | − | 0.868050i | \(-0.334627\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −3.12552 | − | 5.41356i | −0.446503 | − | 0.773365i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.17919 | 1.14532 | ||||||||
\(52\) | −2.84400 | + | 2.21623i | −0.394391 | + | 0.307336i | ||||
\(53\) | −2.48735 | −0.341663 | −0.170832 | − | 0.985300i | \(-0.554645\pi\) | ||||
−0.170832 | + | 0.985300i | \(0.554645\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.432713 | − | 0.749482i | 0.0578238 | − | 0.100154i | ||||
\(57\) | 6.01418i | 0.796597i | ||||||||
\(58\) | −5.62035 | − | 3.24491i | −0.737988 | − | 0.426077i | ||||
\(59\) | 6.09393 | + | 3.51833i | 0.793363 | + | 0.458048i | 0.841145 | − | 0.540810i | \(-0.181882\pi\) |
−0.0477824 | + | 0.998858i | \(0.515215\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.98695 | − | 6.90559i | 0.510476 | − | 0.884171i | −0.489450 | − | 0.872031i | \(-0.662802\pi\) |
0.999926 | − | 0.0121394i | \(-0.00386418\pi\) | |||||||
\(62\) | −3.47529 | − | 6.01937i | −0.441362 | − | 0.764461i | ||||
\(63\) | −0.749482 | + | 0.432713i | −0.0944258 | + | 0.0545168i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.174856 | −0.0215233 | ||||||||
\(67\) | −2.36886 | + | 1.36766i | −0.289402 | + | 0.167086i | −0.637672 | − | 0.770308i | \(-0.720103\pi\) |
0.348270 | + | 0.937394i | \(0.386769\pi\) | |||||||
\(68\) | 4.08960 | + | 7.08339i | 0.495936 | + | 0.858987i | ||||
\(69\) | −1.45614 | + | 2.52211i | −0.175299 | + | 0.303626i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.2677 | + | 7.08275i | 1.45591 | + | 0.840568i | 0.998806 | − | 0.0488476i | \(-0.0155549\pi\) |
0.457100 | + | 0.889415i | \(0.348888\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 12.8706i | 1.50639i | 0.657800 | + | 0.753193i | \(0.271487\pi\) | ||||
−0.657800 | + | 0.753193i | \(0.728513\pi\) | |||||||
\(74\) | 0.879573 | − | 1.52347i | 0.102248 | − | 0.177099i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.20843 | + | 3.00709i | −0.597448 | + | 0.344937i | ||||
\(77\) | 0.151325 | 0.0172451 | ||||||||
\(78\) | 2.21623 | + | 2.84400i | 0.250939 | + | 0.322019i | ||||
\(79\) | −9.48961 | −1.06766 | −0.533832 | − | 0.845590i | \(-0.679249\pi\) | ||||
−0.533832 | + | 0.845590i | \(0.679249\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −4.08960 | + | 7.08339i | −0.451620 | + | 0.782229i | ||||
\(83\) | − | 0.139544i | − | 0.0153169i | −0.999971 | − | 0.00765845i | \(-0.997562\pi\) | ||
0.999971 | − | 0.00765845i | \(-0.00243778\pi\) | |||||||
\(84\) | −0.749482 | − | 0.432713i | −0.0817752 | − | 0.0472129i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.17382i | 0.989238i | ||||||||
\(87\) | −3.24491 | + | 5.62035i | −0.347891 | + | 0.602564i | ||||
\(88\) | −0.0874279 | − | 0.151430i | −0.00931985 | − | 0.0161424i | ||||
\(89\) | 11.3790 | − | 6.56966i | 1.20617 | − | 0.696382i | 0.244249 | − | 0.969713i | \(-0.421459\pi\) |
0.961920 | + | 0.273330i | \(0.0881253\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.91799 | − | 2.46127i | −0.201060 | − | 0.258011i | ||||
\(92\) | −2.91228 | −0.303626 | ||||||||
\(93\) | −6.01937 | + | 3.47529i | −0.624180 | + | 0.360370i | ||||
\(94\) | −5.95105 | − | 10.3075i | −0.613804 | − | 1.06314i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −7.48957 | − | 4.32411i | −0.760451 | − | 0.439047i | 0.0690066 | − | 0.997616i | \(-0.478017\pi\) |
−0.829458 | + | 0.558570i | \(0.811350\pi\) | |||||||
\(98\) | −5.41356 | − | 3.12552i | −0.546852 | − | 0.315725i | ||||
\(99\) | 0.174856i | 0.0175737i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.28276 | − | 9.15001i | −0.525654 | − | 0.910460i | −0.999553 | − | 0.0298810i | \(-0.990487\pi\) |
0.473899 | − | 0.880579i | \(-0.342846\pi\) | |||||||
\(102\) | 7.08339 | − | 4.08960i | 0.701360 | − | 0.404930i | ||||
\(103\) | −8.93568 | −0.880459 | −0.440230 | − | 0.897885i | \(-0.645103\pi\) | ||||
−0.440230 | + | 0.897885i | \(0.645103\pi\) | |||||||
\(104\) | −1.35486 | + | 3.34131i | −0.132855 | + | 0.327642i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.15410 | + | 1.24367i | −0.209225 | + | 0.120796i | ||||
\(107\) | −0.430389 | − | 0.745455i | −0.0416072 | − | 0.0720658i | 0.844472 | − | 0.535600i | \(-0.179914\pi\) |
−0.886079 | + | 0.463534i | \(0.846581\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | − | 5.45336i | − | 0.522337i | −0.965293 | − | 0.261168i | \(-0.915892\pi\) | ||
0.965293 | − | 0.261168i | \(-0.0841078\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.52347 | − | 0.879573i | −0.144601 | − | 0.0834854i | ||||
\(112\) | − | 0.865427i | − | 0.0817752i | ||||||
\(113\) | −5.89106 | + | 10.2036i | −0.554184 | + | 0.959876i | 0.443782 | + | 0.896135i | \(0.353636\pi\) |
−0.997966 | + | 0.0637409i | \(0.979697\pi\) | |||||||
\(114\) | 3.00709 | + | 5.20843i | 0.281640 | + | 0.487814i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.48982 | −0.602564 | ||||||||
\(117\) | 2.84400 | − | 2.21623i | 0.262928 | − | 0.204891i | ||||
\(118\) | 7.03667 | 0.647778 | ||||||||
\(119\) | −6.13015 | + | 3.53925i | −0.561950 | + | 0.324442i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.48471 | + | 9.49980i | −0.498610 | + | 0.863618i | ||||
\(122\) | − | 7.97389i | − | 0.721922i | ||||||
\(123\) | 7.08339 | + | 4.08960i | 0.638688 | + | 0.368746i | ||||
\(124\) | −6.01937 | − | 3.47529i | −0.540555 | − | 0.312090i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.432713 | + | 0.749482i | −0.0385492 | + | 0.0667691i | ||||
\(127\) | 3.47119 | + | 6.01228i | 0.308018 | + | 0.533503i | 0.977929 | − | 0.208939i | \(-0.0670009\pi\) |
−0.669911 | + | 0.742442i | \(0.733668\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 9.17382 | 0.807710 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.27133 | 0.198447 | 0.0992235 | − | 0.995065i | \(-0.468364\pi\) | ||||
0.0992235 | + | 0.995065i | \(0.468364\pi\) | |||||||
\(132\) | −0.151430 | + | 0.0874279i | −0.0131803 | + | 0.00760962i | ||||
\(133\) | −2.60241 | − | 4.50751i | −0.225658 | − | 0.390851i | ||||
\(134\) | −1.36766 | + | 2.36886i | −0.118148 | + | 0.204638i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.08339 | + | 4.08960i | 0.607395 | + | 0.350680i | ||||
\(137\) | 6.38795 | + | 3.68809i | 0.545760 | + | 0.315094i | 0.747410 | − | 0.664363i | \(-0.231297\pi\) |
−0.201650 | + | 0.979458i | \(0.564630\pi\) | |||||||
\(138\) | 2.91228i | 0.247910i | ||||||||
\(139\) | −0.410380 | + | 0.710798i | −0.0348079 | + | 0.0602891i | −0.882905 | − | 0.469552i | \(-0.844415\pi\) |
0.848097 | + | 0.529842i | \(0.177749\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.3075 | + | 5.95105i | −0.868050 | + | 0.501169i | ||||
\(142\) | 14.1655 | 1.18874 | ||||||||
\(143\) | −0.624426 | + | 0.0869582i | −0.0522171 | + | 0.00727181i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.43528 | + | 11.1462i | 0.532588 | + | 0.922469i | ||||
\(147\) | −3.12552 | + | 5.41356i | −0.257788 | + | 0.446503i | ||||
\(148\) | − | 1.75915i | − | 0.144601i | ||||||
\(149\) | 8.90766 | + | 5.14284i | 0.729744 | + | 0.421318i | 0.818329 | − | 0.574751i | \(-0.194901\pi\) |
−0.0885845 | + | 0.996069i | \(0.528234\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 11.7419i | − | 0.955544i | −0.878484 | − | 0.477772i | \(-0.841445\pi\) | ||
0.878484 | − | 0.477772i | \(-0.158555\pi\) | |||||||
\(152\) | −3.00709 | + | 5.20843i | −0.243907 | + | 0.422459i | ||||
\(153\) | −4.08960 | − | 7.08339i | −0.330624 | − | 0.572658i | ||||
\(154\) | 0.131051 | − | 0.0756625i | 0.0105604 | − | 0.00609706i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.34131 | + | 1.35486i | 0.267519 | + | 0.108475i | ||||
\(157\) | −6.76034 | −0.539534 | −0.269767 | − | 0.962926i | \(-0.586947\pi\) | ||||
−0.269767 | + | 0.962926i | \(0.586947\pi\) | |||||||
\(158\) | −8.21824 | + | 4.74480i | −0.653808 | + | 0.377476i | ||||
\(159\) | 1.24367 | + | 2.15410i | 0.0986297 | + | 0.170832i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.52036i | − | 0.198633i | ||||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | 1.23624 | + | 0.713746i | 0.0968301 | + | 0.0559049i | 0.547633 | − | 0.836719i | \(-0.315529\pi\) |
−0.450803 | + | 0.892623i | \(0.648862\pi\) | |||||||
\(164\) | 8.17919i | 0.638688i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.0697718 | − | 0.120848i | −0.00541534 | − | 0.00937964i | ||||
\(167\) | −5.08406 | + | 2.93528i | −0.393416 | + | 0.227139i | −0.683639 | − | 0.729820i | \(-0.739604\pi\) |
0.290223 | + | 0.956959i | \(0.406271\pi\) | |||||||
\(168\) | −0.865427 | −0.0667691 | ||||||||
\(169\) | 9.32872 | + | 9.05401i | 0.717594 | + | 0.696462i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.20843 | − | 3.00709i | 0.398298 | − | 0.229958i | ||||
\(172\) | 4.58691 | + | 7.94476i | 0.349749 | + | 0.605782i | ||||
\(173\) | 6.85138 | − | 11.8669i | 0.520901 | − | 0.902226i | −0.478804 | − | 0.877922i | \(-0.658930\pi\) |
0.999705 | − | 0.0243045i | \(-0.00773712\pi\) | |||||||
\(174\) | 6.48982i | 0.491992i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.151430 | − | 0.0874279i | −0.0114144 | − | 0.00659013i | ||||
\(177\) | − | 7.03667i | − | 0.528908i | ||||||
\(178\) | 6.56966 | − | 11.3790i | 0.492416 | − | 0.852890i | ||||
\(179\) | 7.09191 | + | 12.2835i | 0.530074 | + | 0.918115i | 0.999384 | + | 0.0350821i | \(0.0111693\pi\) |
−0.469310 | + | 0.883033i | \(0.655497\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.7728 | 1.02373 | 0.511863 | − | 0.859067i | \(-0.328956\pi\) | ||||
0.511863 | + | 0.859067i | \(0.328956\pi\) | |||||||
\(182\) | −2.89166 | − | 1.17253i | −0.214344 | − | 0.0869138i | ||||
\(183\) | −7.97389 | −0.589447 | ||||||||
\(184\) | −2.52211 | + | 1.45614i | −0.185932 | + | 0.107348i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.47529 | + | 6.01937i | −0.254820 | + | 0.441362i | ||||
\(187\) | 1.43018i | 0.104585i | ||||||||
\(188\) | −10.3075 | − | 5.95105i | −0.751753 | − | 0.434025i | ||||
\(189\) | 0.749482 | + | 0.432713i | 0.0545168 | + | 0.0314753i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.78821 | − | 4.82932i | 0.201748 | − | 0.349437i | −0.747344 | − | 0.664437i | \(-0.768671\pi\) |
0.949092 | + | 0.315000i | \(0.102005\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −0.191227 | + | 0.110405i | −0.0137648 | + | 0.00794712i | −0.506867 | − | 0.862024i | \(-0.669196\pi\) |
0.493102 | + | 0.869972i | \(0.335863\pi\) | |||||||
\(194\) | −8.64822 | −0.620906 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.25104 | −0.446503 | ||||||||
\(197\) | −1.49286 | + | 0.861905i | −0.106362 | + | 0.0614082i | −0.552237 | − | 0.833687i | \(-0.686226\pi\) |
0.445875 | + | 0.895095i | \(0.352892\pi\) | |||||||
\(198\) | 0.0874279 | + | 0.151430i | 0.00621323 | + | 0.0107616i | ||||
\(199\) | 3.97927 | − | 6.89229i | 0.282083 | − | 0.488581i | −0.689815 | − | 0.723986i | \(-0.742308\pi\) |
0.971898 | + | 0.235404i | \(0.0756414\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.36886 | + | 1.36766i | 0.167086 | + | 0.0964673i | ||||
\(202\) | −9.15001 | − | 5.28276i | −0.643793 | − | 0.371694i | ||||
\(203\) | − | 5.61646i | − | 0.394198i | ||||||
\(204\) | 4.08960 | − | 7.08339i | 0.286329 | − | 0.495936i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.73853 | + | 4.46784i | −0.539169 | + | 0.311289i | ||||
\(207\) | 2.91228 | 0.202417 | ||||||||
\(208\) | 0.497314 | + | 3.57109i | 0.0344825 | + | 0.247610i | ||||
\(209\) | −1.05161 | −0.0727416 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.10991 | + | 3.65448i | 0.145252 | + | 0.251585i | 0.929467 | − | 0.368905i | \(-0.120267\pi\) |
−0.784215 | + | 0.620490i | \(0.786934\pi\) | |||||||
\(212\) | −1.24367 | + | 2.15410i | −0.0854158 | + | 0.147945i | ||||
\(213\) | − | 14.1655i | − | 0.970604i | ||||||
\(214\) | −0.745455 | − | 0.430389i | −0.0509582 | − | 0.0294208i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 3.00761 | − | 5.20933i | 0.204170 | − | 0.353632i | ||||
\(218\) | −2.72668 | − | 4.72274i | −0.184674 | − | 0.319865i | ||||
\(219\) | 11.1462 | − | 6.43528i | 0.753193 | − | 0.434856i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.2616 | − | 18.1270i | 1.56474 | − | 1.21935i | ||||
\(222\) | −1.75915 | −0.118066 | ||||||||
\(223\) | 6.02126 | − | 3.47638i | 0.403214 | − | 0.232795i | −0.284656 | − | 0.958630i | \(-0.591879\pi\) |
0.687870 | + | 0.725834i | \(0.258546\pi\) | |||||||
\(224\) | −0.432713 | − | 0.749482i | −0.0289119 | − | 0.0500769i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.7821i | 0.783735i | ||||||||
\(227\) | 2.50840 | + | 1.44823i | 0.166488 | + | 0.0961221i | 0.580929 | − | 0.813954i | \(-0.302689\pi\) |
−0.414441 | + | 0.910076i | \(0.636023\pi\) | |||||||
\(228\) | 5.20843 | + | 3.00709i | 0.344937 | + | 0.199149i | ||||
\(229\) | − | 7.88800i | − | 0.521254i | −0.965440 | − | 0.260627i | \(-0.916071\pi\) | ||
0.965440 | − | 0.260627i | \(-0.0839293\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0756625 | − | 0.131051i | −0.00497823 | − | 0.00862254i | ||||
\(232\) | −5.62035 | + | 3.24491i | −0.368994 | + | 0.213039i | ||||
\(233\) | 1.42749 | 0.0935181 | 0.0467590 | − | 0.998906i | \(-0.485111\pi\) | ||||
0.0467590 | + | 0.998906i | \(0.485111\pi\) | |||||||
\(234\) | 1.35486 | − | 3.34131i | 0.0885699 | − | 0.218428i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.09393 | − | 3.51833i | 0.396681 | − | 0.229024i | ||||
\(237\) | 4.74480 | + | 8.21824i | 0.308208 | + | 0.533832i | ||||
\(238\) | −3.53925 | + | 6.13015i | −0.229415 | + | 0.397359i | ||||
\(239\) | 10.9084i | 0.705604i | 0.935698 | + | 0.352802i | \(0.114771\pi\) | ||||
−0.935698 | + | 0.352802i | \(0.885229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.4317 | − | 14.6830i | −1.63820 | − | 0.945816i | −0.981452 | − | 0.191707i | \(-0.938598\pi\) |
−0.656749 | − | 0.754109i | \(-0.728069\pi\) | |||||||
\(242\) | 10.9694i | 0.705141i | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −3.98695 | − | 6.90559i | −0.255238 | − | 0.442085i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.17919 | 0.521486 | ||||||||
\(247\) | 13.3288 | + | 17.1043i | 0.848091 | + | 1.08832i | ||||
\(248\) | −6.95057 | −0.441362 | ||||||||
\(249\) | −0.120848 | + | 0.0697718i | −0.00765845 | + | 0.00442161i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.94708 | − | 15.4968i | 0.564735 | − | 0.978150i | −0.432339 | − | 0.901711i | \(-0.642312\pi\) |
0.997074 | − | 0.0764387i | \(-0.0243549\pi\) | |||||||
\(252\) | 0.865427i | 0.0545168i | ||||||||
\(253\) | −0.441005 | − | 0.254615i | −0.0277258 | − | 0.0160075i | ||||
\(254\) | 6.01228 | + | 3.47119i | 0.377244 | + | 0.217802i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −6.08945 | − | 10.5472i | −0.379849 | − | 0.657918i | 0.611191 | − | 0.791483i | \(-0.290691\pi\) |
−0.991040 | + | 0.133565i | \(0.957358\pi\) | |||||||
\(258\) | 7.94476 | − | 4.58691i | 0.494619 | − | 0.285568i | ||||
\(259\) | 1.52241 | 0.0945981 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.48982 | 0.401710 | ||||||||
\(262\) | 1.96703 | − | 1.13567i | 0.121524 | − | 0.0701616i | ||||
\(263\) | 10.5834 | + | 18.3309i | 0.652598 | + | 1.13033i | 0.982490 | + | 0.186314i | \(0.0596542\pi\) |
−0.329892 | + | 0.944019i | \(0.607012\pi\) | |||||||
\(264\) | −0.0874279 | + | 0.151430i | −0.00538082 | + | 0.00931985i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.50751 | − | 2.60241i | −0.276373 | − | 0.159564i | ||||
\(267\) | −11.3790 | − | 6.56966i | −0.696382 | − | 0.402056i | ||||
\(268\) | 2.73532i | 0.167086i | ||||||||
\(269\) | 6.04371 | − | 10.4680i | 0.368492 | − | 0.638246i | −0.620838 | − | 0.783939i | \(-0.713208\pi\) |
0.989330 | + | 0.145692i | \(0.0465410\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.7275 | + | 7.34824i | −0.773142 | + | 0.446374i | −0.833994 | − | 0.551773i | \(-0.813951\pi\) |
0.0608525 | + | 0.998147i | \(0.480618\pi\) | |||||||
\(272\) | 8.17919 | 0.495936 | ||||||||
\(273\) | −1.17253 | + | 2.89166i | −0.0709648 | + | 0.175011i | ||||
\(274\) | 7.37617 | 0.445611 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.45614 | + | 2.52211i | 0.0876493 | + | 0.151813i | ||||
\(277\) | 9.85638 | − | 17.0717i | 0.592212 | − | 1.02574i | −0.401722 | − | 0.915762i | \(-0.631588\pi\) |
0.993934 | − | 0.109980i | \(-0.0350786\pi\) | |||||||
\(278\) | 0.820759i | 0.0492259i | ||||||||
\(279\) | 6.01937 | + | 3.47529i | 0.360370 | + | 0.208060i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.93073i | 0.592418i | 0.955123 | + | 0.296209i | \(0.0957225\pi\) | ||||
−0.955123 | + | 0.296209i | \(0.904278\pi\) | |||||||
\(282\) | −5.95105 | + | 10.3075i | −0.354380 | + | 0.613804i | ||||
\(283\) | −5.81912 | − | 10.0790i | −0.345911 | − | 0.599135i | 0.639608 | − | 0.768701i | \(-0.279097\pi\) |
−0.985519 | + | 0.169566i | \(0.945763\pi\) | |||||||
\(284\) | 12.2677 | − | 7.08275i | 0.727953 | − | 0.420284i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.497290 | + | 0.387521i | −0.0294053 | + | 0.0229146i | ||||
\(287\) | −7.07849 | −0.417830 | ||||||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | −24.9496 | − | 43.2139i | −1.46762 | − | 2.54200i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.64822i | 0.506967i | ||||||||
\(292\) | 11.1462 | + | 6.43528i | 0.652284 | + | 0.376596i | ||||
\(293\) | −11.3906 | − | 6.57636i | −0.665445 | − | 0.384195i | 0.128903 | − | 0.991657i | \(-0.458854\pi\) |
−0.794349 | + | 0.607462i | \(0.792188\pi\) | |||||||
\(294\) | 6.25104i | 0.364568i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.879573 | − | 1.52347i | −0.0511241 | − | 0.0885496i | ||||
\(297\) | 0.151430 | − | 0.0874279i | 0.00878684 | − | 0.00507308i | ||||
\(298\) | 10.2857 | 0.595834 | ||||||||
\(299\) | 1.44832 | + | 10.4000i | 0.0837583 | + | 0.601448i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.87561 | + | 3.96963i | −0.396304 | + | 0.228806i | ||||
\(302\) | −5.87096 | − | 10.1688i | −0.337836 | − | 0.585149i | ||||
\(303\) | −5.28276 | + | 9.15001i | −0.303487 | + | 0.525654i | ||||
\(304\) | 6.01418i | 0.344937i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.08339 | − | 4.08960i | −0.404930 | − | 0.233787i | ||||
\(307\) | − | 14.8609i | − | 0.848155i | −0.905626 | − | 0.424077i | \(-0.860598\pi\) | ||
0.905626 | − | 0.424077i | \(-0.139402\pi\) | |||||||
\(308\) | 0.0756625 | − | 0.131051i | 0.00431127 | − | 0.00746734i | ||||
\(309\) | 4.46784 | + | 7.73853i | 0.254167 | + | 0.440230i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.17666 | 0.520361 | 0.260180 | − | 0.965560i | \(-0.416218\pi\) | ||||
0.260180 | + | 0.965560i | \(0.416218\pi\) | |||||||
\(312\) | 3.57109 | − | 0.497314i | 0.202173 | − | 0.0281548i | ||||
\(313\) | 7.43905 | 0.420480 | 0.210240 | − | 0.977650i | \(-0.432576\pi\) | ||||
0.210240 | + | 0.977650i | \(0.432576\pi\) | |||||||
\(314\) | −5.85463 | + | 3.38017i | −0.330396 | + | 0.190754i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.74480 | + | 8.21824i | −0.266916 | + | 0.462312i | ||||
\(317\) | − | 25.7510i | − | 1.44632i | −0.690679 | − | 0.723161i | \(-0.742688\pi\) | ||
0.690679 | − | 0.723161i | \(-0.257312\pi\) | |||||||
\(318\) | 2.15410 | + | 1.24367i | 0.120796 | + | 0.0697417i | ||||
\(319\) | −0.982750 | − | 0.567391i | −0.0550235 | − | 0.0317678i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.430389 | + | 0.745455i | −0.0240219 | + | 0.0416072i | ||||
\(322\) | −1.26018 | − | 2.18270i | −0.0702272 | − | 0.121637i | ||||
\(323\) | 42.6007 | − | 24.5955i | 2.37037 | − | 1.36853i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.42749 | 0.0790614 | ||||||||
\(327\) | −4.72274 | + | 2.72668i | −0.261168 | + | 0.150786i | ||||
\(328\) | 4.08960 | + | 7.08339i | 0.225810 | + | 0.391115i | ||||
\(329\) | 5.15020 | − | 8.92040i | 0.283940 | − | 0.491798i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.63295 | + | 3.25219i | 0.309615 | + | 0.178756i | 0.646754 | − | 0.762699i | \(-0.276126\pi\) |
−0.337139 | + | 0.941455i | \(0.609459\pi\) | |||||||
\(332\) | −0.120848 | − | 0.0697718i | −0.00663241 | − | 0.00382922i | ||||
\(333\) | 1.75915i | 0.0964006i | ||||||||
\(334\) | −2.93528 | + | 5.08406i | −0.160612 | + | 0.278187i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.749482 | + | 0.432713i | −0.0408876 | + | 0.0236065i | ||||
\(337\) | −18.6696 | −1.01700 | −0.508498 | − | 0.861063i | \(-0.669799\pi\) | ||||
−0.508498 | + | 0.861063i | \(0.669799\pi\) | |||||||
\(338\) | 12.6059 | + | 3.17664i | 0.685671 | + | 0.172786i | ||||
\(339\) | 11.7821 | 0.639917 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.607674 | − | 1.05252i | −0.0329074 | − | 0.0569973i | ||||
\(342\) | 3.00709 | − | 5.20843i | 0.162605 | − | 0.281640i | ||||
\(343\) | − | 11.4678i | − | 0.619203i | ||||||
\(344\) | 7.94476 | + | 4.58691i | 0.428353 | + | 0.247310i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 13.7028i | − | 0.736665i | ||||||
\(347\) | 14.2033 | − | 24.6009i | 0.762474 | − | 1.32064i | −0.179098 | − | 0.983831i | \(-0.557318\pi\) |
0.941572 | − | 0.336813i | \(-0.109349\pi\) | |||||||
\(348\) | 3.24491 | + | 5.62035i | 0.173945 | + | 0.301282i | ||||
\(349\) | −1.93797 | + | 1.11889i | −0.103737 | + | 0.0598926i | −0.550971 | − | 0.834524i | \(-0.685742\pi\) |
0.447234 | + | 0.894417i | \(0.352409\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.34131 | − | 1.35486i | −0.178346 | − | 0.0723170i | ||||
\(352\) | −0.174856 | −0.00931985 | ||||||||
\(353\) | 1.40866 | − | 0.813287i | 0.0749751 | − | 0.0432869i | −0.462044 | − | 0.886857i | \(-0.652884\pi\) |
0.537019 | + | 0.843570i | \(0.319550\pi\) | |||||||
\(354\) | −3.51833 | − | 6.09393i | −0.186997 | − | 0.323889i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 13.1393i | − | 0.696382i | ||||||
\(357\) | 6.13015 | + | 3.53925i | 0.324442 | + | 0.187317i | ||||
\(358\) | 12.2835 | + | 7.09191i | 0.649206 | + | 0.374819i | ||||
\(359\) | 34.4613i | 1.81880i | 0.415923 | + | 0.909400i | \(0.363459\pi\) | ||||
−0.415923 | + | 0.909400i | \(0.636541\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.58515 | + | 14.8699i | 0.451850 | + | 0.782627i | ||||
\(362\) | 11.9276 | − | 6.88641i | 0.626901 | − | 0.361942i | ||||
\(363\) | 10.9694 | 0.575746 | ||||||||
\(364\) | −3.09052 | + | 0.430389i | −0.161987 | + | 0.0225585i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.90559 | + | 3.98695i | −0.360961 | + | 0.208401i | ||||
\(367\) | 7.31703 | + | 12.6735i | 0.381946 | + | 0.661550i | 0.991340 | − | 0.131317i | \(-0.0419207\pi\) |
−0.609394 | + | 0.792867i | \(0.708587\pi\) | |||||||
\(368\) | −1.45614 | + | 2.52211i | −0.0759065 | + | 0.131474i | ||||
\(369\) | − | 8.17919i | − | 0.425792i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.86422 | − | 1.07631i | −0.0967855 | − | 0.0558791i | ||||
\(372\) | 6.95057i | 0.360370i | ||||||||
\(373\) | −11.0370 | + | 19.1166i | −0.571472 | + | 0.989819i | 0.424943 | + | 0.905220i | \(0.360294\pi\) |
−0.996415 | + | 0.0845988i | \(0.973039\pi\) | |||||||
\(374\) | 0.715090 | + | 1.23857i | 0.0369764 | + | 0.0640450i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.9021 | −0.613804 | ||||||||
\(377\) | 3.22747 | + | 23.1757i | 0.166223 | + | 1.19361i | ||||
\(378\) | 0.865427 | 0.0445128 | ||||||||
\(379\) | −12.0573 | + | 6.96127i | −0.619341 | + | 0.357577i | −0.776612 | − | 0.629979i | \(-0.783064\pi\) |
0.157272 | + | 0.987555i | \(0.449730\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.47119 | − | 6.01228i | 0.177834 | − | 0.308018i | ||||
\(382\) | − | 5.57642i | − | 0.285314i | ||||||
\(383\) | 21.3119 | + | 12.3044i | 1.08899 | + | 0.628728i | 0.933307 | − | 0.359080i | \(-0.116909\pi\) |
0.155681 | + | 0.987807i | \(0.450243\pi\) | |||||||
\(384\) | 0.866025 | + | 0.500000i | 0.0441942 | + | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.110405 | + | 0.191227i | −0.00561946 | + | 0.00973319i | ||||
\(387\) | −4.58691 | − | 7.94476i | −0.233166 | − | 0.403855i | ||||
\(388\) | −7.48957 | + | 4.32411i | −0.380226 | + | 0.219523i | ||||
\(389\) | −5.60980 | −0.284428 | −0.142214 | − | 0.989836i | \(-0.545422\pi\) | ||||
−0.142214 | + | 0.989836i | \(0.545422\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.8201 | 1.20463 | ||||||||
\(392\) | −5.41356 | + | 3.12552i | −0.273426 | + | 0.157863i | ||||
\(393\) | −1.13567 | − | 1.96703i | −0.0572867 | − | 0.0992235i | ||||
\(394\) | −0.861905 | + | 1.49286i | −0.0434222 | + | 0.0752094i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.151430 | + | 0.0874279i | 0.00760962 | + | 0.00439342i | ||||
\(397\) | −2.05141 | − | 1.18438i | −0.102957 | − | 0.0594424i | 0.447637 | − | 0.894215i | \(-0.352266\pi\) |
−0.550595 | + | 0.834773i | \(0.685599\pi\) | |||||||
\(398\) | − | 7.95853i | − | 0.398925i | ||||||
\(399\) | −2.60241 | + | 4.50751i | −0.130284 | + | 0.225658i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.2942 | − | 8.25276i | 0.713818 | − | 0.412123i | −0.0986548 | − | 0.995122i | \(-0.531454\pi\) |
0.812473 | + | 0.582998i | \(0.198121\pi\) | |||||||
\(402\) | 2.73532 | 0.136425 | ||||||||
\(403\) | −9.41704 | + | 23.2240i | −0.469096 | + | 1.15687i | ||||
\(404\) | −10.5655 | −0.525654 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.80823 | − | 4.86400i | −0.139370 | − | 0.241396i | ||||
\(407\) | 0.153798 | − | 0.266387i | 0.00762351 | − | 0.0132043i | ||||
\(408\) | − | 8.17919i | − | 0.404930i | ||||||
\(409\) | −28.8448 | − | 16.6535i | −1.42628 | − | 0.823464i | −0.429457 | − | 0.903087i | \(-0.641295\pi\) |
−0.996825 | + | 0.0796230i | \(0.974628\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 7.37617i | − | 0.363840i | ||||||
\(412\) | −4.46784 | + | 7.73853i | −0.220115 | + | 0.381250i | ||||
\(413\) | 3.04486 | + | 5.27385i | 0.149828 | + | 0.259509i | ||||
\(414\) | 2.52211 | − | 1.45614i | 0.123955 | − | 0.0715654i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.21623 | + | 2.84400i | 0.108660 | + | 0.139438i | ||||
\(417\) | 0.820759 | 0.0401927 | ||||||||
\(418\) | −0.910724 | + | 0.525807i | −0.0445450 | + | 0.0257181i | ||||
\(419\) | −15.1303 | − | 26.2065i | −0.739164 | − | 1.28027i | −0.952872 | − | 0.303372i | \(-0.901887\pi\) |
0.213708 | − | 0.976898i | \(-0.431446\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 40.2235i | − | 1.96038i | −0.198070 | − | 0.980188i | \(-0.563467\pi\) | ||
0.198070 | − | 0.980188i | \(-0.436533\pi\) | |||||||
\(422\) | 3.65448 | + | 2.10991i | 0.177897 | + | 0.102709i | ||||
\(423\) | 10.3075 | + | 5.95105i | 0.501169 | + | 0.289350i | ||||
\(424\) | 2.48735i | 0.120796i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.08275 | − | 12.2677i | −0.343160 | − | 0.594371i | ||||
\(427\) | 5.97629 | − | 3.45041i | 0.289213 | − | 0.166977i | ||||
\(428\) | −0.860777 | −0.0416072 | ||||||||
\(429\) | 0.387521 | + | 0.497290i | 0.0187097 | + | 0.0240094i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.1980 | + | 16.2801i | −1.35825 | + | 0.784185i | −0.989388 | − | 0.145300i | \(-0.953585\pi\) |
−0.368860 | + | 0.929485i | \(0.620252\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 15.3663 | − | 26.6153i | 0.738460 | − | 1.27905i | −0.214729 | − | 0.976674i | \(-0.568887\pi\) |
0.953189 | − | 0.302376i | \(-0.0977798\pi\) | |||||||
\(434\) | − | 6.01521i | − | 0.288739i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.72274 | − | 2.72668i | −0.226178 | − | 0.130584i | ||||
\(437\) | 17.5150i | 0.837854i | ||||||||
\(438\) | 6.43528 | − | 11.1462i | 0.307490 | − | 0.532588i | ||||
\(439\) | −3.26422 | − | 5.65380i | −0.155793 | − | 0.269841i | 0.777555 | − | 0.628815i | \(-0.216460\pi\) |
−0.933347 | + | 0.358974i | \(0.883127\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.25104 | 0.297668 | ||||||||
\(442\) | 11.0816 | − | 27.3292i | 0.527100 | − | 1.29992i | ||||
\(443\) | 30.3111 | 1.44012 | 0.720061 | − | 0.693911i | \(-0.244114\pi\) | ||||
0.720061 | + | 0.693911i | \(0.244114\pi\) | |||||||
\(444\) | −1.52347 | + | 0.879573i | −0.0723005 | + | 0.0417427i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.47638 | − | 6.02126i | 0.164611 | − | 0.285115i | ||||
\(447\) | − | 10.2857i | − | 0.486496i | ||||||
\(448\) | −0.749482 | − | 0.432713i | −0.0354097 | − | 0.0204438i | ||||
\(449\) | −13.8034 | − | 7.96938i | −0.651421 | − | 0.376098i | 0.137579 | − | 0.990491i | \(-0.456068\pi\) |
−0.789001 | + | 0.614392i | \(0.789401\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.715090 | + | 1.23857i | −0.0336723 | + | 0.0583221i | ||||
\(452\) | 5.89106 | + | 10.2036i | 0.277092 | + | 0.479938i | ||||
\(453\) | −10.1688 | + | 5.87096i | −0.477772 | + | 0.275842i | ||||
\(454\) | 2.89645 | 0.135937 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.01418 | 0.281640 | ||||||||
\(457\) | −17.1548 | + | 9.90436i | −0.802470 | + | 0.463306i | −0.844334 | − | 0.535817i | \(-0.820004\pi\) |
0.0418642 | + | 0.999123i | \(0.486670\pi\) | |||||||
\(458\) | −3.94400 | − | 6.83121i | −0.184291 | − | 0.319202i | ||||
\(459\) | −4.08960 | + | 7.08339i | −0.190886 | + | 0.330624i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.5898 | − | 6.69139i | −0.539792 | − | 0.311649i | 0.205202 | − | 0.978720i | \(-0.434215\pi\) |
−0.744995 | + | 0.667070i | \(0.767548\pi\) | |||||||
\(462\) | −0.131051 | − | 0.0756625i | −0.00609706 | − | 0.00352014i | ||||
\(463\) | − | 42.3599i | − | 1.96863i | −0.176412 | − | 0.984316i | \(-0.556449\pi\) | ||
0.176412 | − | 0.984316i | \(-0.443551\pi\) | |||||||
\(464\) | −3.24491 | + | 5.62035i | −0.150641 | + | 0.260918i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.23624 | − | 0.713746i | 0.0572679 | − | 0.0330636i | ||||
\(467\) | 33.4593 | 1.54831 | 0.774155 | − | 0.632996i | \(-0.218175\pi\) | ||||
0.774155 | + | 0.632996i | \(0.218175\pi\) | |||||||
\(468\) | −0.497314 | − | 3.57109i | −0.0229883 | − | 0.165074i | ||||
\(469\) | −2.36722 | −0.109308 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.38017 | + | 5.85463i | 0.155750 | + | 0.269767i | ||||
\(472\) | 3.51833 | − | 6.09393i | 0.161944 | − | 0.280496i | ||||
\(473\) | 1.60410i | 0.0737564i | ||||||||
\(474\) | 8.21824 | + | 4.74480i | 0.377476 | + | 0.217936i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.07849i | 0.324442i | ||||||||
\(477\) | 1.24367 | − | 2.15410i | 0.0569439 | − | 0.0986297i | ||||
\(478\) | 5.45418 | + | 9.44692i | 0.249469 | + | 0.432092i | ||||
\(479\) | 19.3387 | − | 11.1652i | 0.883606 | − | 0.510150i | 0.0117600 | − | 0.999931i | \(-0.496257\pi\) |
0.871846 | + | 0.489781i | \(0.162923\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.28207 | + | 0.874847i | −0.286438 | + | 0.0398896i | ||||
\(482\) | −29.3660 | −1.33759 | ||||||||
\(483\) | −2.18270 | + | 1.26018i | −0.0993163 | + | 0.0573403i | ||||
\(484\) | 5.48471 | + | 9.49980i | 0.249305 | + | 0.431809i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | −24.8982 | − | 14.3750i | −1.12824 | − | 0.651392i | −0.184751 | − | 0.982785i | \(-0.559148\pi\) |
−0.943493 | + | 0.331393i | \(0.892481\pi\) | |||||||
\(488\) | −6.90559 | − | 3.98695i | −0.312602 | − | 0.180481i | ||||
\(489\) | − | 1.42749i | − | 0.0645534i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.02546 | + | 13.9005i | 0.362184 | + | 0.627321i | 0.988320 | − | 0.152393i | \(-0.0486978\pi\) |
−0.626136 | + | 0.779714i | \(0.715364\pi\) | |||||||
\(492\) | 7.08339 | − | 4.08960i | 0.319344 | − | 0.184373i | ||||
\(493\) | 53.0815 | 2.39067 | ||||||||
\(494\) | 20.0952 | + | 8.14836i | 0.904127 | + | 0.366612i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.01937 | + | 3.47529i | −0.270278 | + | 0.156045i | ||||
\(497\) | 6.12960 | + | 10.6168i | 0.274950 | + | 0.476228i | ||||
\(498\) | −0.0697718 | + | 0.120848i | −0.00312655 | + | 0.00541534i | ||||
\(499\) | 33.2509i | 1.48851i | 0.667894 | + | 0.744256i | \(0.267196\pi\) | ||||
−0.667894 | + | 0.744256i | \(0.732804\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.08406 | + | 2.93528i | 0.227139 | + | 0.131139i | ||||
\(502\) | − | 17.8942i | − | 0.798656i | ||||||
\(503\) | −12.5710 | + | 21.7736i | −0.560514 | + | 0.970838i | 0.436938 | + | 0.899492i | \(0.356063\pi\) |
−0.997452 | + | 0.0713466i | \(0.977270\pi\) | |||||||
\(504\) | 0.432713 | + | 0.749482i | 0.0192746 | + | 0.0333846i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.509229 | −0.0226380 | ||||||||
\(507\) | 3.17664 | − | 12.6059i | 0.141080 | − | 0.559848i | ||||
\(508\) | 6.94238 | 0.308018 | ||||||||
\(509\) | −22.8809 | + | 13.2103i | −1.01418 | + | 0.585536i | −0.912412 | − | 0.409272i | \(-0.865783\pi\) |
−0.101766 | + | 0.994808i | \(0.532449\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.56927 | + | 9.64625i | −0.246370 | + | 0.426725i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −5.20843 | − | 3.00709i | −0.229958 | − | 0.132766i | ||||
\(514\) | −10.5472 | − | 6.08945i | −0.465219 | − | 0.268594i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.58691 | − | 7.94476i | 0.201927 | − | 0.349749i | ||||
\(517\) | −1.04058 | − | 1.80233i | −0.0457645 | − | 0.0792664i | ||||
\(518\) | 1.31845 | − | 0.761206i | 0.0579293 | − | 0.0334455i | ||||
\(519\) | −13.7028 | −0.601484 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.4462 | −0.983384 | −0.491692 | − | 0.870769i | \(-0.663621\pi\) | ||||
−0.491692 | + | 0.870769i | \(0.663621\pi\) | |||||||
\(522\) | 5.62035 | − | 3.24491i | 0.245996 | − | 0.142026i | ||||
\(523\) | −14.5385 | − | 25.1815i | −0.635726 | − | 1.10111i | −0.986361 | − | 0.164598i | \(-0.947367\pi\) |
0.350635 | − | 0.936512i | \(-0.385966\pi\) | |||||||
\(524\) | 1.13567 | − | 1.96703i | 0.0496118 | − | 0.0859301i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.3309 | + | 10.5834i | 0.799266 | + | 0.461456i | ||||
\(527\) | 49.2336 | + | 28.4250i | 2.14465 | + | 1.23821i | ||||
\(528\) | 0.174856i | 0.00760962i | ||||||||
\(529\) | 7.25931 | − | 12.5735i | 0.315622 | − | 0.546674i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.09393 | + | 3.51833i | −0.264454 | + | 0.152683i | ||||
\(532\) | −5.20483 | −0.225658 | ||||||||
\(533\) | 29.2086 | − | 4.06762i | 1.26517 | − | 0.176188i | ||||
\(534\) | −13.1393 | −0.568594 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.36766 | + | 2.36886i | 0.0590739 | + | 0.102319i | ||||
\(537\) | 7.09191 | − | 12.2835i | 0.306038 | − | 0.530074i | ||||
\(538\) | − | 12.0874i | − | 0.521126i | ||||||
\(539\) | −0.946592 | − | 0.546515i | −0.0407726 | − | 0.0235401i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.17282i | 0.351377i | 0.984446 | + | 0.175688i | \(0.0562151\pi\) | ||||
−0.984446 | + | 0.175688i | \(0.943785\pi\) | |||||||
\(542\) | −7.34824 | + | 12.7275i | −0.315634 | + | 0.546694i | ||||
\(543\) | −6.88641 | − | 11.9276i | −0.295524 | − | 0.511863i | ||||
\(544\) | 7.08339 | − | 4.08960i | 0.303698 | − | 0.175340i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.430389 | + | 3.09052i | 0.0184189 | + | 0.132262i | ||||
\(547\) | 40.7393 | 1.74188 | 0.870942 | − | 0.491385i | \(-0.163509\pi\) | ||||
0.870942 | + | 0.491385i | \(0.163509\pi\) | |||||||
\(548\) | 6.38795 | − | 3.68809i | 0.272880 | − | 0.157547i | ||||
\(549\) | 3.98695 | + | 6.90559i | 0.170159 | + | 0.294724i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 39.0309i | 1.66277i | ||||||||
\(552\) | 2.52211 | + | 1.45614i | 0.107348 | + | 0.0619774i | ||||
\(553\) | −7.11229 | − | 4.10628i | −0.302445 | − | 0.174617i | ||||
\(554\) | − | 19.7128i | − | 0.837515i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.410380 | + | 0.710798i | 0.0174040 | + | 0.0301446i | ||||
\(557\) | 0.794008 | − | 0.458421i | 0.0336432 | − | 0.0194239i | −0.483084 | − | 0.875574i | \(-0.660483\pi\) |
0.516727 | + | 0.856150i | \(0.327150\pi\) | |||||||
\(558\) | 6.95057 | 0.294241 | ||||||||
\(559\) | 26.0903 | − | 20.3313i | 1.10350 | − | 0.859922i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.23857 | − | 0.715090i | 0.0522925 | − | 0.0301911i | ||||
\(562\) | 4.96537 | + | 8.60027i | 0.209451 | + | 0.362780i | ||||
\(563\) | −6.32961 | + | 10.9632i | −0.266761 | + | 0.462044i | −0.968024 | − | 0.250859i | \(-0.919287\pi\) |
0.701262 | + | 0.712903i | \(0.252620\pi\) | |||||||
\(564\) | 11.9021i | 0.501169i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.0790 | − | 5.81912i | −0.423652 | − | 0.244596i | ||||
\(567\) | − | 0.865427i | − | 0.0363445i | ||||||
\(568\) | 7.08275 | − | 12.2677i | 0.297186 | − | 0.514741i | ||||
\(569\) | −12.2559 | − | 21.2279i | −0.513795 | − | 0.889918i | −0.999872 | − | 0.0160026i | \(-0.994906\pi\) |
0.486077 | − | 0.873916i | \(-0.338427\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.1443 | −0.466376 | −0.233188 | − | 0.972432i | \(-0.574916\pi\) | ||||
−0.233188 | + | 0.972432i | \(0.574916\pi\) | |||||||
\(572\) | −0.236905 | + | 0.584248i | −0.00990549 | + | 0.0244286i | ||||
\(573\) | −5.57642 | −0.232958 | ||||||||
\(574\) | −6.13015 | + | 3.53925i | −0.255868 | + | 0.147725i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 23.8325i | 0.992161i | 0.868276 | + | 0.496081i | \(0.165228\pi\) | ||||
−0.868276 | + | 0.496081i | \(0.834772\pi\) | |||||||
\(578\) | −43.2139 | − | 24.9496i | −1.79746 | − | 1.03777i | ||||
\(579\) | 0.191227 | + | 0.110405i | 0.00794712 | + | 0.00458827i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.0603824 | − | 0.104585i | 0.00250508 | − | 0.00433893i | ||||
\(582\) | 4.32411 | + | 7.48957i | 0.179240 | + | 0.310453i | ||||
\(583\) | −0.376658 | + | 0.217463i | −0.0155996 | + | 0.00900642i | ||||
\(584\) | 12.8706 | 0.532588 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.1527 | −0.543334 | ||||||||
\(587\) | −32.3566 | + | 18.6811i | −1.33550 | + | 0.771051i | −0.986136 | − | 0.165937i | \(-0.946935\pi\) |
−0.349362 | + | 0.936988i | \(0.613602\pi\) | |||||||
\(588\) | 3.12552 | + | 5.41356i | 0.128894 | + | 0.223251i | ||||
\(589\) | −20.9010 | + | 36.2016i | −0.861210 | + | 1.49166i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.49286 | + | 0.861905i | 0.0614082 | + | 0.0354540i | ||||
\(592\) | −1.52347 | − | 0.879573i | −0.0626140 | − | 0.0361502i | ||||
\(593\) | − | 6.46136i | − | 0.265336i | −0.991161 | − | 0.132668i | \(-0.957646\pi\) | ||
0.991161 | − | 0.132668i | \(-0.0423544\pi\) | |||||||
\(594\) | 0.0874279 | − | 0.151430i | 0.00358721 | − | 0.00621323i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.90766 | − | 5.14284i | 0.364872 | − | 0.210659i | ||||
\(597\) | −7.95853 | −0.325721 | ||||||||
\(598\) | 6.45428 | + | 8.28251i | 0.263935 | + | 0.338697i | ||||
\(599\) | 38.5057 | 1.57330 | 0.786651 | − | 0.617398i | \(-0.211813\pi\) | ||||
0.786651 | + | 0.617398i | \(0.211813\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.371169 | − | 0.642883i | −0.0151403 | − | 0.0262237i | 0.858356 | − | 0.513055i | \(-0.171486\pi\) |
−0.873496 | + | 0.486831i | \(0.838153\pi\) | |||||||
\(602\) | −3.96963 | + | 6.87561i | −0.161790 | + | 0.280229i | ||||
\(603\) | − | 2.73532i | − | 0.111391i | ||||||
\(604\) | −10.1688 | − | 5.87096i | −0.413763 | − | 0.238886i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.5655i | 0.429195i | ||||||||
\(607\) | −14.7513 | + | 25.5500i | −0.598736 | + | 1.03704i | 0.394272 | + | 0.918994i | \(0.370997\pi\) |
−0.993008 | + | 0.118047i | \(0.962337\pi\) | |||||||
\(608\) | 3.00709 | + | 5.20843i | 0.121954 | + | 0.211230i | ||||
\(609\) | −4.86400 | + | 2.80823i | −0.197099 | + | 0.113795i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.1257 | + | 39.7686i | −0.652374 | + | 1.60887i | ||||
\(612\) | −8.17919 | −0.330624 | ||||||||
\(613\) | −11.8943 | + | 6.86720i | −0.480408 | + | 0.277364i | −0.720587 | − | 0.693365i | \(-0.756127\pi\) |
0.240178 | + | 0.970729i | \(0.422794\pi\) | |||||||
\(614\) | −7.43044 | − | 12.8699i | −0.299868 | − | 0.519387i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 0.151325i | − | 0.00609706i | ||||||
\(617\) | 37.1342 | + | 21.4394i | 1.49497 | + | 0.863119i | 0.999983 | − | 0.00578297i | \(-0.00184079\pi\) |
0.494983 | + | 0.868902i | \(0.335174\pi\) | |||||||
\(618\) | 7.73853 | + | 4.46784i | 0.311289 | + | 0.179723i | ||||
\(619\) | 30.0054i | 1.20602i | 0.797734 | + | 0.603010i | \(0.206032\pi\) | ||||
−0.797734 | + | 0.603010i | \(0.793968\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.45614 | − | 2.52211i | −0.0584329 | − | 0.101209i | ||||
\(622\) | 7.94722 | − | 4.58833i | 0.318655 | − | 0.183975i | ||||
\(623\) | 11.3711 | 0.455574 | ||||||||
\(624\) | 2.84400 | − | 2.21623i | 0.113851 | − | 0.0887202i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.44240 | − | 3.71952i | 0.257490 | − | 0.148662i | ||||
\(627\) | 0.525807 | + | 0.910724i | 0.0209987 | + | 0.0363708i | ||||
\(628\) | −3.38017 | + | 5.85463i | −0.134884 | + | 0.233625i | ||||
\(629\) | 14.3884i | 0.573703i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.73137 | + | 4.46371i | 0.307781 | + | 0.177697i | 0.645933 | − | 0.763394i | \(-0.276468\pi\) |
−0.338152 | + | 0.941091i | \(0.609802\pi\) | |||||||
\(632\) | 9.48961i | 0.377476i | ||||||||
\(633\) | 2.10991 | − | 3.65448i | 0.0838616 | − | 0.145252i | ||||
\(634\) | −12.8755 | − | 22.3011i | −0.511352 | − | 0.885688i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.48735 | 0.0986297 | ||||||||
\(637\) | 3.10873 | + | 22.3230i | 0.123172 | + | 0.884470i | ||||
\(638\) | −1.13478 | −0.0449265 | ||||||||
\(639\) | −12.2677 | + | 7.08275i | −0.485302 | + | 0.280189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.9079 | + | 20.6250i | −0.470332 | + | 0.814639i | −0.999424 | − | 0.0339254i | \(-0.989199\pi\) |
0.529092 | + | 0.848564i | \(0.322532\pi\) | |||||||
\(642\) | 0.860777i | 0.0339722i | ||||||||
\(643\) | 8.30300 | + | 4.79374i | 0.327439 | + | 0.189047i | 0.654703 | − | 0.755886i | \(-0.272794\pi\) |
−0.327265 | + | 0.944933i | \(0.606127\pi\) | |||||||
\(644\) | −2.18270 | − | 1.26018i | −0.0860104 | − | 0.0496581i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.5955 | − | 42.6007i | 0.967699 | − | 1.67610i | ||||
\(647\) | −22.6448 | − | 39.2219i | −0.890259 | − | 1.54197i | −0.839565 | − | 0.543259i | \(-0.817190\pi\) |
−0.0506940 | − | 0.998714i | \(-0.516143\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 1.23040 | 0.0482975 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.01521 | −0.235755 | ||||||||
\(652\) | 1.23624 | − | 0.713746i | 0.0484150 | − | 0.0279524i | ||||
\(653\) | −4.62451 | − | 8.00988i | −0.180971 | − | 0.313451i | 0.761241 | − | 0.648470i | \(-0.224591\pi\) |
−0.942211 | + | 0.335019i | \(0.891257\pi\) | |||||||
\(654\) | −2.72668 | + | 4.72274i | −0.106622 | + | 0.184674i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.08339 | + | 4.08960i | 0.276560 | + | 0.159672i | ||||
\(657\) | −11.1462 | − | 6.43528i | −0.434856 | − | 0.251064i | ||||
\(658\) | − | 10.3004i | − | 0.401551i | ||||||
\(659\) | 11.0666 | − | 19.1679i | 0.431093 | − | 0.746676i | −0.565874 | − | 0.824491i | \(-0.691461\pi\) |
0.996968 | + | 0.0778159i | \(0.0247946\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.75083 | − | 5.05229i | 0.340368 | − | 0.196511i | −0.320067 | − | 0.947395i | \(-0.603705\pi\) |
0.660435 | + | 0.750884i | \(0.270372\pi\) | |||||||
\(662\) | 6.50437 | 0.252800 | ||||||||
\(663\) | −27.3292 | − | 11.0816i | −1.06138 | − | 0.430375i | ||||
\(664\) | −0.139544 | −0.00541534 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.879573 | + | 1.52347i | 0.0340828 | + | 0.0590331i | ||||
\(667\) | −9.45008 | + | 16.3680i | −0.365909 | + | 0.633772i | ||||
\(668\) | 5.87057i | 0.227139i | ||||||||
\(669\) | −6.02126 | − | 3.47638i | −0.232795 | − | 0.134405i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.39428i | − | 0.0538256i | ||||||
\(672\) | −0.432713 | + | 0.749482i | −0.0166923 | + | 0.0289119i | ||||
\(673\) | −6.73157 | − | 11.6594i | −0.259483 | − | 0.449437i | 0.706621 | − | 0.707593i | \(-0.250219\pi\) |
−0.966103 | + | 0.258155i | \(0.916885\pi\) | |||||||
\(674\) | −16.1683 | + | 9.33479i | −0.622781 | + | 0.359562i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.5054 | − | 3.55190i | 0.480975 | − | 0.136612i | ||||
\(677\) | −7.86444 | −0.302255 | −0.151127 | − | 0.988514i | \(-0.548290\pi\) | ||||
−0.151127 | + | 0.988514i | \(0.548290\pi\) | |||||||
\(678\) | 10.2036 | − | 5.89106i | 0.391868 | − | 0.226245i | ||||
\(679\) | −3.74220 | − | 6.48168i | −0.143612 | − | 0.248744i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 2.89645i | − | 0.110992i | ||||||
\(682\) | −1.05252 | − | 0.607674i | −0.0403032 | − | 0.0232690i | ||||
\(683\) | −15.9565 | − | 9.21246i | −0.610557 | − | 0.352505i | 0.162627 | − | 0.986688i | \(-0.448003\pi\) |
−0.773183 | + | 0.634183i | \(0.781337\pi\) | |||||||
\(684\) | − | 6.01418i | − | 0.229958i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.73390 | − | 9.93141i | −0.218921 | − | 0.379183i | ||||
\(687\) | −6.83121 | + | 3.94400i | −0.260627 | + | 0.150473i | ||||
\(688\) | 9.17382 | 0.349749 | ||||||||
\(689\) | 8.31100 | + | 3.37000i | 0.316624 | + | 0.128387i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.5618 | + | 11.8714i | −0.782208 | + | 0.451608i | −0.837212 | − | 0.546878i | \(-0.815816\pi\) |
0.0550042 | + | 0.998486i | \(0.482483\pi\) | |||||||
\(692\) | −6.85138 | − | 11.8669i | −0.260450 | − | 0.451113i | ||||
\(693\) | −0.0756625 | + | 0.131051i | −0.00287418 | + | 0.00497823i | ||||
\(694\) | − | 28.4066i | − | 1.07830i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.62035 | + | 3.24491i | 0.213039 | + | 0.122998i | ||||
\(697\) | − | 66.8992i | − | 2.53399i | ||||||
\(698\) | −1.11889 | + | 1.93797i | −0.0423505 | + | 0.0733532i | ||||
\(699\) | −0.713746 | − | 1.23624i | −0.0269963 | − | 0.0467590i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.52189 | −0.246328 | −0.123164 | − | 0.992386i | \(-0.539304\pi\) | ||||
−0.123164 | + | 0.992386i | \(0.539304\pi\) | |||||||
\(702\) | −3.57109 | + | 0.497314i | −0.134782 | + | 0.0187699i | ||||
\(703\) | −10.5798 | −0.399025 | ||||||||
\(704\) | −0.151430 | + | 0.0874279i | −0.00570722 | + | 0.00329506i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.813287 | − | 1.40866i | 0.0306085 | − | 0.0530154i | ||||
\(707\) | − | 9.14369i | − | 0.343884i | ||||||
\(708\) | −6.09393 | − | 3.51833i | −0.229024 | − | 0.132227i | ||||
\(709\) | −27.5565 | − | 15.9098i | −1.03491 | − | 0.597504i | −0.116521 | − | 0.993188i | \(-0.537174\pi\) |
−0.918387 | + | 0.395684i | \(0.870507\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.74480 | − | 8.21824i | 0.177944 | − | 0.308208i | ||||
\(712\) | −6.56966 | − | 11.3790i | −0.246208 | − | 0.426445i | ||||
\(713\) | −17.5301 | + | 10.1210i | −0.656507 | + | 0.379035i | ||||
\(714\) | 7.07849 | 0.264906 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.1838 | 0.530074 | ||||||||
\(717\) | 9.44692 | − | 5.45418i | 0.352802 | − | 0.203690i | ||||
\(718\) | 17.2307 | + | 29.8444i | 0.643043 | + | 1.11378i | ||||
\(719\) | −11.6970 | + | 20.2597i | −0.436223 | + | 0.755560i | −0.997395 | − | 0.0721392i | \(-0.977017\pi\) |
0.561172 | + | 0.827699i | \(0.310351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.69713 | − | 3.86659i | −0.249414 | − | 0.143999i | ||||
\(722\) | 14.8699 | + | 8.58515i | 0.553401 | + | 0.319506i | ||||
\(723\) | 29.3660i | 1.09213i | ||||||||
\(724\) | 6.88641 | − | 11.9276i | 0.255931 | − | 0.443286i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.49980 | − | 5.48471i | 0.352571 | − | 0.203557i | ||||
\(727\) | −36.0471 | −1.33691 | −0.668457 | − | 0.743750i | \(-0.733045\pi\) | ||||
−0.668457 | + | 0.743750i | \(0.733045\pi\) | |||||||
\(728\) | −2.46127 | + | 1.91799i | −0.0912208 | + | 0.0710853i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.5172 | − | 64.9817i | −1.38762 | − | 2.40344i | ||||
\(732\) | −3.98695 | + | 6.90559i | −0.147362 | + | 0.255238i | ||||
\(733\) | 17.0888i | 0.631189i | 0.948894 | + | 0.315594i | \(0.102204\pi\) | ||||
−0.948894 | + | 0.315594i | \(0.897796\pi\) | |||||||
\(734\) | 12.6735 | + | 7.31703i | 0.467787 | + | 0.270077i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.91228i | 0.107348i | ||||||||
\(737\) | −0.239143 | + | 0.414209i | −0.00880896 | + | 0.0152576i | ||||
\(738\) | −4.08960 | − | 7.08339i | −0.150540 | − | 0.260743i | ||||
\(739\) | −33.4931 | + | 19.3373i | −1.23206 | + | 0.711333i | −0.967460 | − | 0.253024i | \(-0.918575\pi\) |
−0.264604 | + | 0.964357i | \(0.585241\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.14836 | − | 20.0952i | 0.299337 | − | 0.738217i | ||||
\(742\) | −2.15262 | −0.0790250 | ||||||||
\(743\) | 0.390632 | − | 0.225532i | 0.0143309 | − | 0.00827395i | −0.492817 | − | 0.870133i | \(-0.664033\pi\) |
0.507148 | + | 0.861859i | \(0.330700\pi\) | |||||||
\(744\) | 3.47529 | + | 6.01937i | 0.127410 | + | 0.220681i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 22.0739i | 0.808184i | ||||||||
\(747\) | 0.120848 | + | 0.0697718i | 0.00442161 | + | 0.00255282i | ||||
\(748\) | 1.23857 | + | 0.715090i | 0.0452867 | + | 0.0261463i | ||||
\(749\) | − | 0.744940i | − | 0.0272195i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.1206 | − | 19.2614i | −0.405795 | − | 0.702858i | 0.588618 | − | 0.808411i | \(-0.299672\pi\) |
−0.994414 | + | 0.105553i | \(0.966339\pi\) | |||||||
\(752\) | −10.3075 | + | 5.95105i | −0.375876 | + | 0.217012i | ||||
\(753\) | −17.8942 | −0.652100 | ||||||||
\(754\) | 14.3829 | + | 18.4570i | 0.523796 | + | 0.672165i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.749482 | − | 0.432713i | 0.0272584 | − | 0.0157376i | ||||
\(757\) | 4.21654 | + | 7.30326i | 0.153253 | + | 0.265442i | 0.932421 | − | 0.361373i | \(-0.117692\pi\) |
−0.779169 | + | 0.626814i | \(0.784358\pi\) | |||||||
\(758\) | −6.96127 | + | 12.0573i | −0.252845 | + | 0.437940i | ||||
\(759\) | 0.509229i | 0.0184838i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.3585 | + | 10.5993i | 0.665496 | + | 0.384224i | 0.794368 | − | 0.607437i | \(-0.207802\pi\) |
−0.128872 | + | 0.991661i | \(0.541136\pi\) | |||||||
\(762\) | − | 6.94238i | − | 0.251496i | ||||||
\(763\) | 2.35974 | − | 4.08719i | 0.0854283 | − | 0.147966i | ||||
\(764\) | −2.78821 | − | 4.82932i | −0.100874 | − | 0.174719i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.6089 | 0.889155 | ||||||||
\(767\) | −15.5949 | − | 20.0123i | −0.563099 | − | 0.722601i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −3.34820 | + | 1.93308i | −0.120739 | + | 0.0697088i | −0.559153 | − | 0.829064i | \(-0.688874\pi\) |
0.438414 | + | 0.898773i | \(0.355540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.08945 | + | 10.5472i | −0.219306 | + | 0.379849i | ||||
\(772\) | 0.220810i | 0.00794712i | ||||||||
\(773\) | 28.7898 | + | 16.6218i | 1.03550 | + | 0.597845i | 0.918555 | − | 0.395293i | \(-0.129357\pi\) |
0.116944 | + | 0.993139i | \(0.462690\pi\) | |||||||
\(774\) | −7.94476 | − | 4.58691i | −0.285568 | − | 0.164873i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.32411 | + | 7.48957i | −0.155226 | + | 0.268860i | ||||
\(777\) | −0.761206 | − | 1.31845i | −0.0273081 | − | 0.0472990i | ||||
\(778\) | −4.85823 | + | 2.80490i | −0.174176 | + | 0.100561i | ||||
\(779\) | 49.1911 | 1.76245 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.47692 | 0.0886312 | ||||||||
\(782\) | 20.6288 | − | 11.9100i | 0.737684 | − | 0.425902i | ||||
\(783\) | −3.24491 | − | 5.62035i | −0.115964 | − | 0.200855i | ||||
\(784\) | −3.12552 | + | 5.41356i | −0.111626 | + | 0.193341i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.96703 | − | 1.13567i | −0.0701616 | − | 0.0405078i | ||||
\(787\) | 27.6908 | + | 15.9873i | 0.987071 | + | 0.569886i | 0.904398 | − | 0.426691i | \(-0.140321\pi\) |
0.0826737 | + | 0.996577i | \(0.473654\pi\) | |||||||
\(788\) | 1.72381i | 0.0614082i | ||||||||
\(789\) | 10.5834 | − | 18.3309i | 0.376778 | − | 0.652598i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.83049 | + | 5.09828i | −0.313976 | + | 0.181274i | ||||
\(792\) | 0.174856 | 0.00621323 | ||||||||
\(793\) | −22.6777 | + | 17.6720i | −0.805310 | + | 0.627551i | ||||
\(794\) | −2.36876 | −0.0840643 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.97927 | − | 6.89229i | −0.141041 | − | 0.244291i | ||||
\(797\) | −18.0401 | + | 31.2464i | −0.639014 | + | 1.10680i | 0.346635 | + | 0.938000i | \(0.387324\pi\) |
−0.985649 | + | 0.168805i | \(0.946009\pi\) | |||||||
\(798\) | 5.20483i | 0.184249i | ||||||||
\(799\) | 84.3072 | + | 48.6748i | 2.98257 | + | 1.72199i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.1393i | 0.464255i | ||||||||
\(802\) | 8.25276 | − | 14.2942i | 0.291415 | − | 0.504746i | ||||
\(803\) | 1.12525 | + | 1.94898i | 0.0397091 | + | 0.0687782i | ||||
\(804\) | 2.36886 | − | 1.36766i | 0.0835432 | − | 0.0482337i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.45661 | + | 24.8211i | 0.121754 | + | 0.874286i | ||||
\(807\) | −12.0874 | −0.425498 | ||||||||
\(808\) | −9.15001 | + | 5.28276i | −0.321896 | + | 0.185847i | ||||
\(809\) | −12.4162 | − | 21.5054i | −0.436529 | − | 0.756090i | 0.560890 | − | 0.827890i | \(-0.310459\pi\) |
−0.997419 | + | 0.0718003i | \(0.977126\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.3899i | 0.751102i | 0.926802 | + | 0.375551i | \(0.122547\pi\) | ||||
−0.926802 | + | 0.375551i | \(0.877453\pi\) | |||||||
\(812\) | −4.86400 | − | 2.80823i | −0.170693 | − | 0.0985496i | ||||
\(813\) | 12.7275 | + | 7.34824i | 0.446374 | + | 0.257714i | ||||
\(814\) | − | 0.307597i | − | 0.0107813i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.08960 | − | 7.08339i | −0.143164 | − | 0.247968i | ||||
\(817\) | 47.7812 | − | 27.5865i | 1.67165 | − | 0.965129i | ||||
\(818\) | −33.3071 | −1.16455 | ||||||||
\(819\) | 3.09052 | − | 0.430389i | 0.107991 | − | 0.0150390i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.4938 | − | 16.4509i | 0.994441 | − | 0.574141i | 0.0878420 | − | 0.996134i | \(-0.472003\pi\) |
0.906599 | + | 0.421994i | \(0.138670\pi\) | |||||||
\(822\) | −3.68809 | − | 6.38795i | −0.128637 | − | 0.222805i | ||||
\(823\) | −15.9221 | + | 27.5779i | −0.555010 | + | 0.961306i | 0.442893 | + | 0.896575i | \(0.353952\pi\) |
−0.997903 | + | 0.0647309i | \(0.979381\pi\) | |||||||
\(824\) | 8.93568i | 0.311289i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.27385 | + | 3.04486i | 0.183501 | + | 0.105944i | ||||
\(827\) | − | 1.91814i | − | 0.0667004i | −0.999444 | − | 0.0333502i | \(-0.989382\pi\) | ||
0.999444 | − | 0.0333502i | \(-0.0106177\pi\) | |||||||
\(828\) | 1.45614 | − | 2.52211i | 0.0506044 | − | 0.0876493i | ||||
\(829\) | 13.2223 | + | 22.9016i | 0.459228 | + | 0.795407i | 0.998920 | − | 0.0464558i | \(-0.0147927\pi\) |
−0.539692 | + | 0.841863i | \(0.681459\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.7128 | −0.683828 | ||||||||
\(832\) | 3.34131 | + | 1.35486i | 0.115839 | + | 0.0469713i | ||||
\(833\) | 51.1284 | 1.77149 | ||||||||
\(834\) | 0.710798 | − | 0.410380i | 0.0246129 | − | 0.0142103i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.525807 | + | 0.910724i | −0.0181854 | + | 0.0314981i | ||||
\(837\) | − | 6.95057i | − | 0.240247i | ||||||
\(838\) | −26.2065 | − | 15.1303i | −0.905288 | − | 0.522668i | ||||
\(839\) | −25.9126 | − | 14.9607i | −0.894604 | − | 0.516500i | −0.0191582 | − | 0.999816i | \(-0.506099\pi\) |
−0.875446 | + | 0.483317i | \(0.839432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.55886 | + | 11.3603i | −0.226168 | + | 0.391734i | ||||
\(842\) | −20.1118 | − | 34.8346i | −0.693098 | − | 1.20048i | ||||
\(843\) | 8.60027 | − | 4.96537i | 0.296209 | − | 0.171016i | ||||
\(844\) | 4.21983 | 0.145252 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.9021 | 0.409202 | ||||||||
\(847\) | −8.22138 | + | 4.74662i | −0.282490 | + | 0.163096i | ||||
\(848\) | 1.24367 | + | 2.15410i | 0.0427079 | + | 0.0739723i | ||||
\(849\) | −5.81912 | + | 10.0790i | −0.199712 | + | 0.345911i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.43676 | − | 2.56156i | −0.152090 | − | 0.0878092i | ||||
\(852\) | −12.2677 | − | 7.08275i | −0.420284 | − | 0.242651i | ||||
\(853\) | − | 9.19805i | − | 0.314935i | −0.987524 | − | 0.157468i | \(-0.949667\pi\) | ||
0.987524 | − | 0.157468i | \(-0.0503330\pi\) | |||||||
\(854\) | 3.45041 | − | 5.97629i | 0.118071 | − | 0.204504i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.745455 | + | 0.430389i | −0.0254791 | + | 0.0147104i | ||||
\(857\) | −13.1946 | −0.450720 | −0.225360 | − | 0.974276i | \(-0.572356\pi\) | ||||
−0.225360 | + | 0.974276i | \(0.572356\pi\) | |||||||
\(858\) | 0.584248 | + | 0.236905i | 0.0199459 | + | 0.00808780i | ||||
\(859\) | 52.7575 | 1.80006 | 0.900032 | − | 0.435824i | \(-0.143543\pi\) | ||||
0.900032 | + | 0.435824i | \(0.143543\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.53925 | + | 6.13015i | 0.120617 | + | 0.208915i | ||||
\(862\) | −16.2801 | + | 28.1980i | −0.554502 | + | 0.960426i | ||||
\(863\) | 18.6411i | 0.634551i | 0.948333 | + | 0.317276i | \(0.102768\pi\) | ||||
−0.948333 | + | 0.317276i | \(0.897232\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 30.7327i | − | 1.04434i | ||||||
\(867\) | −24.9496 | + | 43.2139i | −0.847332 | + | 1.46762i | ||||
\(868\) | −3.00761 | − | 5.20933i | −0.102085 | − | 0.176816i | ||||
\(869\) | −1.43701 | + | 0.829657i | −0.0487471 | + | 0.0281442i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.76808 | − | 1.36031i | 0.330979 | − | 0.0460924i | ||||
\(872\) | −5.45336 | −0.184674 | ||||||||
\(873\) | 7.48957 | − | 4.32411i | 0.253484 | − | 0.146349i | ||||
\(874\) | 8.75748 | + | 15.1684i | 0.296226 | + | 0.513079i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 12.8706i | − | 0.434856i | ||||||
\(877\) | −39.3640 | − | 22.7268i | −1.32923 | − | 0.767429i | −0.344047 | − | 0.938953i | \(-0.611798\pi\) |
−0.985180 | + | 0.171523i | \(0.945131\pi\) | |||||||
\(878\) | −5.65380 | − | 3.26422i | −0.190807 | − | 0.110162i | ||||
\(879\) | 13.1527i | 0.443630i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.0027 | + | 17.3252i | 0.337000 | + | 0.583701i | 0.983867 | − | 0.178902i | \(-0.0572545\pi\) |
−0.646867 | + | 0.762603i | \(0.723921\pi\) | |||||||
\(882\) | 5.41356 | − | 3.12552i | 0.182284 | − | 0.105242i | ||||
\(883\) | −29.0388 | −0.977233 | −0.488617 | − | 0.872499i | \(-0.662498\pi\) | ||||
−0.488617 | + | 0.872499i | \(0.662498\pi\) | |||||||
\(884\) | −4.06762 | − | 29.2086i | −0.136809 | − | 0.982392i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 26.2501 | − | 15.1555i | 0.881891 | − | 0.509160i | ||||
\(887\) | 1.43623 | + | 2.48763i | 0.0482240 | + | 0.0835264i | 0.889130 | − | 0.457655i | \(-0.151311\pi\) |
−0.840906 | + | 0.541181i | \(0.817977\pi\) | |||||||
\(888\) | −0.879573 | + | 1.52347i | −0.0295165 | + | 0.0511241i | ||||
\(889\) | 6.00812i | 0.201506i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.151430 | − | 0.0874279i | −0.00507308 | − | 0.00292895i | ||||
\(892\) | − | 6.95276i | − | 0.232795i | ||||||
\(893\) | −35.7906 | + | 61.9912i | −1.19769 | + | 2.07446i | ||||
\(894\) | −5.14284 | − | 8.90766i | −0.172002 | − | 0.297917i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.865427 | −0.0289119 | ||||||||
\(897\) | 8.28251 | − | 6.45428i | 0.276545 | − | 0.215502i | ||||
\(898\) | −15.9388 | −0.531883 | ||||||||
\(899\) | −39.0646 | + | 22.5540i | −1.30288 | + | 0.752217i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.1722 | − | 17.6188i | 0.338886 | − | 0.586968i | ||||
\(902\) | 1.43018i | 0.0476198i | ||||||||
\(903\) | 6.87561 | + | 3.96963i | 0.228806 | + | 0.132101i | ||||
\(904\) | 10.2036 | + | 5.89106i | 0.339367 | + | 0.195934i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.87096 | + | 10.1688i | −0.195050 | + | 0.337836i | ||||
\(907\) | −16.7351 | − | 28.9860i | −0.555679 | − | 0.962464i | −0.997850 | − | 0.0655336i | \(-0.979125\pi\) |
0.442171 | − | 0.896931i | \(-0.354208\pi\) | |||||||
\(908\) | 2.50840 | − | 1.44823i | 0.0832442 | − | 0.0480611i | ||||
\(909\) | 10.5655 | 0.350436 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.7528 | 0.687570 | 0.343785 | − | 0.939048i | \(-0.388291\pi\) | ||||
0.343785 | + | 0.939048i | \(0.388291\pi\) | |||||||
\(912\) | 5.20843 | − | 3.00709i | 0.172468 | − | 0.0995746i | ||||
\(913\) | −0.0122000 | − | 0.0211310i | −0.000403761 | − | 0.000699335i | ||||
\(914\) | −9.90436 | + | 17.1548i | −0.327607 | + | 0.567432i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.83121 | − | 3.94400i | −0.225710 | − | 0.130313i | ||||
\(917\) | 1.70232 | + | 0.982835i | 0.0562156 | + | 0.0324561i | ||||
\(918\) | 8.17919i | 0.269954i | ||||||||
\(919\) | 13.7419 | − | 23.8017i | 0.453304 | − | 0.785146i | −0.545285 | − | 0.838251i | \(-0.683579\pi\) |
0.998589 | + | 0.0531051i | \(0.0169118\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.8699 | + | 7.43044i | −0.424077 | + | 0.244841i | ||||
\(922\) | −13.3828 | −0.440739 | ||||||||
\(923\) | −31.3940 | − | 40.2866i | −1.03335 | − | 1.32605i | ||||
\(924\) | −0.151325 | −0.00497823 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21.1800 | − | 36.6848i | −0.696017 | − | 1.20554i | ||||
\(927\) | 4.46784 | − | 7.73853i | 0.146743 | − | 0.254167i | ||||
\(928\) | 6.48982i | 0.213039i | ||||||||
\(929\) | −8.03305 | − | 4.63788i | −0.263556 | − | 0.152164i | 0.362400 | − | 0.932023i | \(-0.381958\pi\) |
−0.625956 | + | 0.779859i | \(0.715291\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.5948i | 1.23212i | ||||||||
\(932\) | 0.713746 | − | 1.23624i | 0.0233795 | − | 0.0404945i | ||||
\(933\) | −4.58833 | − | 7.94722i | −0.150215 | − | 0.260180i | ||||
\(934\) | 28.9766 | − | 16.7296i | 0.948143 | − | 0.547410i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.21623 | − | 2.84400i | −0.0724398 | − | 0.0929590i | ||||
\(937\) | −15.0600 | −0.491989 | −0.245995 | − | 0.969271i | \(-0.579115\pi\) | ||||
−0.245995 | + | 0.969271i | \(0.579115\pi\) | |||||||
\(938\) | −2.05007 | + | 1.18361i | −0.0669373 | + | 0.0386462i | ||||
\(939\) | −3.71952 | − | 6.44240i | −0.121382 | − | 0.210240i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.4194i | 0.633055i | 0.948583 | + | 0.316528i | \(0.102517\pi\) | ||||
−0.948583 | + | 0.316528i | \(0.897483\pi\) | |||||||
\(942\) | 5.85463 | + | 3.38017i | 0.190754 | + | 0.110132i | ||||
\(943\) | 20.6288 | + | 11.9100i | 0.671766 | + | 0.387844i | ||||
\(944\) | − | 7.03667i | − | 0.229024i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.802048 | + | 1.38919i | 0.0260768 | + | 0.0451664i | ||||
\(947\) | 4.71506 | − | 2.72224i | 0.153219 | − | 0.0884610i | −0.421430 | − | 0.906861i | \(-0.638472\pi\) |
0.574649 | + | 0.818400i | \(0.305138\pi\) | |||||||
\(948\) | 9.48961 | 0.308208 | ||||||||
\(949\) | 17.4378 | − | 43.0046i | 0.566055 | − | 1.39599i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.3011 | + | 12.8755i | −0.723161 | + | 0.417517i | ||||
\(952\) | 3.53925 | + | 6.13015i | 0.114708 | + | 0.198679i | ||||
\(953\) | 11.6768 | − | 20.2248i | 0.378249 | − | 0.655146i | −0.612559 | − | 0.790425i | \(-0.709860\pi\) |
0.990808 | + | 0.135279i | \(0.0431930\pi\) | |||||||
\(954\) | − | 2.48735i | − | 0.0805308i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.44692 | + | 5.45418i | 0.305535 | + | 0.176401i | ||||
\(957\) | 1.13478i | 0.0366823i | ||||||||
\(958\) | 11.1652 | − | 19.3387i | 0.360730 | − | 0.624803i | ||||
\(959\) | 3.19177 | + | 5.52831i | 0.103068 | + | 0.178518i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.3104 | −0.558401 | ||||||||
\(962\) | −5.00301 | + | 3.89867i | −0.161303 | + | 0.125698i | ||||
\(963\) | 0.860777 | 0.0277382 | ||||||||
\(964\) | −25.4317 | + | 14.6830i | −0.819101 | + | 0.472908i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.26018 | + | 2.18270i | −0.0405457 | + | 0.0702272i | ||||
\(967\) | 32.2070i | 1.03571i | 0.855469 | + | 0.517854i | \(0.173269\pi\) | ||||
−0.855469 | + | 0.517854i | \(0.826731\pi\) | |||||||
\(968\) | 9.49980 | + | 5.48471i | 0.305335 | + | 0.176285i | ||||
\(969\) | −42.6007 | − | 24.5955i | −1.36853 | − | 0.790123i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.4181 | + | 26.7049i | −0.494789 | + | 0.857000i | −0.999982 | − | 0.00600636i | \(-0.998088\pi\) |
0.505193 | + | 0.863007i | \(0.331421\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −0.615144 | + | 0.355154i | −0.0197206 | + | 0.0113857i | ||||
\(974\) | −28.7499 | −0.921207 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.97389 | −0.255238 | ||||||||
\(977\) | −18.4521 | + | 10.6533i | −0.590334 | + | 0.340829i | −0.765230 | − | 0.643758i | \(-0.777375\pi\) |
0.174896 | + | 0.984587i | \(0.444041\pi\) | |||||||
\(978\) | −0.713746 | − | 1.23624i | −0.0228231 | − | 0.0395307i | ||||
\(979\) | 1.14874 | − | 1.98968i | 0.0367140 | − | 0.0635905i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.72274 | + | 2.72668i | 0.150786 | + | 0.0870561i | ||||
\(982\) | 13.9005 | + | 8.02546i | 0.443583 | + | 0.256103i | ||||
\(983\) | − | 6.15826i | − | 0.196418i | −0.995166 | − | 0.0982090i | \(-0.968689\pi\) | ||
0.995166 | − | 0.0982090i | \(-0.0313114\pi\) | |||||||
\(984\) | 4.08960 | − | 7.08339i | 0.130372 | − | 0.225810i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 45.9699 | − | 26.5407i | 1.46398 | − | 0.845229i | ||||
\(987\) | −10.3004 | −0.327865 | ||||||||
\(988\) | 21.4772 | − | 2.99093i | 0.683279 | − | 0.0951542i | ||||
\(989\) | 26.7167 | 0.849542 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.46451 | − | 4.26866i | −0.0782877 | − | 0.135598i | 0.824224 | − | 0.566265i | \(-0.191612\pi\) |
−0.902511 | + | 0.430666i | \(0.858279\pi\) | |||||||
\(992\) | −3.47529 | + | 6.01937i | −0.110340 | + | 0.191115i | ||||
\(993\) | − | 6.50437i | − | 0.206410i | ||||||
\(994\) | 10.6168 | + | 6.12960i | 0.336744 | + | 0.194419i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.139544i | 0.00442161i | ||||||||
\(997\) | 11.6988 | − | 20.2628i | 0.370503 | − | 0.641730i | −0.619140 | − | 0.785281i | \(-0.712519\pi\) |
0.989643 | + | 0.143550i | \(0.0458519\pi\) | |||||||
\(998\) | 16.6254 | + | 28.7961i | 0.526269 | + | 0.911524i | ||||
\(999\) | 1.52347 | − | 0.879573i | 0.0482003 | − | 0.0278285i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1950.2.bc.i.751.5 | 12 | ||
5.2 | odd | 4 | 390.2.x.b.49.2 | yes | 12 | ||
5.3 | odd | 4 | 390.2.x.a.49.5 | ✓ | 12 | ||
5.4 | even | 2 | 1950.2.bc.j.751.2 | 12 | |||
13.4 | even | 6 | inner | 1950.2.bc.i.901.5 | 12 | ||
15.2 | even | 4 | 1170.2.bj.c.829.4 | 12 | |||
15.8 | even | 4 | 1170.2.bj.d.829.3 | 12 | |||
65.4 | even | 6 | 1950.2.bc.j.901.2 | 12 | |||
65.17 | odd | 12 | 390.2.x.a.199.5 | yes | 12 | ||
65.43 | odd | 12 | 390.2.x.b.199.2 | yes | 12 | ||
195.17 | even | 12 | 1170.2.bj.d.199.3 | 12 | |||
195.173 | even | 12 | 1170.2.bj.c.199.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.x.a.49.5 | ✓ | 12 | 5.3 | odd | 4 | ||
390.2.x.a.199.5 | yes | 12 | 65.17 | odd | 12 | ||
390.2.x.b.49.2 | yes | 12 | 5.2 | odd | 4 | ||
390.2.x.b.199.2 | yes | 12 | 65.43 | odd | 12 | ||
1170.2.bj.c.199.4 | 12 | 195.173 | even | 12 | |||
1170.2.bj.c.829.4 | 12 | 15.2 | even | 4 | |||
1170.2.bj.d.199.3 | 12 | 195.17 | even | 12 | |||
1170.2.bj.d.829.3 | 12 | 15.8 | even | 4 | |||
1950.2.bc.i.751.5 | 12 | 1.1 | even | 1 | trivial | ||
1950.2.bc.i.901.5 | 12 | 13.4 | even | 6 | inner | ||
1950.2.bc.j.751.2 | 12 | 5.4 | even | 2 | |||
1950.2.bc.j.901.2 | 12 | 65.4 | even | 6 |