Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(127,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, 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("819.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.ct (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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.58891012706304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 316.4 | ||
Root | \(1.34408 - 0.439820i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.316 |
Dual form | 819.2.ct.a.127.4 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.104235 | + | 0.0601799i | 0.0737051 | + | 0.0425536i | 0.536400 | − | 0.843964i | \(-0.319784\pi\) |
−0.462695 | + | 0.886518i | \(0.653117\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.992757 | − | 1.71951i | −0.496378 | − | 0.859753i | ||||
\(5\) | 1.68817i | 0.754971i | 0.926016 | + | 0.377485i | \(0.123211\pi\) | ||||
−0.926016 | + | 0.377485i | \(0.876789\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | − | 0.500000i | 0.327327 | − | 0.188982i | ||||
\(8\) | − | 0.479696i | − | 0.169598i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.101594 | + | 0.175965i | −0.0321267 | + | 0.0556452i | ||||
\(11\) | 0.315769 | + | 0.182309i | 0.0952078 | + | 0.0549682i | 0.546848 | − | 0.837232i | \(-0.315828\pi\) |
−0.451640 | + | 0.892200i | \(0.649161\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.80124 | + | 3.12338i | 0.499575 | + | 0.866271i | ||||
\(14\) | 0.120360 | 0.0321675 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.95665 | + | 3.38901i | −0.489161 | + | 0.847252i | ||||
\(17\) | 1.59277 | + | 2.75877i | 0.386304 | + | 0.669099i | 0.991949 | − | 0.126636i | \(-0.0404181\pi\) |
−0.605645 | + | 0.795735i | \(0.707085\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.25046 | − | 0.721954i | 0.286875 | − | 0.165628i | −0.349657 | − | 0.936878i | \(-0.613702\pi\) |
0.636532 | + | 0.771250i | \(0.280368\pi\) | |||||||
\(20\) | 2.90281 | − | 1.67594i | 0.649088 | − | 0.374751i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0219427 | + | 0.0380059i | 0.00467820 | + | 0.00810288i | ||||
\(23\) | 2.54161 | − | 4.40219i | 0.529962 | − | 0.917920i | −0.469428 | − | 0.882971i | \(-0.655540\pi\) |
0.999389 | − | 0.0349493i | \(-0.0111270\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.15010 | 0.430020 | ||||||||
\(26\) | −0.000212944 | 0.433964i | −4.17617e−5 | 0.0851073i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.71951 | − | 0.992757i | −0.324956 | − | 0.187613i | ||||
\(29\) | 4.09831 | − | 7.09848i | 0.761037 | − | 1.31815i | −0.181280 | − | 0.983432i | \(-0.558024\pi\) |
0.942317 | − | 0.334723i | \(-0.108643\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.69775i | − | 0.843742i | −0.906656 | − | 0.421871i | \(-0.861374\pi\) | ||
0.906656 | − | 0.421871i | \(-0.138626\pi\) | |||||||
\(32\) | −1.23876 | + | 0.715198i | −0.218984 | + | 0.126430i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.383412i | 0.0657546i | ||||||||
\(35\) | 0.844083 | + | 1.46199i | 0.142676 | + | 0.247122i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.46967 | + | 3.15792i | 0.899209 | + | 0.519159i | 0.876943 | − | 0.480594i | \(-0.159579\pi\) |
0.0222655 | + | 0.999752i | \(0.492912\pi\) | |||||||
\(38\) | 0.173789 | 0.0281922 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.809806 | 0.128042 | ||||||||
\(41\) | 5.04661 | + | 2.91366i | 0.788148 | + | 0.455037i | 0.839310 | − | 0.543653i | \(-0.182959\pi\) |
−0.0511624 | + | 0.998690i | \(0.516293\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.386561 | − | 0.669543i | −0.0589500 | − | 0.102104i | 0.835044 | − | 0.550183i | \(-0.185442\pi\) |
−0.893994 | + | 0.448078i | \(0.852109\pi\) | |||||||
\(44\) | − | 0.723954i | − | 0.109140i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.529847 | − | 0.305907i | 0.0781217 | − | 0.0451036i | ||||
\(47\) | 12.7905i | 1.86569i | 0.360275 | + | 0.932846i | \(0.382683\pi\) | ||||
−0.360275 | + | 0.932846i | \(0.617317\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | − | 0.866025i | 0.0714286 | − | 0.123718i | ||||
\(50\) | 0.224115 | + | 0.129393i | 0.0316946 | + | 0.0182989i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.58248 | − | 6.19801i | 0.496800 | − | 0.859509i | ||||
\(53\) | −1.37110 | −0.188334 | −0.0941672 | − | 0.995556i | \(-0.530019\pi\) | ||||
−0.0941672 | + | 0.995556i | \(0.530019\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.307768 | + | 0.533070i | −0.0414994 | + | 0.0718791i | ||||
\(56\) | −0.239848 | − | 0.415429i | −0.0320510 | − | 0.0555140i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.854372 | − | 0.493272i | 0.112185 | − | 0.0647698i | ||||
\(59\) | 8.10770 | − | 4.68098i | 1.05553 | − | 0.609412i | 0.131340 | − | 0.991337i | \(-0.458072\pi\) |
0.924193 | + | 0.381925i | \(0.124739\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.51242 | + | 7.81574i | 0.577756 | + | 1.00070i | 0.995736 | + | 0.0922469i | \(0.0294049\pi\) |
−0.417980 | + | 0.908456i | \(0.637262\pi\) | |||||||
\(62\) | 0.282711 | − | 0.489669i | 0.0359043 | − | 0.0621880i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.65442 | 0.956802 | ||||||||
\(65\) | −5.27279 | + | 3.04080i | −0.654009 | + | 0.377164i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.6705 | − | 6.73797i | −1.42578 | − | 0.823174i | −0.428995 | − | 0.903307i | \(-0.641132\pi\) |
−0.996784 | + | 0.0801330i | \(0.974466\pi\) | |||||||
\(68\) | 3.16247 | − | 5.47757i | 0.383506 | − | 0.664252i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.203187i | 0.0242855i | ||||||||
\(71\) | 6.13246 | − | 3.54058i | 0.727789 | − | 0.420189i | −0.0898239 | − | 0.995958i | \(-0.528630\pi\) |
0.817613 | + | 0.575769i | \(0.195297\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.16083i | 0.252906i | 0.991973 | + | 0.126453i | \(0.0403592\pi\) | ||||
−0.991973 | + | 0.126453i | \(0.959641\pi\) | |||||||
\(74\) | 0.380087 | + | 0.658329i | 0.0441842 | + | 0.0765292i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.48281 | − | 1.43345i | −0.284797 | − | 0.164428i | ||||
\(77\) | 0.364618 | 0.0415521 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.88781 | −0.774940 | −0.387470 | − | 0.921882i | \(-0.626651\pi\) | ||||
−0.387470 | + | 0.921882i | \(0.626651\pi\) | |||||||
\(80\) | −5.72121 | − | 3.30314i | −0.639651 | − | 0.369302i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.350688 | + | 0.607409i | 0.0387270 | + | 0.0670771i | ||||
\(83\) | − | 0.567380i | − | 0.0622780i | −0.999515 | − | 0.0311390i | \(-0.990087\pi\) | ||
0.999515 | − | 0.0311390i | \(-0.00991345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.65725 | + | 2.68887i | −0.505150 | + | 0.291648i | ||||
\(86\) | − | 0.0930528i | − | 0.0100341i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.0874529 | − | 0.151473i | 0.00932251 | − | 0.0161471i | ||||
\(89\) | 0.986346 | + | 0.569467i | 0.104553 | + | 0.0603634i | 0.551364 | − | 0.834264i | \(-0.314107\pi\) |
−0.446812 | + | 0.894628i | \(0.647441\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.12161 | + | 1.80431i | 0.327234 | + | 0.189143i | ||||
\(92\) | −10.0928 | −1.05225 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.769734 | + | 1.33322i | −0.0793920 | + | 0.137511i | ||||
\(95\) | 1.21878 | + | 2.11098i | 0.125044 | + | 0.216582i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.86572 | − | 3.96393i | 0.697109 | − | 0.402476i | −0.109161 | − | 0.994024i | \(-0.534816\pi\) |
0.806270 | + | 0.591548i | \(0.201483\pi\) | |||||||
\(98\) | 0.104235 | − | 0.0601799i | 0.0105293 | − | 0.00607909i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.13452 | − | 3.69710i | −0.213452 | − | 0.369710i | ||||
\(101\) | 7.77322 | − | 13.4636i | 0.773465 | − | 1.33968i | −0.162189 | − | 0.986760i | \(-0.551855\pi\) |
0.935653 | − | 0.352920i | \(-0.114811\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.2982 | −1.01471 | −0.507354 | − | 0.861738i | \(-0.669376\pi\) | ||||
−0.507354 | + | 0.861738i | \(0.669376\pi\) | |||||||
\(104\) | 1.49827 | − | 0.864049i | 0.146918 | − | 0.0847270i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.142916 | − | 0.0825124i | −0.0138812 | − | 0.00801432i | ||||
\(107\) | −6.56220 | + | 11.3661i | −0.634391 | + | 1.09880i | 0.352252 | + | 0.935905i | \(0.385416\pi\) |
−0.986644 | + | 0.162893i | \(0.947917\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.4459i | 1.00054i | 0.865871 | + | 0.500268i | \(0.166765\pi\) | ||||
−0.865871 | + | 0.500268i | \(0.833235\pi\) | |||||||
\(110\) | −0.0641602 | + | 0.0370429i | −0.00611743 | + | 0.00353190i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.91329i | 0.369771i | ||||||||
\(113\) | 2.47631 | + | 4.28909i | 0.232952 | + | 0.403484i | 0.958675 | − | 0.284502i | \(-0.0918283\pi\) |
−0.725724 | + | 0.687986i | \(0.758495\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.43163 | + | 4.29065i | 0.693003 | + | 0.400105i | ||||
\(116\) | −16.2745 | −1.51105 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.12681 | 0.103731 | ||||||||
\(119\) | 2.75877 | + | 1.59277i | 0.252896 | + | 0.146009i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.43353 | − | 9.41114i | −0.493957 | − | 0.855559i | ||||
\(122\) | 1.08623i | 0.0983425i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.07781 | + | 4.66373i | −0.725409 | + | 0.418815i | ||||
\(125\) | 12.0705i | 1.07962i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.03366 | − | 6.98650i | 0.357929 | − | 0.619951i | −0.629686 | − | 0.776850i | \(-0.716816\pi\) |
0.987615 | + | 0.156899i | \(0.0501496\pi\) | |||||||
\(128\) | 3.27537 | + | 1.89104i | 0.289505 | + | 0.167146i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.732603 | 0.000359484i | −0.0642535 | 3.15288e-5i | ||||||
\(131\) | −18.9039 | −1.65164 | −0.825820 | − | 0.563934i | \(-0.809287\pi\) | ||||
−0.825820 | + | 0.563934i | \(0.809287\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.721954 | − | 1.25046i | 0.0626013 | − | 0.108429i | ||||
\(134\) | −0.810981 | − | 1.40466i | −0.0700581 | − | 0.121344i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.32337 | − | 0.764047i | 0.113478 | − | 0.0655165i | ||||
\(137\) | −15.7837 | + | 9.11274i | −1.34850 | + | 0.778554i | −0.988036 | − | 0.154221i | \(-0.950713\pi\) |
−0.360459 | + | 0.932775i | \(0.617380\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.62542 | − | 4.54737i | −0.222686 | − | 0.385703i | 0.732937 | − | 0.680297i | \(-0.238149\pi\) |
−0.955623 | + | 0.294594i | \(0.904816\pi\) | |||||||
\(140\) | 1.67594 | − | 2.90281i | 0.141643 | − | 0.245332i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.852287 | 0.0715223 | ||||||||
\(143\) | −0.000645091 | 1.31465i | −5.39452e−5 | 0.109936i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.9834 | + | 6.91862i | 0.995167 | + | 0.574560i | ||||
\(146\) | −0.130038 | + | 0.225233i | −0.0107621 | + | 0.0186404i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 12.5402i | − | 1.03080i | ||||||
\(149\) | −8.03073 | + | 4.63654i | −0.657903 | + | 0.379841i | −0.791478 | − | 0.611198i | \(-0.790688\pi\) |
0.133574 | + | 0.991039i | \(0.457354\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0132i | 1.14038i | 0.821513 | + | 0.570189i | \(0.193130\pi\) | ||||
−0.821513 | + | 0.570189i | \(0.806870\pi\) | |||||||
\(152\) | −0.346318 | − | 0.599841i | −0.0280901 | − | 0.0486535i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.0380059 | + | 0.0219427i | 0.00306260 | + | 0.00176819i | ||||
\(155\) | 7.93059 | 0.637000 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.1825 | −1.37131 | −0.685656 | − | 0.727925i | \(-0.740485\pi\) | ||||
−0.685656 | + | 0.727925i | \(0.740485\pi\) | |||||||
\(158\) | −0.717949 | − | 0.414508i | −0.0571170 | − | 0.0329765i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.20737 | − | 2.09123i | −0.0954511 | − | 0.165326i | ||||
\(161\) | − | 5.08321i | − | 0.400613i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2128 | − | 5.89637i | 0.799930 | − | 0.461840i | −0.0435169 | − | 0.999053i | \(-0.513856\pi\) |
0.843447 | + | 0.537213i | \(0.180523\pi\) | |||||||
\(164\) | − | 11.5702i | − | 0.903482i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0341449 | − | 0.0591407i | 0.00265016 | − | 0.00459021i | ||||
\(167\) | −3.73852 | − | 2.15843i | −0.289295 | − | 0.167025i | 0.348329 | − | 0.937372i | \(-0.386749\pi\) |
−0.637624 | + | 0.770348i | \(0.720083\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.51105 | + | 11.2519i | −0.500850 | + | 0.865534i | ||||
\(170\) | −0.647263 | −0.0496428 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.767522 | + | 1.32939i | −0.0585230 | + | 0.101365i | ||||
\(173\) | −6.25985 | − | 10.8424i | −0.475928 | − | 0.824331i | 0.523692 | − | 0.851908i | \(-0.324554\pi\) |
−0.999620 | + | 0.0275769i | \(0.991221\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.86204 | − | 1.07505i | 0.140757 | − | 0.0812660i | ||||
\(176\) | −1.23569 | + | 0.713428i | −0.0931440 | + | 0.0537767i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.0685410 | + | 0.118717i | 0.00513737 | + | 0.00889818i | ||||
\(179\) | 3.29767 | − | 5.71173i | 0.246479 | − | 0.426915i | −0.716067 | − | 0.698031i | \(-0.754060\pi\) |
0.962547 | + | 0.271117i | \(0.0873929\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.0157 | −0.818791 | −0.409395 | − | 0.912357i | \(-0.634260\pi\) | ||||
−0.409395 | + | 0.912357i | \(0.634260\pi\) | |||||||
\(182\) | 0.216797 | + | 0.375930i | 0.0160701 | + | 0.0278658i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.11171 | − | 1.21920i | −0.155678 | − | 0.0898805i | ||||
\(185\) | −5.33109 | + | 9.23371i | −0.391949 | + | 0.678876i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.16151i | 0.0849379i | ||||||||
\(188\) | 21.9934 | − | 12.6979i | 1.60403 | − | 0.926089i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.293384i | 0.0212843i | ||||||||
\(191\) | 2.96606 | + | 5.13737i | 0.214617 | + | 0.371727i | 0.953154 | − | 0.302486i | \(-0.0978164\pi\) |
−0.738537 | + | 0.674213i | \(0.764483\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.63380 | + | 2.09798i | 0.261567 | + | 0.151016i | 0.625049 | − | 0.780586i | \(-0.285079\pi\) |
−0.363482 | + | 0.931601i | \(0.618412\pi\) | |||||||
\(194\) | 0.954196 | 0.0685073 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.98551 | −0.141822 | ||||||||
\(197\) | −5.00990 | − | 2.89247i | −0.356941 | − | 0.206080i | 0.310797 | − | 0.950476i | \(-0.399404\pi\) |
−0.667738 | + | 0.744396i | \(0.732737\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.97988 | + | 10.3575i | 0.423903 | + | 0.734221i | 0.996317 | − | 0.0857435i | \(-0.0273266\pi\) |
−0.572415 | + | 0.819964i | \(0.693993\pi\) | |||||||
\(200\) | − | 1.03139i | − | 0.0729305i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.62048 | − | 0.935584i | 0.114017 | − | 0.0658275i | ||||
\(203\) | − | 8.19662i | − | 0.575290i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.91874 | + | 8.51951i | −0.343540 | + | 0.595028i | ||||
\(206\) | −1.07343 | − | 0.619743i | −0.0747891 | − | 0.0431795i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.1096 | − | 0.00692349i | −0.978323 | − | 0.000480057i | ||||
\(209\) | 0.526475 | 0.0364170 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.11795 | − | 7.13251i | 0.283492 | − | 0.491022i | −0.688751 | − | 0.724998i | \(-0.741840\pi\) |
0.972242 | + | 0.233976i | \(0.0751738\pi\) | |||||||
\(212\) | 1.36116 | + | 2.35761i | 0.0934851 | + | 0.161921i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.36802 | + | 0.789825i | −0.0935157 | + | 0.0539913i | ||||
\(215\) | 1.13030 | − | 0.652579i | 0.0770858 | − | 0.0445055i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.34888 | − | 4.06838i | −0.159452 | − | 0.276179i | ||||
\(218\) | −0.628633 | + | 1.08882i | −0.0425764 | + | 0.0737445i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.22215 | 0.0823976 | ||||||||
\(221\) | −5.74771 | + | 9.94405i | −0.386633 | + | 0.668909i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.2515 | + | 7.65073i | 0.887383 | + | 0.512331i | 0.873086 | − | 0.487567i | \(-0.162115\pi\) |
0.0142977 | + | 0.999898i | \(0.495449\pi\) | |||||||
\(224\) | −0.715198 | + | 1.23876i | −0.0477861 | + | 0.0827680i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.596097i | 0.0396518i | ||||||||
\(227\) | 6.02292 | − | 3.47733i | 0.399755 | − | 0.230799i | −0.286623 | − | 0.958043i | \(-0.592533\pi\) |
0.686378 | + | 0.727245i | \(0.259199\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 27.4219i | − | 1.81209i | −0.423180 | − | 0.906045i | \(-0.639086\pi\) | ||
0.423180 | − | 0.906045i | \(-0.360914\pi\) | |||||||
\(230\) | 0.516422 | + | 0.894470i | 0.0340519 | + | 0.0589796i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.40511 | − | 1.96594i | −0.223556 | − | 0.129070i | ||||
\(233\) | −6.85333 | −0.448976 | −0.224488 | − | 0.974477i | \(-0.572071\pi\) | ||||
−0.224488 | + | 0.974477i | \(0.572071\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.5926 | −1.40854 | ||||||||
\(236\) | −16.0980 | − | 9.29416i | −1.04789 | − | 0.604998i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.191706 | + | 0.332045i | 0.0124265 | + | 0.0215233i | ||||
\(239\) | − | 22.0754i | − | 1.42794i | −0.700177 | − | 0.713970i | \(-0.746895\pi\) | ||
0.700177 | − | 0.713970i | \(-0.253105\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.6807 | − | 7.89855i | 0.881251 | − | 0.508790i | 0.0101802 | − | 0.999948i | \(-0.496759\pi\) |
0.871071 | + | 0.491158i | \(0.163426\pi\) | |||||||
\(242\) | − | 1.30796i | − | 0.0840787i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.95947 | − | 15.5183i | 0.573571 | − | 0.993455i | ||||
\(245\) | 1.46199 | + | 0.844083i | 0.0934034 | + | 0.0539265i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.50732 | + | 2.60525i | 0.286794 | + | 0.165768i | ||||
\(248\) | −2.25349 | −0.143097 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.726405 | + | 1.25817i | −0.0459419 | + | 0.0795737i | ||||
\(251\) | −11.2783 | − | 19.5346i | −0.711882 | − | 1.23302i | −0.964150 | − | 0.265359i | \(-0.914510\pi\) |
0.252268 | − | 0.967658i | \(-0.418824\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.60512 | − | 0.926716i | 0.100913 | − | 0.0582621i | ||||
\(254\) | 0.840894 | − | 0.485490i | 0.0527624 | − | 0.0304624i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.42681 | − | 12.8636i | −0.464176 | − | 0.803976i | ||||
\(257\) | −10.2064 | + | 17.6781i | −0.636660 | + | 1.10273i | 0.349501 | + | 0.936936i | \(0.386351\pi\) |
−0.986161 | + | 0.165791i | \(0.946982\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.31584 | 0.392447 | ||||||||
\(260\) | 10.4633 | + | 6.04781i | 0.648904 | + | 0.375069i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.97044 | − | 1.13763i | −0.121734 | − | 0.0702833i | ||||
\(263\) | −14.7701 | + | 25.5826i | −0.910764 | + | 1.57749i | −0.0977768 | + | 0.995208i | \(0.531173\pi\) |
−0.812987 | + | 0.582281i | \(0.802160\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.31464i | − | 0.142187i | ||||||
\(266\) | 0.150505 | − | 0.0868943i | 0.00922807 | − | 0.00532783i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 26.7567i | 1.63442i | ||||||||
\(269\) | 13.9581 | + | 24.1762i | 0.851043 | + | 1.47405i | 0.880268 | + | 0.474477i | \(0.157363\pi\) |
−0.0292252 | + | 0.999573i | \(0.509304\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.5036 | − | 14.7245i | −1.54924 | − | 0.894451i | −0.998200 | − | 0.0599690i | \(-0.980900\pi\) |
−0.551035 | − | 0.834482i | \(-0.685767\pi\) | |||||||
\(272\) | −12.4660 | −0.755861 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.19362 | −0.132521 | ||||||||
\(275\) | 0.678933 | + | 0.391982i | 0.0409412 | + | 0.0236374i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.42927 | + | 5.93967i | 0.206045 | + | 0.356880i | 0.950465 | − | 0.310831i | \(-0.100607\pi\) |
−0.744420 | + | 0.667711i | \(0.767274\pi\) | |||||||
\(278\) | − | 0.631992i | − | 0.0379043i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.701313 | − | 0.404903i | 0.0419114 | − | 0.0241976i | ||||
\(281\) | 29.0940i | 1.73561i | 0.496909 | + | 0.867803i | \(0.334468\pi\) | ||||
−0.496909 | + | 0.867803i | \(0.665532\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.80511 | − | 10.0547i | 0.345078 | − | 0.597692i | −0.640290 | − | 0.768133i | \(-0.721186\pi\) |
0.985368 | + | 0.170441i | \(0.0545192\pi\) | |||||||
\(284\) | −12.1761 | − | 7.02986i | −0.722517 | − | 0.417146i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.0791828 | + | 0.136993i | −0.00468217 | + | 0.00810058i | ||||
\(287\) | 5.82732 | 0.343976 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.42614 | − | 5.93425i | 0.201538 | − | 0.349074i | ||||
\(290\) | 0.832724 | + | 1.44232i | 0.0488993 | + | 0.0846960i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.71555 | − | 2.14517i | 0.217436 | − | 0.125537i | ||||
\(293\) | 15.4054 | − | 8.89430i | 0.899992 | − | 0.519610i | 0.0227942 | − | 0.999740i | \(-0.492744\pi\) |
0.877197 | + | 0.480130i | \(0.159410\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.90228 | + | 13.6871i | 0.460088 | + | 0.796896i | ||||
\(296\) | 1.51484 | − | 2.62378i | 0.0880483 | − | 0.152504i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.11611 | −0.0646544 | ||||||||
\(299\) | 18.3278 | + | 0.00899334i | 1.05992 | + | 0.000520098i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.669543 | − | 0.386561i | −0.0385918 | − | 0.0222810i | ||||
\(302\) | −0.843314 | + | 1.46066i | −0.0485273 | + | 0.0840517i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.65043i | 0.324074i | ||||||||
\(305\) | −13.1943 | + | 7.61771i | −0.755501 | + | 0.436189i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.07966i | 0.518204i | 0.965850 | + | 0.259102i | \(0.0834265\pi\) | ||||
−0.965850 | + | 0.259102i | \(0.916573\pi\) | |||||||
\(308\) | −0.361977 | − | 0.626963i | −0.0206256 | − | 0.0357245i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.826643 | + | 0.477262i | 0.0469501 | + | 0.0271067i | ||||
\(311\) | 1.57073 | 0.0890677 | 0.0445338 | − | 0.999008i | \(-0.485820\pi\) | ||||
0.0445338 | + | 0.999008i | \(0.485820\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.6232 | 1.16569 | 0.582846 | − | 0.812582i | \(-0.301939\pi\) | ||||
0.582846 | + | 0.812582i | \(0.301939\pi\) | |||||||
\(314\) | −1.79101 | − | 1.03404i | −0.101073 | − | 0.0583544i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.83792 | + | 11.8436i | 0.384663 | + | 0.666256i | ||||
\(317\) | − | 30.5435i | − | 1.71549i | −0.514072 | − | 0.857747i | \(-0.671863\pi\) | ||
0.514072 | − | 0.857747i | \(-0.328137\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.58823 | − | 1.49432i | 0.144913 | − | 0.0836657i | ||||
\(320\) | 12.9219i | 0.722358i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.305907 | − | 0.529847i | 0.0170476 | − | 0.0295272i | ||||
\(323\) | 3.98340 | + | 2.29982i | 0.221642 | + | 0.127965i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.87285 | + | 6.71558i | 0.214827 | + | 0.372513i | ||||
\(326\) | 1.41937 | 0.0786118 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.39767 | − | 2.42084i | 0.0771735 | − | 0.133668i | ||||
\(329\) | 6.39527 | + | 11.0769i | 0.352583 | + | 0.610691i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.3894 | + | 12.9265i | −1.23063 | + | 0.710507i | −0.967162 | − | 0.254161i | \(-0.918201\pi\) |
−0.263472 | + | 0.964667i | \(0.584868\pi\) | |||||||
\(332\) | −0.975612 | + | 0.563270i | −0.0535437 | + | 0.0309135i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.259789 | − | 0.449967i | −0.0142150 | − | 0.0246211i | ||||
\(335\) | 11.3748 | − | 19.7017i | 0.621472 | − | 1.07642i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.3954 | −1.16548 | −0.582742 | − | 0.812657i | \(-0.698020\pi\) | ||||
−0.582742 | + | 0.812657i | \(0.698020\pi\) | |||||||
\(338\) | −1.35582 | + | 0.781009i | −0.0737468 | + | 0.0424813i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.24704 | + | 5.33878i | 0.501491 | + | 0.289536i | ||||
\(341\) | 0.856443 | − | 1.48340i | 0.0463790 | − | 0.0803308i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −0.321177 | + | 0.185432i | −0.0173167 | + | 0.00999781i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 1.50687i | − | 0.0810098i | ||||||
\(347\) | 1.10442 | + | 1.91291i | 0.0592882 | + | 0.102690i | 0.894146 | − | 0.447775i | \(-0.147784\pi\) |
−0.834858 | + | 0.550466i | \(0.814450\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.77843 | − | 5.64558i | −0.523427 | − | 0.302201i | 0.214908 | − | 0.976634i | \(-0.431055\pi\) |
−0.738336 | + | 0.674433i | \(0.764388\pi\) | |||||||
\(350\) | 0.258786 | 0.0138327 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.521548 | −0.0277986 | ||||||||
\(353\) | 30.8680 | + | 17.8217i | 1.64294 | + | 0.948552i | 0.979781 | + | 0.200072i | \(0.0641177\pi\) |
0.663158 | + | 0.748479i | \(0.269216\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.97708 | + | 10.3526i | 0.317230 | + | 0.549459i | ||||
\(356\) | − | 2.26137i | − | 0.119852i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.687464 | − | 0.396907i | 0.0363336 | − | 0.0209772i | ||||
\(359\) | − | 19.3218i | − | 1.01976i | −0.860244 | − | 0.509882i | \(-0.829689\pi\) | ||
0.860244 | − | 0.509882i | \(-0.170311\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.45757 | + | 14.6489i | −0.445135 | + | 0.770997i | ||||
\(362\) | −1.14822 | − | 0.662924i | −0.0603490 | − | 0.0348425i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.00351282 | − | 7.15887i | 0.000184122 | − | 0.375227i | ||||
\(365\) | −3.64783 | −0.190936 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.86032 | − | 3.22218i | 0.0971082 | − | 0.168196i | −0.813378 | − | 0.581735i | \(-0.802374\pi\) |
0.910487 | + | 0.413539i | \(0.135707\pi\) | |||||||
\(368\) | 9.94604 | + | 17.2271i | 0.518473 | + | 0.898022i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.11137 | + | 0.641649i | −0.0577773 | + | 0.0333578i | ||||
\(371\) | −1.18740 | + | 0.685548i | −0.0616469 | + | 0.0355919i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.75638 | + | 3.04214i | 0.0909420 | + | 0.157516i | 0.907908 | − | 0.419170i | \(-0.137679\pi\) |
−0.816966 | + | 0.576686i | \(0.804346\pi\) | |||||||
\(374\) | −0.0698995 | + | 0.121070i | −0.00361442 | + | 0.00626035i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.13557 | 0.316418 | ||||||||
\(377\) | 29.5533 | + | 0.0145016i | 1.52207 | + | 0.000746873i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.6647 | + | 12.5081i | 1.11284 | + | 0.642500i | 0.939564 | − | 0.342373i | \(-0.111230\pi\) |
0.173279 | + | 0.984873i | \(0.444564\pi\) | |||||||
\(380\) | 2.41990 | − | 4.19139i | 0.124138 | − | 0.215014i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.713990i | 0.0365309i | ||||||||
\(383\) | 19.4556 | − | 11.2327i | 0.994134 | − | 0.573964i | 0.0876266 | − | 0.996153i | \(-0.472072\pi\) |
0.906507 | + | 0.422190i | \(0.138738\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.615536i | 0.0313706i | ||||||||
\(386\) | 0.252512 | + | 0.437364i | 0.0128525 | + | 0.0222612i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.6320 | − | 7.87043i | −0.692059 | − | 0.399561i | ||||
\(389\) | −13.3364 | −0.676184 | −0.338092 | − | 0.941113i | \(-0.609781\pi\) | ||||
−0.338092 | + | 0.941113i | \(0.609781\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.1928 | 0.818906 | ||||||||
\(392\) | −0.415429 | − | 0.239848i | −0.0209823 | − | 0.0121142i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.348137 | − | 0.602991i | −0.0175389 | − | 0.0303783i | ||||
\(395\) | − | 11.6278i | − | 0.585057i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.3723 | + | 12.9166i | −1.12283 | + | 0.648268i | −0.942123 | − | 0.335268i | \(-0.891173\pi\) |
−0.180710 | + | 0.983536i | \(0.557840\pi\) | |||||||
\(398\) | 1.43948i | 0.0721544i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.20698 | + | 7.28670i | −0.210349 | + | 0.364335i | ||||
\(401\) | −15.2078 | − | 8.78025i | −0.759443 | − | 0.438465i | 0.0696524 | − | 0.997571i | \(-0.477811\pi\) |
−0.829096 | + | 0.559106i | \(0.811144\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.6729 | − | 8.46180i | 0.730909 | − | 0.421512i | ||||
\(404\) | −30.8677 | −1.53572 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.493272 | − | 0.854372i | 0.0244807 | − | 0.0424018i | ||||
\(407\) | 1.15143 | + | 1.99434i | 0.0570745 | + | 0.0988559i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.5818 | − | 7.26410i | 0.622129 | − | 0.359186i | −0.155568 | − | 0.987825i | \(-0.549721\pi\) |
0.777698 | + | 0.628639i | \(0.216388\pi\) | |||||||
\(410\) | −1.02541 | + | 0.592019i | −0.0506412 | + | 0.0292377i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.2236 | + | 17.7077i | 0.503679 | + | 0.872398i | ||||
\(413\) | 4.68098 | − | 8.10770i | 0.230336 | − | 0.398954i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.957831 | 0.0470181 | ||||||||
\(416\) | −4.46514 | − | 2.58087i | −0.218922 | − | 0.126538i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.0548769 | + | 0.0316832i | 0.00268412 | + | 0.00154968i | ||||
\(419\) | −2.30096 | + | 3.98538i | −0.112409 | + | 0.194699i | −0.916741 | − | 0.399482i | \(-0.869190\pi\) |
0.804332 | + | 0.594180i | \(0.202523\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 19.2645i | − | 0.938895i | −0.882960 | − | 0.469447i | \(-0.844453\pi\) | ||
0.882960 | − | 0.469447i | \(-0.155547\pi\) | |||||||
\(422\) | 0.858468 | − | 0.495637i | 0.0417896 | − | 0.0241272i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.657709i | 0.0319412i | ||||||||
\(425\) | 3.42462 | + | 5.93161i | 0.166118 | + | 0.287726i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.81574 | + | 4.51242i | 0.378230 | + | 0.218371i | ||||
\(428\) | 26.0587 | 1.25959 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.157089 | 0.00757548 | ||||||||
\(431\) | 24.5649 | + | 14.1825i | 1.18325 | + | 0.683149i | 0.956764 | − | 0.290865i | \(-0.0939432\pi\) |
0.226485 | + | 0.974015i | \(0.427277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.26014 | − | 10.8429i | −0.300843 | − | 0.521076i | 0.675484 | − | 0.737375i | \(-0.263935\pi\) |
−0.976327 | + | 0.216299i | \(0.930601\pi\) | |||||||
\(434\) | − | 0.565421i | − | 0.0271411i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.9618 | − | 10.3702i | 0.860213 | − | 0.496644i | ||||
\(437\) | − | 7.33969i | − | 0.351105i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.8637 | − | 27.4767i | 0.757132 | − | 1.31139i | −0.187176 | − | 0.982326i | \(-0.559933\pi\) |
0.944307 | − | 0.329064i | \(-0.106733\pi\) | |||||||
\(440\) | 0.255711 | + | 0.147635i | 0.0121906 | + | 0.00703822i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.19754 | + | 0.690619i | −0.0569613 | + | 0.0328494i | ||||
\(443\) | −1.73048 | −0.0822177 | −0.0411088 | − | 0.999155i | \(-0.513089\pi\) | ||||
−0.0411088 | + | 0.999155i | \(0.513089\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.961355 | + | 1.66512i | −0.0455726 | + | 0.0789341i | ||||
\(446\) | 0.920842 | + | 1.59494i | 0.0436031 | + | 0.0755228i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.62892 | − | 3.82721i | 0.313187 | − | 0.180819i | ||||
\(449\) | 9.14208 | − | 5.27818i | 0.431442 | − | 0.249093i | −0.268519 | − | 0.963274i | \(-0.586534\pi\) |
0.699961 | + | 0.714181i | \(0.253201\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.06237 | + | 1.84008i | 0.0500252 | + | 0.0866462i | ||||
\(452\) | 4.91675 | − | 8.51605i | 0.231264 | − | 0.400561i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.837063 | 0.0392853 | ||||||||
\(455\) | −3.04597 | + | 5.26980i | −0.142797 | + | 0.247052i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.88399 | − | 3.97447i | −0.322019 | − | 0.185918i | 0.330273 | − | 0.943885i | \(-0.392859\pi\) |
−0.652292 | + | 0.757968i | \(0.726193\pi\) | |||||||
\(458\) | 1.65025 | − | 2.85832i | 0.0771111 | − | 0.133560i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 17.0383i | − | 0.794415i | ||||||
\(461\) | −9.43262 | + | 5.44592i | −0.439321 | + | 0.253642i | −0.703309 | − | 0.710884i | \(-0.748295\pi\) |
0.263989 | + | 0.964526i | \(0.414962\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 35.8227i | − | 1.66482i | −0.554158 | − | 0.832411i | \(-0.686960\pi\) | ||
0.554158 | − | 0.832411i | \(-0.313040\pi\) | |||||||
\(464\) | 16.0379 | + | 27.7784i | 0.744539 | + | 1.28958i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.714355 | − | 0.412433i | −0.0330918 | − | 0.0191056i | ||||
\(467\) | 19.8983 | 0.920785 | 0.460393 | − | 0.887715i | \(-0.347709\pi\) | ||||
0.460393 | + | 0.887715i | \(0.347709\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.4759 | −0.622261 | ||||||||
\(470\) | −2.25069 | − | 1.29944i | −0.103817 | − | 0.0599386i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.24545 | − | 3.88923i | −0.103355 | − | 0.179016i | ||||
\(473\) | − | 0.281894i | − | 0.0129615i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.68861 | − | 1.55227i | 0.123362 | − | 0.0712231i | ||||
\(476\) | − | 6.32495i | − | 0.289904i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.32850 | − | 2.30102i | 0.0607640 | − | 0.105246i | ||||
\(479\) | −22.7680 | − | 13.1451i | −1.04030 | − | 0.600615i | −0.120379 | − | 0.992728i | \(-0.538411\pi\) |
−0.919917 | + | 0.392113i | \(0.871744\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0111741 | + | 22.7721i | −0.000509496 | + | 1.03832i | ||||
\(482\) | 1.90134 | 0.0866035 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.7883 | + | 18.6860i | −0.490379 | + | 0.849362i | ||||
\(485\) | 6.69177 | + | 11.5905i | 0.303857 | + | 0.526296i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.52491 | − | 3.18981i | 0.250358 | − | 0.144544i | −0.369570 | − | 0.929203i | \(-0.620495\pi\) |
0.619928 | + | 0.784659i | \(0.287162\pi\) | |||||||
\(488\) | 3.74918 | − | 2.16459i | 0.169717 | − | 0.0979864i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.101594 | + | 0.175965i | 0.00458954 | + | 0.00794931i | ||||
\(491\) | 1.48384 | − | 2.57008i | 0.0669647 | − | 0.115986i | −0.830599 | − | 0.556871i | \(-0.812002\pi\) |
0.897564 | + | 0.440885i | \(0.145335\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.1107 | 1.17597 | ||||||||
\(494\) | 0.313035 | + | 0.542808i | 0.0140841 | + | 0.0244221i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.9207 | + | 9.19184i | 0.714862 | + | 0.412726i | ||||
\(497\) | 3.54058 | − | 6.13246i | 0.158817 | − | 0.275078i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 28.1331i | − | 1.25941i | −0.776835 | − | 0.629704i | \(-0.783176\pi\) | ||
0.776835 | − | 0.629704i | \(-0.216824\pi\) | |||||||
\(500\) | 20.7554 | − | 11.9831i | 0.928208 | − | 0.535901i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 2.71492i | − | 0.121173i | ||||||
\(503\) | −15.7688 | − | 27.3124i | −0.703097 | − | 1.21780i | −0.967374 | − | 0.253353i | \(-0.918467\pi\) |
0.264277 | − | 0.964447i | \(-0.414867\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.7288 | + | 13.1225i | 1.01142 | + | 0.583943i | ||||
\(506\) | 0.223079 | 0.00991706 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.0178 | −0.710673 | ||||||||
\(509\) | −11.7731 | − | 6.79719i | −0.521832 | − | 0.301280i | 0.215852 | − | 0.976426i | \(-0.430747\pi\) |
−0.737684 | + | 0.675146i | \(0.764081\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.08041 | + | 1.87133i | 0.0477947 | + | 0.0827828i | ||||
\(512\) | − | 9.35193i | − | 0.413301i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.12773 | + | 1.22845i | −0.0938502 | + | 0.0541844i | ||||
\(515\) | − | 17.3850i | − | 0.766074i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.33183 | + | 4.03885i | −0.102554 | + | 0.177628i | ||||
\(518\) | 0.658329 | + | 0.380087i | 0.0289253 | + | 0.0167000i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.45866 | + | 2.52933i | 0.0639664 | + | 0.110919i | ||||
\(521\) | −8.78344 | −0.384810 | −0.192405 | − | 0.981316i | \(-0.561629\pi\) | ||||
−0.192405 | + | 0.981316i | \(0.561629\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.2849 | + | 28.2063i | −0.712088 | + | 1.23337i | 0.251983 | + | 0.967732i | \(0.418917\pi\) |
−0.964072 | + | 0.265642i | \(0.914416\pi\) | |||||||
\(524\) | 18.7670 | + | 32.5053i | 0.819838 | + | 1.42000i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.07912 | + | 1.77773i | −0.134256 | + | 0.0775127i | ||||
\(527\) | 12.9600 | − | 7.48246i | 0.564547 | − | 0.325941i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.41953 | − | 2.45869i | −0.0617185 | − | 0.106900i | ||||
\(530\) | 0.139295 | − | 0.241265i | 0.00605057 | − | 0.0104799i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.86690 | −0.124296 | ||||||||
\(533\) | −0.0103098 | + | 21.0107i | −0.000446568 | + | 0.910074i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.1878 | − | 11.0781i | −0.829560 | − | 0.478947i | ||||
\(536\) | −3.23218 | + | 5.59829i | −0.139609 | + | 0.241809i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.36000i | 0.144860i | ||||||||
\(539\) | 0.315769 | − | 0.182309i | 0.0136011 | − | 0.00785261i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 6.94870i | − | 0.298748i | −0.988781 | − | 0.149374i | \(-0.952274\pi\) | ||
0.988781 | − | 0.149374i | \(-0.0477258\pi\) | |||||||
\(542\) | −1.77224 | − | 3.06961i | −0.0761243 | − | 0.131851i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.94612 | − | 2.27830i | −0.169189 | − | 0.0976811i | ||||
\(545\) | −17.6344 | −0.755375 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.9095 | 0.466457 | 0.233229 | − | 0.972422i | \(-0.425071\pi\) | ||||
0.233229 | + | 0.972422i | \(0.425071\pi\) | |||||||
\(548\) | 31.3388 | + | 18.0935i | 1.33873 | + | 0.772915i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.0471789 | + | 0.0817163i | 0.00201172 | + | 0.00348440i | ||||
\(551\) | − | 11.8352i | − | 0.504194i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.96502 | + | 3.44391i | −0.253659 | + | 0.146450i | ||||
\(554\) | 0.825493i | 0.0350718i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.21282 | + | 9.02886i | −0.221073 | + | 0.382909i | ||||
\(557\) | −29.9901 | − | 17.3148i | −1.27072 | − | 0.733650i | −0.295596 | − | 0.955313i | \(-0.595518\pi\) |
−0.975123 | + | 0.221662i | \(0.928852\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.39495 | − | 2.41339i | 0.0590001 | − | 0.102075i | ||||
\(560\) | −6.60628 | −0.279166 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.75088 | + | 3.03261i | −0.0738563 | + | 0.127923i | ||||
\(563\) | −4.56839 | − | 7.91269i | −0.192535 | − | 0.333480i | 0.753555 | − | 0.657385i | \(-0.228338\pi\) |
−0.946090 | + | 0.323905i | \(0.895004\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.24070 | + | 4.18042i | −0.304618 | + | 0.175872i | ||||
\(566\) | 1.21019 | − | 0.698702i | 0.0508680 | − | 0.0293686i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.69840 | − | 2.94172i | −0.0712633 | − | 0.123432i | ||||
\(569\) | −9.15000 | + | 15.8483i | −0.383588 | + | 0.664394i | −0.991572 | − | 0.129555i | \(-0.958645\pi\) |
0.607984 | + | 0.793949i | \(0.291978\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.1791 | −0.425981 | −0.212990 | − | 0.977054i | \(-0.568320\pi\) | ||||
−0.212990 | + | 0.977054i | \(0.568320\pi\) | |||||||
\(572\) | 2.26119 | − | 1.30402i | 0.0945450 | − | 0.0545237i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.607409 | + | 0.350688i | 0.0253528 | + | 0.0146374i | ||||
\(575\) | 5.46470 | − | 9.46514i | 0.227894 | − | 0.394724i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.5165i | 0.812482i | 0.913766 | + | 0.406241i | \(0.133161\pi\) | ||||
−0.913766 | + | 0.406241i | \(0.866839\pi\) | |||||||
\(578\) | 0.714246 | − | 0.412370i | 0.0297087 | − | 0.0171523i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 27.4740i | − | 1.14080i | ||||||
\(581\) | −0.283690 | − | 0.491365i | −0.0117694 | − | 0.0203853i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.432949 | − | 0.249963i | −0.0179309 | − | 0.0103524i | ||||
\(584\) | 1.03654 | 0.0428923 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.14103 | 0.0884453 | ||||||||
\(587\) | 30.6486 | + | 17.6950i | 1.26501 | + | 0.730351i | 0.974039 | − | 0.226382i | \(-0.0726898\pi\) |
0.290967 | + | 0.956733i | \(0.406023\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.39156 | − | 5.87436i | −0.139747 | − | 0.242049i | ||||
\(590\) | 1.90223i | 0.0783137i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −21.4044 | + | 12.3579i | −0.879716 | + | 0.507905i | ||||
\(593\) | 18.0881i | 0.742790i | 0.928475 | + | 0.371395i | \(0.121120\pi\) | ||||
−0.928475 | + | 0.371395i | \(0.878880\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.68887 | + | 4.65725i | −0.110233 | + | 0.190929i | ||||
\(596\) | 15.9451 | + | 9.20592i | 0.653138 | + | 0.377089i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.90985 | + | 1.10390i | 0.0780996 | + | 0.0451419i | ||||
\(599\) | −9.05992 | −0.370178 | −0.185089 | − | 0.982722i | \(-0.559257\pi\) | ||||
−0.185089 | + | 0.982722i | \(0.559257\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.6440 | + | 25.3642i | −0.597343 | + | 1.03463i | 0.395869 | + | 0.918307i | \(0.370444\pi\) |
−0.993212 | + | 0.116321i | \(0.962890\pi\) | |||||||
\(602\) | −0.0465264 | − | 0.0805861i | −0.00189628 | − | 0.00328444i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 24.0958 | − | 13.9117i | 0.980444 | − | 0.566059i | ||||
\(605\) | 15.8876 | − | 9.17269i | 0.645922 | − | 0.372923i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.6825 | + | 34.0911i | 0.798887 | + | 1.38371i | 0.920341 | + | 0.391116i | \(0.127911\pi\) |
−0.121454 | + | 0.992597i | \(0.538756\pi\) | |||||||
\(608\) | −1.03268 | + | 1.78865i | −0.0418807 | + | 0.0725394i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.83373 | −0.0742457 | ||||||||
\(611\) | −39.9498 | + | 23.0389i | −1.61619 | + | 0.932053i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.79186 | + | 2.76658i | 0.193541 | + | 0.111741i | 0.593639 | − | 0.804731i | \(-0.297691\pi\) |
−0.400098 | + | 0.916472i | \(0.631024\pi\) | |||||||
\(614\) | −0.546413 | + | 0.946416i | −0.0220514 | + | 0.0381942i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 0.174906i | − | 0.00704716i | ||||||
\(617\) | −10.8959 | + | 6.29077i | −0.438654 | + | 0.253257i | −0.703026 | − | 0.711164i | \(-0.748168\pi\) |
0.264373 | + | 0.964421i | \(0.414835\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.3955i | 0.900149i | 0.892991 | + | 0.450075i | \(0.148603\pi\) | ||||
−0.892991 | + | 0.450075i | \(0.851397\pi\) | |||||||
\(620\) | −7.87314 | − | 13.6367i | −0.316193 | − | 0.547662i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.163724 | + | 0.0945262i | 0.00656474 | + | 0.00379015i | ||||
\(623\) | 1.13893 | 0.0456305 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.62659 | −0.385064 | ||||||||
\(626\) | 2.14965 | + | 1.24110i | 0.0859175 | + | 0.0496045i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.0580 | + | 29.5454i | 0.680690 | + | 1.17899i | ||||
\(629\) | 20.1194i | 0.802213i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.68778 | − | 0.974439i | 0.0671894 | − | 0.0387918i | −0.466029 | − | 0.884769i | \(-0.654316\pi\) |
0.533218 | + | 0.845978i | \(0.320982\pi\) | |||||||
\(632\) | 3.30406i | 0.131428i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.83811 | − | 3.18369i | 0.0730005 | − | 0.126441i | ||||
\(635\) | 11.7944 | + | 6.80948i | 0.468045 | + | 0.270226i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.60555 | + | 0.00176922i | 0.142857 | + | 7.00992e-5i | ||||
\(638\) | 0.359712 | 0.0142411 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.19238 | + | 5.52937i | −0.126190 | + | 0.218568i | ||||
\(641\) | −5.21051 | − | 9.02487i | −0.205803 | − | 0.356461i | 0.744585 | − | 0.667527i | \(-0.232647\pi\) |
−0.950388 | + | 0.311066i | \(0.899314\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.2247 | − | 7.63531i | 0.521533 | − | 0.301107i | −0.216029 | − | 0.976387i | \(-0.569310\pi\) |
0.737562 | + | 0.675280i | \(0.235977\pi\) | |||||||
\(644\) | −8.74061 | + | 5.04639i | −0.344428 | + | 0.198856i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.276806 | + | 0.479442i | 0.0108908 | + | 0.0188634i | ||||
\(647\) | −8.75328 | + | 15.1611i | −0.344127 | + | 0.596045i | −0.985195 | − | 0.171439i | \(-0.945158\pi\) |
0.641068 | + | 0.767484i | \(0.278492\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.41354 | 0.133993 | ||||||||
\(650\) | −0.000457849 | 0.933064i | −1.79583e−5 | 0.0365978i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.2777 | − | 11.7073i | −0.794136 | − | 0.458494i | ||||
\(653\) | −5.09169 | + | 8.81906i | −0.199253 | + | 0.345117i | −0.948287 | − | 0.317416i | \(-0.897185\pi\) |
0.749033 | + | 0.662532i | \(0.230518\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 31.9129i | − | 1.24694i | ||||||
\(656\) | −19.7488 | + | 11.4020i | −0.771063 | + | 0.445173i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.53947i | 0.0600147i | ||||||||
\(659\) | −21.9294 | − | 37.9828i | −0.854247 | − | 1.47960i | −0.877342 | − | 0.479866i | \(-0.840685\pi\) |
0.0230945 | − | 0.999733i | \(-0.492648\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.5156 | − | 16.4635i | −1.10913 | − | 0.640356i | −0.170526 | − | 0.985353i | \(-0.554547\pi\) |
−0.938604 | + | 0.344997i | \(0.887880\pi\) | |||||||
\(662\) | −3.11167 | −0.120939 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.272170 | −0.0105622 | ||||||||
\(665\) | 2.11098 | + | 1.21878i | 0.0818604 | + | 0.0472621i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.8326 | − | 36.0831i | −0.806640 | − | 1.39714i | ||||
\(668\) | 8.57120i | 0.331630i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.37130 | − | 1.36907i | 0.0916113 | − | 0.0528918i | ||||
\(671\) | 3.29062i | 0.127033i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.3423 | − | 23.1095i | 0.514307 | − | 0.890806i | −0.485555 | − | 0.874206i | \(-0.661383\pi\) |
0.999862 | − | 0.0165997i | \(-0.00528409\pi\) | |||||||
\(674\) | −2.23015 | − | 1.28758i | −0.0859021 | − | 0.0495956i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.8117 | + | 0.0253313i | 0.992756 | + | 0.000974280i | ||||
\(677\) | −29.5328 | −1.13504 | −0.567519 | − | 0.823361i | \(-0.692096\pi\) | ||||
−0.567519 | + | 0.823361i | \(0.692096\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.96393 | − | 6.86572i | 0.152122 | − | 0.263482i | ||||
\(680\) | 1.28984 | + | 2.23406i | 0.0494630 | + | 0.0856725i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.178542 | − | 0.103081i | 0.00683674 | − | 0.00394719i | ||||
\(683\) | 15.8379 | − | 9.14400i | 0.606019 | − | 0.349885i | −0.165387 | − | 0.986229i | \(-0.552887\pi\) |
0.771406 | + | 0.636343i | \(0.219554\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.3838 | − | 26.6456i | −0.587786 | − | 1.01807i | ||||
\(686\) | 0.0601799 | − | 0.104235i | 0.00229768 | − | 0.00397970i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.02545 | 0.115344 | ||||||||
\(689\) | −2.46968 | − | 4.28246i | −0.0940872 | − | 0.163149i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.95525 | − | 5.17031i | −0.340674 | − | 0.196688i | 0.319896 | − | 0.947453i | \(-0.396352\pi\) |
−0.660570 | + | 0.750765i | \(0.729685\pi\) | |||||||
\(692\) | −12.4290 | + | 21.5277i | −0.472480 | + | 0.818360i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.265855i | 0.0100917i | ||||||||
\(695\) | 7.67671 | − | 4.43215i | 0.291194 | − | 0.168121i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.5632i | 0.703131i | ||||||||
\(698\) | −0.679501 | − | 1.17693i | −0.0257195 | − | 0.0445475i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.69710 | − | 2.13452i | −0.139737 | − | 0.0806774i | ||||
\(701\) | −41.6959 | −1.57483 | −0.787415 | − | 0.616423i | \(-0.788581\pi\) | ||||
−0.787415 | + | 0.616423i | \(0.788581\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.11948 | 0.343948 | ||||||||
\(704\) | 2.41702 | + | 1.39547i | 0.0910951 | + | 0.0525938i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.14501 | + | 3.71527i | 0.0807287 | + | 0.139826i | ||||
\(707\) | − | 15.5464i | − | 0.584684i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.00947974 | − | 0.00547313i | 0.000356019 | − | 0.000205548i | −0.499822 | − | 0.866128i | \(-0.666601\pi\) |
0.500178 | + | 0.865923i | \(0.333268\pi\) | |||||||
\(710\) | 1.43880i | 0.0539972i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.273171 | − | 0.473146i | 0.0102375 | − | 0.0177319i | ||||
\(713\) | −20.6804 | − | 11.9398i | −0.774488 | − | 0.447151i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.21935 | − | 0.00108902i | −0.0829988 | − | 4.07271e-5i | ||||
\(716\) | −13.0951 | −0.489388 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.16278 | − | 2.01400i | 0.0433947 | − | 0.0751618i | ||||
\(719\) | 12.7330 | + | 22.0542i | 0.474861 | + | 0.822484i | 0.999586 | − | 0.0287885i | \(-0.00916494\pi\) |
−0.524724 | + | 0.851272i | \(0.675832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.91847 | + | 5.14908i | −0.332141 | + | 0.191762i | ||||
\(722\) | −1.76314 | + | 1.01795i | −0.0656174 | + | 0.0378842i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.9359 | + | 18.9416i | 0.406430 | + | 0.703957i | ||||
\(725\) | 8.81176 | − | 15.2624i | 0.327261 | − | 0.566832i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.5565 | −0.873663 | −0.436831 | − | 0.899543i | \(-0.643899\pi\) | ||||
−0.436831 | + | 0.899543i | \(0.643899\pi\) | |||||||
\(728\) | 0.865519 | − | 1.49743i | 0.0320783 | − | 0.0554983i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.380231 | − | 0.219526i | −0.0140730 | − | 0.00812503i | ||||
\(731\) | 1.23141 | − | 2.13286i | 0.0455453 | − | 0.0788867i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.23249i | 0.230202i | 0.993354 | + | 0.115101i | \(0.0367192\pi\) | ||||
−0.993354 | + | 0.115101i | \(0.963281\pi\) | |||||||
\(734\) | 0.387821 | − | 0.223909i | 0.0143147 | − | 0.00826461i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.27100i | 0.268013i | ||||||||
\(737\) | −2.45679 | − | 4.25528i | −0.0904969 | − | 0.156745i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.12339 | + | 0.648588i | 0.0413244 | + | 0.0238587i | 0.520520 | − | 0.853850i | \(-0.325738\pi\) |
−0.479195 | + | 0.877708i | \(0.659071\pi\) | |||||||
\(740\) | 21.1699 | 0.778221 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.165025 | −0.00605825 | ||||||||
\(743\) | −5.25627 | − | 3.03471i | −0.192834 | − | 0.111333i | 0.400475 | − | 0.916308i | \(-0.368845\pi\) |
−0.593309 | + | 0.804975i | \(0.702179\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.82725 | − | 13.5572i | −0.286768 | − | 0.496697i | ||||
\(746\) | 0.422796i | 0.0154797i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.99722 | − | 1.15310i | 0.0730256 | − | 0.0421613i | ||||
\(749\) | 13.1244i | 0.479555i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.3023 | + | 31.7005i | −0.667860 | + | 1.15677i | 0.310641 | + | 0.950527i | \(0.399456\pi\) |
−0.978501 | + | 0.206241i | \(0.933877\pi\) | |||||||
\(752\) | −43.3473 | − | 25.0266i | −1.58071 | − | 0.912625i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.07961 | + | 1.78003i | 0.112153 | + | 0.0648248i | ||||
\(755\) | −23.6566 | −0.860952 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.83991 | + | 10.1150i | −0.212255 | + | 0.367636i | −0.952420 | − | 0.304789i | \(-0.901414\pi\) |
0.740165 | + | 0.672425i | \(0.234747\pi\) | |||||||
\(758\) | 1.50548 | + | 2.60757i | 0.0546815 | + | 0.0947111i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.01263 | − | 0.584642i | 0.0367320 | − | 0.0212072i | ||||
\(761\) | 34.4408 | − | 19.8844i | 1.24848 | − | 0.720810i | 0.277673 | − | 0.960676i | \(-0.410437\pi\) |
0.970806 | + | 0.239866i | \(0.0771035\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.22295 | + | 9.04641i | 0.189083 | + | 0.327502i | ||||
\(764\) | 5.88916 | − | 10.2003i | 0.213062 | − | 0.369035i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.70393 | 0.0976970 | ||||||||
\(767\) | 29.2245 | + | 16.8919i | 1.05523 | + | 0.609930i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.62507 | − | 4.97969i | −0.311028 | − | 0.179572i | 0.336358 | − | 0.941734i | \(-0.390805\pi\) |
−0.647386 | + | 0.762162i | \(0.724138\pi\) | |||||||
\(770\) | −0.0370429 | + | 0.0641602i | −0.00133493 | + | 0.00231217i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 8.33112i | − | 0.299843i | ||||||
\(773\) | −11.0433 | + | 6.37588i | −0.397201 | + | 0.229324i | −0.685276 | − | 0.728284i | \(-0.740318\pi\) |
0.288074 | + | 0.957608i | \(0.406985\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10.1006i | − | 0.362825i | ||||||
\(776\) | −1.90148 | − | 3.29346i | −0.0682592 | − | 0.118228i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.39012 | − | 0.802586i | −0.0498382 | − | 0.0287741i | ||||
\(779\) | 8.41411 | 0.301467 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.58192 | 0.0923882 | ||||||||
\(782\) | 1.68785 | + | 0.974483i | 0.0603575 | + | 0.0348474i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.95665 | + | 3.38901i | 0.0698802 | + | 0.121036i | ||||
\(785\) | − | 29.0069i | − | 1.03530i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.52380 | − | 4.34387i | 0.268194 | − | 0.154842i | −0.359872 | − | 0.933002i | \(-0.617180\pi\) |
0.628067 | + | 0.778159i | \(0.283846\pi\) | |||||||
\(788\) | 11.4861i | 0.409174i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.699759 | − | 1.21202i | 0.0248963 | − | 0.0431216i | ||||
\(791\) | 4.28909 | + | 2.47631i | 0.152503 | + | 0.0880474i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.2836 | + | 28.1721i | −0.578247 | + | 1.00042i | ||||
\(794\) | −3.10929 | −0.110345 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.8731 | − | 20.5649i | 0.420832 | − | 0.728903i | ||||
\(797\) | −19.3719 | − | 33.5531i | −0.686187 | − | 1.18851i | −0.973062 | − | 0.230543i | \(-0.925950\pi\) |
0.286875 | − | 0.957968i | \(-0.407384\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.2861 | + | 20.3724i | −1.24833 | + | 0.720725i | ||||
\(800\) | −2.66345 | + | 1.53774i | −0.0941672 | + | 0.0543675i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.05679 | − | 1.83041i | −0.0373166 | − | 0.0646342i | ||||
\(803\) | −0.393938 | + | 0.682321i | −0.0139018 | + | 0.0240786i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.58130 | 0.302451 | ||||||||
\(806\) | 2.03866 | + | 0.00100036i | 0.0718086 | + | 3.52361e-5i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.45844 | − | 3.72878i | −0.227207 | − | 0.131178i | ||||
\(809\) | 14.4275 | − | 24.9892i | 0.507244 | − | 0.878573i | −0.492721 | − | 0.870188i | \(-0.663998\pi\) |
0.999965 | − | 0.00838530i | \(-0.00266915\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 12.3917i | − | 0.435131i | −0.976046 | − | 0.217566i | \(-0.930188\pi\) | ||
0.976046 | − | 0.217566i | \(-0.0698116\pi\) | |||||||
\(812\) | −14.0941 | + | 8.13725i | −0.494607 | + | 0.285561i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.277173i | 0.00971491i | ||||||||
\(815\) | 9.95405 | + | 17.2409i | 0.348675 | + | 0.603923i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.966758 | − | 0.558158i | −0.0338226 | − | 0.0195275i | ||||
\(818\) | 1.74861 | 0.0611388 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.5324 | 0.682103 | ||||||||
\(821\) | −35.5277 | − | 20.5119i | −1.23992 | − | 0.715870i | −0.270845 | − | 0.962623i | \(-0.587303\pi\) |
−0.969079 | + | 0.246753i | \(0.920636\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.06806 | − | 1.84994i | −0.0372304 | − | 0.0644849i | 0.846810 | − | 0.531896i | \(-0.178520\pi\) |
−0.884040 | + | 0.467411i | \(0.845187\pi\) | |||||||
\(824\) | 4.93999i | 0.172093i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.975842 | − | 0.563403i | 0.0339539 | − | 0.0196033i | ||||
\(827\) | − | 8.54938i | − | 0.297291i | −0.988891 | − | 0.148645i | \(-0.952509\pi\) | ||
0.988891 | − | 0.148645i | \(-0.0474913\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.37844 | + | 12.7798i | −0.256264 | + | 0.443862i | −0.965238 | − | 0.261373i | \(-0.915825\pi\) |
0.708974 | + | 0.705234i | \(0.249158\pi\) | |||||||
\(830\) | 0.0998392 | + | 0.0576422i | 0.00346547 | + | 0.00200079i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.7875 | + | 23.9077i | 0.477995 | + | 0.828850i | ||||
\(833\) | 3.18555 | 0.110373 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.64379 | − | 6.31123i | 0.126099 | − | 0.218409i | ||||
\(836\) | −0.522661 | − | 0.905276i | −0.0180766 | − | 0.0313096i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.479680 | + | 0.276943i | −0.0165703 | + | 0.00956685i | ||||
\(839\) | −23.3581 | + | 13.4858i | −0.806411 | + | 0.465582i | −0.845708 | − | 0.533646i | \(-0.820822\pi\) |
0.0392968 | + | 0.999228i | \(0.487488\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0923 | − | 33.0687i | −0.658353 | − | 1.14030i | ||||
\(842\) | 1.15934 | − | 2.00803i | 0.0399534 | − | 0.0692013i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.3525 | −0.562877 | ||||||||
\(845\) | −18.9951 | − | 10.9917i | −0.653453 | − | 0.378127i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.41114 | − | 5.43353i | −0.323371 | − | 0.186698i | ||||
\(848\) | 2.68275 | − | 4.64665i | 0.0921259 | − | 0.159567i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.824374i | 0.0282758i | ||||||||
\(851\) | 27.8035 | − | 16.0524i | 0.953092 | − | 0.550268i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.6332i | 0.877665i | 0.898569 | + | 0.438832i | \(0.144608\pi\) | ||||
−0.898569 | + | 0.438832i | \(0.855392\pi\) | |||||||
\(854\) | 0.543114 | + | 0.940702i | 0.0185850 | + | 0.0321902i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.45225 | + | 3.14786i | 0.186354 | + | 0.107592i | ||||
\(857\) | 11.7653 | 0.401894 | 0.200947 | − | 0.979602i | \(-0.435598\pi\) | ||||
0.200947 | + | 0.979602i | \(0.435598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.7761 | −0.742992 | −0.371496 | − | 0.928435i | \(-0.621155\pi\) | ||||
−0.371496 | + | 0.928435i | \(0.621155\pi\) | |||||||
\(860\) | −2.24422 | − | 1.29570i | −0.0765274 | − | 0.0441831i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.70701 | + | 2.95663i | 0.0581410 | + | 0.100703i | ||||
\(863\) | − | 41.0575i | − | 1.39761i | −0.715310 | − | 0.698807i | \(-0.753715\pi\) | ||
0.715310 | − | 0.698807i | \(-0.246285\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.3037 | − | 10.5677i | 0.622345 | − | 0.359311i | ||||
\(866\) | − | 1.50694i | − | 0.0512079i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.66373 | + | 8.07781i | −0.158297 | + | 0.274179i | ||||
\(869\) | −2.17496 | − | 1.25571i | −0.0737803 | − | 0.0425971i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0238420 | − | 48.5882i | 0.000807854 | − | 1.64635i | ||||
\(872\) | 5.01085 | 0.169689 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.441702 | − | 0.765050i | 0.0149408 | − | 0.0258782i | ||||
\(875\) | 6.03527 | + | 10.4534i | 0.204029 | + | 0.353389i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.96788 | − | 3.44556i | 0.201521 | − | 0.116348i | −0.395844 | − | 0.918318i | \(-0.629548\pi\) |
0.597365 | + | 0.801970i | \(0.296214\pi\) | |||||||
\(878\) | 3.30709 | − | 1.90935i | 0.111609 | − | 0.0644374i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.20439 | − | 2.08606i | −0.0405998 | − | 0.0703209i | ||||
\(881\) | 5.32288 | − | 9.21950i | 0.179332 | − | 0.310613i | −0.762320 | − | 0.647201i | \(-0.775940\pi\) |
0.941652 | + | 0.336588i | \(0.109273\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.3844 | 0.719641 | 0.359821 | − | 0.933022i | \(-0.382838\pi\) | ||||
0.359821 | + | 0.933022i | \(0.382838\pi\) | |||||||
\(884\) | 22.8049 | + | 0.0111902i | 0.767012 | + | 0.000376369i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.180376 | − | 0.104140i | −0.00605986 | − | 0.00349866i | ||||
\(887\) | −17.0575 | + | 29.5445i | −0.572735 | + | 0.992007i | 0.423548 | + | 0.905874i | \(0.360784\pi\) |
−0.996284 | + | 0.0861333i | \(0.972549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.06731i | − | 0.270569i | ||||||
\(890\) | −0.200413 | + | 0.115709i | −0.00671786 | + | 0.00387856i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 30.3813i | − | 1.01724i | ||||||
\(893\) | 9.23418 | + | 15.9941i | 0.309010 | + | 0.535221i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.64235 | + | 5.56701i | 0.322308 | + | 0.186085i | ||||
\(896\) | 3.78208 | 0.126350 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.27056 | 0.0423992 | ||||||||
\(899\) | −33.3469 | − | 19.2528i | −1.11218 | − | 0.642118i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.18384 | − | 3.78253i | −0.0727544 | − | 0.126014i | ||||
\(902\) | 0.255734i | 0.00851502i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.05746 | − | 1.18788i | 0.0684301 | − | 0.0395081i | ||||
\(905\) | − | 18.5963i | − | 0.618163i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.0758 | − | 36.5043i | 0.699810 | − | 1.21211i | −0.268723 | − | 0.963218i | \(-0.586601\pi\) |
0.968532 | − | 0.248888i | \(-0.0800652\pi\) | |||||||
\(908\) | −11.9586 | − | 6.90429i | −0.396860 | − | 0.229127i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.634632 | + | 0.365990i | −0.0210379 | + | 0.0121324i | ||||
\(911\) | −20.9947 | −0.695584 | −0.347792 | − | 0.937572i | \(-0.613068\pi\) | ||||
−0.347792 | + | 0.937572i | \(0.613068\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.103438 | − | 0.179161i | 0.00342331 | − | 0.00592935i | ||||
\(914\) | −0.478367 | − | 0.828556i | −0.0158230 | − | 0.0274062i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −47.1521 | + | 27.2233i | −1.55795 | + | 0.899483i | ||||
\(917\) | −16.3712 | + | 9.45194i | −0.540626 | + | 0.312131i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.14699 | + | 12.3789i | 0.235757 | + | 0.408344i | 0.959493 | − | 0.281734i | \(-0.0909096\pi\) |
−0.723735 | + | 0.690078i | \(0.757576\pi\) | |||||||
\(920\) | 2.05821 | − | 3.56492i | 0.0678571 | − | 0.117532i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.31094 | −0.0431736 | ||||||||
\(923\) | 22.1046 | + | 12.7766i | 0.727583 | + | 0.420546i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.7603 | + | 6.78983i | 0.386677 | + | 0.223248i | ||||
\(926\) | 2.15581 | − | 3.73397i | 0.0708443 | − | 0.122706i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11.7244i | 0.384872i | ||||||||
\(929\) | −5.89524 | + | 3.40362i | −0.193416 | + | 0.111669i | −0.593581 | − | 0.804774i | \(-0.702286\pi\) |
0.400164 | + | 0.916443i | \(0.368953\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.44391i | − | 0.0473221i | ||||||
\(932\) | 6.80369 | + | 11.7843i | 0.222862 | + | 0.386009i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.07410 | + | 1.19748i | 0.0678666 | + | 0.0391828i | ||||
\(935\) | −1.96082 | −0.0641256 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.22890 | −0.170821 | −0.0854104 | − | 0.996346i | \(-0.527220\pi\) | ||||
−0.0854104 | + | 0.996346i | \(0.527220\pi\) | |||||||
\(938\) | −1.40466 | − | 0.810981i | −0.0458638 | − | 0.0264795i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 21.4362 | + | 37.1285i | 0.699170 | + | 1.21100i | ||||
\(941\) | 56.4403i | 1.83990i | 0.392033 | + | 0.919951i | \(0.371772\pi\) | ||||
−0.392033 | + | 0.919951i | \(0.628228\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.6530 | − | 14.8108i | 0.835376 | − | 0.482304i | ||||
\(944\) | 36.6361i | 1.19240i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0169644 | − | 0.0293832i | 0.000551559 | − | 0.000955329i | ||||
\(947\) | 5.06648 | + | 2.92513i | 0.164639 | + | 0.0950541i | 0.580055 | − | 0.814577i | \(-0.303031\pi\) |
−0.415417 | + | 0.909631i | \(0.636364\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.74909 | + | 3.89217i | −0.219085 | + | 0.126345i | ||||
\(950\) | 0.373662 | 0.0121232 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.764047 | − | 1.32337i | 0.0247629 | − | 0.0428906i | ||||
\(953\) | 10.8742 | + | 18.8346i | 0.352249 | + | 0.610114i | 0.986643 | − | 0.162896i | \(-0.0520836\pi\) |
−0.634394 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.67273 | + | 5.00720i | −0.280643 | + | 0.162029i | ||||
\(956\) | −37.9588 | + | 21.9155i | −1.22767 | + | 0.708798i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.58214 | − | 2.74035i | −0.0511167 | − | 0.0885368i | ||||
\(959\) | −9.11274 | + | 15.7837i | −0.294266 | + | 0.509683i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.93110 | 0.288100 | ||||||||
\(962\) | −1.37159 | + | 2.37297i | −0.0442217 | + | 0.0765075i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −27.1632 | − | 15.6827i | −0.874868 | − | 0.505105i | ||||
\(965\) | −3.54173 | + | 6.13446i | −0.114012 | + | 0.197475i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.3251i | 0.428507i | 0.976778 | + | 0.214253i | \(0.0687318\pi\) | ||||
−0.976778 | + | 0.214253i | \(0.931268\pi\) | |||||||
\(968\) | −4.51449 | + | 2.60644i | −0.145101 | + | 0.0837742i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.61084i | 0.0517210i | ||||||||
\(971\) | 3.73092 | + | 6.46215i | 0.119731 | + | 0.207380i | 0.919661 | − | 0.392713i | \(-0.128463\pi\) |
−0.799930 | + | 0.600093i | \(0.795130\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.54737 | − | 2.62542i | −0.145782 | − | 0.0841673i | ||||
\(974\) | 0.767850 | 0.0246035 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −35.3168 | −1.13046 | ||||||||
\(977\) | 9.49204 | + | 5.48023i | 0.303677 | + | 0.175328i | 0.644094 | − | 0.764947i | \(-0.277235\pi\) |
−0.340416 | + | 0.940275i | \(0.610568\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.207638 | + | 0.359640i | 0.00663614 | + | 0.0114941i | ||||
\(980\) | − | 3.35188i | − | 0.107072i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.309335 | − | 0.178595i | 0.00987127 | − | 0.00569918i | ||||
\(983\) | − | 16.1441i | − | 0.514918i | −0.966289 | − | 0.257459i | \(-0.917115\pi\) | ||
0.966289 | − | 0.257459i | \(-0.0828852\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.88296 | − | 8.45754i | 0.155584 | − | 0.269480i | ||||
\(986\) | 2.72164 | + | 1.57134i | 0.0866747 | + | 0.0500417i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.00507218 | − | 10.3367i | 0.000161368 | − | 0.328856i | ||||
\(989\) | −3.92994 | −0.124965 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.35748 | + | 5.81533i | −0.106654 | + | 0.184730i | −0.914413 | − | 0.404783i | \(-0.867347\pi\) |
0.807759 | + | 0.589513i | \(0.200680\pi\) | |||||||
\(992\) | 3.35982 | + | 5.81938i | 0.106674 | + | 0.184766i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.738102 | − | 0.426143i | 0.0234112 | − | 0.0135164i | ||||
\(995\) | −17.4851 | + | 10.0950i | −0.554315 | + | 0.320034i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.22057 | + | 15.9705i | 0.292018 | + | 0.505791i | 0.974287 | − | 0.225311i | \(-0.0723399\pi\) |
−0.682269 | + | 0.731102i | \(0.739007\pi\) | |||||||
\(998\) | 1.69305 | − | 2.93244i | 0.0535924 | − | 0.0928248i | ||||
\(999\) | 0 | 0 |
(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 | 819.2.ct.a.316.4 | 12 | ||
3.2 | odd | 2 | 91.2.q.a.43.3 | yes | 12 | ||
12.11 | even | 2 | 1456.2.cc.c.225.3 | 12 | |||
13.10 | even | 6 | inner | 819.2.ct.a.127.4 | 12 | ||
21.2 | odd | 6 | 637.2.k.h.459.4 | 12 | |||
21.5 | even | 6 | 637.2.k.g.459.4 | 12 | |||
21.11 | odd | 6 | 637.2.u.h.30.4 | 12 | |||
21.17 | even | 6 | 637.2.u.i.30.4 | 12 | |||
21.20 | even | 2 | 637.2.q.h.589.3 | 12 | |||
39.17 | odd | 6 | 1183.2.c.i.337.6 | 12 | |||
39.20 | even | 12 | 1183.2.a.m.1.4 | 6 | |||
39.23 | odd | 6 | 91.2.q.a.36.3 | ✓ | 12 | ||
39.32 | even | 12 | 1183.2.a.p.1.3 | 6 | |||
39.35 | odd | 6 | 1183.2.c.i.337.7 | 12 | |||
156.23 | even | 6 | 1456.2.cc.c.673.3 | 12 | |||
273.20 | odd | 12 | 8281.2.a.by.1.4 | 6 | |||
273.23 | odd | 6 | 637.2.u.h.361.4 | 12 | |||
273.62 | even | 6 | 637.2.q.h.491.3 | 12 | |||
273.101 | even | 6 | 637.2.k.g.569.3 | 12 | |||
273.179 | odd | 6 | 637.2.k.h.569.3 | 12 | |||
273.188 | odd | 12 | 8281.2.a.ch.1.3 | 6 | |||
273.257 | even | 6 | 637.2.u.i.361.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.3 | ✓ | 12 | 39.23 | odd | 6 | ||
91.2.q.a.43.3 | yes | 12 | 3.2 | odd | 2 | ||
637.2.k.g.459.4 | 12 | 21.5 | even | 6 | |||
637.2.k.g.569.3 | 12 | 273.101 | even | 6 | |||
637.2.k.h.459.4 | 12 | 21.2 | odd | 6 | |||
637.2.k.h.569.3 | 12 | 273.179 | odd | 6 | |||
637.2.q.h.491.3 | 12 | 273.62 | even | 6 | |||
637.2.q.h.589.3 | 12 | 21.20 | even | 2 | |||
637.2.u.h.30.4 | 12 | 21.11 | odd | 6 | |||
637.2.u.h.361.4 | 12 | 273.23 | odd | 6 | |||
637.2.u.i.30.4 | 12 | 21.17 | even | 6 | |||
637.2.u.i.361.4 | 12 | 273.257 | even | 6 | |||
819.2.ct.a.127.4 | 12 | 13.10 | even | 6 | inner | ||
819.2.ct.a.316.4 | 12 | 1.1 | even | 1 | trivial | ||
1183.2.a.m.1.4 | 6 | 39.20 | even | 12 | |||
1183.2.a.p.1.3 | 6 | 39.32 | even | 12 | |||
1183.2.c.i.337.6 | 12 | 39.17 | odd | 6 | |||
1183.2.c.i.337.7 | 12 | 39.35 | odd | 6 | |||
1456.2.cc.c.225.3 | 12 | 12.11 | even | 2 | |||
1456.2.cc.c.673.3 | 12 | 156.23 | even | 6 | |||
8281.2.a.by.1.4 | 6 | 273.20 | odd | 12 | |||
8281.2.a.ch.1.3 | 6 | 273.188 | odd | 12 |