Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(491,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("637.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.q (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: | \(5.08647060876\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 589.3 | ||
Root | \(1.34408 - 0.439820i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.589 |
Dual form | 637.2.q.h.491.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | 0.462695 | − | 0.886518i | \(-0.346883\pi\) |
−0.536400 | + | 0.843964i | \(0.680216\pi\) | |||||||
\(3\) | −0.291146 | + | 0.504280i | −0.168093 | + | 0.291146i | −0.937749 | − | 0.347313i | \(-0.887094\pi\) |
0.769656 | + | 0.638459i | \(0.220428\pi\) | |||||||
\(4\) | −0.992757 | − | 1.71951i | −0.496378 | − | 0.859753i | ||||
\(5\) | 1.68817i | 0.754971i | 0.926016 | + | 0.377485i | \(0.123211\pi\) | ||||
−0.926016 | + | 0.377485i | \(0.876789\pi\) | |||||||
\(6\) | 0.0606950 | − | 0.0350423i | 0.0247786 | − | 0.0143060i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.479696i | 0.169598i | ||||||||
\(9\) | 1.33047 | + | 2.30444i | 0.443489 | + | 0.768146i | ||||
\(10\) | 0.101594 | − | 0.175965i | 0.0321267 | − | 0.0556452i | ||||
\(11\) | −0.315769 | − | 0.182309i | −0.0952078 | − | 0.0549682i | 0.451640 | − | 0.892200i | \(-0.350839\pi\) |
−0.546848 | + | 0.837232i | \(0.684172\pi\) | |||||||
\(12\) | 1.15615 | 0.333751 | ||||||||
\(13\) | −1.80124 | − | 3.12338i | −0.499575 | − | 0.866271i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.851308 | − | 0.491503i | −0.219807 | − | 0.126905i | ||||
\(16\) | −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 | \(0.707085\pi\) | |||||||
\(18\) | − | 0.320270i | − | 0.0754884i | ||||||
\(19\) | −1.25046 | + | 0.721954i | −0.286875 | + | 0.165628i | −0.636532 | − | 0.771250i | \(-0.719632\pi\) |
0.349657 | + | 0.936878i | \(0.386298\pi\) | |||||||
\(20\) | 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 | \(0.344460\pi\) |
−0.999389 | + | 0.0349493i | \(0.988873\pi\) | |||||||
\(24\) | −0.241901 | − | 0.139662i | −0.0493778 | − | 0.0285083i | ||||
\(25\) | 2.15010 | 0.430020 | ||||||||
\(26\) | −0.000212944 | 0.433964i | −4.17617e−5 | 0.0851073i | ||||||
\(27\) | −3.29632 | −0.634377 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.09831 | + | 7.09848i | −0.761037 | + | 1.31815i | 0.181280 | + | 0.983432i | \(0.441976\pi\) |
−0.942317 | + | 0.334723i | \(0.891357\pi\) | |||||||
\(30\) | 0.0591572 | + | 0.102463i | 0.0108006 | + | 0.0187071i | ||||
\(31\) | 4.69775i | 0.843742i | 0.906656 | + | 0.421871i | \(0.138626\pi\) | ||||
−0.906656 | + | 0.421871i | \(0.861374\pi\) | |||||||
\(32\) | 1.23876 | − | 0.715198i | 0.218984 | − | 0.126430i | ||||
\(33\) | 0.183870 | − | 0.106157i | 0.0320076 | − | 0.0184796i | ||||
\(34\) | − | 0.383412i | − | 0.0657546i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.64166 | − | 4.57549i | 0.440277 | − | 0.762582i | ||||
\(37\) | 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 | ||||||||
\(39\) | 2.09948 | + | 0.00103020i | 0.336186 | + | 0.000164965i | ||||
\(40\) | −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 | ||||||||
\(45\) | −3.89027 | + | 2.24605i | −0.579928 | + | 0.334821i | ||||
\(46\) | 0.529847 | − | 0.305907i | 0.0781217 | − | 0.0451036i | ||||
\(47\) | 12.7905i | 1.86569i | 0.360275 | + | 0.932846i | \(0.382683\pi\) | ||||
−0.360275 | + | 0.932846i | \(0.617317\pi\) | |||||||
\(48\) | −1.13934 | − | 1.97339i | −0.164449 | − | 0.284835i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.224115 | − | 0.129393i | −0.0316946 | − | 0.0182989i | ||||
\(51\) | −1.85492 | −0.259741 | ||||||||
\(52\) | −3.58248 | + | 6.19801i | −0.496800 | + | 0.859509i | ||||
\(53\) | 1.37110 | 0.188334 | 0.0941672 | − | 0.995556i | \(-0.469981\pi\) | ||||
0.0941672 | + | 0.995556i | \(0.469981\pi\) | |||||||
\(54\) | 0.343591 | + | 0.198372i | 0.0467568 | + | 0.0269950i | ||||
\(55\) | 0.307768 | − | 0.533070i | 0.0414994 | − | 0.0718791i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.840776i | − | 0.111363i | ||||||
\(58\) | 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 | \(0.124739\pi\) | |||||||
\(60\) | 1.95177i | 0.251972i | ||||||||
\(61\) | −4.51242 | − | 7.81574i | −0.577756 | − | 1.00070i | −0.995736 | − | 0.0922469i | \(-0.970595\pi\) |
0.417980 | − | 0.908456i | \(-0.362738\pi\) | |||||||
\(62\) | 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 | ||||
\(66\) | −0.0255541 | −0.00314549 | ||||||||
\(67\) | −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 | ||||
\(69\) | −1.47996 | − | 2.56336i | −0.178166 | − | 0.308592i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.13246 | + | 3.54058i | −0.727789 | + | 0.420189i | −0.817613 | − | 0.575769i | \(-0.804703\pi\) |
0.0898239 | + | 0.995958i | \(0.471370\pi\) | |||||||
\(72\) | −1.10543 | + | 0.638220i | −0.130276 | + | 0.0752150i | ||||
\(73\) | − | 2.16083i | − | 0.252906i | −0.991973 | − | 0.126453i | \(-0.959641\pi\) | ||
0.991973 | − | 0.126453i | \(-0.0403592\pi\) | |||||||
\(74\) | −0.380087 | − | 0.658329i | −0.0441842 | − | 0.0765292i | ||||
\(75\) | −0.625992 | + | 1.08425i | −0.0722834 | + | 0.125198i | ||||
\(76\) | 2.48281 | + | 1.43345i | 0.284797 | + | 0.164428i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.218777 | − | 0.126454i | −0.0247716 | − | 0.0143181i | ||||
\(79\) | −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 | ||||
\(81\) | −3.03169 | + | 5.25105i | −0.336855 | + | 0.583450i | ||||
\(82\) | −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 | ||||||||
\(87\) | −2.38641 | − | 4.13339i | −0.255850 | − | 0.443146i | ||||
\(88\) | 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 | \(0.647441\pi\) | |||||||
\(90\) | 0.540669 | 0.0569915 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.0928 | 1.05225 | ||||||||
\(93\) | −2.36898 | − | 1.36773i | −0.245652 | − | 0.141827i | ||||
\(94\) | 0.769734 | − | 1.33322i | 0.0793920 | − | 0.137511i | ||||
\(95\) | −1.21878 | − | 2.11098i | −0.125044 | − | 0.216582i | ||||
\(96\) | 0.832908i | 0.0850083i | ||||||||
\(97\) | −6.86572 | + | 3.96393i | −0.697109 | + | 0.402476i | −0.806270 | − | 0.591548i | \(-0.798517\pi\) |
0.109161 | + | 0.994024i | \(0.465184\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 0.970225i | − | 0.0975113i | ||||||
\(100\) | −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 | \(-0.114811\pi\) | |||||||
\(102\) | 0.193347 | + | 0.111629i | 0.0191442 | + | 0.0110529i | ||||
\(103\) | 10.2982 | 1.01471 | 0.507354 | − | 0.861738i | \(-0.330624\pi\) | ||||
0.507354 | + | 0.861738i | \(0.330624\pi\) | |||||||
\(104\) | 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 | \(-0.614584\pi\) |
0.986644 | − | 0.162893i | \(-0.0520826\pi\) | |||||||
\(108\) | 3.27244 | + | 5.66804i | 0.314891 | + | 0.545407i | ||||
\(109\) | 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 | ||||
\(111\) | −3.18495 | + | 1.83883i | −0.302302 | + | 0.174534i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.47631 | − | 4.28909i | −0.232952 | − | 0.403484i | 0.725724 | − | 0.687986i | \(-0.241505\pi\) |
−0.958675 | + | 0.284502i | \(0.908172\pi\) | |||||||
\(114\) | −0.0505978 | + | 0.0876380i | −0.00473892 | + | 0.00820805i | ||||
\(115\) | −7.43163 | − | 4.29065i | −0.693003 | − | 0.400105i | ||||
\(116\) | 16.2745 | 1.51105 | ||||||||
\(117\) | 4.80115 | − | 8.30642i | 0.443866 | − | 0.767928i | ||||
\(118\) | −1.12681 | −0.103731 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.235772 | − | 0.408369i | 0.0215229 | − | 0.0372788i | ||||
\(121\) | −5.43353 | − | 9.41114i | −0.493957 | − | 0.855559i | ||||
\(122\) | 1.08623i | 0.0983425i | ||||||||
\(123\) | −2.93860 | + | 1.69660i | −0.264965 | + | 0.152977i | ||||
\(124\) | 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 | ||||
\(129\) | 0.450183 | 0.0396364 | ||||||||
\(130\) | −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 | \(0.809287\pi\) | |||||||
\(132\) | −0.365075 | − | 0.210776i | −0.0317757 | − | 0.0183457i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.810981 | + | 1.40466i | 0.0700581 | + | 0.121344i | ||||
\(135\) | − | 5.56473i | − | 0.478936i | ||||||
\(136\) | −1.32337 | + | 0.764047i | −0.113478 | + | 0.0655165i | ||||
\(137\) | 15.7837 | − | 9.11274i | 1.34850 | − | 0.778554i | 0.360459 | − | 0.932775i | \(-0.382620\pi\) |
0.988036 | + | 0.154221i | \(0.0492867\pi\) | |||||||
\(138\) | 0.356255i | 0.0303264i | ||||||||
\(139\) | 2.62542 | + | 4.54737i | 0.222686 | + | 0.385703i | 0.955623 | − | 0.294594i | \(-0.0951843\pi\) |
−0.732937 | + | 0.680297i | \(0.761851\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.45001 | − | 3.72392i | −0.543189 | − | 0.313610i | ||||
\(142\) | 0.852287 | 0.0715223 | ||||||||
\(143\) | −0.000645091 | 1.31465i | −5.39452e−5 | 0.109936i | ||||||
\(144\) | −10.4130 | −0.867751 | ||||||||
\(145\) | −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 | −0.133574 | − | 0.991039i | \(-0.542646\pi\) |
0.791478 | + | 0.611198i | \(0.209312\pi\) | |||||||
\(150\) | 0.130500 | − | 0.0753444i | 0.0106553 | − | 0.00615184i | ||||
\(151\) | 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 | ||||
\(153\) | −4.23827 | + | 7.34090i | −0.342644 | + | 0.593476i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.93059 | −0.637000 | ||||||||
\(156\) | −2.08250 | − | 3.61110i | −0.166734 | − | 0.289119i | ||||
\(157\) | 17.1825 | 1.37131 | 0.685656 | − | 0.727925i | \(-0.259515\pi\) | ||||
0.685656 | + | 0.727925i | \(0.259515\pi\) | |||||||
\(158\) | 0.717949 | + | 0.414508i | 0.0571170 | + | 0.0329765i | ||||
\(159\) | −0.399189 | + | 0.691415i | −0.0316577 | + | 0.0548328i | ||||
\(160\) | 1.20737 | + | 2.09123i | 0.0954511 | + | 0.165326i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.632016 | − | 0.364894i | 0.0496558 | − | 0.0286688i | ||||
\(163\) | 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 | ||||||
\(165\) | 0.179211 | + | 0.310402i | 0.0139515 | + | 0.0241648i | ||||
\(166\) | −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 | ||||||||
\(171\) | −3.32739 | − | 1.92107i | −0.254452 | − | 0.146908i | ||||
\(172\) | −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 | \(0.991221\pi\) | |||||||
\(174\) | 0.574457i | 0.0435494i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.23569 | − | 0.713428i | 0.0931440 | − | 0.0537767i | ||||
\(177\) | 5.45140i | 0.409752i | ||||||||
\(178\) | −0.0685410 | − | 0.118717i | −0.00513737 | − | 0.00889818i | ||||
\(179\) | −3.29767 | + | 5.71173i | −0.246479 | + | 0.426915i | −0.962547 | − | 0.271117i | \(-0.912607\pi\) |
0.716067 | + | 0.698031i | \(0.245940\pi\) | |||||||
\(180\) | 7.72419 | + | 4.45956i | 0.575727 | + | 0.332396i | ||||
\(181\) | 11.0157 | 0.818791 | 0.409395 | − | 0.912357i | \(-0.365740\pi\) | ||||
0.409395 | + | 0.912357i | \(0.365740\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.25509 | 0.388468 | ||||||||
\(184\) | −2.11171 | − | 1.21920i | −0.155678 | − | 0.0898805i | ||||
\(185\) | −5.33109 | + | 9.23371i | −0.391949 | + | 0.678876i | ||||
\(186\) | 0.164620 | + | 0.285130i | 0.0120705 | + | 0.0209068i | ||||
\(187\) | − | 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 | 0.738537 | − | 0.674213i | \(-0.235517\pi\) |
−0.953154 | + | 0.302486i | \(0.902184\pi\) | |||||||
\(192\) | −2.22855 | + | 3.85997i | −0.160832 | + | 0.278569i | ||||
\(193\) | 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 | ||||||||
\(195\) | −0.00173916 | + | 3.54428i | −0.000124544 | + | 0.253811i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00990 | + | 2.89247i | 0.356941 | + | 0.206080i | 0.667738 | − | 0.744396i | \(-0.267263\pi\) |
−0.310797 | + | 0.950476i | \(0.600596\pi\) | |||||||
\(198\) | −0.0583881 | + | 0.101131i | −0.00414946 | + | 0.00718708i | ||||
\(199\) | −5.97988 | − | 10.3575i | −0.423903 | − | 0.734221i | 0.572415 | − | 0.819964i | \(-0.306007\pi\) |
−0.996317 | + | 0.0857435i | \(0.972673\pi\) | |||||||
\(200\) | 1.03139i | 0.0729305i | ||||||||
\(201\) | 6.79564 | − | 3.92347i | 0.479328 | − | 0.276740i | ||||
\(202\) | −1.62048 | + | 0.935584i | −0.114017 | + | 0.0658275i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.84148 | + | 3.18954i | 0.128930 | + | 0.223313i | ||||
\(205\) | −4.91874 | + | 8.51951i | −0.343540 | + | 0.595028i | ||||
\(206\) | −1.07343 | − | 0.619743i | −0.0747891 | − | 0.0431795i | ||||
\(207\) | −13.5261 | −0.940129 | ||||||||
\(208\) | 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 | ||||
\(213\) | − | 4.12330i | − | 0.282524i | ||||||
\(214\) | −1.36802 | + | 0.789825i | −0.0935157 | + | 0.0539913i | ||||
\(215\) | 1.13030 | − | 0.652579i | 0.0770858 | − | 0.0445055i | ||||
\(216\) | − | 1.58123i | − | 0.107589i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.628633 | − | 1.08882i | 0.0425764 | − | 0.0737445i | ||||
\(219\) | 1.08966 | + | 0.629116i | 0.0736325 | + | 0.0425117i | ||||
\(220\) | −1.22215 | −0.0823976 | ||||||||
\(221\) | 5.74771 | − | 9.94405i | 0.386633 | − | 0.668909i | ||||
\(222\) | 0.442643 | 0.0297082 | ||||||||
\(223\) | −13.2515 | − | 7.65073i | −0.887383 | − | 0.512331i | −0.0142977 | − | 0.999898i | \(-0.504551\pi\) |
−0.873086 | + | 0.487567i | \(0.837885\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.86064 | + | 4.95477i | 0.190709 | + | 0.330318i | ||||
\(226\) | 0.596097i | 0.0396518i | ||||||||
\(227\) | 6.02292 | − | 3.47733i | 0.399755 | − | 0.230799i | −0.286623 | − | 0.958043i | \(-0.592533\pi\) |
0.686378 | + | 0.727245i | \(0.259199\pi\) | |||||||
\(228\) | −1.44572 | + | 0.834686i | −0.0957450 | + | 0.0552784i | ||||
\(229\) | 27.4219i | 1.81209i | 0.423180 | + | 0.906045i | \(0.360914\pi\) | ||||
−0.423180 | + | 0.906045i | \(0.639086\pi\) | |||||||
\(230\) | 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 | \(-0.427929\pi\) | ||||
0.224488 | + | 0.974477i | \(0.427929\pi\) | |||||||
\(234\) | −1.00033 | + | 0.576884i | −0.0653933 | + | 0.0377121i | ||||
\(235\) | −21.5926 | −1.40854 | ||||||||
\(236\) | −16.0980 | − | 9.29416i | −1.04789 | − | 0.604998i | ||||
\(237\) | 2.00536 | − | 3.47338i | 0.130262 | − | 0.225621i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.0754i | 1.42794i | 0.700177 | + | 0.713970i | \(0.253105\pi\) | ||||
−0.700177 | + | 0.713970i | \(0.746895\pi\) | |||||||
\(240\) | 3.33141 | − | 1.92339i | 0.215042 | − | 0.124154i | ||||
\(241\) | −13.6807 | + | 7.89855i | −0.881251 | + | 0.508790i | −0.871071 | − | 0.491158i | \(-0.836574\pi\) |
−0.0101802 | + | 0.999948i | \(0.503241\pi\) | |||||||
\(242\) | 1.30796i | 0.0840787i | ||||||||
\(243\) | −6.70981 | − | 11.6217i | −0.430434 | − | 0.745534i | ||||
\(244\) | −8.95947 | + | 15.5183i | −0.573571 | + | 0.993455i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.408405 | 0.0260390 | ||||||||
\(247\) | 4.50732 | + | 2.60525i | 0.286794 | + | 0.165768i | ||||
\(248\) | −2.25349 | −0.143097 | ||||||||
\(249\) | 0.286118 | + | 0.165190i | 0.0181320 | + | 0.0104685i | ||||
\(250\) | 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 | ||||
\(255\) | − | 3.13141i | − | 0.196097i | ||||||
\(256\) | −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 | \(0.946982\pi\) | |||||||
\(258\) | −0.0469247 | − | 0.0270920i | −0.00292140 | − | 0.00168667i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −10.4633 | − | 6.04781i | −0.648904 | − | 0.375069i | ||||
\(261\) | −21.8107 | −1.35005 | ||||||||
\(262\) | 1.97044 | + | 1.13763i | 0.121734 | + | 0.0702833i | ||||
\(263\) | 14.7701 | − | 25.5826i | 0.910764 | − | 1.57749i | 0.0977768 | − | 0.995208i | \(-0.468827\pi\) |
0.812987 | − | 0.582281i | \(-0.197840\pi\) | |||||||
\(264\) | 0.0509231 | + | 0.0882015i | 0.00313410 | + | 0.00542842i | ||||
\(265\) | 2.31464i | 0.142187i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.574342 | + | 0.331596i | −0.0351491 | + | 0.0202934i | ||||
\(268\) | 26.7567i | 1.63442i | ||||||||
\(269\) | 13.9581 | + | 24.1762i | 0.851043 | + | 1.47405i | 0.880268 | + | 0.474477i | \(0.157363\pi\) |
−0.0292252 | + | 0.999573i | \(0.509304\pi\) | |||||||
\(270\) | −0.334885 | + | 0.580038i | −0.0203805 | + | 0.0353000i | ||||
\(271\) | 25.5036 | + | 14.7245i | 1.54924 | + | 0.894451i | 0.998200 | + | 0.0599690i | \(0.0191002\pi\) |
0.551035 | + | 0.834482i | \(0.314233\pi\) | |||||||
\(272\) | −12.4660 | −0.755861 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.19362 | −0.132521 | ||||||||
\(275\) | −0.678933 | − | 0.391982i | −0.0409412 | − | 0.0236374i | ||||
\(276\) | −2.93847 | + | 5.08959i | −0.176875 | + | 0.306357i | ||||
\(277\) | 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 | ||||||
\(279\) | −10.8257 | + | 6.25021i | −0.648117 | + | 0.374190i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 29.0940i | − | 1.73561i | −0.496909 | − | 0.867803i | \(-0.665532\pi\) | ||
0.496909 | − | 0.867803i | \(-0.334468\pi\) | |||||||
\(282\) | 0.448210 | + | 0.776323i | 0.0266905 | + | 0.0462293i | ||||
\(283\) | −5.80511 | + | 10.0547i | −0.345078 | + | 0.597692i | −0.985368 | − | 0.170441i | \(-0.945481\pi\) |
0.640290 | + | 0.768133i | \(0.278814\pi\) | |||||||
\(284\) | 12.1761 | + | 7.02986i | 0.722517 | + | 0.417146i | ||||
\(285\) | 1.41937 | 0.0840761 | ||||||||
\(286\) | 0.0791828 | − | 0.136993i | 0.00468217 | − | 0.00810058i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.29626 | + | 1.90310i | 0.194234 | + | 0.112141i | ||||
\(289\) | 3.42614 | − | 5.93425i | 0.201538 | − | 0.349074i | ||||
\(290\) | 0.832724 | + | 1.44232i | 0.0488993 | + | 0.0846960i | ||||
\(291\) | − | 4.61633i | − | 0.270614i | ||||||
\(292\) | −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 | ||||
\(297\) | 1.04087 | + | 0.600949i | 0.0603976 | + | 0.0348706i | ||||
\(298\) | −1.11611 | −0.0646544 | ||||||||
\(299\) | 18.3278 | + | 0.00899334i | 1.05992 | + | 0.000520098i | ||||
\(300\) | 2.48583 | 0.143520 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.843314 | − | 1.46066i | 0.0485273 | − | 0.0840517i | ||||
\(303\) | 4.52629 | + | 7.83976i | 0.260028 | + | 0.450382i | ||||
\(304\) | − | 5.65043i | − | 0.324074i | ||||||
\(305\) | 13.1943 | − | 7.61771i | 0.755501 | − | 0.436189i | ||||
\(306\) | 0.883550 | − | 0.510118i | 0.0505092 | − | 0.0291615i | ||||
\(307\) | − | 9.07966i | − | 0.518204i | −0.965850 | − | 0.259102i | \(-0.916573\pi\) | ||
0.965850 | − | 0.259102i | \(-0.0834265\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.99827 | + | 5.19315i | −0.170566 | + | 0.295428i | ||||
\(310\) | 0.826643 | + | 0.477262i | 0.0469501 | + | 0.0271067i | ||||
\(311\) | 1.57073 | 0.0890677 | 0.0445338 | − | 0.999008i | \(-0.485820\pi\) | ||||
0.0445338 | + | 0.999008i | \(0.485820\pi\) | |||||||
\(312\) | −0.000494185 | 1.00711i | −2.79777e−5 | 0.0570166i | ||||||
\(313\) | −20.6232 | −1.16569 | −0.582846 | − | 0.812582i | \(-0.698061\pi\) | ||||
−0.582846 | + | 0.812582i | \(0.698061\pi\) | |||||||
\(314\) | −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 | \(0.328137\pi\) | ||||
−0.514072 | + | 0.857747i | \(0.671863\pi\) | |||||||
\(318\) | 0.0832187 | − | 0.0480463i | 0.00466667 | − | 0.00269430i | ||||
\(319\) | 2.58823 | − | 1.49432i | 0.144913 | − | 0.0836657i | ||||
\(320\) | 12.9219i | 0.722358i | ||||||||
\(321\) | 3.82111 | + | 6.61836i | 0.213274 | + | 0.369401i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.98340 | − | 2.29982i | −0.221642 | − | 0.127965i | ||||
\(324\) | 12.0389 | 0.668830 | ||||||||
\(325\) | −3.87285 | − | 6.71558i | −0.214827 | − | 0.372513i | ||||
\(326\) | −1.41937 | −0.0786118 | ||||||||
\(327\) | −5.26765 | − | 3.04128i | −0.291302 | − | 0.168183i | ||||
\(328\) | −1.39767 | + | 2.42084i | −0.0771735 | + | 0.133668i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 0.0431396i | − | 0.00237476i | ||||||
\(331\) | −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 | ||||
\(333\) | 16.8060i | 0.920965i | ||||||||
\(334\) | 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 | ||||
\(339\) | 2.88387 | 0.156630 | ||||||||
\(340\) | 9.24704 | + | 5.33878i | 0.501491 | + | 0.289536i | ||||
\(341\) | 0.856443 | − | 1.48340i | 0.0463790 | − | 0.0803308i | ||||
\(342\) | 0.231220 | + | 0.400485i | 0.0125029 | + | 0.0216557i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.321177 | − | 0.185432i | 0.0173167 | − | 0.00999781i | ||||
\(345\) | 4.32738 | − | 2.49841i | 0.232978 | − | 0.134510i | ||||
\(346\) | 1.50687i | 0.0810098i | ||||||||
\(347\) | −1.10442 | − | 1.91291i | −0.0592882 | − | 0.102690i | 0.834858 | − | 0.550466i | \(-0.185550\pi\) |
−0.894146 | + | 0.447775i | \(0.852216\pi\) | |||||||
\(348\) | −4.73825 | + | 8.20689i | −0.253997 | + | 0.439936i | ||||
\(349\) | 9.77843 | + | 5.64558i | 0.523427 | + | 0.302201i | 0.738336 | − | 0.674433i | \(-0.235612\pi\) |
−0.214908 | + | 0.976634i | \(0.568945\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.93747 | + | 10.2957i | 0.316919 | + | 0.549542i | ||||
\(352\) | −0.521548 | −0.0277986 | ||||||||
\(353\) | 30.8680 | + | 17.8217i | 1.64294 | + | 0.948552i | 0.979781 | + | 0.200072i | \(0.0641177\pi\) |
0.663158 | + | 0.748479i | \(0.269216\pi\) | |||||||
\(354\) | 0.328065 | − | 0.568225i | 0.0174365 | − | 0.0302008i | ||||
\(355\) | −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 | \(0.170311\pi\) | ||||
−0.860244 | + | 0.509882i | \(0.829689\pi\) | |||||||
\(360\) | −1.07742 | − | 1.86615i | −0.0567851 | − | 0.0983546i | ||||
\(361\) | −8.45757 | + | 14.6489i | −0.445135 | + | 0.770997i | ||||
\(362\) | −1.14822 | − | 0.662924i | −0.0603490 | − | 0.0348425i | ||||
\(363\) | 6.32780 | 0.332123 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.64783 | 0.190936 | ||||||||
\(366\) | −0.547763 | − | 0.316251i | −0.0286320 | − | 0.0165307i | ||||
\(367\) | −1.86032 | + | 3.22218i | −0.0971082 | + | 0.168196i | −0.910487 | − | 0.413539i | \(-0.864293\pi\) |
0.813378 | + | 0.581735i | \(0.197626\pi\) | |||||||
\(368\) | −9.94604 | − | 17.2271i | −0.518473 | − | 0.898022i | ||||
\(369\) | 15.5061i | 0.807217i | ||||||||
\(370\) | 1.11137 | − | 0.641649i | 0.0577773 | − | 0.0333578i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.43130i | 0.281600i | ||||||||
\(373\) | 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 | ||||
\(375\) | −6.08693 | − | 3.51429i | −0.314328 | − | 0.181477i | ||||
\(376\) | −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 | ||||
\(381\) | 2.34877 | + | 4.06818i | 0.120331 | + | 0.208419i | ||||
\(382\) | 0.713990i | 0.0365309i | ||||||||
\(383\) | 19.4556 | − | 11.2327i | 0.994134 | − | 0.573964i | 0.0876266 | − | 0.996153i | \(-0.472072\pi\) |
0.906507 | + | 0.422190i | \(0.138738\pi\) | |||||||
\(384\) | 1.90722 | − | 1.10114i | 0.0973276 | − | 0.0561921i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.252512 | − | 0.437364i | −0.0128525 | − | 0.0222612i | ||||
\(387\) | 1.02861 | − | 1.78161i | 0.0522874 | − | 0.0905644i | ||||
\(388\) | 13.6320 | + | 7.87043i | 0.692059 | + | 0.399561i | ||||
\(389\) | 13.3364 | 0.676184 | 0.338092 | − | 0.941113i | \(-0.390219\pi\) | ||||
0.338092 | + | 0.941113i | \(0.390219\pi\) | |||||||
\(390\) | 0.213476 | − | 0.369332i | 0.0108098 | − | 0.0187018i | ||||
\(391\) | −16.1928 | −0.818906 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.50379 | − | 9.53284i | 0.277629 | − | 0.480868i | ||||
\(394\) | −0.348137 | − | 0.602991i | −0.0175389 | − | 0.0303783i | ||||
\(395\) | − | 11.6278i | − | 0.585057i | ||||||
\(396\) | −1.66831 | + | 0.963198i | −0.0838356 | + | 0.0484025i | ||||
\(397\) | 22.3723 | − | 12.9166i | 1.12283 | − | 0.648268i | 0.180710 | − | 0.983536i | \(-0.442160\pi\) |
0.942123 | + | 0.335268i | \(0.108827\pi\) | |||||||
\(398\) | 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 | 0.829096 | − | 0.559106i | \(-0.188856\pi\) |
−0.0696524 | + | 0.997571i | \(0.522189\pi\) | |||||||
\(402\) | −0.944456 | −0.0471052 | ||||||||
\(403\) | 14.6729 | − | 8.46180i | 0.730909 | − | 0.421512i | ||||
\(404\) | −30.8677 | −1.53572 | ||||||||
\(405\) | −8.86464 | − | 5.11800i | −0.440487 | − | 0.254316i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.15143 | − | 1.99434i | −0.0570745 | − | 0.0988559i | ||||
\(408\) | − | 0.889797i | − | 0.0440515i | ||||||
\(409\) | −12.5818 | + | 7.26410i | −0.622129 | + | 0.359186i | −0.777698 | − | 0.628639i | \(-0.783612\pi\) |
0.155568 | + | 0.987825i | \(0.450279\pi\) | |||||||
\(410\) | 1.02541 | − | 0.592019i | 0.0506412 | − | 0.0292377i | ||||
\(411\) | 10.6126i | 0.523479i | ||||||||
\(412\) | −10.2236 | − | 17.7077i | −0.503679 | − | 0.872398i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.40989 | + | 0.814000i | 0.0692923 | + | 0.0400059i | ||||
\(415\) | 0.957831 | 0.0470181 | ||||||||
\(416\) | −4.46514 | − | 2.58087i | −0.218922 | − | 0.126538i | ||||
\(417\) | −3.05753 | −0.149728 | ||||||||
\(418\) | −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 | ||||
\(423\) | −29.4750 | + | 17.0174i | −1.43312 | + | 0.827415i | ||||
\(424\) | 0.657709i | 0.0319412i | ||||||||
\(425\) | 3.42462 | + | 5.93161i | 0.166118 | + | 0.287726i | ||||
\(426\) | −0.248140 | + | 0.429791i | −0.0120224 | + | 0.0208234i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −26.0587 | −1.25959 | ||||||||
\(429\) | −0.662763 | − | 0.383080i | −0.0319985 | − | 0.0184953i | ||||
\(430\) | −0.157089 | −0.00757548 | ||||||||
\(431\) | −24.5649 | − | 14.1825i | −1.18325 | − | 0.683149i | −0.226485 | − | 0.974015i | \(-0.572723\pi\) |
−0.956764 | + | 0.290865i | \(0.906057\pi\) | |||||||
\(432\) | 6.44973 | − | 11.1713i | 0.310313 | − | 0.537477i | ||||
\(433\) | 6.26014 | + | 10.8429i | 0.300843 | + | 0.521076i | 0.976327 | − | 0.216299i | \(-0.0693986\pi\) |
−0.675484 | + | 0.737375i | \(0.736065\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.97784 | − | 4.02866i | 0.334562 | − | 0.193159i | ||||
\(436\) | 17.9618 | − | 10.3702i | 0.860213 | − | 0.496644i | ||||
\(437\) | − | 7.33969i | − | 0.351105i | ||||||
\(438\) | −0.0757203 | − | 0.131151i | −0.00361806 | − | 0.00626666i | ||||
\(439\) | −15.8637 | + | 27.4767i | −0.757132 | + | 1.31139i | 0.187176 | + | 0.982326i | \(0.440067\pi\) |
−0.944307 | + | 0.329064i | \(0.893267\pi\) | |||||||
\(440\) | 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 | \(-0.486911\pi\) | ||||
0.0411088 | + | 0.999155i | \(0.486911\pi\) | |||||||
\(444\) | 6.32376 | + | 3.65102i | 0.300112 | + | 0.173270i | ||||
\(445\) | −0.961355 | + | 1.66512i | −0.0455726 | + | 0.0789341i | ||||
\(446\) | 0.920842 | + | 1.59494i | 0.0436031 | + | 0.0755228i | ||||
\(447\) | 5.39965i | 0.255394i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.14208 | + | 5.27818i | −0.431442 | + | 0.249093i | −0.699961 | − | 0.714181i | \(-0.746799\pi\) |
0.268519 | + | 0.963274i | \(0.413466\pi\) | |||||||
\(450\) | − | 0.688612i | − | 0.0324615i | ||||||
\(451\) | −1.06237 | − | 1.84008i | −0.0500252 | − | 0.0866462i | ||||
\(452\) | −4.91675 | + | 8.51605i | −0.231264 | + | 0.400561i | ||||
\(453\) | −7.06658 | − | 4.07989i | −0.332017 | − | 0.191690i | ||||
\(454\) | −0.837063 | −0.0392853 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.403317 | 0.0188870 | ||||||||
\(457\) | −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 | ||||
\(459\) | −5.25029 | − | 9.09377i | −0.245062 | − | 0.424461i | ||||
\(460\) | 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 | ||||
\(465\) | 2.30896 | − | 3.99923i | 0.107075 | − | 0.185460i | ||||
\(466\) | −0.714355 | − | 0.412433i | −0.0330918 | − | 0.0191056i | ||||
\(467\) | 19.8983 | 0.920785 | 0.460393 | − | 0.887715i | \(-0.347709\pi\) | ||||
0.460393 | + | 0.887715i | \(0.347709\pi\) | |||||||
\(468\) | −19.0493 | − | 0.00934738i | −0.880554 | − | 0.000432083i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.25069 | + | 1.29944i | 0.103817 | + | 0.0599386i | ||||
\(471\) | −5.00262 | + | 8.66479i | −0.230508 | + | 0.399252i | ||||
\(472\) | 2.24545 | + | 3.88923i | 0.103355 | + | 0.179016i | ||||
\(473\) | 0.281894i | 0.0129615i | ||||||||
\(474\) | −0.418056 | + | 0.241365i | −0.0192020 | + | 0.0110863i | ||||
\(475\) | −2.68861 | + | 1.55227i | −0.123362 | + | 0.0712231i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.82420 | + | 3.15960i | 0.0835243 | + | 0.144668i | ||||
\(478\) | 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 | \(0.871744\pi\) | |||||||
\(480\) | −1.40609 | −0.0641788 | ||||||||
\(481\) | 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 | ||||
\(486\) | 1.61518i | 0.0732662i | ||||||||
\(487\) | 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 | ||||
\(489\) | 6.86682i | 0.310528i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.48384 | + | 2.57008i | −0.0669647 | + | 0.115986i | −0.897564 | − | 0.440885i | \(-0.854665\pi\) |
0.830599 | + | 0.556871i | \(0.187998\pi\) | |||||||
\(492\) | 5.83463 | + | 3.36862i | 0.263045 | + | 0.151869i | ||||
\(493\) | −26.1107 | −1.17597 | ||||||||
\(494\) | −0.313035 | − | 0.542808i | −0.0140841 | − | 0.0244221i | ||||
\(495\) | 1.63790 | 0.0736182 | ||||||||
\(496\) | −15.9207 | − | 9.19184i | −0.714862 | − | 0.412726i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.0198823 | − | 0.0344371i | −0.000890947 | − | 0.00154316i | ||||
\(499\) | − | 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 | ||||
\(501\) | 2.17691 | − | 1.25684i | 0.0972571 | − | 0.0561514i | ||||
\(502\) | 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 | ||||||||
\(507\) | −3.77846 | − | 6.55935i | −0.167807 | − | 0.291311i | ||||
\(508\) | −16.0178 | −0.710673 | ||||||||
\(509\) | −11.7731 | − | 6.79719i | −0.521832 | − | 0.301280i | 0.215852 | − | 0.976426i | \(-0.430747\pi\) |
−0.737684 | + | 0.675146i | \(0.764081\pi\) | |||||||
\(510\) | −0.188448 | + | 0.326402i | −0.00834462 | + | 0.0144533i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 9.35193i | 0.413301i | ||||||||
\(513\) | 4.12191 | − | 2.37979i | 0.181987 | − | 0.105070i | ||||
\(514\) | 2.12773 | − | 1.22845i | 0.0938502 | − | 0.0541844i | ||||
\(515\) | 17.3850i | 0.766074i | ||||||||
\(516\) | −0.446922 | − | 0.774091i | −0.0196746 | − | 0.0340775i | ||||
\(517\) | 2.33183 | − | 4.03885i | 0.102554 | − | 0.177628i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.29012 | 0.320001 | ||||||||
\(520\) | 1.45866 | + | 2.52933i | 0.0639664 | + | 0.110919i | ||||
\(521\) | −8.78344 | −0.384810 | −0.192405 | − | 0.981316i | \(-0.561629\pi\) | ||||
−0.192405 | + | 0.981316i | \(0.561629\pi\) | |||||||
\(522\) | 2.27343 | + | 1.31256i | 0.0995053 | + | 0.0574494i | ||||
\(523\) | 16.2849 | − | 28.2063i | 0.712088 | − | 1.23337i | −0.251983 | − | 0.967732i | \(-0.581083\pi\) |
0.964072 | − | 0.265642i | \(-0.0855839\pi\) | |||||||
\(524\) | 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 | ||||
\(528\) | 0.830847i | 0.0361580i | ||||||||
\(529\) | −1.41953 | − | 2.45869i | −0.0617185 | − | 0.106900i | ||||
\(530\) | 0.139295 | − | 0.241265i | 0.00605057 | − | 0.0104799i | ||||
\(531\) | 21.5741 | + | 12.4558i | 0.936235 | + | 0.540536i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.0103098 | − | 21.0107i | 0.000446568 | − | 0.910074i | ||||
\(534\) | 0.0798218 | 0.00345423 | ||||||||
\(535\) | 19.1878 | + | 11.0781i | 0.829560 | + | 0.478947i | ||||
\(536\) | 3.23218 | − | 5.59829i | 0.139609 | − | 0.241809i | ||||
\(537\) | −1.92021 | − | 3.32590i | −0.0828631 | − | 0.143523i | ||||
\(538\) | − | 3.36000i | − | 0.144860i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −9.56858 | + | 5.52442i | −0.411766 | + | 0.237733i | ||||
\(541\) | − | 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 | ||||
\(543\) | −3.20718 | + | 5.55500i | −0.137633 | + | 0.238388i | ||||
\(544\) | 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 | ||||
\(549\) | 12.0073 | − | 20.7972i | 0.512457 | − | 0.887602i | ||||
\(550\) | 0.0471789 | + | 0.0817163i | 0.00201172 | + | 0.00348440i | ||||
\(551\) | − | 11.8352i | − | 0.504194i | ||||||
\(552\) | 1.22963 | − | 0.709929i | 0.0523367 | − | 0.0302166i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 0.825493i | − | 0.0350718i | ||||||
\(555\) | −3.10425 | − | 5.37672i | −0.131768 | − | 0.228229i | ||||
\(556\) | 5.21282 | − | 9.02886i | 0.221073 | − | 0.382909i | ||||
\(557\) | 29.9901 | + | 17.3148i | 1.27072 | + | 0.733650i | 0.975123 | − | 0.221662i | \(-0.0711483\pi\) |
0.295596 | + | 0.955313i | \(0.404482\pi\) | |||||||
\(558\) | 1.50455 | 0.0636927 | ||||||||
\(559\) | −1.39495 | + | 2.41339i | −0.0590001 | + | 0.102075i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.585725 | + | 0.338169i | 0.0247293 | + | 0.0142775i | ||||
\(562\) | −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 | \(0.895004\pi\) | |||||||
\(564\) | 14.7878i | 0.622677i | ||||||||
\(565\) | 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 | −0.607984 | − | 0.793949i | \(-0.708022\pi\) |
0.991572 | + | 0.129555i | \(0.0413549\pi\) | |||||||
\(570\) | −0.147947 | − | 0.0854175i | −0.00619684 | − | 0.00357775i | ||||
\(571\) | −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 | ||||
\(573\) | 3.45423 | 0.144303 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.46470 | + | 9.46514i | −0.227894 | + | 0.394724i | ||||
\(576\) | 10.1840 | + | 17.6391i | 0.424332 | + | 0.734964i | ||||
\(577\) | − | 19.5165i | − | 0.812482i | −0.913766 | − | 0.406241i | \(-0.866839\pi\) | ||
0.913766 | − | 0.406241i | \(-0.133161\pi\) | |||||||
\(578\) | −0.714246 | + | 0.412370i | −0.0297087 | + | 0.0171523i | ||||
\(579\) | −2.11593 | + | 1.22163i | −0.0879352 | + | 0.0507694i | ||||
\(580\) | 27.4740i | 1.14080i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.277810 | + | 0.481182i | −0.0115156 | + | 0.0199456i | ||||
\(583\) | −0.432949 | − | 0.249963i | −0.0179309 | − | 0.0103524i | ||||
\(584\) | 1.03654 | 0.0428923 | ||||||||
\(585\) | 14.0226 | + | 8.10513i | 0.579763 | + | 0.335106i | ||||
\(586\) | −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 | ||||||
\(591\) | −2.91723 | + | 1.68426i | −0.119999 | + | 0.0692812i | ||||
\(592\) | −21.4044 | + | 12.3579i | −0.879716 | + | 0.507905i | ||||
\(593\) | 18.0881i | 0.742790i | 0.928475 | + | 0.371395i | \(0.121120\pi\) | ||||
−0.928475 | + | 0.371395i | \(0.878880\pi\) | |||||||
\(594\) | −0.0723301 | − | 0.125279i | −0.00296774 | − | 0.00514028i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.9451 | − | 9.20592i | −0.653138 | − | 0.377089i | ||||
\(597\) | 6.96407 | 0.285021 | ||||||||
\(598\) | −1.90985 | − | 1.10390i | −0.0780996 | − | 0.0451419i | ||||
\(599\) | 9.05992 | 0.370178 | 0.185089 | − | 0.982722i | \(-0.440743\pi\) | ||||
0.185089 | + | 0.982722i | \(0.440743\pi\) | |||||||
\(600\) | −0.520111 | − | 0.300286i | −0.0212334 | − | 0.0122591i | ||||
\(601\) | 14.6440 | − | 25.3642i | 0.597343 | − | 1.03463i | −0.395869 | − | 0.918307i | \(-0.629556\pi\) |
0.993212 | − | 0.116321i | \(-0.0371102\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 35.8586i | − | 1.46028i | ||||||
\(604\) | 24.0958 | − | 13.9117i | 0.980444 | − | 0.566059i | ||||
\(605\) | 15.8876 | − | 9.17269i | 0.645922 | − | 0.372923i | ||||
\(606\) | − | 1.08957i | − | 0.0442606i | ||||||
\(607\) | −19.6825 | − | 34.0911i | −0.798887 | − | 1.38371i | −0.920341 | − | 0.391116i | \(-0.872089\pi\) |
0.121454 | − | 0.992597i | \(-0.461244\pi\) | |||||||
\(608\) | −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 | ||||
\(612\) | 16.8303 | 0.680324 | ||||||||
\(613\) | 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 | ||||
\(615\) | −2.86414 | − | 4.96084i | −0.115493 | − | 0.200040i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.8959 | − | 6.29077i | 0.438654 | − | 0.253257i | −0.264373 | − | 0.964421i | \(-0.585165\pi\) |
0.703026 | + | 0.711164i | \(0.251832\pi\) | |||||||
\(618\) | 0.625047 | − | 0.360871i | 0.0251431 | − | 0.0145164i | ||||
\(619\) | − | 22.3955i | − | 0.900149i | −0.892991 | − | 0.450075i | \(-0.851397\pi\) | ||
0.892991 | − | 0.450075i | \(-0.148603\pi\) | |||||||
\(620\) | 7.87314 | + | 13.6367i | 0.316193 | + | 0.547662i | ||||
\(621\) | 8.37794 | − | 14.5110i | 0.336195 | − | 0.582307i | ||||
\(622\) | −0.163724 | − | 0.0945262i | −0.00656474 | − | 0.00379015i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.11144 | + | 7.11315i | −0.164589 | + | 0.284754i | ||||
\(625\) | −9.62659 | −0.385064 | ||||||||
\(626\) | 2.14965 | + | 1.24110i | 0.0859175 | + | 0.0496045i | ||||
\(627\) | −0.153281 | + | 0.265491i | −0.00612145 | + | 0.0106027i | ||||
\(628\) | −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 | ||||||
\(633\) | 2.39785 | + | 4.15320i | 0.0953061 | + | 0.165075i | ||||
\(634\) | 1.83811 | − | 3.18369i | 0.0730005 | − | 0.126441i | ||||
\(635\) | 11.7944 | + | 6.80948i | 0.468045 | + | 0.270226i | ||||
\(636\) | 1.58519 | 0.0628569 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.359712 | −0.0142411 | ||||||||
\(639\) | −16.3181 | − | 9.42125i | −0.645533 | − | 0.372699i | ||||
\(640\) | 3.19238 | − | 5.52937i | 0.126190 | − | 0.218568i | ||||
\(641\) | 5.21051 | + | 9.02487i | 0.205803 | + | 0.356461i | 0.950388 | − | 0.311066i | \(-0.100686\pi\) |
−0.744585 | + | 0.667527i | \(0.767353\pi\) | |||||||
\(642\) | − | 0.919818i | − | 0.0363023i | ||||||
\(643\) | −13.2247 | + | 7.63531i | −0.521533 | + | 0.301107i | −0.737562 | − | 0.675280i | \(-0.764023\pi\) |
0.216029 | + | 0.976387i | \(0.430690\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.759983i | 0.0299243i | ||||||||
\(646\) | 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 | \(0.278492\pi\) | |||||||
\(648\) | −2.51891 | − | 1.45429i | −0.0989520 | − | 0.0571300i | ||||
\(649\) | −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 | −0.749033 | − | 0.662532i | \(-0.769482\pi\) |
0.948287 | + | 0.317416i | \(0.102815\pi\) | |||||||
\(654\) | 0.366048 | + | 0.634014i | 0.0143136 | + | 0.0247919i | ||||
\(655\) | − | 31.9129i | − | 1.24694i | ||||||
\(656\) | −19.7488 | + | 11.4020i | −0.771063 | + | 0.445173i | ||||
\(657\) | 4.97949 | − | 2.87491i | 0.194268 | − | 0.112161i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.9294 | + | 37.9828i | 0.854247 | + | 1.47960i | 0.877342 | + | 0.479866i | \(0.159315\pi\) |
−0.0230945 | + | 0.999733i | \(0.507352\pi\) | |||||||
\(660\) | 0.355825 | − | 0.616308i | 0.0138505 | − | 0.0239897i | ||||
\(661\) | 28.5156 | + | 16.4635i | 1.10913 | + | 0.640356i | 0.938604 | − | 0.344997i | \(-0.112120\pi\) |
0.170526 | + | 0.985353i | \(0.445453\pi\) | |||||||
\(662\) | 3.11167 | 0.120939 | ||||||||
\(663\) | 3.34116 | + | 5.79362i | 0.129760 | + | 0.225006i | ||||
\(664\) | 0.272170 | 0.0105622 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.01139 | − | 1.75177i | 0.0391904 | − | 0.0678798i | ||||
\(667\) | −20.8326 | − | 36.0831i | −0.806640 | − | 1.39714i | ||||
\(668\) | 8.57120i | 0.331630i | ||||||||
\(669\) | 7.71622 | − | 4.45496i | 0.298326 | − | 0.172239i | ||||
\(670\) | −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 | ||||
\(675\) | −7.08740 | −0.272794 | ||||||||
\(676\) | 25.8117 | + | 0.0253313i | 0.992756 | + | 0.000974280i | ||||
\(677\) | −29.5328 | −1.13504 | −0.567519 | − | 0.823361i | \(-0.692096\pi\) | ||||
−0.567519 | + | 0.823361i | \(0.692096\pi\) | |||||||
\(678\) | −0.300599 | − | 0.173551i | −0.0115444 | − | 0.00666519i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.28984 | − | 2.23406i | −0.0494630 | − | 0.0856725i | ||||
\(681\) | 4.04965i | 0.155183i | ||||||||
\(682\) | −0.178542 | + | 0.103081i | −0.00683674 | + | 0.00394719i | ||||
\(683\) | −15.8379 | + | 9.14400i | −0.606019 | + | 0.349885i | −0.771406 | − | 0.636343i | \(-0.780446\pi\) |
0.165387 | + | 0.986229i | \(0.447113\pi\) | |||||||
\(684\) | 7.62863i | 0.291688i | ||||||||
\(685\) | 15.3838 | + | 26.6456i | 0.587786 | + | 1.01807i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.8283 | − | 7.98378i | −0.527583 | − | 0.304600i | ||||
\(688\) | 3.02545 | 0.115344 | ||||||||
\(689\) | −2.46968 | − | 4.28246i | −0.0940872 | − | 0.163149i | ||||
\(690\) | −0.601417 | −0.0228956 | ||||||||
\(691\) | 8.95525 | + | 5.17031i | 0.340674 | + | 0.196688i | 0.660570 | − | 0.750765i | \(-0.270315\pi\) |
−0.319896 | + | 0.947453i | \(0.603648\pi\) | |||||||
\(692\) | −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 | ||||
\(696\) | 1.98277 | − | 1.14475i | 0.0751567 | − | 0.0433917i | ||||
\(697\) | 18.5632i | 0.703131i | ||||||||
\(698\) | −0.679501 | − | 1.17693i | −0.0257195 | − | 0.0445475i | ||||
\(699\) | −1.99532 | + | 3.45599i | −0.0754699 | + | 0.130718i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.6959 | 1.57483 | 0.787415 | − | 0.616423i | \(-0.211419\pi\) | ||||
0.787415 | + | 0.616423i | \(0.211419\pi\) | |||||||
\(702\) | 0.000701930 | − | 1.43048i | 2.64926e−5 | − | 0.0539901i | ||||
\(703\) | −9.11948 | −0.343948 | ||||||||
\(704\) | −2.41702 | − | 1.39547i | −0.0910951 | − | 0.0525938i | ||||
\(705\) | 6.28659 | − | 10.8887i | 0.236766 | − | 0.410092i | ||||
\(706\) | −2.14501 | − | 3.71527i | −0.0807287 | − | 0.139826i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.37371 | − | 5.41191i | 0.352286 | − | 0.203392i | ||||
\(709\) | 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 | ||||||||
\(711\) | −9.16402 | − | 15.8725i | −0.343677 | − | 0.595267i | ||||
\(712\) | −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 | ||||||||
\(717\) | −11.1322 | − | 6.42717i | −0.415739 | − | 0.240027i | ||||
\(718\) | 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 | \(0.675832\pi\) | |||||||
\(720\) | − | 17.5789i | − | 0.655127i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.76314 | − | 1.01795i | 0.0656174 | − | 0.0378842i | ||||
\(723\) | − | 9.19853i | − | 0.342097i | ||||||
\(724\) | −10.9359 | − | 18.9416i | −0.406430 | − | 0.703957i | ||||
\(725\) | −8.81176 | + | 15.2624i | −0.327261 | + | 0.566832i | ||||
\(726\) | −0.659576 | − | 0.380807i | −0.0244792 | − | 0.0141331i | ||||
\(727\) | 23.5565 | 0.873663 | 0.436831 | − | 0.899543i | \(-0.356101\pi\) | ||||
0.436831 | + | 0.899543i | \(0.356101\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.3760 | −0.384297 | ||||||||
\(730\) | −0.380231 | − | 0.219526i | −0.0140730 | − | 0.00812503i | ||||
\(731\) | 1.23141 | − | 2.13286i | 0.0455453 | − | 0.0788867i | ||||
\(732\) | −5.21703 | − | 9.03616i | −0.192827 | − | 0.333986i | ||||
\(733\) | − | 6.23249i | − | 0.230202i | −0.993354 | − | 0.115101i | \(-0.963281\pi\) | ||
0.993354 | − | 0.115101i | \(-0.0367192\pi\) | |||||||
\(734\) | 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 | ||||
\(738\) | 0.933158 | − | 1.61628i | 0.0343500 | − | 0.0594960i | ||||
\(739\) | 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 | ||||||||
\(741\) | −2.62606 | + | 1.51444i | −0.0964709 | + | 0.0556344i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.25627 | + | 3.03471i | 0.192834 | + | 0.111333i | 0.593309 | − | 0.804975i | \(-0.297821\pi\) |
−0.400475 | + | 0.916308i | \(0.631155\pi\) | |||||||
\(744\) | 0.656096 | − | 1.13639i | 0.0240536 | − | 0.0416621i | ||||
\(745\) | 7.82725 | + | 13.5572i | 0.286768 | + | 0.496697i | ||||
\(746\) | − | 0.422796i | − | 0.0154797i | ||||||
\(747\) | 1.30749 | − | 0.754880i | 0.0478386 | − | 0.0276196i | ||||
\(748\) | −1.99722 | + | 1.15310i | −0.0730256 | + | 0.0421613i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.422980 | + | 0.732622i | 0.0154450 | + | 0.0267516i | ||||
\(751\) | −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 | ||||
\(753\) | 13.1346 | 0.478650 | ||||||||
\(754\) | −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 | ||||
\(759\) | 1.07924i | 0.0391739i | ||||||||
\(760\) | 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 | \(0.0771035\pi\) | |||||||
\(762\) | − | 0.565394i | − | 0.0204821i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.88916 | + | 10.2003i | −0.213062 | + | 0.369035i | ||||
\(765\) | −12.3926 | − | 7.15490i | −0.448057 | − | 0.258686i | ||||
\(766\) | −2.70393 | −0.0976970 | ||||||||
\(767\) | −29.2245 | − | 16.8919i | −1.05523 | − | 0.609930i | ||||
\(768\) | 8.64915 | 0.312099 | ||||||||
\(769\) | 8.62507 | + | 4.97969i | 0.311028 | + | 0.179572i | 0.647386 | − | 0.762162i | \(-0.275862\pi\) |
−0.336358 | + | 0.941734i | \(0.609195\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.94313 | − | 10.2938i | −0.214036 | − | 0.370722i | ||||
\(772\) | − | 8.33112i | − | 0.299843i | ||||||
\(773\) | −11.0433 | + | 6.37588i | −0.397201 | + | 0.229324i | −0.685276 | − | 0.728284i | \(-0.740318\pi\) |
0.288074 | + | 0.957608i | \(0.406985\pi\) | |||||||
\(774\) | −0.214435 | + | 0.123804i | −0.00770769 | + | 0.00445004i | ||||
\(775\) | 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 | ||||||||
\(780\) | 6.09613 | − | 3.51561i | 0.218276 | − | 0.125879i | ||||
\(781\) | 2.58192 | 0.0923882 | ||||||||
\(782\) | 1.68785 | + | 0.974483i | 0.0603575 | + | 0.0348474i | ||||
\(783\) | 13.5093 | − | 23.3988i | 0.482784 | − | 0.836206i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 29.0069i | 1.03530i | ||||||||
\(786\) | −1.14737 | + | 0.662435i | −0.0409254 | + | 0.0236283i | ||||
\(787\) | −7.52380 | + | 4.34387i | −0.268194 | + | 0.154842i | −0.628067 | − | 0.778159i | \(-0.716154\pi\) |
0.359872 | + | 0.933002i | \(0.382820\pi\) | |||||||
\(788\) | − | 11.4861i | − | 0.409174i | ||||||
\(789\) | 8.60052 | + | 14.8965i | 0.306187 | + | 0.530331i | ||||
\(790\) | −0.699759 | + | 1.21202i | −0.0248963 | + | 0.0431216i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.465413 | 0.0165377 | ||||||||
\(793\) | −16.2836 | + | 28.1721i | −0.578247 | + | 1.00042i | ||||
\(794\) | −3.10929 | −0.110345 | ||||||||
\(795\) | −1.16722 | − | 0.673897i | −0.0413972 | − | 0.0239007i | ||||
\(796\) | −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 | ||||
\(801\) | 3.03063i | 0.107082i | ||||||||
\(802\) | −1.05679 | − | 1.83041i | −0.0373166 | − | 0.0646342i | ||||
\(803\) | −0.393938 | + | 0.682321i | −0.0139018 | + | 0.0240786i | ||||
\(804\) | −13.4928 | − | 7.79009i | −0.475856 | − | 0.274735i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.03866 | − | 0.00100036i | −0.0718086 | − | 3.52361e-5i | ||||
\(807\) | −16.2554 | −0.572218 | ||||||||
\(808\) | 6.45844 | + | 3.72878i | 0.227207 | + | 0.131178i | ||||
\(809\) | −14.4275 | + | 24.9892i | −0.507244 | + | 0.878573i | 0.492721 | + | 0.870188i | \(0.336002\pi\) |
−0.999965 | + | 0.00838530i | \(0.997331\pi\) | |||||||
\(810\) | 0.616002 | + | 1.06695i | 0.0216441 | + | 0.0374887i | ||||
\(811\) | 12.3917i | 0.435131i | 0.976046 | + | 0.217566i | \(0.0698116\pi\) | ||||
−0.976046 | + | 0.217566i | \(0.930188\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.8506 | + | 8.57397i | −0.520832 | + | 0.300702i | ||||
\(814\) | 0.277173i | 0.00971491i | ||||||||
\(815\) | 9.95405 | + | 17.2409i | 0.348675 | + | 0.603923i | ||||
\(816\) | 3.62942 | − | 6.28634i | 0.127055 | − | 0.220066i | ||||
\(817\) | 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 | 0.969079 | − | 0.246753i | \(-0.0793635\pi\) |
0.270845 | + | 0.962623i | \(0.412697\pi\) | |||||||
\(822\) | 0.638663 | − | 1.10620i | 0.0222759 | − | 0.0385830i | ||||
\(823\) | −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 | ||||||||
\(825\) | 0.395337 | − | 0.228248i | 0.0137639 | − | 0.00794658i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.54938i | 0.297291i | 0.988891 | + | 0.148645i | \(0.0474913\pi\) | ||||
−0.988891 | + | 0.148645i | \(0.952509\pi\) | |||||||
\(828\) | 13.4281 | + | 23.2582i | 0.466660 | + | 0.808278i | ||||
\(829\) | 7.37844 | − | 12.7798i | 0.256264 | − | 0.443862i | −0.708974 | − | 0.705234i | \(-0.750842\pi\) |
0.965238 | + | 0.261373i | \(0.0841751\pi\) | |||||||
\(830\) | −0.0998392 | − | 0.0576422i | −0.00346547 | − | 0.00200079i | ||||
\(831\) | −3.99367 | −0.138539 | ||||||||
\(832\) | −13.7875 | − | 23.9077i | −0.477995 | − | 0.828850i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.318701 | + | 0.184002i | 0.0110357 | + | 0.00637146i | ||||
\(835\) | 3.64379 | − | 6.31123i | 0.126099 | − | 0.218409i | ||||
\(836\) | −0.522661 | − | 0.905276i | −0.0180766 | − | 0.0313096i | ||||
\(837\) | − | 15.4853i | − | 0.535250i | ||||||
\(838\) | 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 | ||||
\(843\) | 14.6715 | + | 8.47062i | 0.505315 | + | 0.291743i | ||||
\(844\) | −16.3525 | −0.562877 | ||||||||
\(845\) | −18.9951 | − | 10.9917i | −0.653453 | − | 0.378127i | ||||
\(846\) | 4.09643 | 0.140838 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.68275 | + | 4.64665i | −0.0921259 | + | 0.159567i | ||||
\(849\) | −3.38027 | − | 5.85479i | −0.116010 | − | 0.200936i | ||||
\(850\) | − | 0.824374i | − | 0.0282758i | ||||||
\(851\) | −27.8035 | + | 16.0524i | −0.953092 | + | 0.550268i | ||||
\(852\) | −7.09003 | + | 4.09343i | −0.242901 | + | 0.140239i | ||||
\(853\) | − | 25.6332i | − | 0.877665i | −0.898569 | − | 0.438832i | \(-0.855392\pi\) | ||
0.898569 | − | 0.438832i | \(-0.144608\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.24309 | − | 5.61719i | 0.110911 | − | 0.192104i | ||||
\(856\) | 5.45225 | + | 3.14786i | 0.186354 | + | 0.107592i | ||||
\(857\) | 11.7653 | 0.401894 | 0.200947 | − | 0.979602i | \(-0.435598\pi\) | ||||
0.200947 | + | 0.979602i | \(0.435598\pi\) | |||||||
\(858\) | 0.0460292 | + | 0.0798153i | 0.00157141 | + | 0.00272485i | ||||
\(859\) | 21.7761 | 0.742992 | 0.371496 | − | 0.928435i | \(-0.378845\pi\) | ||||
0.371496 | + | 0.928435i | \(0.378845\pi\) | |||||||
\(860\) | −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 | \(0.246285\pi\) | ||||
−0.715310 | + | 0.698807i | \(0.753715\pi\) | |||||||
\(864\) | −4.08334 | + | 2.35752i | −0.138918 | + | 0.0802044i | ||||
\(865\) | 18.3037 | − | 10.5677i | 0.622345 | − | 0.359311i | ||||
\(866\) | − | 1.50694i | − | 0.0512079i | ||||||
\(867\) | 1.99502 | + | 3.45547i | 0.0677543 | + | 0.117354i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.17496 | + | 1.25571i | 0.0737803 | + | 0.0425971i | ||||
\(870\) | −0.969778 | −0.0328785 | ||||||||
\(871\) | −0.0238420 | + | 48.5882i | −0.000807854 | + | 1.64635i | ||||
\(872\) | −5.01085 | −0.169689 | ||||||||
\(873\) | −18.2693 | − | 10.5478i | −0.618320 | − | 0.356987i | ||||
\(874\) | −0.441702 | + | 0.765050i | −0.0149408 | + | 0.0258782i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 2.49824i | − | 0.0844076i | ||||||
\(877\) | 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 | ||||
\(879\) | 10.3582i | 0.349372i | ||||||||
\(880\) | 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 | ||||
\(885\) | −9.20286 | −0.309351 | ||||||||
\(886\) | −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 | \(0.972549\pi\) | |||||||
\(888\) | −0.882080 | − | 1.52781i | −0.0296007 | − | 0.0512698i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.200413 | − | 0.115709i | 0.00671786 | − | 0.00387856i | ||||
\(891\) | 1.91463 | − | 1.10541i | 0.0641424 | − | 0.0370326i | ||||
\(892\) | 30.3813i | 1.01724i | ||||||||
\(893\) | −9.23418 | − | 15.9941i | −0.309010 | − | 0.535221i | ||||
\(894\) | 0.324950 | − | 0.562831i | 0.0108680 | − | 0.0188239i | ||||
\(895\) | −9.64235 | − | 5.56701i | −0.322308 | − | 0.186085i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.34060 | + | 9.23971i | −0.178317 | + | 0.308505i | ||||
\(898\) | 1.27056 | 0.0423992 | ||||||||
\(899\) | −33.3469 | − | 19.2528i | −1.11218 | − | 0.642118i | ||||
\(900\) | 5.67983 | − | 9.83776i | 0.189328 | − | 0.327925i | ||||
\(901\) | 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 | ||||||||
\(906\) | 0.491055 | + | 0.850532i | 0.0163142 | + | 0.0282570i | ||||
\(907\) | 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 | ||||
\(909\) | 41.3681 | 1.37209 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.9947 | 0.695584 | 0.347792 | − | 0.937572i | \(-0.386932\pi\) | ||||
0.347792 | + | 0.937572i | \(0.386932\pi\) | |||||||
\(912\) | 2.84940 | + | 1.64510i | 0.0943529 | + | 0.0544747i | ||||
\(913\) | −0.103438 | + | 0.179161i | −0.00342331 | + | 0.00592935i | ||||
\(914\) | 0.478367 | + | 0.828556i | 0.0158230 | + | 0.0274062i | ||||
\(915\) | 8.87147i | 0.293282i | ||||||||
\(916\) | 47.1521 | − | 27.2233i | 1.55795 | − | 0.899483i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.26385i | 0.0417132i | ||||||||
\(919\) | 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 | ||||
\(921\) | 4.57869 | + | 2.64351i | 0.150873 | + | 0.0871065i | ||||
\(922\) | 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 | ||||
\(927\) | 13.7014 | + | 23.7315i | 0.450012 | + | 0.779444i | ||||
\(928\) | 11.7244i | 0.384872i | ||||||||
\(929\) | −5.89524 | + | 3.40362i | −0.193416 | + | 0.111669i | −0.593581 | − | 0.804774i | \(-0.702286\pi\) |
0.400164 | + | 0.916443i | \(0.368953\pi\) | |||||||
\(930\) | −0.481347 | + | 0.277906i | −0.0157840 | + | 0.00911290i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.80369 | − | 11.7843i | −0.222862 | − | 0.386009i | ||||
\(933\) | −0.457310 | + | 0.792085i | −0.0149717 | + | 0.0259317i | ||||
\(934\) | −2.07410 | − | 1.19748i | −0.0678666 | − | 0.0391828i | ||||
\(935\) | 1.96082 | 0.0641256 | ||||||||
\(936\) | 3.98455 | + | 2.30309i | 0.130239 | + | 0.0752789i | ||||
\(937\) | 5.22890 | 0.170821 | 0.0854104 | − | 0.996346i | \(-0.472780\pi\) | ||||
0.0854104 | + | 0.996346i | \(0.472780\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.00437 | − | 10.3999i | 0.195945 | − | 0.339387i | ||||
\(940\) | 21.4362 | + | 37.1285i | 0.699170 | + | 1.21100i | ||||
\(941\) | 56.4403i | 1.83990i | 0.392033 | + | 0.919951i | \(0.371772\pi\) | ||||
−0.392033 | + | 0.919951i | \(0.628228\pi\) | |||||||
\(942\) | 1.04289 | − | 0.602114i | 0.0339793 | − | 0.0196179i | ||||
\(943\) | −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 | 0.415417 | − | 0.909631i | \(-0.363636\pi\) |
−0.580055 | + | 0.814577i | \(0.696969\pi\) | |||||||
\(948\) | −7.96334 | −0.258637 | ||||||||
\(949\) | −6.74909 | + | 3.89217i | −0.219085 | + | 0.126345i | ||||
\(950\) | 0.373662 | 0.0121232 | ||||||||
\(951\) | −15.4025 | − | 8.89262i | −0.499459 | − | 0.288363i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.8742 | − | 18.8346i | −0.352249 | − | 0.610114i | 0.634394 | − | 0.773010i | \(-0.281250\pi\) |
−0.986643 | + | 0.162896i | \(0.947916\pi\) | |||||||
\(954\) | − | 0.439121i | − | 0.0142171i | ||||||
\(955\) | 8.67273 | − | 5.00720i | 0.280643 | − | 0.162029i | ||||
\(956\) | 37.9588 | − | 21.9155i | 1.22767 | − | 0.708798i | ||||
\(957\) | 1.74026i | 0.0562546i | ||||||||
\(958\) | 1.58214 | + | 2.74035i | 0.0511167 | + | 0.0885368i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6.51626 | − | 3.76217i | −0.210312 | − | 0.121423i | ||||
\(961\) | 8.93110 | 0.288100 | ||||||||
\(962\) | −1.37159 | + | 2.37297i | −0.0442217 | + | 0.0765075i | ||||
\(963\) | 34.9232 | 1.12538 | ||||||||
\(964\) | 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 | ||||
\(969\) | 2.31950 | − | 1.33917i | 0.0745132 | − | 0.0430202i | ||||
\(970\) | 1.61084i | 0.0517210i | ||||||||
\(971\) | 3.73092 | + | 6.46215i | 0.119731 | + | 0.207380i | 0.919661 | − | 0.392713i | \(-0.128463\pi\) |
−0.799930 | + | 0.600093i | \(0.795130\pi\) | |||||||
\(972\) | −13.3224 | + | 23.0751i | −0.427317 | + | 0.740134i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.767850 | −0.0246035 | ||||||||
\(975\) | 4.51409 | + | 0.00221504i | 0.144567 | + | 7.09381e-5i | ||||
\(976\) | 35.3168 | 1.13046 | ||||||||
\(977\) | −9.49204 | − | 5.48023i | −0.303677 | − | 0.175328i | 0.340416 | − | 0.940275i | \(-0.389432\pi\) |
−0.644094 | + | 0.764947i | \(0.722765\pi\) | |||||||
\(978\) | 0.413245 | − | 0.715761i | 0.0132141 | − | 0.0228875i | ||||
\(979\) | −0.207638 | − | 0.359640i | −0.00663614 | − | 0.0114941i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.0719 | + | 13.8979i | −0.768557 | + | 0.443727i | ||||
\(982\) | 0.309335 | − | 0.178595i | 0.00987127 | − | 0.00569918i | ||||
\(983\) | − | 16.1441i | − | 0.514918i | −0.966289 | − | 0.257459i | \(-0.917115\pi\) | ||
0.966289 | − | 0.257459i | \(-0.0828852\pi\) | |||||||
\(984\) | −0.813853 | − | 1.40963i | −0.0259447 | − | 0.0449375i | ||||
\(985\) | −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 | ||||||||
\(990\) | −0.170726 | − | 0.0985688i | −0.00542603 | − | 0.00313272i | ||||
\(991\) | −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 | ||||
\(993\) | − | 15.0540i | − | 0.477725i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.4851 | − | 10.0950i | 0.554315 | − | 0.320034i | ||||
\(996\) | − | 0.655975i | − | 0.0207854i | ||||||
\(997\) | −9.22057 | − | 15.9705i | −0.292018 | − | 0.505791i | 0.682269 | − | 0.731102i | \(-0.260993\pi\) |
−0.974287 | + | 0.225311i | \(0.927660\pi\) | |||||||
\(998\) | −1.69305 | + | 2.93244i | −0.0535924 | + | 0.0928248i | ||||
\(999\) | −18.0298 | − | 10.4095i | −0.570437 | − | 0.329342i |
(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 | 637.2.q.h.589.3 | 12 | ||
7.2 | even | 3 | 637.2.k.g.459.4 | 12 | |||
7.3 | odd | 6 | 637.2.u.h.30.4 | 12 | |||
7.4 | even | 3 | 637.2.u.i.30.4 | 12 | |||
7.5 | odd | 6 | 637.2.k.h.459.4 | 12 | |||
7.6 | odd | 2 | 91.2.q.a.43.3 | yes | 12 | ||
13.6 | odd | 12 | 8281.2.a.ch.1.3 | 6 | |||
13.7 | odd | 12 | 8281.2.a.by.1.4 | 6 | |||
13.10 | even | 6 | inner | 637.2.q.h.491.3 | 12 | ||
21.20 | even | 2 | 819.2.ct.a.316.4 | 12 | |||
28.27 | even | 2 | 1456.2.cc.c.225.3 | 12 | |||
91.6 | even | 12 | 1183.2.a.p.1.3 | 6 | |||
91.10 | odd | 6 | 637.2.k.h.569.3 | 12 | |||
91.20 | even | 12 | 1183.2.a.m.1.4 | 6 | |||
91.23 | even | 6 | 637.2.u.i.361.4 | 12 | |||
91.48 | odd | 6 | 1183.2.c.i.337.7 | 12 | |||
91.62 | odd | 6 | 91.2.q.a.36.3 | ✓ | 12 | ||
91.69 | odd | 6 | 1183.2.c.i.337.6 | 12 | |||
91.75 | odd | 6 | 637.2.u.h.361.4 | 12 | |||
91.88 | even | 6 | 637.2.k.g.569.3 | 12 | |||
273.62 | even | 6 | 819.2.ct.a.127.4 | 12 | |||
364.335 | even | 6 | 1456.2.cc.c.673.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.3 | ✓ | 12 | 91.62 | odd | 6 | ||
91.2.q.a.43.3 | yes | 12 | 7.6 | odd | 2 | ||
637.2.k.g.459.4 | 12 | 7.2 | even | 3 | |||
637.2.k.g.569.3 | 12 | 91.88 | even | 6 | |||
637.2.k.h.459.4 | 12 | 7.5 | odd | 6 | |||
637.2.k.h.569.3 | 12 | 91.10 | odd | 6 | |||
637.2.q.h.491.3 | 12 | 13.10 | even | 6 | inner | ||
637.2.q.h.589.3 | 12 | 1.1 | even | 1 | trivial | ||
637.2.u.h.30.4 | 12 | 7.3 | odd | 6 | |||
637.2.u.h.361.4 | 12 | 91.75 | odd | 6 | |||
637.2.u.i.30.4 | 12 | 7.4 | even | 3 | |||
637.2.u.i.361.4 | 12 | 91.23 | even | 6 | |||
819.2.ct.a.127.4 | 12 | 273.62 | even | 6 | |||
819.2.ct.a.316.4 | 12 | 21.20 | even | 2 | |||
1183.2.a.m.1.4 | 6 | 91.20 | even | 12 | |||
1183.2.a.p.1.3 | 6 | 91.6 | even | 12 | |||
1183.2.c.i.337.6 | 12 | 91.69 | odd | 6 | |||
1183.2.c.i.337.7 | 12 | 91.48 | odd | 6 | |||
1456.2.cc.c.225.3 | 12 | 28.27 | even | 2 | |||
1456.2.cc.c.673.3 | 12 | 364.335 | even | 6 | |||
8281.2.a.by.1.4 | 6 | 13.7 | odd | 12 | |||
8281.2.a.ch.1.3 | 6 | 13.6 | odd | 12 |