Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(459,637)]
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([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
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 | 459.4 | ||
Root | \(1.34408 - 0.439820i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.459 |
Dual form | 637.2.k.g.569.3 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.120360i | 0.0851073i | 0.999094 | + | 0.0425536i | \(0.0135493\pi\) | ||||
−0.999094 | + | 0.0425536i | \(0.986451\pi\) | |||||||
\(3\) | −0.291146 | − | 0.504280i | −0.168093 | − | 0.291146i | 0.769656 | − | 0.638459i | \(-0.220428\pi\) |
−0.937749 | + | 0.347313i | \(0.887094\pi\) | |||||||
\(4\) | 1.98551 | 0.992757 | ||||||||
\(5\) | 1.46199 | − | 0.844083i | 0.653824 | − | 0.377485i | −0.136096 | − | 0.990696i | \(-0.543456\pi\) |
0.789920 | + | 0.613210i | \(0.210122\pi\) | |||||||
\(6\) | 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 | \(-0.649161\pi\) |
0.546848 | + | 0.837232i | \(0.315828\pi\) | |||||||
\(12\) | −0.578074 | − | 1.00125i | −0.166876 | − | 0.289037i | ||||
\(13\) | −1.80124 | − | 3.12338i | −0.499575 | − | 0.866271i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.851308 | − | 0.491503i | −0.219807 | − | 0.126905i | ||||
\(16\) | 3.91329 | 0.978323 | ||||||||
\(17\) | −3.18555 | −0.772609 | −0.386304 | − | 0.922371i | \(-0.626249\pi\) | ||||
−0.386304 | + | 0.922371i | \(0.626249\pi\) | |||||||
\(18\) | 0.277362 | + | 0.160135i | 0.0653748 | + | 0.0377442i | ||||
\(19\) | 1.25046 | + | 0.721954i | 0.286875 | + | 0.165628i | 0.636532 | − | 0.771250i | \(-0.280368\pi\) |
−0.349657 | + | 0.936878i | \(0.613702\pi\) | |||||||
\(20\) | 2.90281 | − | 1.67594i | 0.649088 | − | 0.374751i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0219427 | + | 0.0380059i | 0.00467820 | + | 0.00810288i | ||||
\(23\) | 5.08321 | 1.05992 | 0.529962 | − | 0.848022i | \(-0.322206\pi\) | ||||
0.529962 | + | 0.848022i | \(0.322206\pi\) | |||||||
\(24\) | 0.241901 | − | 0.139662i | 0.0493778 | − | 0.0285083i | ||||
\(25\) | −1.07505 | + | 1.86204i | −0.215010 | + | 0.372408i | ||||
\(26\) | 0.375930 | − | 0.216797i | 0.0737260 | − | 0.0425175i | ||||
\(27\) | −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 | ||||
\(31\) | −4.06838 | − | 2.34888i | −0.730702 | − | 0.421871i | 0.0879771 | − | 0.996122i | \(-0.471960\pi\) |
−0.818679 | + | 0.574252i | \(0.805293\pi\) | |||||||
\(32\) | 1.43040i | 0.252861i | ||||||||
\(33\) | −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 | ||||
\(37\) | − | 6.31584i | − | 1.03832i | −0.854678 | − | 0.519159i | \(-0.826245\pi\) | ||
0.854678 | − | 0.519159i | \(-0.173755\pi\) | |||||||
\(38\) | −0.0868943 | + | 0.150505i | −0.0140961 | + | 0.0244152i | ||||
\(39\) | −1.05063 | + | 1.81769i | −0.168236 | + | 0.291063i | ||||
\(40\) | 0.404903 | + | 0.701313i | 0.0640208 | + | 0.110887i | ||||
\(41\) | 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 | \(0.852109\pi\) | |||||||
\(44\) | 0.626963 | − | 0.361977i | 0.0945182 | − | 0.0545701i | ||||
\(45\) | − | 4.49210i | − | 0.669643i | ||||||
\(46\) | 0.611815i | 0.0902072i | ||||||||
\(47\) | 11.0769 | − | 6.39527i | 1.61574 | − | 0.932846i | 0.627731 | − | 0.778430i | \(-0.283984\pi\) |
0.988006 | − | 0.154416i | \(-0.0493495\pi\) | |||||||
\(48\) | −1.13934 | − | 1.97339i | −0.164449 | − | 0.284835i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.224115 | − | 0.129393i | −0.0316946 | − | 0.0182989i | ||||
\(51\) | 0.927459 | + | 1.60641i | 0.129870 | + | 0.224942i | ||||
\(52\) | −3.57639 | − | 6.20152i | −0.495956 | − | 0.859996i | ||||
\(53\) | −0.685548 | + | 1.18740i | −0.0941672 | + | 0.163102i | −0.909261 | − | 0.416227i | \(-0.863352\pi\) |
0.815094 | + | 0.579329i | \(0.196685\pi\) | |||||||
\(54\) | − | 0.396744i | − | 0.0539901i | ||||||
\(55\) | 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 | ||||
\(59\) | 9.36197i | 1.21882i | 0.792854 | + | 0.609412i | \(0.208595\pi\) | ||||
−0.792854 | + | 0.609412i | \(0.791405\pi\) | |||||||
\(60\) | −1.69028 | − | 0.975885i | −0.218215 | − | 0.125986i | ||||
\(61\) | −4.51242 | + | 7.81574i | −0.577756 | + | 1.00070i | 0.417980 | + | 0.908456i | \(0.362738\pi\) |
−0.995736 | + | 0.0922469i | \(0.970595\pi\) | |||||||
\(62\) | 0.282711 | − | 0.489669i | 0.0359043 | − | 0.0621880i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.65442 | 0.956802 | ||||||||
\(65\) | −5.26980 | − | 3.04597i | −0.653638 | − | 0.377806i | ||||
\(66\) | 0.0127771 | − | 0.0221305i | 0.00157275 | − | 0.00272408i | ||||
\(67\) | 11.6705 | − | 6.73797i | 1.42578 | − | 0.823174i | 0.428995 | − | 0.903307i | \(-0.358868\pi\) |
0.996784 | + | 0.0801330i | \(0.0255345\pi\) | |||||||
\(68\) | −6.32495 | −0.767013 | ||||||||
\(69\) | −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 | ||||
\(73\) | 1.87133 | + | 1.08041i | 0.219023 | + | 0.126453i | 0.605498 | − | 0.795847i | \(-0.292974\pi\) |
−0.386475 | + | 0.922300i | \(0.626307\pi\) | |||||||
\(74\) | 0.760173 | 0.0883684 | ||||||||
\(75\) | 1.25198 | 0.144567 | ||||||||
\(76\) | 2.48281 | + | 1.43345i | 0.284797 | + | 0.164428i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.218777 | − | 0.126454i | −0.0247716 | − | 0.0143181i | ||||
\(79\) | 3.44391 | + | 5.96502i | 0.387470 | + | 0.671117i | 0.992108 | − | 0.125382i | \(-0.0400158\pi\) |
−0.604639 | + | 0.796500i | \(0.706682\pi\) | |||||||
\(80\) | 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 | ||||
\(86\) | 0.0805861 | − | 0.0465264i | 0.00868982 | − | 0.00501707i | ||||
\(87\) | 4.77282 | 0.511700 | ||||||||
\(88\) | 0.0874529 | + | 0.151473i | 0.00932251 | + | 0.0161471i | ||||
\(89\) | − | 1.13893i | − | 0.120727i | −0.998176 | − | 0.0603634i | \(-0.980774\pi\) | ||
0.998176 | − | 0.0603634i | \(-0.0192260\pi\) | |||||||
\(90\) | 0.540669 | 0.0569915 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.0928 | 1.05225 | ||||||||
\(93\) | 2.73547i | 0.283655i | ||||||||
\(94\) | 0.769734 | + | 1.33322i | 0.0793920 | + | 0.137511i | ||||
\(95\) | 2.43755 | 0.250088 | ||||||||
\(96\) | 0.721319 | − | 0.416454i | 0.0736193 | − | 0.0425041i | ||||
\(97\) | −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 | 0.935653 | + | 0.352920i | \(0.114811\pi\) |
−0.162189 | + | 0.986760i | \(0.551855\pi\) | |||||||
\(102\) | −0.193347 | + | 0.111629i | −0.0191442 | + | 0.0110529i | ||||
\(103\) | −5.14908 | − | 8.91847i | −0.507354 | − | 0.878763i | −0.999964 | − | 0.00851245i | \(-0.997290\pi\) |
0.492610 | − | 0.870250i | \(-0.336043\pi\) | |||||||
\(104\) | 1.49827 | − | 0.864049i | 0.146918 | − | 0.0847270i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.142916 | − | 0.0825124i | −0.0138812 | − | 0.00801432i | ||||
\(107\) | −13.1244 | −1.26878 | −0.634391 | − | 0.773012i | \(-0.718749\pi\) | ||||
−0.634391 | + | 0.773012i | \(0.718749\pi\) | |||||||
\(108\) | −6.54488 | −0.629782 | ||||||||
\(109\) | −9.04641 | − | 5.22295i | −0.866489 | − | 0.500268i | −0.000309035 | − | 1.00000i | \(-0.500098\pi\) |
−0.866180 | + | 0.499732i | \(0.833432\pi\) | |||||||
\(110\) | 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 | \(0.908172\pi\) | |||||||
\(114\) | 0.101196 | 0.00947784 | ||||||||
\(115\) | 7.43163 | − | 4.29065i | 0.693003 | − | 0.400105i | ||||
\(116\) | −8.13725 | + | 14.0941i | −0.755524 | + | 1.30861i | ||||
\(117\) | −9.59414 | − | 0.00470779i | −0.886979 | − | 0.000435235i | ||||
\(118\) | −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 | ||||
\(122\) | −0.940702 | − | 0.543114i | −0.0851671 | − | 0.0491713i | ||||
\(123\) | − | 3.39320i | − | 0.305955i | ||||||
\(124\) | −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 | \(0.0501496\pi\) | |||||||
\(128\) | 3.78208i | 0.334291i | ||||||||
\(129\) | −0.225091 | + | 0.389870i | −0.0198182 | + | 0.0343261i | ||||
\(130\) | 0.366613 | − | 0.634273i | 0.0321541 | − | 0.0556294i | ||||
\(131\) | 9.45194 | + | 16.3712i | 0.825820 | + | 1.43036i | 0.901291 | + | 0.433214i | \(0.142620\pi\) |
−0.0754716 | + | 0.997148i | \(0.524046\pi\) | |||||||
\(132\) | −0.365075 | − | 0.210776i | −0.0317757 | − | 0.0183457i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.810981 | + | 1.40466i | 0.0700581 | + | 0.121344i | ||||
\(135\) | −4.81920 | + | 2.78236i | −0.414770 | + | 0.239468i | ||||
\(136\) | − | 1.52809i | − | 0.131033i | ||||||
\(137\) | 18.2255i | 1.55711i | 0.627577 | + | 0.778554i | \(0.284047\pi\) | ||||
−0.627577 | + | 0.778554i | \(0.715953\pi\) | |||||||
\(138\) | 0.308526 | − | 0.178127i | 0.0262635 | − | 0.0151632i | ||||
\(139\) | 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 | ||||
\(142\) | −0.426143 | − | 0.738102i | −0.0357612 | − | 0.0619401i | ||||
\(143\) | −1.13820 | − | 0.657883i | −0.0951808 | − | 0.0550150i | ||||
\(144\) | 5.20651 | − | 9.01794i | 0.433876 | − | 0.751495i | ||||
\(145\) | 13.8372i | 1.14912i | ||||||||
\(146\) | −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 | \(-0.457354\pi\) |
−0.791478 | + | 0.611198i | \(0.790688\pi\) | |||||||
\(150\) | 0.150689i | 0.0123037i | ||||||||
\(151\) | −12.1358 | − | 7.00661i | −0.987597 | − | 0.570189i | −0.0830419 | − | 0.996546i | \(-0.526464\pi\) |
−0.904555 | + | 0.426357i | \(0.859797\pi\) | |||||||
\(152\) | −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 | ||||||||
\(156\) | −2.08605 | + | 3.60905i | −0.167017 | + | 0.288955i | ||||
\(157\) | −8.59125 | + | 14.8805i | −0.685656 | + | 1.18759i | 0.287574 | + | 0.957759i | \(0.407151\pi\) |
−0.973230 | + | 0.229833i | \(0.926182\pi\) | |||||||
\(158\) | −0.717949 | + | 0.414508i | −0.0571170 | + | 0.0329765i | ||||
\(159\) | 0.798378 | 0.0633155 | ||||||||
\(160\) | 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 | \(-0.486144\pi\) |
−0.843447 | + | 0.537213i | \(0.819477\pi\) | |||||||
\(164\) | 10.0201 | + | 5.78511i | 0.782439 | + | 0.451741i | ||||
\(165\) | −0.358422 | −0.0279031 | ||||||||
\(166\) | 0.0682898 | 0.00530031 | ||||||||
\(167\) | −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 | ||||
\(170\) | −0.323632 | − | 0.560546i | −0.0248214 | − | 0.0429919i | ||||
\(171\) | 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 | −0.999620 | − | 0.0275769i | \(-0.991221\pi\) |
0.523692 | + | 0.851908i | \(0.324554\pi\) | |||||||
\(174\) | 0.574457i | 0.0435494i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.23569 | − | 0.713428i | 0.0931440 | − | 0.0537767i | ||||
\(177\) | 4.72105 | − | 2.72570i | 0.354856 | − | 0.204876i | ||||
\(178\) | 0.137082 | 0.0102747 | ||||||||
\(179\) | −3.29767 | − | 5.71173i | −0.246479 | − | 0.426915i | 0.716067 | − | 0.698031i | \(-0.245940\pi\) |
−0.962547 | + | 0.271117i | \(0.912607\pi\) | |||||||
\(180\) | − | 8.91913i | − | 0.664792i | ||||||
\(181\) | 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 | ||||||||
\(184\) | 2.43840i | 0.179761i | ||||||||
\(185\) | −5.33109 | − | 9.23371i | −0.391949 | − | 0.678876i | ||||
\(186\) | −0.329240 | −0.0241411 | ||||||||
\(187\) | −1.00590 | + | 0.580754i | −0.0735584 | + | 0.0424690i | ||||
\(188\) | 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 | \(-0.902184\pi\) |
0.738537 | + | 0.674213i | \(0.235517\pi\) | |||||||
\(192\) | −2.22855 | − | 3.85997i | −0.160832 | − | 0.278569i | ||||
\(193\) | −3.63380 | + | 2.09798i | −0.261567 | + | 0.151016i | −0.625049 | − | 0.780586i | \(-0.714921\pi\) |
0.363482 | + | 0.931601i | \(0.381588\pi\) | |||||||
\(194\) | −0.477098 | − | 0.826358i | −0.0342536 | − | 0.0593290i | ||||
\(195\) | −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 | \(0.600596\pi\) | |||||||
\(198\) | 0.116776 | 0.00829893 | ||||||||
\(199\) | 11.9598 | 0.847805 | 0.423903 | − | 0.905708i | \(-0.360660\pi\) | ||||
0.423903 | + | 0.905708i | \(0.360660\pi\) | |||||||
\(200\) | −0.893213 | − | 0.515697i | −0.0631597 | − | 0.0364653i | ||||
\(201\) | −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 | ||||
\(205\) | 9.83748 | 0.687079 | ||||||||
\(206\) | 1.07343 | − | 0.619743i | 0.0747891 | − | 0.0431795i | ||||
\(207\) | 6.76305 | − | 11.7139i | 0.470065 | − | 0.814176i | ||||
\(208\) | −7.04879 | − | 12.2227i | −0.488746 | − | 0.847492i | ||||
\(209\) | 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 | ||||
\(213\) | 3.57088 | + | 2.06165i | 0.244673 | + | 0.141262i | ||||
\(214\) | − | 1.57965i | − | 0.107983i | ||||||
\(215\) | −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 | ||||
\(219\) | − | 1.25823i | − | 0.0850234i | ||||||
\(220\) | 0.611077 | − | 1.05842i | 0.0411988 | − | 0.0713584i | ||||
\(221\) | 5.73795 | + | 9.94969i | 0.385976 | + | 0.669288i | ||||
\(222\) | −0.221321 | − | 0.383340i | −0.0148541 | − | 0.0257281i | ||||
\(223\) | −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 | ||||
\(226\) | 0.516235 | − | 0.298048i | 0.0343394 | − | 0.0198259i | ||||
\(227\) | 6.95467i | 0.461598i | 0.973002 | + | 0.230799i | \(0.0741339\pi\) | ||||
−0.973002 | + | 0.230799i | \(0.925866\pi\) | |||||||
\(228\) | − | 1.66937i | − | 0.110557i | ||||||
\(229\) | 23.7481 | − | 13.7110i | 1.56932 | − | 0.906045i | 0.573068 | − | 0.819508i | \(-0.305753\pi\) |
0.996249 | − | 0.0865377i | \(-0.0275803\pi\) | |||||||
\(230\) | 0.516422 | + | 0.894470i | 0.0340519 | + | 0.0589796i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.40511 | − | 1.96594i | −0.223556 | − | 0.129070i | ||||
\(233\) | −3.42666 | − | 5.93515i | −0.224488 | − | 0.388825i | 0.731678 | − | 0.681651i | \(-0.238738\pi\) |
−0.956166 | + | 0.292826i | \(0.905404\pi\) | |||||||
\(234\) | 0.000566629 | − | 1.15475i | 3.70417e−5 | − | 0.0754883i | ||||
\(235\) | 10.7963 | − | 18.6997i | 0.704271 | − | 1.21983i | ||||
\(236\) | 18.5883i | 1.21000i | ||||||||
\(237\) | 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 | ||||
\(241\) | − | 15.7971i | − | 1.01758i | −0.860890 | − | 0.508790i | \(-0.830093\pi\) | ||
0.860890 | − | 0.508790i | \(-0.169907\pi\) | |||||||
\(242\) | −1.13272 | − | 0.653979i | −0.0728143 | − | 0.0420393i | ||||
\(243\) | −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 | ||||||||
\(247\) | 0.00255459 | − | 5.20608i | 0.000162545 | − | 0.331255i | ||||
\(248\) | 1.12675 | − | 1.95158i | 0.0715485 | − | 0.123926i | ||||
\(249\) | −0.286118 | + | 0.165190i | −0.0181320 | + | 0.0104685i | ||||
\(250\) | −1.45281 | −0.0918838 | ||||||||
\(251\) | −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 | ||||
\(255\) | 2.71188 | + | 1.56570i | 0.169825 | + | 0.0980483i | ||||
\(256\) | 14.8536 | 0.928352 | ||||||||
\(257\) | 20.4129 | 1.27332 | 0.636660 | − | 0.771145i | \(-0.280315\pi\) | ||||
0.636660 | + | 0.771145i | \(0.280315\pi\) | |||||||
\(258\) | −0.0469247 | − | 0.0270920i | −0.00292140 | − | 0.00168667i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −10.4633 | − | 6.04781i | −0.648904 | − | 0.375069i | ||||
\(261\) | 10.9053 | + | 18.8886i | 0.675023 | + | 1.16917i | ||||
\(262\) | −1.97044 | + | 1.13763i | −0.121734 | + | 0.0702833i | ||||
\(263\) | 14.7701 | + | 25.5826i | 0.910764 | + | 1.57749i | 0.812987 | + | 0.582281i | \(0.197840\pi\) |
0.0977768 | + | 0.995208i | \(0.468827\pi\) | |||||||
\(264\) | 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 | ||||
\(268\) | 23.1719 | − | 13.3783i | 1.41545 | − | 0.817211i | ||||
\(269\) | −27.9163 | −1.70209 | −0.851043 | − | 0.525096i | \(-0.824029\pi\) | ||||
−0.851043 | + | 0.525096i | \(0.824029\pi\) | |||||||
\(270\) | −0.334885 | − | 0.580038i | −0.0203805 | − | 0.0353000i | ||||
\(271\) | − | 29.4491i | − | 1.78890i | −0.447165 | − | 0.894451i | \(-0.647566\pi\) | ||
0.447165 | − | 0.894451i | \(-0.352434\pi\) | |||||||
\(272\) | −12.4660 | −0.755861 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.19362 | −0.132521 | ||||||||
\(275\) | 0.783965i | 0.0472748i | ||||||||
\(276\) | −2.93847 | − | 5.08959i | −0.176875 | − | 0.306357i | ||||
\(277\) | −6.85854 | −0.412090 | −0.206045 | − | 0.978543i | \(-0.566059\pi\) | ||||
−0.206045 | + | 0.978543i | \(0.566059\pi\) | |||||||
\(278\) | −0.547321 | + | 0.315996i | −0.0328261 | + | 0.0189522i | ||||
\(279\) | −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 | 0.640290 | − | 0.768133i | \(-0.278814\pi\) |
−0.985368 | + | 0.170441i | \(0.945481\pi\) | |||||||
\(284\) | −12.1761 | + | 7.02986i | −0.722517 | + | 0.417146i | ||||
\(285\) | −0.709684 | − | 1.22921i | −0.0420381 | − | 0.0728121i | ||||
\(286\) | 0.0791828 | − | 0.136993i | 0.00468217 | − | 0.00810058i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.29626 | + | 1.90310i | 0.194234 | + | 0.112141i | ||||
\(289\) | −6.85229 | −0.403076 | ||||||||
\(290\) | −1.66545 | −0.0977985 | ||||||||
\(291\) | 3.99786 | + | 2.30816i | 0.234358 | + | 0.135307i | ||||
\(292\) | 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 | ||||
\(296\) | 3.02968 | 0.176097 | ||||||||
\(297\) | −1.04087 | + | 0.600949i | −0.0603976 | + | 0.0348706i | ||||
\(298\) | 0.558054 | − | 0.966578i | 0.0323272 | − | 0.0559924i | ||||
\(299\) | −9.15610 | − | 15.8768i | −0.529511 | − | 0.918180i | ||||
\(300\) | 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 | ||||
\(304\) | 4.89341 | + | 2.82521i | 0.280657 | + | 0.162037i | ||||
\(305\) | 15.2354i | 0.872378i | ||||||||
\(306\) | −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 | ||||
\(310\) | − | 0.954525i | − | 0.0542134i | ||||||
\(311\) | −0.785363 | + | 1.36029i | −0.0445338 | + | 0.0771349i | −0.887433 | − | 0.460937i | \(-0.847514\pi\) |
0.842899 | + | 0.538071i | \(0.180847\pi\) | |||||||
\(312\) | −0.871939 | − | 0.503985i | −0.0493638 | − | 0.0285325i | ||||
\(313\) | 10.3116 | + | 17.8602i | 0.582846 | + | 1.00952i | 0.995140 | + | 0.0984686i | \(0.0313944\pi\) |
−0.412294 | + | 0.911051i | \(0.635272\pi\) | |||||||
\(314\) | −1.79101 | − | 1.03404i | −0.101073 | − | 0.0583544i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.83792 | + | 11.8436i | 0.384663 | + | 0.666256i | ||||
\(317\) | 26.4515 | − | 15.2718i | 1.48566 | − | 0.857747i | 0.485795 | − | 0.874073i | \(-0.338530\pi\) |
0.999867 | + | 0.0163255i | \(0.00519681\pi\) | |||||||
\(318\) | 0.0960927i | 0.00538861i | ||||||||
\(319\) | 2.98863i | 0.167331i | ||||||||
\(320\) | 11.1907 | − | 6.46096i | 0.625580 | − | 0.361179i | ||||
\(321\) | 3.82111 | + | 6.61836i | 0.213274 | + | 0.369401i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.98340 | − | 2.29982i | −0.221642 | − | 0.127965i | ||||
\(324\) | −6.01947 | − | 10.4260i | −0.334415 | − | 0.579224i | ||||
\(325\) | 7.75229 | + | 0.00380400i | 0.430019 | + | 0.000211008i | ||||
\(326\) | 0.709687 | − | 1.22921i | 0.0393059 | − | 0.0680799i | ||||
\(327\) | 6.08256i | 0.336366i | ||||||||
\(328\) | −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 | \(-0.0817992\pi\) |
0.263472 | + | 0.964667i | \(0.415132\pi\) | |||||||
\(332\) | − | 1.12654i | − | 0.0618269i | ||||||
\(333\) | −14.5545 | − | 8.40302i | −0.797579 | − | 0.460483i | ||||
\(334\) | 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 | \(0.698020\pi\) | |||||||
\(338\) | −1.35428 | − | 0.783669i | −0.0736633 | − | 0.0426260i | ||||
\(339\) | −1.44194 | + | 2.49750i | −0.0783152 | + | 0.135646i | ||||
\(340\) | −9.24704 | + | 5.33878i | −0.501491 | + | 0.289536i | ||||
\(341\) | −1.71289 | −0.0927580 | ||||||||
\(342\) | 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 | ||||
\(346\) | −1.30499 | − | 0.753435i | −0.0701566 | − | 0.0405049i | ||||
\(347\) | 2.20883 | 0.118576 | 0.0592882 | − | 0.998241i | \(-0.481117\pi\) | ||||
0.0592882 | + | 0.998241i | \(0.481117\pi\) | |||||||
\(348\) | 9.47651 | 0.507994 | ||||||||
\(349\) | 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 | ||||
\(352\) | 0.260774 | + | 0.451674i | 0.0138993 | + | 0.0240743i | ||||
\(353\) | −30.8680 | + | 17.8217i | −1.64294 | + | 0.948552i | −0.663158 | + | 0.748479i | \(0.730784\pi\) |
−0.979781 | + | 0.200072i | \(0.935882\pi\) | |||||||
\(354\) | 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 | ||||
\(359\) | 16.7331 | − | 9.66089i | 0.883142 | − | 0.509882i | 0.0114488 | − | 0.999934i | \(-0.496356\pi\) |
0.871693 | + | 0.490052i | \(0.163022\pi\) | |||||||
\(360\) | 2.15484 | 0.113570 | ||||||||
\(361\) | −8.45757 | − | 14.6489i | −0.445135 | − | 0.770997i | ||||
\(362\) | 1.32585i | 0.0696851i | ||||||||
\(363\) | 6.32780 | 0.332123 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.64783 | 0.190936 | ||||||||
\(366\) | 0.632502i | 0.0330614i | ||||||||
\(367\) | −1.86032 | − | 3.22218i | −0.0971082 | − | 0.168196i | 0.813378 | − | 0.581735i | \(-0.197626\pi\) |
−0.910487 | + | 0.413539i | \(0.864293\pi\) | |||||||
\(368\) | 19.8921 | 1.03695 | ||||||||
\(369\) | 13.4287 | − | 7.75306i | 0.699070 | − | 0.403608i | ||||
\(370\) | 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 | −0.816966 | − | 0.576686i | \(-0.804346\pi\) |
0.907908 | + | 0.419170i | \(0.137679\pi\) | |||||||
\(374\) | −0.0698995 | − | 0.121070i | −0.00361442 | − | 0.00626035i | ||||
\(375\) | 6.08693 | − | 3.51429i | 0.314328 | − | 0.181477i | ||||
\(376\) | 3.06779 | + | 5.31356i | 0.158209 | + | 0.274026i | ||||
\(377\) | 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 | \(0.444564\pi\) | |||||||
\(380\) | 4.83980 | 0.248276 | ||||||||
\(381\) | −4.69753 | −0.240662 | ||||||||
\(382\) | −0.618333 | − | 0.356995i | −0.0316367 | − | 0.0182655i | ||||
\(383\) | −19.4556 | − | 11.2327i | −0.994134 | − | 0.573964i | −0.0876266 | − | 0.996153i | \(-0.527928\pi\) |
−0.906507 | + | 0.422190i | \(0.861262\pi\) | |||||||
\(384\) | 1.90722 | − | 1.10114i | 0.0973276 | − | 0.0561921i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.252512 | − | 0.437364i | −0.0128525 | − | 0.0222612i | ||||
\(387\) | −2.05723 | −0.104575 | ||||||||
\(388\) | −13.6320 | + | 7.87043i | −0.692059 | + | 0.399561i | ||||
\(389\) | −6.66822 | + | 11.5497i | −0.338092 | + | 0.585592i | −0.984074 | − | 0.177760i | \(-0.943115\pi\) |
0.645982 | + | 0.763353i | \(0.276448\pi\) | |||||||
\(390\) | −0.426589 | 0.000209325i | −0.0216012 | 1.05996e-5i | ||||||
\(391\) | −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 | ||||
\(395\) | 10.0699 | + | 5.81388i | 0.506674 | + | 0.292528i | ||||
\(396\) | − | 1.92640i | − | 0.0968050i | ||||||
\(397\) | −22.3723 | − | 12.9166i | −1.12283 | − | 0.648268i | −0.180710 | − | 0.983536i | \(-0.557840\pi\) |
−0.942123 | + | 0.335268i | \(0.891173\pi\) | |||||||
\(398\) | 1.43948i | 0.0721544i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.20698 | + | 7.28670i | −0.210349 | + | 0.364335i | ||||
\(401\) | − | 17.5605i | − | 0.876930i | −0.898748 | − | 0.438465i | \(-0.855522\pi\) | ||
0.898748 | − | 0.438465i | \(-0.144478\pi\) | |||||||
\(402\) | 0.472228 | − | 0.817923i | 0.0235526 | − | 0.0407943i | ||||
\(403\) | −0.00831138 | + | 16.9380i | −0.000414019 | + | 0.843742i | ||||
\(404\) | 15.4338 | + | 26.7322i | 0.767862 | + | 1.32998i | ||||
\(405\) | −8.86464 | − | 5.11800i | −0.440487 | − | 0.254316i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.15143 | − | 1.99434i | −0.0570745 | − | 0.0988559i | ||||
\(408\) | −0.770587 | + | 0.444899i | −0.0381497 | + | 0.0220258i | ||||
\(409\) | − | 14.5282i | − | 0.718373i | −0.933266 | − | 0.359186i | \(-0.883054\pi\) | ||
0.933266 | − | 0.359186i | \(-0.116946\pi\) | |||||||
\(410\) | 1.18404i | 0.0584755i | ||||||||
\(411\) | 9.19074 | − | 5.30628i | 0.453346 | − | 0.261739i | ||||
\(412\) | −10.2236 | − | 17.7077i | −0.503679 | − | 0.872398i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.40989 | + | 0.814000i | 0.0692923 | + | 0.0400059i | ||||
\(415\) | −0.478915 | − | 0.829506i | −0.0235090 | − | 0.0407188i | ||||
\(416\) | 4.46767 | − | 2.57649i | 0.219046 | − | 0.126323i | ||||
\(417\) | 1.52876 | − | 2.64790i | 0.0748639 | − | 0.129668i | ||||
\(418\) | 0.0633664i | 0.00309935i | ||||||||
\(419\) | −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 | ||||
\(423\) | − | 34.0348i | − | 1.65483i | ||||||
\(424\) | −0.569593 | − | 0.328854i | −0.0276619 | − | 0.0159706i | ||||
\(425\) | 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 | ||||||||
\(429\) | −0.000375631 | 0.765510i | −1.81357e−5 | 0.0369592i | ||||||
\(430\) | 0.0785443 | − | 0.136043i | 0.00378774 | − | 0.00656056i | ||||
\(431\) | 24.5649 | − | 14.1825i | 1.18325 | − | 0.683149i | 0.226485 | − | 0.974015i | \(-0.427277\pi\) |
0.956764 | + | 0.290865i | \(0.0939432\pi\) | |||||||
\(432\) | −12.8995 | −0.620625 | ||||||||
\(433\) | 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 | ||||
\(437\) | 6.35636 | + | 3.66984i | 0.304066 | + | 0.175552i | ||||
\(438\) | 0.151441 | 0.00723611 | ||||||||
\(439\) | 31.7273 | 1.51426 | 0.757132 | − | 0.653262i | \(-0.226600\pi\) | ||||
0.757132 | + | 0.653262i | \(0.226600\pi\) | |||||||
\(440\) | 0.255711 | + | 0.147635i | 0.0121906 | + | 0.00703822i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.19754 | + | 0.690619i | −0.0569613 | + | 0.0328494i | ||||
\(443\) | −0.865241 | − | 1.49864i | −0.0411088 | − | 0.0712026i | 0.844739 | − | 0.535179i | \(-0.179756\pi\) |
−0.885848 | + | 0.463976i | \(0.846422\pi\) | |||||||
\(444\) | −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 | \(0.413466\pi\) | |||||||
\(450\) | −0.596355 | + | 0.344306i | −0.0281125 | + | 0.0162307i | ||||
\(451\) | 2.12475 | 0.100050 | ||||||||
\(452\) | −4.91675 | − | 8.51605i | −0.231264 | − | 0.400561i | ||||
\(453\) | 8.15978i | 0.383380i | ||||||||
\(454\) | −0.837063 | −0.0392853 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.403317 | 0.0188870 | ||||||||
\(457\) | 7.94894i | 0.371836i | 0.982565 | + | 0.185918i | \(0.0595259\pi\) | ||||
−0.982565 | + | 0.185918i | \(0.940474\pi\) | |||||||
\(458\) | 1.65025 | + | 2.85832i | 0.0771111 | + | 0.133560i | ||||
\(459\) | 10.5006 | 0.490125 | ||||||||
\(460\) | 14.7556 | − | 8.51915i | 0.687983 | − | 0.397207i | ||||
\(461\) | −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 | ||||
\(467\) | −9.94917 | − | 17.2325i | −0.460393 | − | 0.797423i | 0.538588 | − | 0.842569i | \(-0.318958\pi\) |
−0.998980 | + | 0.0451460i | \(0.985625\pi\) | |||||||
\(468\) | −19.0493 | − | 0.00934738i | −0.880554 | − | 0.000432083i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.25069 | + | 1.29944i | 0.103817 | + | 0.0599386i | ||||
\(471\) | 10.0052 | 0.461017 | ||||||||
\(472\) | −4.49090 | −0.206710 | ||||||||
\(473\) | −0.244127 | − | 0.140947i | −0.0112250 | − | 0.00648075i | ||||
\(474\) | 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 | ||||
\(478\) | −2.65699 | −0.121528 | ||||||||
\(479\) | 22.7680 | − | 13.1451i | 1.04030 | − | 0.600615i | 0.120379 | − | 0.992728i | \(-0.461589\pi\) |
0.919917 | + | 0.392113i | \(0.128256\pi\) | |||||||
\(480\) | 0.703043 | − | 1.21771i | 0.0320894 | − | 0.0555804i | ||||
\(481\) | −19.7268 | + | 11.3764i | −0.899464 | + | 0.518717i | ||||
\(482\) | 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 | ||||
\(486\) | −1.39879 | − | 0.807592i | −0.0634504 | − | 0.0366331i | ||||
\(487\) | 6.37962i | 0.289088i | 0.989498 | + | 0.144544i | \(0.0461716\pi\) | ||||
−0.989498 | + | 0.144544i | \(0.953828\pi\) | |||||||
\(488\) | −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 | \(0.187998\pi\) | |||||||
\(492\) | − | 6.73725i | − | 0.303739i | ||||||
\(493\) | 13.0554 | − | 22.6125i | 0.587984 | − | 1.01842i | ||||
\(494\) | 0.626603 | 0.000307471i | 0.0281922 | 1.38338e-5i | ||||||
\(495\) | −0.818951 | − | 1.41846i | −0.0368091 | − | 0.0637552i | ||||
\(496\) | −15.9207 | − | 9.19184i | −0.714862 | − | 0.412726i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.0198823 | − | 0.0344371i | −0.000890947 | − | 0.00154316i | ||||
\(499\) | −24.3639 | + | 14.0665i | −1.09068 | + | 0.629704i | −0.933757 | − | 0.357906i | \(-0.883491\pi\) |
−0.156923 | + | 0.987611i | \(0.550157\pi\) | |||||||
\(500\) | 23.9662i | 1.07180i | ||||||||
\(501\) | 2.51368i | 0.112303i | ||||||||
\(502\) | 2.35119 | − | 1.35746i | 0.104939 | − | 0.0605864i | ||||
\(503\) | −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 | ||||
\(506\) | 0.111539 | + | 0.193192i | 0.00495853 | + | 0.00858843i | ||||
\(507\) | 7.56979 | + | 0.00742891i | 0.336186 | + | 0.000329930i | ||||
\(508\) | 8.00888 | − | 13.8718i | 0.355336 | − | 0.615461i | ||||
\(509\) | 13.5944i | 0.602560i | 0.953536 | + | 0.301280i | \(0.0974139\pi\) | ||||
−0.953536 | + | 0.301280i | \(0.902586\pi\) | |||||||
\(510\) | −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 | ||||
\(514\) | 2.45689i | 0.108369i | ||||||||
\(515\) | −15.0558 | − | 8.69250i | −0.663440 | − | 0.383037i | ||||
\(516\) | −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 | ||||||||
\(520\) | 1.46114 | − | 2.52790i | 0.0640752 | − | 0.110856i | ||||
\(521\) | 4.39172 | − | 7.60669i | 0.192405 | − | 0.333255i | −0.753642 | − | 0.657285i | \(-0.771705\pi\) |
0.946047 | + | 0.324030i | \(0.105038\pi\) | |||||||
\(522\) | −2.27343 | + | 1.31256i | −0.0995053 | + | 0.0574494i | ||||
\(523\) | −32.5698 | −1.42418 | −0.712088 | − | 0.702090i | \(-0.752251\pi\) | ||||
−0.712088 | + | 0.702090i | \(0.752251\pi\) | |||||||
\(524\) | 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 | ||||
\(528\) | −0.719535 | − | 0.415424i | −0.0313137 | − | 0.0180790i | ||||
\(529\) | 2.83905 | 0.123437 | ||||||||
\(530\) | −0.278589 | −0.0121011 | ||||||||
\(531\) | 21.5741 | + | 12.4558i | 0.936235 | + | 0.540536i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.0103098 | − | 21.0107i | 0.000446568 | − | 0.910074i | ||||
\(534\) | −0.0399109 | − | 0.0691277i | −0.00172711 | − | 0.00299145i | ||||
\(535\) | −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 | ||||
\(541\) | −6.01775 | + | 3.47435i | −0.258723 | + | 0.149374i | −0.623752 | − | 0.781622i | \(-0.714392\pi\) |
0.365029 | + | 0.930996i | \(0.381059\pi\) | |||||||
\(542\) | 3.54448 | 0.152249 | ||||||||
\(543\) | −3.20718 | − | 5.55500i | −0.137633 | − | 0.238388i | ||||
\(544\) | − | 4.55659i | − | 0.195362i | ||||||
\(545\) | −17.6344 | −0.755375 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.9095 | 0.466457 | 0.233229 | − | 0.972422i | \(-0.425071\pi\) | ||||
0.233229 | + | 0.972422i | \(0.425071\pi\) | |||||||
\(548\) | 36.1870i | 1.54583i | ||||||||
\(549\) | 12.0073 | + | 20.7972i | 0.512457 | + | 0.887602i | ||||
\(550\) | −0.0943579 | −0.00402343 | ||||||||
\(551\) | −10.2495 | + | 5.91758i | −0.436645 | + | 0.252097i | ||||
\(552\) | 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 | \(-0.928852\pi\) |
−0.295596 | + | 0.955313i | \(0.595518\pi\) | |||||||
\(558\) | −0.752275 | − | 1.30298i | −0.0318463 | − | 0.0551595i | ||||
\(559\) | −1.39495 | + | 2.41339i | −0.0590001 | + | 0.102075i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.585725 | + | 0.338169i | 0.0247293 | + | 0.0142775i | ||||
\(562\) | 3.50176 | 0.147713 | ||||||||
\(563\) | 9.13679 | 0.385070 | 0.192535 | − | 0.981290i | \(-0.438329\pi\) | ||||
0.192535 | + | 0.981290i | \(0.438329\pi\) | |||||||
\(564\) | −12.8066 | − | 7.39388i | −0.539254 | − | 0.311339i | ||||
\(565\) | −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 | ||||
\(569\) | −18.3000 | −0.767176 | −0.383588 | − | 0.923504i | \(-0.625312\pi\) | ||||
−0.383588 | + | 0.923504i | \(0.625312\pi\) | |||||||
\(570\) | 0.147947 | − | 0.0854175i | 0.00619684 | − | 0.00357775i | ||||
\(571\) | 5.08954 | − | 8.81533i | 0.212990 | − | 0.368910i | −0.739659 | − | 0.672982i | \(-0.765013\pi\) |
0.952649 | + | 0.304072i | \(0.0983464\pi\) | |||||||
\(572\) | −2.25991 | − | 1.30624i | −0.0944914 | − | 0.0546165i | ||||
\(573\) | 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 | ||||
\(577\) | 16.9018 | + | 9.75824i | 0.703630 | + | 0.406241i | 0.808698 | − | 0.588224i | \(-0.200173\pi\) |
−0.105068 | + | 0.994465i | \(0.533506\pi\) | |||||||
\(578\) | − | 0.824740i | − | 0.0343047i | ||||||
\(579\) | 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 | ||||
\(583\) | 0.499926i | 0.0207048i | ||||||||
\(584\) | −0.518270 | + | 0.897670i | −0.0214462 | + | 0.0371458i | ||||
\(585\) | −14.0306 | + | 8.09136i | −0.580092 | + | 0.334537i | ||||
\(586\) | 1.07052 | + | 1.85419i | 0.0442226 | + | 0.0765959i | ||||
\(587\) | 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 | ||||
\(590\) | −1.64738 | + | 0.951117i | −0.0678217 | + | 0.0391569i | ||||
\(591\) | − | 3.36852i | − | 0.138562i | ||||||
\(592\) | − | 24.7157i | − | 1.01581i | ||||||
\(593\) | 15.6648 | − | 9.04406i | 0.643275 | − | 0.371395i | −0.142600 | − | 0.989780i | \(-0.545546\pi\) |
0.785875 | + | 0.618385i | \(0.212213\pi\) | |||||||
\(594\) | −0.0723301 | − | 0.125279i | −0.00296774 | − | 0.00514028i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.9451 | − | 9.20592i | −0.653138 | − | 0.377089i | ||||
\(597\) | −3.48204 | − | 6.03107i | −0.142510 | − | 0.246835i | ||||
\(598\) | 1.91093 | − | 1.10203i | 0.0781438 | − | 0.0450653i | ||||
\(599\) | −4.52996 | + | 7.84612i | −0.185089 | + | 0.320584i | −0.943607 | − | 0.331069i | \(-0.892591\pi\) |
0.758517 | + | 0.651653i | \(0.225924\pi\) | |||||||
\(600\) | 0.600572i | 0.0245182i | ||||||||
\(601\) | 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 | ||||
\(605\) | 18.3454i | 0.745846i | ||||||||
\(606\) | 0.943592 | + | 0.544783i | 0.0383308 | + | 0.0221303i | ||||
\(607\) | −19.6825 | + | 34.0911i | −0.798887 | + | 1.38371i | 0.121454 | + | 0.992597i | \(0.461244\pi\) |
−0.920341 | + | 0.391116i | \(0.872089\pi\) | |||||||
\(608\) | −1.03268 | + | 1.78865i | −0.0418807 | + | 0.0725394i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.83373 | −0.0742457 | ||||||||
\(611\) | −39.9271 | − | 23.0781i | −1.61528 | − | 0.933639i | ||||
\(612\) | −8.41514 | + | 14.5755i | −0.340162 | + | 0.589178i | ||||
\(613\) | −4.79186 | + | 2.76658i | −0.193541 | + | 0.111741i | −0.593639 | − | 0.804731i | \(-0.702309\pi\) |
0.400098 | + | 0.916472i | \(0.368976\pi\) | |||||||
\(614\) | 1.09283 | 0.0441029 | ||||||||
\(615\) | −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 | ||||
\(619\) | 19.3950 | + | 11.1977i | 0.779552 | + | 0.450075i | 0.836272 | − | 0.548316i | \(-0.184731\pi\) |
−0.0567194 | + | 0.998390i | \(0.518064\pi\) | |||||||
\(620\) | −15.7463 | −0.632386 | ||||||||
\(621\) | −16.7559 | −0.672390 | ||||||||
\(622\) | −0.163724 | − | 0.0945262i | −0.00656474 | − | 0.00379015i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.11144 | + | 7.11315i | −0.164589 | + | 0.284754i | ||||
\(625\) | 4.81330 | + | 8.33687i | 0.192532 | + | 0.333475i | ||||
\(626\) | −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 | \(0.320982\pi\) | |||||||
\(632\) | −2.86140 | + | 1.65203i | −0.113820 | + | 0.0657142i | ||||
\(633\) | −4.79570 | −0.190612 | ||||||||
\(634\) | 1.83811 | + | 3.18369i | 0.0730005 | + | 0.126441i | ||||
\(635\) | − | 13.6190i | − | 0.540452i | ||||||
\(636\) | 1.58519 | 0.0628569 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.359712 | −0.0142411 | ||||||||
\(639\) | 18.8425i | 0.745397i | ||||||||
\(640\) | 3.19238 | + | 5.52937i | 0.126190 | + | 0.218568i | ||||
\(641\) | −10.4210 | −0.411605 | −0.205803 | − | 0.978594i | \(-0.565981\pi\) | ||||
−0.205803 | + | 0.978594i | \(0.565981\pi\) | |||||||
\(642\) | −0.796586 | + | 0.459909i | −0.0314387 | + | 0.0181512i | ||||
\(643\) | −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 | 0.641068 | − | 0.767484i | \(-0.278492\pi\) |
−0.985195 | + | 0.171439i | \(0.945158\pi\) | |||||||
\(648\) | 2.51891 | − | 1.45429i | 0.0989520 | − | 0.0571300i | ||||
\(649\) | 1.70677 | + | 2.95622i | 0.0669966 | + | 0.116042i | ||||
\(650\) | −0.000457849 | 0.933064i | −1.79583e−5 | 0.0365978i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.2777 | − | 11.7073i | −0.794136 | − | 0.458494i | ||||
\(653\) | −10.1834 | −0.398506 | −0.199253 | − | 0.979948i | \(-0.563852\pi\) | ||||
−0.199253 | + | 0.979948i | \(0.563852\pi\) | |||||||
\(654\) | −0.732096 | −0.0286272 | ||||||||
\(655\) | 27.6374 | + | 15.9564i | 1.07988 | + | 0.623470i | ||||
\(656\) | 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 | \(0.507352\pi\) | |||||||
\(660\) | −0.711651 | −0.0277010 | ||||||||
\(661\) | −28.5156 | + | 16.4635i | −1.10913 | + | 0.640356i | −0.938604 | − | 0.344997i | \(-0.887880\pi\) |
−0.170526 | + | 0.985353i | \(0.554547\pi\) | |||||||
\(662\) | −1.55584 | + | 2.69479i | −0.0604693 | + | 0.104736i | ||||
\(663\) | 3.34684 | − | 5.79034i | 0.129981 | − | 0.224878i | ||||
\(664\) | 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 | ||||
\(668\) | −7.42287 | − | 4.28560i | −0.287200 | − | 0.165815i | ||||
\(669\) | 8.90992i | 0.344478i | ||||||||
\(670\) | 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 | \(-0.00528409\pi\) | |||||||
\(674\) | − | 2.57515i | − | 0.0991912i | ||||||
\(675\) | 3.54370 | − | 6.13787i | 0.136397 | − | 0.236247i | ||||
\(676\) | −12.9278 | + | 22.3409i | −0.497222 | + | 0.859265i | ||||
\(677\) | 14.7664 | + | 25.5761i | 0.567519 | + | 0.982971i | 0.996810 | + | 0.0798052i | \(0.0254298\pi\) |
−0.429292 | + | 0.903166i | \(0.641237\pi\) | |||||||
\(678\) | −0.300599 | − | 0.173551i | −0.0115444 | − | 0.00666519i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.28984 | − | 2.23406i | −0.0494630 | − | 0.0856725i | ||||
\(681\) | 3.50710 | − | 2.02482i | 0.134392 | − | 0.0775914i | ||||
\(682\) | − | 0.206163i | − | 0.00789438i | ||||||
\(683\) | − | 18.2880i | − | 0.699771i | −0.936793 | − | 0.349885i | \(-0.886221\pi\) | ||
0.936793 | − | 0.349885i | \(-0.113779\pi\) | |||||||
\(684\) | 6.60659 | − | 3.81431i | 0.252609 | − | 0.145844i | ||||
\(685\) | 15.3838 | + | 26.6456i | 0.587786 | + | 1.01807i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.8283 | − | 7.98378i | −0.527583 | − | 0.304600i | ||||
\(688\) | −1.51272 | − | 2.62012i | −0.0576721 | − | 0.0998910i | ||||
\(689\) | 4.94355 | + | 0.00242577i | 0.188334 | + | 9.24146e-5i | ||||
\(690\) | 0.300709 | − | 0.520843i | 0.0114478 | − | 0.0198281i | ||||
\(691\) | − | 10.3406i | − | 0.393376i | −0.980466 | − | 0.196688i | \(-0.936981\pi\) | ||
0.980466 | − | 0.196688i | \(-0.0630186\pi\) | |||||||
\(692\) | −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 | ||||
\(696\) | 2.28950i | 0.0867834i | ||||||||
\(697\) | −16.0762 | − | 9.28160i | −0.608930 | − | 0.351566i | ||||
\(698\) | −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 | \(0.211419\pi\) | |||||||
\(702\) | −1.23918 | + | 0.714633i | −0.0467700 | + | 0.0269721i | ||||
\(703\) | 4.55974 | − | 7.89770i | 0.171974 | − | 0.297867i | ||||
\(704\) | 2.41702 | − | 1.39547i | 0.0910951 | − | 0.0525938i | ||||
\(705\) | −12.5732 | −0.473533 | ||||||||
\(706\) | −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 | \(-0.333399\pi\) |
−0.500178 | + | 0.865923i | \(0.666732\pi\) | |||||||
\(710\) | −1.24604 | − | 0.719400i | −0.0467630 | − | 0.0269986i | ||||
\(711\) | 18.3280 | 0.687355 | ||||||||
\(712\) | 0.546342 | 0.0204750 | ||||||||
\(713\) | −20.6804 | − | 11.9398i | −0.774488 | − | 0.447151i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.21935 | − | 0.00108902i | −0.0829988 | − | 4.07271e-5i | ||||
\(716\) | −6.54757 | − | 11.3407i | −0.244694 | − | 0.423823i | ||||
\(717\) | 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 | −0.524724 | − | 0.851272i | \(-0.675832\pi\) |
0.999586 | + | 0.0287885i | \(0.00916494\pi\) | |||||||
\(720\) | − | 17.5789i | − | 0.655127i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.76314 | − | 1.01795i | 0.0656174 | − | 0.0378842i | ||||
\(723\) | −7.96616 | + | 4.59926i | −0.296265 | + | 0.171048i | ||||
\(724\) | 21.8718 | 0.812860 | ||||||||
\(725\) | −8.81176 | − | 15.2624i | −0.327261 | − | 0.566832i | ||||
\(726\) | 0.761613i | 0.0282661i | ||||||||
\(727\) | 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 | ||||||||
\(730\) | 0.439053i | 0.0162501i | ||||||||
\(731\) | 1.23141 | + | 2.13286i | 0.0455453 | + | 0.0788867i | ||||
\(732\) | 10.4341 | 0.385654 | ||||||||
\(733\) | −5.39750 | + | 3.11625i | −0.199361 | + | 0.115101i | −0.596357 | − | 0.802719i | \(-0.703386\pi\) |
0.396996 | + | 0.917820i | \(0.370053\pi\) | |||||||
\(734\) | 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 | \(-0.674262\pi\) |
0.479195 | + | 0.877708i | \(0.340929\pi\) | |||||||
\(740\) | −10.5849 | − | 18.3337i | −0.389110 | − | 0.673959i | ||||
\(741\) | −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 | \(0.631155\pi\) | |||||||
\(744\) | −1.31219 | −0.0481073 | ||||||||
\(745\) | −15.6545 | −0.573537 | ||||||||
\(746\) | 0.366152 | + | 0.211398i | 0.0134058 | + | 0.00773983i | ||||
\(747\) | −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 | ||||
\(751\) | 36.6046 | 1.33572 | 0.667860 | − | 0.744287i | \(-0.267210\pi\) | ||||
0.667860 | + | 0.744287i | \(0.267210\pi\) | |||||||
\(752\) | 43.3473 | − | 25.0266i | 1.58071 | − | 0.912625i | ||||
\(753\) | −6.56728 | + | 11.3749i | −0.239325 | + | 0.414523i | ||||
\(754\) | −0.00174542 | + | 3.55703i | −6.35643e−5 | + | 0.129540i | ||||
\(755\) | −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 | ||||
\(759\) | −0.934648 | − | 0.539619i | −0.0339256 | − | 0.0195869i | ||||
\(760\) | 1.16928i | 0.0424144i | ||||||||
\(761\) | −34.4408 | − | 19.8844i | −1.24848 | − | 0.720810i | −0.277673 | − | 0.960676i | \(-0.589563\pi\) |
−0.970806 | + | 0.239866i | \(0.922896\pi\) | |||||||
\(762\) | − | 0.565394i | − | 0.0204821i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.88916 | + | 10.2003i | −0.213062 | + | 0.369035i | ||||
\(765\) | 14.3098i | 0.517372i | ||||||||
\(766\) | 1.35197 | − | 2.34167i | 0.0488485 | − | 0.0846081i | ||||
\(767\) | 29.2410 | − | 16.8632i | 1.05583 | − | 0.608894i | ||||
\(768\) | −4.32457 | − | 7.49038i | −0.156050 | − | 0.270286i | ||||
\(769\) | 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 | ||||
\(772\) | −7.21496 | + | 4.16556i | −0.259672 | + | 0.149922i | ||||
\(773\) | − | 12.7518i | − | 0.458649i | −0.973350 | − | 0.229324i | \(-0.926348\pi\) | ||
0.973350 | − | 0.229324i | \(-0.0736517\pi\) | |||||||
\(774\) | − | 0.247608i | − | 0.00890007i | ||||||
\(775\) | 8.74740 | − | 5.05032i | 0.314216 | − | 0.181413i | ||||
\(776\) | −1.90148 | − | 3.29346i | −0.0682592 | − | 0.118228i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.39012 | − | 0.802586i | −0.0498382 | − | 0.0287741i | ||||
\(779\) | 4.20705 | + | 7.28683i | 0.150733 | + | 0.261078i | ||||
\(780\) | −0.00345312 | + | 7.03721i | −0.000123641 | + | 0.251972i | ||||
\(781\) | −1.29096 | + | 2.23601i | −0.0461941 | + | 0.0800106i | ||||
\(782\) | − | 1.94897i | − | 0.0696949i | ||||||
\(783\) | 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 | ||||
\(787\) | − | 8.68773i | − | 0.309684i | −0.987939 | − | 0.154842i | \(-0.950513\pi\) | ||
0.987939 | − | 0.154842i | \(-0.0494869\pi\) | |||||||
\(788\) | 9.94723 | + | 5.74303i | 0.354355 | + | 0.204587i | ||||
\(789\) | 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 | ||||||||
\(793\) | 32.5395 | + | 0.0159670i | 1.15551 | + | 0.000567003i | ||||
\(794\) | 1.55465 | − | 2.69273i | 0.0551723 | − | 0.0955613i | ||||
\(795\) | 1.16722 | − | 0.673897i | 0.0413972 | − | 0.0239007i | ||||
\(796\) | 23.7463 | 0.841664 | ||||||||
\(797\) | −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 | ||||
\(801\) | −2.62460 | − | 1.51532i | −0.0927358 | − | 0.0535411i | ||||
\(802\) | 2.11358 | 0.0746331 | ||||||||
\(803\) | 0.787876 | 0.0278036 | ||||||||
\(804\) | −13.4928 | − | 7.79009i | −0.475856 | − | 0.274735i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.03866 | − | 0.00100036i | −0.0718086 | − | 3.52361e-5i | ||||
\(807\) | 8.12771 | + | 14.0776i | 0.286109 | + | 0.495555i | ||||
\(808\) | −6.45844 | + | 3.72878i | −0.227207 | + | 0.131178i | ||||
\(809\) | −14.4275 | − | 24.9892i | −0.507244 | − | 0.878573i | −0.999965 | − | 0.00838530i | \(-0.997331\pi\) |
0.492721 | − | 0.870188i | \(-0.336002\pi\) | |||||||
\(810\) | 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 | ||||
\(814\) | 0.240039 | − | 0.138586i | 0.00841336 | − | 0.00485745i | ||||
\(815\) | −19.9081 | −0.697351 | ||||||||
\(816\) | 3.62942 | + | 6.28634i | 0.127055 | + | 0.220066i | ||||
\(817\) | − | 1.11632i | − | 0.0390549i | ||||||
\(818\) | 1.74861 | 0.0611388 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.5324 | 0.682103 | ||||||||
\(821\) | − | 41.0238i | − | 1.43174i | −0.698233 | − | 0.715870i | \(-0.746030\pi\) | ||
0.698233 | − | 0.715870i | \(-0.253970\pi\) | |||||||
\(822\) | 0.638663 | + | 1.10620i | 0.0222759 | + | 0.0385830i | ||||
\(823\) | 2.13613 | 0.0744608 | 0.0372304 | − | 0.999307i | \(-0.488146\pi\) | ||||
0.0372304 | + | 0.999307i | \(0.488146\pi\) | |||||||
\(824\) | 4.27815 | − | 2.46999i | 0.149037 | − | 0.0860463i | ||||
\(825\) | 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 | 0.965238 | − | 0.261373i | \(-0.0841751\pi\) |
−0.708974 | + | 0.705234i | \(0.750842\pi\) | |||||||
\(830\) | 0.0998392 | − | 0.0576422i | 0.00346547 | − | 0.00200079i | ||||
\(831\) | 1.99684 | + | 3.45862i | 0.0692695 | + | 0.119978i | ||||
\(832\) | −13.7875 | − | 23.9077i | −0.477995 | − | 0.828850i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.318701 | + | 0.184002i | 0.0110357 | + | 0.00637146i | ||||
\(835\) | −7.28758 | −0.252197 | ||||||||
\(836\) | 1.04532 | 0.0361532 | ||||||||
\(837\) | 13.4107 | + | 7.74265i | 0.463540 | + | 0.267625i | ||||
\(838\) | −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 | ||||
\(842\) | 2.31867 | 0.0799068 | ||||||||
\(843\) | −14.6715 | + | 8.47062i | −0.505315 | + | 0.291743i | ||||
\(844\) | 8.17626 | − | 14.1617i | 0.281438 | − | 0.487465i | ||||
\(845\) | −0.0215377 | + | 21.9461i | −0.000740920 | + | 0.754970i | ||||
\(846\) | 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 | ||||
\(850\) | 0.713928 | + | 0.412187i | 0.0244875 | + | 0.0141379i | ||||
\(851\) | − | 32.1047i | − | 1.10054i | ||||||
\(852\) | 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 | ||||
\(856\) | − | 6.29572i | − | 0.215183i | ||||||
\(857\) | −5.88263 | + | 10.1890i | −0.200947 | + | 0.348050i | −0.948834 | − | 0.315776i | \(-0.897735\pi\) |
0.747887 | + | 0.663826i | \(0.231068\pi\) | |||||||
\(858\) | −0.0921367 | 4.52110e-5i | −0.00314549 | 1.54348e-6i | ||||||
\(859\) | −10.8881 | − | 18.8587i | −0.371496 | − | 0.643450i | 0.618300 | − | 0.785942i | \(-0.287822\pi\) |
−0.989796 | + | 0.142492i | \(0.954488\pi\) | |||||||
\(860\) | −2.24422 | − | 1.29570i | −0.0765274 | − | 0.0441831i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.70701 | + | 2.95663i | 0.0581410 | + | 0.100703i | ||||
\(863\) | 35.5569 | − | 20.5288i | 1.21037 | − | 0.698807i | 0.247530 | − | 0.968880i | \(-0.420381\pi\) |
0.962840 | + | 0.270073i | \(0.0870479\pi\) | |||||||
\(864\) | − | 4.71504i | − | 0.160409i | ||||||
\(865\) | 21.1353i | 0.718623i | ||||||||
\(866\) | −1.30505 | + | 0.753470i | −0.0443473 | + | 0.0256040i | ||||
\(867\) | 1.99502 | + | 3.45547i | 0.0677543 | + | 0.117354i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.17496 | + | 1.25571i | 0.0737803 | + | 0.0425971i | ||||
\(870\) | 0.484889 | + | 0.839852i | 0.0164393 | + | 0.0284737i | ||||
\(871\) | −42.0667 | − | 24.3147i | −1.42538 | − | 0.823873i | ||||
\(872\) | 2.50543 | − | 4.33953i | 0.0848445 | − | 0.146955i | ||||
\(873\) | 21.0955i | 0.713975i | ||||||||
\(874\) | −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 | \(-0.370452\pi\) |
−0.597365 | + | 0.801970i | \(0.703786\pi\) | |||||||
\(878\) | 3.81870i | 0.128875i | ||||||||
\(879\) | −8.97043 | − | 5.17908i | −0.302565 | − | 0.174686i | ||||
\(880\) | 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 | \(0.382838\pi\) | |||||||
\(884\) | 11.3928 | + | 19.7552i | 0.383180 | + | 0.664440i | ||||
\(885\) | 4.60143 | − | 7.96991i | 0.154675 | − | 0.267906i | ||||
\(886\) | 0.180376 | − | 0.104140i | 0.00605986 | − | 0.00349866i | ||||
\(887\) | 34.1150 | 1.14547 | 0.572735 | − | 0.819740i | \(-0.305882\pi\) | ||||
0.572735 | + | 0.819740i | \(0.305882\pi\) | |||||||
\(888\) | −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 | ||||
\(892\) | −26.3110 | − | 15.1906i | −0.880956 | − | 0.508620i | ||||
\(893\) | 18.4684 | 0.618020 | ||||||||
\(894\) | −0.649901 | −0.0217359 | ||||||||
\(895\) | −9.64235 | − | 5.56701i | −0.322308 | − | 0.186085i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.34060 | + | 9.23971i | −0.178317 | + | 0.308505i | ||||
\(898\) | −0.635282 | − | 1.10034i | −0.0211996 | − | 0.0367188i | ||||
\(899\) | 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 | ||||
\(905\) | 16.1049 | − | 9.29816i | 0.535345 | − | 0.309081i | ||||
\(906\) | −0.982110 | −0.0326284 | ||||||||
\(907\) | 21.0758 | + | 36.5043i | 0.699810 | + | 1.21211i | 0.968532 | + | 0.248888i | \(0.0800652\pi\) |
−0.268723 | + | 0.963218i | \(0.586601\pi\) | |||||||
\(908\) | 13.8086i | 0.458254i | ||||||||
\(909\) | 41.3681 | 1.37209 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.9947 | 0.695584 | 0.347792 | − | 0.937572i | \(-0.386932\pi\) | ||||
0.347792 | + | 0.937572i | \(0.386932\pi\) | |||||||
\(912\) | − | 3.29020i | − | 0.108949i | ||||||
\(913\) | −0.103438 | − | 0.179161i | −0.00342331 | − | 0.00592935i | ||||
\(914\) | −0.956734 | −0.0316459 | ||||||||
\(915\) | 7.68291 | − | 4.43573i | 0.253989 | − | 0.146641i | ||||
\(916\) | 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 | −0.723735 | − | 0.690078i | \(-0.757576\pi\) |
0.959493 | + | 0.281734i | \(0.0909096\pi\) | |||||||
\(920\) | 2.05821 | + | 3.56492i | 0.0678571 | + | 0.117532i | ||||
\(921\) | −4.57869 | + | 2.64351i | −0.150873 | + | 0.0871065i | ||||
\(922\) | −0.655471 | − | 1.13531i | −0.0215868 | − | 0.0373894i | ||||
\(923\) | 22.1046 | + | 12.7766i | 0.727583 | + | 0.420546i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.7603 | + | 6.78983i | 0.386677 | + | 0.223248i | ||||
\(926\) | 4.31162 | 0.141689 | ||||||||
\(927\) | −27.4027 | −0.900024 | ||||||||
\(928\) | −10.1536 | − | 5.86220i | −0.333309 | − | 0.192436i | ||||
\(929\) | 5.89524 | + | 3.40362i | 0.193416 | + | 0.111669i | 0.593581 | − | 0.804774i | \(-0.297714\pi\) |
−0.400164 | + | 0.916443i | \(0.631047\pi\) | |||||||
\(930\) | −0.481347 | + | 0.277906i | −0.0157840 | + | 0.00911290i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.80369 | − | 11.7843i | −0.222862 | − | 0.386009i | ||||
\(933\) | 0.914621 | 0.0299433 | ||||||||
\(934\) | 2.07410 | − | 1.19748i | 0.0678666 | − | 0.0391828i | ||||
\(935\) | −0.980409 | + | 1.69812i | −0.0320628 | + | 0.0555344i | ||||
\(936\) | 0.00225831 | − | 4.60227i | 7.38151e−5 | − | 0.150430i | ||||
\(937\) | 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 | ||||
\(941\) | −48.8788 | − | 28.2202i | −1.59340 | − | 0.919951i | −0.992718 | − | 0.120465i | \(-0.961561\pi\) |
−0.600685 | − | 0.799486i | \(-0.705105\pi\) | |||||||
\(942\) | 1.20423i | 0.0392359i | ||||||||
\(943\) | 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 | ||||
\(947\) | 5.85027i | 0.190108i | 0.995472 | + | 0.0950541i | \(0.0303024\pi\) | ||||
−0.995472 | + | 0.0950541i | \(0.969698\pi\) | |||||||
\(948\) | 3.98167 | − | 6.89645i | 0.129319 | − | 0.223986i | ||||
\(949\) | 0.00382299 | − | 7.79097i | 0.000124099 | − | 0.252906i | ||||
\(950\) | −0.186831 | − | 0.323601i | −0.00606160 | − | 0.0104990i | ||||
\(951\) | −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 | \(0.947916\pi\) | |||||||
\(954\) | −0.380290 | + | 0.219560i | −0.0123123 | + | 0.00710853i | ||||
\(955\) | 10.0144i | 0.324059i | ||||||||
\(956\) | 43.8310i | 1.41760i | ||||||||
\(957\) | 1.50711 | − | 0.870129i | 0.0487179 | − | 0.0281273i | ||||
\(958\) | 1.58214 | + | 2.74035i | 0.0511167 | + | 0.0885368i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6.51626 | − | 3.76217i | −0.210312 | − | 0.121423i | ||||
\(961\) | −4.46555 | − | 7.73456i | −0.144050 | − | 0.249502i | ||||
\(962\) | −1.36926 | − | 2.37431i | −0.0441466 | − | 0.0765509i | ||||
\(963\) | −17.4616 | + | 30.2444i | −0.562692 | + | 0.974611i | ||||
\(964\) | − | 31.3654i | − | 1.01021i | ||||||
\(965\) | −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 | ||||
\(969\) | 2.67833i | 0.0860404i | ||||||||
\(970\) | −1.39503 | − | 0.805420i | −0.0447917 | − | 0.0258605i | ||||
\(971\) | 3.73092 | − | 6.46215i | 0.119731 | − | 0.207380i | −0.799930 | − | 0.600093i | \(-0.795130\pi\) |
0.919661 | + | 0.392713i | \(0.128463\pi\) | |||||||
\(972\) | −13.3224 | + | 23.0751i | −0.427317 | + | 0.740134i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.767850 | −0.0246035 | ||||||||
\(975\) | −2.25513 | − | 3.91043i | −0.0722219 | − | 0.125234i | ||||
\(976\) | −17.6584 | + | 30.5853i | −0.565232 | + | 0.979011i | ||||
\(977\) | 9.49204 | − | 5.48023i | 0.303677 | − | 0.175328i | −0.340416 | − | 0.940275i | \(-0.610568\pi\) |
0.644094 | + | 0.764947i | \(0.277235\pi\) | |||||||
\(978\) | −0.826490 | −0.0264282 | ||||||||
\(979\) | −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 | ||||
\(983\) | 13.9812 | + | 8.07206i | 0.445932 | + | 0.257459i | 0.706111 | − | 0.708102i | \(-0.250448\pi\) |
−0.260179 | + | 0.965560i | \(0.583781\pi\) | |||||||
\(984\) | 1.62771 | 0.0518893 | ||||||||
\(985\) | 9.76593 | 0.311168 | ||||||||
\(986\) | 2.72164 | + | 1.57134i | 0.0866747 | + | 0.0500417i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.00507218 | − | 10.3367i | 0.000161368 | − | 0.328856i | ||||
\(989\) | −1.96497 | − | 3.40343i | −0.0624824 | − | 0.108223i | ||||
\(990\) | 0.170726 | − | 0.0985688i | 0.00542603 | − | 0.00313272i | ||||
\(991\) | −3.35748 | − | 5.81533i | −0.106654 | − | 0.184730i | 0.807759 | − | 0.589513i | \(-0.200680\pi\) |
−0.914413 | + | 0.404783i | \(0.867347\pi\) | |||||||
\(992\) | 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 | ||||
\(996\) | −0.568091 | + | 0.327988i | −0.0180007 | + | 0.0103927i | ||||
\(997\) | 18.4411 | 0.584037 | 0.292018 | − | 0.956413i | \(-0.405673\pi\) | ||||
0.292018 | + | 0.956413i | \(0.405673\pi\) | |||||||
\(998\) | −1.69305 | − | 2.93244i | −0.0535924 | − | 0.0928248i | ||||
\(999\) | 20.8190i | 0.658684i |
(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.k.g.459.4 | 12 | ||
7.2 | even | 3 | 637.2.u.i.30.4 | 12 | |||
7.3 | odd | 6 | 91.2.q.a.43.3 | yes | 12 | ||
7.4 | even | 3 | 637.2.q.h.589.3 | 12 | |||
7.5 | odd | 6 | 637.2.u.h.30.4 | 12 | |||
7.6 | odd | 2 | 637.2.k.h.459.4 | 12 | |||
13.10 | even | 6 | 637.2.u.i.361.4 | 12 | |||
21.17 | even | 6 | 819.2.ct.a.316.4 | 12 | |||
28.3 | even | 6 | 1456.2.cc.c.225.3 | 12 | |||
91.10 | odd | 6 | 91.2.q.a.36.3 | ✓ | 12 | ||
91.17 | odd | 6 | 1183.2.c.i.337.6 | 12 | |||
91.23 | even | 6 | inner | 637.2.k.g.569.3 | 12 | ||
91.32 | odd | 12 | 8281.2.a.ch.1.3 | 6 | |||
91.45 | even | 12 | 1183.2.a.p.1.3 | 6 | |||
91.46 | odd | 12 | 8281.2.a.by.1.4 | 6 | |||
91.59 | even | 12 | 1183.2.a.m.1.4 | 6 | |||
91.62 | odd | 6 | 637.2.u.h.361.4 | 12 | |||
91.75 | odd | 6 | 637.2.k.h.569.3 | 12 | |||
91.87 | odd | 6 | 1183.2.c.i.337.7 | 12 | |||
91.88 | even | 6 | 637.2.q.h.491.3 | 12 | |||
273.101 | even | 6 | 819.2.ct.a.127.4 | 12 | |||
364.283 | 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 | 91.10 | odd | 6 | ||
91.2.q.a.43.3 | yes | 12 | 7.3 | odd | 6 | ||
637.2.k.g.459.4 | 12 | 1.1 | even | 1 | trivial | ||
637.2.k.g.569.3 | 12 | 91.23 | even | 6 | inner | ||
637.2.k.h.459.4 | 12 | 7.6 | odd | 2 | |||
637.2.k.h.569.3 | 12 | 91.75 | odd | 6 | |||
637.2.q.h.491.3 | 12 | 91.88 | even | 6 | |||
637.2.q.h.589.3 | 12 | 7.4 | even | 3 | |||
637.2.u.h.30.4 | 12 | 7.5 | odd | 6 | |||
637.2.u.h.361.4 | 12 | 91.62 | odd | 6 | |||
637.2.u.i.30.4 | 12 | 7.2 | even | 3 | |||
637.2.u.i.361.4 | 12 | 13.10 | even | 6 | |||
819.2.ct.a.127.4 | 12 | 273.101 | even | 6 | |||
819.2.ct.a.316.4 | 12 | 21.17 | even | 6 | |||
1183.2.a.m.1.4 | 6 | 91.59 | even | 12 | |||
1183.2.a.p.1.3 | 6 | 91.45 | even | 12 | |||
1183.2.c.i.337.6 | 12 | 91.17 | odd | 6 | |||
1183.2.c.i.337.7 | 12 | 91.87 | odd | 6 | |||
1456.2.cc.c.225.3 | 12 | 28.3 | even | 6 | |||
1456.2.cc.c.673.3 | 12 | 364.283 | even | 6 | |||
8281.2.a.by.1.4 | 6 | 91.46 | odd | 12 | |||
8281.2.a.ch.1.3 | 6 | 91.32 | odd | 12 |