Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(30,637)]
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([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.30");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.u (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: | \(\Z[a_1, a_2, a_3]\) |
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 | 361.4 | ||
Root | \(1.34408 - 0.439820i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.361 |
Dual form | 637.2.u.i.30.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.104235 | + | 0.0601799i | 0.0737051 | + | 0.0425536i | 0.536400 | − | 0.843964i | \(-0.319784\pi\) |
−0.462695 | + | 0.886518i | \(0.653117\pi\) | |||||||
\(3\) | 0.582292 | 0.336186 | 0.168093 | − | 0.985771i | \(-0.446239\pi\) | ||||
0.168093 | + | 0.985771i | \(0.446239\pi\) | |||||||
\(4\) | −0.992757 | − | 1.71951i | −0.496378 | − | 0.859753i | ||||
\(5\) | −1.46199 | + | 0.844083i | −0.653824 | + | 0.377485i | −0.789920 | − | 0.613210i | \(-0.789878\pi\) |
0.136096 | + | 0.990696i | \(0.456544\pi\) | |||||||
\(6\) | 0.0606950 | + | 0.0350423i | 0.0247786 | + | 0.0143060i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 0.479696i | − | 0.169598i | ||||||
\(9\) | −2.66094 | −0.886979 | ||||||||
\(10\) | −0.203187 | −0.0642535 | ||||||||
\(11\) | − | 0.364618i | − | 0.109936i | −0.998488 | − | 0.0549682i | \(-0.982494\pi\) | ||
0.998488 | − | 0.0549682i | \(-0.0175058\pi\) | |||||||
\(12\) | −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 | ||||
\(16\) | −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 | \(0.707085\pi\) | |||||||
\(18\) | −0.277362 | − | 0.160135i | −0.0653748 | − | 0.0377442i | ||||
\(19\) | 1.44391i | 0.331255i | 0.986188 | + | 0.165628i | \(0.0529649\pi\) | ||||
−0.986188 | + | 0.165628i | \(0.947035\pi\) | |||||||
\(20\) | 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 | \(0.988873\pi\) | |||||||
\(24\) | − | 0.279323i | − | 0.0570166i | ||||||
\(25\) | −1.07505 | + | 1.86204i | −0.215010 | + | 0.372408i | ||||
\(26\) | −0.375717 | + | 0.217166i | −0.0736842 | + | 0.0425898i | ||||
\(27\) | −3.29632 | −0.634377 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.09831 | − | 7.09848i | −0.761037 | − | 1.31815i | −0.942317 | − | 0.334723i | \(-0.891357\pi\) |
0.181280 | − | 0.983432i | \(-0.441976\pi\) | |||||||
\(30\) | −0.118314 | −0.0216012 | ||||||||
\(31\) | 4.06838 | + | 2.34888i | 0.730702 | + | 0.421871i | 0.818679 | − | 0.574252i | \(-0.194707\pi\) |
−0.0879771 | + | 0.996122i | \(0.528040\pi\) | |||||||
\(32\) | −1.23876 | + | 0.715198i | −0.218984 | + | 0.126430i | ||||
\(33\) | − | 0.212314i | − | 0.0369592i | ||||||
\(34\) | 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 | −0.0222655 | − | 0.999752i | \(-0.507088\pi\) |
−0.876943 | + | 0.480594i | \(0.840421\pi\) | |||||||
\(38\) | −0.0868943 | + | 0.150505i | −0.0140961 | + | 0.0244152i | ||||
\(39\) | −1.04885 | + | 1.81872i | −0.167950 | + | 0.291228i | ||||
\(40\) | 0.404903 | + | 0.701313i | 0.0640208 | + | 0.110887i | ||||
\(41\) | 5.04661 | − | 2.91366i | 0.788148 | − | 0.455037i | −0.0511624 | − | 0.998690i | \(-0.516293\pi\) |
0.839310 | + | 0.543653i | \(0.182959\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.386561 | + | 0.669543i | −0.0589500 | + | 0.102104i | −0.893994 | − | 0.448078i | \(-0.852109\pi\) |
0.835044 | + | 0.550183i | \(0.185442\pi\) | |||||||
\(44\) | −0.626963 | + | 0.361977i | −0.0945182 | + | 0.0545701i | ||||
\(45\) | 3.89027 | − | 2.24605i | 0.579928 | − | 0.334821i | ||||
\(46\) | −0.529847 | + | 0.305907i | −0.0781217 | + | 0.0451036i | ||||
\(47\) | −11.0769 | + | 6.39527i | −1.61574 | + | 0.932846i | −0.627731 | + | 0.778430i | \(0.716016\pi\) |
−0.988006 | + | 0.154416i | \(0.950650\pi\) | |||||||
\(48\) | −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 | ||||
\(52\) | 7.15887 | − | 0.00351282i | 0.992757 | − | 0.000487140i | ||||
\(53\) | −0.685548 | + | 1.18740i | −0.0941672 | + | 0.163102i | −0.909261 | − | 0.416227i | \(-0.863352\pi\) |
0.815094 | + | 0.579329i | \(0.196685\pi\) | |||||||
\(54\) | −0.343591 | − | 0.198372i | −0.0467568 | − | 0.0269950i | ||||
\(55\) | 0.307768 | + | 0.533070i | 0.0414994 | + | 0.0718791i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.840776i | 0.111363i | ||||||||
\(58\) | − | 0.986544i | − | 0.129540i | ||||||
\(59\) | −8.10770 | + | 4.68098i | −1.05553 | + | 0.609412i | −0.924193 | − | 0.381925i | \(-0.875261\pi\) |
−0.131340 | + | 0.991337i | \(0.541928\pi\) | |||||||
\(60\) | 1.69028 | + | 0.975885i | 0.218215 | + | 0.125986i | ||||
\(61\) | 9.02484 | 1.15551 | 0.577756 | − | 0.816209i | \(-0.303928\pi\) | ||||
0.577756 | + | 0.816209i | \(0.303928\pi\) | |||||||
\(62\) | 0.282711 | + | 0.489669i | 0.0359043 | + | 0.0621880i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.65442 | 0.956802 | ||||||||
\(65\) | −0.00298674 | − | 6.08677i | −0.000370460 | − | 0.754970i | ||||
\(66\) | 0.0127771 | − | 0.0221305i | 0.00157275 | − | 0.00272408i | ||||
\(67\) | − | 13.4759i | − | 1.64635i | −0.567789 | − | 0.823174i | \(-0.692201\pi\) | ||
0.567789 | − | 0.823174i | \(-0.307799\pi\) | |||||||
\(68\) | 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 | 0.0898239 | − | 0.995958i | \(-0.471370\pi\) |
−0.817613 | + | 0.575769i | \(0.804703\pi\) | |||||||
\(72\) | 1.27644i | 0.150430i | ||||||||
\(73\) | −1.87133 | − | 1.08041i | −0.219023 | − | 0.126453i | 0.386475 | − | 0.922300i | \(-0.373693\pi\) |
−0.605498 | + | 0.795847i | \(0.707026\pi\) | |||||||
\(74\) | −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 | ||||
\(79\) | 3.44391 | + | 5.96502i | 0.387470 | + | 0.671117i | 0.992108 | − | 0.125382i | \(-0.0400158\pi\) |
−0.604639 | + | 0.796500i | \(0.706682\pi\) | |||||||
\(80\) | − | 6.60628i | − | 0.738605i | ||||||
\(81\) | 6.06339 | 0.673710 | ||||||||
\(82\) | 0.701376 | 0.0774540 | ||||||||
\(83\) | 0.567380i | 0.0622780i | 0.999515 | + | 0.0311390i | \(0.00991345\pi\) | ||||
−0.999515 | + | 0.0311390i | \(0.990087\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.65725 | − | 2.68887i | −0.505150 | − | 0.291648i | ||||
\(86\) | −0.0805861 | + | 0.0465264i | −0.00868982 | + | 0.00501707i | ||||
\(87\) | −2.38641 | − | 4.13339i | −0.255850 | − | 0.443146i | ||||
\(88\) | −0.174906 | −0.0186450 | ||||||||
\(89\) | −0.986346 | − | 0.569467i | −0.104553 | − | 0.0603634i | 0.446812 | − | 0.894628i | \(-0.352559\pi\) |
−0.551364 | + | 0.834264i | \(0.685893\pi\) | |||||||
\(90\) | 0.540669 | 0.0569915 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.0928 | 1.05225 | ||||||||
\(93\) | 2.36898 | + | 1.36773i | 0.245652 | + | 0.141827i | ||||
\(94\) | −1.53947 | −0.158784 | ||||||||
\(95\) | −1.21878 | − | 2.11098i | −0.125044 | − | 0.216582i | ||||
\(96\) | −0.721319 | + | 0.416454i | −0.0736193 | + | 0.0425041i | ||||
\(97\) | −6.86572 | − | 3.96393i | −0.697109 | − | 0.402476i | 0.109161 | − | 0.994024i | \(-0.465184\pi\) |
−0.806270 | + | 0.591548i | \(0.798517\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.970225i | 0.0975113i | ||||||||
\(100\) | 4.26905 | 0.426905 | ||||||||
\(101\) | −15.5464 | −1.54693 | −0.773465 | − | 0.633839i | \(-0.781478\pi\) | ||||
−0.773465 | + | 0.633839i | \(0.781478\pi\) | |||||||
\(102\) | 0.223258i | 0.0221058i | ||||||||
\(103\) | −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 | ||||
\(107\) | 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 | ||||
\(109\) | 9.04641 | + | 5.22295i | 0.866489 | + | 0.500268i | 0.866180 | − | 0.499732i | \(-0.166568\pi\) |
0.000309035 | 1.00000i | \(0.499902\pi\) | ||||||||
\(110\) | 0.0740858i | 0.00706380i | ||||||||
\(111\) | −3.18495 | − | 1.83883i | −0.302302 | − | 0.174534i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.47631 | + | 4.28909i | −0.232952 | + | 0.403484i | −0.958675 | − | 0.284502i | \(-0.908172\pi\) |
0.725724 | + | 0.687986i | \(0.241505\pi\) | |||||||
\(114\) | −0.0505978 | + | 0.0876380i | −0.00473892 | + | 0.00820805i | ||||
\(115\) | − | 8.58130i | − | 0.800211i | ||||||
\(116\) | −8.13725 | + | 14.0941i | −0.755524 | + | 1.30861i | ||||
\(117\) | 4.79299 | − | 8.31112i | 0.443112 | − | 0.768364i | ||||
\(118\) | −1.12681 | −0.103731 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.235772 | + | 0.408369i | 0.0215229 | + | 0.0372788i | ||||
\(121\) | 10.8671 | 0.987914 | ||||||||
\(122\) | 0.940702 | + | 0.543114i | 0.0851671 | + | 0.0491713i | ||||
\(123\) | 2.93860 | − | 1.69660i | 0.264965 | − | 0.152977i | ||||
\(124\) | − | 9.32746i | − | 0.837630i | ||||||
\(125\) | − | 12.0705i | − | 1.07962i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.03366 | + | 6.98650i | 0.357929 | + | 0.619951i | 0.987615 | − | 0.156899i | \(-0.0501496\pi\) |
−0.629686 | + | 0.776850i | \(0.716816\pi\) | |||||||
\(128\) | 3.27537 | + | 1.89104i | 0.289505 | + | 0.167146i | ||||
\(129\) | −0.225091 | + | 0.389870i | −0.0198182 | + | 0.0343261i | ||||
\(130\) | 0.365990 | − | 0.634632i | 0.0320994 | − | 0.0556609i | ||||
\(131\) | 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 | ||||
\(136\) | 1.32337 | − | 0.764047i | 0.113478 | − | 0.0655165i | ||||
\(137\) | −15.7837 | + | 9.11274i | −1.34850 | + | 0.778554i | −0.988036 | − | 0.154221i | \(-0.950713\pi\) |
−0.360459 | + | 0.932775i | \(0.617380\pi\) | |||||||
\(138\) | −0.308526 | + | 0.178127i | −0.0262635 | + | 0.0151632i | ||||
\(139\) | 2.62542 | − | 4.54737i | 0.222686 | − | 0.385703i | −0.732937 | − | 0.680297i | \(-0.761851\pi\) |
0.955623 | + | 0.294594i | \(0.0951843\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.45001 | + | 3.72392i | −0.543189 | + | 0.313610i | ||||
\(142\) | −0.426143 | − | 0.738102i | −0.0357612 | − | 0.0619401i | ||||
\(143\) | 1.13884 | + | 0.656766i | 0.0952348 | + | 0.0549215i | ||||
\(144\) | 5.20651 | − | 9.01794i | 0.433876 | − | 0.751495i | ||||
\(145\) | 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 | ||||||||
\(149\) | − | 9.27309i | − | 0.759681i | −0.925052 | − | 0.379841i | \(-0.875979\pi\) | ||
0.925052 | − | 0.379841i | \(-0.124021\pi\) | |||||||
\(150\) | −0.130500 | + | 0.0753444i | −0.0106553 | + | 0.00615184i | ||||
\(151\) | 12.1358 | + | 7.00661i | 0.987597 | + | 0.570189i | 0.904555 | − | 0.426357i | \(-0.140203\pi\) |
0.0830419 | + | 0.996546i | \(0.473536\pi\) | |||||||
\(152\) | 0.692636 | 0.0561802 | ||||||||
\(153\) | −4.23827 | − | 7.34090i | −0.342644 | − | 0.593476i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.93059 | −0.637000 | ||||||||
\(156\) | 4.16855 | − | 0.00204549i | 0.333751 | − | 0.000163770i | ||||
\(157\) | −8.59125 | + | 14.8805i | −0.685656 | + | 1.18759i | 0.287574 | + | 0.957759i | \(0.407151\pi\) |
−0.973230 | + | 0.229833i | \(0.926182\pi\) | |||||||
\(158\) | 0.829017i | 0.0659530i | ||||||||
\(159\) | −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 | ||||
\(163\) | − | 11.7927i | − | 0.923679i | −0.886963 | − | 0.461840i | \(-0.847190\pi\) | ||
0.886963 | − | 0.461840i | \(-0.152810\pi\) | |||||||
\(164\) | −10.0201 | − | 5.78511i | −0.782439 | − | 0.451741i | ||||
\(165\) | 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 | −0.637624 | − | 0.770348i | \(-0.720083\pi\) |
0.348329 | + | 0.937372i | \(0.386749\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.51105 | − | 11.2519i | −0.500850 | − | 0.865534i | ||||
\(170\) | −0.323632 | − | 0.560546i | −0.0248214 | − | 0.0429919i | ||||
\(171\) | − | 3.84214i | − | 0.293816i | ||||||
\(172\) | 1.53504 | 0.117046 | ||||||||
\(173\) | 12.5197 | 0.951855 | 0.475928 | − | 0.879484i | \(-0.342112\pi\) | ||||
0.475928 | + | 0.879484i | \(0.342112\pi\) | |||||||
\(174\) | − | 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 | ||||
\(178\) | −0.0685410 | − | 0.118717i | −0.00513737 | − | 0.00889818i | ||||
\(179\) | 6.59534 | 0.492959 | 0.246479 | − | 0.969148i | \(-0.420726\pi\) | ||||
0.246479 | + | 0.969148i | \(0.420726\pi\) | |||||||
\(180\) | −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 | ||||
\(185\) | 10.6622 | 0.783899 | ||||||||
\(186\) | 0.164620 | + | 0.285130i | 0.0120705 | + | 0.0209068i | ||||
\(187\) | 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 | ||||||
\(191\) | 5.93213 | 0.429234 | 0.214617 | − | 0.976698i | \(-0.431150\pi\) | ||||
0.214617 | + | 0.976698i | \(0.431150\pi\) | |||||||
\(192\) | 4.45711 | 0.321664 | ||||||||
\(193\) | 4.19595i | 0.302031i | 0.988531 | + | 0.151016i | \(0.0482544\pi\) | ||||
−0.988531 | + | 0.151016i | \(0.951746\pi\) | |||||||
\(194\) | −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 | −0.310797 | − | 0.950476i | \(-0.600596\pi\) |
0.667738 | + | 0.744396i | \(0.267263\pi\) | |||||||
\(198\) | −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 | \(0.972673\pi\) | |||||||
\(200\) | 0.893213 | + | 0.515697i | 0.0631597 | + | 0.0364653i | ||||
\(201\) | − | 7.84693i | − | 0.553480i | ||||||
\(202\) | −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 | ||||
\(206\) | − | 1.23949i | − | 0.0863590i | ||||||
\(207\) | 6.76305 | − | 11.7139i | 0.470065 | − | 0.814176i | ||||
\(208\) | −7.06078 | − | 12.2158i | −0.489577 | − | 0.847012i | ||||
\(209\) | 0.526475 | 0.0364170 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.11795 | + | 7.13251i | 0.283492 | + | 0.491022i | 0.972242 | − | 0.233976i | \(-0.0751738\pi\) |
−0.688751 | + | 0.724998i | \(0.741840\pi\) | |||||||
\(212\) | 2.72233 | 0.186970 | ||||||||
\(213\) | −3.57088 | − | 2.06165i | −0.244673 | − | 0.141262i | ||||
\(214\) | 1.36802 | − | 0.789825i | 0.0935157 | − | 0.0539913i | ||||
\(215\) | − | 1.30516i | − | 0.0890110i | ||||||
\(216\) | 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 | ||||
\(220\) | 0.611077 | − | 1.05842i | 0.0411988 | − | 0.0713584i | ||||
\(221\) | −11.4857 | + | 0.00563595i | −0.772609 | + | 0.000379115i | ||||
\(222\) | −0.221321 | − | 0.383340i | −0.0148541 | − | 0.0257281i | ||||
\(223\) | −13.2515 | + | 7.65073i | −0.887383 | + | 0.512331i | −0.873086 | − | 0.487567i | \(-0.837885\pi\) |
−0.0142977 | + | 0.999898i | \(0.504551\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.86064 | − | 4.95477i | 0.190709 | − | 0.330318i | ||||
\(226\) | −0.516235 | + | 0.298048i | −0.0343394 | + | 0.0198259i | ||||
\(227\) | −6.02292 | + | 3.47733i | −0.399755 | + | 0.230799i | −0.686378 | − | 0.727245i | \(-0.740801\pi\) |
0.286623 | + | 0.958043i | \(0.407467\pi\) | |||||||
\(228\) | 1.44572 | − | 0.834686i | 0.0957450 | − | 0.0552784i | ||||
\(229\) | −23.7481 | + | 13.7110i | −1.56932 | + | 0.906045i | −0.573068 | + | 0.819508i | \(0.694247\pi\) |
−0.996249 | + | 0.0865377i | \(0.972420\pi\) | |||||||
\(230\) | 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 | \(0.905404\pi\) | |||||||
\(234\) | 0.999759 | − | 0.577866i | 0.0653563 | − | 0.0377763i | ||||
\(235\) | 10.7963 | − | 18.6997i | 0.704271 | − | 1.21983i | ||||
\(236\) | 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 | \(-0.746895\pi\) | ||
0.700177 | − | 0.713970i | \(-0.253105\pi\) | |||||||
\(240\) | − | 3.84679i | − | 0.248309i | ||||||
\(241\) | 13.6807 | − | 7.89855i | 0.881251 | − | 0.508790i | 0.0101802 | − | 0.999948i | \(-0.496759\pi\) |
0.871071 | + | 0.491158i | \(0.163426\pi\) | |||||||
\(242\) | 1.13272 | + | 0.653979i | 0.0728143 | + | 0.0420393i | ||||
\(243\) | 13.4196 | 0.860869 | ||||||||
\(244\) | −8.95947 | − | 15.5183i | −0.573571 | − | 0.993455i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.408405 | 0.0260390 | ||||||||
\(247\) | −4.50988 | − | 2.60083i | −0.286957 | − | 0.165487i | ||||
\(248\) | 1.12675 | − | 1.95158i | 0.0715485 | − | 0.123926i | ||||
\(249\) | 0.330381i | 0.0209370i | ||||||||
\(250\) | 0.726405 | − | 1.25817i | 0.0459419 | − | 0.0795737i | ||||
\(251\) | −11.2783 | + | 19.5346i | −0.711882 | + | 1.23302i | 0.252268 | + | 0.967658i | \(0.418824\pi\) |
−0.964150 | + | 0.265359i | \(0.914510\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.60512 | + | 0.926716i | 0.100913 | + | 0.0582621i | ||||
\(254\) | 0.970981i | 0.0609247i | ||||||||
\(255\) | −2.71188 | − | 1.56570i | −0.169825 | − | 0.0980483i | ||||
\(256\) | −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 | ||||
\(261\) | 10.9053 | + | 18.8886i | 0.675023 | + | 1.16917i | ||||
\(262\) | 2.27527i | 0.140567i | ||||||||
\(263\) | −29.5402 | −1.82153 | −0.910764 | − | 0.412927i | \(-0.864506\pi\) | ||||
−0.910764 | + | 0.412927i | \(0.864506\pi\) | |||||||
\(264\) | −0.101846 | −0.00626820 | ||||||||
\(265\) | − | 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 | ||||
\(269\) | 13.9581 | + | 24.1762i | 0.851043 | + | 1.47405i | 0.880268 | + | 0.474477i | \(0.157363\pi\) |
−0.0292252 | + | 0.999573i | \(0.509304\pi\) | |||||||
\(270\) | 0.669770 | 0.0407609 | ||||||||
\(271\) | −25.5036 | − | 14.7245i | −1.54924 | − | 0.894451i | −0.998200 | − | 0.0599690i | \(-0.980900\pi\) |
−0.551035 | − | 0.834482i | \(-0.685767\pi\) | |||||||
\(272\) | −12.4660 | −0.755861 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.19362 | −0.132521 | ||||||||
\(275\) | 0.678933 | + | 0.391982i | 0.0409412 | + | 0.0236374i | ||||
\(276\) | 5.87695 | 0.353751 | ||||||||
\(277\) | 3.42927 | + | 5.93967i | 0.206045 | + | 0.356880i | 0.950465 | − | 0.310831i | \(-0.100607\pi\) |
−0.744420 | + | 0.667711i | \(0.767274\pi\) | |||||||
\(278\) | 0.547321 | − | 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 | \(0.334468\pi\) | ||||
−0.496909 | + | 0.867803i | \(0.665532\pi\) | |||||||
\(282\) | −0.896420 | −0.0533810 | ||||||||
\(283\) | 11.6102 | 0.690156 | 0.345078 | − | 0.938574i | \(-0.387853\pi\) | ||||
0.345078 | + | 0.938574i | \(0.387853\pi\) | |||||||
\(284\) | 14.0597i | 0.834291i | ||||||||
\(285\) | −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 | ||||
\(289\) | 3.42614 | − | 5.93425i | 0.201538 | − | 0.349074i | ||||
\(290\) | 0.832724 | + | 1.44232i | 0.0488993 | + | 0.0846960i | ||||
\(291\) | −3.99786 | − | 2.30816i | −0.234358 | − | 0.135307i | ||||
\(292\) | 4.29035i | 0.251074i | ||||||||
\(293\) | 15.4054 | + | 8.89430i | 0.899992 | + | 0.519610i | 0.877197 | − | 0.480130i | \(-0.159410\pi\) |
0.0227942 | + | 0.999740i | \(0.492744\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.90228 | − | 13.6871i | 0.460088 | − | 0.796896i | ||||
\(296\) | −1.51484 | + | 2.62378i | −0.0880483 | + | 0.152504i | ||||
\(297\) | 1.20190i | 0.0697412i | ||||||||
\(298\) | 0.558054 | − | 0.966578i | 0.0323272 | − | 0.0559924i | ||||
\(299\) | −9.17168 | − | 15.8678i | −0.530412 | − | 0.917660i | ||||
\(300\) | 2.48583 | 0.143520 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.843314 | + | 1.46066i | 0.0485273 | + | 0.0840517i | ||||
\(303\) | −9.05257 | −0.520057 | ||||||||
\(304\) | −4.89341 | − | 2.82521i | −0.280657 | − | 0.162037i | ||||
\(305\) | −13.1943 | + | 7.61771i | −0.755501 | + | 0.436189i | ||||
\(306\) | − | 1.02024i | − | 0.0583230i | ||||||
\(307\) | 9.07966i | 0.518204i | 0.965850 | + | 0.259102i | \(0.0834265\pi\) | ||||
−0.965850 | + | 0.259102i | \(0.916573\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.99827 | − | 5.19315i | −0.170566 | − | 0.295428i | ||||
\(310\) | −0.826643 | − | 0.477262i | −0.0469501 | − | 0.0271067i | ||||
\(311\) | −0.785363 | + | 1.36029i | −0.0445338 | + | 0.0771349i | −0.887433 | − | 0.460937i | \(-0.847514\pi\) |
0.842899 | + | 0.538071i | \(0.180847\pi\) | |||||||
\(312\) | 0.872433 | + | 0.503129i | 0.0493918 | + | 0.0284841i | ||||
\(313\) | 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 | −0.999867 | − | 0.0163255i | \(-0.994803\pi\) |
−0.485795 | + | 0.874073i | \(0.661470\pi\) | |||||||
\(318\) | −0.0832187 | + | 0.0480463i | −0.00466667 | + | 0.00269430i | ||||
\(319\) | −2.58823 | + | 1.49432i | −0.144913 | + | 0.0836657i | ||||
\(320\) | −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 | ||||
\(325\) | −3.87944 | − | 6.71177i | −0.215192 | − | 0.372302i | ||||
\(326\) | 0.709687 | − | 1.22921i | 0.0393059 | − | 0.0680799i | ||||
\(327\) | 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 | ||||||||
\(331\) | 25.8531i | 1.42101i | 0.703690 | + | 0.710507i | \(0.251534\pi\) | ||||
−0.703690 | + | 0.710507i | \(0.748466\pi\) | |||||||
\(332\) | 0.975612 | − | 0.563270i | 0.0535437 | − | 0.0309135i | ||||
\(333\) | 14.5545 | + | 8.40302i | 0.797579 | + | 0.460483i | ||||
\(334\) | −0.519578 | −0.0284300 | ||||||||
\(335\) | 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 | \(0.698020\pi\) | |||||||
\(338\) | −0.00153556 | − | 1.56468i | −8.35233e−5 | − | 0.0851073i | ||||
\(339\) | −1.44194 | + | 2.49750i | −0.0783152 | + | 0.135646i | ||||
\(340\) | 10.6776i | 0.579072i | ||||||||
\(341\) | 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 | ||||
\(345\) | − | 4.99682i | − | 0.269020i | ||||||
\(346\) | 1.30499 | + | 0.753435i | 0.0701566 | + | 0.0405049i | ||||
\(347\) | −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 | −0.214908 | − | 0.976634i | \(-0.568945\pi\) |
0.738336 | + | 0.674433i | \(0.235612\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.93747 | − | 10.2957i | 0.316919 | − | 0.549542i | ||||
\(352\) | 0.260774 | + | 0.451674i | 0.0138993 | + | 0.0240743i | ||||
\(353\) | 35.6433i | 1.89710i | 0.316623 | + | 0.948552i | \(0.397451\pi\) | ||||
−0.316623 | + | 0.948552i | \(0.602549\pi\) | |||||||
\(354\) | −0.656130 | −0.0348729 | ||||||||
\(355\) | 11.9542 | 0.634461 | ||||||||
\(356\) | 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 | −0.871693 | − | 0.490052i | \(-0.836978\pi\) |
−0.0114488 | + | 0.999934i | \(0.503644\pi\) | |||||||
\(360\) | −1.07742 | − | 1.86615i | −0.0567851 | − | 0.0983546i | ||||
\(361\) | 16.9151 | 0.890270 | ||||||||
\(362\) | 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 | ||||
\(367\) | 3.72065 | 0.194216 | 0.0971082 | − | 0.995274i | \(-0.469041\pi\) | ||||
0.0971082 | + | 0.995274i | \(0.469041\pi\) | |||||||
\(368\) | −9.94604 | − | 17.2271i | −0.518473 | − | 0.898022i | ||||
\(369\) | −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 | ||||||
\(373\) | −3.51276 | −0.181884 | −0.0909420 | − | 0.995856i | \(-0.528988\pi\) | ||||
−0.0909420 | + | 0.995856i | \(0.528988\pi\) | |||||||
\(374\) | 0.139799 | 0.00722884 | ||||||||
\(375\) | − | 7.02858i | − | 0.362954i | ||||||
\(376\) | 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 | 0.173279 | − | 0.984873i | \(-0.444564\pi\) |
0.939564 | + | 0.342373i | \(0.111230\pi\) | |||||||
\(380\) | −2.41990 | + | 4.19139i | −0.124138 | + | 0.215014i | ||||
\(381\) | 2.34877 | + | 4.06818i | 0.120331 | + | 0.208419i | ||||
\(382\) | 0.618333 | + | 0.356995i | 0.0316367 | + | 0.0182655i | ||||
\(383\) | − | 22.4654i | − | 1.14793i | −0.818881 | − | 0.573964i | \(-0.805405\pi\) | ||
0.818881 | − | 0.573964i | \(-0.194595\pi\) | |||||||
\(384\) | 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 | ||||
\(388\) | 15.7409i | 0.799121i | ||||||||
\(389\) | −6.66822 | + | 11.5497i | −0.338092 | + | 0.585592i | −0.984074 | − | 0.177760i | \(-0.943115\pi\) |
0.645982 | + | 0.763353i | \(0.276448\pi\) | |||||||
\(390\) | 0.213113 | − | 0.369541i | 0.0107914 | − | 0.0187124i | ||||
\(391\) | −16.1928 | −0.818906 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.50379 | + | 9.53284i | 0.277629 | + | 0.480868i | ||||
\(394\) | 0.696274 | 0.0350778 | ||||||||
\(395\) | −10.0699 | − | 5.81388i | −0.506674 | − | 0.292528i | ||||
\(396\) | 1.66831 | − | 0.963198i | 0.0838356 | − | 0.0484025i | ||||
\(397\) | − | 25.8333i | − | 1.29654i | −0.761412 | − | 0.648268i | \(-0.775494\pi\) | ||
0.761412 | − | 0.648268i | \(-0.224506\pi\) | |||||||
\(398\) | − | 1.43948i | − | 0.0721544i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.20698 | − | 7.28670i | −0.210349 | − | 0.364335i | ||||
\(401\) | −15.2078 | − | 8.78025i | −0.759443 | − | 0.438465i | 0.0696524 | − | 0.997571i | \(-0.477811\pi\) |
−0.829096 | + | 0.559106i | \(0.811144\pi\) | |||||||
\(402\) | 0.472228 | − | 0.817923i | 0.0235526 | − | 0.0407943i | ||||
\(403\) | −14.6646 | + | 8.47620i | −0.730495 | + | 0.422229i | ||||
\(404\) | 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 | ||||
\(409\) | 12.5818 | − | 7.26410i | 0.622129 | − | 0.359186i | −0.155568 | − | 0.987825i | \(-0.549721\pi\) |
0.777698 | + | 0.628639i | \(0.216388\pi\) | |||||||
\(410\) | −1.02541 | + | 0.592019i | −0.0506412 | + | 0.0292377i | ||||
\(411\) | −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 | ||||
\(416\) | −0.00253069 | − | 5.15736i | −0.000124077 | − | 0.252861i | ||||
\(417\) | 1.52876 | − | 2.64790i | 0.0748639 | − | 0.129668i | ||||
\(418\) | 0.0548769 | + | 0.0316832i | 0.00268412 | + | 0.00154968i | ||||
\(419\) | −2.30096 | − | 3.98538i | −0.112409 | − | 0.194699i | 0.804332 | − | 0.594180i | \(-0.202523\pi\) |
−0.916741 | + | 0.399482i | \(0.869190\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.2645i | 0.938895i | 0.882960 | + | 0.469447i | \(0.155547\pi\) | ||||
−0.882960 | + | 0.469447i | \(0.844453\pi\) | |||||||
\(422\) | 0.991273i | 0.0482544i | ||||||||
\(423\) | 29.4750 | − | 17.0174i | 1.43312 | − | 0.827415i | ||||
\(424\) | 0.569593 | + | 0.328854i | 0.0276619 | + | 0.0159706i | ||||
\(425\) | −6.84924 | −0.332237 | ||||||||
\(426\) | −0.248140 | − | 0.429791i | −0.0120224 | − | 0.0208234i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −26.0587 | −1.25959 | ||||||||
\(429\) | 0.663139 | + | 0.382430i | 0.0320166 | + | 0.0184639i | ||||
\(430\) | 0.0785443 | − | 0.136043i | 0.00378774 | − | 0.00656056i | ||||
\(431\) | − | 28.3651i | − | 1.36630i | −0.730279 | − | 0.683149i | \(-0.760610\pi\) | ||
0.730279 | − | 0.683149i | \(-0.239390\pi\) | |||||||
\(432\) | 6.44973 | − | 11.1713i | 0.310313 | − | 0.537477i | ||||
\(433\) | 6.26014 | − | 10.8429i | 0.300843 | − | 0.521076i | −0.675484 | − | 0.737375i | \(-0.736065\pi\) |
0.976327 | + | 0.216299i | \(0.0693986\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.97784 | + | 4.02866i | 0.334562 | + | 0.193159i | ||||
\(436\) | − | 20.7405i | − | 0.993288i | ||||||
\(437\) | −6.35636 | − | 3.66984i | −0.304066 | − | 0.175552i | ||||
\(438\) | −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 | ||||
\(443\) | −0.865241 | − | 1.49864i | −0.0411088 | − | 0.0712026i | 0.844739 | − | 0.535179i | \(-0.179756\pi\) |
−0.885848 | + | 0.463976i | \(0.846422\pi\) | |||||||
\(444\) | 7.30205i | 0.346540i | ||||||||
\(445\) | 1.92271 | 0.0911452 | ||||||||
\(446\) | −1.84168 | −0.0872062 | ||||||||
\(447\) | − | 5.39965i | − | 0.255394i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.14208 | − | 5.27818i | −0.431442 | − | 0.249093i | 0.268519 | − | 0.963274i | \(-0.413466\pi\) |
−0.699961 | + | 0.714181i | \(0.746799\pi\) | |||||||
\(450\) | 0.596355 | − | 0.344306i | 0.0281125 | − | 0.0162307i | ||||
\(451\) | −1.06237 | − | 1.84008i | −0.0500252 | − | 0.0866462i | ||||
\(452\) | 9.83349 | 0.462528 | ||||||||
\(453\) | 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 | 0.652292 | − | 0.757968i | \(-0.273807\pi\) |
−0.330273 | + | 0.943885i | \(0.607141\pi\) | |||||||
\(458\) | −3.30050 | −0.154222 | ||||||||
\(459\) | −5.25029 | − | 9.09377i | −0.245062 | − | 0.424461i | ||||
\(460\) | −14.7556 | + | 8.51915i | −0.687983 | + | 0.397207i | ||||
\(461\) | −9.43262 | − | 5.44592i | −0.439321 | − | 0.253642i | 0.263989 | − | 0.964526i | \(-0.414962\pi\) |
−0.703309 | + | 0.710884i | \(0.748295\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.8227i | 1.66482i | 0.554158 | + | 0.832411i | \(0.313040\pi\) | ||||
−0.554158 | + | 0.832411i | \(0.686960\pi\) | |||||||
\(464\) | 32.0757 | 1.48908 | ||||||||
\(465\) | −4.61792 | −0.214151 | ||||||||
\(466\) | − | 0.824866i | − | 0.0382112i | ||||||
\(467\) | −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 | ||||
\(471\) | −5.00262 | + | 8.66479i | −0.230508 | + | 0.399252i | ||||
\(472\) | 2.24545 | + | 3.88923i | 0.103355 | + | 0.179016i | ||||
\(473\) | 0.244127 | + | 0.140947i | 0.0112250 | + | 0.00648075i | ||||
\(474\) | 0.482730i | 0.0221725i | ||||||||
\(475\) | −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 | ||||
\(479\) | − | 26.2902i | − | 1.20123i | −0.799538 | − | 0.600615i | \(-0.794922\pi\) | ||
0.799538 | − | 0.600615i | \(-0.205078\pi\) | |||||||
\(480\) | 0.703043 | − | 1.21771i | 0.0320894 | − | 0.0555804i | ||||
\(481\) | 19.7156 | − | 11.3957i | 0.898954 | − | 0.519600i | ||||
\(482\) | 1.90134 | 0.0866035 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.7883 | − | 18.6860i | −0.490379 | − | 0.849362i | ||||
\(485\) | 13.3835 | 0.607715 | ||||||||
\(486\) | 1.39879 | + | 0.807592i | 0.0634504 | + | 0.0366331i | ||||
\(487\) | −5.52491 | + | 3.18981i | −0.250358 | + | 0.144544i | −0.619928 | − | 0.784659i | \(-0.712838\pi\) |
0.369570 | + | 0.929203i | \(0.379505\pi\) | |||||||
\(488\) | − | 4.32918i | − | 0.195973i | ||||||
\(489\) | − | 6.86682i | − | 0.310528i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.48384 | − | 2.57008i | −0.0669647 | − | 0.115986i | 0.830599 | − | 0.556871i | \(-0.187998\pi\) |
−0.897564 | + | 0.440885i | \(0.854665\pi\) | |||||||
\(492\) | −5.83463 | − | 3.36862i | −0.263045 | − | 0.151869i | ||||
\(493\) | 13.0554 | − | 22.6125i | 0.587984 | − | 1.01842i | ||||
\(494\) | −0.313568 | − | 0.542501i | −0.0141081 | − | 0.0244083i | ||||
\(495\) | −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 | 0.156923 | − | 0.987611i | \(-0.449843\pi\) |
0.933757 | + | 0.357906i | \(0.116509\pi\) | |||||||
\(500\) | −20.7554 | + | 11.9831i | −0.928208 | + | 0.535901i | ||||
\(501\) | −2.17691 | + | 1.25684i | −0.0972571 | + | 0.0561514i | ||||
\(502\) | −2.35119 | + | 1.35746i | −0.104939 | + | 0.0605864i | ||||
\(503\) | −15.7688 | + | 27.3124i | −0.703097 | + | 1.21780i | 0.264277 | + | 0.964447i | \(0.414867\pi\) |
−0.967374 | + | 0.253353i | \(0.918467\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.7288 | − | 13.1225i | 1.01142 | − | 0.583943i | ||||
\(506\) | 0.111539 | + | 0.193192i | 0.00495853 | + | 0.00858843i | ||||
\(507\) | −3.79133 | − | 6.55192i | −0.168379 | − | 0.290981i | ||||
\(508\) | 8.00888 | − | 13.8718i | 0.355336 | − | 0.615461i | ||||
\(509\) | 11.7731 | + | 6.79719i | 0.521832 | + | 0.301280i | 0.737684 | − | 0.675146i | \(-0.235919\pi\) |
−0.215852 | + | 0.976426i | \(0.569253\pi\) | |||||||
\(510\) | −0.188448 | − | 0.326402i | −0.00834462 | − | 0.0144533i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 9.35193i | − | 0.413301i | ||||||
\(513\) | − | 4.75958i | − | 0.210140i | ||||||
\(514\) | −2.12773 | + | 1.22845i | −0.0938502 | + | 0.0541844i | ||||
\(515\) | 15.0558 | + | 8.69250i | 0.663440 | + | 0.383037i | ||||
\(516\) | 0.893844 | 0.0393493 | ||||||||
\(517\) | 2.33183 | + | 4.03885i | 0.102554 | + | 0.177628i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.29012 | 0.320001 | ||||||||
\(520\) | −2.91980 | + | 0.00143273i | −0.128042 | + | 6.28293e-5i | ||||
\(521\) | 4.39172 | − | 7.60669i | 0.192405 | − | 0.333255i | −0.753642 | − | 0.657285i | \(-0.771705\pi\) |
0.946047 | + | 0.324030i | \(0.105038\pi\) | |||||||
\(522\) | 2.62513i | 0.114899i | ||||||||
\(523\) | 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 | ||||
\(527\) | 14.9649i | 0.651882i | ||||||||
\(528\) | 0.719535 | + | 0.415424i | 0.0313137 | + | 0.0180790i | ||||
\(529\) | −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 | ||||
\(534\) | −0.0399109 | − | 0.0691277i | −0.00172711 | − | 0.00299145i | ||||
\(535\) | 22.1561i | 0.957894i | ||||||||
\(536\) | −6.46435 | −0.279218 | ||||||||
\(537\) | 3.84041 | 0.165726 | ||||||||
\(538\) | 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 | −0.365029 | − | 0.930996i | \(-0.618941\pi\) |
0.623752 | + | 0.781622i | \(0.285608\pi\) | |||||||
\(542\) | −1.77224 | − | 3.06961i | −0.0761243 | − | 0.131851i | ||||
\(543\) | 6.41436 | 0.275266 | ||||||||
\(544\) | −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 | ||||
\(549\) | −24.0145 | −1.02491 | ||||||||
\(550\) | 0.0471789 | + | 0.0817163i | 0.00201172 | + | 0.00348440i | ||||
\(551\) | 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 | ||||||||
\(555\) | 6.20850 | 0.263536 | ||||||||
\(556\) | −10.4256 | −0.442145 | ||||||||
\(557\) | 34.6295i | 1.46730i | 0.679527 | + | 0.733650i | \(0.262185\pi\) | ||||
−0.679527 | + | 0.733650i | \(0.737815\pi\) | |||||||
\(558\) | −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 | ||||
\(562\) | −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 | \(0.895004\pi\) | |||||||
\(564\) | 12.8066 | + | 7.39388i | 0.539254 | + | 0.311339i | ||||
\(565\) | − | 8.36084i | − | 0.351743i | ||||||
\(566\) | 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 | \(0.0413549\pi\) | |||||||
\(570\) | − | 0.170835i | − | 0.00715549i | ||||||
\(571\) | 5.08954 | − | 8.81533i | 0.212990 | − | 0.368910i | −0.739659 | − | 0.672982i | \(-0.765013\pi\) |
0.952649 | + | 0.304072i | \(0.0983464\pi\) | |||||||
\(572\) | −0.00128084 | − | 2.61025i | −5.35545e−5 | − | 0.109140i | ||||
\(573\) | 3.45423 | 0.144303 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.46470 | − | 9.46514i | −0.227894 | − | 0.394724i | ||||
\(576\) | −20.3679 | −0.848663 | ||||||||
\(577\) | −16.9018 | − | 9.75824i | −0.703630 | − | 0.406241i | 0.105068 | − | 0.994465i | \(-0.466494\pi\) |
−0.808698 | + | 0.588224i | \(0.799827\pi\) | |||||||
\(578\) | 0.714246 | − | 0.412370i | 0.0297087 | − | 0.0171523i | ||||
\(579\) | 2.44327i | 0.101539i | ||||||||
\(580\) | − | 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 | ||||
\(584\) | −0.518270 | + | 0.897670i | −0.0214462 | + | 0.0371458i | ||||
\(585\) | 0.00794753 | + | 16.1965i | 0.000328590 | + | 0.669643i | ||||
\(586\) | 1.07052 | + | 1.85419i | 0.0442226 | + | 0.0765959i | ||||
\(587\) | 30.6486 | − | 17.6950i | 1.26501 | − | 0.730351i | 0.290967 | − | 0.956733i | \(-0.406023\pi\) |
0.974039 | + | 0.226382i | \(0.0726898\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.39156 | + | 5.87436i | −0.139747 | + | 0.242049i | ||||
\(590\) | 1.64738 | − | 0.951117i | 0.0678217 | − | 0.0391569i | ||||
\(591\) | 2.91723 | − | 1.68426i | 0.119999 | − | 0.0692812i | ||||
\(592\) | 21.4044 | − | 12.3579i | 0.879716 | − | 0.507905i | ||||
\(593\) | −15.6648 | + | 9.04406i | −0.643275 | + | 0.371395i | −0.785875 | − | 0.618385i | \(-0.787787\pi\) |
0.142600 | + | 0.989780i | \(0.454454\pi\) | |||||||
\(594\) | −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 | ||||
\(598\) | −0.00108244 | − | 2.20593i | −4.42642e−5 | − | 0.0902072i | ||||
\(599\) | −4.52996 | + | 7.84612i | −0.185089 | + | 0.320584i | −0.943607 | − | 0.331069i | \(-0.892591\pi\) |
0.758517 | + | 0.651653i | \(0.225924\pi\) | |||||||
\(600\) | 0.520111 | + | 0.300286i | 0.0212334 | + | 0.0122591i | ||||
\(601\) | 14.6440 | + | 25.3642i | 0.597343 | + | 1.03463i | 0.993212 | + | 0.116321i | \(0.0371102\pi\) |
−0.395869 | + | 0.918307i | \(0.629556\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 35.8586i | 1.46028i | ||||||||
\(604\) | − | 27.8234i | − | 1.13212i | ||||||
\(605\) | −15.8876 | + | 9.17269i | −0.645922 | + | 0.372923i | ||||
\(606\) | −0.943592 | − | 0.544783i | −0.0383308 | − | 0.0221303i | ||||
\(607\) | 39.3650 | 1.59777 | 0.798887 | − | 0.601481i | \(-0.205422\pi\) | ||||
0.798887 | + | 0.601481i | \(0.205422\pi\) | |||||||
\(608\) | −1.03268 | − | 1.78865i | −0.0418807 | − | 0.0725394i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.83373 | −0.0742457 | ||||||||
\(611\) | −0.0226293 | − | 46.1170i | −0.000915485 | − | 1.86569i | ||||
\(612\) | −8.41514 | + | 14.5755i | −0.340162 | + | 0.589178i | ||||
\(613\) | 5.53316i | 0.223482i | 0.993737 | + | 0.111741i | \(0.0356427\pi\) | ||||
−0.993737 | + | 0.111741i | \(0.964357\pi\) | |||||||
\(614\) | −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 | 0.703026 | − | 0.711164i | \(-0.251832\pi\) |
−0.264373 | + | 0.964421i | \(0.585165\pi\) | |||||||
\(618\) | − | 0.721742i | − | 0.0290327i | ||||||
\(619\) | −19.3950 | − | 11.1977i | −0.779552 | − | 0.450075i | 0.0567194 | − | 0.998390i | \(-0.481936\pi\) |
−0.836272 | + | 0.548316i | \(0.815269\pi\) | |||||||
\(620\) | 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 | ||||
\(625\) | 4.81330 | + | 8.33687i | 0.192532 | + | 0.333475i | ||||
\(626\) | 2.48221i | 0.0992090i | ||||||||
\(627\) | 0.306562 | 0.0122429 | ||||||||
\(628\) | 34.1161 | 1.36138 | ||||||||
\(629\) | − | 20.1194i | − | 0.802213i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.68778 | + | 0.974439i | 0.0671894 | + | 0.0387918i | 0.533218 | − | 0.845978i | \(-0.320982\pi\) |
−0.466029 | + | 0.884769i | \(0.654316\pi\) | |||||||
\(632\) | 2.86140 | − | 1.65203i | 0.113820 | − | 0.0657142i | ||||
\(633\) | 2.39785 | + | 4.15320i | 0.0953061 | + | 0.165075i | ||||
\(634\) | −3.67621 | −0.146001 | ||||||||
\(635\) | −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 | ||||
\(640\) | −6.38477 | −0.252380 | ||||||||
\(641\) | 5.21051 | + | 9.02487i | 0.205803 | + | 0.356461i | 0.950388 | − | 0.311066i | \(-0.100686\pi\) |
−0.744585 | + | 0.667527i | \(0.767353\pi\) | |||||||
\(642\) | 0.796586 | − | 0.459909i | 0.0314387 | − | 0.0181512i | ||||
\(643\) | −13.2247 | − | 7.63531i | −0.521533 | − | 0.301107i | 0.216029 | − | 0.976387i | \(-0.430690\pi\) |
−0.737562 | + | 0.675280i | \(0.764023\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 0.759983i | − | 0.0299243i | ||||||
\(646\) | −0.553612 | −0.0217816 | ||||||||
\(647\) | 17.5066 | 0.688254 | 0.344127 | − | 0.938923i | \(-0.388175\pi\) | ||||
0.344127 | + | 0.938923i | \(0.388175\pi\) | |||||||
\(648\) | − | 2.90858i | − | 0.114260i | ||||||
\(649\) | 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 | ||||
\(653\) | 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 | ||||
\(655\) | −27.6374 | − | 15.9564i | −1.07988 | − | 0.623470i | ||||
\(656\) | 22.8040i | 0.890346i | ||||||||
\(657\) | 4.97949 | + | 2.87491i | 0.194268 | + | 0.112161i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.9294 | − | 37.9828i | 0.854247 | − | 1.47960i | −0.0230945 | − | 0.999733i | \(-0.507352\pi\) |
0.877342 | − | 0.479866i | \(-0.159315\pi\) | |||||||
\(660\) | 0.355825 | − | 0.616308i | 0.0138505 | − | 0.0239897i | ||||
\(661\) | 32.9270i | 1.28071i | 0.768078 | + | 0.640356i | \(0.221213\pi\) | ||||
−0.768078 | + | 0.640356i | \(0.778787\pi\) | |||||||
\(662\) | −1.55584 | + | 2.69479i | −0.0604693 | + | 0.104736i | ||||
\(663\) | −6.68800 | + | 0.00328177i | −0.259741 | + | 0.000127453i | ||||
\(664\) | 0.272170 | 0.0105622 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.01139 | + | 1.75177i | 0.0391904 | + | 0.0678798i | ||||
\(667\) | 41.6651 | 1.61328 | ||||||||
\(668\) | 7.42287 | + | 4.28560i | 0.287200 | + | 0.165815i | ||||
\(669\) | −7.71622 | + | 4.45496i | −0.298326 | + | 0.172239i | ||||
\(670\) | 2.73814i | 0.105784i | ||||||||
\(671\) | − | 3.29062i | − | 0.127033i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.3423 | + | 23.1095i | 0.514307 | + | 0.890806i | 0.999862 | + | 0.0165997i | \(0.00528409\pi\) |
−0.485555 | + | 0.874206i | \(0.661383\pi\) | |||||||
\(674\) | −2.23015 | − | 1.28758i | −0.0859021 | − | 0.0495956i | ||||
\(675\) | 3.54370 | − | 6.13787i | 0.136397 | − | 0.236247i | ||||
\(676\) | −12.8839 | + | 22.3662i | −0.495534 | + | 0.860239i | ||||
\(677\) | 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 | ||||
\(682\) | 0.178542 | − | 0.103081i | 0.00683674 | − | 0.00394719i | ||||
\(683\) | 15.8379 | − | 9.14400i | 0.606019 | − | 0.349885i | −0.165387 | − | 0.986229i | \(-0.552887\pi\) |
0.771406 | + | 0.636343i | \(0.219554\pi\) | |||||||
\(684\) | −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 | ||||
\(689\) | −2.47388 | − | 4.28003i | −0.0942472 | − | 0.163056i | ||||
\(690\) | 0.300709 | − | 0.520843i | 0.0114478 | − | 0.0198281i | ||||
\(691\) | −8.95525 | − | 5.17031i | −0.340674 | − | 0.196688i | 0.319896 | − | 0.947453i | \(-0.396352\pi\) |
−0.660570 | + | 0.750765i | \(0.729685\pi\) | |||||||
\(692\) | −12.4290 | − | 21.5277i | −0.472480 | − | 0.818360i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 0.265855i | − | 0.0100917i | ||||||
\(695\) | 8.86430i | 0.336242i | ||||||||
\(696\) | −1.98277 | + | 1.14475i | −0.0751567 | + | 0.0433917i | ||||
\(697\) | 16.0762 | + | 9.28160i | 0.608930 | + | 0.351566i | ||||
\(698\) | 1.35900 | 0.0514390 | ||||||||
\(699\) | −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 | \(0.211419\pi\) | |||||||
\(702\) | 1.23848 | − | 0.715849i | 0.0467435 | − | 0.0270180i | ||||
\(703\) | 4.55974 | − | 7.89770i | 0.171974 | − | 0.297867i | ||||
\(704\) | − | 2.79094i | − | 0.105188i | ||||||
\(705\) | 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 | ||||
\(709\) | − | 0.0109463i | − | 0.000411095i | −1.00000 | 0.000205548i | \(-0.999935\pi\) | |||
1.00000 | 0.000205548i | \(-6.54279e-5\pi\) | ||||||||
\(710\) | 1.24604 | + | 0.719400i | 0.0467630 | + | 0.0269986i | ||||
\(711\) | −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 | ||||
\(716\) | −6.54757 | − | 11.3407i | −0.244694 | − | 0.423823i | ||||
\(717\) | − | 12.8543i | − | 0.480054i | ||||||
\(718\) | −2.32557 | −0.0867894 | ||||||||
\(719\) | −25.4660 | −0.949722 | −0.474861 | − | 0.880061i | \(-0.657502\pi\) | ||||
−0.474861 | + | 0.880061i | \(0.657502\pi\) | |||||||
\(720\) | 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 | ||||
\(724\) | −10.9359 | − | 18.9416i | −0.406430 | − | 0.703957i | ||||
\(725\) | 17.6235 | 0.654521 | ||||||||
\(726\) | 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 | ||||
\(731\) | −2.46282 | −0.0910905 | ||||||||
\(732\) | −5.21703 | − | 9.03616i | −0.192827 | − | 0.333986i | ||||
\(733\) | 5.39750 | − | 3.11625i | 0.199361 | − | 0.115101i | −0.396996 | − | 0.917820i | \(-0.629947\pi\) |
0.596357 | + | 0.802719i | \(0.296614\pi\) | |||||||
\(734\) | 0.387821 | + | 0.223909i | 0.0143147 | + | 0.00826461i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 7.27100i | − | 0.268013i | ||||||
\(737\) | −4.91357 | −0.180994 | ||||||||
\(738\) | −1.86632 | −0.0687000 | ||||||||
\(739\) | 1.29718i | 0.0477174i | 0.999715 | + | 0.0238587i | \(0.00759517\pi\) | ||||
−0.999715 | + | 0.0238587i | \(0.992405\pi\) | |||||||
\(740\) | −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 | −0.400475 | − | 0.916308i | \(-0.631155\pi\) |
0.593309 | + | 0.804975i | \(0.297821\pi\) | |||||||
\(744\) | 0.656096 | − | 1.13639i | 0.0240536 | − | 0.0416621i | ||||
\(745\) | 7.82725 | + | 13.5572i | 0.286768 | + | 0.496697i | ||||
\(746\) | −0.366152 | − | 0.211398i | −0.0134058 | − | 0.00773983i | ||||
\(747\) | − | 1.50976i | − | 0.0552393i | ||||||
\(748\) | −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 | \(0.933877\pi\) | |||||||
\(752\) | − | 50.0531i | − | 1.82525i | ||||||
\(753\) | −6.56728 | + | 11.3749i | −0.239325 | + | 0.414523i | ||||
\(754\) | 3.08135 | + | 1.77701i | 0.112216 | + | 0.0647147i | ||||
\(755\) | −23.6566 | −0.860952 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.83991 | − | 10.1150i | −0.212255 | − | 0.367636i | 0.740165 | − | 0.672425i | \(-0.234747\pi\) |
−0.952420 | + | 0.304789i | \(0.901414\pi\) | |||||||
\(758\) | 3.01096 | 0.109363 | ||||||||
\(759\) | 0.934648 | + | 0.539619i | 0.0339256 | + | 0.0195869i | ||||
\(760\) | −1.01263 | + | 0.584642i | −0.0367320 | + | 0.0212072i | ||||
\(761\) | − | 39.7688i | − | 1.44162i | −0.693133 | − | 0.720810i | \(-0.743770\pi\) | ||
0.693133 | − | 0.720810i | \(-0.256230\pi\) | |||||||
\(762\) | 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 | ||||
\(766\) | 1.35197 | − | 2.34167i | 0.0488485 | − | 0.0846081i | ||||
\(767\) | −0.0165634 | − | 33.7551i | −0.000598070 | − | 1.21882i | ||||
\(768\) | −4.32457 | − | 7.49038i | −0.156050 | − | 0.270286i | ||||
\(769\) | 8.62507 | − | 4.97969i | 0.311028 | − | 0.179572i | −0.336358 | − | 0.941734i | \(-0.609195\pi\) |
0.647386 | + | 0.762162i | \(0.275862\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.94313 | + | 10.2938i | −0.214036 | + | 0.370722i | ||||
\(772\) | 7.21496 | − | 4.16556i | 0.259672 | − | 0.149922i | ||||
\(773\) | 11.0433 | − | 6.37588i | 0.397201 | − | 0.229324i | −0.288074 | − | 0.957608i | \(-0.593015\pi\) |
0.685276 | + | 0.728284i | \(0.259682\pi\) | |||||||
\(774\) | 0.214435 | − | 0.123804i | 0.00770769 | − | 0.00445004i | ||||
\(775\) | −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 | ||||
\(780\) | −6.09267 | + | 3.52159i | −0.218153 | + | 0.126093i | ||||
\(781\) | −1.29096 | + | 2.23601i | −0.0461941 | + | 0.0800106i | ||||
\(782\) | −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 | ||||||
\(786\) | 1.32487i | 0.0472566i | ||||||||
\(787\) | 7.52380 | − | 4.34387i | 0.268194 | − | 0.154842i | −0.359872 | − | 0.933002i | \(-0.617180\pi\) |
0.628067 | + | 0.778159i | \(0.283846\pi\) | |||||||
\(788\) | −9.94723 | − | 5.74303i | −0.354355 | − | 0.204587i | ||||
\(789\) | −17.2010 | −0.612373 | ||||||||
\(790\) | −0.699759 | − | 1.21202i | −0.0248963 | − | 0.0431216i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.465413 | 0.0165377 | ||||||||
\(793\) | −16.2559 | + | 28.1880i | −0.577265 | + | 1.00099i | ||||
\(794\) | 1.55465 | − | 2.69273i | 0.0551723 | − | 0.0955613i | ||||
\(795\) | − | 1.34779i | − | 0.0478013i | ||||||
\(796\) | −11.8731 | + | 20.5649i | −0.420832 | + | 0.728903i | ||||
\(797\) | −19.3719 | + | 33.5531i | −0.686187 | + | 1.18851i | 0.286875 | + | 0.957968i | \(0.407384\pi\) |
−0.973062 | + | 0.230543i | \(0.925950\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.2861 | − | 20.3724i | −1.24833 | − | 0.720725i | ||||
\(800\) | − | 3.07549i | − | 0.108735i | ||||||
\(801\) | 2.62460 | + | 1.51532i | 0.0927358 | + | 0.0535411i | ||||
\(802\) | −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 | ||||
\(807\) | 8.12771 | + | 14.0776i | 0.286109 | + | 0.495555i | ||||
\(808\) | 7.45757i | 0.262356i | ||||||||
\(809\) | 28.8550 | 1.01449 | 0.507244 | − | 0.861802i | \(-0.330664\pi\) | ||||
0.507244 | + | 0.861802i | \(0.330664\pi\) | |||||||
\(810\) | −1.23200 | −0.0432882 | ||||||||
\(811\) | − | 12.3917i | − | 0.435131i | −0.976046 | − | 0.217566i | \(-0.930188\pi\) | ||
0.976046 | − | 0.217566i | \(-0.0698116\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.8506 | − | 8.57397i | −0.520832 | − | 0.300702i | ||||
\(814\) | −0.240039 | + | 0.138586i | −0.00841336 | + | 0.00485745i | ||||
\(815\) | 9.95405 | + | 17.2409i | 0.348675 | + | 0.603923i | ||||
\(816\) | −7.25884 | −0.254110 | ||||||||
\(817\) | −0.966758 | − | 0.558158i | −0.0338226 | − | 0.0195275i | ||||
\(818\) | 1.74861 | 0.0611388 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.5324 | 0.682103 | ||||||||
\(821\) | −35.5277 | − | 20.5119i | −1.23992 | − | 0.715870i | −0.270845 | − | 0.962623i | \(-0.587303\pi\) |
−0.969079 | + | 0.246753i | \(0.920636\pi\) | |||||||
\(822\) | −1.27733 | −0.0445519 | ||||||||
\(823\) | −1.06806 | − | 1.84994i | −0.0372304 | − | 0.0644849i | 0.846810 | − | 0.531896i | \(-0.178520\pi\) |
−0.884040 | + | 0.467411i | \(0.845187\pi\) | |||||||
\(824\) | −4.27815 | + | 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 | \(-0.952509\pi\) | ||
0.988891 | − | 0.148645i | \(-0.0474913\pi\) | |||||||
\(828\) | −26.8563 | −0.933320 | ||||||||
\(829\) | −14.7569 | −0.512528 | −0.256264 | − | 0.966607i | \(-0.582492\pi\) | ||||
−0.256264 | + | 0.966607i | \(0.582492\pi\) | |||||||
\(830\) | − | 0.115284i | − | 0.00400158i | ||||||
\(831\) | 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 | ||||
\(835\) | 3.64379 | − | 6.31123i | 0.126099 | − | 0.218409i | ||||
\(836\) | −0.522661 | − | 0.905276i | −0.0180766 | − | 0.0313096i | ||||
\(837\) | −13.4107 | − | 7.74265i | −0.463540 | − | 0.267625i | ||||
\(838\) | − | 0.553887i | − | 0.0191337i | ||||||
\(839\) | −23.3581 | − | 13.4858i | −0.806411 | − | 0.465582i | 0.0392968 | − | 0.999228i | \(-0.487488\pi\) |
−0.845708 | + | 0.533646i | \(0.820822\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0923 | + | 33.0687i | −0.658353 | + | 1.14030i | ||||
\(842\) | −1.15934 | + | 2.00803i | −0.0399534 | + | 0.0692013i | ||||
\(843\) | 16.9412i | 0.583487i | ||||||||
\(844\) | 8.17626 | − | 14.1617i | 0.281438 | − | 0.487465i | ||||
\(845\) | 19.0167 | + | 10.9544i | 0.654194 | + | 0.376843i | ||||
\(846\) | 4.09643 | 0.140838 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.68275 | − | 4.64665i | −0.0921259 | − | 0.159567i | ||||
\(849\) | 6.76053 | 0.232021 | ||||||||
\(850\) | −0.713928 | − | 0.412187i | −0.0244875 | − | 0.0141379i | ||||
\(851\) | 27.8035 | − | 16.0524i | 0.953092 | − | 0.550268i | ||||
\(852\) | 8.18686i | 0.280477i | ||||||||
\(853\) | 25.6332i | 0.877665i | 0.898569 | + | 0.438832i | \(0.144608\pi\) | ||||
−0.898569 | + | 0.438832i | \(0.855392\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.24309 | + | 5.61719i | 0.110911 | + | 0.192104i | ||||
\(856\) | −5.45225 | − | 3.14786i | −0.186354 | − | 0.107592i | ||||
\(857\) | −5.88263 | + | 10.1890i | −0.200947 | + | 0.348050i | −0.948834 | − | 0.315776i | \(-0.897735\pi\) |
0.747887 | + | 0.663826i | \(0.231068\pi\) | |||||||
\(858\) | 0.0461075 | + | 0.0797701i | 0.00157408 | + | 0.00272331i | ||||
\(859\) | −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 | −0.962840 | − | 0.270073i | \(-0.912952\pi\) |
−0.247530 | + | 0.968880i | \(0.579619\pi\) | |||||||
\(864\) | 4.08334 | − | 2.35752i | 0.138918 | − | 0.0802044i | ||||
\(865\) | −18.3037 | + | 10.5677i | −0.622345 | + | 0.359311i | ||||
\(866\) | 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 | ||||
\(871\) | 42.0905 | + | 24.2734i | 1.42618 | + | 0.822474i | ||||
\(872\) | 2.50543 | − | 4.33953i | 0.0848445 | − | 0.146955i | ||||
\(873\) | 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 | ||||||||
\(877\) | − | 6.89112i | − | 0.232696i | −0.993208 | − | 0.116348i | \(-0.962881\pi\) | ||
0.993208 | − | 0.116348i | \(-0.0371189\pi\) | |||||||
\(878\) | −3.30709 | + | 1.90935i | −0.111609 | + | 0.0644374i | ||||
\(879\) | 8.97043 | + | 5.17908i | 0.302565 | + | 0.174686i | ||||
\(880\) | −2.40877 | −0.0811996 | ||||||||
\(881\) | 5.32288 | + | 9.21950i | 0.179332 | + | 0.310613i | 0.941652 | − | 0.336588i | \(-0.109273\pi\) |
−0.762320 | + | 0.647201i | \(0.775940\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.3844 | 0.719641 | 0.359821 | − | 0.933022i | \(-0.382838\pi\) | ||||
0.359821 | + | 0.933022i | \(0.382838\pi\) | |||||||
\(884\) | 11.4122 | + | 19.7440i | 0.383832 | + | 0.664064i | ||||
\(885\) | 4.60143 | − | 7.96991i | 0.154675 | − | 0.267906i | ||||
\(886\) | − | 0.208281i | − | 0.00699732i | ||||||
\(887\) | −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 | ||||
\(891\) | − | 2.21082i | − | 0.0740653i | ||||||
\(892\) | 26.3110 | + | 15.1906i | 0.880956 | + | 0.508620i | ||||
\(893\) | −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 | ||||
\(898\) | −0.635282 | − | 1.10034i | −0.0211996 | − | 0.0367188i | ||||
\(899\) | − | 38.5057i | − | 1.28424i | ||||||
\(900\) | −11.3597 | −0.378655 | ||||||||
\(901\) | −4.36769 | −0.145509 | ||||||||
\(902\) | − | 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 | ||||
\(906\) | 0.491055 | + | 0.850532i | 0.0163142 | + | 0.0282570i | ||||
\(907\) | −42.1515 | −1.39962 | −0.699810 | − | 0.714329i | \(-0.746732\pi\) | ||||
−0.699810 | + | 0.714329i | \(0.746732\pi\) | |||||||
\(908\) | 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 | ||||
\(913\) | 0.206877 | 0.00684663 | ||||||||
\(914\) | 0.478367 | + | 0.828556i | 0.0158230 | + | 0.0274062i | ||||
\(915\) | −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 | ||||||
\(919\) | −14.2940 | −0.471515 | −0.235757 | − | 0.971812i | \(-0.575757\pi\) | ||||
−0.235757 | + | 0.971812i | \(0.575757\pi\) | |||||||
\(920\) | −4.11642 | −0.135714 | ||||||||
\(921\) | 5.28701i | 0.174213i | ||||||||
\(922\) | −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 | ||||
\(926\) | −2.15581 | + | 3.73397i | −0.0708443 | + | 0.122706i | ||||
\(927\) | 13.7014 | + | 23.7315i | 0.450012 | + | 0.779444i | ||||
\(928\) | 10.1536 | + | 5.86220i | 0.333309 | + | 0.192436i | ||||
\(929\) | 6.80723i | 0.223338i | 0.993745 | + | 0.111669i | \(0.0356197\pi\) | ||||
−0.993745 | + | 0.111669i | \(0.964380\pi\) | |||||||
\(930\) | −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 | ||||
\(934\) | − | 2.39496i | − | 0.0783655i | ||||||
\(935\) | −0.980409 | + | 1.69812i | −0.0320628 | + | 0.0555344i | ||||
\(936\) | −3.98681 | − | 2.29918i | −0.130313 | − | 0.0751510i | ||||
\(937\) | 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 | ||||
\(940\) | −42.8723 | −1.39834 | ||||||||
\(941\) | 48.8788 | + | 28.2202i | 1.59340 | + | 0.919951i | 0.992718 | + | 0.120465i | \(0.0384386\pi\) |
0.600685 | + | 0.799486i | \(0.294895\pi\) | |||||||
\(942\) | −1.04289 | + | 0.602114i | −0.0339793 | + | 0.0196179i | ||||
\(943\) | 29.6215i | 0.964609i | ||||||||
\(944\) | − | 36.6361i | − | 1.19240i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0169644 | + | 0.0293832i | 0.000551559 | + | 0.000955329i | ||||
\(947\) | 5.06648 | + | 2.92513i | 0.164639 | + | 0.0950541i | 0.580055 | − | 0.814577i | \(-0.303031\pi\) |
−0.415417 | + | 0.909631i | \(0.636364\pi\) | |||||||
\(948\) | 3.98167 | − | 6.89645i | 0.129319 | − | 0.223986i | ||||
\(949\) | 6.74527 | − | 3.89880i | 0.218961 | − | 0.126560i | ||||
\(950\) | −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 | −0.986643 | − | 0.162896i | \(-0.947916\pi\) |
0.634394 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(954\) | 0.380290 | − | 0.219560i | 0.0123123 | − | 0.00710853i | ||||
\(955\) | −8.67273 | + | 5.00720i | −0.280643 | + | 0.162029i | ||||
\(956\) | −37.9588 | + | 21.9155i | −1.22767 | + | 0.708798i | ||||
\(957\) | −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 | ||||
\(962\) | 2.74084 | − | 0.00134492i | 0.0883683 | − | 4.33619e-5i | ||||
\(963\) | −17.4616 | + | 30.2444i | −0.562692 | + | 0.974611i | ||||
\(964\) | −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 | \(-0.931268\pi\) | ||
0.976778 | − | 0.214253i | \(-0.0687318\pi\) | |||||||
\(968\) | − | 5.21288i | − | 0.167548i | ||||||
\(969\) | −2.31950 | + | 1.33917i | −0.0745132 | + | 0.0430202i | ||||
\(970\) | 1.39503 | + | 0.805420i | 0.0447917 | + | 0.0258605i | ||||
\(971\) | −7.46185 | −0.239462 | −0.119731 | − | 0.992806i | \(-0.538203\pi\) | ||||
−0.119731 | + | 0.992806i | \(0.538203\pi\) | |||||||
\(972\) | −13.3224 | − | 23.0751i | −0.427317 | − | 0.740134i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.767850 | −0.0246035 | ||||||||
\(975\) | −2.25897 | − | 3.90821i | −0.0723448 | − | 0.125163i | ||||
\(976\) | −17.6584 | + | 30.5853i | −0.565232 | + | 0.979011i | ||||
\(977\) | − | 10.9605i | − | 0.350656i | −0.984510 | − | 0.175328i | \(-0.943901\pi\) | ||
0.984510 | − | 0.175328i | \(-0.0560986\pi\) | |||||||
\(978\) | 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 | ||||
\(982\) | − | 0.357189i | − | 0.0113984i | ||||||
\(983\) | −13.9812 | − | 8.07206i | −0.445932 | − | 0.257459i | 0.260179 | − | 0.965560i | \(-0.416219\pi\) |
−0.706111 | + | 0.708102i | \(0.749552\pi\) | |||||||
\(984\) | −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 | ||||
\(989\) | −1.96497 | − | 3.40343i | −0.0624824 | − | 0.108223i | ||||
\(990\) | − | 0.197138i | − | 0.00626544i | ||||||
\(991\) | 6.71496 | 0.213308 | 0.106654 | − | 0.994296i | \(-0.465986\pi\) | ||||
0.106654 | + | 0.994296i | \(0.465986\pi\) | |||||||
\(992\) | −6.71965 | −0.213349 | ||||||||
\(993\) | 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 | ||||
\(997\) | −9.22057 | − | 15.9705i | −0.292018 | − | 0.505791i | 0.682269 | − | 0.731102i | \(-0.260993\pi\) |
−0.974287 | + | 0.225311i | \(0.927660\pi\) | |||||||
\(998\) | 3.38609 | 0.107185 | ||||||||
\(999\) | 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.u.i.361.4 | 12 | ||
7.2 | even | 3 | 637.2.k.g.569.3 | 12 | |||
7.3 | odd | 6 | 91.2.q.a.36.3 | ✓ | 12 | ||
7.4 | even | 3 | 637.2.q.h.491.3 | 12 | |||
7.5 | odd | 6 | 637.2.k.h.569.3 | 12 | |||
7.6 | odd | 2 | 637.2.u.h.361.4 | 12 | |||
13.4 | even | 6 | 637.2.k.g.459.4 | 12 | |||
21.17 | even | 6 | 819.2.ct.a.127.4 | 12 | |||
28.3 | even | 6 | 1456.2.cc.c.673.3 | 12 | |||
91.3 | odd | 6 | 1183.2.c.i.337.6 | 12 | |||
91.4 | even | 6 | 637.2.q.h.589.3 | 12 | |||
91.10 | odd | 6 | 1183.2.c.i.337.7 | 12 | |||
91.11 | odd | 12 | 8281.2.a.ch.1.3 | 6 | |||
91.17 | odd | 6 | 91.2.q.a.43.3 | yes | 12 | ||
91.24 | even | 12 | 1183.2.a.p.1.3 | 6 | |||
91.30 | even | 6 | inner | 637.2.u.i.30.4 | 12 | ||
91.67 | odd | 12 | 8281.2.a.by.1.4 | 6 | |||
91.69 | odd | 6 | 637.2.k.h.459.4 | 12 | |||
91.80 | even | 12 | 1183.2.a.m.1.4 | 6 | |||
91.82 | odd | 6 | 637.2.u.h.30.4 | 12 | |||
273.17 | even | 6 | 819.2.ct.a.316.4 | 12 | |||
364.199 | even | 6 | 1456.2.cc.c.225.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.3 | ✓ | 12 | 7.3 | odd | 6 | ||
91.2.q.a.43.3 | yes | 12 | 91.17 | odd | 6 | ||
637.2.k.g.459.4 | 12 | 13.4 | even | 6 | |||
637.2.k.g.569.3 | 12 | 7.2 | even | 3 | |||
637.2.k.h.459.4 | 12 | 91.69 | odd | 6 | |||
637.2.k.h.569.3 | 12 | 7.5 | odd | 6 | |||
637.2.q.h.491.3 | 12 | 7.4 | even | 3 | |||
637.2.q.h.589.3 | 12 | 91.4 | even | 6 | |||
637.2.u.h.30.4 | 12 | 91.82 | odd | 6 | |||
637.2.u.h.361.4 | 12 | 7.6 | odd | 2 | |||
637.2.u.i.30.4 | 12 | 91.30 | even | 6 | inner | ||
637.2.u.i.361.4 | 12 | 1.1 | even | 1 | trivial | ||
819.2.ct.a.127.4 | 12 | 21.17 | even | 6 | |||
819.2.ct.a.316.4 | 12 | 273.17 | even | 6 | |||
1183.2.a.m.1.4 | 6 | 91.80 | even | 12 | |||
1183.2.a.p.1.3 | 6 | 91.24 | even | 12 | |||
1183.2.c.i.337.6 | 12 | 91.3 | odd | 6 | |||
1183.2.c.i.337.7 | 12 | 91.10 | odd | 6 | |||
1456.2.cc.c.225.3 | 12 | 364.199 | even | 6 | |||
1456.2.cc.c.673.3 | 12 | 28.3 | even | 6 | |||
8281.2.a.by.1.4 | 6 | 91.67 | odd | 12 | |||
8281.2.a.ch.1.3 | 6 | 91.11 | odd | 12 |