Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,19,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 19, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 19);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 19 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.d (of order \(2\), degree \(1\), 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: | \(16.4308910168\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} + 56971 x^{14} - 14457953 x^{13} + 5222713963 x^{12} - 1887111404561 x^{11} + \cdots + 32\!\cdots\!30 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{120}\cdot 3^{13}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.1 | ||
Root | \(-226.199 - 141.712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.19.d.b.3.2 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −426.398 | − | 283.424i | −0.832808 | − | 0.553562i | ||||
\(3\) | 35846.9 | 1.82121 | 0.910607 | − | 0.413274i | \(-0.135615\pi\) | ||||
0.910607 | + | 0.413274i | \(0.135615\pi\) | |||||||
\(4\) | 101486. | + | 241703.i | 0.387138 | + | 0.922022i | ||||
\(5\) | − | 3.47680e6i | − | 1.78012i | −0.455844 | − | 0.890060i | \(-0.650663\pi\) | ||
0.455844 | − | 0.890060i | \(-0.349337\pi\) | |||||||
\(6\) | −1.52851e7 | − | 1.01599e7i | −1.51672 | − | 1.00816i | ||||
\(7\) | 1.08296e7i | 0.268367i | 0.990956 | + | 0.134184i | \(0.0428412\pi\) | ||||
−0.990956 | + | 0.134184i | \(0.957159\pi\) | |||||||
\(8\) | 2.52310e7 | − | 1.31825e8i | 0.187985 | − | 0.982172i | ||||
\(9\) | 8.97583e8 | 2.31682 | ||||||||
\(10\) | −9.85407e8 | + | 1.48250e9i | −0.985407 | + | 1.48250i | ||||
\(11\) | −1.36275e8 | −0.0577939 | −0.0288970 | − | 0.999582i | \(-0.509199\pi\) | ||||
−0.0288970 | + | 0.999582i | \(0.509199\pi\) | |||||||
\(12\) | 3.63796e9 | + | 8.66430e9i | 0.705060 | + | 1.67920i | ||||
\(13\) | − | 2.80141e9i | − | 0.264172i | −0.991238 | − | 0.132086i | \(-0.957832\pi\) | ||
0.991238 | − | 0.132086i | \(-0.0421675\pi\) | |||||||
\(14\) | 3.06936e9 | − | 4.61771e9i | 0.148558 | − | 0.223498i | ||||
\(15\) | − | 1.24633e11i | − | 3.24198i | ||||||
\(16\) | −4.81207e10 | + | 4.90587e10i | −0.700249 | + | 0.713899i | ||||
\(17\) | 2.99849e10 | 0.252849 | 0.126425 | − | 0.991976i | \(-0.459650\pi\) | ||||
0.126425 | + | 0.991976i | \(0.459650\pi\) | |||||||
\(18\) | −3.82727e11 | − | 2.54397e11i | −1.92946 | − | 1.28250i | ||||
\(19\) | −5.03309e10 | −0.155974 | −0.0779871 | − | 0.996954i | \(-0.524849\pi\) | ||||
−0.0779871 | + | 0.996954i | \(0.524849\pi\) | |||||||
\(20\) | 8.40350e11 | − | 3.52845e11i | 1.64131 | − | 0.689151i | ||||
\(21\) | 3.88208e11i | 0.488754i | ||||||||
\(22\) | 5.81073e10 | + | 3.86236e10i | 0.0481312 | + | 0.0319925i | ||||
\(23\) | − | 1.64351e12i | − | 0.912475i | −0.889858 | − | 0.456237i | \(-0.849197\pi\) | ||
0.889858 | − | 0.456237i | \(-0.150803\pi\) | |||||||
\(24\) | 9.04453e11 | − | 4.72552e12i | 0.342362 | − | 1.78874i | ||||
\(25\) | −8.27341e12 | −2.16883 | ||||||||
\(26\) | −7.93988e11 | + | 1.19452e12i | −0.146236 | + | 0.220005i | ||||
\(27\) | 1.82878e13 | 2.39821 | ||||||||
\(28\) | −2.61754e12 | + | 1.09905e12i | −0.247441 | + | 0.103895i | ||||
\(29\) | − | 5.13731e12i | − | 0.354123i | −0.984200 | − | 0.177061i | \(-0.943341\pi\) | ||
0.984200 | − | 0.177061i | \(-0.0566591\pi\) | |||||||
\(30\) | −3.53238e13 | + | 5.31430e13i | −1.79464 | + | 2.69994i | ||||
\(31\) | − | 3.37595e13i | − | 1.27685i | −0.769683 | − | 0.638426i | \(-0.779586\pi\) | ||
0.769683 | − | 0.638426i | \(-0.220414\pi\) | |||||||
\(32\) | 3.44230e13 | − | 7.27996e12i | 0.978360 | − | 0.206909i | ||||
\(33\) | −4.88504e12 | −0.105255 | ||||||||
\(34\) | −1.27855e13 | − | 8.49843e12i | −0.210575 | − | 0.139968i | ||||
\(35\) | 3.76523e13 | 0.477726 | ||||||||
\(36\) | 9.10919e13 | + | 2.16948e14i | 0.896928 | + | 2.13616i | ||||
\(37\) | 1.22733e14i | 0.944376i | 0.881498 | + | 0.472188i | \(0.156536\pi\) | ||||
−0.881498 | + | 0.472188i | \(0.843464\pi\) | |||||||
\(38\) | 2.14610e13 | + | 1.42650e13i | 0.129896 | + | 0.0863414i | ||||
\(39\) | − | 1.00422e14i | − | 0.481114i | ||||||
\(40\) | −4.58328e14 | − | 8.77229e13i | −1.74838 | − | 0.334636i | ||||
\(41\) | 4.29547e14 | 1.31207 | 0.656033 | − | 0.754732i | \(-0.272233\pi\) | ||||
0.656033 | + | 0.754732i | \(0.272233\pi\) | |||||||
\(42\) | 1.10027e14 | − | 1.65531e14i | 0.270556 | − | 0.407038i | ||||
\(43\) | −5.15040e14 | −1.02477 | −0.512383 | − | 0.858757i | \(-0.671237\pi\) | ||||
−0.512383 | + | 0.858757i | \(0.671237\pi\) | |||||||
\(44\) | −1.38300e13 | − | 3.29380e13i | −0.0223742 | − | 0.0532873i | ||||
\(45\) | − | 3.12071e15i | − | 4.12421i | ||||||
\(46\) | −4.65809e14 | + | 7.00787e14i | −0.505112 | + | 0.759916i | ||||
\(47\) | − | 4.52697e14i | − | 0.404508i | −0.979333 | − | 0.202254i | \(-0.935173\pi\) | ||
0.979333 | − | 0.202254i | \(-0.0648266\pi\) | |||||||
\(48\) | −1.72498e15 | + | 1.75861e15i | −1.27530 | + | 1.30016i | ||||
\(49\) | 1.51113e15 | 0.927979 | ||||||||
\(50\) | 3.52776e15 | + | 2.34488e15i | 1.80621 | + | 1.20058i | ||||
\(51\) | 1.07487e15 | 0.460493 | ||||||||
\(52\) | 6.77109e14 | − | 2.84304e14i | 0.243573 | − | 0.102271i | ||||
\(53\) | 3.85227e15i | 1.16744i | 0.811956 | + | 0.583719i | \(0.198403\pi\) | ||||
−0.811956 | + | 0.583719i | \(0.801597\pi\) | |||||||
\(54\) | −7.79786e15 | − | 5.18319e15i | −1.99725 | − | 1.32756i | ||||
\(55\) | 4.73800e14i | 0.102880i | ||||||||
\(56\) | 1.42761e15 | + | 2.73241e14i | 0.263583 | + | 0.0504492i | ||||
\(57\) | −1.80421e15 | −0.284062 | ||||||||
\(58\) | −1.45604e15 | + | 2.19054e15i | −0.196029 | + | 0.294916i | ||||
\(59\) | −8.14938e15 | −0.940711 | −0.470356 | − | 0.882477i | \(-0.655874\pi\) | ||||
−0.470356 | + | 0.882477i | \(0.655874\pi\) | |||||||
\(60\) | 3.01240e16 | − | 1.26484e16i | 2.98917 | − | 1.25509i | ||||
\(61\) | 1.63847e16i | 1.40110i | 0.713603 | + | 0.700551i | \(0.247062\pi\) | ||||
−0.713603 | + | 0.700551i | \(0.752938\pi\) | |||||||
\(62\) | −9.56825e15 | + | 1.43950e16i | −0.706817 | + | 1.06337i | ||||
\(63\) | 9.72046e15i | 0.621759i | ||||||||
\(64\) | −1.67412e16 | − | 6.65214e15i | −0.929323 | − | 0.369268i | ||||
\(65\) | −9.73995e15 | −0.470258 | ||||||||
\(66\) | 2.08297e15 | + | 1.38454e15i | 0.0876572 | + | 0.0582652i | ||||
\(67\) | 3.10380e16 | 1.14083 | 0.570414 | − | 0.821357i | \(-0.306783\pi\) | ||||
0.570414 | + | 0.821357i | \(0.306783\pi\) | |||||||
\(68\) | 3.04304e15 | + | 7.24742e15i | 0.0978875 | + | 0.233133i | ||||
\(69\) | − | 5.89147e16i | − | 1.66181i | ||||||
\(70\) | −1.60548e16 | − | 1.06716e16i | −0.397854 | − | 0.264451i | ||||
\(71\) | 4.98018e16i | 1.08623i | 0.839660 | + | 0.543113i | \(0.182755\pi\) | ||||
−0.839660 | + | 0.543113i | \(0.817245\pi\) | |||||||
\(72\) | 2.26469e16 | − | 1.18324e17i | 0.435528 | − | 2.27551i | ||||
\(73\) | 7.59692e16 | 1.29042 | 0.645211 | − | 0.764005i | \(-0.276770\pi\) | ||||
0.645211 | + | 0.764005i | \(0.276770\pi\) | |||||||
\(74\) | 3.47854e16 | − | 5.23330e16i | 0.522771 | − | 0.786484i | ||||
\(75\) | −2.96577e17 | −3.94989 | ||||||||
\(76\) | −5.10788e15 | − | 1.21651e16i | −0.0603835 | − | 0.143812i | ||||
\(77\) | − | 1.47580e15i | − | 0.0155100i | ||||||
\(78\) | −2.84620e16 | + | 4.28198e16i | −0.266327 | + | 0.400676i | ||||
\(79\) | 1.64362e17i | 1.37138i | 0.727893 | + | 0.685690i | \(0.240500\pi\) | ||||
−0.727893 | + | 0.685690i | \(0.759500\pi\) | |||||||
\(80\) | 1.70567e17 | + | 1.67306e17i | 1.27082 | + | 1.24653i | ||||
\(81\) | 3.07819e17 | 2.05083 | ||||||||
\(82\) | −1.83158e17 | − | 1.21744e17i | −1.09270 | − | 0.726310i | ||||
\(83\) | 4.04293e16 | 0.216268 | 0.108134 | − | 0.994136i | \(-0.465512\pi\) | ||||
0.108134 | + | 0.994136i | \(0.465512\pi\) | |||||||
\(84\) | −9.38308e16 | + | 3.93976e16i | −0.450642 | + | 0.189215i | ||||
\(85\) | − | 1.04251e17i | − | 0.450102i | ||||||
\(86\) | 2.19612e17 | + | 1.45975e17i | 0.853433 | + | 0.567272i | ||||
\(87\) | − | 1.84157e17i | − | 0.644933i | ||||||
\(88\) | −3.43835e15 | + | 1.79644e16i | −0.0108644 | + | 0.0567636i | ||||
\(89\) | 1.65081e17 | 0.471182 | 0.235591 | − | 0.971852i | \(-0.424298\pi\) | ||||
0.235591 | + | 0.971852i | \(0.424298\pi\) | |||||||
\(90\) | −8.84485e17 | + | 1.33066e18i | −2.28301 | + | 3.43468i | ||||
\(91\) | 3.03382e16 | 0.0708952 | ||||||||
\(92\) | 3.97240e17 | − | 1.66793e17i | 0.841322 | − | 0.353253i | ||||
\(93\) | − | 1.21017e18i | − | 2.32542i | ||||||
\(94\) | −1.28305e17 | + | 1.93029e17i | −0.223920 | + | 0.336877i | ||||
\(95\) | 1.74990e17i | 0.277653i | ||||||||
\(96\) | 1.23396e18 | − | 2.60964e17i | 1.78180 | − | 0.376825i | ||||
\(97\) | −4.02901e17 | −0.529972 | −0.264986 | − | 0.964252i | \(-0.585367\pi\) | ||||
−0.264986 | + | 0.964252i | \(0.585367\pi\) | |||||||
\(98\) | −6.44344e17 | − | 4.28291e17i | −0.772828 | − | 0.513694i | ||||
\(99\) | −1.22318e17 | −0.133898 | ||||||||
\(100\) | −8.39634e17 | − | 1.99970e18i | −0.839634 | − | 1.99970i | ||||
\(101\) | 1.24060e18i | 1.13433i | 0.823606 | + | 0.567163i | \(0.191959\pi\) | ||||
−0.823606 | + | 0.567163i | \(0.808041\pi\) | |||||||
\(102\) | −4.58320e17 | − | 3.04643e17i | −0.383502 | − | 0.254911i | ||||
\(103\) | − | 1.12022e18i | − | 0.858556i | −0.903172 | − | 0.429278i | \(-0.858768\pi\) | ||
0.903172 | − | 0.429278i | \(-0.141232\pi\) | |||||||
\(104\) | −3.69296e17 | − | 7.06824e16i | −0.259463 | − | 0.0496605i | ||||
\(105\) | 1.34972e18 | 0.870041 | ||||||||
\(106\) | 1.09183e18 | − | 1.64260e18i | 0.646250 | − | 0.972252i | ||||
\(107\) | −1.14037e18 | −0.620287 | −0.310144 | − | 0.950690i | \(-0.600377\pi\) | ||||
−0.310144 | + | 0.950690i | \(0.600377\pi\) | |||||||
\(108\) | 1.85595e18 | + | 4.42020e18i | 0.928437 | + | 2.21120i | ||||
\(109\) | 2.82963e16i | 0.0130284i | 0.999979 | + | 0.00651419i | \(0.00207355\pi\) | ||||
−0.999979 | + | 0.00651419i | \(0.997926\pi\) | |||||||
\(110\) | 1.34286e17 | − | 2.02027e17i | 0.0569505 | − | 0.0856793i | ||||
\(111\) | 4.39960e18i | 1.71991i | ||||||||
\(112\) | −5.31286e17 | − | 5.21128e17i | −0.191587 | − | 0.187924i | ||||
\(113\) | 2.32500e18 | 0.773956 | 0.386978 | − | 0.922089i | \(-0.373519\pi\) | ||||
0.386978 | + | 0.922089i | \(0.373519\pi\) | |||||||
\(114\) | 7.69311e17 | + | 5.11356e17i | 0.236569 | + | 0.157246i | ||||
\(115\) | −5.71413e18 | −1.62431 | ||||||||
\(116\) | 1.24170e18 | − | 5.21364e17i | 0.326509 | − | 0.137094i | ||||
\(117\) | − | 2.51450e18i | − | 0.612039i | ||||||
\(118\) | 3.47487e18 | + | 2.30973e18i | 0.783432 | + | 0.520742i | ||||
\(119\) | 3.24724e17i | 0.0678565i | ||||||||
\(120\) | −1.64297e19 | − | 3.14460e18i | −3.18418 | − | 0.609445i | ||||
\(121\) | −5.54135e18 | −0.996660 | ||||||||
\(122\) | 4.64381e18 | − | 6.98639e18i | 0.775597 | − | 1.16685i | ||||
\(123\) | 1.53979e19 | 2.38955 | ||||||||
\(124\) | 8.15975e18 | − | 3.42611e18i | 1.17729 | − | 0.494317i | ||||
\(125\) | 1.55020e19i | 2.08065i | ||||||||
\(126\) | 2.75501e18 | − | 4.14478e18i | 0.344182 | − | 0.517805i | ||||
\(127\) | 9.14710e18i | 1.06427i | 0.846661 | + | 0.532133i | \(0.178609\pi\) | ||||
−0.846661 | + | 0.532133i | \(0.821391\pi\) | |||||||
\(128\) | 5.25303e18 | + | 7.58131e18i | 0.569535 | + | 0.821967i | ||||
\(129\) | −1.84626e19 | −1.86632 | ||||||||
\(130\) | 4.15309e18 | + | 2.76053e18i | 0.391635 | + | 0.260317i | ||||
\(131\) | 1.00187e18 | 0.0881796 | 0.0440898 | − | 0.999028i | \(-0.485961\pi\) | ||||
0.0440898 | + | 0.999028i | \(0.485961\pi\) | |||||||
\(132\) | −4.95763e17 | − | 1.18073e18i | −0.0407482 | − | 0.0970475i | ||||
\(133\) | − | 5.45064e17i | − | 0.0418584i | ||||||
\(134\) | −1.32345e19 | − | 8.79691e18i | −0.950091 | − | 0.631520i | ||||
\(135\) | − | 6.35828e19i | − | 4.26910i | ||||||
\(136\) | 7.56548e17 | − | 3.95275e18i | 0.0475320 | − | 0.248342i | ||||
\(137\) | 3.46626e18 | 0.203881 | 0.101940 | − | 0.994791i | \(-0.467495\pi\) | ||||
0.101940 | + | 0.994791i | \(0.467495\pi\) | |||||||
\(138\) | −1.66978e19 | + | 2.51211e19i | −0.919916 | + | 1.38397i | ||||
\(139\) | 2.01094e19 | 1.03817 | 0.519083 | − | 0.854724i | \(-0.326274\pi\) | ||||
0.519083 | + | 0.854724i | \(0.326274\pi\) | |||||||
\(140\) | 3.82117e18 | + | 9.10065e18i | 0.184946 | + | 0.440474i | ||||
\(141\) | − | 1.62278e19i | − | 0.736695i | ||||||
\(142\) | 1.41150e19 | − | 2.12354e19i | 0.601294 | − | 0.904618i | ||||
\(143\) | 3.81763e17i | 0.0152675i | ||||||||
\(144\) | −4.31924e19 | + | 4.40343e19i | −1.62235 | + | 1.65397i | ||||
\(145\) | −1.78614e19 | −0.630381 | ||||||||
\(146\) | −3.23931e19 | − | 2.15315e19i | −1.07467 | − | 0.714329i | ||||
\(147\) | 5.41695e19 | 1.69005 | ||||||||
\(148\) | −2.96648e19 | + | 1.24556e19i | −0.870736 | + | 0.365604i | ||||
\(149\) | 2.79939e19i | 0.773369i | 0.922212 | + | 0.386684i | \(0.126380\pi\) | ||||
−0.922212 | + | 0.386684i | \(0.873620\pi\) | |||||||
\(150\) | 1.26460e20 | + | 8.40569e19i | 3.28950 | + | 2.18651i | ||||
\(151\) | 3.64407e19i | 0.892882i | 0.894813 | + | 0.446441i | \(0.147309\pi\) | ||||
−0.894813 | + | 0.446441i | \(0.852691\pi\) | |||||||
\(152\) | −1.26990e18 | + | 6.63487e18i | −0.0293209 | + | 0.153193i | ||||
\(153\) | 2.69139e19 | 0.585806 | ||||||||
\(154\) | −4.18278e17 | + | 6.29279e17i | −0.00858575 | + | 0.0129168i | ||||
\(155\) | −1.17375e20 | −2.27295 | ||||||||
\(156\) | 2.42723e19 | − | 1.01914e19i | 0.443598 | − | 0.186257i | ||||
\(157\) | − | 5.65222e19i | − | 0.975264i | −0.873049 | − | 0.487632i | \(-0.837861\pi\) | ||
0.873049 | − | 0.487632i | \(-0.162139\pi\) | |||||||
\(158\) | 4.65842e19 | − | 7.00836e19i | 0.759145 | − | 1.14210i | ||||
\(159\) | 1.38092e20i | 2.12615i | ||||||||
\(160\) | −2.53109e19 | − | 1.19682e20i | −0.368323 | − | 1.74160i | ||||
\(161\) | 1.77985e19 | 0.244878 | ||||||||
\(162\) | −1.31253e20 | − | 8.72432e19i | −1.70795 | − | 1.13526i | ||||
\(163\) | 2.32565e18 | 0.0286323 | 0.0143161 | − | 0.999898i | \(-0.495443\pi\) | ||||
0.0143161 | + | 0.999898i | \(0.495443\pi\) | |||||||
\(164\) | 4.35929e19 | + | 1.03823e20i | 0.507950 | + | 1.20975i | ||||
\(165\) | 1.69843e19i | 0.187367i | ||||||||
\(166\) | −1.72389e19 | − | 1.14586e19i | −0.180110 | − | 0.119718i | ||||
\(167\) | − | 1.78856e20i | − | 1.77033i | −0.465274 | − | 0.885167i | \(-0.654044\pi\) | ||
0.465274 | − | 0.885167i | \(-0.345956\pi\) | |||||||
\(168\) | 5.11754e19 | + | 9.79486e18i | 0.480041 | + | 0.0918787i | ||||
\(169\) | 1.04607e20 | 0.930213 | ||||||||
\(170\) | −2.95473e19 | + | 4.44525e19i | −0.249160 | + | 0.374849i | ||||
\(171\) | −4.51762e19 | −0.361364 | ||||||||
\(172\) | −5.22692e19 | − | 1.24486e20i | −0.396725 | − | 0.944857i | ||||
\(173\) | 1.63126e20i | 1.17519i | 0.809154 | + | 0.587597i | \(0.199926\pi\) | ||||
−0.809154 | + | 0.587597i | \(0.800074\pi\) | |||||||
\(174\) | −5.21945e19 | + | 7.85241e19i | −0.357011 | + | 0.537105i | ||||
\(175\) | − | 8.95977e19i | − | 0.582042i | ||||||
\(176\) | 6.55766e18 | − | 6.68548e18i | 0.0404701 | − | 0.0412590i | ||||
\(177\) | −2.92130e20 | −1.71324 | ||||||||
\(178\) | −7.03903e19 | − | 4.67880e19i | −0.392404 | − | 0.260828i | ||||
\(179\) | −2.69767e19 | −0.142992 | −0.0714961 | − | 0.997441i | \(-0.522777\pi\) | ||||
−0.0714961 | + | 0.997441i | \(0.522777\pi\) | |||||||
\(180\) | 7.54284e20 | − | 3.16708e20i | 3.80262 | − | 1.59664i | ||||
\(181\) | − | 2.69695e20i | − | 1.29350i | −0.762703 | − | 0.646749i | \(-0.776128\pi\) | ||
0.762703 | − | 0.646749i | \(-0.223872\pi\) | |||||||
\(182\) | −1.29361e19 | − | 8.59856e18i | −0.0590421 | − | 0.0392449i | ||||
\(183\) | 5.87341e20i | 2.55171i | ||||||||
\(184\) | −2.16655e20 | − | 4.14673e19i | −0.896207 | − | 0.171532i | ||||
\(185\) | 4.26717e20 | 1.68110 | ||||||||
\(186\) | −3.42992e20 | + | 5.16016e20i | −1.28727 | + | 1.93663i | ||||
\(187\) | −4.08619e18 | −0.0146132 | ||||||||
\(188\) | 1.09418e20 | − | 4.59423e19i | 0.372965 | − | 0.156600i | ||||
\(189\) | 1.98049e20i | 0.643601i | ||||||||
\(190\) | 4.95965e19 | − | 7.46155e19i | 0.153698 | − | 0.231231i | ||||
\(191\) | 1.48397e20i | 0.438658i | 0.975651 | + | 0.219329i | \(0.0703867\pi\) | ||||
−0.975651 | + | 0.219329i | \(0.929613\pi\) | |||||||
\(192\) | −6.00121e20 | − | 2.38459e20i | −1.69250 | − | 0.672516i | ||||
\(193\) | −1.72513e20 | −0.464309 | −0.232154 | − | 0.972679i | \(-0.574577\pi\) | ||||
−0.232154 | + | 0.972679i | \(0.574577\pi\) | |||||||
\(194\) | 1.71796e20 | + | 1.14192e20i | 0.441365 | + | 0.293372i | ||||
\(195\) | −3.49147e20 | −0.856440 | ||||||||
\(196\) | 1.53359e20 | + | 3.65245e20i | 0.359256 | + | 0.855617i | ||||
\(197\) | − | 3.97468e20i | − | 0.889418i | −0.895675 | − | 0.444709i | \(-0.853307\pi\) | ||
0.895675 | − | 0.444709i | \(-0.146693\pi\) | |||||||
\(198\) | 5.21562e19 | + | 3.46679e19i | 0.111511 | + | 0.0741209i | ||||
\(199\) | − | 3.99187e20i | − | 0.815640i | −0.913062 | − | 0.407820i | \(-0.866289\pi\) | ||
0.913062 | − | 0.407820i | \(-0.133711\pi\) | |||||||
\(200\) | −2.08746e20 | + | 1.09064e21i | −0.407707 | + | 2.13016i | ||||
\(201\) | 1.11262e21 | 2.07769 | ||||||||
\(202\) | 3.51614e20 | − | 5.28987e20i | 0.627920 | − | 0.944675i | ||||
\(203\) | 5.56350e19 | 0.0950350 | ||||||||
\(204\) | 1.09084e20 | + | 2.59798e20i | 0.178274 | + | 0.424585i | ||||
\(205\) | − | 1.49345e21i | − | 2.33563i | ||||||
\(206\) | −3.17497e20 | + | 4.77660e20i | −0.475264 | + | 0.715012i | ||||
\(207\) | − | 1.47518e21i | − | 2.11404i | ||||||
\(208\) | 1.37434e20 | + | 1.34806e20i | 0.188592 | + | 0.184986i | ||||
\(209\) | 6.85885e18 | 0.00901436 | ||||||||
\(210\) | −5.75517e20 | − | 3.82543e20i | −0.724577 | − | 0.481622i | ||||
\(211\) | −1.19555e21 | −1.44220 | −0.721100 | − | 0.692831i | \(-0.756363\pi\) | ||||
−0.721100 | + | 0.692831i | \(0.756363\pi\) | |||||||
\(212\) | −9.31104e20 | + | 3.90951e20i | −1.07640 | + | 0.451959i | ||||
\(213\) | 1.78524e21i | 1.97825i | ||||||||
\(214\) | 4.86252e20 | + | 3.23209e20i | 0.516580 | + | 0.343368i | ||||
\(215\) | 1.79069e21i | 1.82421i | ||||||||
\(216\) | 4.61418e20 | − | 2.41078e21i | 0.450828 | − | 2.35545i | ||||
\(217\) | 3.65601e20 | 0.342665 | ||||||||
\(218\) | 8.01984e18 | − | 1.20655e19i | 0.00721202 | − | 0.0108501i | ||||
\(219\) | 2.72326e21 | 2.35013 | ||||||||
\(220\) | −1.14519e20 | + | 4.80840e19i | −0.0948577 | + | 0.0398287i | ||||
\(221\) | − | 8.40001e19i | − | 0.0667958i | ||||||
\(222\) | 1.24695e21 | − | 1.87598e21i | 0.952078 | − | 1.43236i | ||||
\(223\) | − | 9.47274e20i | − | 0.694595i | −0.937755 | − | 0.347298i | \(-0.887099\pi\) | ||
0.937755 | − | 0.347298i | \(-0.112901\pi\) | |||||||
\(224\) | 7.88390e19 | + | 3.72787e20i | 0.0555276 | + | 0.262560i | ||||
\(225\) | −7.42607e21 | −5.02477 | ||||||||
\(226\) | −9.91373e20 | − | 6.58960e20i | −0.644557 | − | 0.428433i | ||||
\(227\) | 2.11701e21 | 1.32279 | 0.661395 | − | 0.750038i | \(-0.269965\pi\) | ||||
0.661395 | + | 0.750038i | \(0.269965\pi\) | |||||||
\(228\) | −1.83102e20 | − | 4.36082e20i | −0.109971 | − | 0.261912i | ||||
\(229\) | 1.70342e21i | 0.983561i | 0.870719 | + | 0.491781i | \(0.163654\pi\) | ||||
−0.870719 | + | 0.491781i | \(0.836346\pi\) | |||||||
\(230\) | 2.43649e21 | + | 1.61952e21i | 1.35274 | + | 0.899159i | ||||
\(231\) | − | 5.29030e19i | − | 0.0282470i | ||||||
\(232\) | −6.77225e20 | − | 1.29619e20i | −0.347809 | − | 0.0665699i | ||||
\(233\) | 2.47054e21 | 1.22064 | 0.610321 | − | 0.792154i | \(-0.291040\pi\) | ||||
0.610321 | + | 0.792154i | \(0.291040\pi\) | |||||||
\(234\) | −7.12670e20 | + | 1.07218e21i | −0.338802 | + | 0.509711i | ||||
\(235\) | −1.57393e21 | −0.720072 | ||||||||
\(236\) | −8.27046e20 | − | 1.96973e21i | −0.364185 | − | 0.867356i | ||||
\(237\) | 5.89188e21i | 2.49758i | ||||||||
\(238\) | 9.20345e19 | − | 1.38462e20i | 0.0375628 | − | 0.0565115i | ||||
\(239\) | − | 2.48664e20i | − | 0.0977307i | −0.998805 | − | 0.0488654i | \(-0.984439\pi\) | ||
0.998805 | − | 0.0488654i | \(-0.0155605\pi\) | |||||||
\(240\) | 6.11431e21 | + | 5.99741e21i | 2.31444 | + | 2.27019i | ||||
\(241\) | 1.90611e21 | 0.695016 | 0.347508 | − | 0.937677i | \(-0.387028\pi\) | ||||
0.347508 | + | 0.937677i | \(0.387028\pi\) | |||||||
\(242\) | 2.36282e21 | + | 1.57055e21i | 0.830026 | + | 0.551713i | ||||
\(243\) | 3.94930e21 | 1.33679 | ||||||||
\(244\) | −3.96022e21 | + | 1.66281e21i | −1.29185 | + | 0.542419i | ||||
\(245\) | − | 5.25390e21i | − | 1.65191i | ||||||
\(246\) | −6.56564e21 | − | 4.36414e21i | −1.99004 | − | 1.32277i | ||||
\(247\) | 1.40998e20i | 0.0412040i | ||||||||
\(248\) | −4.45034e21 | − | 8.51785e20i | −1.25409 | − | 0.240030i | ||||
\(249\) | 1.44927e21 | 0.393871 | ||||||||
\(250\) | 4.39365e21 | − | 6.61003e21i | 1.15177 | − | 1.73278i | ||||
\(251\) | −7.71308e21 | −1.95058 | −0.975292 | − | 0.220921i | \(-0.929094\pi\) | ||||
−0.975292 | + | 0.220921i | \(0.929094\pi\) | |||||||
\(252\) | −2.34946e21 | + | 9.86488e20i | −0.573275 | + | 0.240706i | ||||
\(253\) | 2.23969e20i | 0.0527355i | ||||||||
\(254\) | 2.59251e21 | − | 3.90030e21i | 0.589137 | − | 0.886329i | ||||
\(255\) | − | 3.73709e21i | − | 0.819732i | ||||||
\(256\) | −9.11542e19 | − | 4.72149e21i | −0.0193027 | − | 0.999814i | ||||
\(257\) | −7.58318e21 | −1.55043 | −0.775217 | − | 0.631695i | \(-0.782359\pi\) | ||||
−0.775217 | + | 0.631695i | \(0.782359\pi\) | |||||||
\(258\) | 7.87241e21 | + | 5.23274e21i | 1.55428 | + | 1.03312i | ||||
\(259\) | −1.32915e21 | −0.253440 | ||||||||
\(260\) | −9.88466e20 | − | 2.35417e21i | −0.182055 | − | 0.433588i | ||||
\(261\) | − | 4.61116e21i | − | 0.820438i | ||||||
\(262\) | −4.27193e20 | − | 2.83953e20i | −0.0734366 | − | 0.0488129i | ||||
\(263\) | 3.30248e21i | 0.548578i | 0.961647 | + | 0.274289i | \(0.0884425\pi\) | ||||
−0.961647 | + | 0.274289i | \(0.911558\pi\) | |||||||
\(264\) | −1.23254e20 | + | 6.43970e20i | −0.0197864 | + | 0.103379i | ||||
\(265\) | 1.33936e22 | 2.07818 | ||||||||
\(266\) | −1.54484e20 | + | 2.32414e20i | −0.0231712 | + | 0.0348600i | ||||
\(267\) | 5.91767e21 | 0.858122 | ||||||||
\(268\) | 3.14992e21 | + | 7.50196e21i | 0.441658 | + | 1.05187i | ||||
\(269\) | − | 1.42430e22i | − | 1.93122i | −0.259994 | − | 0.965610i | \(-0.583721\pi\) | ||
0.259994 | − | 0.965610i | \(-0.416279\pi\) | |||||||
\(270\) | −1.80209e22 | + | 2.71116e22i | −2.36321 | + | 3.55534i | ||||
\(271\) | 1.37402e22i | 1.74289i | 0.490491 | + | 0.871446i | \(0.336817\pi\) | ||||
−0.490491 | + | 0.871446i | \(0.663183\pi\) | |||||||
\(272\) | −1.44289e21 | + | 1.47102e21i | −0.177058 | + | 0.180509i | ||||
\(273\) | 1.08753e21 | 0.129115 | ||||||||
\(274\) | −1.47801e21 | − | 9.82422e20i | −0.169794 | − | 0.112861i | ||||
\(275\) | 1.12746e21 | 0.125345 | ||||||||
\(276\) | 1.42398e22 | − | 5.97900e21i | 1.53223 | − | 0.643350i | ||||
\(277\) | 9.97314e21i | 1.03876i | 0.854544 | + | 0.519379i | \(0.173837\pi\) | ||||
−0.854544 | + | 0.519379i | \(0.826163\pi\) | |||||||
\(278\) | −8.57461e21 | − | 5.69949e21i | −0.864592 | − | 0.574689i | ||||
\(279\) | − | 3.03020e22i | − | 2.95824i | ||||||
\(280\) | 9.50004e20 | − | 4.96351e21i | 0.0898055 | − | 0.469209i | ||||
\(281\) | 4.87172e21 | 0.445990 | 0.222995 | − | 0.974820i | \(-0.428417\pi\) | ||||
0.222995 | + | 0.974820i | \(0.428417\pi\) | |||||||
\(282\) | −4.59935e21 | + | 6.91949e21i | −0.407806 | + | 0.613525i | ||||
\(283\) | −2.09871e21 | −0.180249 | −0.0901247 | − | 0.995930i | \(-0.528727\pi\) | ||||
−0.0901247 | + | 0.995930i | \(0.528727\pi\) | |||||||
\(284\) | −1.20372e22 | + | 5.05418e21i | −1.00152 | + | 0.420519i | ||||
\(285\) | 6.27287e21i | 0.505665i | ||||||||
\(286\) | 1.08201e20 | − | 1.62783e20i | 0.00845154 | − | 0.0127149i | ||||
\(287\) | 4.65181e21i | 0.352116i | ||||||||
\(288\) | 3.08975e22 | − | 6.53437e21i | 2.26668 | − | 0.479370i | ||||
\(289\) | −1.31640e22 | −0.936067 | ||||||||
\(290\) | 7.61605e21 | + | 5.06234e21i | 0.524986 | + | 0.348955i | ||||
\(291\) | −1.44428e22 | −0.965192 | ||||||||
\(292\) | 7.70979e21 | + | 1.83619e22i | 0.499571 | + | 1.18980i | ||||
\(293\) | 1.17383e22i | 0.737557i | 0.929517 | + | 0.368779i | \(0.120224\pi\) | ||||
−0.929517 | + | 0.368779i | \(0.879776\pi\) | |||||||
\(294\) | −2.30978e22 | − | 1.53529e22i | −1.40749 | − | 0.935547i | ||||
\(295\) | 2.83337e22i | 1.67458i | ||||||||
\(296\) | 1.61792e22 | + | 3.09667e21i | 0.927540 | + | 0.177529i | ||||
\(297\) | −2.49217e21 | −0.138602 | ||||||||
\(298\) | 7.93413e21 | − | 1.19365e22i | 0.428108 | − | 0.644068i | ||||
\(299\) | −4.60414e21 | −0.241050 | ||||||||
\(300\) | −3.00983e22 | − | 7.16833e22i | −1.52915 | − | 3.64189i | ||||
\(301\) | − | 5.57767e21i | − | 0.275014i | ||||||
\(302\) | 1.03282e22 | − | 1.55382e22i | 0.494266 | − | 0.743599i | ||||
\(303\) | 4.44715e22i | 2.06585i | ||||||||
\(304\) | 2.42196e21 | − | 2.46917e21i | 0.109221 | − | 0.111350i | ||||
\(305\) | 5.69662e22 | 2.49413 | ||||||||
\(306\) | −1.14760e22 | − | 7.62805e21i | −0.487864 | − | 0.324280i | ||||
\(307\) | −3.79319e22 | −1.56588 | −0.782941 | − | 0.622096i | \(-0.786282\pi\) | ||||
−0.782941 | + | 0.622096i | \(0.786282\pi\) | |||||||
\(308\) | 3.56705e20 | − | 1.49773e20i | 0.0143006 | − | 0.00600450i | ||||
\(309\) | − | 4.01565e22i | − | 1.56361i | ||||||
\(310\) | 5.00484e22 | + | 3.32668e22i | 1.89293 | + | 1.25822i | ||||
\(311\) | − | 3.70263e22i | − | 1.36040i | −0.733026 | − | 0.680201i | \(-0.761893\pi\) | ||
0.733026 | − | 0.680201i | \(-0.238107\pi\) | |||||||
\(312\) | −1.32381e22 | − | 2.53375e21i | −0.472537 | − | 0.0904424i | ||||
\(313\) | −2.78803e22 | −0.966938 | −0.483469 | − | 0.875361i | \(-0.660623\pi\) | ||||
−0.483469 | + | 0.875361i | \(0.660623\pi\) | |||||||
\(314\) | −1.60197e22 | + | 2.41009e22i | −0.539870 | + | 0.812208i | ||||
\(315\) | 3.37960e22 | 1.10680 | ||||||||
\(316\) | −3.97268e22 | + | 1.66804e22i | −1.26444 | + | 0.530913i | ||||
\(317\) | − | 8.83287e21i | − | 0.273255i | −0.990622 | − | 0.136628i | \(-0.956374\pi\) | ||
0.990622 | − | 0.136628i | \(-0.0436264\pi\) | |||||||
\(318\) | 3.91386e22 | − | 5.88822e22i | 1.17696 | − | 1.77068i | ||||
\(319\) | 7.00087e20i | 0.0204661i | ||||||||
\(320\) | −2.31281e22 | + | 5.82057e22i | −0.657341 | + | 1.65431i | ||||
\(321\) | −4.08789e22 | −1.12968 | ||||||||
\(322\) | −7.58924e21 | − | 5.04452e21i | −0.203937 | − | 0.135555i | ||||
\(323\) | −1.50917e21 | −0.0394380 | ||||||||
\(324\) | 3.12392e22 | + | 7.44006e22i | 0.793954 | + | 1.89091i | ||||
\(325\) | 2.31773e22i | 0.572943i | ||||||||
\(326\) | −9.91651e20 | − | 6.59144e20i | −0.0238452 | − | 0.0158497i | ||||
\(327\) | 1.01433e21i | 0.0237275i | ||||||||
\(328\) | 1.08379e22 | − | 5.66249e22i | 0.246649 | − | 1.28867i | ||||
\(329\) | 4.90252e21 | 0.108557 | ||||||||
\(330\) | 4.81376e21 | − | 7.24206e21i | 0.103719 | − | 0.156040i | ||||
\(331\) | 2.27336e22 | 0.476669 | 0.238335 | − | 0.971183i | \(-0.423399\pi\) | ||||
0.238335 | + | 0.971183i | \(0.423399\pi\) | |||||||
\(332\) | 4.10300e21 | + | 9.77186e21i | 0.0837256 | + | 0.199404i | ||||
\(333\) | 1.10163e23i | 2.18795i | ||||||||
\(334\) | −5.06920e22 | + | 7.62637e22i | −0.979990 | + | 1.47435i | ||||
\(335\) | − | 1.07913e23i | − | 2.03081i | ||||||
\(336\) | −1.90450e22 | − | 1.86808e22i | −0.348921 | − | 0.342250i | ||||
\(337\) | 6.91628e22 | 1.23368 | 0.616842 | − | 0.787087i | \(-0.288412\pi\) | ||||
0.616842 | + | 0.787087i | \(0.288412\pi\) | |||||||
\(338\) | −4.46044e22 | − | 2.96483e22i | −0.774689 | − | 0.514931i | ||||
\(339\) | 8.33440e22 | 1.40954 | ||||||||
\(340\) | 2.51978e22 | − | 1.05800e22i | 0.415004 | − | 0.174251i | ||||
\(341\) | 4.60058e21i | 0.0737943i | ||||||||
\(342\) | 1.92630e22 | + | 1.28040e22i | 0.300947 | + | 0.200037i | ||||
\(343\) | 3.40000e22i | 0.517407i | ||||||||
\(344\) | −1.29950e22 | + | 6.78950e22i | −0.192641 | + | 1.00650i | ||||
\(345\) | −2.04834e23 | −2.95822 | ||||||||
\(346\) | 4.62339e22 | − | 6.95567e22i | 0.650543 | − | 0.978710i | ||||
\(347\) | 3.56633e22 | 0.488941 | 0.244471 | − | 0.969657i | \(-0.421386\pi\) | ||||
0.244471 | + | 0.969657i | \(0.421386\pi\) | |||||||
\(348\) | 4.45112e22 | − | 1.86893e22i | 0.594643 | − | 0.249678i | ||||
\(349\) | − | 6.57517e22i | − | 0.856008i | −0.903777 | − | 0.428004i | \(-0.859217\pi\) | ||
0.903777 | − | 0.428004i | \(-0.140783\pi\) | |||||||
\(350\) | −2.53941e22 | + | 3.82042e22i | −0.322196 | + | 0.484729i | ||||
\(351\) | − | 5.12316e22i | − | 0.633540i | ||||||
\(352\) | −4.69099e21 | + | 9.92077e20i | −0.0565433 | + | 0.0119581i | ||||
\(353\) | −2.20900e22 | −0.259552 | −0.129776 | − | 0.991543i | \(-0.541426\pi\) | ||||
−0.129776 | + | 0.991543i | \(0.541426\pi\) | |||||||
\(354\) | 1.24564e23 | + | 8.27967e22i | 1.42680 | + | 0.948383i | ||||
\(355\) | 1.73151e23 | 1.93361 | ||||||||
\(356\) | 1.67534e22 | + | 3.99006e22i | 0.182412 | + | 0.434440i | ||||
\(357\) | 1.16404e22i | 0.123581i | ||||||||
\(358\) | 1.15028e22 | + | 7.64585e21i | 0.119085 | + | 0.0791551i | ||||
\(359\) | − | 1.38349e23i | − | 1.39678i | −0.715719 | − | 0.698389i | \(-0.753901\pi\) | ||
0.715719 | − | 0.698389i | \(-0.246099\pi\) | |||||||
\(360\) | −4.11388e23 | − | 7.87386e22i | −4.05069 | − | 0.775292i | ||||
\(361\) | −1.01594e23 | −0.975672 | ||||||||
\(362\) | −7.64380e22 | + | 1.14997e23i | −0.716032 | + | 1.07723i | ||||
\(363\) | −1.98640e23 | −1.81513 | ||||||||
\(364\) | 3.07889e21 | + | 7.33281e21i | 0.0274462 | + | 0.0653669i | ||||
\(365\) | − | 2.64129e23i | − | 2.29710i | ||||||
\(366\) | 1.66466e23 | − | 2.50441e23i | 1.41253 | − | 2.12508i | ||||
\(367\) | − | 2.17842e22i | − | 0.180363i | −0.995925 | − | 0.0901813i | \(-0.971255\pi\) | ||
0.995925 | − | 0.0901813i | \(-0.0287447\pi\) | |||||||
\(368\) | 8.06283e22 | + | 7.90867e22i | 0.651414 | + | 0.638959i | ||||
\(369\) | 3.85554e23 | 3.03982 | ||||||||
\(370\) | −1.81951e23 | − | 1.20942e23i | −1.40004 | − | 0.930595i | ||||
\(371\) | −4.17185e22 | −0.313302 | ||||||||
\(372\) | 2.92502e23 | − | 1.22816e23i | 2.14409 | − | 0.900258i | ||||
\(373\) | 1.59981e23i | 1.14469i | 0.820013 | + | 0.572345i | \(0.193966\pi\) | ||||
−0.820013 | + | 0.572345i | \(0.806034\pi\) | |||||||
\(374\) | 1.74234e21 | + | 1.15812e21i | 0.0121700 | + | 0.00808929i | ||||
\(375\) | 5.55701e23i | 3.78930i | ||||||||
\(376\) | −5.96767e22 | − | 1.14220e22i | −0.397296 | − | 0.0760415i | ||||
\(377\) | −1.43917e22 | −0.0935494 | ||||||||
\(378\) | 5.61318e22 | − | 8.44477e22i | 0.356273 | − | 0.535996i | ||||
\(379\) | −1.69897e23 | −1.05301 | −0.526506 | − | 0.850171i | \(-0.676498\pi\) | ||||
−0.526506 | + | 0.850171i | \(0.676498\pi\) | |||||||
\(380\) | −4.22956e22 | + | 1.77590e22i | −0.256002 | + | 0.107490i | ||||
\(381\) | 3.27896e23i | 1.93825i | ||||||||
\(382\) | 4.20593e22 | − | 6.32762e22i | 0.242824 | − | 0.365317i | ||||
\(383\) | − | 1.52269e22i | − | 0.0858665i | −0.999078 | − | 0.0429333i | \(-0.986330\pi\) | ||
0.999078 | − | 0.0429333i | \(-0.0136703\pi\) | |||||||
\(384\) | 1.88305e23 | + | 2.71767e23i | 1.03724 | + | 1.49698i | ||||
\(385\) | −5.13106e21 | −0.0276097 | ||||||||
\(386\) | 7.35593e22 | + | 4.88944e22i | 0.386680 | + | 0.257024i | ||||
\(387\) | −4.62291e23 | −2.37420 | ||||||||
\(388\) | −4.08887e22 | − | 9.73822e22i | −0.205172 | − | 0.488646i | ||||
\(389\) | 8.21497e22i | 0.402772i | 0.979512 | + | 0.201386i | \(0.0645446\pi\) | ||||
−0.979512 | + | 0.201386i | \(0.935455\pi\) | |||||||
\(390\) | 1.48876e23 | + | 9.89567e22i | 0.713250 | + | 0.474093i | ||||
\(391\) | − | 4.92803e22i | − | 0.230719i | ||||||
\(392\) | 3.81274e22 | − | 1.99205e23i | 0.174447 | − | 0.911435i | ||||
\(393\) | 3.59138e22 | 0.160594 | ||||||||
\(394\) | −1.12652e23 | + | 1.69479e23i | −0.492348 | + | 0.740714i | ||||
\(395\) | 5.71454e23 | 2.44122 | ||||||||
\(396\) | −1.24136e22 | − | 2.95646e22i | −0.0518370 | − | 0.123457i | ||||
\(397\) | 7.33206e22i | 0.299303i | 0.988739 | + | 0.149652i | \(0.0478152\pi\) | ||||
−0.988739 | + | 0.149652i | \(0.952185\pi\) | |||||||
\(398\) | −1.13139e23 | + | 1.70212e23i | −0.451508 | + | 0.679272i | ||||
\(399\) | − | 1.95389e22i | − | 0.0762330i | ||||||
\(400\) | 3.98123e23 | − | 4.05883e23i | 1.51872 | − | 1.54832i | ||||
\(401\) | −1.38921e23 | −0.518167 | −0.259083 | − | 0.965855i | \(-0.583420\pi\) | ||||
−0.259083 | + | 0.965855i | \(0.583420\pi\) | |||||||
\(402\) | −4.74417e23 | − | 3.15342e23i | −1.73032 | − | 1.15013i | ||||
\(403\) | −9.45743e22 | −0.337309 | ||||||||
\(404\) | −2.99855e23 | + | 1.25903e23i | −1.04587 | + | 0.439140i | ||||
\(405\) | − | 1.07022e24i | − | 3.65072i | ||||||
\(406\) | −2.37226e22 | − | 1.57683e22i | −0.0791459 | − | 0.0526078i | ||||
\(407\) | − | 1.67254e22i | − | 0.0545792i | ||||||
\(408\) | 2.71199e22 | − | 1.41694e23i | 0.0865659 | − | 0.452283i | ||||
\(409\) | −9.61573e22 | −0.300243 | −0.150121 | − | 0.988668i | \(-0.547966\pi\) | ||||
−0.150121 | + | 0.988668i | \(0.547966\pi\) | |||||||
\(410\) | −4.23278e23 | + | 6.36802e23i | −1.29292 | + | 1.94513i | ||||
\(411\) | 1.24255e23 | 0.371311 | ||||||||
\(412\) | 2.70760e23 | − | 1.13687e23i | 0.791608 | − | 0.332379i | ||||
\(413\) | − | 8.82544e22i | − | 0.252456i | ||||||
\(414\) | −4.18102e23 | + | 6.29015e23i | −1.17025 | + | 1.76059i | ||||
\(415\) | − | 1.40564e23i | − | 0.384984i | ||||||
\(416\) | −2.03942e22 | − | 9.64331e22i | −0.0546596 | − | 0.258456i | ||||
\(417\) | 7.20862e23 | 1.89072 | ||||||||
\(418\) | −2.92460e21 | − | 1.94396e21i | −0.00750723 | − | 0.00499001i | ||||
\(419\) | −3.85125e22 | −0.0967554 | −0.0483777 | − | 0.998829i | \(-0.515405\pi\) | ||||
−0.0483777 | + | 0.998829i | \(0.515405\pi\) | |||||||
\(420\) | 1.36977e23 | + | 3.26231e23i | 0.336826 | + | 0.802197i | ||||
\(421\) | 4.63719e23i | 1.11613i | 0.829796 | + | 0.558066i | \(0.188457\pi\) | ||||
−0.829796 | + | 0.558066i | \(0.811543\pi\) | |||||||
\(422\) | 5.09780e23 | + | 3.38847e23i | 1.20108 | + | 0.798348i | ||||
\(423\) | − | 4.06333e23i | − | 0.937171i | ||||||
\(424\) | 5.07825e23 | + | 9.71966e22i | 1.14663 | + | 0.219461i | ||||
\(425\) | −2.48077e23 | −0.548386 | ||||||||
\(426\) | 5.05981e23 | − | 7.61224e23i | 1.09508 | − | 1.64750i | ||||
\(427\) | −1.77439e23 | −0.376010 | ||||||||
\(428\) | −1.15732e23 | − | 2.75631e23i | −0.240137 | − | 0.571919i | ||||
\(429\) | 1.36850e22i | 0.0278055i | ||||||||
\(430\) | 5.07524e23 | − | 7.63545e23i | 1.00981 | − | 1.51921i | ||||
\(431\) | 2.54794e23i | 0.496471i | 0.968700 | + | 0.248235i | \(0.0798507\pi\) | ||||
−0.968700 | + | 0.248235i | \(0.920149\pi\) | |||||||
\(432\) | −8.80021e23 | + | 8.97175e23i | −1.67934 | + | 1.71208i | ||||
\(433\) | −5.45490e23 | −1.01952 | −0.509760 | − | 0.860316i | \(-0.670266\pi\) | ||||
−0.509760 | + | 0.860316i | \(0.670266\pi\) | |||||||
\(434\) | −1.55892e23 | − | 1.03620e23i | −0.285374 | − | 0.189687i | ||||
\(435\) | −6.40276e23 | −1.14806 | ||||||||
\(436\) | −6.83928e21 | + | 2.87167e21i | −0.0120125 | + | 0.00504378i | ||||
\(437\) | 8.27192e22i | 0.142322i | ||||||||
\(438\) | −1.16119e24 | − | 7.71838e23i | −1.95721 | − | 1.30095i | ||||
\(439\) | − | 3.40557e23i | − | 0.562352i | −0.959656 | − | 0.281176i | \(-0.909275\pi\) | ||
0.959656 | − | 0.281176i | \(-0.0907245\pi\) | |||||||
\(440\) | 6.24587e22 | + | 1.19544e22i | 0.101046 | + | 0.0193400i | ||||
\(441\) | 1.35637e24 | 2.14996 | ||||||||
\(442\) | −2.38076e22 | + | 3.58174e22i | −0.0369756 | + | 0.0556281i | ||||
\(443\) | 3.64770e23 | 0.555118 | 0.277559 | − | 0.960709i | \(-0.410475\pi\) | ||||
0.277559 | + | 0.960709i | \(0.410475\pi\) | |||||||
\(444\) | −1.06339e24 | + | 4.46496e23i | −1.58580 | + | 0.665842i | ||||
\(445\) | − | 5.73955e23i | − | 0.838759i | ||||||
\(446\) | −2.68480e23 | + | 4.03915e23i | −0.384502 | + | 0.578465i | ||||
\(447\) | 1.00350e24i | 1.40847i | ||||||||
\(448\) | 7.20400e22 | − | 1.81300e23i | 0.0990995 | − | 0.249400i | ||||
\(449\) | 1.21112e23 | 0.163294 | 0.0816468 | − | 0.996661i | \(-0.473982\pi\) | ||||
0.0816468 | + | 0.996661i | \(0.473982\pi\) | |||||||
\(450\) | 3.16646e24 | + | 2.10473e24i | 4.18467 | + | 2.78153i | ||||
\(451\) | −5.85365e22 | −0.0758294 | ||||||||
\(452\) | 2.35954e23 | + | 5.61958e23i | 0.299628 | + | 0.713605i | ||||
\(453\) | 1.30629e24i | 1.62613i | ||||||||
\(454\) | −9.02689e23 | − | 6.00012e23i | −1.10163 | − | 0.732246i | ||||
\(455\) | − | 1.05480e23i | − | 0.126202i | ||||||
\(456\) | −4.55220e22 | + | 2.37840e23i | −0.0533996 | + | 0.278998i | ||||
\(457\) | −1.16172e23 | −0.133615 | −0.0668077 | − | 0.997766i | \(-0.521281\pi\) | ||||
−0.0668077 | + | 0.997766i | \(0.521281\pi\) | |||||||
\(458\) | 4.82789e23 | − | 7.26332e23i | 0.544462 | − | 0.819117i | ||||
\(459\) | 5.48357e23 | 0.606386 | ||||||||
\(460\) | −5.79904e23 | − | 1.38112e24i | −0.628833 | − | 1.49765i | ||||
\(461\) | − | 1.17462e24i | − | 1.24908i | −0.780992 | − | 0.624541i | \(-0.785286\pi\) | ||
0.780992 | − | 0.624541i | \(-0.214714\pi\) | |||||||
\(462\) | −1.49940e22 | + | 2.25577e22i | −0.0156365 | + | 0.0235243i | ||||
\(463\) | 7.75697e23i | 0.793347i | 0.917960 | + | 0.396673i | \(0.129835\pi\) | ||||
−0.917960 | + | 0.396673i | \(0.870165\pi\) | |||||||
\(464\) | 2.52030e23 | + | 2.47211e23i | 0.252808 | + | 0.247974i | ||||
\(465\) | −4.20753e24 | −4.13953 | ||||||||
\(466\) | −1.05343e24 | − | 7.00210e23i | −1.01656 | − | 0.675701i | ||||
\(467\) | 1.68463e24 | 1.59460 | 0.797300 | − | 0.603584i | \(-0.206261\pi\) | ||||
0.797300 | + | 0.603584i | \(0.206261\pi\) | |||||||
\(468\) | 6.07762e23 | − | 2.55186e23i | 0.564314 | − | 0.236943i | ||||
\(469\) | 3.36129e23i | 0.306161i | ||||||||
\(470\) | 6.71122e23 | + | 4.46091e23i | 0.599681 | + | 0.398605i | ||||
\(471\) | − | 2.02615e24i | − | 1.77616i | ||||||
\(472\) | −2.05617e23 | + | 1.07429e24i | −0.176840 | + | 0.923940i | ||||
\(473\) | 7.01871e22 | 0.0592252 | ||||||||
\(474\) | 1.66990e24 | − | 2.51228e24i | 1.38256 | − | 2.08000i | ||||
\(475\) | 4.16409e23 | 0.338281 | ||||||||
\(476\) | −7.84866e22 | + | 3.29549e22i | −0.0625652 | + | 0.0262698i | ||||
\(477\) | 3.45773e24i | 2.70474i | ||||||||
\(478\) | −7.04772e22 | + | 1.06030e23i | −0.0541000 | + | 0.0813909i | ||||
\(479\) | − | 1.30173e24i | − | 0.980619i | −0.871548 | − | 0.490310i | \(-0.836884\pi\) | ||
0.871548 | − | 0.490310i | \(-0.163116\pi\) | |||||||
\(480\) | −9.07320e23 | − | 4.29022e24i | −0.670794 | − | 3.17182i | ||||
\(481\) | 3.43825e23 | 0.249478 | ||||||||
\(482\) | −8.12761e23 | − | 5.40237e23i | −0.578814 | − | 0.384734i | ||||
\(483\) | 6.38022e23 | 0.445976 | ||||||||
\(484\) | −5.62368e23 | − | 1.33936e24i | −0.385844 | − | 0.918942i | ||||
\(485\) | 1.40080e24i | 0.943413i | ||||||||
\(486\) | −1.68397e24 | − | 1.11933e24i | −1.11329 | − | 0.739998i | ||||
\(487\) | 1.08221e24i | 0.702348i | 0.936310 | + | 0.351174i | \(0.114217\pi\) | ||||
−0.936310 | + | 0.351174i | \(0.885783\pi\) | |||||||
\(488\) | 2.15991e24 | + | 4.13402e23i | 1.37612 | + | 0.263387i | ||||
\(489\) | 8.33674e22 | 0.0521455 | ||||||||
\(490\) | −1.48908e24 | + | 2.24025e24i | −0.914437 | + | 1.37573i | ||||
\(491\) | −2.27518e24 | −1.37177 | −0.685887 | − | 0.727708i | \(-0.740586\pi\) | ||||
−0.685887 | + | 0.727708i | \(0.740586\pi\) | |||||||
\(492\) | 1.56267e24 | + | 3.72172e24i | 0.925085 | + | 2.20322i | ||||
\(493\) | − | 1.54042e23i | − | 0.0895398i | ||||||
\(494\) | 3.99622e22 | − | 6.01211e22i | 0.0228090 | − | 0.0343150i | ||||
\(495\) | 4.25275e23i | 0.238354i | ||||||||
\(496\) | 1.65620e24 | + | 1.62453e24i | 0.911543 | + | 0.894115i | ||||
\(497\) | −5.39334e23 | −0.291508 | ||||||||
\(498\) | −6.17964e23 | − | 4.10757e23i | −0.328019 | − | 0.218032i | ||||
\(499\) | −7.54183e23 | −0.393162 | −0.196581 | − | 0.980488i | \(-0.562984\pi\) | ||||
−0.196581 | + | 0.980488i | \(0.562984\pi\) | |||||||
\(500\) | −3.74688e24 | + | 1.57324e24i | −1.91840 | + | 0.805497i | ||||
\(501\) | − | 6.41144e24i | − | 3.22415i | ||||||
\(502\) | 3.28884e24 | + | 2.18607e24i | 1.62446 | + | 1.07977i | ||||
\(503\) | − | 2.48165e24i | − | 1.20401i | −0.798494 | − | 0.602003i | \(-0.794370\pi\) | ||
0.798494 | − | 0.602003i | \(-0.205630\pi\) | |||||||
\(504\) | 1.28140e24 | + | 2.45257e23i | 0.610674 | + | 0.116882i | ||||
\(505\) | 4.31330e24 | 2.01923 | ||||||||
\(506\) | 6.34781e22 | − | 9.54998e22i | 0.0291924 | − | 0.0439185i | ||||
\(507\) | 3.74986e24 | 1.69412 | ||||||||
\(508\) | −2.21088e24 | + | 9.28301e23i | −0.981276 | + | 0.412017i | ||||
\(509\) | 2.65070e23i | 0.115585i | 0.998329 | + | 0.0577925i | \(0.0184062\pi\) | ||||
−0.998329 | + | 0.0577925i | \(0.981594\pi\) | |||||||
\(510\) | −1.05918e24 | + | 1.59349e24i | −0.453773 | + | 0.682679i | ||||
\(511\) | 8.22715e23i | 0.346307i | ||||||||
\(512\) | −1.29931e24 | + | 2.03907e24i | −0.537384 | + | 0.843338i | ||||
\(513\) | −9.20441e23 | −0.374059 | ||||||||
\(514\) | 3.23345e24 | + | 2.14925e24i | 1.29121 | + | 0.858262i | ||||
\(515\) | −3.89478e24 | −1.52833 | ||||||||
\(516\) | −1.87369e24 | − | 4.46246e24i | −0.722522 | − | 1.72079i | ||||
\(517\) | 6.16913e22i | 0.0233781i | ||||||||
\(518\) | 5.66745e23 | + | 3.76712e23i | 0.211067 | + | 0.140295i | ||||
\(519\) | 5.84758e24i | 2.14028i | ||||||||
\(520\) | −2.45748e23 | + | 1.28397e24i | −0.0884017 | + | 0.461874i | ||||
\(521\) | 4.48105e24 | 1.58431 | 0.792155 | − | 0.610320i | \(-0.208959\pi\) | ||||
0.792155 | + | 0.610320i | \(0.208959\pi\) | |||||||
\(522\) | −1.30691e24 | + | 1.96619e24i | −0.454164 | + | 0.683267i | ||||
\(523\) | 1.94656e24 | 0.664895 | 0.332448 | − | 0.943122i | \(-0.392126\pi\) | ||||
0.332448 | + | 0.943122i | \(0.392126\pi\) | |||||||
\(524\) | 1.01675e23 | + | 2.42154e23i | 0.0341376 | + | 0.0813035i | ||||
\(525\) | − | 3.21180e24i | − | 1.06002i | ||||||
\(526\) | 9.36002e23 | − | 1.40817e24i | 0.303672 | − | 0.456860i | ||||
\(527\) | − | 1.01227e24i | − | 0.322851i | ||||||
\(528\) | 2.35072e23 | − | 2.39654e23i | 0.0737048 | − | 0.0751415i | ||||
\(529\) | 5.43039e23 | 0.167390 | ||||||||
\(530\) | −5.71098e24 | − | 3.79605e24i | −1.73072 | − | 1.15040i | ||||
\(531\) | −7.31474e24 | −2.17946 | ||||||||
\(532\) | 1.31743e23 | − | 5.53162e22i | 0.0385943 | − | 0.0162049i | ||||
\(533\) | − | 1.20334e24i | − | 0.346611i | ||||||
\(534\) | −2.52328e24 | − | 1.67721e24i | −0.714651 | − | 0.475024i | ||||
\(535\) | 3.96484e24i | 1.10419i | ||||||||
\(536\) | 7.83119e23 | − | 4.09158e24i | 0.214459 | − | 1.12049i | ||||
\(537\) | −9.67034e23 | −0.260419 | ||||||||
\(538\) | −4.03681e24 | + | 6.07319e24i | −1.06905 | + | 1.60834i | ||||
\(539\) | −2.05930e23 | −0.0536315 | ||||||||
\(540\) | 1.53681e25 | − | 6.45276e24i | 3.93620 | − | 1.65273i | ||||
\(541\) | − | 3.82714e24i | − | 0.964050i | −0.876158 | − | 0.482025i | \(-0.839901\pi\) | ||
0.876158 | − | 0.482025i | \(-0.160099\pi\) | |||||||
\(542\) | 3.89431e24 | − | 5.85880e24i | 0.964799 | − | 1.45149i | ||||
\(543\) | − | 9.66774e24i | − | 2.35574i | ||||||
\(544\) | 1.03217e24 | − | 2.18289e23i | 0.247378 | − | 0.0523168i | ||||
\(545\) | 9.83803e22 | 0.0231921 | ||||||||
\(546\) | −4.63721e23 | − | 3.08232e23i | −0.107528 | − | 0.0714734i | ||||
\(547\) | −8.31133e24 | −1.89577 | −0.947883 | − | 0.318620i | \(-0.896781\pi\) | ||||
−0.947883 | + | 0.318620i | \(0.896781\pi\) | |||||||
\(548\) | 3.51777e23 | + | 8.37805e23i | 0.0789300 | + | 0.187983i | ||||
\(549\) | 1.47066e25i | 3.24610i | ||||||||
\(550\) | −4.80746e23 | − | 3.19549e23i | −0.104388 | − | 0.0693862i | ||||
\(551\) | 2.58566e23i | 0.0552340i | ||||||||
\(552\) | −7.76642e24 | − | 1.48647e24i | −1.63218 | − | 0.312396i | ||||
\(553\) | −1.77998e24 | −0.368034 | ||||||||
\(554\) | 2.82663e24 | − | 4.25252e24i | 0.575017 | − | 0.865085i | ||||
\(555\) | 1.52965e25 | 3.06165 | ||||||||
\(556\) | 2.04082e24 | + | 4.86050e24i | 0.401913 | + | 0.957211i | ||||
\(557\) | 8.43060e23i | 0.163366i | 0.996658 | + | 0.0816830i | \(0.0260295\pi\) | ||||
−0.996658 | + | 0.0816830i | \(0.973970\pi\) | |||||||
\(558\) | −8.58830e24 | + | 1.29207e25i | −1.63757 | + | 2.46364i | ||||
\(559\) | 1.44284e24i | 0.270715i | ||||||||
\(560\) | −1.81186e24 | + | 1.84717e24i | −0.334527 | + | 0.341048i | ||||
\(561\) | −1.46477e23 | −0.0266137 | ||||||||
\(562\) | −2.07729e24 | − | 1.38076e24i | −0.371424 | − | 0.246883i | ||||
\(563\) | 5.66512e24 | 0.996858 | 0.498429 | − | 0.866930i | \(-0.333910\pi\) | ||||
0.498429 | + | 0.866930i | \(0.333910\pi\) | |||||||
\(564\) | 3.92230e24 | − | 1.64689e24i | 0.679249 | − | 0.285202i | ||||
\(565\) | − | 8.08354e24i | − | 1.37773i | ||||||
\(566\) | 8.94884e23 | + | 5.94824e23i | 0.150113 | + | 0.0997793i | ||||
\(567\) | 3.33355e24i | 0.550376i | ||||||||
\(568\) | 6.56512e24 | + | 1.25655e24i | 1.06686 | + | 0.204195i | ||||
\(569\) | −7.57789e24 | −1.21210 | −0.606049 | − | 0.795427i | \(-0.707246\pi\) | ||||
−0.606049 | + | 0.795427i | \(0.707246\pi\) | |||||||
\(570\) | 1.77788e24 | − | 2.67474e24i | 0.279917 | − | 0.421122i | ||||
\(571\) | −5.34260e24 | −0.827995 | −0.413997 | − | 0.910278i | \(-0.635868\pi\) | ||||
−0.413997 | + | 0.910278i | \(0.635868\pi\) | |||||||
\(572\) | −9.22730e22 | + | 3.87435e22i | −0.0140770 | + | 0.00591064i | ||||
\(573\) | 5.31959e24i | 0.798889i | ||||||||
\(574\) | 1.31844e24 | − | 1.98352e24i | 0.194918 | − | 0.293245i | ||||
\(575\) | 1.35974e25i | 1.97900i | ||||||||
\(576\) | −1.50266e25 | − | 5.97085e24i | −2.15307 | − | 0.855527i | ||||
\(577\) | 8.76279e24 | 1.23612 | 0.618059 | − | 0.786132i | \(-0.287919\pi\) | ||||
0.618059 | + | 0.786132i | \(0.287919\pi\) | |||||||
\(578\) | 5.61309e24 | + | 3.73099e24i | 0.779564 | + | 0.518171i | ||||
\(579\) | −6.18408e24 | −0.845605 | ||||||||
\(580\) | −1.81268e24 | − | 4.31714e24i | −0.244044 | − | 0.581225i | ||||
\(581\) | 4.37833e23i | 0.0580394i | ||||||||
\(582\) | 6.15836e24 | + | 4.09343e24i | 0.803819 | + | 0.534294i | ||||
\(583\) | − | 5.24968e23i | − | 0.0674708i | ||||||
\(584\) | 1.91678e24 | − | 1.00146e25i | 0.242580 | − | 1.26742i | ||||
\(585\) | −8.74241e24 | −1.08950 | ||||||||
\(586\) | 3.32691e24 | − | 5.00517e24i | 0.408284 | − | 0.614244i | ||||
\(587\) | −7.96895e24 | −0.963071 | −0.481535 | − | 0.876427i | \(-0.659921\pi\) | ||||
−0.481535 | + | 0.876427i | \(0.659921\pi\) | |||||||
\(588\) | 5.49744e24 | + | 1.30929e25i | 0.654281 | + | 1.55826i | ||||
\(589\) | 1.69915e24i | 0.199156i | ||||||||
\(590\) | 8.03045e24 | − | 1.20814e25i | 0.926983 | − | 1.39460i | ||||
\(591\) | − | 1.42480e25i | − | 1.61982i | ||||||
\(592\) | −6.02112e24 | − | 5.90599e24i | −0.674189 | − | 0.661299i | ||||
\(593\) | 3.11221e24 | 0.343224 | 0.171612 | − | 0.985165i | \(-0.445103\pi\) | ||||
0.171612 | + | 0.985165i | \(0.445103\pi\) | |||||||
\(594\) | 1.06265e24 | + | 7.06340e23i | 0.115429 | + | 0.0767248i | ||||
\(595\) | 1.12900e24 | 0.120793 | ||||||||
\(596\) | −6.76619e24 | + | 2.84098e24i | −0.713063 | + | 0.299400i | ||||
\(597\) | − | 1.43096e25i | − | 1.48546i | ||||||
\(598\) | 1.96319e24 | + | 1.30492e24i | 0.200749 | + | 0.133436i | ||||
\(599\) | 1.18101e25i | 1.18963i | 0.803864 | + | 0.594814i | \(0.202774\pi\) | ||||
−0.803864 | + | 0.594814i | \(0.797226\pi\) | |||||||
\(600\) | −7.48292e24 | + | 3.90962e25i | −0.742522 | + | 3.87947i | ||||
\(601\) | 4.63978e24 | 0.453552 | 0.226776 | − | 0.973947i | \(-0.427182\pi\) | ||||
0.226776 | + | 0.973947i | \(0.427182\pi\) | |||||||
\(602\) | −1.58084e24 | + | 2.37830e24i | −0.152237 | + | 0.229034i | ||||
\(603\) | 2.78592e25 | 2.64309 | ||||||||
\(604\) | −8.80781e24 | + | 3.69821e24i | −0.823257 | + | 0.345668i | ||||
\(605\) | 1.92661e25i | 1.77417i | ||||||||
\(606\) | 1.26043e25 | − | 1.89626e25i | 1.14358 | − | 1.72045i | ||||
\(607\) | − | 7.64084e24i | − | 0.683035i | −0.939875 | − | 0.341518i | \(-0.889059\pi\) | ||
0.939875 | − | 0.341518i | \(-0.110941\pi\) | |||||||
\(608\) | −1.73254e24 | + | 3.66407e23i | −0.152599 | + | 0.0322724i | ||||
\(609\) | 1.99434e24 | 0.173079 | ||||||||
\(610\) | −2.42903e25 | − | 1.61456e25i | −2.07713 | − | 1.38066i | ||||
\(611\) | −1.26819e24 | −0.106860 | ||||||||
\(612\) | 2.73138e24 | + | 6.50516e24i | 0.226788 | + | 0.540126i | ||||
\(613\) | 1.33533e24i | 0.109255i | 0.998507 | + | 0.0546277i | \(0.0173972\pi\) | ||||
−0.998507 | + | 0.0546277i | \(0.982603\pi\) | |||||||
\(614\) | 1.61741e25 | + | 1.07508e25i | 1.30408 | + | 0.866814i | ||||
\(615\) | − | 5.35355e25i | − | 4.25369i | ||||||
\(616\) | −1.94548e23 | − | 3.72359e22i | −0.0152335 | − | 0.00291565i | ||||
\(617\) | −1.43061e25 | −1.10396 | −0.551982 | − | 0.833856i | \(-0.686128\pi\) | ||||
−0.551982 | + | 0.833856i | \(0.686128\pi\) | |||||||
\(618\) | −1.13813e25 | + | 1.71226e25i | −0.865558 | + | 1.30219i | ||||
\(619\) | −7.11980e24 | −0.533644 | −0.266822 | − | 0.963746i | \(-0.585974\pi\) | ||||
−0.266822 | + | 0.963746i | \(0.585974\pi\) | |||||||
\(620\) | −1.19119e25 | − | 2.83698e25i | −0.879944 | − | 2.09571i | ||||
\(621\) | − | 3.00561e25i | − | 2.18830i | ||||||
\(622\) | −1.04941e25 | + | 1.57879e25i | −0.753067 | + | 1.13295i | ||||
\(623\) | 1.78776e24i | 0.126450i | ||||||||
\(624\) | 4.92658e24 | + | 4.83239e24i | 0.343467 | + | 0.336900i | ||||
\(625\) | 2.23369e25 | 1.53498 | ||||||||
\(626\) | 1.18881e25 | + | 7.90195e24i | 0.805273 | + | 0.535260i | ||||
\(627\) | 2.45869e23 | 0.0164171 | ||||||||
\(628\) | 1.36616e25 | − | 5.73620e24i | 0.899215 | − | 0.377561i | ||||
\(629\) | 3.68013e24i | 0.238785i | ||||||||
\(630\) | −1.44106e25 | − | 9.57861e24i | −0.921755 | − | 0.612685i | ||||
\(631\) | 4.13788e23i | 0.0260924i | 0.999915 | + | 0.0130462i | \(0.00415285\pi\) | ||||
−0.999915 | + | 0.0130462i | \(0.995847\pi\) | |||||||
\(632\) | 2.16670e25 | + | 4.14702e24i | 1.34693 | + | 0.257800i | ||||
\(633\) | −4.28568e25 | −2.62656 | ||||||||
\(634\) | −2.50345e24 | + | 3.76632e24i | −0.151264 | + | 0.227569i | ||||
\(635\) | 3.18026e25 | 1.89452 | ||||||||
\(636\) | −3.33772e25 | + | 1.40144e25i | −1.96036 | + | 0.823114i | ||||
\(637\) | − | 4.23331e24i | − | 0.245146i | ||||||
\(638\) | 1.98421e23 | − | 2.98515e23i | 0.0113293 | − | 0.0170444i | ||||
\(639\) | 4.47013e25i | 2.51659i | ||||||||
\(640\) | 2.63587e25 | − | 1.82637e25i | 1.46320 | − | 1.01384i | ||||
\(641\) | −2.79818e25 | −1.53163 | −0.765815 | − | 0.643061i | \(-0.777664\pi\) | ||||
−0.765815 | + | 0.643061i | \(0.777664\pi\) | |||||||
\(642\) | 1.74307e25 | + | 1.15861e25i | 0.940803 | + | 0.625346i | ||||
\(643\) | −6.06624e24 | −0.322865 | −0.161432 | − | 0.986884i | \(-0.551611\pi\) | ||||
−0.161432 | + | 0.986884i | \(0.551611\pi\) | |||||||
\(644\) | 1.80629e24 | + | 4.30194e24i | 0.0948016 | + | 0.225783i | ||||
\(645\) | 6.41907e25i | 3.32227i | ||||||||
\(646\) | 6.43505e23 | + | 4.27734e23i | 0.0328443 | + | 0.0218314i | ||||
\(647\) | 2.42292e25i | 1.21955i | 0.792574 | + | 0.609775i | \(0.208740\pi\) | ||||
−0.792574 | + | 0.609775i | \(0.791260\pi\) | |||||||
\(648\) | 7.76657e24 | − | 4.05782e25i | 0.385526 | − | 2.01427i | ||||
\(649\) | 1.11056e24 | 0.0543674 | ||||||||
\(650\) | 6.56899e24 | − | 9.88272e24i | 0.317160 | − | 0.477152i | ||||
\(651\) | 1.31057e25 | 0.624067 | ||||||||
\(652\) | 2.36020e23 | + | 5.62115e23i | 0.0110846 | + | 0.0263996i | ||||
\(653\) | 2.57769e25i | 1.19402i | 0.802233 | + | 0.597011i | \(0.203645\pi\) | ||||
−0.802233 | + | 0.597011i | \(0.796355\pi\) | |||||||
\(654\) | 2.87487e23 | − | 4.32510e23i | 0.0131346 | − | 0.0197604i | ||||
\(655\) | − | 3.48328e24i | − | 0.156970i | ||||||
\(656\) | −2.06701e25 | + | 2.10730e25i | −0.918773 | + | 0.936682i | ||||
\(657\) | 6.81887e25 | 2.98967 | ||||||||
\(658\) | −2.09042e24 | − | 1.38949e24i | −0.0904068 | − | 0.0600929i | ||||
\(659\) | −2.16127e25 | −0.922021 | −0.461010 | − | 0.887395i | \(-0.652513\pi\) | ||||
−0.461010 | + | 0.887395i | \(0.652513\pi\) | |||||||
\(660\) | −4.10515e24 | + | 1.72367e24i | −0.172756 | + | 0.0725366i | ||||
\(661\) | − | 3.80929e25i | − | 1.58136i | −0.612230 | − | 0.790680i | \(-0.709727\pi\) | ||
0.612230 | − | 0.790680i | \(-0.290273\pi\) | |||||||
\(662\) | −9.69357e24 | − | 6.44326e24i | −0.396974 | − | 0.263866i | ||||
\(663\) | − | 3.01115e24i | − | 0.121649i | ||||||
\(664\) | 1.02007e24 | − | 5.32958e24i | 0.0406553 | − | 0.212413i | ||||
\(665\) | −1.89507e24 | −0.0745129 | ||||||||
\(666\) | 3.12228e25 | − | 4.69732e25i | 1.21117 | − | 1.82214i | ||||
\(667\) | −8.44320e24 | −0.323128 | ||||||||
\(668\) | 4.32299e25 | − | 1.81513e25i | 1.63229 | − | 0.685362i | ||||
\(669\) | − | 3.39569e25i | − | 1.26501i | ||||||
\(670\) | −3.05851e25 | + | 4.60137e25i | −1.12418 | + | 1.69128i | ||||
\(671\) | − | 2.23282e24i | − | 0.0809751i | ||||||
\(672\) | 2.82614e24 | + | 1.33633e25i | 0.101128 | + | 0.478178i | ||||
\(673\) | −1.42553e25 | −0.503317 | −0.251658 | − | 0.967816i | \(-0.580976\pi\) | ||||
−0.251658 | + | 0.967816i | \(0.580976\pi\) | |||||||
\(674\) | −2.94909e25 | − | 1.96024e25i | −1.02742 | − | 0.682920i | ||||
\(675\) | −1.51302e26 | −5.20129 | ||||||||
\(676\) | 1.06162e25 | + | 2.52839e25i | 0.360120 | + | 0.857677i | ||||
\(677\) | − | 3.50982e25i | − | 1.17486i | −0.809275 | − | 0.587430i | \(-0.800140\pi\) | ||
0.809275 | − | 0.587430i | \(-0.199860\pi\) | |||||||
\(678\) | −3.55377e25 | − | 2.36217e25i | −1.17388 | − | 0.780268i | ||||
\(679\) | − | 4.36325e24i | − | 0.142227i | ||||||
\(680\) | −1.37429e25 | − | 2.63036e24i | −0.442078 | − | 0.0846127i | ||||
\(681\) | 7.58884e25 | 2.40908 | ||||||||
\(682\) | 1.30391e24 | − | 1.96167e24i | 0.0408497 | − | 0.0614565i | ||||
\(683\) | 5.18583e25 | 1.60336 | 0.801681 | − | 0.597752i | \(-0.203939\pi\) | ||||
0.801681 | + | 0.597752i | \(0.203939\pi\) | |||||||
\(684\) | −4.58474e24 | − | 1.09192e25i | −0.139898 | − | 0.333185i | ||||
\(685\) | − | 1.20515e25i | − | 0.362932i | ||||||
\(686\) | 9.63642e24 | − | 1.44975e25i | 0.286417 | − | 0.430900i | ||||
\(687\) | 6.10623e25i | 1.79127i | ||||||||
\(688\) | 2.47841e25 | − | 2.52672e25i | 0.717591 | − | 0.731579i | ||||
\(689\) | 1.07918e25 | 0.308405 | ||||||||
\(690\) | 8.73408e25 | + | 5.80549e25i | 2.46363 | + | 1.63756i | ||||
\(691\) | −1.96292e25 | −0.546513 | −0.273256 | − | 0.961941i | \(-0.588101\pi\) | ||||
−0.273256 | + | 0.961941i | \(0.588101\pi\) | |||||||
\(692\) | −3.94281e25 | + | 1.65550e25i | −1.08355 | + | 0.454961i | ||||
\(693\) | − | 1.32466e24i | − | 0.0359339i | ||||||
\(694\) | −1.52068e25 | − | 1.01078e25i | −0.407194 | − | 0.270659i | ||||
\(695\) | − | 6.99164e25i | − | 1.84806i | ||||||
\(696\) | −2.42765e25 | − | 4.64646e24i | −0.633435 | − | 0.121238i | ||||
\(697\) | 1.28799e25 | 0.331755 | ||||||||
\(698\) | −1.86356e25 | + | 2.80363e25i | −0.473854 | + | 0.712890i | ||||
\(699\) | 8.85613e25 | 2.22305 | ||||||||
\(700\) | 2.16560e25 | − | 9.09289e24i | 0.536655 | − | 0.225330i | ||||
\(701\) | 5.39698e25i | 1.32035i | 0.751112 | + | 0.660174i | \(0.229518\pi\) | ||||
−0.751112 | + | 0.660174i | \(0.770482\pi\) | |||||||
\(702\) | −1.45203e25 | + | 2.18450e25i | −0.350704 | + | 0.527617i | ||||
\(703\) | − | 6.17726e24i | − | 0.147298i | ||||||
\(704\) | 2.28141e24 | + | 9.06521e23i | 0.0537092 | + | 0.0213414i | ||||
\(705\) | −5.64207e25 | −1.31140 | ||||||||
\(706\) | 9.41914e24 | + | 6.26084e24i | 0.216157 | + | 0.143678i | ||||
\(707\) | −1.34351e25 | −0.304416 | ||||||||
\(708\) | −2.96471e25 | − | 7.06086e25i | −0.663258 | − | 1.57964i | ||||
\(709\) | − | 6.68291e25i | − | 1.47622i | −0.674683 | − | 0.738108i | \(-0.735720\pi\) | ||
0.674683 | − | 0.738108i | \(-0.264280\pi\) | |||||||
\(710\) | −7.38311e25 | − | 4.90751e25i | −1.61033 | − | 1.07037i | ||||
\(711\) | 1.47529e26i | 3.17724i | ||||||||
\(712\) | 4.16517e24 | − | 2.17618e25i | 0.0885753 | − | 0.462781i | ||||
\(713\) | −5.54839e25 | −1.16510 | ||||||||
\(714\) | 3.29916e24 | − | 4.96342e24i | 0.0684099 | − | 0.102919i | ||||
\(715\) | 1.32731e24 | 0.0271781 | ||||||||
\(716\) | −2.73776e24 | − | 6.52035e24i | −0.0553576 | − | 0.131842i | ||||
\(717\) | − | 8.91383e24i | − | 0.177988i | ||||||
\(718\) | −3.92115e25 | + | 5.89919e25i | −0.773204 | + | 1.16325i | ||||
\(719\) | − | 9.75703e25i | − | 1.90002i | −0.312222 | − | 0.950009i | \(-0.601073\pi\) | ||
0.312222 | − | 0.950009i | \(-0.398927\pi\) | |||||||
\(720\) | 1.53098e26 | + | 1.50171e26i | 2.94427 | + | 2.88798i | ||||
\(721\) | 1.21315e25 | 0.230408 | ||||||||
\(722\) | 4.33195e25 | + | 2.87942e25i | 0.812547 | + | 0.540095i | ||||
\(723\) | 6.83282e25 | 1.26577 | ||||||||
\(724\) | 6.51860e25 | − | 2.73702e25i | 1.19263 | − | 0.500762i | ||||
\(725\) | 4.25031e25i | 0.768030i | ||||||||
\(726\) | 8.46998e25 | + | 5.62994e25i | 1.51165 | + | 1.00479i | ||||
\(727\) | − | 3.21406e24i | − | 0.0566558i | −0.999599 | − | 0.0283279i | \(-0.990982\pi\) | ||
0.999599 | − | 0.0283279i | \(-0.00901825\pi\) | |||||||
\(728\) | 7.65462e23 | − | 3.99933e24i | 0.0133273 | − | 0.0696313i | ||||
\(729\) | 2.23152e25 | 0.383754 | ||||||||
\(730\) | −7.48606e25 | + | 1.12624e26i | −1.27159 | + | 1.91305i | ||||
\(731\) | −1.54434e25 | −0.259112 | ||||||||
\(732\) | −1.41962e26 | + | 5.96068e25i | −2.35273 | + | 0.987861i | ||||
\(733\) | 3.47572e25i | 0.568996i | 0.958677 | + | 0.284498i | \(0.0918270\pi\) | ||||
−0.958677 | + | 0.284498i | \(0.908173\pi\) | |||||||
\(734\) | −6.17415e24 | + | 9.28872e24i | −0.0998419 | + | 0.150207i | ||||
\(735\) | − | 1.88336e26i | − | 3.00849i | ||||||
\(736\) | −1.19647e25 | − | 5.65744e25i | −0.188799 | − | 0.892729i | ||||
\(737\) | −4.22970e24 | −0.0659330 | ||||||||
\(738\) | −1.64399e26 | − | 1.09275e26i | −2.53158 | − | 1.68273i | ||||
\(739\) | −3.36930e25 | −0.512554 | −0.256277 | − | 0.966603i | \(-0.582496\pi\) | ||||
−0.256277 | + | 0.966603i | \(0.582496\pi\) | |||||||
\(740\) | 4.33057e25 | + | 1.03139e26i | 0.650818 | + | 1.55001i | ||||
\(741\) | 5.05434e24i | 0.0750414i | ||||||||
\(742\) | 1.77887e25 | + | 1.18240e25i | 0.260921 | + | 0.173432i | ||||
\(743\) | − | 6.47870e25i | − | 0.938833i | −0.882977 | − | 0.469416i | \(-0.844464\pi\) | ||
0.882977 | − | 0.469416i | \(-0.155536\pi\) | |||||||
\(744\) | −1.59531e26 | − | 3.05339e25i | −2.28396 | − | 0.437145i | ||||
\(745\) | 9.73290e25 | 1.37669 | ||||||||
\(746\) | 4.53423e25 | − | 6.82153e25i | 0.633657 | − | 0.953307i | ||||
\(747\) | 3.62886e25 | 0.501055 | ||||||||
\(748\) | −4.14690e23 | − | 9.87643e23i | −0.00565730 | − | 0.0134737i | ||||
\(749\) | − | 1.23498e25i | − | 0.166465i | ||||||
\(750\) | 1.57499e26 | − | 2.36949e26i | 2.09762 | − | 3.15576i | ||||
\(751\) | 1.29075e26i | 1.69856i | 0.527939 | + | 0.849282i | \(0.322965\pi\) | ||||
−0.527939 | + | 0.849282i | \(0.677035\pi\) | |||||||
\(752\) | 2.22087e25 | + | 2.17841e25i | 0.288777 | + | 0.283256i | ||||
\(753\) | −2.76490e26 | −3.55243 | ||||||||
\(754\) | 6.13660e24 | + | 4.07896e24i | 0.0779087 | + | 0.0517854i | ||||
\(755\) | 1.26697e26 | 1.58944 | ||||||||
\(756\) | −4.78690e25 | + | 2.00992e25i | −0.593414 | + | 0.249162i | ||||
\(757\) | 8.91927e25i | 1.09261i | 0.837585 | + | 0.546306i | \(0.183967\pi\) | ||||
−0.837585 | + | 0.546306i | \(0.816033\pi\) | |||||||
\(758\) | 7.24438e25 | + | 4.81530e25i | 0.876957 | + | 0.582908i | ||||
\(759\) | 8.02860e24i | 0.0960426i | ||||||||
\(760\) | 2.30681e25 | + | 4.41518e24i | 0.272703 | + | 0.0521946i | ||||
\(761\) | 1.25661e26 | 1.46804 | 0.734022 | − | 0.679125i | \(-0.237641\pi\) | ||||
0.734022 | + | 0.679125i | \(0.237641\pi\) | |||||||
\(762\) | 9.29335e25 | − | 1.39814e26i | 1.07294 | − | 1.61419i | ||||
\(763\) | −3.06437e23 | −0.00349639 | ||||||||
\(764\) | −3.58680e25 | + | 1.50602e25i | −0.404452 | + | 0.169821i | ||||
\(765\) | − | 9.35742e25i | − | 1.04281i | ||||||
\(766\) | −4.31568e24 | + | 6.49273e24i | −0.0475325 | + | 0.0715103i | ||||
\(767\) | 2.28298e25i | 0.248510i | ||||||||
\(768\) | −3.26760e24 | − | 1.69251e26i | −0.0351543 | − | 1.82087i | ||||
\(769\) | 3.35301e25 | 0.356531 | 0.178266 | − | 0.983982i | \(-0.442951\pi\) | ||||
0.178266 | + | 0.983982i | \(0.442951\pi\) | |||||||
\(770\) | 2.18787e24 | + | 1.45427e24i | 0.0229935 | + | 0.0152837i | ||||
\(771\) | −2.71834e26 | −2.82367 | ||||||||
\(772\) | −1.75077e25 | − | 4.16969e25i | −0.179751 | − | 0.428103i | ||||
\(773\) | 6.15259e25i | 0.624371i | 0.950021 | + | 0.312185i | \(0.101061\pi\) | ||||
−0.950021 | + | 0.312185i | \(0.898939\pi\) | |||||||
\(774\) | 1.97120e26 | + | 1.31024e26i | 1.97725 | + | 1.31427i | ||||
\(775\) | 2.79306e26i | 2.76927i | ||||||||
\(776\) | −1.01656e25 | + | 5.31124e25i | −0.0996270 | + | 0.520523i | ||||
\(777\) | −4.76458e25 | −0.461568 | ||||||||
\(778\) | 2.32832e25 | − | 3.50284e25i | 0.222960 | − | 0.335432i | ||||
\(779\) | −2.16195e25 | −0.204648 | ||||||||
\(780\) | −3.54335e25 | − | 8.43898e25i | −0.331560 | − | 0.789657i | ||||
\(781\) | − | 6.78675e24i | − | 0.0627773i | ||||||
\(782\) | −1.39672e25 | + | 2.10130e25i | −0.127717 | + | 0.192144i | ||||
\(783\) | − | 9.39500e25i | − | 0.849260i | ||||||
\(784\) | −7.27169e25 | + | 7.41343e25i | −0.649816 | + | 0.662483i | ||||
\(785\) | −1.96516e26 | −1.73609 | ||||||||
\(786\) | −1.53136e25 | − | 1.01788e25i | −0.133744 | − | 0.0888987i | ||||
\(787\) | −7.75132e24 | −0.0669273 | −0.0334636 | − | 0.999440i | \(-0.510654\pi\) | ||||
−0.0334636 | + | 0.999440i | \(0.510654\pi\) | |||||||
\(788\) | 9.60689e25 | − | 4.03373e25i | 0.820063 | − | 0.344327i | ||||
\(789\) | 1.18384e26i | 0.999078i | ||||||||
\(790\) | −2.43666e26 | − | 1.61964e26i | −2.03307 | − | 1.35137i | ||||
\(791\) | 2.51788e25i | 0.207705i | ||||||||
\(792\) | −3.08621e24 | + | 1.61246e25i | −0.0251709 | + | 0.131511i | ||||
\(793\) | 4.59003e25 | 0.370132 | ||||||||
\(794\) | 2.07808e25 | − | 3.12637e25i | 0.165683 | − | 0.249262i | ||||
\(795\) | 4.80118e26 | 3.78481 | ||||||||
\(796\) | 9.64845e25 | − | 4.05118e25i | 0.752038 | − | 0.315765i | ||||
\(797\) | − | 1.14334e26i | − | 0.881155i | −0.897715 | − | 0.440578i | \(-0.854774\pi\) | ||
0.897715 | − | 0.440578i | \(-0.145226\pi\) | |||||||
\(798\) | −5.53778e24 | + | 8.33132e24i | −0.0421997 | + | 0.0634875i | ||||
\(799\) | − | 1.35741e25i | − | 0.102280i | ||||||
\(800\) | −2.84796e26 | + | 6.02301e25i | −2.12189 | + | 0.448749i | ||||
\(801\) | 1.48174e26 | 1.09164 | ||||||||
\(802\) | 5.92357e25 | + | 3.93736e25i | 0.431533 | + | 0.286838i | ||||
\(803\) | −1.03527e25 | −0.0745785 | ||||||||
\(804\) | 1.12915e26 | + | 2.68922e26i | 0.804353 | + | 1.91568i | ||||
\(805\) | − | 6.18817e25i | − | 0.435913i | ||||||
\(806\) | 4.03263e25 | + | 2.68046e25i | 0.280914 | + | 0.186722i | ||||
\(807\) | − | 5.10569e26i | − | 3.51716i | ||||||
\(808\) | 1.63541e26 | + | 3.13014e25i | 1.11410 | + | 0.213237i | ||||
\(809\) | −6.96753e25 | −0.469399 | −0.234699 | − | 0.972068i | \(-0.575411\pi\) | ||||
−0.234699 | + | 0.972068i | \(0.575411\pi\) | |||||||
\(810\) | −3.03327e26 | + | 4.56340e26i | −2.02090 | + | 3.04035i | ||||
\(811\) | −2.24307e26 | −1.47793 | −0.738967 | − | 0.673741i | \(-0.764686\pi\) | ||||
−0.738967 | + | 0.673741i | \(0.764686\pi\) | |||||||
\(812\) | 5.64616e24 | + | 1.34471e25i | 0.0367916 | + | 0.0876244i | ||||
\(813\) | 4.92545e26i | 3.17418i | ||||||||
\(814\) | −4.74038e24 | + | 7.13168e24i | −0.0302130 | + | 0.0454540i | ||||
\(815\) | − | 8.08580e24i | − | 0.0509688i | ||||||
\(816\) | −5.17234e25 | + | 5.27316e25i | −0.322460 | + | 0.328745i | ||||
\(817\) | 2.59224e25 | 0.159837 | ||||||||
\(818\) | 4.10013e25 | + | 2.72533e25i | 0.250045 | + | 0.166203i | ||||
\(819\) | 2.72310e25 | 0.164251 | ||||||||
\(820\) | 3.60970e26 | − | 1.51564e26i | 2.15351 | − | 0.904212i | ||||
\(821\) | − | 1.51175e26i | − | 0.892055i | −0.895019 | − | 0.446027i | \(-0.852838\pi\) | ||
0.895019 | − | 0.446027i | \(-0.147162\pi\) | |||||||
\(822\) | −5.29820e25 | − | 3.52168e25i | −0.309230 | − | 0.205544i | ||||
\(823\) | 1.32029e26i | 0.762203i | 0.924533 | + | 0.381101i | \(0.124455\pi\) | ||||
−0.924533 | + | 0.381101i | \(0.875545\pi\) | |||||||
\(824\) | −1.47673e26 | − | 2.82643e25i | −0.843250 | − | 0.161396i | ||||
\(825\) | 4.04160e25 | 0.228280 | ||||||||
\(826\) | −2.50134e25 | + | 3.76315e25i | −0.139750 | + | 0.210247i | ||||
\(827\) | 1.71500e26 | 0.947797 | 0.473898 | − | 0.880580i | \(-0.342846\pi\) | ||||
0.473898 | + | 0.880580i | \(0.342846\pi\) | |||||||
\(828\) | 3.56556e26 | − | 1.49710e26i | 1.94919 | − | 0.818424i | ||||
\(829\) | − | 1.01192e26i | − | 0.547210i | −0.961842 | − | 0.273605i | \(-0.911784\pi\) | ||
0.961842 | − | 0.273605i | \(-0.0882160\pi\) | |||||||
\(830\) | −3.98393e25 | + | 5.99363e25i | −0.213112 | + | 0.320617i | ||||
\(831\) | 3.57507e26i | 1.89180i | ||||||||
\(832\) | −1.86354e25 | + | 4.68990e25i | −0.0975503 | + | 0.245501i | ||||
\(833\) | 4.53112e25 | 0.234639 | ||||||||
\(834\) | −3.07374e26 | − | 2.04309e26i | −1.57461 | − | 1.04663i | ||||
\(835\) | −6.21845e26 | −3.15140 | ||||||||
\(836\) | 6.96076e23 | + | 1.65780e24i | 0.00348980 | + | 0.00831144i | ||||
\(837\) | − | 6.17386e26i | − | 3.06216i | ||||||
\(838\) | 1.64216e25 | + | 1.09154e25i | 0.0805787 | + | 0.0535601i | ||||
\(839\) | − | 1.53518e26i | − | 0.745252i | −0.927982 | − | 0.372626i | \(-0.878458\pi\) | ||
0.927982 | − | 0.372626i | \(-0.121542\pi\) | |||||||
\(840\) | 3.40547e25 | − | 1.77927e26i | 0.163555 | − | 0.854530i | ||||
\(841\) | 1.84065e26 | 0.874597 | ||||||||
\(842\) | 1.31429e26 | − | 1.97729e26i | 0.617849 | − | 0.929524i | ||||
\(843\) | 1.74636e26 | 0.812244 | ||||||||
\(844\) | −1.21331e26 | − | 2.88968e26i | −0.558330 | − | 1.32974i | ||||
\(845\) | − | 3.63699e26i | − | 1.65589i | ||||||
\(846\) | −1.15164e26 | + | 1.73259e26i | −0.518782 | + | 0.780483i | ||||
\(847\) | − | 6.00105e25i | − | 0.267471i | ||||||
\(848\) | −1.88988e26 | − | 1.85374e26i | −0.833433 | − | 0.817498i | ||||
\(849\) | −7.52322e25 | −0.328273 | ||||||||
\(850\) | 1.05780e26 | + | 7.03110e25i | 0.456700 | + | 0.303566i | ||||
\(851\) | 2.01712e26 | 0.861719 | ||||||||
\(852\) | −4.31498e26 | + | 1.81177e26i | −1.82399 | + | 0.765855i | ||||
\(853\) | 2.05890e26i | 0.861178i | 0.902548 | + | 0.430589i | \(0.141694\pi\) | ||||
−0.902548 | + | 0.430589i | \(0.858306\pi\) | |||||||
\(854\) | 7.56598e25 | + | 5.02906e25i | 0.313144 | + | 0.208145i | ||||
\(855\) | 1.57068e26i | 0.643271i | ||||||||
\(856\) | −2.87727e25 | + | 1.50330e26i | −0.116605 | + | 0.609229i | ||||
\(857\) | 1.36020e26 | 0.545476 | 0.272738 | − | 0.962088i | \(-0.412071\pi\) | ||||
0.272738 | + | 0.962088i | \(0.412071\pi\) | |||||||
\(858\) | 3.87867e24 | − | 5.83526e24i | 0.0153921 | − | 0.0231566i | ||||
\(859\) | −1.80946e26 | −0.710576 | −0.355288 | − | 0.934757i | \(-0.615617\pi\) | ||||
−0.355288 | + | 0.934757i | \(0.615617\pi\) | |||||||
\(860\) | −4.32814e26 | + | 1.81729e26i | −1.68196 | + | 0.706219i | ||||
\(861\) | 1.66753e26i | 0.641278i | ||||||||
\(862\) | 7.22147e25 | − | 1.08644e26i | 0.274828 | − | 0.413465i | ||||
\(863\) | 2.20461e26i | 0.830298i | 0.909754 | + | 0.415149i | \(0.136271\pi\) | ||||
−0.909754 | + | 0.415149i | \(0.863729\pi\) | |||||||
\(864\) | 6.29520e26 | − | 1.33134e26i | 2.34631 | − | 0.496211i | ||||
\(865\) | 5.67157e26 | 2.09198 | ||||||||
\(866\) | 2.32596e26 | + | 1.54605e26i | 0.849065 | + | 0.564368i | ||||
\(867\) | −4.71889e26 | −1.70478 | ||||||||
\(868\) | 3.71034e25 | + | 8.83668e25i | 0.132659 | + | 0.315945i | ||||
\(869\) | − | 2.23985e25i | − | 0.0792575i | ||||||
\(870\) | 2.73012e26 | + | 1.81470e26i | 0.956112 | + | 0.635522i | ||||
\(871\) | − | 8.69503e25i | − | 0.301375i | ||||||
\(872\) | 3.73015e24 | + | 7.13943e23i | 0.0127961 | + | 0.00244915i | ||||
\(873\) | −3.61637e26 | −1.22785 | ||||||||
\(874\) | 2.34446e25 | − | 3.52713e25i | 0.0787844 | − | 0.118527i | ||||
\(875\) | −1.67881e26 | −0.558378 | ||||||||
\(876\) | 2.76373e26 | + | 6.58220e26i | 0.909825 | + | 2.16687i | ||||
\(877\) | − | 4.77671e26i | − | 1.55644i | −0.627991 | − | 0.778221i | \(-0.716123\pi\) | ||
0.627991 | − | 0.778221i | \(-0.283877\pi\) | |||||||
\(878\) | −9.65219e25 | + | 1.45212e26i | −0.311297 | + | 0.468331i | ||||
\(879\) | 4.20781e26i | 1.34325i | ||||||||
\(880\) | −2.32441e25 | − | 2.27996e25i | −0.0734459 | − | 0.0720417i | ||||
\(881\) | 3.98413e26 | 1.24609 | 0.623047 | − | 0.782184i | \(-0.285895\pi\) | ||||
0.623047 | + | 0.782184i | \(0.285895\pi\) | |||||||
\(882\) | −5.78352e26 | − | 3.84427e26i | −1.79050 | − | 1.19014i | ||||
\(883\) | 2.83034e26 | 0.867346 | 0.433673 | − | 0.901070i | \(-0.357217\pi\) | ||||
0.433673 | + | 0.901070i | \(0.357217\pi\) | |||||||
\(884\) | 2.03030e25 | − | 8.52481e24i | 0.0615872 | − | 0.0258592i | ||||
\(885\) | 1.01568e27i | 3.04976i | ||||||||
\(886\) | −1.55537e26 | − | 1.03384e26i | −0.462307 | − | 0.307292i | ||||
\(887\) | − | 1.96588e26i | − | 0.578422i | −0.957265 | − | 0.289211i | \(-0.906607\pi\) | ||
0.957265 | − | 0.289211i | \(-0.0933929\pi\) | |||||||
\(888\) | 5.79976e26 | + | 1.11006e26i | 1.68925 | + | 0.323318i | ||||
\(889\) | −9.90594e25 | −0.285614 | ||||||||
\(890\) | −1.62672e26 | + | 2.44733e26i | −0.464306 | + | 0.698525i | ||||
\(891\) | −4.19480e25 | −0.118526 | ||||||||
\(892\) | 2.28959e26 | − | 9.61349e25i | 0.640432 | − | 0.268904i | ||||
\(893\) | 2.27847e25i | 0.0630927i | ||||||||
\(894\) | 2.84414e26 | − | 4.27888e26i | 0.779676 | − | 1.17298i | ||||
\(895\) | 9.37926e25i | 0.254543i | ||||||||
\(896\) | −8.21025e25 | + | 5.68882e25i | −0.220589 | + | 0.152844i | ||||
\(897\) | −1.65044e26 | −0.439004 | ||||||||
\(898\) | −5.16418e25 | − | 3.43260e25i | −0.135992 | − | 0.0903932i | ||||
\(899\) | −1.73433e26 | −0.452162 | ||||||||
\(900\) | −7.53641e26 | − | 1.79490e27i | −1.94528 | − | 4.63295i | ||||
\(901\) | 1.15510e26i | 0.295186i | ||||||||
\(902\) | 2.49598e25 | + | 1.65906e25i | 0.0631513 | + | 0.0419763i | ||||
\(903\) | − | 1.99942e26i | − | 0.500859i | ||||||
\(904\) | 5.86619e25 | − | 3.06492e26i | 0.145492 | − | 0.760158i | ||||
\(905\) | −9.37674e26 | −2.30258 | ||||||||
\(906\) | 3.70233e26 | − | 5.56998e26i | 0.900164 | − | 1.35425i | ||||
\(907\) | −1.92019e26 | −0.462252 | −0.231126 | − | 0.972924i | \(-0.574241\pi\) | ||||
−0.231126 | + | 0.972924i | \(0.574241\pi\) | |||||||
\(908\) | 2.14847e26 | + | 5.11687e26i | 0.512102 | + | 1.21964i | ||||
\(909\) | 1.11354e27i | 2.62803i | ||||||||
\(910\) | −2.98954e25 | + | 4.49763e25i | −0.0698606 | + | 0.105102i | ||||
\(911\) | − | 2.22110e26i | − | 0.513927i | −0.966421 | − | 0.256964i | \(-0.917278\pi\) | ||
0.966421 | − | 0.256964i | \(-0.0827221\pi\) | |||||||
\(912\) | 8.68200e25 | − | 8.85123e25i | 0.198914 | − | 0.202792i | ||||
\(913\) | −5.50950e24 | −0.0124990 | ||||||||
\(914\) | 4.95355e25 | + | 3.29260e25i | 0.111276 | + | 0.0739644i | ||||
\(915\) | 2.04206e27 | 4.54234 | ||||||||
\(916\) | −4.11720e26 | + | 1.72873e26i | −0.906865 | + | 0.380773i | ||||
\(917\) | 1.08498e25i | 0.0236645i | ||||||||
\(918\) | −2.33818e26 | − | 1.55417e26i | −0.505003 | − | 0.335672i | ||||
\(919\) | 4.44214e26i | 0.950064i | 0.879969 | + | 0.475032i | \(0.157563\pi\) | ||||
−0.879969 | + | 0.475032i | \(0.842437\pi\) | |||||||
\(920\) | −1.44173e26 | + | 7.53265e26i | −0.305347 | + | 1.59536i | ||||
\(921\) | −1.35974e27 | −2.85181 | ||||||||
\(922\) | −3.32917e26 | + | 5.00857e26i | −0.691445 | + | 1.04025i | ||||
\(923\) | 1.39516e26 | 0.286951 | ||||||||
\(924\) | 1.27868e25 | − | 5.36891e24i | 0.0260444 | − | 0.0109355i | ||||
\(925\) | − | 1.01542e27i | − | 2.04819i | ||||||
\(926\) | 2.19851e26 | − | 3.30755e26i | 0.439167 | − | 0.660705i | ||||
\(927\) | − | 1.00549e27i | − | 1.98912i | ||||||
\(928\) | −3.73994e25 | − | 1.76842e26i | −0.0732712 | − | 0.346460i | ||||
\(929\) | 9.19897e25 | 0.178483 | 0.0892417 | − | 0.996010i | \(-0.471556\pi\) | ||||
0.0892417 | + | 0.996010i | \(0.471556\pi\) | |||||||
\(930\) | 1.79408e27 | + | 1.19251e27i | 3.44743 | + | 2.29149i | ||||
\(931\) | −7.60568e25 | −0.144741 | ||||||||
\(932\) | 2.50725e26 | + | 5.97135e26i | 0.472556 | + | 1.12546i | ||||
\(933\) | − | 1.32728e27i | − | 2.47758i | ||||||
\(934\) | −7.18320e26 | − | 4.77463e26i | −1.32799 | − | 0.882710i | ||||
\(935\) | 1.42068e25i | 0.0260132i | ||||||||
\(936\) | −3.31474e26 | − | 6.34433e25i | −0.601128 | − | 0.115054i | ||||
\(937\) | 6.97243e26 | 1.25236 | 0.626178 | − | 0.779680i | \(-0.284618\pi\) | ||||
0.626178 | + | 0.779680i | \(0.284618\pi\) | |||||||
\(938\) | 9.52669e25 | − | 1.43325e26i | 0.169479 | − | 0.254973i | ||||
\(939\) | −9.99424e26 | −1.76100 | ||||||||
\(940\) | −1.59732e26 | − | 3.80424e26i | −0.278767 | − | 0.663922i | ||||
\(941\) | 7.71125e26i | 1.33296i | 0.745522 | + | 0.666481i | \(0.232200\pi\) | ||||
−0.745522 | + | 0.666481i | \(0.767800\pi\) | |||||||
\(942\) | −5.74259e26 | + | 8.63945e26i | −0.983218 | + | 1.47920i | ||||
\(943\) | − | 7.05963e26i | − | 1.19723i | ||||||
\(944\) | 3.92154e26 | − | 3.99798e26i | 0.658732 | − | 0.671573i | ||||
\(945\) | 6.88576e26 | 1.14569 | ||||||||
\(946\) | −2.99276e25 | − | 1.98927e25i | −0.0493232 | − | 0.0327849i | ||||
\(947\) | 5.01052e26 | 0.817962 | 0.408981 | − | 0.912543i | \(-0.365884\pi\) | ||||
0.408981 | + | 0.912543i | \(0.365884\pi\) | |||||||
\(948\) | −1.42408e27 | + | 5.97942e26i | −2.30282 | + | 0.966906i | ||||
\(949\) | − | 2.12821e26i | − | 0.340894i | ||||||
\(950\) | −1.77556e26 | − | 1.18020e26i | −0.281723 | − | 0.187259i | ||||
\(951\) | − | 3.16632e26i | − | 0.497656i | ||||||
\(952\) | 4.28067e25 | + | 8.19310e24i | 0.0666468 | + | 0.0127560i | ||||
\(953\) | 7.95510e26 | 1.22690 | 0.613451 | − | 0.789733i | \(-0.289781\pi\) | ||||
0.613451 | + | 0.789733i | \(0.289781\pi\) | |||||||
\(954\) | 9.80004e26 | − | 1.47437e27i | 1.49724 | − | 2.25253i | ||||
\(955\) | 5.15947e26 | 0.780863 | ||||||||
\(956\) | 6.01026e25 | − | 2.52358e25i | 0.0901099 | − | 0.0378352i | ||||
\(957\) | 2.50960e25i | 0.0372732i | ||||||||
\(958\) | −3.68941e26 | + | 5.55053e26i | −0.542834 | + | 0.816667i | ||||
\(959\) | 3.75382e25i | 0.0547150i | ||||||||
\(960\) | −8.29073e26 | + | 2.08650e27i | −1.19716 | + | 3.01284i | ||||
\(961\) | −4.40650e26 | −0.630352 | ||||||||
\(962\) | −1.46606e26 | − | 9.74483e25i | −0.207767 | − | 0.138102i | ||||
\(963\) | −1.02358e27 | −1.43709 | ||||||||
\(964\) | 1.93443e26 | + | 4.60712e26i | 0.269067 | + | 0.640820i | ||||
\(965\) | 5.99794e26i | 0.826525i | ||||||||
\(966\) | −2.72051e26 | − | 1.80831e26i | −0.371412 | − | 0.246875i | ||||
\(967\) | 9.39317e26i | 1.27050i | 0.772307 | + | 0.635249i | \(0.219103\pi\) | ||||
−0.772307 | + | 0.635249i | \(0.780897\pi\) | |||||||
\(968\) | −1.39814e26 | + | 7.30487e26i | −0.187358 | + | 0.978891i | ||||
\(969\) | −5.40990e25 | −0.0718250 | ||||||||
\(970\) | 3.97022e26 | − | 5.97300e26i | 0.522238 | − | 0.785682i | ||||
\(971\) | 1.28565e26 | 0.167551 | 0.0837757 | − | 0.996485i | \(-0.473302\pi\) | ||||
0.0837757 | + | 0.996485i | \(0.473302\pi\) | |||||||
\(972\) | 4.00798e26 | + | 9.54557e26i | 0.517523 | + | 1.23255i | ||||
\(973\) | 2.17777e26i | 0.278610i | ||||||||
\(974\) | 3.06725e26 | − | 4.61453e26i | 0.388793 | − | 0.584921i | ||||
\(975\) | 8.30834e26i | 1.04345i | ||||||||
\(976\) | −8.03812e26 | − | 7.88443e26i | −1.00024 | − | 0.981120i | ||||
\(977\) | 3.96171e26 | 0.488463 | 0.244232 | − | 0.969717i | \(-0.421464\pi\) | ||||
0.244232 | + | 0.969717i | \(0.421464\pi\) | |||||||
\(978\) | −3.55477e25 | − | 2.36283e25i | −0.0434271 | − | 0.0288658i | ||||
\(979\) | −2.24965e25 | −0.0272314 | ||||||||
\(980\) | 1.26988e27 | − | 5.33196e26i | 1.52310 | − | 0.639518i | ||||
\(981\) | 2.53983e25i | 0.0301844i | ||||||||
\(982\) | 9.70132e26 | + | 6.44841e26i | 1.14242 | + | 0.759363i | ||||
\(983\) | − | 3.94343e26i | − | 0.460143i | −0.973174 | − | 0.230071i | \(-0.926104\pi\) | ||
0.973174 | − | 0.230071i | \(-0.0738960\pi\) | |||||||
\(984\) | 3.88505e26 | − | 2.02983e27i | 0.449201 | − | 2.34695i | ||||
\(985\) | −1.38191e27 | −1.58327 | ||||||||
\(986\) | −4.36591e25 | + | 6.56830e25i | −0.0495658 | + | 0.0745694i | ||||
\(987\) | 1.75740e26 | 0.197705 | ||||||||
\(988\) | −3.40795e25 | + | 1.43093e25i | −0.0379910 | + | 0.0159516i | ||||
\(989\) | 8.46471e26i | 0.935073i | ||||||||
\(990\) | 1.20533e26 | − | 1.81336e26i | 0.131944 | − | 0.198503i | ||||
\(991\) | − | 1.21537e27i | − | 1.31840i | −0.751968 | − | 0.659200i | \(-0.770895\pi\) | ||
0.751968 | − | 0.659200i | \(-0.229105\pi\) | |||||||
\(992\) | −2.45768e26 | − | 1.16210e27i | −0.264192 | − | 1.24922i | ||||
\(993\) | 8.14932e26 | 0.868116 | ||||||||
\(994\) | 2.29971e26 | + | 1.52860e26i | 0.242770 | + | 0.161368i | ||||
\(995\) | −1.38789e27 | −1.45194 | ||||||||
\(996\) | 1.47080e26 | + | 3.50291e26i | 0.152482 | + | 0.363158i | ||||
\(997\) | 8.41591e25i | 0.0864659i | 0.999065 | + | 0.0432330i | \(0.0137658\pi\) | ||||
−0.999065 | + | 0.0432330i | \(0.986234\pi\) | |||||||
\(998\) | 3.21582e26 | + | 2.13753e26i | 0.327429 | + | 0.217640i | ||||
\(999\) | 2.24451e27i | 2.26481i |
(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 | 8.19.d.b.3.1 | ✓ | 16 | |
3.2 | odd | 2 | 72.19.b.b.19.16 | 16 | |||
4.3 | odd | 2 | 32.19.d.b.15.1 | 16 | |||
8.3 | odd | 2 | inner | 8.19.d.b.3.2 | yes | 16 | |
8.5 | even | 2 | 32.19.d.b.15.2 | 16 | |||
24.11 | even | 2 | 72.19.b.b.19.15 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.19.d.b.3.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
8.19.d.b.3.2 | yes | 16 | 8.3 | odd | 2 | inner | |
32.19.d.b.15.1 | 16 | 4.3 | odd | 2 | |||
32.19.d.b.15.2 | 16 | 8.5 | even | 2 | |||
72.19.b.b.19.15 | 16 | 24.11 | even | 2 | |||
72.19.b.b.19.16 | 16 | 3.2 | odd | 2 |