Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [24,11,Mod(17,24)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("24.17");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.e (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: | \(15.2485740642\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 532 x^{8} - 1350 x^{7} + 106101 x^{6} + 516780 x^{5} - 8879077 x^{4} - 65126430 x^{3} + \cdots + 6338653425 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{72}\cdot 3^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 17.7 | ||
Root | \(10.3554 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 24.17 |
Dual form | 24.11.e.a.17.8 |
$q$-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 \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(13\) | \(17\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 171.197 | − | 172.454i | 0.704516 | − | 0.709688i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2896.26i | 0.926804i | 0.886148 | + | 0.463402i | \(0.153371\pi\) | ||||
−0.886148 | + | 0.463402i | \(0.846629\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −28955.7 | −1.72284 | −0.861419 | − | 0.507895i | \(-0.830424\pi\) | ||||
−0.861419 | + | 0.507895i | \(0.830424\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −431.864 | − | 59047.4i | −0.00731365 | − | 0.999973i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 194676.i | 1.20879i | 0.796687 | + | 0.604393i | \(0.206584\pi\) | ||||
−0.796687 | + | 0.604393i | \(0.793416\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −114481. | −0.308331 | −0.154166 | − | 0.988045i | \(-0.549269\pi\) | ||||
−0.154166 | + | 0.988045i | \(0.549269\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 499472. | + | 495833.i | 0.657741 | + | 0.652948i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 39710.7i | 0.0279681i | 0.999902 | + | 0.0139840i | \(0.00445140\pi\) | ||||
−0.999902 | + | 0.0139840i | \(0.995549\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.65684e6 | −1.88071 | −0.940357 | − | 0.340188i | \(-0.889509\pi\) | ||||
−0.940357 | + | 0.340188i | \(0.889509\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.95715e6 | + | 4.99354e6i | −1.21377 | + | 1.22268i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.57809e6i | 1.17739i | 0.808355 | + | 0.588695i | \(0.200358\pi\) | ||||
−0.808355 | + | 0.588695i | \(0.799642\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.37729e6 | 0.141035 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.02569e7 | − | 1.00343e7i | −0.714821 | − | 0.699307i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.03229e7i | 0.990824i | 0.868658 | + | 0.495412i | \(0.164983\pi\) | ||||
−0.868658 | + | 0.495412i | \(0.835017\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.24006e6 | −0.287821 | −0.143910 | − | 0.989591i | \(-0.545968\pi\) | ||||
−0.143910 | + | 0.989591i | \(0.545968\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.35727e7 | + | 3.33281e7i | 0.857860 | + | 0.851609i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 8.38634e7i | − | 1.59673i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.91039e7 | 0.275496 | 0.137748 | − | 0.990467i | \(-0.456014\pi\) | ||||
0.137748 | + | 0.990467i | \(0.456014\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.95989e7 | + | 1.97428e7i | −0.217225 | + | 0.218819i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.15568e8i | − | 0.997516i | −0.866741 | − | 0.498758i | \(-0.833790\pi\) | ||
0.866741 | − | 0.498758i | \(-0.166210\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.08453e6 | −0.0277843 | −0.0138922 | − | 0.999903i | \(-0.504422\pi\) | ||||
−0.0138922 | + | 0.999903i | \(0.504422\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.71017e8 | − | 1.25079e6i | 0.926779 | − | 0.00677832i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 2.81165e8i | − | 1.22595i | −0.790104 | − | 0.612973i | \(-0.789973\pi\) | ||
0.790104 | − | 0.612973i | \(-0.210027\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.55960e8 | 1.96817 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.84827e6 | + | 6.79836e6i | 0.0198486 | + | 0.0197040i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.33283e8i | 0.796954i | 0.917178 | + | 0.398477i | \(0.130461\pi\) | ||||
−0.917178 | + | 0.398477i | \(0.869539\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.63833e8 | −1.12031 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.97239e8 | + | 8.03091e8i | −1.32499 | + | 1.33472i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.23488e9i | − | 1.72729i | −0.504102 | − | 0.863644i | \(-0.668176\pi\) | ||
0.504102 | − | 0.863644i | \(-0.331824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.77494e8 | −0.683751 | −0.341876 | − | 0.939745i | \(-0.611062\pi\) | ||||
−0.341876 | + | 0.939745i | \(0.611062\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.25049e7 | + | 1.70976e9i | 0.0126002 | + | 1.72279i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 3.31568e8i | − | 0.285763i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.61148e8 | −0.637828 | −0.318914 | − | 0.947784i | \(-0.603318\pi\) | ||||
−0.318914 | + | 0.947784i | \(0.603318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.30687e9 | + | 1.29735e9i | 0.835579 | + | 0.829490i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.70435e9i | 0.944641i | 0.881427 | + | 0.472320i | \(0.156583\pi\) | ||||
−0.881427 | + | 0.472320i | \(0.843417\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.23189e8 | −0.397087 | −0.198543 | − | 0.980092i | \(-0.563621\pi\) | ||||
−0.198543 | + | 0.980092i | \(0.563621\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.35789e8 | − | 2.37520e8i | 0.0993612 | − | 0.100091i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.63699e9i | − | 2.08254i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.61377e9 | 1.17442 | 0.587212 | − | 0.809433i | \(-0.300225\pi\) | ||||
0.587212 | + | 0.809433i | \(0.300225\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.48641e9 | + | 5.10009e7i | −0.999893 | + | 0.0146269i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.05763e8i | 0.179171i | 0.995979 | + | 0.0895856i | \(0.0285543\pi\) | ||||
−0.995979 | + | 0.0895856i | \(0.971446\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.15012e8 | −0.0259209 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.50477e9 | + | 3.47923e9i | 0.703176 | + | 0.698052i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.89745e9i | − | 1.23520i | −0.786491 | − | 0.617602i | \(-0.788104\pi\) | ||
0.786491 | − | 0.617602i | \(-0.211896\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.31489e9 | 0.531205 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.41068e9 | + | 1.42103e9i | −0.202774 | + | 0.204263i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 1.34874e10i | − | 1.74305i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.18738e10 | 1.38271 | 0.691353 | − | 0.722517i | \(-0.257015\pi\) | ||||
0.691353 | + | 0.722517i | \(0.257015\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.14951e10 | − | 8.40736e7i | 1.20875 | − | 0.00884063i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.31279e10i | 1.24907i | 0.780995 | + | 0.624537i | \(0.214712\pi\) | ||||
−0.780995 | + | 0.624537i | \(0.785288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.80950e10 | −1.56089 | −0.780445 | − | 0.625225i | \(-0.785007\pi\) | ||||
−0.780445 | + | 0.625225i | \(0.785007\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.44626e10 | − | 1.43572e10i | −1.13318 | − | 1.12492i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.72427e10i | 1.94237i | 0.238334 | + | 0.971183i | \(0.423399\pi\) | ||||
−0.238334 | + | 0.971183i | \(0.576601\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.20673e9 | −0.208416 | −0.104208 | − | 0.994556i | \(-0.533231\pi\) | ||||
−0.104208 | + | 0.994556i | \(0.533231\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.27055e9 | − | 3.29456e9i | 0.194091 | − | 0.195516i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.35851e10i | 0.737342i | 0.929560 | + | 0.368671i | \(0.120187\pi\) | ||||
−0.929560 | + | 0.368671i | \(0.879813\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.19481e10 | −1.09121 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.94403e7 | + | 6.75983e9i | 0.00225503 | + | 0.308323i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.14985e9i | − | 0.0481844i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.19614e10 | −0.461162 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.99303e10 | − | 1.97850e10i | −0.707925 | − | 0.702766i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.22728e10i | 1.05752i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.49525e9 | −0.0755259 | −0.0377629 | − | 0.999287i | \(-0.512023\pi\) | ||||
−0.0377629 | + | 0.999287i | \(0.512023\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.99261e8 | + | 7.04394e8i | −0.0195745 | + | 0.0197182i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.63293e9i | 0.197849i | 0.995095 | + | 0.0989247i | \(0.0315403\pi\) | ||||
−0.995095 | + | 0.0989247i | \(0.968460\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.34842e11 | 3.24017 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.90619e10 | − | 2.97067e10i | 0.648120 | − | 0.662499i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.02271e9i | − | 0.166233i | −0.996540 | − | 0.0831167i | \(-0.973513\pi\) | ||
0.996540 | − | 0.0831167i | \(-0.0264874\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.71352e10 | −0.908389 | −0.454194 | − | 0.890903i | \(-0.650073\pi\) | ||||
−0.454194 | + | 0.890903i | \(0.650073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.84880e10 | − | 4.81347e10i | −0.870039 | − | 0.863699i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2.22868e10i | − | 0.372707i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.88605e10 | −0.918299 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.51789e10 | − | 9.58776e10i | 1.38661 | − | 1.39679i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.14868e10i | 1.24574i | 0.782325 | + | 0.622870i | \(0.214033\pi\) | ||||
−0.782325 | + | 0.622870i | \(0.785967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.96294e10 | −0.759583 | −0.379792 | − | 0.925072i | \(-0.624004\pi\) | ||||
−0.379792 | + | 0.925072i | \(0.624004\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.34481e9 | − | 1.71496e7i | 0.0279673 | − | 0.000204549i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.38654e10i | − | 0.266753i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.63632e11 | 1.71542 | 0.857711 | − | 0.514133i | \(-0.171886\pi\) | ||||
0.857711 | + | 0.514133i | \(0.171886\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.74760e10 | + | 5.70571e10i | 0.565589 | + | 0.561467i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.19429e11i | − | 2.02845i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.15923e10 | 0.448380 | 0.224190 | − | 0.974545i | \(-0.428026\pi\) | ||||
0.224190 | + | 0.974545i | \(0.428026\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.65268e10 | + | 9.72353e10i | −0.789275 | + | 0.795068i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.56828e11i | 1.20737i | 0.797222 | + | 0.603686i | \(0.206302\pi\) | ||||
−0.797222 | + | 0.603686i | \(0.793698\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.24753e11 | −0.904932 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.01112e9 | + | 2.74974e11i | 0.0137549 | + | 1.88066i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.19891e9i | − | 0.0400023i | −0.999800 | − | 0.0200012i | \(-0.993633\pi\) | ||
0.999800 | − | 0.0200012i | \(-0.00636699\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.98805e10 | −0.242980 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.12960e11 | − | 2.11408e11i | −1.22584 | − | 1.21690i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 6.16221e10i | − | 0.335329i | −0.985844 | − | 0.167665i | \(-0.946377\pi\) | ||
0.985844 | − | 0.167665i | \(-0.0536226\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.01755e11 | −1.03856 | −0.519280 | − | 0.854604i | \(-0.673800\pi\) | ||||
−0.519280 | + | 0.854604i | \(0.673800\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.88655e10 | + | 9.95912e10i | −0.481714 | + | 0.485250i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.53300e10i | 0.255330i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.73072e9 | −0.0338074 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.96996e11 | + | 2.90550e11i | 1.23152 | + | 1.20479i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.09166e9i | 0.0318325i | 0.999873 | + | 0.0159163i | \(0.00506651\pi\) | ||||
−0.999873 | + | 0.0159163i | \(0.994933\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.16879e11 | −0.436465 | −0.218232 | − | 0.975897i | \(-0.570029\pi\) | ||||
−0.218232 | + | 0.975897i | \(0.570029\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.71802e10 | − | 5.67636e10i | −0.202802 | − | 0.201325i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.95881e10i | 0.167127i | 0.996502 | + | 0.0835634i | \(0.0266301\pi\) | ||||
−0.996502 | + | 0.0835634i | \(0.973370\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.11416e11 | 0.997872 | 0.498936 | − | 0.866639i | \(-0.333724\pi\) | ||||
0.498936 | + | 0.866639i | \(0.333724\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.47426e11 | + | 1.48509e11i | −0.449360 | + | 0.452659i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 5.88466e11i | − | 1.70703i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.34716e11 | 0.924502 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.47466e11 | − | 3.27270e9i | 1.17736 | − | 0.00861102i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 9.06575e11i | − | 2.27338i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.14486e11 | −0.273740 | −0.136870 | − | 0.990589i | \(-0.543704\pi\) | ||||
−0.136870 | + | 0.990589i | \(0.543704\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.93922e11 | + | 2.91780e11i | 0.670400 | + | 0.665515i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.18299e10i | − | 0.0257506i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.38597e11 | 0.495869 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.40928e11 | + | 1.41962e11i | −0.279754 | + | 0.281808i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4.54613e9i | − | 0.00862343i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.84007e11 | −1.05899 | −0.529497 | − | 0.848312i | \(-0.677619\pi\) | ||||
−0.529497 | + | 0.848312i | \(0.677619\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.94802e8 | − | 8.13255e10i | −0.00103148 | − | 0.141031i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.76098e11i | 0.789891i | 0.918705 | + | 0.394946i | \(0.129237\pi\) | ||||
−0.918705 | + | 0.394946i | \(0.870763\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.81466e11 | 0.605729 | 0.302864 | − | 0.953034i | \(-0.402057\pi\) | ||||
0.302864 | + | 0.953034i | \(0.402057\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.72123e11 | − | 9.65039e11i | −1.47795 | − | 1.46718i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.06247e11i | 1.17405i | 0.809567 | + | 0.587027i | \(0.199702\pi\) | ||||
−0.809567 | + | 0.587027i | \(0.800298\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.14326e11 | 1.13621 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.18668e11 | − | 6.23210e11i | 0.827401 | − | 0.833475i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.67498e11i | − | 1.11245i | −0.831033 | − | 0.556223i | \(-0.812250\pi\) | ||
0.831033 | − | 0.556223i | \(-0.187750\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.44941e11 | −0.916298 | −0.458149 | − | 0.888875i | \(-0.651487\pi\) | ||||
−0.458149 | + | 0.888875i | \(0.651487\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.88069e11 | + | 6.09977e11i | −0.694060 | + | 0.719917i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.61021e12i | 1.82411i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.33121e11 | 0.579884 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.21712e11 | + | 1.20825e11i | 0.127156 | + | 0.126229i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.82693e11i | 0.986391i | 0.869919 | + | 0.493195i | \(0.164171\pi\) | ||||
−0.869919 | + | 0.493195i | \(0.835829\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.47527e12 | −1.42321 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.96898e10 | + | 1.98344e10i | −0.0182617 | + | 0.0183958i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.47313e11i | 0.488169i | 0.969754 | + | 0.244084i | \(0.0784874\pi\) | ||||
−0.969754 | + | 0.244084i | \(0.921513\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.53169e11 | −0.474634 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.20002e12 | − | 8.77674e9i | 0.990797 | − | 0.00724654i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.74576e11i | 0.297688i | 0.988861 | + | 0.148844i | \(0.0475552\pi\) | ||||
−0.988861 | + | 0.148844i | \(0.952445\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.65274e11 | −0.738620 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.18949e12 | − | 1.18083e12i | −0.876609 | − | 0.870221i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.13820e11i | − | 0.222802i | −0.993776 | − | 0.111401i | \(-0.964466\pi\) | ||
0.993776 | − | 0.111401i | \(-0.0355338\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.64330e11 | −0.249257 | −0.124629 | − | 0.992203i | \(-0.539774\pi\) | ||||
−0.124629 | + | 0.992203i | \(0.539774\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.67501e11 | − | 5.71667e11i | 0.374243 | − | 0.376990i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.68126e11i | 0.170481i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.46521e11 | −0.396446 | −0.198223 | − | 0.980157i | \(-0.563517\pi\) | ||||
−0.198223 | + | 0.980157i | \(0.563517\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.55858e9 | + | 4.86554e11i | 0.00210502 | + | 0.287813i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.02357e11i | − | 0.286735i | −0.989670 | − | 0.143367i | \(-0.954207\pi\) | ||
0.989670 | − | 0.143367i | \(-0.0457931\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.08013e12 | 1.69682 | 0.848412 | − | 0.529337i | \(-0.177559\pi\) | ||||
0.848412 | + | 0.529337i | \(0.177559\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.32596e12 | − | 2.30901e12i | −1.23702 | − | 1.22801i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.34637e12i | 1.71856i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.01442e12 | 0.999218 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.03276e12 | − | 2.04768e12i | 0.974139 | − | 0.981290i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.63922e12i | − | 0.759102i | −0.925171 | − | 0.379551i | \(-0.876078\pi\) | ||
0.925171 | − | 0.379551i | \(-0.123922\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.57654e12 | 1.60086 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.95344e12 | − | 1.99677e12i | 0.845312 | − | 0.864066i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 8.67549e11i | − | 0.363026i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.18271e11 | 0.0478679 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.26396e12 | + | 2.24746e12i | 0.886453 | + | 0.879993i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.67257e12i | − | 0.633703i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.92793e12 | −0.706968 | −0.353484 | − | 0.935441i | \(-0.615003\pi\) | ||||
−0.353484 | + | 0.935441i | \(0.615003\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.09781e12 | + | 3.12055e12i | −1.09967 | + | 1.10774i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2.19382e12i | − | 0.754048i | −0.926203 | − | 0.377024i | \(-0.876947\pi\) | ||
0.926203 | − | 0.377024i | \(-0.123053\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.54264e12 | −0.846377 | −0.423189 | − | 0.906042i | \(-0.639089\pi\) | ||||
−0.423189 | + | 0.906042i | \(0.639089\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.95192e12 | + | 3.62176e10i | −1.59669 | + | 0.0116779i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4.30864e12i | − | 1.34600i | −0.739645 | − | 0.672998i | \(-0.765006\pi\) | ||
0.739645 | − | 0.672998i | \(-0.234994\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.95639e12 | −1.19769 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.69812e12 | + | 4.66388e12i | 1.37847 | + | 1.36843i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.84926e11i | − | 0.0526000i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.57674e11 | −0.0434854 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.48984e11 | + | 5.53014e11i | −0.146832 | + | 0.147910i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.14133e12i | 2.11211i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.00163e12 | 1.25884 | 0.629422 | − | 0.777064i | \(-0.283292\pi\) | ||||
0.629422 | + | 0.777064i | \(0.283292\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.25030e9 | − | 1.12804e12i | −0.00201488 | − | 0.275488i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 2.49411e12i | − | 0.591142i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.46058e12 | −0.336028 | −0.168014 | − | 0.985785i | \(-0.553735\pi\) | ||||
−0.168014 | + | 0.985785i | \(0.553735\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.34280e12 | + | 2.32573e12i | 0.523283 | + | 0.519470i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.60414e12i | − | 0.347914i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.91895e12 | −1.66800 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.75746e12 | + | 3.78504e12i | −0.768775 | + | 0.774418i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.30574e12i | 0.259543i | 0.991544 | + | 0.129772i | \(0.0414244\pi\) | ||||
−0.991544 | + | 0.129772i | \(0.958576\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.59463e11 | 0.0307987 | 0.0153993 | − | 0.999881i | \(-0.495098\pi\) | ||||
0.0153993 | + | 0.999881i | \(0.495098\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.17422e12 | + | 1.14874e12i | 0.220402 | + | 0.215618i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.32899e12i | 0.607350i | 0.952776 | + | 0.303675i | \(0.0982138\pi\) | ||||
−0.952776 | + | 0.303675i | \(0.901786\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.93624e12 | −0.875497 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.98297e11 | − | 1.96852e11i | −0.0341959 | − | 0.0339467i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.56753e12i | − | 1.10136i | −0.834716 | − | 0.550681i | \(-0.814368\pi\) | ||
0.834716 | − | 0.550681i | \(-0.185632\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.55551e13 | 2.53709 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.04776e12 | + | 2.06279e12i | −0.324896 | + | 0.327281i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 2.38417e12i | − | 0.368021i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.57363e12 | −0.386559 | −0.193279 | − | 0.981144i | \(-0.561912\pi\) | ||||
−0.193279 | + | 0.981144i | \(0.561912\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.82402e12 | + | 4.99098e10i | −0.997489 | + | 0.00729548i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 9.65045e12i | − | 1.37302i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.63844e12 | −0.365428 | −0.182714 | − | 0.983166i | \(-0.558488\pi\) | ||||
−0.182714 | + | 0.983166i | \(0.558488\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.56558e12 | + | 5.52502e12i | 0.750506 | + | 0.745037i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.32660e12i | − | 0.305502i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.18638e12 | −0.151715 | −0.0758573 | − | 0.997119i | \(-0.524169\pi\) | ||||
−0.0758573 | + | 0.997119i | \(0.524169\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.27181e11 | + | 4.30317e11i | −0.0532092 | + | 0.0535998i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.81521e11i | 0.0341599i | 0.999854 | + | 0.0170799i | \(0.00543698\pi\) | ||||
−0.999854 | + | 0.0170799i | \(0.994563\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.63262e13 | 1.93011 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.76396e9 | + | 2.41181e11i | 0.000203205 | + | 0.0277836i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 9.28352e12i | − | 1.04223i | −0.853486 | − | 0.521117i | \(-0.825516\pi\) | ||
0.853486 | − | 0.521117i | \(-0.174484\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.00931e11 | −0.0329293 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.31633e12 | + | 1.30674e12i | 0.140411 | + | 0.139388i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.04664e13i | 1.08846i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.05417e12 | −0.613907 | −0.306953 | − | 0.951725i | \(-0.599310\pi\) | ||||
−0.306953 | + | 0.951725i | \(0.599310\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.30846e13 | − | 2.32541e13i | 2.28275 | − | 2.29951i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.02940e13i | − | 0.992803i | −0.868093 | − | 0.496401i | \(-0.834654\pi\) | ||
0.868093 | − | 0.496401i | \(-0.165346\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.43333e11 | 0.0887442 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.47712e11 | − | 1.00976e13i | −0.0135563 | − | 0.926705i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.71908e12i | 0.333015i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.30585e11 | 0.0376220 | 0.0188110 | − | 0.999823i | \(-0.494012\pi\) | ||||
0.0188110 | + | 0.999823i | \(0.494012\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.38355e12 | − | 1.37347e12i | −0.117974 | − | 0.117114i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.57569e13i | 2.97584i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.04407e12 | −0.166057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.06943e12 | + | 8.12867e12i | −0.639974 | + | 0.644672i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.34433e12i | 0.258964i | 0.991582 | + | 0.129482i | \(0.0413315\pi\) | ||||
−0.991582 | + | 0.129482i | \(0.958669\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.21958e13 | −0.922145 | −0.461073 | − | 0.887362i | \(-0.652535\pi\) | ||||
−0.461073 | + | 0.887362i | \(0.652535\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.66020e13 | + | 1.21425e11i | −1.22591 | + | 0.00896614i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.46931e10i | 0.00394446i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.67218e13 | 1.17799 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.84345e12 | − | 3.81544e12i | −0.264505 | − | 0.262578i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.44756e13i | 1.64568i | 0.568270 | + | 0.822842i | \(0.307613\pi\) | ||||
−0.568270 | + | 0.822842i | \(0.692387\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.53458e13 | −1.66520 | −0.832601 | − | 0.553873i | \(-0.813149\pi\) | ||||
−0.832601 | + | 0.553873i | \(0.813149\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.00768e13 | + | 1.01507e13i | −0.646957 | + | 0.651706i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 3.52899e13i | − | 2.21433i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.40755e13 | −1.47656 | −0.738282 | − | 0.674492i | \(-0.764363\pi\) | ||||
−0.738282 | + | 0.674492i | \(0.764363\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.40099e11 | − | 3.28280e13i | −0.0143945 | − | 1.96812i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.24137e13i | 0.727585i | 0.931480 | + | 0.363792i | \(0.118518\pi\) | ||||
−0.931480 | + | 0.363792i | \(0.881482\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.99768e13 | 1.14479 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.57773e13 | + | 1.56623e13i | 0.884086 | + | 0.877644i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.90273e13i | 1.59065i | 0.606181 | + | 0.795327i | \(0.292701\pi\) | ||||
−0.606181 | + | 0.795327i | \(0.707299\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.24984e13 | 1.20578 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.02084e13 | + | 1.02833e13i | −0.535139 | + | 0.539067i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.60079e12i | 0.492323i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.83053e12 | −0.342668 | −0.171334 | − | 0.985213i | \(-0.554808\pi\) | ||||
−0.171334 | + | 0.985213i | \(0.554808\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.98468e11 | − | 4.07308e11i | 0.0195583 | − | 0.0199922i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.98477e12i | 0.431522i | 0.976446 | + | 0.215761i | \(0.0692231\pi\) | ||||
−0.976446 | + | 0.215761i | \(0.930777\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.37787e13 | −0.647595 | −0.323797 | − | 0.946126i | \(-0.604960\pi\) | ||||
−0.323797 | + | 0.946126i | \(0.604960\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.11568e12 | − | 4.08569e12i | −0.189312 | − | 0.187932i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 1.44791e13i | − | 0.651866i | −0.945393 | − | 0.325933i | \(-0.894322\pi\) | ||
0.945393 | − | 0.325933i | \(-0.105678\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.49352e13 | 1.09887 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.80134e13 | − | 2.82191e13i | 1.20854 | − | 1.21741i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7.95161e11i | − | 0.0335853i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.41382e12 | −0.265246 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.96795e13 | − | 1.43933e11i | 0.796933 | − | 0.00582864i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 1.56308e13i | − | 0.619876i | −0.950757 | − | 0.309938i | \(-0.899692\pi\) | ||
0.950757 | − | 0.309938i | \(-0.100308\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.18704e12 | −0.0849439 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.78415e13 | − | 3.75657e13i | −1.43957 | − | 1.42908i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.43896e13i | 1.28150i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.42315e12 | 0.124963 | 0.0624815 | − | 0.998046i | \(-0.480099\pi\) | ||||
0.0624815 | + | 0.998046i | \(0.480099\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.83246e12 | − | 8.89730e12i | 0.315891 | − | 0.318210i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4.18001e13i | − | 1.46477i | −0.680891 | − | 0.732385i | \(-0.738407\pi\) | ||
0.680891 | − | 0.732385i | \(-0.261593\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.07037e11 | −0.0277114 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.43499e11 | + | 3.32929e13i | 0.00819353 | + | 1.12028i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 4.93507e13i | − | 1.62746i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.50002e12 | 0.307059 | 0.153529 | − | 0.988144i | \(-0.450936\pi\) | ||||
0.153529 | + | 0.988144i | \(0.450936\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.70456e13 | + | 2.68485e13i | 0.856857 | + | 0.850613i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.27832e12i | − | 0.0397007i | −0.999803 | − | 0.0198504i | \(-0.993681\pi\) | ||
0.999803 | − | 0.0198504i | \(-0.00631898\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.80218e13 | −1.15765 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.13573e13 | + | 2.15141e13i | −0.637539 | + | 0.642219i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.67555e11i | 0.0283196i | 0.999900 | + | 0.0141598i | \(0.00450735\pi\) | ||||
−0.999900 | + | 0.0141598i | \(0.995493\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.38361e13 | 0.684116 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.77647e13 | + | 4.67281e13i | 1.34438 | + | 1.31520i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 5.24078e13i | − | 1.44664i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.47360e13 | 1.48191 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.06903e12 | − | 1.06124e12i | −0.0283891 | − | 0.0281823i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2.98648e13i | − | 0.777985i | −0.921241 | − | 0.388992i | \(-0.872823\pi\) | ||
0.921241 | − | 0.388992i | \(-0.127177\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.68489e13 | 1.45283 | 0.726413 | − | 0.687259i | \(-0.241186\pi\) | ||||
0.726413 | + | 0.687259i | \(0.241186\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.82744e12 | + | 6.87755e12i | −0.171183 | + | 0.172440i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 3.27218e11i | − | 0.00804979i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.60009e13 | −0.386247 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.29165e13 | + | 5.33300e11i | −1.72724 | + | 0.0126328i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.32304e13i | 0.307566i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.89020e13 | −1.80019 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.06270e13 | − | 1.05496e13i | −0.237979 | − | 0.236245i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.08232e14i | 2.37910i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.15417e13 | −0.680610 | −0.340305 | − | 0.940315i | \(-0.610530\pi\) | ||||
−0.340305 | + | 0.940315i | \(0.610530\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.45400e13 | + | 3.47935e13i | −0.731683 | + | 0.737054i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 9.28754e12i | − | 0.193160i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.80363e13 | 0.572511 | 0.286256 | − | 0.958153i | \(-0.407589\pi\) | ||||
0.286256 | + | 0.958153i | \(0.407589\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.49399e11 | + | 3.40995e13i | 0.00500072 | + | 0.683733i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 9.46406e13i | − | 1.86346i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.04639e14 | −2.02334 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.54190e12 | + | 9.47236e12i | 0.181205 | + | 0.179884i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.80012e13i | 0.708796i | 0.935095 | + | 0.354398i | \(0.115314\pi\) | ||||
−0.935095 | + | 0.354398i | \(0.884686\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.67602e11 | 0.00856678 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.32348e12 | + | 1.33319e12i | −0.0238179 | + | 0.0239927i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.97052e13i | 1.58590i | 0.609287 | + | 0.792950i | \(0.291456\pi\) | ||||
−0.609287 | + | 0.792950i | \(0.708544\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.93459e13 | −0.683372 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00952e14 | − | 1.47677e12i | 1.72265 | − | 0.0251998i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 7.70896e13i | − | 1.29251i | −0.763121 | − | 0.646256i | \(-0.776334\pi\) | ||
0.763121 | − | 0.646256i | \(-0.223666\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.45952e13 | 0.899444 | 0.449722 | − | 0.893169i | \(-0.351523\pi\) | ||||
0.449722 | + | 0.893169i | \(0.351523\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.39544e12 | + | 1.38527e12i | 0.0225911 | + | 0.0224265i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.04372e13i | 0.166053i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.32936e13 | 0.676932 | 0.338466 | − | 0.940979i | \(-0.390092\pi\) | ||||
0.338466 | + | 0.940979i | \(0.390092\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.00093e13 | + | 2.01562e13i | −0.307496 | + | 0.309754i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.04359e13i | − | 0.308683i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.48822e13 | −0.963347 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.95782e13 | + | 1.43192e11i | −0.285755 | + | 0.00208997i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 6.69167e13i | − | 0.960161i | −0.877224 | − | 0.480080i | \(-0.840607\pi\) | ||
0.877224 | − | 0.480080i | \(-0.159393\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.83726e13 | 0.541309 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.55167e12 | + | 8.48935e12i | 0.118608 | + | 0.117744i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.42544e13i | 0.467136i | 0.972340 | + | 0.233568i | \(0.0750401\pi\) | ||||
−0.972340 | + | 0.233568i | \(0.924960\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.33027e12 | 0.0446575 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.33136e13 | − | 5.37049e13i | 0.703017 | − | 0.708178i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.09769e14i | − | 1.42346i | −0.702455 | − | 0.711728i | \(-0.747913\pi\) | ||
0.702455 | − | 0.711728i | \(-0.252087\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.21221e14 | 1.54598 | 0.772990 | − | 0.634418i | \(-0.218760\pi\) | ||||
0.772990 | + | 0.634418i | \(0.218760\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.71899e11 | + | 5.08486e13i | 0.00466485 | + | 0.637811i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 3.46432e13i | − | 0.427407i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.42306e14 | 1.72695 | 0.863473 | − | 0.504394i | \(-0.168284\pi\) | ||||
0.863473 | + | 0.504394i | \(0.168284\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.01483e14 | − | 1.00744e14i | −1.21146 | − | 1.20263i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.21881e13i | 0.377998i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.15590e14 | −1.33542 | −0.667711 | − | 0.744421i | \(-0.732726\pi\) | ||||
−0.667711 | + | 0.744421i | \(0.732726\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.73026e13 | − | 5.77232e13i | 0.651326 | − | 0.656108i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.06571e13i | 0.902021i | 0.892519 | + | 0.451011i | \(0.148936\pi\) | ||||
−0.892519 | + | 0.451011i | \(0.851064\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.74323e14 | 1.91823 | 0.959115 | − | 0.283015i | \(-0.0913347\pi\) | ||||
0.959115 | + | 0.283015i | \(0.0913347\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.60407e13 | − | 7.77277e13i | 0.823357 | − | 0.841624i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.99721e14i | 2.12806i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.00204e13 | −0.839075 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.56343e14 | − | 1.55203e14i | −1.61339 | − | 1.60163i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.58630e11i | 0.00770508i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.66535e14 | −1.66479 | −0.832393 | − | 0.554185i | \(-0.813030\pi\) | ||||
−0.832393 | + | 0.554185i | \(0.813030\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.95996e13 | + | 1.97435e13i | −0.192854 | + | 0.194270i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 7.22690e12i | − | 0.0699977i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.36470e13 | −0.606849 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.00637e14 | − | 7.36046e11i | 0.944616 | − | 0.00690877i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 3.87340e13i | − | 0.357933i | −0.983855 | − | 0.178967i | \(-0.942725\pi\) | ||
0.983855 | − | 0.178967i | \(-0.0572754\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.69076e13 | −0.881664 | −0.440832 | − | 0.897590i | \(-0.645316\pi\) | ||||
−0.440832 | + | 0.897590i | \(0.645316\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.04011e12 | − | 2.02524e12i | −0.0182749 | − | 0.0181417i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.22038e14i | 1.95842i | 0.202856 | + | 0.979209i | \(0.434978\pi\) | ||||
−0.202856 | + | 0.979209i | \(0.565022\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.40402e14 | 2.08792 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.08472e13 | − | 4.11471e13i | 0.349347 | − | 0.351912i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.00663e14i | − | 0.847823i | −0.905704 | − | 0.423912i | \(-0.860657\pi\) | ||
0.905704 | − | 0.423912i | \(-0.139343\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.21070e13 | −0.183368 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.55506e11 | + | 4.86072e13i | 0.00290415 | + | 0.397076i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.49486e14i | − | 1.20274i | −0.798970 | − | 0.601371i | \(-0.794621\pi\) | ||
0.798970 | − | 0.601371i | \(-0.205379\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.32290e14 | 1.04838 | 0.524191 | − | 0.851601i | \(-0.324368\pi\) | ||||
0.524191 | + | 0.851601i | \(0.324368\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.83998e11 | − | 7.78285e11i | −0.00611995 | − | 0.00607535i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.90538e14i | 3.00300i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.54009e14 | −1.16659 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.99805e13 | + | 1.00714e14i | −0.746079 | + | 0.751556i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.12424e14i | − | 0.826509i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.71199e13 | −0.413726 | −0.206863 | − | 0.978370i | \(-0.566325\pi\) | ||||
−0.206863 | + | 0.978370i | \(0.566325\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.41267e13 | − | 1.38201e13i | −0.100815 | − | 0.0986265i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.69430e13i | 0.189454i | 0.995503 | + | 0.0947269i | \(0.0301978\pi\) | ||||
−0.995503 | + | 0.0947269i | \(0.969802\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.43814e14 | −2.38218 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.21051e13 | + | 8.15068e13i | 0.560576 | + | 0.556491i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.11908e14i | 1.42575i | 0.701289 | + | 0.712877i | \(0.252608\pi\) | ||||
−0.701289 | + | 0.712877i | \(0.747392\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.32359e13 | 0.154066 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.53060e13 | − | 6.57854e13i | 0.426746 | − | 0.429878i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 3.81546e13i | − | 0.245726i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.02683e13 | 0.446035 | 0.223018 | − | 0.974814i | \(-0.428409\pi\) | ||||
0.223018 | + | 0.974814i | \(0.428409\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.32850e14 | + | 2.43441e12i | −2.08249 | + | 0.0152310i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 1.36516e14i | − | 0.841898i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.58930e12 | 0.0278986 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.39041e14 | + | 1.38027e14i | 0.833212 | + | 0.827141i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.48408e14i | 0.876734i | 0.898796 | + | 0.438367i | \(0.144443\pi\) | ||||
−0.898796 | + | 0.438367i | \(0.855557\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.89640e13 | −0.518129 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.39411e14 | − | 1.40434e14i | 0.800479 | − | 0.806355i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 3.80128e14i | − | 2.15195i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.47672e13 | −0.417330 | −0.208665 | − | 0.977987i | \(-0.566912\pi\) | ||||
−0.208665 | + | 0.977987i | \(0.566912\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.56066e12 | − | 2.13384e14i | −0.00858933 | − | 1.17439i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.24439e13i | − | 0.338877i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.45483e13 | 0.345426 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.49604e14 | − | 1.48514e14i | −0.789490 | − | 0.783737i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.07074e14i | 1.07766i | 0.842415 | + | 0.538829i | \(0.181133\pi\) | ||||
−0.842415 | + | 0.538829i | \(0.818867\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.23954e14 | 2.68916 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.27532e14 | + | 1.28468e14i | −0.645547 | + | 0.650286i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.79906e13i | 0.139740i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.67871e14 | 0.826615 | 0.413307 | − | 0.910592i | \(-0.364374\pi\) | ||||
0.413307 | + | 0.910592i | \(0.364374\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.51713e12 | + | 2.05842e14i | 0.0219394 | + | 0.999759i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.62199e11i | − | 0.000777074i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.75732e14 | 1.30307 | 0.651535 | − | 0.758618i | \(-0.274125\pi\) | ||||
0.651535 | + | 0.758618i | \(0.274125\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.77687e14 | + | 2.75663e14i | 1.29455 | + | 1.28511i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.67645e14i | − | 0.770998i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.56316e13 | 0.0709220 | 0.0354610 | − | 0.999371i | \(-0.488710\pi\) | ||||
0.0354610 | + | 0.999371i | \(0.488710\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.12689e13 | − | 9.19389e13i | 0.408537 | − | 0.411536i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.10001e14i | − | 0.927420i | −0.885987 | − | 0.463710i | \(-0.846518\pi\) | ||
0.885987 | − | 0.463710i | \(-0.153482\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.64970e14 | −1.15456 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.16735e13 | − | 3.04793e11i | 0.179166 | − | 0.00131040i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 7.88832e14i | − | 3.34638i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.85250e14 | 0.775457 | 0.387729 | − | 0.921774i | \(-0.373260\pi\) | ||||
0.387729 | + | 0.921774i | \(0.373260\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.69469e14 | + | 1.68234e14i | 0.700030 | + | 0.694928i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.72702e14i | − | 0.703985i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.17483e14 | −1.27715 | −0.638574 | − | 0.769561i | \(-0.720475\pi\) | ||||
−0.638574 | + | 0.769561i | \(0.720475\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.52563e14 | + | 2.54417e14i | −1.00268 | + | 1.01004i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.60646e14i | − | 1.02124i | −0.859807 | − | 0.510620i | \(-0.829416\pi\) | ||
0.859807 | − | 0.510620i | \(-0.170584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.28533e13 | 0.359066 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.96697e10 | + | 6.79119e12i | 0.000189576 | + | 0.0259202i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.41371e14i | 0.532577i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.97900e14 | −1.47959 | −0.739797 | − | 0.672830i | \(-0.765079\pi\) | ||||
−0.739797 | + | 0.672830i | \(0.765079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.43864e13 | + | 9.36986e13i | 0.346448 | + | 0.343923i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.65561e13i | 0.349850i | 0.984582 | + | 0.174925i | \(0.0559683\pi\) | ||||
−0.984582 | + | 0.174925i | \(0.944032\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.13490e13 | −0.0405927 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.47011e13 | + | 9.53963e13i | −0.334388 | + | 0.336842i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.38183e14i | 1.87604i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.31796e14 | −1.14187 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.03926e14 | − | 2.08450e14i | 0.692890 | − | 0.708262i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.73922e14i | 1.58986i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.67204e14 | −0.553826 | −0.276913 | − | 0.960895i | \(-0.589311\pi\) | ||||
−0.276913 | + | 0.960895i | \(0.589311\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.45972e13 | + | 6.41265e13i | 0.211266 | + | 0.209726i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.93365e14i | − | 1.27032i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.61122e13 | 0.210822 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.65252e14 | + | 1.66465e14i | −0.520370 | + | 0.524190i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.24257e14i | 0.697355i | 0.937243 | + | 0.348678i | \(0.113369\pi\) | ||||
−0.937243 | + | 0.348678i | \(0.886631\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.11652e13 | 0.0342873 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.07277e14 | + | 2.97876e12i | −1.23517 | + | 0.00903385i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.60255e14i | − | 0.479993i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.35524e14 | 1.87998 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.41196e13 | − | 5.37252e13i | −0.158120 | − | 0.156968i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.61446e13i | − | 0.162019i | −0.996713 | − | 0.0810094i | \(-0.974186\pi\) | ||
0.996713 | − | 0.0810094i | \(-0.0258144\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.29094e14 | 0.652994 | 0.326497 | − | 0.945198i | \(-0.394132\pi\) | ||||
0.326497 | + | 0.945198i | \(0.394132\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.23723e13 | + | 6.28302e13i | −0.175606 | + | 0.176895i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.49425e14i | 0.415561i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.90210e13 | 0.0522544 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.43158e12 | − | 1.95736e14i | −0.00388505 | − | 0.531191i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.07005e13i | 0.0286872i | 0.999897 | + | 0.0143436i | \(0.00456586\pi\) | ||||
−0.999897 | + | 0.0143436i | \(0.995434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.45374e14 | −0.385023 | −0.192511 | − | 0.981295i | \(-0.561663\pi\) | ||||
−0.192511 | + | 0.981295i | \(0.561663\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.62394e13 | + | 4.59024e13i | 0.120988 | + | 0.120106i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.18994e14i | 1.85865i | 0.369263 | + | 0.929325i | \(0.379610\pi\) | ||||
−0.369263 | + | 0.929325i | \(0.620390\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.70290e14 | −1.45654 | −0.728272 | − | 0.685288i | \(-0.759676\pi\) | ||||
−0.728272 | + | 0.685288i | \(0.759676\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.10683e14 | + | 1.11495e14i | −0.279302 | + | 0.281353i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.20775e13i | 0.0550459i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.54215e14 | −1.11900 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.45176e13 | + | 8.26832e13i | 0.205740 | + | 0.201275i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 2.29884e14i | − | 0.552967i | −0.961019 | − | 0.276483i | \(-0.910831\pi\) | ||
0.961019 | − | 0.276483i | \(-0.0891690\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.68552e12 | 0.0182681 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.66335e13 | − | 8.60022e13i | −0.203492 | − | 0.202009i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 3.61316e14i | − | 0.838694i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.46350e14 | 0.794508 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.27310e14 | − | 5.31181e14i | 1.19544 | − | 1.20421i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.44771e14i | 0.324366i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.32069e13 | −0.0956772 | −0.0478386 | − | 0.998855i | \(-0.515233\pi\) | ||||
−0.0478386 | + | 0.998855i | \(0.515233\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.96397e14 | + | 5.82473e12i | −1.74301 | + | 0.0127481i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 4.26827e14i | − | 0.923311i | −0.887059 | − | 0.461656i | \(-0.847256\pi\) | ||
0.887059 | − | 0.461656i | \(-0.152744\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.71870e14 | 1.43655 | 0.718273 | − | 0.695761i | \(-0.244933\pi\) | ||||
0.718273 | + | 0.695761i | \(0.244933\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.77095e14 | + | 5.72890e14i | 1.21964 | + | 1.21075i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 4.48581e13i | − | 0.0937102i | −0.998902 | − | 0.0468551i | \(-0.985080\pi\) | ||
0.998902 | − | 0.0468551i | \(-0.0149199\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.79537e13 | 0.0370743 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.44863e14 | − | 3.47395e14i | 0.703965 | − | 0.709133i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.03515e14i | 1.41963i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.85853e13 | 0.196662 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.12785e12 | − | 7.01116e14i | −0.0101126 | − | 1.38267i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 9.34483e14i | − | 1.82193i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.48985e14 | 0.287174 | 0.143587 | − | 0.989638i | \(-0.454136\pi\) | ||||
0.143587 | + | 0.989638i | \(0.454136\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.82691e14 | − | 2.80631e14i | −0.538726 | − | 0.534800i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.70640e14i | 1.45202i | 0.687685 | + | 0.726009i | \(0.258627\pi\) | ||||
−0.687685 | + | 0.726009i | \(0.741373\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.72274e14 | −0.693521 | −0.346761 | − | 0.937954i | \(-0.612718\pi\) | ||||
−0.346761 | + | 0.937954i | \(0.612718\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.12294e14 | − | 6.16789e14i | 1.12783 | − | 1.13611i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.00591e14i | − | 0.183207i | −0.995796 | − | 0.0916034i | \(-0.970801\pi\) | ||
0.995796 | − | 0.0916034i | \(-0.0291992\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.22519e13 | 0.130119 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.92865e12 | − | 6.78721e14i | −0.0176808 | − | 1.20866i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.30934e15i | 2.30565i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.78474e14 | 0.310785 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.49612e14 | − | 1.48522e14i | −0.257635 | − | 0.255758i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1.67462e14i | − | 0.285180i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.32349e13 | −0.0222893 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.02476e13 | − | 2.03963e13i | 0.0337237 | − | 0.0339713i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 5.84336e14i | − | 0.962542i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.35465e14 | 1.19819 | 0.599095 | − | 0.800678i | \(-0.295527\pi\) | ||||
0.599095 | + | 0.800678i | \(0.295527\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.75168e14 | − | 5.66946e12i | 1.24904 | − | 0.00913529i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.08632e14i | 1.44809i | 0.689751 | + | 0.724046i | \(0.257720\pi\) | ||||
−0.689751 | + | 0.724046i | \(0.742280\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.37395e14 | −0.216580 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.88442e14 | − | 2.86340e14i | −0.449732 | − | 0.446454i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.21017e14i | − | 0.340863i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.54977e14 | 1.30430 | 0.652149 | − | 0.758091i | \(-0.273868\pi\) | ||||
0.652149 | + | 0.758091i | \(0.273868\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.30057e14 | + | 3.32480e14i | −0.498071 | + | 0.501727i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.95116e14i | − | 0.291262i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.63117e13 | 0.0388544 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.81457e12 | + | 1.06846e15i | 0.0114158 | + | 1.56085i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 7.98341e13i | − | 0.115375i | −0.998335 | − | 0.0576873i | \(-0.981627\pi\) | ||
0.998335 | − | 0.0576873i | \(-0.0183726\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.58901e15 | −3.70157 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.78333e14 | − | 3.75576e14i | −0.535139 | − | 0.531239i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2.23902e13i | − | 0.0313328i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.34741e14 | −1.01727 | −0.508635 | − | 0.860982i | \(-0.669850\pi\) | ||||
−0.508635 | + | 0.860982i | \(0.669850\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.35294e14 | + | 4.38489e14i | −0.596286 | + | 0.600663i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.61320e14i | 0.625251i | 0.949876 | + | 0.312626i | \(0.101209\pi\) | ||||
−0.949876 | + | 0.312626i | \(0.898791\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.75787e14 | 1.17447 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.41510e14 | + | 8.60179e14i | −1.11661 | + | 1.14138i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.37004e14i | 0.705063i | 0.935800 | + | 0.352531i | \(0.114679\pi\) | ||||
−0.935800 | + | 0.352531i | \(0.885321\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.42398e13 | 0.122434 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.43042e14 | − | 7.37627e14i | −0.955236 | − | 0.948275i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 5.35229e14i | − | 0.680887i | −0.940265 | − | 0.340443i | \(-0.889423\pi\) | ||
0.940265 | − | 0.340443i | \(-0.110577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.34356e13 | −0.0295025 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.77324e14 | + | 6.82296e14i | −0.843795 | + | 0.849989i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.32304e14i | 0.286393i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.51730e14 | −0.917159 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.60861e15 | − | 1.17651e13i | 1.94231 | − | 0.0142058i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 3.38511e14i | − | 0.404517i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.03515e14 | −0.477229 | −0.238614 | − | 0.971114i | \(-0.576693\pi\) | ||||
−0.238614 | + | 0.971114i | \(0.576693\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.18913e13 | − | 3.16589e13i | −0.0373295 | − | 0.0370575i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.59080e14i | 0.300149i | 0.988675 | + | 0.150075i | \(0.0479514\pi\) | ||||
−0.988675 | + | 0.150075i | \(0.952049\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.36484e15 | 1.56501 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.69934e13 | + | 2.71915e13i | −0.0306362 | + | 0.0308611i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.64717e15i | − | 1.85040i | −0.379476 | − | 0.925202i | \(-0.623896\pi\) | ||
0.379476 | − | 0.925202i | \(-0.376104\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.34277e15 | 1.49310 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.38487e12 | + | 1.89349e14i | 0.00152428 | + | 0.208410i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.13285e15i | 1.23425i | 0.786863 | + | 0.617127i | \(0.211704\pi\) | ||||
−0.786863 | + | 0.617127i | \(0.788296\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.43620e14 | −0.154894 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.40401e15 | + | 1.39377e15i | 1.49894 | + | 1.48801i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 3.09529e13i | − | 0.0327130i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.14488e15 | −1.19782 | −0.598910 | − | 0.800816i | \(-0.704399\pi\) | ||||
−0.598910 | + | 0.800816i | \(0.704399\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.56267e14 | − | 8.62552e14i | 0.886876 | − | 0.893386i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.01941e14i | 0.924832i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.48757e14 | −0.963118 | −0.481559 | − | 0.876414i | \(-0.659929\pi\) | ||||
−0.481559 | + | 0.876414i | \(0.659929\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.95947e14 | − | 1.91695e14i | −0.196930 | − | 0.192656i |
(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 | 24.11.e.a.17.7 | ✓ | 10 | |
3.2 | odd | 2 | inner | 24.11.e.a.17.8 | yes | 10 | |
4.3 | odd | 2 | 48.11.e.e.17.4 | 10 | |||
8.3 | odd | 2 | 192.11.e.i.65.7 | 10 | |||
8.5 | even | 2 | 192.11.e.j.65.4 | 10 | |||
12.11 | even | 2 | 48.11.e.e.17.3 | 10 | |||
24.5 | odd | 2 | 192.11.e.j.65.3 | 10 | |||
24.11 | even | 2 | 192.11.e.i.65.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.11.e.a.17.7 | ✓ | 10 | 1.1 | even | 1 | trivial | |
24.11.e.a.17.8 | yes | 10 | 3.2 | odd | 2 | inner | |
48.11.e.e.17.3 | 10 | 12.11 | even | 2 | |||
48.11.e.e.17.4 | 10 | 4.3 | odd | 2 | |||
192.11.e.i.65.7 | 10 | 8.3 | odd | 2 | |||
192.11.e.i.65.8 | 10 | 24.11 | even | 2 | |||
192.11.e.j.65.3 | 10 | 24.5 | odd | 2 | |||
192.11.e.j.65.4 | 10 | 8.5 | even | 2 |