Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,10,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.a (trivial) |
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: | yes |
Analytic conductor: | \(22.1465409550\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} + \cdots + 52\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(15.9205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −17.9205 | −0.791983 | −0.395991 | − | 0.918254i | \(-0.629599\pi\) | ||||
−0.395991 | + | 0.918254i | \(0.629599\pi\) | |||||||
\(3\) | −172.986 | −1.23300 | −0.616501 | − | 0.787354i | \(-0.711451\pi\) | ||||
−0.616501 | + | 0.787354i | \(0.711451\pi\) | |||||||
\(4\) | −190.855 | −0.372763 | ||||||||
\(5\) | 238.484 | 0.170645 | 0.0853226 | − | 0.996353i | \(-0.472808\pi\) | ||||
0.0853226 | + | 0.996353i | \(0.472808\pi\) | |||||||
\(6\) | 3099.99 | 0.976517 | ||||||||
\(7\) | −4524.82 | −0.712295 | −0.356148 | − | 0.934430i | \(-0.615910\pi\) | ||||
−0.356148 | + | 0.934430i | \(0.615910\pi\) | |||||||
\(8\) | 12595.5 | 1.08720 | ||||||||
\(9\) | 10241.0 | 0.520296 | ||||||||
\(10\) | −4273.75 | −0.135148 | ||||||||
\(11\) | 66772.1 | 1.37508 | 0.687540 | − | 0.726146i | \(-0.258690\pi\) | ||||
0.687540 | + | 0.726146i | \(0.258690\pi\) | |||||||
\(12\) | 33015.1 | 0.459618 | ||||||||
\(13\) | 45566.0 | 0.442482 | 0.221241 | − | 0.975219i | \(-0.428989\pi\) | ||||
0.221241 | + | 0.975219i | \(0.428989\pi\) | |||||||
\(14\) | 81087.1 | 0.564126 | ||||||||
\(15\) | −41254.2 | −0.210406 | ||||||||
\(16\) | −128001. | −0.488284 | ||||||||
\(17\) | 494574. | 1.43619 | 0.718094 | − | 0.695947i | \(-0.245015\pi\) | ||||
0.718094 | + | 0.695947i | \(0.245015\pi\) | |||||||
\(18\) | −183524. | −0.412065 | ||||||||
\(19\) | −1.08372e6 | −1.90776 | −0.953881 | − | 0.300184i | \(-0.902952\pi\) | ||||
−0.953881 | + | 0.300184i | \(0.902952\pi\) | |||||||
\(20\) | −45515.8 | −0.0636103 | ||||||||
\(21\) | 782728. | 0.878262 | ||||||||
\(22\) | −1.19659e6 | −1.08904 | ||||||||
\(23\) | 1.35193e6 | 1.00735 | 0.503675 | − | 0.863893i | \(-0.331981\pi\) | ||||
0.503675 | + | 0.863893i | \(0.331981\pi\) | |||||||
\(24\) | −2.17884e6 | −1.34053 | ||||||||
\(25\) | −1.89625e6 | −0.970880 | ||||||||
\(26\) | −816566. | −0.350438 | ||||||||
\(27\) | 1.63333e6 | 0.591476 | ||||||||
\(28\) | 863584. | 0.265518 | ||||||||
\(29\) | −4.85463e6 | −1.27457 | −0.637287 | − | 0.770627i | \(-0.719943\pi\) | ||||
−0.637287 | + | 0.770627i | \(0.719943\pi\) | |||||||
\(30\) | 739298. | 0.166638 | ||||||||
\(31\) | 5.69784e6 | 1.10811 | 0.554054 | − | 0.832481i | \(-0.313080\pi\) | ||||
0.554054 | + | 0.832481i | \(0.313080\pi\) | |||||||
\(32\) | −4.15507e6 | −0.700492 | ||||||||
\(33\) | −1.15506e7 | −1.69548 | ||||||||
\(34\) | −8.86302e6 | −1.13744 | ||||||||
\(35\) | −1.07910e6 | −0.121550 | ||||||||
\(36\) | −1.95454e6 | −0.193947 | ||||||||
\(37\) | −1.59658e7 | −1.40050 | −0.700249 | − | 0.713898i | \(-0.746928\pi\) | ||||
−0.700249 | + | 0.713898i | \(0.746928\pi\) | |||||||
\(38\) | 1.94208e7 | 1.51091 | ||||||||
\(39\) | −7.88225e6 | −0.545581 | ||||||||
\(40\) | 3.00383e6 | 0.185526 | ||||||||
\(41\) | 1.10007e7 | 0.607988 | 0.303994 | − | 0.952674i | \(-0.401680\pi\) | ||||
0.303994 | + | 0.952674i | \(0.401680\pi\) | |||||||
\(42\) | −1.40269e7 | −0.695568 | ||||||||
\(43\) | −3.41880e6 | −0.152499 | ||||||||
\(44\) | −1.27438e7 | −0.512580 | ||||||||
\(45\) | 2.44231e6 | 0.0887860 | ||||||||
\(46\) | −2.42274e7 | −0.797803 | ||||||||
\(47\) | 2.98409e7 | 0.892014 | 0.446007 | − | 0.895029i | \(-0.352846\pi\) | ||||
0.446007 | + | 0.895029i | \(0.352846\pi\) | |||||||
\(48\) | 2.21423e7 | 0.602056 | ||||||||
\(49\) | −1.98796e7 | −0.492635 | ||||||||
\(50\) | 3.39818e7 | 0.768920 | ||||||||
\(51\) | −8.55541e7 | −1.77082 | ||||||||
\(52\) | −8.69648e6 | −0.164941 | ||||||||
\(53\) | 7.43943e6 | 0.129509 | 0.0647543 | − | 0.997901i | \(-0.479374\pi\) | ||||
0.0647543 | + | 0.997901i | \(0.479374\pi\) | |||||||
\(54\) | −2.92702e7 | −0.468439 | ||||||||
\(55\) | 1.59241e7 | 0.234651 | ||||||||
\(56\) | −5.69925e7 | −0.774411 | ||||||||
\(57\) | 1.87467e8 | 2.35228 | ||||||||
\(58\) | 8.69975e7 | 1.00944 | ||||||||
\(59\) | 1.08119e8 | 1.16163 | 0.580815 | − | 0.814036i | \(-0.302734\pi\) | ||||
0.580815 | + | 0.814036i | \(0.302734\pi\) | |||||||
\(60\) | 7.87357e6 | 0.0784316 | ||||||||
\(61\) | 1.99515e8 | 1.84497 | 0.922487 | − | 0.386028i | \(-0.126153\pi\) | ||||
0.922487 | + | 0.386028i | \(0.126153\pi\) | |||||||
\(62\) | −1.02108e8 | −0.877603 | ||||||||
\(63\) | −4.63386e7 | −0.370604 | ||||||||
\(64\) | 1.39997e8 | 1.04306 | ||||||||
\(65\) | 1.08667e7 | 0.0755073 | ||||||||
\(66\) | 2.06993e8 | 1.34279 | ||||||||
\(67\) | −2.61727e8 | −1.58677 | −0.793383 | − | 0.608723i | \(-0.791682\pi\) | ||||
−0.793383 | + | 0.608723i | \(0.791682\pi\) | |||||||
\(68\) | −9.43918e7 | −0.535358 | ||||||||
\(69\) | −2.33865e8 | −1.24206 | ||||||||
\(70\) | 1.93380e7 | 0.0962653 | ||||||||
\(71\) | 6.58887e7 | 0.307715 | 0.153857 | − | 0.988093i | \(-0.450830\pi\) | ||||
0.153857 | + | 0.988093i | \(0.450830\pi\) | |||||||
\(72\) | 1.28991e8 | 0.565668 | ||||||||
\(73\) | −4.01146e8 | −1.65329 | −0.826646 | − | 0.562722i | \(-0.809754\pi\) | ||||
−0.826646 | + | 0.562722i | \(0.809754\pi\) | |||||||
\(74\) | 2.86115e8 | 1.10917 | ||||||||
\(75\) | 3.28024e8 | 1.19710 | ||||||||
\(76\) | 2.06832e8 | 0.711144 | ||||||||
\(77\) | −3.02132e8 | −0.979464 | ||||||||
\(78\) | 1.41254e8 | 0.432091 | ||||||||
\(79\) | 1.23252e8 | 0.356019 | 0.178009 | − | 0.984029i | \(-0.443034\pi\) | ||||
0.178009 | + | 0.984029i | \(0.443034\pi\) | |||||||
\(80\) | −3.05261e7 | −0.0833233 | ||||||||
\(81\) | −4.84116e8 | −1.24959 | ||||||||
\(82\) | −1.97139e8 | −0.481516 | ||||||||
\(83\) | −3.81346e8 | −0.881998 | −0.440999 | − | 0.897507i | \(-0.645376\pi\) | ||||
−0.440999 | + | 0.897507i | \(0.645376\pi\) | |||||||
\(84\) | −1.49388e8 | −0.327384 | ||||||||
\(85\) | 1.17948e8 | 0.245078 | ||||||||
\(86\) | 6.12667e7 | 0.120776 | ||||||||
\(87\) | 8.39780e8 | 1.57155 | ||||||||
\(88\) | 8.41030e8 | 1.49499 | ||||||||
\(89\) | −3.81633e8 | −0.644749 | −0.322375 | − | 0.946612i | \(-0.604481\pi\) | ||||
−0.322375 | + | 0.946612i | \(0.604481\pi\) | |||||||
\(90\) | −4.37675e7 | −0.0703169 | ||||||||
\(91\) | −2.06178e8 | −0.315178 | ||||||||
\(92\) | −2.58023e8 | −0.375503 | ||||||||
\(93\) | −9.85643e8 | −1.36630 | ||||||||
\(94\) | −5.34765e8 | −0.706460 | ||||||||
\(95\) | −2.58449e8 | −0.325550 | ||||||||
\(96\) | 7.18767e8 | 0.863709 | ||||||||
\(97\) | −5.93343e8 | −0.680507 | −0.340254 | − | 0.940334i | \(-0.610513\pi\) | ||||
−0.340254 | + | 0.940334i | \(0.610513\pi\) | |||||||
\(98\) | 3.56253e8 | 0.390159 | ||||||||
\(99\) | 6.83813e8 | 0.715449 | ||||||||
\(100\) | 3.61909e8 | 0.361909 | ||||||||
\(101\) | 1.22816e8 | 0.117438 | 0.0587190 | − | 0.998275i | \(-0.481298\pi\) | ||||
0.0587190 | + | 0.998275i | \(0.481298\pi\) | |||||||
\(102\) | 1.53317e9 | 1.40246 | ||||||||
\(103\) | −1.45390e9 | −1.27282 | −0.636408 | − | 0.771353i | \(-0.719580\pi\) | ||||
−0.636408 | + | 0.771353i | \(0.719580\pi\) | |||||||
\(104\) | 5.73927e8 | 0.481068 | ||||||||
\(105\) | 1.86668e8 | 0.149871 | ||||||||
\(106\) | −1.33319e8 | −0.102569 | ||||||||
\(107\) | −1.05553e9 | −0.778475 | −0.389237 | − | 0.921138i | \(-0.627261\pi\) | ||||
−0.389237 | + | 0.921138i | \(0.627261\pi\) | |||||||
\(108\) | −3.11729e8 | −0.220481 | ||||||||
\(109\) | −1.48849e9 | −1.01001 | −0.505006 | − | 0.863116i | \(-0.668510\pi\) | ||||
−0.505006 | + | 0.863116i | \(0.668510\pi\) | |||||||
\(110\) | −2.85368e8 | −0.185839 | ||||||||
\(111\) | 2.76185e9 | 1.72682 | ||||||||
\(112\) | 5.79180e8 | 0.347802 | ||||||||
\(113\) | −2.40872e9 | −1.38974 | −0.694869 | − | 0.719137i | \(-0.744538\pi\) | ||||
−0.694869 | + | 0.719137i | \(0.744538\pi\) | |||||||
\(114\) | −3.35951e9 | −1.86296 | ||||||||
\(115\) | 3.22414e8 | 0.171899 | ||||||||
\(116\) | 9.26530e8 | 0.475115 | ||||||||
\(117\) | 4.66640e8 | 0.230221 | ||||||||
\(118\) | −1.93755e9 | −0.919991 | ||||||||
\(119\) | −2.23786e9 | −1.02299 | ||||||||
\(120\) | −5.19619e8 | −0.228754 | ||||||||
\(121\) | 2.10057e9 | 0.890847 | ||||||||
\(122\) | −3.57541e9 | −1.46119 | ||||||||
\(123\) | −1.90297e9 | −0.749651 | ||||||||
\(124\) | −1.08746e9 | −0.413062 | ||||||||
\(125\) | −9.18014e8 | −0.336321 | ||||||||
\(126\) | 8.30412e8 | 0.293512 | ||||||||
\(127\) | 1.63138e9 | 0.556464 | 0.278232 | − | 0.960514i | \(-0.410252\pi\) | ||||
0.278232 | + | 0.960514i | \(0.410252\pi\) | |||||||
\(128\) | −3.81431e8 | −0.125595 | ||||||||
\(129\) | 5.91403e8 | 0.188031 | ||||||||
\(130\) | −1.94738e8 | −0.0598005 | ||||||||
\(131\) | −2.34159e9 | −0.694690 | −0.347345 | − | 0.937737i | \(-0.612917\pi\) | ||||
−0.347345 | + | 0.937737i | \(0.612917\pi\) | |||||||
\(132\) | 2.20449e9 | 0.632012 | ||||||||
\(133\) | 4.90362e9 | 1.35889 | ||||||||
\(134\) | 4.69029e9 | 1.25669 | ||||||||
\(135\) | 3.89523e8 | 0.100933 | ||||||||
\(136\) | 6.22942e9 | 1.56143 | ||||||||
\(137\) | 4.87195e9 | 1.18157 | 0.590786 | − | 0.806828i | \(-0.298818\pi\) | ||||
0.590786 | + | 0.806828i | \(0.298818\pi\) | |||||||
\(138\) | 4.19098e9 | 0.983693 | ||||||||
\(139\) | 3.89560e9 | 0.885131 | 0.442566 | − | 0.896736i | \(-0.354068\pi\) | ||||
0.442566 | + | 0.896736i | \(0.354068\pi\) | |||||||
\(140\) | 2.05951e8 | 0.0453093 | ||||||||
\(141\) | −5.16205e9 | −1.09986 | ||||||||
\(142\) | −1.18076e9 | −0.243705 | ||||||||
\(143\) | 3.04254e9 | 0.608448 | ||||||||
\(144\) | −1.31085e9 | −0.254052 | ||||||||
\(145\) | −1.15775e9 | −0.217500 | ||||||||
\(146\) | 7.18875e9 | 1.30938 | ||||||||
\(147\) | 3.43888e9 | 0.607421 | ||||||||
\(148\) | 3.04715e9 | 0.522055 | ||||||||
\(149\) | 3.97719e9 | 0.661056 | 0.330528 | − | 0.943796i | \(-0.392773\pi\) | ||||
0.330528 | + | 0.943796i | \(0.392773\pi\) | |||||||
\(150\) | −5.87836e9 | −0.948081 | ||||||||
\(151\) | 1.04756e9 | 0.163977 | 0.0819886 | − | 0.996633i | \(-0.473873\pi\) | ||||
0.0819886 | + | 0.996633i | \(0.473873\pi\) | |||||||
\(152\) | −1.36500e10 | −2.07413 | ||||||||
\(153\) | 5.06492e9 | 0.747242 | ||||||||
\(154\) | 5.41436e9 | 0.775718 | ||||||||
\(155\) | 1.35884e9 | 0.189093 | ||||||||
\(156\) | 1.50437e9 | 0.203373 | ||||||||
\(157\) | −6.06273e9 | −0.796379 | −0.398189 | − | 0.917303i | \(-0.630361\pi\) | ||||
−0.398189 | + | 0.917303i | \(0.630361\pi\) | |||||||
\(158\) | −2.20874e9 | −0.281961 | ||||||||
\(159\) | −1.28691e9 | −0.159684 | ||||||||
\(160\) | −9.90917e8 | −0.119536 | ||||||||
\(161\) | −6.11726e9 | −0.717530 | ||||||||
\(162\) | 8.67561e9 | 0.989652 | ||||||||
\(163\) | 4.36837e9 | 0.484702 | 0.242351 | − | 0.970189i | \(-0.422081\pi\) | ||||
0.242351 | + | 0.970189i | \(0.422081\pi\) | |||||||
\(164\) | −2.09955e9 | −0.226636 | ||||||||
\(165\) | −2.75463e9 | −0.289325 | ||||||||
\(166\) | 6.83392e9 | 0.698528 | ||||||||
\(167\) | −9.06833e9 | −0.902200 | −0.451100 | − | 0.892473i | \(-0.648968\pi\) | ||||
−0.451100 | + | 0.892473i | \(0.648968\pi\) | |||||||
\(168\) | 9.85888e9 | 0.954851 | ||||||||
\(169\) | −8.52824e9 | −0.804210 | ||||||||
\(170\) | −2.11369e9 | −0.194098 | ||||||||
\(171\) | −1.10983e10 | −0.992601 | ||||||||
\(172\) | 6.52495e8 | 0.0568459 | ||||||||
\(173\) | −1.41700e10 | −1.20272 | −0.601359 | − | 0.798979i | \(-0.705374\pi\) | ||||
−0.601359 | + | 0.798979i | \(0.705374\pi\) | |||||||
\(174\) | −1.50493e10 | −1.24464 | ||||||||
\(175\) | 8.58019e9 | 0.691554 | ||||||||
\(176\) | −8.54688e9 | −0.671430 | ||||||||
\(177\) | −1.87030e10 | −1.43229 | ||||||||
\(178\) | 6.83906e9 | 0.510630 | ||||||||
\(179\) | 2.05552e10 | 1.49652 | 0.748260 | − | 0.663405i | \(-0.230889\pi\) | ||||
0.748260 | + | 0.663405i | \(0.230889\pi\) | |||||||
\(180\) | −4.66127e8 | −0.0330962 | ||||||||
\(181\) | −1.98258e10 | −1.37302 | −0.686511 | − | 0.727119i | \(-0.740859\pi\) | ||||
−0.686511 | + | 0.727119i | \(0.740859\pi\) | |||||||
\(182\) | 3.69481e9 | 0.249615 | ||||||||
\(183\) | −3.45131e10 | −2.27486 | ||||||||
\(184\) | 1.70283e10 | 1.09519 | ||||||||
\(185\) | −3.80758e9 | −0.238988 | ||||||||
\(186\) | 1.76632e10 | 1.08209 | ||||||||
\(187\) | 3.30238e10 | 1.97487 | ||||||||
\(188\) | −5.69528e9 | −0.332510 | ||||||||
\(189\) | −7.39053e9 | −0.421306 | ||||||||
\(190\) | 4.63154e9 | 0.257830 | ||||||||
\(191\) | −1.93769e10 | −1.05350 | −0.526750 | − | 0.850020i | \(-0.676590\pi\) | ||||
−0.526750 | + | 0.850020i | \(0.676590\pi\) | |||||||
\(192\) | −2.42175e10 | −1.28610 | ||||||||
\(193\) | 2.44314e10 | 1.26748 | 0.633740 | − | 0.773546i | \(-0.281519\pi\) | ||||
0.633740 | + | 0.773546i | \(0.281519\pi\) | |||||||
\(194\) | 1.06330e10 | 0.538950 | ||||||||
\(195\) | −1.87979e9 | −0.0931008 | ||||||||
\(196\) | 3.79412e9 | 0.183636 | ||||||||
\(197\) | −1.22473e10 | −0.579354 | −0.289677 | − | 0.957124i | \(-0.593548\pi\) | ||||
−0.289677 | + | 0.957124i | \(0.593548\pi\) | |||||||
\(198\) | −1.22543e10 | −0.566623 | ||||||||
\(199\) | −2.12982e10 | −0.962731 | −0.481366 | − | 0.876520i | \(-0.659859\pi\) | ||||
−0.481366 | + | 0.876520i | \(0.659859\pi\) | |||||||
\(200\) | −2.38843e10 | −1.05555 | ||||||||
\(201\) | 4.52751e10 | 1.95649 | ||||||||
\(202\) | −2.20092e9 | −0.0930088 | ||||||||
\(203\) | 2.19663e10 | 0.907873 | ||||||||
\(204\) | 1.63284e10 | 0.660098 | ||||||||
\(205\) | 2.62350e9 | 0.103750 | ||||||||
\(206\) | 2.60546e10 | 1.00805 | ||||||||
\(207\) | 1.38451e10 | 0.524120 | ||||||||
\(208\) | −5.83247e9 | −0.216057 | ||||||||
\(209\) | −7.23620e10 | −2.62333 | ||||||||
\(210\) | −3.34519e9 | −0.118695 | ||||||||
\(211\) | −3.57352e10 | −1.24115 | −0.620576 | − | 0.784146i | \(-0.713101\pi\) | ||||
−0.620576 | + | 0.784146i | \(0.713101\pi\) | |||||||
\(212\) | −1.41985e9 | −0.0482761 | ||||||||
\(213\) | −1.13978e10 | −0.379413 | ||||||||
\(214\) | 1.89157e10 | 0.616538 | ||||||||
\(215\) | −8.15329e8 | −0.0260231 | ||||||||
\(216\) | 2.05727e10 | 0.643056 | ||||||||
\(217\) | −2.57817e10 | −0.789301 | ||||||||
\(218\) | 2.66745e10 | 0.799912 | ||||||||
\(219\) | 6.93925e10 | 2.03851 | ||||||||
\(220\) | −3.03919e9 | −0.0874692 | ||||||||
\(221\) | 2.25357e10 | 0.635487 | ||||||||
\(222\) | −4.94938e10 | −1.36761 | ||||||||
\(223\) | 1.10106e10 | 0.298153 | 0.149076 | − | 0.988826i | \(-0.452370\pi\) | ||||
0.149076 | + | 0.988826i | \(0.452370\pi\) | |||||||
\(224\) | 1.88009e10 | 0.498958 | ||||||||
\(225\) | −1.94195e10 | −0.505145 | ||||||||
\(226\) | 4.31655e10 | 1.10065 | ||||||||
\(227\) | 1.50858e10 | 0.377096 | 0.188548 | − | 0.982064i | \(-0.439622\pi\) | ||||
0.188548 | + | 0.982064i | \(0.439622\pi\) | |||||||
\(228\) | −3.57790e10 | −0.876843 | ||||||||
\(229\) | 1.14580e10 | 0.275327 | 0.137664 | − | 0.990479i | \(-0.456041\pi\) | ||||
0.137664 | + | 0.990479i | \(0.456041\pi\) | |||||||
\(230\) | −5.77783e9 | −0.136141 | ||||||||
\(231\) | 5.22644e10 | 1.20768 | ||||||||
\(232\) | −6.11466e10 | −1.38572 | ||||||||
\(233\) | −1.02658e10 | −0.228187 | −0.114094 | − | 0.993470i | \(-0.536396\pi\) | ||||
−0.114094 | + | 0.993470i | \(0.536396\pi\) | |||||||
\(234\) | −8.36244e9 | −0.182331 | ||||||||
\(235\) | 7.11658e9 | 0.152218 | ||||||||
\(236\) | −2.06350e10 | −0.433013 | ||||||||
\(237\) | −2.13208e10 | −0.438972 | ||||||||
\(238\) | 4.01036e10 | 0.810190 | ||||||||
\(239\) | 3.71284e10 | 0.736064 | 0.368032 | − | 0.929813i | \(-0.380032\pi\) | ||||
0.368032 | + | 0.929813i | \(0.380032\pi\) | |||||||
\(240\) | 5.28057e9 | 0.102738 | ||||||||
\(241\) | 4.83626e10 | 0.923492 | 0.461746 | − | 0.887012i | \(-0.347223\pi\) | ||||
0.461746 | + | 0.887012i | \(0.347223\pi\) | |||||||
\(242\) | −3.76433e10 | −0.705536 | ||||||||
\(243\) | 5.15962e10 | 0.949269 | ||||||||
\(244\) | −3.80783e10 | −0.687739 | ||||||||
\(245\) | −4.74096e9 | −0.0840658 | ||||||||
\(246\) | 3.41022e10 | 0.593710 | ||||||||
\(247\) | −4.93806e10 | −0.844150 | ||||||||
\(248\) | 7.17672e10 | 1.20474 | ||||||||
\(249\) | 6.59673e10 | 1.08751 | ||||||||
\(250\) | 1.64513e10 | 0.266360 | ||||||||
\(251\) | 3.34140e10 | 0.531369 | 0.265684 | − | 0.964060i | \(-0.414402\pi\) | ||||
0.265684 | + | 0.964060i | \(0.414402\pi\) | |||||||
\(252\) | 8.84395e9 | 0.138148 | ||||||||
\(253\) | 9.02715e10 | 1.38519 | ||||||||
\(254\) | −2.92351e10 | −0.440710 | ||||||||
\(255\) | −2.04033e10 | −0.302182 | ||||||||
\(256\) | −6.48432e10 | −0.943593 | ||||||||
\(257\) | −8.20412e10 | −1.17309 | −0.586547 | − | 0.809915i | \(-0.699513\pi\) | ||||
−0.586547 | + | 0.809915i | \(0.699513\pi\) | |||||||
\(258\) | −1.05983e10 | −0.148917 | ||||||||
\(259\) | 7.22423e10 | 0.997569 | ||||||||
\(260\) | −2.07397e9 | −0.0281464 | ||||||||
\(261\) | −4.97162e10 | −0.663156 | ||||||||
\(262\) | 4.19626e10 | 0.550182 | ||||||||
\(263\) | 4.19397e10 | 0.540536 | 0.270268 | − | 0.962785i | \(-0.412888\pi\) | ||||
0.270268 | + | 0.962785i | \(0.412888\pi\) | |||||||
\(264\) | −1.45486e11 | −1.84333 | ||||||||
\(265\) | 1.77418e9 | 0.0221000 | ||||||||
\(266\) | −8.78754e10 | −1.07622 | ||||||||
\(267\) | 6.60170e10 | 0.794977 | ||||||||
\(268\) | 4.99520e10 | 0.591488 | ||||||||
\(269\) | 1.06374e11 | 1.23866 | 0.619328 | − | 0.785132i | \(-0.287405\pi\) | ||||
0.619328 | + | 0.785132i | \(0.287405\pi\) | |||||||
\(270\) | −6.98046e9 | −0.0799368 | ||||||||
\(271\) | −8.12651e10 | −0.915255 | −0.457628 | − | 0.889144i | \(-0.651301\pi\) | ||||
−0.457628 | + | 0.889144i | \(0.651301\pi\) | |||||||
\(272\) | −6.33058e10 | −0.701267 | ||||||||
\(273\) | 3.56658e10 | 0.388615 | ||||||||
\(274\) | −8.73079e10 | −0.935785 | ||||||||
\(275\) | −1.26617e11 | −1.33504 | ||||||||
\(276\) | 4.46343e10 | 0.462996 | ||||||||
\(277\) | 2.01089e10 | 0.205225 | 0.102612 | − | 0.994721i | \(-0.467280\pi\) | ||||
0.102612 | + | 0.994721i | \(0.467280\pi\) | |||||||
\(278\) | −6.98112e10 | −0.701009 | ||||||||
\(279\) | 5.83514e10 | 0.576544 | ||||||||
\(280\) | −1.35918e10 | −0.132149 | ||||||||
\(281\) | −1.16967e11 | −1.11914 | −0.559572 | − | 0.828782i | \(-0.689035\pi\) | ||||
−0.559572 | + | 0.828782i | \(0.689035\pi\) | |||||||
\(282\) | 9.25066e10 | 0.871067 | ||||||||
\(283\) | −9.10743e10 | −0.844028 | −0.422014 | − | 0.906589i | \(-0.638677\pi\) | ||||
−0.422014 | + | 0.906589i | \(0.638677\pi\) | |||||||
\(284\) | −1.25752e10 | −0.114705 | ||||||||
\(285\) | 4.47079e10 | 0.401404 | ||||||||
\(286\) | −5.45238e10 | −0.481880 | ||||||||
\(287\) | −4.97764e10 | −0.433067 | ||||||||
\(288\) | −4.25520e10 | −0.364463 | ||||||||
\(289\) | 1.26015e11 | 1.06263 | ||||||||
\(290\) | 2.07475e10 | 0.172256 | ||||||||
\(291\) | 1.02640e11 | 0.839067 | ||||||||
\(292\) | 7.65607e10 | 0.616287 | ||||||||
\(293\) | −7.51554e10 | −0.595739 | −0.297869 | − | 0.954607i | \(-0.596276\pi\) | ||||
−0.297869 | + | 0.954607i | \(0.596276\pi\) | |||||||
\(294\) | −6.16266e10 | −0.481067 | ||||||||
\(295\) | 2.57846e10 | 0.198226 | ||||||||
\(296\) | −2.01098e11 | −1.52263 | ||||||||
\(297\) | 1.09061e11 | 0.813328 | ||||||||
\(298\) | −7.12733e10 | −0.523545 | ||||||||
\(299\) | 6.16021e10 | 0.445734 | ||||||||
\(300\) | −6.26049e10 | −0.446234 | ||||||||
\(301\) | 1.54695e10 | 0.108624 | ||||||||
\(302\) | −1.87729e10 | −0.129867 | ||||||||
\(303\) | −2.12454e10 | −0.144801 | ||||||||
\(304\) | 1.38716e11 | 0.931530 | ||||||||
\(305\) | 4.75810e10 | 0.314836 | ||||||||
\(306\) | −9.07661e10 | −0.591803 | ||||||||
\(307\) | 2.57354e10 | 0.165352 | 0.0826759 | − | 0.996576i | \(-0.473653\pi\) | ||||
0.0826759 | + | 0.996576i | \(0.473653\pi\) | |||||||
\(308\) | 5.76634e10 | 0.365108 | ||||||||
\(309\) | 2.51503e11 | 1.56939 | ||||||||
\(310\) | −2.43511e10 | −0.149759 | ||||||||
\(311\) | 5.97715e10 | 0.362304 | 0.181152 | − | 0.983455i | \(-0.442017\pi\) | ||||
0.181152 | + | 0.983455i | \(0.442017\pi\) | |||||||
\(312\) | −9.92811e10 | −0.593159 | ||||||||
\(313\) | −6.89838e10 | −0.406254 | −0.203127 | − | 0.979152i | \(-0.565110\pi\) | ||||
−0.203127 | + | 0.979152i | \(0.565110\pi\) | |||||||
\(314\) | 1.08647e11 | 0.630718 | ||||||||
\(315\) | −1.10510e10 | −0.0632418 | ||||||||
\(316\) | −2.35233e10 | −0.132711 | ||||||||
\(317\) | −3.11421e11 | −1.73213 | −0.866067 | − | 0.499928i | \(-0.833360\pi\) | ||||
−0.866067 | + | 0.499928i | \(0.833360\pi\) | |||||||
\(318\) | 2.30622e10 | 0.126467 | ||||||||
\(319\) | −3.24154e11 | −1.75264 | ||||||||
\(320\) | 3.33871e10 | 0.177993 | ||||||||
\(321\) | 1.82592e11 | 0.959861 | ||||||||
\(322\) | 1.09624e11 | 0.568271 | ||||||||
\(323\) | −5.35978e11 | −2.73990 | ||||||||
\(324\) | 9.23959e10 | 0.465801 | ||||||||
\(325\) | −8.64045e10 | −0.429597 | ||||||||
\(326\) | −7.82835e10 | −0.383876 | ||||||||
\(327\) | 2.57487e11 | 1.24535 | ||||||||
\(328\) | 1.38560e11 | 0.661007 | ||||||||
\(329\) | −1.35025e11 | −0.635378 | ||||||||
\(330\) | 4.93645e10 | 0.229140 | ||||||||
\(331\) | −1.00401e11 | −0.459738 | −0.229869 | − | 0.973222i | \(-0.573830\pi\) | ||||
−0.229869 | + | 0.973222i | \(0.573830\pi\) | |||||||
\(332\) | 7.27818e10 | 0.328777 | ||||||||
\(333\) | −1.63505e11 | −0.728674 | ||||||||
\(334\) | 1.62509e11 | 0.714527 | ||||||||
\(335\) | −6.24178e10 | −0.270774 | ||||||||
\(336\) | −1.00190e11 | −0.428841 | ||||||||
\(337\) | −3.46652e11 | −1.46406 | −0.732030 | − | 0.681273i | \(-0.761427\pi\) | ||||
−0.732030 | + | 0.681273i | \(0.761427\pi\) | |||||||
\(338\) | 1.52831e11 | 0.636920 | ||||||||
\(339\) | 4.16673e11 | 1.71355 | ||||||||
\(340\) | −2.25109e10 | −0.0913562 | ||||||||
\(341\) | 3.80457e11 | 1.52374 | ||||||||
\(342\) | 1.98888e11 | 0.786123 | ||||||||
\(343\) | 2.72544e11 | 1.06320 | ||||||||
\(344\) | −4.30616e10 | −0.165797 | ||||||||
\(345\) | −5.57730e10 | −0.211952 | ||||||||
\(346\) | 2.53935e11 | 0.952531 | ||||||||
\(347\) | 4.59014e10 | 0.169959 | 0.0849794 | − | 0.996383i | \(-0.472918\pi\) | ||||
0.0849794 | + | 0.996383i | \(0.472918\pi\) | |||||||
\(348\) | −1.60276e11 | −0.585818 | ||||||||
\(349\) | −5.52760e11 | −1.99445 | −0.997224 | − | 0.0744645i | \(-0.976275\pi\) | ||||
−0.997224 | + | 0.0744645i | \(0.976275\pi\) | |||||||
\(350\) | −1.53762e11 | −0.547698 | ||||||||
\(351\) | 7.44243e10 | 0.261718 | ||||||||
\(352\) | −2.77443e11 | −0.963234 | ||||||||
\(353\) | −3.24055e11 | −1.11079 | −0.555395 | − | 0.831586i | \(-0.687433\pi\) | ||||
−0.555395 | + | 0.831586i | \(0.687433\pi\) | |||||||
\(354\) | 3.35168e11 | 1.13435 | ||||||||
\(355\) | 1.57134e10 | 0.0525100 | ||||||||
\(356\) | 7.28365e10 | 0.240339 | ||||||||
\(357\) | 3.87117e11 | 1.26135 | ||||||||
\(358\) | −3.68360e11 | −1.18522 | ||||||||
\(359\) | 2.90617e11 | 0.923413 | 0.461707 | − | 0.887033i | \(-0.347237\pi\) | ||||
0.461707 | + | 0.887033i | \(0.347237\pi\) | |||||||
\(360\) | 3.07622e10 | 0.0965285 | ||||||||
\(361\) | 8.51753e11 | 2.63956 | ||||||||
\(362\) | 3.55289e11 | 1.08741 | ||||||||
\(363\) | −3.63368e11 | −1.09842 | ||||||||
\(364\) | 3.93500e10 | 0.117487 | ||||||||
\(365\) | −9.56668e10 | −0.282126 | ||||||||
\(366\) | 6.18493e11 | 1.80165 | ||||||||
\(367\) | −1.08398e11 | −0.311906 | −0.155953 | − | 0.987764i | \(-0.549845\pi\) | ||||
−0.155953 | + | 0.987764i | \(0.549845\pi\) | |||||||
\(368\) | −1.73048e11 | −0.491872 | ||||||||
\(369\) | 1.12658e11 | 0.316334 | ||||||||
\(370\) | 6.82339e10 | 0.189275 | ||||||||
\(371\) | −3.36621e10 | −0.0922483 | ||||||||
\(372\) | 1.88115e11 | 0.509307 | ||||||||
\(373\) | −4.17071e11 | −1.11563 | −0.557815 | − | 0.829965i | \(-0.688360\pi\) | ||||
−0.557815 | + | 0.829965i | \(0.688360\pi\) | |||||||
\(374\) | −5.91803e11 | −1.56407 | ||||||||
\(375\) | 1.58803e11 | 0.414685 | ||||||||
\(376\) | 3.75862e11 | 0.969802 | ||||||||
\(377\) | −2.21206e11 | −0.563976 | ||||||||
\(378\) | 1.32442e11 | 0.333667 | ||||||||
\(379\) | −2.63908e11 | −0.657015 | −0.328508 | − | 0.944501i | \(-0.606546\pi\) | ||||
−0.328508 | + | 0.944501i | \(0.606546\pi\) | |||||||
\(380\) | 4.93262e10 | 0.121353 | ||||||||
\(381\) | −2.82204e11 | −0.686122 | ||||||||
\(382\) | 3.47245e11 | 0.834354 | ||||||||
\(383\) | 8.16196e11 | 1.93821 | 0.969103 | − | 0.246658i | \(-0.0793325\pi\) | ||||
0.969103 | + | 0.246658i | \(0.0793325\pi\) | |||||||
\(384\) | 6.59820e10 | 0.154858 | ||||||||
\(385\) | −7.20536e10 | −0.167141 | ||||||||
\(386\) | −4.37824e11 | −1.00382 | ||||||||
\(387\) | −3.50119e10 | −0.0793444 | ||||||||
\(388\) | 1.13242e11 | 0.253668 | ||||||||
\(389\) | 6.95765e11 | 1.54060 | 0.770299 | − | 0.637683i | \(-0.220107\pi\) | ||||
0.770299 | + | 0.637683i | \(0.220107\pi\) | |||||||
\(390\) | 3.36868e10 | 0.0737342 | ||||||||
\(391\) | 6.68631e11 | 1.44674 | ||||||||
\(392\) | −2.50394e11 | −0.535595 | ||||||||
\(393\) | 4.05062e11 | 0.856554 | ||||||||
\(394\) | 2.19479e11 | 0.458838 | ||||||||
\(395\) | 2.93937e10 | 0.0607528 | ||||||||
\(396\) | −1.30509e11 | −0.266693 | ||||||||
\(397\) | 2.39129e10 | 0.0483143 | 0.0241571 | − | 0.999708i | \(-0.492310\pi\) | ||||
0.0241571 | + | 0.999708i | \(0.492310\pi\) | |||||||
\(398\) | 3.81676e11 | 0.762466 | ||||||||
\(399\) | −8.48255e11 | −1.67552 | ||||||||
\(400\) | 2.42721e11 | 0.474065 | ||||||||
\(401\) | −1.31846e11 | −0.254634 | −0.127317 | − | 0.991862i | \(-0.540637\pi\) | ||||
−0.127317 | + | 0.991862i | \(0.540637\pi\) | |||||||
\(402\) | −8.11353e11 | −1.54950 | ||||||||
\(403\) | 2.59627e11 | 0.490318 | ||||||||
\(404\) | −2.34400e10 | −0.0437766 | ||||||||
\(405\) | −1.15454e11 | −0.213236 | ||||||||
\(406\) | −3.93648e11 | −0.719020 | ||||||||
\(407\) | −1.06607e12 | −1.92580 | ||||||||
\(408\) | −1.07760e12 | −1.92525 | ||||||||
\(409\) | 2.22821e11 | 0.393732 | 0.196866 | − | 0.980430i | \(-0.436924\pi\) | ||||
0.196866 | + | 0.980430i | \(0.436924\pi\) | |||||||
\(410\) | −4.70145e10 | −0.0821683 | ||||||||
\(411\) | −8.42777e11 | −1.45688 | ||||||||
\(412\) | 2.77483e11 | 0.474459 | ||||||||
\(413\) | −4.89219e11 | −0.827423 | ||||||||
\(414\) | −2.48112e11 | −0.415094 | ||||||||
\(415\) | −9.09449e10 | −0.150509 | ||||||||
\(416\) | −1.89330e11 | −0.309955 | ||||||||
\(417\) | −6.73882e11 | −1.09137 | ||||||||
\(418\) | 1.29677e12 | 2.07763 | ||||||||
\(419\) | −8.93132e11 | −1.41564 | −0.707820 | − | 0.706393i | \(-0.750321\pi\) | ||||
−0.707820 | + | 0.706393i | \(0.750321\pi\) | |||||||
\(420\) | −3.56265e10 | −0.0558665 | ||||||||
\(421\) | 4.93105e11 | 0.765014 | 0.382507 | − | 0.923953i | \(-0.375061\pi\) | ||||
0.382507 | + | 0.923953i | \(0.375061\pi\) | |||||||
\(422\) | 6.40393e11 | 0.982971 | ||||||||
\(423\) | 3.05600e11 | 0.464111 | ||||||||
\(424\) | 9.37036e10 | 0.140802 | ||||||||
\(425\) | −9.37836e11 | −1.39437 | ||||||||
\(426\) | 2.04254e11 | 0.300489 | ||||||||
\(427\) | −9.02768e11 | −1.31417 | ||||||||
\(428\) | 2.01453e11 | 0.290187 | ||||||||
\(429\) | −5.26315e11 | −0.750218 | ||||||||
\(430\) | 1.46111e10 | 0.0206099 | ||||||||
\(431\) | 1.09242e12 | 1.52490 | 0.762449 | − | 0.647048i | \(-0.223997\pi\) | ||||
0.762449 | + | 0.647048i | \(0.223997\pi\) | |||||||
\(432\) | −2.09068e11 | −0.288808 | ||||||||
\(433\) | −6.73980e11 | −0.921406 | −0.460703 | − | 0.887554i | \(-0.652403\pi\) | ||||
−0.460703 | + | 0.887554i | \(0.652403\pi\) | |||||||
\(434\) | 4.62021e11 | 0.625112 | ||||||||
\(435\) | 2.00274e11 | 0.268178 | ||||||||
\(436\) | 2.84085e11 | 0.376495 | ||||||||
\(437\) | −1.46511e12 | −1.92178 | ||||||||
\(438\) | −1.24355e12 | −1.61447 | ||||||||
\(439\) | 2.78225e11 | 0.357524 | 0.178762 | − | 0.983892i | \(-0.442791\pi\) | ||||
0.178762 | + | 0.983892i | \(0.442791\pi\) | |||||||
\(440\) | 2.00572e11 | 0.255114 | ||||||||
\(441\) | −2.03587e11 | −0.256316 | ||||||||
\(442\) | −4.03852e11 | −0.503294 | ||||||||
\(443\) | 3.25574e11 | 0.401636 | 0.200818 | − | 0.979629i | \(-0.435640\pi\) | ||||
0.200818 | + | 0.979629i | \(0.435640\pi\) | |||||||
\(444\) | −5.27113e11 | −0.643695 | ||||||||
\(445\) | −9.10133e10 | −0.110023 | ||||||||
\(446\) | −1.97316e11 | −0.236132 | ||||||||
\(447\) | −6.87996e11 | −0.815083 | ||||||||
\(448\) | −6.33463e11 | −0.742968 | ||||||||
\(449\) | 9.27680e11 | 1.07718 | 0.538592 | − | 0.842567i | \(-0.318956\pi\) | ||||
0.538592 | + | 0.842567i | \(0.318956\pi\) | |||||||
\(450\) | 3.48007e11 | 0.400066 | ||||||||
\(451\) | 7.34544e11 | 0.836032 | ||||||||
\(452\) | 4.59715e11 | 0.518043 | ||||||||
\(453\) | −1.81213e11 | −0.202184 | ||||||||
\(454\) | −2.70346e11 | −0.298654 | ||||||||
\(455\) | −4.91700e10 | −0.0537835 | ||||||||
\(456\) | 2.36125e12 | 2.55741 | ||||||||
\(457\) | 1.08416e12 | 1.16271 | 0.581355 | − | 0.813650i | \(-0.302523\pi\) | ||||
0.581355 | + | 0.813650i | \(0.302523\pi\) | |||||||
\(458\) | −2.05333e11 | −0.218055 | ||||||||
\(459\) | 8.07803e11 | 0.849471 | ||||||||
\(460\) | −6.15343e10 | −0.0640777 | ||||||||
\(461\) | 5.03578e11 | 0.519293 | 0.259647 | − | 0.965704i | \(-0.416394\pi\) | ||||
0.259647 | + | 0.965704i | \(0.416394\pi\) | |||||||
\(462\) | −9.36606e11 | −0.956463 | ||||||||
\(463\) | −1.27085e12 | −1.28523 | −0.642613 | − | 0.766191i | \(-0.722150\pi\) | ||||
−0.642613 | + | 0.766191i | \(0.722150\pi\) | |||||||
\(464\) | 6.21396e11 | 0.622354 | ||||||||
\(465\) | −2.35060e11 | −0.233153 | ||||||||
\(466\) | 1.83968e11 | 0.180720 | ||||||||
\(467\) | 1.68815e12 | 1.64243 | 0.821214 | − | 0.570621i | \(-0.193297\pi\) | ||||
0.821214 | + | 0.570621i | \(0.193297\pi\) | |||||||
\(468\) | −8.90606e10 | −0.0858181 | ||||||||
\(469\) | 1.18427e12 | 1.13025 | ||||||||
\(470\) | −1.27533e11 | −0.120554 | ||||||||
\(471\) | 1.04876e12 | 0.981937 | ||||||||
\(472\) | 1.36181e12 | 1.26293 | ||||||||
\(473\) | −2.28281e11 | −0.209698 | ||||||||
\(474\) | 3.82081e11 | 0.347658 | ||||||||
\(475\) | 2.05500e12 | 1.85221 | ||||||||
\(476\) | 4.27106e11 | 0.381333 | ||||||||
\(477\) | 7.61871e10 | 0.0673828 | ||||||||
\(478\) | −6.65360e11 | −0.582950 | ||||||||
\(479\) | −1.34770e12 | −1.16972 | −0.584862 | − | 0.811133i | \(-0.698851\pi\) | ||||
−0.584862 | + | 0.811133i | \(0.698851\pi\) | |||||||
\(480\) | 1.71414e11 | 0.147388 | ||||||||
\(481\) | −7.27496e11 | −0.619695 | ||||||||
\(482\) | −8.66684e11 | −0.731390 | ||||||||
\(483\) | 1.05820e12 | 0.884717 | ||||||||
\(484\) | −4.00904e11 | −0.332075 | ||||||||
\(485\) | −1.41503e11 | −0.116125 | ||||||||
\(486\) | −9.24631e11 | −0.751805 | ||||||||
\(487\) | 4.15547e11 | 0.334765 | 0.167382 | − | 0.985892i | \(-0.446469\pi\) | ||||
0.167382 | + | 0.985892i | \(0.446469\pi\) | |||||||
\(488\) | 2.51299e12 | 2.00587 | ||||||||
\(489\) | −7.55665e11 | −0.597640 | ||||||||
\(490\) | 8.49606e10 | 0.0665787 | ||||||||
\(491\) | 2.51440e11 | 0.195239 | 0.0976197 | − | 0.995224i | \(-0.468877\pi\) | ||||
0.0976197 | + | 0.995224i | \(0.468877\pi\) | |||||||
\(492\) | 3.63191e11 | 0.279442 | ||||||||
\(493\) | −2.40097e12 | −1.83053 | ||||||||
\(494\) | 8.84925e11 | 0.668552 | ||||||||
\(495\) | 1.63078e11 | 0.122088 | ||||||||
\(496\) | −7.29327e11 | −0.541072 | ||||||||
\(497\) | −2.98134e11 | −0.219184 | ||||||||
\(498\) | −1.18217e12 | −0.861286 | ||||||||
\(499\) | −1.18872e12 | −0.858273 | −0.429137 | − | 0.903240i | \(-0.641182\pi\) | ||||
−0.429137 | + | 0.903240i | \(0.641182\pi\) | |||||||
\(500\) | 1.75207e11 | 0.125368 | ||||||||
\(501\) | 1.56869e12 | 1.11242 | ||||||||
\(502\) | −5.98796e11 | −0.420835 | ||||||||
\(503\) | −2.74830e10 | −0.0191430 | −0.00957148 | − | 0.999954i | \(-0.503047\pi\) | ||||
−0.00957148 | + | 0.999954i | \(0.503047\pi\) | |||||||
\(504\) | −5.83659e11 | −0.402923 | ||||||||
\(505\) | 2.92896e10 | 0.0200402 | ||||||||
\(506\) | −1.61771e12 | −1.09704 | ||||||||
\(507\) | 1.47526e12 | 0.991593 | ||||||||
\(508\) | −3.11356e11 | −0.207430 | ||||||||
\(509\) | −2.56804e12 | −1.69579 | −0.847894 | − | 0.530165i | \(-0.822130\pi\) | ||||
−0.847894 | + | 0.530165i | \(0.822130\pi\) | |||||||
\(510\) | 3.65637e11 | 0.239323 | ||||||||
\(511\) | 1.81511e12 | 1.17763 | ||||||||
\(512\) | 1.35732e12 | 0.872904 | ||||||||
\(513\) | −1.77007e12 | −1.12840 | ||||||||
\(514\) | 1.47022e12 | 0.929070 | ||||||||
\(515\) | −3.46730e11 | −0.217200 | ||||||||
\(516\) | −1.12872e11 | −0.0700911 | ||||||||
\(517\) | 1.99254e12 | 1.22659 | ||||||||
\(518\) | −1.29462e12 | −0.790057 | ||||||||
\(519\) | 2.45121e12 | 1.48295 | ||||||||
\(520\) | 1.36872e11 | 0.0820920 | ||||||||
\(521\) | −5.58805e11 | −0.332269 | −0.166135 | − | 0.986103i | \(-0.553129\pi\) | ||||
−0.166135 | + | 0.986103i | \(0.553129\pi\) | |||||||
\(522\) | 8.90940e11 | 0.525208 | ||||||||
\(523\) | −1.74645e12 | −1.02070 | −0.510350 | − | 0.859967i | \(-0.670484\pi\) | ||||
−0.510350 | + | 0.859967i | \(0.670484\pi\) | |||||||
\(524\) | 4.46905e11 | 0.258955 | ||||||||
\(525\) | −1.48425e12 | −0.852687 | ||||||||
\(526\) | −7.51581e11 | −0.428095 | ||||||||
\(527\) | 2.81800e12 | 1.59145 | ||||||||
\(528\) | 1.47849e12 | 0.827875 | ||||||||
\(529\) | 2.65711e10 | 0.0147523 | ||||||||
\(530\) | −3.17943e10 | −0.0175028 | ||||||||
\(531\) | 1.10724e12 | 0.604391 | ||||||||
\(532\) | −9.35880e11 | −0.506545 | ||||||||
\(533\) | 5.01260e11 | 0.269024 | ||||||||
\(534\) | −1.18306e12 | −0.629608 | ||||||||
\(535\) | −2.51727e11 | −0.132843 | ||||||||
\(536\) | −3.29660e12 | −1.72514 | ||||||||
\(537\) | −3.55575e12 | −1.84521 | ||||||||
\(538\) | −1.90628e12 | −0.980994 | ||||||||
\(539\) | −1.32740e12 | −0.677413 | ||||||||
\(540\) | −7.43424e10 | −0.0376240 | ||||||||
\(541\) | 1.23556e12 | 0.620122 | 0.310061 | − | 0.950717i | \(-0.399650\pi\) | ||||
0.310061 | + | 0.950717i | \(0.399650\pi\) | |||||||
\(542\) | 1.45631e12 | 0.724866 | ||||||||
\(543\) | 3.42958e12 | 1.69294 | ||||||||
\(544\) | −2.05499e12 | −1.00604 | ||||||||
\(545\) | −3.54981e11 | −0.172354 | ||||||||
\(546\) | −6.39149e11 | −0.307776 | ||||||||
\(547\) | −1.66722e11 | −0.0796251 | −0.0398126 | − | 0.999207i | \(-0.512676\pi\) | ||||
−0.0398126 | + | 0.999207i | \(0.512676\pi\) | |||||||
\(548\) | −9.29835e11 | −0.440447 | ||||||||
\(549\) | 2.04323e12 | 0.959933 | ||||||||
\(550\) | 2.26904e12 | 1.05733 | ||||||||
\(551\) | 5.26104e12 | 2.43158 | ||||||||
\(552\) | −2.94565e12 | −1.35038 | ||||||||
\(553\) | −5.57694e11 | −0.253590 | ||||||||
\(554\) | −3.60362e11 | −0.162534 | ||||||||
\(555\) | 6.58656e11 | 0.294673 | ||||||||
\(556\) | −7.43494e11 | −0.329945 | ||||||||
\(557\) | 5.10355e11 | 0.224659 | 0.112330 | − | 0.993671i | \(-0.464169\pi\) | ||||
0.112330 | + | 0.993671i | \(0.464169\pi\) | |||||||
\(558\) | −1.04569e12 | −0.456613 | ||||||||
\(559\) | −1.55781e11 | −0.0674778 | ||||||||
\(560\) | 1.38125e11 | 0.0593508 | ||||||||
\(561\) | −5.71263e12 | −2.43502 | ||||||||
\(562\) | 2.09612e12 | 0.886343 | ||||||||
\(563\) | 6.39701e11 | 0.268342 | 0.134171 | − | 0.990958i | \(-0.457163\pi\) | ||||
0.134171 | + | 0.990958i | \(0.457163\pi\) | |||||||
\(564\) | 9.85202e11 | 0.409986 | ||||||||
\(565\) | −5.74440e11 | −0.237152 | ||||||||
\(566\) | 1.63210e12 | 0.668456 | ||||||||
\(567\) | 2.19054e12 | 0.890076 | ||||||||
\(568\) | 8.29903e11 | 0.334549 | ||||||||
\(569\) | 2.50583e12 | 1.00218 | 0.501090 | − | 0.865395i | \(-0.332933\pi\) | ||||
0.501090 | + | 0.865395i | \(0.332933\pi\) | |||||||
\(570\) | −8.01189e11 | −0.317905 | ||||||||
\(571\) | −2.06826e12 | −0.814220 | −0.407110 | − | 0.913379i | \(-0.633463\pi\) | ||||
−0.407110 | + | 0.913379i | \(0.633463\pi\) | |||||||
\(572\) | −5.80683e11 | −0.226807 | ||||||||
\(573\) | 3.35193e12 | 1.29897 | ||||||||
\(574\) | 8.92019e11 | 0.342982 | ||||||||
\(575\) | −2.56360e12 | −0.978015 | ||||||||
\(576\) | 1.43371e12 | 0.542701 | ||||||||
\(577\) | −1.61115e12 | −0.605124 | −0.302562 | − | 0.953130i | \(-0.597842\pi\) | ||||
−0.302562 | + | 0.953130i | \(0.597842\pi\) | |||||||
\(578\) | −2.25826e12 | −0.841587 | ||||||||
\(579\) | −4.22629e12 | −1.56281 | ||||||||
\(580\) | 2.20962e11 | 0.0810760 | ||||||||
\(581\) | 1.72552e12 | 0.628243 | ||||||||
\(582\) | −1.83936e12 | −0.664527 | ||||||||
\(583\) | 4.96747e11 | 0.178085 | ||||||||
\(584\) | −5.05265e12 | −1.79747 | ||||||||
\(585\) | 1.11286e11 | 0.0392862 | ||||||||
\(586\) | 1.34682e12 | 0.471815 | ||||||||
\(587\) | 2.54415e12 | 0.884446 | 0.442223 | − | 0.896905i | \(-0.354190\pi\) | ||||
0.442223 | + | 0.896905i | \(0.354190\pi\) | |||||||
\(588\) | −6.56328e11 | −0.226424 | ||||||||
\(589\) | −6.17484e12 | −2.11401 | ||||||||
\(590\) | −4.62074e11 | −0.156992 | ||||||||
\(591\) | 2.11861e12 | 0.714345 | ||||||||
\(592\) | 2.04363e12 | 0.683841 | ||||||||
\(593\) | 1.32235e11 | 0.0439137 | 0.0219569 | − | 0.999759i | \(-0.493010\pi\) | ||||
0.0219569 | + | 0.999759i | \(0.493010\pi\) | |||||||
\(594\) | −1.95443e12 | −0.644142 | ||||||||
\(595\) | −5.33693e11 | −0.174568 | ||||||||
\(596\) | −7.59066e11 | −0.246417 | ||||||||
\(597\) | 3.68429e12 | 1.18705 | ||||||||
\(598\) | −1.10394e12 | −0.353013 | ||||||||
\(599\) | 2.32737e12 | 0.738660 | 0.369330 | − | 0.929298i | \(-0.379587\pi\) | ||||
0.369330 | + | 0.929298i | \(0.379587\pi\) | |||||||
\(600\) | 4.13163e12 | 1.30149 | ||||||||
\(601\) | −5.87945e12 | −1.83824 | −0.919119 | − | 0.393981i | \(-0.871098\pi\) | ||||
−0.919119 | + | 0.393981i | \(0.871098\pi\) | |||||||
\(602\) | −2.77221e11 | −0.0860284 | ||||||||
\(603\) | −2.68035e12 | −0.825588 | ||||||||
\(604\) | −1.99932e11 | −0.0611247 | ||||||||
\(605\) | 5.00952e11 | 0.152019 | ||||||||
\(606\) | 3.80728e11 | 0.114680 | ||||||||
\(607\) | −2.28556e12 | −0.683351 | −0.341675 | − | 0.939818i | \(-0.610994\pi\) | ||||
−0.341675 | + | 0.939818i | \(0.610994\pi\) | |||||||
\(608\) | 4.50292e12 | 1.33637 | ||||||||
\(609\) | −3.79986e12 | −1.11941 | ||||||||
\(610\) | −8.52676e11 | −0.249345 | ||||||||
\(611\) | 1.35973e12 | 0.394700 | ||||||||
\(612\) | −9.66665e11 | −0.278545 | ||||||||
\(613\) | −2.72675e12 | −0.779960 | −0.389980 | − | 0.920823i | \(-0.627518\pi\) | ||||
−0.389980 | + | 0.920823i | \(0.627518\pi\) | |||||||
\(614\) | −4.61192e11 | −0.130956 | ||||||||
\(615\) | −4.53828e11 | −0.127924 | ||||||||
\(616\) | −3.80551e12 | −1.06488 | ||||||||
\(617\) | 1.68755e12 | 0.468784 | 0.234392 | − | 0.972142i | \(-0.424690\pi\) | ||||
0.234392 | + | 0.972142i | \(0.424690\pi\) | |||||||
\(618\) | −4.50706e12 | −1.24293 | ||||||||
\(619\) | −5.29229e12 | −1.44889 | −0.724445 | − | 0.689332i | \(-0.757904\pi\) | ||||
−0.724445 | + | 0.689332i | \(0.757904\pi\) | |||||||
\(620\) | −2.59341e11 | −0.0704871 | ||||||||
\(621\) | 2.20816e12 | 0.595823 | ||||||||
\(622\) | −1.07114e12 | −0.286938 | ||||||||
\(623\) | 1.72682e12 | 0.459252 | ||||||||
\(624\) | 1.00893e12 | 0.266399 | ||||||||
\(625\) | 3.48468e12 | 0.913489 | ||||||||
\(626\) | 1.23623e12 | 0.321746 | ||||||||
\(627\) | 1.25176e13 | 3.23457 | ||||||||
\(628\) | 1.15710e12 | 0.296861 | ||||||||
\(629\) | −7.89626e12 | −2.01138 | ||||||||
\(630\) | 1.98040e11 | 0.0500864 | ||||||||
\(631\) | −2.78836e12 | −0.700191 | −0.350095 | − | 0.936714i | \(-0.613851\pi\) | ||||
−0.350095 | + | 0.936714i | \(0.613851\pi\) | |||||||
\(632\) | 1.55243e12 | 0.387065 | ||||||||
\(633\) | 6.18167e12 | 1.53034 | ||||||||
\(634\) | 5.58083e12 | 1.37182 | ||||||||
\(635\) | 3.89057e11 | 0.0949579 | ||||||||
\(636\) | 2.45614e11 | 0.0595245 | ||||||||
\(637\) | −9.05833e11 | −0.217982 | ||||||||
\(638\) | 5.80901e12 | 1.38806 | ||||||||
\(639\) | 6.74765e11 | 0.160103 | ||||||||
\(640\) | −9.09650e10 | −0.0214321 | ||||||||
\(641\) | 5.16942e12 | 1.20943 | 0.604715 | − | 0.796442i | \(-0.293287\pi\) | ||||
0.604715 | + | 0.796442i | \(0.293287\pi\) | |||||||
\(642\) | −3.27214e12 | −0.760194 | ||||||||
\(643\) | −3.58293e12 | −0.826589 | −0.413294 | − | 0.910598i | \(-0.635622\pi\) | ||||
−0.413294 | + | 0.910598i | \(0.635622\pi\) | |||||||
\(644\) | 1.16751e12 | 0.267469 | ||||||||
\(645\) | 1.41040e11 | 0.0320866 | ||||||||
\(646\) | 9.60500e12 | 2.16996 | ||||||||
\(647\) | 3.89598e12 | 0.874074 | 0.437037 | − | 0.899444i | \(-0.356028\pi\) | ||||
0.437037 | + | 0.899444i | \(0.356028\pi\) | |||||||
\(648\) | −6.09770e12 | −1.35856 | ||||||||
\(649\) | 7.21933e12 | 1.59733 | ||||||||
\(650\) | 1.54841e12 | 0.340233 | ||||||||
\(651\) | 4.45986e12 | 0.973210 | ||||||||
\(652\) | −8.33725e11 | −0.180679 | ||||||||
\(653\) | −6.62700e10 | −0.0142629 | −0.00713145 | − | 0.999975i | \(-0.502270\pi\) | ||||
−0.00713145 | + | 0.999975i | \(0.502270\pi\) | |||||||
\(654\) | −4.61430e12 | −0.986294 | ||||||||
\(655\) | −5.58432e11 | −0.118545 | ||||||||
\(656\) | −1.40810e12 | −0.296871 | ||||||||
\(657\) | −4.10813e12 | −0.860201 | ||||||||
\(658\) | 2.41971e12 | 0.503208 | ||||||||
\(659\) | 1.84962e12 | 0.382030 | 0.191015 | − | 0.981587i | \(-0.438822\pi\) | ||||
0.191015 | + | 0.981587i | \(0.438822\pi\) | |||||||
\(660\) | 5.25735e11 | 0.107850 | ||||||||
\(661\) | −3.74337e12 | −0.762705 | −0.381352 | − | 0.924430i | \(-0.624542\pi\) | ||||
−0.381352 | + | 0.924430i | \(0.624542\pi\) | |||||||
\(662\) | 1.79923e12 | 0.364104 | ||||||||
\(663\) | −3.89835e12 | −0.783557 | ||||||||
\(664\) | −4.80325e12 | −0.958913 | ||||||||
\(665\) | 1.16943e12 | 0.231888 | ||||||||
\(666\) | 2.93010e12 | 0.577097 | ||||||||
\(667\) | −6.56314e12 | −1.28394 | ||||||||
\(668\) | 1.73073e12 | 0.336307 | ||||||||
\(669\) | −1.90467e12 | −0.367623 | ||||||||
\(670\) | 1.11856e12 | 0.214448 | ||||||||
\(671\) | 1.33220e13 | 2.53699 | ||||||||
\(672\) | −3.25229e12 | −0.615216 | ||||||||
\(673\) | 2.59774e12 | 0.488122 | 0.244061 | − | 0.969760i | \(-0.421520\pi\) | ||||
0.244061 | + | 0.969760i | \(0.421520\pi\) | |||||||
\(674\) | 6.21218e12 | 1.15951 | ||||||||
\(675\) | −3.09721e12 | −0.574253 | ||||||||
\(676\) | 1.62766e12 | 0.299780 | ||||||||
\(677\) | −7.57984e12 | −1.38679 | −0.693396 | − | 0.720557i | \(-0.743886\pi\) | ||||
−0.693396 | + | 0.720557i | \(0.743886\pi\) | |||||||
\(678\) | −7.46700e12 | −1.35710 | ||||||||
\(679\) | 2.68477e12 | 0.484722 | ||||||||
\(680\) | 1.48562e12 | 0.266450 | ||||||||
\(681\) | −2.60963e12 | −0.464961 | ||||||||
\(682\) | −6.81798e12 | −1.20677 | ||||||||
\(683\) | −9.09946e12 | −1.60001 | −0.800004 | − | 0.599994i | \(-0.795170\pi\) | ||||
−0.800004 | + | 0.599994i | \(0.795170\pi\) | |||||||
\(684\) | 2.11817e12 | 0.370005 | ||||||||
\(685\) | 1.16188e12 | 0.201630 | ||||||||
\(686\) | −4.88414e12 | −0.842034 | ||||||||
\(687\) | −1.98207e12 | −0.339479 | ||||||||
\(688\) | 4.37609e11 | 0.0744626 | ||||||||
\(689\) | 3.38985e11 | 0.0573052 | ||||||||
\(690\) | 9.99481e11 | 0.167862 | ||||||||
\(691\) | 1.40526e10 | 0.00234480 | 0.00117240 | − | 0.999999i | \(-0.499627\pi\) | ||||
0.00117240 | + | 0.999999i | \(0.499627\pi\) | |||||||
\(692\) | 2.70442e12 | 0.448329 | ||||||||
\(693\) | −3.09413e12 | −0.509611 | ||||||||
\(694\) | −8.22578e11 | −0.134604 | ||||||||
\(695\) | 9.29037e11 | 0.151043 | ||||||||
\(696\) | 1.05775e13 | 1.70860 | ||||||||
\(697\) | 5.44068e12 | 0.873184 | ||||||||
\(698\) | 9.90576e12 | 1.57957 | ||||||||
\(699\) | 1.77583e12 | 0.281355 | ||||||||
\(700\) | −1.63757e12 | −0.257786 | ||||||||
\(701\) | −9.00853e12 | −1.40904 | −0.704519 | − | 0.709685i | \(-0.748837\pi\) | ||||
−0.704519 | + | 0.709685i | \(0.748837\pi\) | |||||||
\(702\) | −1.33372e12 | −0.207276 | ||||||||
\(703\) | 1.73024e13 | 2.67182 | ||||||||
\(704\) | 9.34793e12 | 1.43429 | ||||||||
\(705\) | −1.23106e12 | −0.187685 | ||||||||
\(706\) | 5.80723e12 | 0.879727 | ||||||||
\(707\) | −5.55720e11 | −0.0836505 | ||||||||
\(708\) | 3.56956e12 | 0.533906 | ||||||||
\(709\) | −1.15494e13 | −1.71653 | −0.858264 | − | 0.513209i | \(-0.828457\pi\) | ||||
−0.858264 | + | 0.513209i | \(0.828457\pi\) | |||||||
\(710\) | −2.81592e11 | −0.0415870 | ||||||||
\(711\) | 1.26222e12 | 0.185235 | ||||||||
\(712\) | −4.80687e12 | −0.700974 | ||||||||
\(713\) | 7.70309e12 | 1.11625 | ||||||||
\(714\) | −6.93734e12 | −0.998966 | ||||||||
\(715\) | 7.25596e11 | 0.103829 | ||||||||
\(716\) | −3.92306e12 | −0.557848 | ||||||||
\(717\) | −6.42268e12 | −0.907569 | ||||||||
\(718\) | −5.20801e12 | −0.731327 | ||||||||
\(719\) | −2.80308e12 | −0.391161 | −0.195580 | − | 0.980688i | \(-0.562659\pi\) | ||||
−0.195580 | + | 0.980688i | \(0.562659\pi\) | |||||||
\(720\) | −3.12617e11 | −0.0433528 | ||||||||
\(721\) | 6.57861e12 | 0.906621 | ||||||||
\(722\) | −1.52639e13 | −2.09048 | ||||||||
\(723\) | −8.36603e12 | −1.13867 | ||||||||
\(724\) | 3.78386e12 | 0.511813 | ||||||||
\(725\) | 9.20559e12 | 1.23746 | ||||||||
\(726\) | 6.51175e12 | 0.869927 | ||||||||
\(727\) | −5.45780e12 | −0.724625 | −0.362312 | − | 0.932057i | \(-0.618013\pi\) | ||||
−0.362312 | + | 0.932057i | \(0.618013\pi\) | |||||||
\(728\) | −2.59692e12 | −0.342663 | ||||||||
\(729\) | 6.03463e11 | 0.0791366 | ||||||||
\(730\) | 1.71440e12 | 0.223439 | ||||||||
\(731\) | −1.69085e12 | −0.219016 | ||||||||
\(732\) | 6.58700e12 | 0.847984 | ||||||||
\(733\) | −3.95238e12 | −0.505697 | −0.252849 | − | 0.967506i | \(-0.581367\pi\) | ||||
−0.252849 | + | 0.967506i | \(0.581367\pi\) | |||||||
\(734\) | 1.94255e12 | 0.247024 | ||||||||
\(735\) | 8.20118e11 | 0.103653 | ||||||||
\(736\) | −5.61738e12 | −0.705640 | ||||||||
\(737\) | −1.74761e13 | −2.18193 | ||||||||
\(738\) | −2.01890e12 | −0.250531 | ||||||||
\(739\) | 2.12821e11 | 0.0262491 | 0.0131246 | − | 0.999914i | \(-0.495822\pi\) | ||||
0.0131246 | + | 0.999914i | \(0.495822\pi\) | |||||||
\(740\) | 7.26696e11 | 0.0890861 | ||||||||
\(741\) | 8.54212e12 | 1.04084 | ||||||||
\(742\) | 6.03242e11 | 0.0730591 | ||||||||
\(743\) | −4.10800e12 | −0.494516 | −0.247258 | − | 0.968950i | \(-0.579530\pi\) | ||||
−0.247258 | + | 0.968950i | \(0.579530\pi\) | |||||||
\(744\) | −1.24147e13 | −1.48545 | ||||||||
\(745\) | 9.48495e11 | 0.112806 | ||||||||
\(746\) | 7.47413e12 | 0.883560 | ||||||||
\(747\) | −3.90536e12 | −0.458900 | ||||||||
\(748\) | −6.30274e12 | −0.736161 | ||||||||
\(749\) | 4.77609e12 | 0.554504 | ||||||||
\(750\) | −2.84583e12 | −0.328423 | ||||||||
\(751\) | 5.19165e12 | 0.595560 | 0.297780 | − | 0.954634i | \(-0.403754\pi\) | ||||
0.297780 | + | 0.954634i | \(0.403754\pi\) | |||||||
\(752\) | −3.81966e12 | −0.435556 | ||||||||
\(753\) | −5.78013e12 | −0.655179 | ||||||||
\(754\) | 3.96412e12 | 0.446659 | ||||||||
\(755\) | 2.49826e11 | 0.0279819 | ||||||||
\(756\) | 1.41052e12 | 0.157047 | ||||||||
\(757\) | −1.20035e13 | −1.32854 | −0.664272 | − | 0.747491i | \(-0.731258\pi\) | ||||
−0.664272 | + | 0.747491i | \(0.731258\pi\) | |||||||
\(758\) | 4.72936e12 | 0.520345 | ||||||||
\(759\) | −1.56157e13 | −1.70794 | ||||||||
\(760\) | −3.25530e12 | −0.353940 | ||||||||
\(761\) | −1.27185e12 | −0.137469 | −0.0687345 | − | 0.997635i | \(-0.521896\pi\) | ||||
−0.0687345 | + | 0.997635i | \(0.521896\pi\) | |||||||
\(762\) | 5.05725e12 | 0.543397 | ||||||||
\(763\) | 6.73515e12 | 0.719427 | ||||||||
\(764\) | 3.69818e12 | 0.392706 | ||||||||
\(765\) | 1.20790e12 | 0.127513 | ||||||||
\(766\) | −1.46267e13 | −1.53502 | ||||||||
\(767\) | 4.92654e12 | 0.514000 | ||||||||
\(768\) | 1.12169e13 | 1.16345 | ||||||||
\(769\) | 1.49703e13 | 1.54370 | 0.771849 | − | 0.635806i | \(-0.219332\pi\) | ||||
0.771849 | + | 0.635806i | \(0.219332\pi\) | |||||||
\(770\) | 1.29124e12 | 0.132373 | ||||||||
\(771\) | 1.41919e13 | 1.44643 | ||||||||
\(772\) | −4.66286e12 | −0.472470 | ||||||||
\(773\) | 1.59529e13 | 1.60706 | 0.803529 | − | 0.595266i | \(-0.202953\pi\) | ||||
0.803529 | + | 0.595266i | \(0.202953\pi\) | |||||||
\(774\) | 6.27431e11 | 0.0628394 | ||||||||
\(775\) | −1.08045e13 | −1.07584 | ||||||||
\(776\) | −7.47346e12 | −0.739851 | ||||||||
\(777\) | −1.24969e13 | −1.23000 | ||||||||
\(778\) | −1.24685e13 | −1.22013 | ||||||||
\(779\) | −1.19217e13 | −1.15990 | ||||||||
\(780\) | 3.58767e11 | 0.0347046 | ||||||||
\(781\) | 4.39953e12 | 0.423133 | ||||||||
\(782\) | −1.19822e13 | −1.14579 | ||||||||
\(783\) | −7.92922e12 | −0.753881 | ||||||||
\(784\) | 2.54460e12 | 0.240546 | ||||||||
\(785\) | −1.44586e12 | −0.135898 | ||||||||
\(786\) | −7.25892e12 | −0.678376 | ||||||||
\(787\) | −4.64442e12 | −0.431564 | −0.215782 | − | 0.976442i | \(-0.569230\pi\) | ||||
−0.215782 | + | 0.976442i | \(0.569230\pi\) | |||||||
\(788\) | 2.33747e12 | 0.215962 | ||||||||
\(789\) | −7.25496e12 | −0.666482 | ||||||||
\(790\) | −5.26750e11 | −0.0481152 | ||||||||
\(791\) | 1.08990e13 | 0.989904 | ||||||||
\(792\) | 8.61298e12 | 0.777840 | ||||||||
\(793\) | 9.09107e12 | 0.816368 | ||||||||
\(794\) | −4.28532e11 | −0.0382641 | ||||||||
\(795\) | −3.06908e11 | −0.0272494 | ||||||||
\(796\) | 4.06487e12 | 0.358871 | ||||||||
\(797\) | 1.24077e13 | 1.08925 | 0.544625 | − | 0.838680i | \(-0.316672\pi\) | ||||
0.544625 | + | 0.838680i | \(0.316672\pi\) | |||||||
\(798\) | 1.52012e13 | 1.32698 | ||||||||
\(799\) | 1.47585e13 | 1.28110 | ||||||||
\(800\) | 7.87905e12 | 0.680094 | ||||||||
\(801\) | −3.90830e12 | −0.335460 | ||||||||
\(802\) | 2.36275e12 | 0.201666 | ||||||||
\(803\) | −2.67854e13 | −2.27341 | ||||||||
\(804\) | −8.64097e12 | −0.729306 | ||||||||
\(805\) | −1.45887e12 | −0.122443 | ||||||||
\(806\) | −4.65266e12 | −0.388323 | ||||||||
\(807\) | −1.84012e13 | −1.52727 | ||||||||
\(808\) | 1.54693e12 | 0.127679 | ||||||||
\(809\) | −9.50544e12 | −0.780196 | −0.390098 | − | 0.920773i | \(-0.627559\pi\) | ||||
−0.390098 | + | 0.920773i | \(0.627559\pi\) | |||||||
\(810\) | 2.06899e12 | 0.168879 | ||||||||
\(811\) | −6.56385e12 | −0.532801 | −0.266400 | − | 0.963862i | \(-0.585834\pi\) | ||||
−0.266400 | + | 0.963862i | \(0.585834\pi\) | |||||||
\(812\) | −4.19238e12 | −0.338422 | ||||||||
\(813\) | 1.40577e13 | 1.12851 | ||||||||
\(814\) | 1.91045e13 | 1.52520 | ||||||||
\(815\) | 1.04179e12 | 0.0827121 | ||||||||
\(816\) | 1.09510e13 | 0.864664 | ||||||||
\(817\) | 3.70501e12 | 0.290931 | ||||||||
\(818\) | −3.99306e12 | −0.311829 | ||||||||
\(819\) | −2.11146e12 | −0.163986 | ||||||||
\(820\) | −5.00708e11 | −0.0386743 | ||||||||
\(821\) | 3.96939e12 | 0.304915 | 0.152458 | − | 0.988310i | \(-0.451281\pi\) | ||||
0.152458 | + | 0.988310i | \(0.451281\pi\) | |||||||
\(822\) | 1.51030e13 | 1.15383 | ||||||||
\(823\) | 2.57352e13 | 1.95537 | 0.977683 | − | 0.210086i | \(-0.0673743\pi\) | ||||
0.977683 | + | 0.210086i | \(0.0673743\pi\) | |||||||
\(824\) | −1.83126e13 | −1.38381 | ||||||||
\(825\) | 2.19029e13 | 1.64611 | ||||||||
\(826\) | 8.76706e12 | 0.655305 | ||||||||
\(827\) | −1.59944e13 | −1.18903 | −0.594516 | − | 0.804084i | \(-0.702656\pi\) | ||||
−0.594516 | + | 0.804084i | \(0.702656\pi\) | |||||||
\(828\) | −2.64241e12 | −0.195373 | ||||||||
\(829\) | 5.84546e12 | 0.429856 | 0.214928 | − | 0.976630i | \(-0.431048\pi\) | ||||
0.214928 | + | 0.976630i | \(0.431048\pi\) | |||||||
\(830\) | 1.62978e12 | 0.119200 | ||||||||
\(831\) | −3.47855e12 | −0.253043 | ||||||||
\(832\) | 6.37911e12 | 0.461536 | ||||||||
\(833\) | −9.83194e12 | −0.707516 | ||||||||
\(834\) | 1.20763e13 | 0.864346 | ||||||||
\(835\) | −2.16265e12 | −0.153956 | ||||||||
\(836\) | 1.38106e13 | 0.977881 | ||||||||
\(837\) | 9.30646e12 | 0.655420 | ||||||||
\(838\) | 1.60054e13 | 1.12116 | ||||||||
\(839\) | −2.45685e12 | −0.171178 | −0.0855892 | − | 0.996331i | \(-0.527277\pi\) | ||||
−0.0855892 | + | 0.996331i | \(0.527277\pi\) | |||||||
\(840\) | 2.35118e12 | 0.162941 | ||||||||
\(841\) | 9.06028e12 | 0.624539 | ||||||||
\(842\) | −8.83669e12 | −0.605878 | ||||||||
\(843\) | 2.02337e13 | 1.37991 | ||||||||
\(844\) | 6.82023e12 | 0.462656 | ||||||||
\(845\) | −2.03385e12 | −0.137234 | ||||||||
\(846\) | −5.47652e12 | −0.367568 | ||||||||
\(847\) | −9.50471e12 | −0.634546 | ||||||||
\(848\) | −9.52253e11 | −0.0632370 | ||||||||
\(849\) | 1.57545e13 | 1.04069 | ||||||||
\(850\) | 1.68065e13 | 1.10431 | ||||||||
\(851\) | −2.15847e13 | −1.41079 | ||||||||
\(852\) | 2.17532e12 | 0.141431 | ||||||||
\(853\) | 1.38158e11 | 0.00893523 | 0.00446761 | − | 0.999990i | \(-0.498578\pi\) | ||||
0.00446761 | + | 0.999990i | \(0.498578\pi\) | |||||||
\(854\) | 1.61781e13 | 1.04080 | ||||||||
\(855\) | −2.64677e12 | −0.169383 | ||||||||
\(856\) | −1.32950e13 | −0.846361 | ||||||||
\(857\) | −4.58334e12 | −0.290248 | −0.145124 | − | 0.989414i | \(-0.546358\pi\) | ||||
−0.145124 | + | 0.989414i | \(0.546358\pi\) | |||||||
\(858\) | 9.43183e12 | 0.594160 | ||||||||
\(859\) | 1.34992e13 | 0.845938 | 0.422969 | − | 0.906144i | \(-0.360988\pi\) | ||||
0.422969 | + | 0.906144i | \(0.360988\pi\) | |||||||
\(860\) | 1.55609e11 | 0.00970047 | ||||||||
\(861\) | 8.61060e12 | 0.533973 | ||||||||
\(862\) | −1.95767e13 | −1.20769 | ||||||||
\(863\) | 1.87111e13 | 1.14829 | 0.574144 | − | 0.818754i | \(-0.305335\pi\) | ||||
0.574144 | + | 0.818754i | \(0.305335\pi\) | |||||||
\(864\) | −6.78661e12 | −0.414325 | ||||||||
\(865\) | −3.37932e12 | −0.205238 | ||||||||
\(866\) | 1.20781e13 | 0.729738 | ||||||||
\(867\) | −2.17988e13 | −1.31023 | ||||||||
\(868\) | 4.92056e12 | 0.294222 | ||||||||
\(869\) | 8.22981e12 | 0.489554 | ||||||||
\(870\) | −3.58902e12 | −0.212392 | ||||||||
\(871\) | −1.19259e13 | −0.702115 | ||||||||
\(872\) | −1.87483e13 | −1.09809 | ||||||||
\(873\) | −6.07641e12 | −0.354065 | ||||||||
\(874\) | 2.62556e13 | 1.52202 | ||||||||
\(875\) | 4.15385e12 | 0.239560 | ||||||||
\(876\) | −1.32439e13 | −0.759884 | ||||||||
\(877\) | −2.55346e13 | −1.45757 | −0.728786 | − | 0.684741i | \(-0.759915\pi\) | ||||
−0.728786 | + | 0.684741i | \(0.759915\pi\) | |||||||
\(878\) | −4.98593e12 | −0.283153 | ||||||||
\(879\) | 1.30008e13 | 0.734548 | ||||||||
\(880\) | −2.03829e12 | −0.114576 | ||||||||
\(881\) | 3.99929e12 | 0.223662 | 0.111831 | − | 0.993727i | \(-0.464329\pi\) | ||||
0.111831 | + | 0.993727i | \(0.464329\pi\) | |||||||
\(882\) | 3.64838e12 | 0.202998 | ||||||||
\(883\) | −1.35158e12 | −0.0748204 | −0.0374102 | − | 0.999300i | \(-0.511911\pi\) | ||||
−0.0374102 | + | 0.999300i | \(0.511911\pi\) | |||||||
\(884\) | −4.30105e12 | −0.236886 | ||||||||
\(885\) | −4.46036e12 | −0.244414 | ||||||||
\(886\) | −5.83445e12 | −0.318089 | ||||||||
\(887\) | −1.75151e13 | −0.950074 | −0.475037 | − | 0.879966i | \(-0.657565\pi\) | ||||
−0.475037 | + | 0.879966i | \(0.657565\pi\) | |||||||
\(888\) | 3.47870e13 | 1.87741 | ||||||||
\(889\) | −7.38168e12 | −0.396367 | ||||||||
\(890\) | 1.63101e12 | 0.0871365 | ||||||||
\(891\) | −3.23255e13 | −1.71828 | ||||||||
\(892\) | −2.10143e12 | −0.111140 | ||||||||
\(893\) | −3.23391e13 | −1.70175 | ||||||||
\(894\) | 1.23292e13 | 0.645532 | ||||||||
\(895\) | 4.90208e12 | 0.255374 | ||||||||
\(896\) | 1.72591e12 | 0.0894604 | ||||||||
\(897\) | −1.06563e13 | −0.549591 | ||||||||
\(898\) | −1.66245e13 | −0.853111 | ||||||||
\(899\) | −2.76609e13 | −1.41237 | ||||||||
\(900\) | 3.70630e12 | 0.188300 | ||||||||
\(901\) | 3.67935e12 | 0.185999 | ||||||||
\(902\) | −1.31634e13 | −0.662123 | ||||||||
\(903\) | −2.67599e12 | −0.133934 | ||||||||
\(904\) | −3.03391e13 | −1.51093 | ||||||||
\(905\) | −4.72814e12 | −0.234300 | ||||||||
\(906\) | 3.24743e12 | 0.160126 | ||||||||
\(907\) | 3.20478e13 | 1.57241 | 0.786204 | − | 0.617967i | \(-0.212044\pi\) | ||||
0.786204 | + | 0.617967i | \(0.212044\pi\) | |||||||
\(908\) | −2.87920e12 | −0.140568 | ||||||||
\(909\) | 1.25776e12 | 0.0611025 | ||||||||
\(910\) | 8.81153e11 | 0.0425956 | ||||||||
\(911\) | 3.17963e13 | 1.52948 | 0.764740 | − | 0.644340i | \(-0.222868\pi\) | ||||
0.764740 | + | 0.644340i | \(0.222868\pi\) | |||||||
\(912\) | −2.39959e13 | −1.14858 | ||||||||
\(913\) | −2.54633e13 | −1.21282 | ||||||||
\(914\) | −1.94287e13 | −0.920846 | ||||||||
\(915\) | −8.23082e12 | −0.388194 | ||||||||
\(916\) | −2.18682e12 | −0.102632 | ||||||||
\(917\) | 1.05953e13 | 0.494824 | ||||||||
\(918\) | −1.44763e13 | −0.672766 | ||||||||
\(919\) | 6.46550e12 | 0.299008 | 0.149504 | − | 0.988761i | \(-0.452232\pi\) | ||||
0.149504 | + | 0.988761i | \(0.452232\pi\) | |||||||
\(920\) | 4.06098e12 | 0.186890 | ||||||||
\(921\) | −4.45186e12 | −0.203879 | ||||||||
\(922\) | −9.02438e12 | −0.411271 | ||||||||
\(923\) | 3.00228e12 | 0.136158 | ||||||||
\(924\) | −9.97492e12 | −0.450180 | ||||||||
\(925\) | 3.02751e13 | 1.35972 | ||||||||
\(926\) | 2.27743e13 | 1.01788 | ||||||||
\(927\) | −1.48893e13 | −0.662241 | ||||||||
\(928\) | 2.01713e13 | 0.892829 | ||||||||
\(929\) | 3.58746e12 | 0.158022 | 0.0790109 | − | 0.996874i | \(-0.474824\pi\) | ||||
0.0790109 | + | 0.996874i | \(0.474824\pi\) | |||||||
\(930\) | 4.21240e12 | 0.184653 | ||||||||
\(931\) | 2.15439e13 | 0.939831 | ||||||||
\(932\) | 1.95928e12 | 0.0850598 | ||||||||
\(933\) | −1.03396e13 | −0.446721 | ||||||||
\(934\) | −3.02526e13 | −1.30077 | ||||||||
\(935\) | 7.87563e12 | 0.337002 | ||||||||
\(936\) | 5.87758e12 | 0.250298 | ||||||||
\(937\) | 4.03654e13 | 1.71073 | 0.855364 | − | 0.518027i | \(-0.173333\pi\) | ||||
0.855364 | + | 0.518027i | \(0.173333\pi\) | |||||||
\(938\) | −2.12227e13 | −0.895135 | ||||||||
\(939\) | 1.19332e13 | 0.500912 | ||||||||
\(940\) | −1.35823e12 | −0.0567413 | ||||||||
\(941\) | −1.34172e13 | −0.557840 | −0.278920 | − | 0.960314i | \(-0.589977\pi\) | ||||
−0.278920 | + | 0.960314i | \(0.589977\pi\) | |||||||
\(942\) | −1.87944e13 | −0.777677 | ||||||||
\(943\) | 1.48723e13 | 0.612456 | ||||||||
\(944\) | −1.38393e13 | −0.567205 | ||||||||
\(945\) | −1.76252e12 | −0.0718938 | ||||||||
\(946\) | 4.09091e12 | 0.166077 | ||||||||
\(947\) | −8.00627e12 | −0.323486 | −0.161743 | − | 0.986833i | \(-0.551712\pi\) | ||||
−0.161743 | + | 0.986833i | \(0.551712\pi\) | |||||||
\(948\) | 4.06919e12 | 0.163633 | ||||||||
\(949\) | −1.82786e13 | −0.731552 | ||||||||
\(950\) | −3.68266e13 | −1.46692 | ||||||||
\(951\) | 5.38714e13 | 2.13573 | ||||||||
\(952\) | −2.81870e13 | −1.11220 | ||||||||
\(953\) | −2.74035e13 | −1.07619 | −0.538094 | − | 0.842885i | \(-0.680855\pi\) | ||||
−0.538094 | + | 0.842885i | \(0.680855\pi\) | |||||||
\(954\) | −1.36531e12 | −0.0533660 | ||||||||
\(955\) | −4.62108e12 | −0.179775 | ||||||||
\(956\) | −7.08614e12 | −0.274378 | ||||||||
\(957\) | 5.60739e13 | 2.16101 | ||||||||
\(958\) | 2.41515e13 | 0.926402 | ||||||||
\(959\) | −2.20447e13 | −0.841628 | ||||||||
\(960\) | −5.77549e12 | −0.219466 | ||||||||
\(961\) | 6.02571e12 | 0.227904 | ||||||||
\(962\) | 1.30371e13 | 0.490788 | ||||||||
\(963\) | −1.08097e13 | −0.405037 | ||||||||
\(964\) | −9.23024e12 | −0.344244 | ||||||||
\(965\) | 5.82650e12 | 0.216289 | ||||||||
\(966\) | −1.89634e13 | −0.700680 | ||||||||
\(967\) | −1.14021e13 | −0.419341 | −0.209671 | − | 0.977772i | \(-0.567239\pi\) | ||||
−0.209671 | + | 0.977772i | \(0.567239\pi\) | |||||||
\(968\) | 2.64578e13 | 0.968534 | ||||||||
\(969\) | 9.27164e13 | 3.37831 | ||||||||
\(970\) | 2.53580e12 | 0.0919692 | ||||||||
\(971\) | 3.11540e13 | 1.12467 | 0.562337 | − | 0.826908i | \(-0.309902\pi\) | ||||
0.562337 | + | 0.826908i | \(0.309902\pi\) | |||||||
\(972\) | −9.84738e12 | −0.353853 | ||||||||
\(973\) | −1.76269e13 | −0.630475 | ||||||||
\(974\) | −7.44682e12 | −0.265128 | ||||||||
\(975\) | 1.49467e13 | 0.529694 | ||||||||
\(976\) | −2.55380e13 | −0.900872 | ||||||||
\(977\) | −4.42114e13 | −1.55242 | −0.776209 | − | 0.630475i | \(-0.782860\pi\) | ||||
−0.776209 | + | 0.630475i | \(0.782860\pi\) | |||||||
\(978\) | 1.35419e13 | 0.473320 | ||||||||
\(979\) | −2.54824e13 | −0.886582 | ||||||||
\(980\) | 9.04836e11 | 0.0313367 | ||||||||
\(981\) | −1.52436e13 | −0.525505 | ||||||||
\(982\) | −4.50594e12 | −0.154626 | ||||||||
\(983\) | 1.16477e13 | 0.397877 | 0.198939 | − | 0.980012i | \(-0.436251\pi\) | ||||
0.198939 | + | 0.980012i | \(0.436251\pi\) | |||||||
\(984\) | −2.39689e13 | −0.815024 | ||||||||
\(985\) | −2.92079e12 | −0.0988639 | ||||||||
\(986\) | 4.30267e13 | 1.44975 | ||||||||
\(987\) | 2.33573e13 | 0.783422 | ||||||||
\(988\) | 9.42452e12 | 0.314668 | ||||||||
\(989\) | −4.62199e12 | −0.153619 | ||||||||
\(990\) | −2.92245e12 | −0.0966915 | ||||||||
\(991\) | 4.19672e12 | 0.138222 | 0.0691112 | − | 0.997609i | \(-0.477984\pi\) | ||||
0.0691112 | + | 0.997609i | \(0.477984\pi\) | |||||||
\(992\) | −2.36749e13 | −0.776222 | ||||||||
\(993\) | 1.73678e13 | 0.566858 | ||||||||
\(994\) | 5.34273e12 | 0.173590 | ||||||||
\(995\) | −5.07929e12 | −0.164285 | ||||||||
\(996\) | −1.25902e13 | −0.405383 | ||||||||
\(997\) | 3.39392e13 | 1.08786 | 0.543930 | − | 0.839131i | \(-0.316936\pi\) | ||||
0.543930 | + | 0.839131i | \(0.316936\pi\) | |||||||
\(998\) | 2.13024e13 | 0.679737 | ||||||||
\(999\) | −2.60774e13 | −0.828362 |
(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 | 43.10.a.a.1.6 | ✓ | 15 | |
3.2 | odd | 2 | 387.10.a.c.1.10 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.10.a.a.1.6 | ✓ | 15 | 1.1 | even | 1 | trivial | |
387.10.a.c.1.10 | 15 | 3.2 | odd | 2 |