Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [547,8,Mod(1,547)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("547.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.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: | \(170.874608940\) |
Analytic rank: | \(1\) |
Dimension: | \(156\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 547.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −20.7147 | −1.83094 | −0.915469 | − | 0.402389i | \(-0.868180\pi\) | ||||
−0.915469 | + | 0.402389i | \(0.868180\pi\) | |||||||
\(3\) | 73.8020 | 1.57813 | 0.789067 | − | 0.614307i | \(-0.210564\pi\) | ||||
0.789067 | + | 0.614307i | \(0.210564\pi\) | |||||||
\(4\) | 301.098 | 2.35233 | ||||||||
\(5\) | 73.8971 | 0.264382 | 0.132191 | − | 0.991224i | \(-0.457799\pi\) | ||||
0.132191 | + | 0.991224i | \(0.457799\pi\) | |||||||
\(6\) | −1528.79 | −2.88946 | ||||||||
\(7\) | 1490.12 | 1.64202 | 0.821011 | − | 0.570913i | \(-0.193411\pi\) | ||||
0.821011 | + | 0.570913i | \(0.193411\pi\) | |||||||
\(8\) | −3585.68 | −2.47603 | ||||||||
\(9\) | 3259.74 | 1.49051 | ||||||||
\(10\) | −1530.76 | −0.484067 | ||||||||
\(11\) | −3255.54 | −0.737478 | −0.368739 | − | 0.929533i | \(-0.620210\pi\) | ||||
−0.368739 | + | 0.929533i | \(0.620210\pi\) | |||||||
\(12\) | 22221.7 | 3.71229 | ||||||||
\(13\) | −9643.42 | −1.21739 | −0.608694 | − | 0.793405i | \(-0.708306\pi\) | ||||
−0.608694 | + | 0.793405i | \(0.708306\pi\) | |||||||
\(14\) | −30867.4 | −3.00644 | ||||||||
\(15\) | 5453.76 | 0.417231 | ||||||||
\(16\) | 35735.7 | 2.18113 | ||||||||
\(17\) | 23212.3 | 1.14590 | 0.572951 | − | 0.819590i | \(-0.305799\pi\) | ||||
0.572951 | + | 0.819590i | \(0.305799\pi\) | |||||||
\(18\) | −67524.5 | −2.72903 | ||||||||
\(19\) | −26830.9 | −0.897423 | −0.448711 | − | 0.893677i | \(-0.648117\pi\) | ||||
−0.448711 | + | 0.893677i | \(0.648117\pi\) | |||||||
\(20\) | 22250.3 | 0.621915 | ||||||||
\(21\) | 109974. | 2.59133 | ||||||||
\(22\) | 67437.6 | 1.35028 | ||||||||
\(23\) | −96604.9 | −1.65559 | −0.827793 | − | 0.561034i | \(-0.810404\pi\) | ||||
−0.827793 | + | 0.561034i | \(0.810404\pi\) | |||||||
\(24\) | −264631. | −3.90751 | ||||||||
\(25\) | −72664.2 | −0.930102 | ||||||||
\(26\) | 199760. | 2.22896 | ||||||||
\(27\) | 79170.4 | 0.774086 | ||||||||
\(28\) | 448673. | 3.86258 | ||||||||
\(29\) | −43668.4 | −0.332487 | −0.166243 | − | 0.986085i | \(-0.553164\pi\) | ||||
−0.166243 | + | 0.986085i | \(0.553164\pi\) | |||||||
\(30\) | −112973. | −0.763923 | ||||||||
\(31\) | 84751.2 | 0.510952 | 0.255476 | − | 0.966815i | \(-0.417768\pi\) | ||||
0.255476 | + | 0.966815i | \(0.417768\pi\) | |||||||
\(32\) | −281286. | −1.51748 | ||||||||
\(33\) | −240266. | −1.16384 | ||||||||
\(34\) | −480836. | −2.09807 | ||||||||
\(35\) | 110116. | 0.434121 | ||||||||
\(36\) | 981503. | 3.50617 | ||||||||
\(37\) | 236077. | 0.766208 | 0.383104 | − | 0.923705i | \(-0.374855\pi\) | ||||
0.383104 | + | 0.923705i | \(0.374855\pi\) | |||||||
\(38\) | 555793. | 1.64312 | ||||||||
\(39\) | −711704. | −1.92120 | ||||||||
\(40\) | −264971. | −0.654620 | ||||||||
\(41\) | −539942. | −1.22350 | −0.611749 | − | 0.791052i | \(-0.709534\pi\) | ||||
−0.611749 | + | 0.791052i | \(0.709534\pi\) | |||||||
\(42\) | −2.27808e6 | −4.74456 | ||||||||
\(43\) | 481095. | 0.922766 | 0.461383 | − | 0.887201i | \(-0.347353\pi\) | ||||
0.461383 | + | 0.887201i | \(0.347353\pi\) | |||||||
\(44\) | −980239. | −1.73479 | ||||||||
\(45\) | 240885. | 0.394064 | ||||||||
\(46\) | 2.00114e6 | 3.03127 | ||||||||
\(47\) | 93118.1 | 0.130825 | 0.0654127 | − | 0.997858i | \(-0.479164\pi\) | ||||
0.0654127 | + | 0.997858i | \(0.479164\pi\) | |||||||
\(48\) | 2.63737e6 | 3.44212 | ||||||||
\(49\) | 1.39692e6 | 1.69623 | ||||||||
\(50\) | 1.50522e6 | 1.70296 | ||||||||
\(51\) | 1.71312e6 | 1.80839 | ||||||||
\(52\) | −2.90362e6 | −2.86370 | ||||||||
\(53\) | 1.53295e6 | 1.41437 | 0.707185 | − | 0.707028i | \(-0.249965\pi\) | ||||
0.707185 | + | 0.707028i | \(0.249965\pi\) | |||||||
\(54\) | −1.63999e6 | −1.41730 | ||||||||
\(55\) | −240575. | −0.194976 | ||||||||
\(56\) | −5.34310e6 | −4.06570 | ||||||||
\(57\) | −1.98017e6 | −1.41625 | ||||||||
\(58\) | 904578. | 0.608763 | ||||||||
\(59\) | −2.65658e6 | −1.68400 | −0.841998 | − | 0.539480i | \(-0.818621\pi\) | ||||
−0.841998 | + | 0.539480i | \(0.818621\pi\) | |||||||
\(60\) | 1.64212e6 | 0.981465 | ||||||||
\(61\) | −1.48574e6 | −0.838087 | −0.419044 | − | 0.907966i | \(-0.637635\pi\) | ||||
−0.419044 | + | 0.907966i | \(0.637635\pi\) | |||||||
\(62\) | −1.75559e6 | −0.935521 | ||||||||
\(63\) | 4.85741e6 | 2.44744 | ||||||||
\(64\) | 1.25259e6 | 0.597283 | ||||||||
\(65\) | −712621. | −0.321856 | ||||||||
\(66\) | 4.97703e6 | 2.13092 | ||||||||
\(67\) | −2.58945e6 | −1.05183 | −0.525916 | − | 0.850537i | \(-0.676277\pi\) | ||||
−0.525916 | + | 0.850537i | \(0.676277\pi\) | |||||||
\(68\) | 6.98919e6 | 2.69554 | ||||||||
\(69\) | −7.12964e6 | −2.61274 | ||||||||
\(70\) | −2.28101e6 | −0.794849 | ||||||||
\(71\) | −1.00423e6 | −0.332987 | −0.166494 | − | 0.986043i | \(-0.553245\pi\) | ||||
−0.166494 | + | 0.986043i | \(0.553245\pi\) | |||||||
\(72\) | −1.16884e7 | −3.69055 | ||||||||
\(73\) | −2.40816e6 | −0.724529 | −0.362264 | − | 0.932075i | \(-0.617996\pi\) | ||||
−0.362264 | + | 0.932075i | \(0.617996\pi\) | |||||||
\(74\) | −4.89025e6 | −1.40288 | ||||||||
\(75\) | −5.36277e6 | −1.46783 | ||||||||
\(76\) | −8.07873e6 | −2.11104 | ||||||||
\(77\) | −4.85116e6 | −1.21095 | ||||||||
\(78\) | 1.47427e7 | 3.51760 | ||||||||
\(79\) | −5.50752e6 | −1.25679 | −0.628393 | − | 0.777896i | \(-0.716287\pi\) | ||||
−0.628393 | + | 0.777896i | \(0.716287\pi\) | |||||||
\(80\) | 2.64076e6 | 0.576653 | ||||||||
\(81\) | −1.28612e6 | −0.268895 | ||||||||
\(82\) | 1.11847e7 | 2.24015 | ||||||||
\(83\) | −1.52341e6 | −0.292444 | −0.146222 | − | 0.989252i | \(-0.546711\pi\) | ||||
−0.146222 | + | 0.989252i | \(0.546711\pi\) | |||||||
\(84\) | 3.31130e7 | 6.09567 | ||||||||
\(85\) | 1.71532e6 | 0.302956 | ||||||||
\(86\) | −9.96574e6 | −1.68953 | ||||||||
\(87\) | −3.22282e6 | −0.524709 | ||||||||
\(88\) | 1.16733e7 | 1.82602 | ||||||||
\(89\) | −1.23720e7 | −1.86026 | −0.930130 | − | 0.367230i | \(-0.880306\pi\) | ||||
−0.930130 | + | 0.367230i | \(0.880306\pi\) | |||||||
\(90\) | −4.98987e6 | −0.721506 | ||||||||
\(91\) | −1.43699e7 | −1.99898 | ||||||||
\(92\) | −2.90876e7 | −3.89449 | ||||||||
\(93\) | 6.25481e6 | 0.806350 | ||||||||
\(94\) | −1.92891e6 | −0.239533 | ||||||||
\(95\) | −1.98272e6 | −0.237263 | ||||||||
\(96\) | −2.07595e7 | −2.39479 | ||||||||
\(97\) | 1.34239e7 | 1.49340 | 0.746702 | − | 0.665159i | \(-0.231636\pi\) | ||||
0.746702 | + | 0.665159i | \(0.231636\pi\) | |||||||
\(98\) | −2.89368e7 | −3.10570 | ||||||||
\(99\) | −1.06122e7 | −1.09922 | ||||||||
\(100\) | −2.18791e7 | −2.18791 | ||||||||
\(101\) | 7.79543e6 | 0.752862 | 0.376431 | − | 0.926445i | \(-0.377151\pi\) | ||||
0.376431 | + | 0.926445i | \(0.377151\pi\) | |||||||
\(102\) | −3.54867e7 | −3.31104 | ||||||||
\(103\) | −5.82875e6 | −0.525588 | −0.262794 | − | 0.964852i | \(-0.584644\pi\) | ||||
−0.262794 | + | 0.964852i | \(0.584644\pi\) | |||||||
\(104\) | 3.45782e7 | 3.01430 | ||||||||
\(105\) | 8.12676e6 | 0.685102 | ||||||||
\(106\) | −3.17546e7 | −2.58962 | ||||||||
\(107\) | −1.11500e7 | −0.879897 | −0.439949 | − | 0.898023i | \(-0.645003\pi\) | ||||
−0.439949 | + | 0.898023i | \(0.645003\pi\) | |||||||
\(108\) | 2.38381e7 | 1.82091 | ||||||||
\(109\) | 1.96029e7 | 1.44986 | 0.724932 | − | 0.688821i | \(-0.241871\pi\) | ||||
0.724932 | + | 0.688821i | \(0.241871\pi\) | |||||||
\(110\) | 4.98344e6 | 0.356989 | ||||||||
\(111\) | 1.74229e7 | 1.20918 | ||||||||
\(112\) | 5.32505e7 | 3.58147 | ||||||||
\(113\) | −748612. | −0.0488070 | −0.0244035 | − | 0.999702i | \(-0.507769\pi\) | ||||
−0.0244035 | + | 0.999702i | \(0.507769\pi\) | |||||||
\(114\) | 4.10187e7 | 2.59307 | ||||||||
\(115\) | −7.13882e6 | −0.437708 | ||||||||
\(116\) | −1.31485e7 | −0.782120 | ||||||||
\(117\) | −3.14350e7 | −1.81453 | ||||||||
\(118\) | 5.50303e7 | 3.08329 | ||||||||
\(119\) | 3.45892e7 | 1.88159 | ||||||||
\(120\) | −1.95554e7 | −1.03308 | ||||||||
\(121\) | −8.88860e6 | −0.456126 | ||||||||
\(122\) | 3.07767e7 | 1.53448 | ||||||||
\(123\) | −3.98488e7 | −1.93084 | ||||||||
\(124\) | 2.55185e7 | 1.20193 | ||||||||
\(125\) | −1.11429e7 | −0.510285 | ||||||||
\(126\) | −1.00620e8 | −4.48112 | ||||||||
\(127\) | −1.06282e7 | −0.460413 | −0.230207 | − | 0.973142i | \(-0.573940\pi\) | ||||
−0.230207 | + | 0.973142i | \(0.573940\pi\) | |||||||
\(128\) | 1.00576e7 | 0.423895 | ||||||||
\(129\) | 3.55058e7 | 1.45625 | ||||||||
\(130\) | 1.47617e7 | 0.589298 | ||||||||
\(131\) | −3.82747e7 | −1.48752 | −0.743760 | − | 0.668447i | \(-0.766959\pi\) | ||||
−0.743760 | + | 0.668447i | \(0.766959\pi\) | |||||||
\(132\) | −7.23436e7 | −2.73774 | ||||||||
\(133\) | −3.99813e7 | −1.47359 | ||||||||
\(134\) | 5.36397e7 | 1.92584 | ||||||||
\(135\) | 5.85046e6 | 0.204655 | ||||||||
\(136\) | −8.32320e7 | −2.83729 | ||||||||
\(137\) | 6.16888e6 | 0.204967 | 0.102484 | − | 0.994735i | \(-0.467321\pi\) | ||||
0.102484 | + | 0.994735i | \(0.467321\pi\) | |||||||
\(138\) | 1.47688e8 | 4.78376 | ||||||||
\(139\) | 5.42813e7 | 1.71435 | 0.857173 | − | 0.515029i | \(-0.172219\pi\) | ||||
0.857173 | + | 0.515029i | \(0.172219\pi\) | |||||||
\(140\) | 3.31557e7 | 1.02120 | ||||||||
\(141\) | 6.87231e6 | 0.206460 | ||||||||
\(142\) | 2.08022e7 | 0.609679 | ||||||||
\(143\) | 3.13946e7 | 0.897798 | ||||||||
\(144\) | 1.16489e8 | 3.25099 | ||||||||
\(145\) | −3.22697e6 | −0.0879037 | ||||||||
\(146\) | 4.98843e7 | 1.32657 | ||||||||
\(147\) | 1.03096e8 | 2.67688 | ||||||||
\(148\) | 7.10823e7 | 1.80238 | ||||||||
\(149\) | −5.48491e7 | −1.35837 | −0.679184 | − | 0.733968i | \(-0.737666\pi\) | ||||
−0.679184 | + | 0.733968i | \(0.737666\pi\) | |||||||
\(150\) | 1.11088e8 | 2.68750 | ||||||||
\(151\) | 4.78971e7 | 1.13211 | 0.566057 | − | 0.824366i | \(-0.308468\pi\) | ||||
0.566057 | + | 0.824366i | \(0.308468\pi\) | |||||||
\(152\) | 9.62069e7 | 2.22205 | ||||||||
\(153\) | 7.56661e7 | 1.70797 | ||||||||
\(154\) | 1.00490e8 | 2.21718 | ||||||||
\(155\) | 6.26287e6 | 0.135087 | ||||||||
\(156\) | −2.14293e8 | −4.51931 | ||||||||
\(157\) | −7.96894e7 | −1.64343 | −0.821716 | − | 0.569897i | \(-0.806983\pi\) | ||||
−0.821716 | + | 0.569897i | \(0.806983\pi\) | |||||||
\(158\) | 1.14087e8 | 2.30110 | ||||||||
\(159\) | 1.13135e8 | 2.23207 | ||||||||
\(160\) | −2.07862e7 | −0.401196 | ||||||||
\(161\) | −1.43953e8 | −2.71851 | ||||||||
\(162\) | 2.66415e7 | 0.492330 | ||||||||
\(163\) | 5.76508e7 | 1.04267 | 0.521337 | − | 0.853351i | \(-0.325433\pi\) | ||||
0.521337 | + | 0.853351i | \(0.325433\pi\) | |||||||
\(164\) | −1.62576e8 | −2.87807 | ||||||||
\(165\) | −1.77549e7 | −0.307699 | ||||||||
\(166\) | 3.15569e7 | 0.535446 | ||||||||
\(167\) | 1.91556e6 | 0.0318264 | 0.0159132 | − | 0.999873i | \(-0.494934\pi\) | ||||
0.0159132 | + | 0.999873i | \(0.494934\pi\) | |||||||
\(168\) | −3.94332e8 | −6.41622 | ||||||||
\(169\) | 3.02470e7 | 0.482036 | ||||||||
\(170\) | −3.55324e7 | −0.554694 | ||||||||
\(171\) | −8.74616e7 | −1.33762 | ||||||||
\(172\) | 1.44857e8 | 2.17065 | ||||||||
\(173\) | −8.14785e7 | −1.19642 | −0.598208 | − | 0.801341i | \(-0.704120\pi\) | ||||
−0.598208 | + | 0.801341i | \(0.704120\pi\) | |||||||
\(174\) | 6.67597e7 | 0.960709 | ||||||||
\(175\) | −1.08279e8 | −1.52725 | ||||||||
\(176\) | −1.16339e8 | −1.60854 | ||||||||
\(177\) | −1.96061e8 | −2.65757 | ||||||||
\(178\) | 2.56282e8 | 3.40602 | ||||||||
\(179\) | −3.48393e7 | −0.454029 | −0.227015 | − | 0.973891i | \(-0.572897\pi\) | ||||
−0.227015 | + | 0.973891i | \(0.572897\pi\) | |||||||
\(180\) | 7.25302e7 | 0.926969 | ||||||||
\(181\) | 7.40560e7 | 0.928293 | 0.464147 | − | 0.885758i | \(-0.346361\pi\) | ||||
0.464147 | + | 0.885758i | \(0.346361\pi\) | |||||||
\(182\) | 2.97668e8 | 3.66000 | ||||||||
\(183\) | −1.09651e8 | −1.32261 | ||||||||
\(184\) | 3.46394e8 | 4.09929 | ||||||||
\(185\) | 1.74454e7 | 0.202572 | ||||||||
\(186\) | −1.29566e8 | −1.47638 | ||||||||
\(187\) | −7.55687e7 | −0.845077 | ||||||||
\(188\) | 2.80377e7 | 0.307745 | ||||||||
\(189\) | 1.17974e8 | 1.27107 | ||||||||
\(190\) | 4.10715e7 | 0.434413 | ||||||||
\(191\) | 1.87132e8 | 1.94326 | 0.971632 | − | 0.236499i | \(-0.0760001\pi\) | ||||
0.971632 | + | 0.236499i | \(0.0760001\pi\) | |||||||
\(192\) | 9.24439e7 | 0.942593 | ||||||||
\(193\) | 3.37092e7 | 0.337519 | 0.168759 | − | 0.985657i | \(-0.446024\pi\) | ||||
0.168759 | + | 0.985657i | \(0.446024\pi\) | |||||||
\(194\) | −2.78072e8 | −2.73433 | ||||||||
\(195\) | −5.25929e7 | −0.507932 | ||||||||
\(196\) | 4.20611e8 | 3.99010 | ||||||||
\(197\) | 9.49367e7 | 0.884713 | 0.442356 | − | 0.896839i | \(-0.354143\pi\) | ||||
0.442356 | + | 0.896839i | \(0.354143\pi\) | |||||||
\(198\) | 2.19829e8 | 2.01260 | ||||||||
\(199\) | 1.01890e8 | 0.916524 | 0.458262 | − | 0.888817i | \(-0.348472\pi\) | ||||
0.458262 | + | 0.888817i | \(0.348472\pi\) | |||||||
\(200\) | 2.60551e8 | 2.30296 | ||||||||
\(201\) | −1.91107e8 | −1.65993 | ||||||||
\(202\) | −1.61480e8 | −1.37844 | ||||||||
\(203\) | −6.50713e7 | −0.545951 | ||||||||
\(204\) | 5.15817e8 | 4.25392 | ||||||||
\(205\) | −3.99001e7 | −0.323471 | ||||||||
\(206\) | 1.20741e8 | 0.962319 | ||||||||
\(207\) | −3.14907e8 | −2.46766 | ||||||||
\(208\) | −3.44614e8 | −2.65529 | ||||||||
\(209\) | 8.73490e7 | 0.661830 | ||||||||
\(210\) | −1.68343e8 | −1.25438 | ||||||||
\(211\) | −1.09208e8 | −0.800321 | −0.400161 | − | 0.916445i | \(-0.631046\pi\) | ||||
−0.400161 | + | 0.916445i | \(0.631046\pi\) | |||||||
\(212\) | 4.61570e8 | 3.32707 | ||||||||
\(213\) | −7.41140e7 | −0.525498 | ||||||||
\(214\) | 2.30969e8 | 1.61104 | ||||||||
\(215\) | 3.55515e7 | 0.243963 | ||||||||
\(216\) | −2.83880e8 | −1.91666 | ||||||||
\(217\) | 1.26290e8 | 0.838994 | ||||||||
\(218\) | −4.06068e8 | −2.65461 | ||||||||
\(219\) | −1.77727e8 | −1.14340 | ||||||||
\(220\) | −7.24368e7 | −0.458649 | ||||||||
\(221\) | −2.23846e8 | −1.39501 | ||||||||
\(222\) | −3.60911e8 | −2.21393 | ||||||||
\(223\) | 2.85379e8 | 1.72327 | 0.861637 | − | 0.507524i | \(-0.169439\pi\) | ||||
0.861637 | + | 0.507524i | \(0.169439\pi\) | |||||||
\(224\) | −4.19151e8 | −2.49174 | ||||||||
\(225\) | −2.36866e8 | −1.38632 | ||||||||
\(226\) | 1.55073e7 | 0.0893625 | ||||||||
\(227\) | −6.21605e7 | −0.352715 | −0.176357 | − | 0.984326i | \(-0.556431\pi\) | ||||
−0.176357 | + | 0.984326i | \(0.556431\pi\) | |||||||
\(228\) | −5.96227e8 | −3.33150 | ||||||||
\(229\) | −3.96137e7 | −0.217982 | −0.108991 | − | 0.994043i | \(-0.534762\pi\) | ||||
−0.108991 | + | 0.994043i | \(0.534762\pi\) | |||||||
\(230\) | 1.47879e8 | 0.801415 | ||||||||
\(231\) | −3.58025e8 | −1.91105 | ||||||||
\(232\) | 1.56581e8 | 0.823249 | ||||||||
\(233\) | −2.98931e7 | −0.154819 | −0.0774096 | − | 0.996999i | \(-0.524665\pi\) | ||||
−0.0774096 | + | 0.996999i | \(0.524665\pi\) | |||||||
\(234\) | 6.51167e8 | 3.32229 | ||||||||
\(235\) | 6.88116e6 | 0.0345879 | ||||||||
\(236\) | −7.99893e8 | −3.96132 | ||||||||
\(237\) | −4.06466e8 | −1.98338 | ||||||||
\(238\) | −7.16504e8 | −3.44508 | ||||||||
\(239\) | −3.10037e8 | −1.46900 | −0.734499 | − | 0.678609i | \(-0.762583\pi\) | ||||
−0.734499 | + | 0.678609i | \(0.762583\pi\) | |||||||
\(240\) | 1.94894e8 | 0.910036 | ||||||||
\(241\) | −8.93025e7 | −0.410964 | −0.205482 | − | 0.978661i | \(-0.565876\pi\) | ||||
−0.205482 | + | 0.978661i | \(0.565876\pi\) | |||||||
\(242\) | 1.84125e8 | 0.835138 | ||||||||
\(243\) | −2.68064e8 | −1.19844 | ||||||||
\(244\) | −4.47355e8 | −1.97146 | ||||||||
\(245\) | 1.03228e8 | 0.448454 | ||||||||
\(246\) | 8.25455e8 | 3.53525 | ||||||||
\(247\) | 2.58741e8 | 1.09251 | ||||||||
\(248\) | −3.03891e8 | −1.26513 | ||||||||
\(249\) | −1.12430e8 | −0.461515 | ||||||||
\(250\) | 2.30821e8 | 0.934300 | ||||||||
\(251\) | −1.04502e8 | −0.417126 | −0.208563 | − | 0.978009i | \(-0.566879\pi\) | ||||
−0.208563 | + | 0.978009i | \(0.566879\pi\) | |||||||
\(252\) | 1.46256e9 | 5.75720 | ||||||||
\(253\) | 3.14502e8 | 1.22096 | ||||||||
\(254\) | 2.20160e8 | 0.842988 | ||||||||
\(255\) | 1.26594e8 | 0.478105 | ||||||||
\(256\) | −3.68671e8 | −1.37341 | ||||||||
\(257\) | −3.65475e8 | −1.34305 | −0.671523 | − | 0.740983i | \(-0.734360\pi\) | ||||
−0.671523 | + | 0.740983i | \(0.734360\pi\) | |||||||
\(258\) | −7.35492e8 | −2.66630 | ||||||||
\(259\) | 3.51783e8 | 1.25813 | ||||||||
\(260\) | −2.14569e8 | −0.757112 | ||||||||
\(261\) | −1.42348e8 | −0.495574 | ||||||||
\(262\) | 7.92849e8 | 2.72355 | ||||||||
\(263\) | 4.81180e8 | 1.63103 | 0.815516 | − | 0.578734i | \(-0.196453\pi\) | ||||
0.815516 | + | 0.578734i | \(0.196453\pi\) | |||||||
\(264\) | 8.61516e8 | 2.88171 | ||||||||
\(265\) | 1.13281e8 | 0.373935 | ||||||||
\(266\) | 8.28200e8 | 2.69805 | ||||||||
\(267\) | −9.13076e8 | −2.93574 | ||||||||
\(268\) | −7.79680e8 | −2.47426 | ||||||||
\(269\) | −5.61063e8 | −1.75743 | −0.878717 | − | 0.477344i | \(-0.841600\pi\) | ||||
−0.878717 | + | 0.477344i | \(0.841600\pi\) | |||||||
\(270\) | −1.21190e8 | −0.374710 | ||||||||
\(271\) | −6.31875e7 | −0.192858 | −0.0964292 | − | 0.995340i | \(-0.530742\pi\) | ||||
−0.0964292 | + | 0.995340i | \(0.530742\pi\) | |||||||
\(272\) | 8.29508e8 | 2.49936 | ||||||||
\(273\) | −1.06053e9 | −3.15466 | ||||||||
\(274\) | −1.27787e8 | −0.375282 | ||||||||
\(275\) | 2.36562e8 | 0.685930 | ||||||||
\(276\) | −2.14672e9 | −6.14602 | ||||||||
\(277\) | 1.99282e8 | 0.563365 | 0.281682 | − | 0.959508i | \(-0.409108\pi\) | ||||
0.281682 | + | 0.959508i | \(0.409108\pi\) | |||||||
\(278\) | −1.12442e9 | −3.13886 | ||||||||
\(279\) | 2.76267e8 | 0.761577 | ||||||||
\(280\) | −3.94840e8 | −1.07490 | ||||||||
\(281\) | 3.34142e8 | 0.898378 | 0.449189 | − | 0.893437i | \(-0.351713\pi\) | ||||
0.449189 | + | 0.893437i | \(0.351713\pi\) | |||||||
\(282\) | −1.42358e8 | −0.378015 | ||||||||
\(283\) | −3.41530e8 | −0.895729 | −0.447865 | − | 0.894101i | \(-0.647815\pi\) | ||||
−0.447865 | + | 0.894101i | \(0.647815\pi\) | |||||||
\(284\) | −3.02371e8 | −0.783296 | ||||||||
\(285\) | −1.46329e8 | −0.374432 | ||||||||
\(286\) | −6.50329e8 | −1.64381 | ||||||||
\(287\) | −8.04579e8 | −2.00901 | ||||||||
\(288\) | −9.16920e8 | −2.26182 | ||||||||
\(289\) | 1.28473e8 | 0.313090 | ||||||||
\(290\) | 6.68457e7 | 0.160946 | ||||||||
\(291\) | 9.90710e8 | 2.35679 | ||||||||
\(292\) | −7.25094e8 | −1.70433 | ||||||||
\(293\) | −5.18982e8 | −1.20536 | −0.602678 | − | 0.797985i | \(-0.705900\pi\) | ||||
−0.602678 | + | 0.797985i | \(0.705900\pi\) | |||||||
\(294\) | −2.13559e9 | −4.90121 | ||||||||
\(295\) | −1.96314e8 | −0.445219 | ||||||||
\(296\) | −8.46495e8 | −1.89716 | ||||||||
\(297\) | −2.57743e8 | −0.570872 | ||||||||
\(298\) | 1.13618e9 | 2.48709 | ||||||||
\(299\) | 9.31602e8 | 2.01549 | ||||||||
\(300\) | −1.61472e9 | −3.45281 | ||||||||
\(301\) | 7.16891e8 | 1.51520 | ||||||||
\(302\) | −9.92175e8 | −2.07283 | ||||||||
\(303\) | 5.75318e8 | 1.18812 | ||||||||
\(304\) | −9.58819e8 | −1.95740 | ||||||||
\(305\) | −1.09792e8 | −0.221575 | ||||||||
\(306\) | −1.56740e9 | −3.12719 | ||||||||
\(307\) | 7.56489e8 | 1.49217 | 0.746085 | − | 0.665850i | \(-0.231931\pi\) | ||||
0.746085 | + | 0.665850i | \(0.231931\pi\) | |||||||
\(308\) | −1.46068e9 | −2.84857 | ||||||||
\(309\) | −4.30174e8 | −0.829448 | ||||||||
\(310\) | −1.29733e8 | −0.247335 | ||||||||
\(311\) | −7.71933e8 | −1.45518 | −0.727592 | − | 0.686010i | \(-0.759361\pi\) | ||||
−0.727592 | + | 0.686010i | \(0.759361\pi\) | |||||||
\(312\) | 2.55194e9 | 4.75696 | ||||||||
\(313\) | 1.57966e8 | 0.291177 | 0.145589 | − | 0.989345i | \(-0.453492\pi\) | ||||
0.145589 | + | 0.989345i | \(0.453492\pi\) | |||||||
\(314\) | 1.65074e9 | 3.00902 | ||||||||
\(315\) | 3.58949e8 | 0.647061 | ||||||||
\(316\) | −1.65831e9 | −2.95638 | ||||||||
\(317\) | 5.54573e8 | 0.977803 | 0.488901 | − | 0.872339i | \(-0.337398\pi\) | ||||
0.488901 | + | 0.872339i | \(0.337398\pi\) | |||||||
\(318\) | −2.34356e9 | −4.08677 | ||||||||
\(319\) | 1.42164e8 | 0.245202 | ||||||||
\(320\) | 9.25630e7 | 0.157911 | ||||||||
\(321\) | −8.22893e8 | −1.38860 | ||||||||
\(322\) | 2.98194e9 | 4.97742 | ||||||||
\(323\) | −6.22807e8 | −1.02836 | ||||||||
\(324\) | −3.87248e8 | −0.632530 | ||||||||
\(325\) | 7.00732e8 | 1.13230 | ||||||||
\(326\) | −1.19422e9 | −1.90907 | ||||||||
\(327\) | 1.44673e9 | 2.28808 | ||||||||
\(328\) | 1.93606e9 | 3.02942 | ||||||||
\(329\) | 1.38757e8 | 0.214818 | ||||||||
\(330\) | 3.67788e8 | 0.563377 | ||||||||
\(331\) | 3.19945e8 | 0.484927 | 0.242464 | − | 0.970160i | \(-0.422044\pi\) | ||||
0.242464 | + | 0.970160i | \(0.422044\pi\) | |||||||
\(332\) | −4.58695e8 | −0.687925 | ||||||||
\(333\) | 7.69548e8 | 1.14204 | ||||||||
\(334\) | −3.96802e7 | −0.0582722 | ||||||||
\(335\) | −1.91353e8 | −0.278086 | ||||||||
\(336\) | 3.93000e9 | 5.65203 | ||||||||
\(337\) | 1.24573e8 | 0.177304 | 0.0886522 | − | 0.996063i | \(-0.471744\pi\) | ||||
0.0886522 | + | 0.996063i | \(0.471744\pi\) | |||||||
\(338\) | −6.26558e8 | −0.882577 | ||||||||
\(339\) | −5.52491e7 | −0.0770240 | ||||||||
\(340\) | 5.16481e8 | 0.712653 | ||||||||
\(341\) | −2.75911e8 | −0.376816 | ||||||||
\(342\) | 1.81174e9 | 2.44909 | ||||||||
\(343\) | 8.54404e8 | 1.14323 | ||||||||
\(344\) | −1.72505e9 | −2.28480 | ||||||||
\(345\) | −5.26860e8 | −0.690761 | ||||||||
\(346\) | 1.68780e9 | 2.19056 | ||||||||
\(347\) | 6.62089e8 | 0.850674 | 0.425337 | − | 0.905035i | \(-0.360156\pi\) | ||||
0.425337 | + | 0.905035i | \(0.360156\pi\) | |||||||
\(348\) | −9.70386e8 | −1.23429 | ||||||||
\(349\) | −9.31176e8 | −1.17258 | −0.586291 | − | 0.810101i | \(-0.699412\pi\) | ||||
−0.586291 | + | 0.810101i | \(0.699412\pi\) | |||||||
\(350\) | 2.24296e9 | 2.79629 | ||||||||
\(351\) | −7.63473e8 | −0.942364 | ||||||||
\(352\) | 9.15740e8 | 1.11911 | ||||||||
\(353\) | 7.55790e8 | 0.914513 | 0.457256 | − | 0.889335i | \(-0.348832\pi\) | ||||
0.457256 | + | 0.889335i | \(0.348832\pi\) | |||||||
\(354\) | 4.06135e9 | 4.86585 | ||||||||
\(355\) | −7.42094e7 | −0.0880359 | ||||||||
\(356\) | −3.72518e9 | −4.37595 | ||||||||
\(357\) | 2.55275e9 | 2.96941 | ||||||||
\(358\) | 7.21686e8 | 0.831299 | ||||||||
\(359\) | 8.55845e8 | 0.976258 | 0.488129 | − | 0.872772i | \(-0.337680\pi\) | ||||
0.488129 | + | 0.872772i | \(0.337680\pi\) | |||||||
\(360\) | −8.63738e8 | −0.975716 | ||||||||
\(361\) | −1.73977e8 | −0.194633 | ||||||||
\(362\) | −1.53405e9 | −1.69965 | ||||||||
\(363\) | −6.55997e8 | −0.719828 | ||||||||
\(364\) | −4.32675e9 | −4.70226 | ||||||||
\(365\) | −1.77956e8 | −0.191553 | ||||||||
\(366\) | 2.27138e9 | 2.42162 | ||||||||
\(367\) | −7.91187e8 | −0.835503 | −0.417751 | − | 0.908561i | \(-0.637182\pi\) | ||||
−0.417751 | + | 0.908561i | \(0.637182\pi\) | |||||||
\(368\) | −3.45224e9 | −3.61105 | ||||||||
\(369\) | −1.76007e9 | −1.82363 | ||||||||
\(370\) | −3.61376e8 | −0.370897 | ||||||||
\(371\) | 2.28429e9 | 2.32243 | ||||||||
\(372\) | 1.88331e9 | 1.89680 | ||||||||
\(373\) | 1.38399e9 | 1.38087 | 0.690433 | − | 0.723396i | \(-0.257420\pi\) | ||||
0.690433 | + | 0.723396i | \(0.257420\pi\) | |||||||
\(374\) | 1.56538e9 | 1.54728 | ||||||||
\(375\) | −8.22368e8 | −0.805298 | ||||||||
\(376\) | −3.33892e8 | −0.323928 | ||||||||
\(377\) | 4.21113e8 | 0.404766 | ||||||||
\(378\) | −2.44379e9 | −2.32724 | ||||||||
\(379\) | −1.33706e8 | −0.126158 | −0.0630788 | − | 0.998009i | \(-0.520092\pi\) | ||||
−0.0630788 | + | 0.998009i | \(0.520092\pi\) | |||||||
\(380\) | −5.96995e8 | −0.558121 | ||||||||
\(381\) | −7.84385e8 | −0.726594 | ||||||||
\(382\) | −3.87638e9 | −3.55799 | ||||||||
\(383\) | 1.90252e9 | 1.73035 | 0.865174 | − | 0.501471i | \(-0.167208\pi\) | ||||
0.865174 | + | 0.501471i | \(0.167208\pi\) | |||||||
\(384\) | 7.42269e8 | 0.668963 | ||||||||
\(385\) | −3.58487e8 | −0.320155 | ||||||||
\(386\) | −6.98276e8 | −0.617976 | ||||||||
\(387\) | 1.56825e9 | 1.37539 | ||||||||
\(388\) | 4.04191e9 | 3.51298 | ||||||||
\(389\) | −3.74686e8 | −0.322733 | −0.161367 | − | 0.986895i | \(-0.551590\pi\) | ||||
−0.161367 | + | 0.986895i | \(0.551590\pi\) | |||||||
\(390\) | 1.08944e9 | 0.929992 | ||||||||
\(391\) | −2.24242e9 | −1.89714 | ||||||||
\(392\) | −5.00891e9 | −4.19993 | ||||||||
\(393\) | −2.82475e9 | −2.34751 | ||||||||
\(394\) | −1.96658e9 | −1.61985 | ||||||||
\(395\) | −4.06990e8 | −0.332272 | ||||||||
\(396\) | −3.19532e9 | −2.58572 | ||||||||
\(397\) | 1.86096e8 | 0.149269 | 0.0746347 | − | 0.997211i | \(-0.476221\pi\) | ||||
0.0746347 | + | 0.997211i | \(0.476221\pi\) | |||||||
\(398\) | −2.11061e9 | −1.67810 | ||||||||
\(399\) | −2.95070e9 | −2.32552 | ||||||||
\(400\) | −2.59670e9 | −2.02868 | ||||||||
\(401\) | −1.28243e9 | −0.993179 | −0.496590 | − | 0.867986i | \(-0.665415\pi\) | ||||
−0.496590 | + | 0.867986i | \(0.665415\pi\) | |||||||
\(402\) | 3.95872e9 | 3.03923 | ||||||||
\(403\) | −8.17291e8 | −0.622027 | ||||||||
\(404\) | 2.34719e9 | 1.77098 | ||||||||
\(405\) | −9.50403e7 | −0.0710911 | ||||||||
\(406\) | 1.34793e9 | 0.999601 | ||||||||
\(407\) | −7.68558e8 | −0.565062 | ||||||||
\(408\) | −6.14269e9 | −4.47763 | ||||||||
\(409\) | −7.56893e7 | −0.0547020 | −0.0273510 | − | 0.999626i | \(-0.508707\pi\) | ||||
−0.0273510 | + | 0.999626i | \(0.508707\pi\) | |||||||
\(410\) | 8.26519e8 | 0.592256 | ||||||||
\(411\) | 4.55276e8 | 0.323466 | ||||||||
\(412\) | −1.75503e9 | −1.23636 | ||||||||
\(413\) | −3.95863e9 | −2.76516 | ||||||||
\(414\) | 6.52320e9 | 4.51814 | ||||||||
\(415\) | −1.12575e8 | −0.0773169 | ||||||||
\(416\) | 2.71256e9 | 1.84737 | ||||||||
\(417\) | 4.00607e9 | 2.70547 | ||||||||
\(418\) | −1.80941e9 | −1.21177 | ||||||||
\(419\) | −1.16121e9 | −0.771189 | −0.385594 | − | 0.922668i | \(-0.626004\pi\) | ||||
−0.385594 | + | 0.922668i | \(0.626004\pi\) | |||||||
\(420\) | 2.44696e9 | 1.61159 | ||||||||
\(421\) | −8.64920e8 | −0.564922 | −0.282461 | − | 0.959279i | \(-0.591151\pi\) | ||||
−0.282461 | + | 0.959279i | \(0.591151\pi\) | |||||||
\(422\) | 2.26220e9 | 1.46534 | ||||||||
\(423\) | 3.03541e8 | 0.194996 | ||||||||
\(424\) | −5.49668e9 | −3.50203 | ||||||||
\(425\) | −1.68670e9 | −1.06581 | ||||||||
\(426\) | 1.53525e9 | 0.962155 | ||||||||
\(427\) | −2.21394e9 | −1.37616 | ||||||||
\(428\) | −3.35725e9 | −2.06981 | ||||||||
\(429\) | 2.31698e9 | 1.41685 | ||||||||
\(430\) | −7.36439e8 | −0.446681 | ||||||||
\(431\) | −1.29106e9 | −0.776742 | −0.388371 | − | 0.921503i | \(-0.626962\pi\) | ||||
−0.388371 | + | 0.921503i | \(0.626962\pi\) | |||||||
\(432\) | 2.82921e9 | 1.68839 | ||||||||
\(433\) | 2.17469e8 | 0.128733 | 0.0643666 | − | 0.997926i | \(-0.479497\pi\) | ||||
0.0643666 | + | 0.997926i | \(0.479497\pi\) | |||||||
\(434\) | −2.61605e9 | −1.53614 | ||||||||
\(435\) | −2.38157e8 | −0.138724 | ||||||||
\(436\) | 5.90240e9 | 3.41056 | ||||||||
\(437\) | 2.59199e9 | 1.48576 | ||||||||
\(438\) | 3.68156e9 | 2.09350 | ||||||||
\(439\) | −9.39396e8 | −0.529935 | −0.264968 | − | 0.964257i | \(-0.585361\pi\) | ||||
−0.264968 | + | 0.964257i | \(0.585361\pi\) | |||||||
\(440\) | 8.62626e8 | 0.482768 | ||||||||
\(441\) | 4.55360e9 | 2.52825 | ||||||||
\(442\) | 4.63690e9 | 2.55417 | ||||||||
\(443\) | 8.17201e8 | 0.446597 | 0.223298 | − | 0.974750i | \(-0.428318\pi\) | ||||
0.223298 | + | 0.974750i | \(0.428318\pi\) | |||||||
\(444\) | 5.24602e9 | 2.84439 | ||||||||
\(445\) | −9.14253e8 | −0.491820 | ||||||||
\(446\) | −5.91153e9 | −3.15521 | ||||||||
\(447\) | −4.04798e9 | −2.14369 | ||||||||
\(448\) | 1.86652e9 | 0.980751 | ||||||||
\(449\) | 2.04702e8 | 0.106724 | 0.0533618 | − | 0.998575i | \(-0.483006\pi\) | ||||
0.0533618 | + | 0.998575i | \(0.483006\pi\) | |||||||
\(450\) | 4.90662e9 | 2.53827 | ||||||||
\(451\) | 1.75780e9 | 0.902303 | ||||||||
\(452\) | −2.25406e8 | −0.114810 | ||||||||
\(453\) | 3.53491e9 | 1.78663 | ||||||||
\(454\) | 1.28764e9 | 0.645799 | ||||||||
\(455\) | −1.06189e9 | −0.528495 | ||||||||
\(456\) | 7.10027e9 | 3.50669 | ||||||||
\(457\) | 1.45321e9 | 0.712235 | 0.356117 | − | 0.934441i | \(-0.384100\pi\) | ||||
0.356117 | + | 0.934441i | \(0.384100\pi\) | |||||||
\(458\) | 8.20586e8 | 0.399112 | ||||||||
\(459\) | 1.83773e9 | 0.887027 | ||||||||
\(460\) | −2.14949e9 | −1.02963 | ||||||||
\(461\) | −2.51711e9 | −1.19660 | −0.598301 | − | 0.801272i | \(-0.704157\pi\) | ||||
−0.598301 | + | 0.801272i | \(0.704157\pi\) | |||||||
\(462\) | 7.41638e9 | 3.49901 | ||||||||
\(463\) | −2.48995e9 | −1.16589 | −0.582944 | − | 0.812512i | \(-0.698099\pi\) | ||||
−0.582944 | + | 0.812512i | \(0.698099\pi\) | |||||||
\(464\) | −1.56052e9 | −0.725198 | ||||||||
\(465\) | 4.62212e8 | 0.213185 | ||||||||
\(466\) | 6.19226e8 | 0.283464 | ||||||||
\(467\) | 1.38614e9 | 0.629792 | 0.314896 | − | 0.949126i | \(-0.398030\pi\) | ||||
0.314896 | + | 0.949126i | \(0.398030\pi\) | |||||||
\(468\) | −9.46504e9 | −4.26837 | ||||||||
\(469\) | −3.85860e9 | −1.72713 | ||||||||
\(470\) | −1.42541e8 | −0.0633283 | ||||||||
\(471\) | −5.88124e9 | −2.59356 | ||||||||
\(472\) | 9.52565e9 | 4.16963 | ||||||||
\(473\) | −1.56623e9 | −0.680520 | ||||||||
\(474\) | 8.41982e9 | 3.63144 | ||||||||
\(475\) | 1.94964e9 | 0.834695 | ||||||||
\(476\) | 1.04148e10 | 4.42613 | ||||||||
\(477\) | 4.99703e9 | 2.10813 | ||||||||
\(478\) | 6.42233e9 | 2.68964 | ||||||||
\(479\) | −3.31140e9 | −1.37669 | −0.688347 | − | 0.725381i | \(-0.741664\pi\) | ||||
−0.688347 | + | 0.725381i | \(0.741664\pi\) | |||||||
\(480\) | −1.53407e9 | −0.633140 | ||||||||
\(481\) | −2.27659e9 | −0.932773 | ||||||||
\(482\) | 1.84987e9 | 0.752450 | ||||||||
\(483\) | −1.06240e10 | −4.29017 | ||||||||
\(484\) | −2.67635e9 | −1.07296 | ||||||||
\(485\) | 9.91986e8 | 0.394830 | ||||||||
\(486\) | 5.55286e9 | 2.19427 | ||||||||
\(487\) | 3.75492e9 | 1.47316 | 0.736580 | − | 0.676351i | \(-0.236440\pi\) | ||||
0.736580 | + | 0.676351i | \(0.236440\pi\) | |||||||
\(488\) | 5.32740e9 | 2.07513 | ||||||||
\(489\) | 4.25474e9 | 1.64548 | ||||||||
\(490\) | −2.13835e9 | −0.821091 | ||||||||
\(491\) | 3.06437e8 | 0.116830 | 0.0584151 | − | 0.998292i | \(-0.481395\pi\) | ||||
0.0584151 | + | 0.998292i | \(0.481395\pi\) | |||||||
\(492\) | −1.19984e10 | −4.54198 | ||||||||
\(493\) | −1.01365e9 | −0.380997 | ||||||||
\(494\) | −5.35975e9 | −2.00032 | ||||||||
\(495\) | −7.84213e8 | −0.290613 | ||||||||
\(496\) | 3.02864e9 | 1.11445 | ||||||||
\(497\) | −1.49642e9 | −0.546772 | ||||||||
\(498\) | 2.32896e9 | 0.845006 | ||||||||
\(499\) | −1.33384e9 | −0.480566 | −0.240283 | − | 0.970703i | \(-0.577240\pi\) | ||||
−0.240283 | + | 0.970703i | \(0.577240\pi\) | |||||||
\(500\) | −3.35511e9 | −1.20036 | ||||||||
\(501\) | 1.41372e8 | 0.0502264 | ||||||||
\(502\) | 2.16473e9 | 0.763732 | ||||||||
\(503\) | 8.59977e8 | 0.301300 | 0.150650 | − | 0.988587i | \(-0.451863\pi\) | ||||
0.150650 | + | 0.988587i | \(0.451863\pi\) | |||||||
\(504\) | −1.74171e10 | −6.05996 | ||||||||
\(505\) | 5.76060e8 | 0.199043 | ||||||||
\(506\) | −6.51480e9 | −2.23550 | ||||||||
\(507\) | 2.23229e9 | 0.760717 | ||||||||
\(508\) | −3.20014e9 | −1.08304 | ||||||||
\(509\) | 1.11628e9 | 0.375198 | 0.187599 | − | 0.982246i | \(-0.439929\pi\) | ||||
0.187599 | + | 0.982246i | \(0.439929\pi\) | |||||||
\(510\) | −2.62236e9 | −0.875381 | ||||||||
\(511\) | −3.58846e9 | −1.18969 | ||||||||
\(512\) | 6.34954e9 | 2.09073 | ||||||||
\(513\) | −2.12421e9 | −0.694683 | ||||||||
\(514\) | 7.57069e9 | 2.45903 | ||||||||
\(515\) | −4.30728e8 | −0.138956 | ||||||||
\(516\) | 1.06907e10 | 3.42558 | ||||||||
\(517\) | −3.03150e8 | −0.0964808 | ||||||||
\(518\) | −7.28708e9 | −2.30356 | ||||||||
\(519\) | −6.01328e9 | −1.88810 | ||||||||
\(520\) | 2.55523e9 | 0.796927 | ||||||||
\(521\) | −4.36175e9 | −1.35123 | −0.675614 | − | 0.737256i | \(-0.736121\pi\) | ||||
−0.675614 | + | 0.737256i | \(0.736121\pi\) | |||||||
\(522\) | 2.94869e9 | 0.907365 | ||||||||
\(523\) | 3.02705e9 | 0.925259 | 0.462629 | − | 0.886552i | \(-0.346906\pi\) | ||||
0.462629 | + | 0.886552i | \(0.346906\pi\) | |||||||
\(524\) | −1.15245e10 | −3.49914 | ||||||||
\(525\) | −7.99118e9 | −2.41020 | ||||||||
\(526\) | −9.96750e9 | −2.98632 | ||||||||
\(527\) | 1.96727e9 | 0.585500 | ||||||||
\(528\) | −8.58606e9 | −2.53849 | ||||||||
\(529\) | 5.92768e9 | 1.74097 | ||||||||
\(530\) | −2.34658e9 | −0.684651 | ||||||||
\(531\) | −8.65976e9 | −2.51001 | ||||||||
\(532\) | −1.20383e10 | −3.46637 | ||||||||
\(533\) | 5.20688e9 | 1.48947 | ||||||||
\(534\) | 1.89141e10 | 5.37516 | ||||||||
\(535\) | −8.23953e8 | −0.232629 | ||||||||
\(536\) | 9.28495e9 | 2.60437 | ||||||||
\(537\) | −2.57121e9 | −0.716519 | ||||||||
\(538\) | 1.16223e10 | 3.21775 | ||||||||
\(539\) | −4.54774e9 | −1.25094 | ||||||||
\(540\) | 1.76156e9 | 0.481416 | ||||||||
\(541\) | 3.28479e9 | 0.891903 | 0.445952 | − | 0.895057i | \(-0.352865\pi\) | ||||
0.445952 | + | 0.895057i | \(0.352865\pi\) | |||||||
\(542\) | 1.30891e9 | 0.353112 | ||||||||
\(543\) | 5.46548e9 | 1.46497 | ||||||||
\(544\) | −6.52931e9 | −1.73889 | ||||||||
\(545\) | 1.44860e9 | 0.383318 | ||||||||
\(546\) | 2.19685e10 | 5.77598 | ||||||||
\(547\) | 1.63667e8 | 0.0427569 | ||||||||
\(548\) | 1.85744e9 | 0.482151 | ||||||||
\(549\) | −4.84313e9 | −1.24917 | ||||||||
\(550\) | −4.90030e9 | −1.25589 | ||||||||
\(551\) | 1.17166e9 | 0.298381 | ||||||||
\(552\) | 2.55646e10 | 6.46923 | ||||||||
\(553\) | −8.20688e9 | −2.06367 | ||||||||
\(554\) | −4.12807e9 | −1.03149 | ||||||||
\(555\) | 1.28750e9 | 0.319686 | ||||||||
\(556\) | 1.63440e10 | 4.03271 | ||||||||
\(557\) | 1.55094e9 | 0.380280 | 0.190140 | − | 0.981757i | \(-0.439106\pi\) | ||||
0.190140 | + | 0.981757i | \(0.439106\pi\) | |||||||
\(558\) | −5.72278e9 | −1.39440 | ||||||||
\(559\) | −4.63940e9 | −1.12336 | ||||||||
\(560\) | 3.93506e9 | 0.946876 | ||||||||
\(561\) | −5.57713e9 | −1.33365 | ||||||||
\(562\) | −6.92165e9 | −1.64487 | ||||||||
\(563\) | 6.31801e9 | 1.49211 | 0.746056 | − | 0.665884i | \(-0.231945\pi\) | ||||
0.746056 | + | 0.665884i | \(0.231945\pi\) | |||||||
\(564\) | 2.06924e9 | 0.485662 | ||||||||
\(565\) | −5.53202e7 | −0.0129037 | ||||||||
\(566\) | 7.07470e9 | 1.64002 | ||||||||
\(567\) | −1.91647e9 | −0.441531 | ||||||||
\(568\) | 3.60084e9 | 0.824488 | ||||||||
\(569\) | 3.41487e9 | 0.777109 | 0.388554 | − | 0.921426i | \(-0.372975\pi\) | ||||
0.388554 | + | 0.921426i | \(0.372975\pi\) | |||||||
\(570\) | 3.03116e9 | 0.685562 | ||||||||
\(571\) | −2.10563e9 | −0.473321 | −0.236660 | − | 0.971592i | \(-0.576053\pi\) | ||||
−0.236660 | + | 0.971592i | \(0.576053\pi\) | |||||||
\(572\) | 9.45286e9 | 2.11192 | ||||||||
\(573\) | 1.38107e10 | 3.06673 | ||||||||
\(574\) | 1.66666e10 | 3.67837 | ||||||||
\(575\) | 7.01972e9 | 1.53986 | ||||||||
\(576\) | 4.08313e9 | 0.890255 | ||||||||
\(577\) | −5.35199e9 | −1.15985 | −0.579923 | − | 0.814671i | \(-0.696917\pi\) | ||||
−0.579923 | + | 0.814671i | \(0.696917\pi\) | |||||||
\(578\) | −2.66128e9 | −0.573249 | ||||||||
\(579\) | 2.48781e9 | 0.532650 | ||||||||
\(580\) | −9.71636e8 | −0.206779 | ||||||||
\(581\) | −2.27006e9 | −0.480199 | ||||||||
\(582\) | −2.05223e10 | −4.31514 | ||||||||
\(583\) | −4.99059e9 | −1.04307 | ||||||||
\(584\) | 8.63490e9 | 1.79396 | ||||||||
\(585\) | −2.32296e9 | −0.479729 | ||||||||
\(586\) | 1.07505e10 | 2.20693 | ||||||||
\(587\) | −4.97991e9 | −1.01622 | −0.508111 | − | 0.861292i | \(-0.669656\pi\) | ||||
−0.508111 | + | 0.861292i | \(0.669656\pi\) | |||||||
\(588\) | 3.10419e10 | 6.29692 | ||||||||
\(589\) | −2.27395e9 | −0.458540 | ||||||||
\(590\) | 4.06658e9 | 0.815168 | ||||||||
\(591\) | 7.00652e9 | 1.39620 | ||||||||
\(592\) | 8.43636e9 | 1.67120 | ||||||||
\(593\) | 2.96746e8 | 0.0584377 | 0.0292188 | − | 0.999573i | \(-0.490698\pi\) | ||||
0.0292188 | + | 0.999573i | \(0.490698\pi\) | |||||||
\(594\) | 5.33906e9 | 1.04523 | ||||||||
\(595\) | 2.55604e9 | 0.497460 | ||||||||
\(596\) | −1.65150e10 | −3.19533 | ||||||||
\(597\) | 7.51966e9 | 1.44640 | ||||||||
\(598\) | −1.92978e10 | −3.69024 | ||||||||
\(599\) | 6.91564e9 | 1.31474 | 0.657368 | − | 0.753570i | \(-0.271670\pi\) | ||||
0.657368 | + | 0.753570i | \(0.271670\pi\) | |||||||
\(600\) | 1.92292e10 | 3.63439 | ||||||||
\(601\) | 2.80612e9 | 0.527285 | 0.263642 | − | 0.964620i | \(-0.415076\pi\) | ||||
0.263642 | + | 0.964620i | \(0.415076\pi\) | |||||||
\(602\) | −1.48502e10 | −2.77424 | ||||||||
\(603\) | −8.44094e9 | −1.56776 | ||||||||
\(604\) | 1.44218e10 | 2.66311 | ||||||||
\(605\) | −6.56842e8 | −0.120592 | ||||||||
\(606\) | −1.19175e10 | −2.17537 | ||||||||
\(607\) | −9.13664e8 | −0.165816 | −0.0829079 | − | 0.996557i | \(-0.526421\pi\) | ||||
−0.0829079 | + | 0.996557i | \(0.526421\pi\) | |||||||
\(608\) | 7.54715e9 | 1.36182 | ||||||||
\(609\) | −4.80239e9 | −0.861583 | ||||||||
\(610\) | 2.27431e9 | 0.405691 | ||||||||
\(611\) | −8.97977e8 | −0.159265 | ||||||||
\(612\) | 2.27830e10 | 4.01772 | ||||||||
\(613\) | 1.14941e9 | 0.201540 | 0.100770 | − | 0.994910i | \(-0.467869\pi\) | ||||
0.100770 | + | 0.994910i | \(0.467869\pi\) | |||||||
\(614\) | −1.56704e10 | −2.73207 | ||||||||
\(615\) | −2.94471e9 | −0.510481 | ||||||||
\(616\) | 1.73947e10 | 2.99837 | ||||||||
\(617\) | −1.14126e10 | −1.95608 | −0.978041 | − | 0.208413i | \(-0.933170\pi\) | ||||
−0.978041 | + | 0.208413i | \(0.933170\pi\) | |||||||
\(618\) | 8.91092e9 | 1.51867 | ||||||||
\(619\) | 6.04418e9 | 1.02428 | 0.512142 | − | 0.858901i | \(-0.328852\pi\) | ||||
0.512142 | + | 0.858901i | \(0.328852\pi\) | |||||||
\(620\) | 1.88574e9 | 0.317769 | ||||||||
\(621\) | −7.64825e9 | −1.28157 | ||||||||
\(622\) | 1.59903e10 | 2.66435 | ||||||||
\(623\) | −1.84357e10 | −3.05459 | ||||||||
\(624\) | −2.54332e10 | −4.19040 | ||||||||
\(625\) | 4.85346e9 | 0.795192 | ||||||||
\(626\) | −3.27221e9 | −0.533128 | ||||||||
\(627\) | 6.44654e9 | 1.04446 | ||||||||
\(628\) | −2.39944e10 | −3.86590 | ||||||||
\(629\) | 5.47988e9 | 0.877999 | ||||||||
\(630\) | −7.43551e9 | −1.18473 | ||||||||
\(631\) | −9.36059e9 | −1.48320 | −0.741602 | − | 0.670841i | \(-0.765933\pi\) | ||||
−0.741602 | + | 0.670841i | \(0.765933\pi\) | |||||||
\(632\) | 1.97482e10 | 3.11185 | ||||||||
\(633\) | −8.05974e9 | −1.26301 | ||||||||
\(634\) | −1.14878e10 | −1.79030 | ||||||||
\(635\) | −7.85395e8 | −0.121725 | ||||||||
\(636\) | 3.40648e10 | 5.25056 | ||||||||
\(637\) | −1.34711e10 | −2.06498 | ||||||||
\(638\) | −2.94489e9 | −0.448949 | ||||||||
\(639\) | −3.27352e9 | −0.496320 | ||||||||
\(640\) | 7.43225e8 | 0.112070 | ||||||||
\(641\) | −4.42697e9 | −0.663901 | −0.331950 | − | 0.943297i | \(-0.607707\pi\) | ||||
−0.331950 | + | 0.943297i | \(0.607707\pi\) | |||||||
\(642\) | 1.70460e10 | 2.54243 | ||||||||
\(643\) | −1.19909e10 | −1.77875 | −0.889374 | − | 0.457181i | \(-0.848859\pi\) | ||||
−0.889374 | + | 0.457181i | \(0.848859\pi\) | |||||||
\(644\) | −4.33441e10 | −6.39483 | ||||||||
\(645\) | 2.62378e9 | 0.385006 | ||||||||
\(646\) | 1.29012e10 | 1.88286 | ||||||||
\(647\) | −8.03624e9 | −1.16651 | −0.583254 | − | 0.812289i | \(-0.698221\pi\) | ||||
−0.583254 | + | 0.812289i | \(0.698221\pi\) | |||||||
\(648\) | 4.61160e9 | 0.665794 | ||||||||
\(649\) | 8.64862e9 | 1.24191 | ||||||||
\(650\) | −1.45154e10 | −2.07316 | ||||||||
\(651\) | 9.32043e9 | 1.32404 | ||||||||
\(652\) | 1.73586e10 | 2.45272 | ||||||||
\(653\) | 8.01372e9 | 1.12626 | 0.563129 | − | 0.826369i | \(-0.309597\pi\) | ||||
0.563129 | + | 0.826369i | \(0.309597\pi\) | |||||||
\(654\) | −2.99686e10 | −4.18933 | ||||||||
\(655\) | −2.82839e9 | −0.393274 | ||||||||
\(656\) | −1.92952e10 | −2.66861 | ||||||||
\(657\) | −7.84998e9 | −1.07992 | ||||||||
\(658\) | −2.87432e9 | −0.393318 | ||||||||
\(659\) | 3.08292e9 | 0.419627 | 0.209813 | − | 0.977741i | \(-0.432714\pi\) | ||||
0.209813 | + | 0.977741i | \(0.432714\pi\) | |||||||
\(660\) | −5.34599e9 | −0.723809 | ||||||||
\(661\) | −3.22412e8 | −0.0434217 | −0.0217108 | − | 0.999764i | \(-0.506911\pi\) | ||||
−0.0217108 | + | 0.999764i | \(0.506911\pi\) | |||||||
\(662\) | −6.62755e9 | −0.887872 | ||||||||
\(663\) | −1.65203e10 | −2.20151 | ||||||||
\(664\) | 5.46245e9 | 0.724101 | ||||||||
\(665\) | −2.95450e9 | −0.389590 | ||||||||
\(666\) | −1.59410e10 | −2.09100 | ||||||||
\(667\) | 4.21858e9 | 0.550461 | ||||||||
\(668\) | 5.76772e8 | 0.0748663 | ||||||||
\(669\) | 2.10615e10 | 2.71956 | ||||||||
\(670\) | 3.96382e9 | 0.509157 | ||||||||
\(671\) | 4.83690e9 | 0.618071 | ||||||||
\(672\) | −3.09342e10 | −3.93230 | ||||||||
\(673\) | 1.25539e10 | 1.58755 | 0.793775 | − | 0.608211i | \(-0.208113\pi\) | ||||
0.793775 | + | 0.608211i | \(0.208113\pi\) | |||||||
\(674\) | −2.58049e9 | −0.324633 | ||||||||
\(675\) | −5.75285e9 | −0.719979 | ||||||||
\(676\) | 9.10733e9 | 1.13391 | ||||||||
\(677\) | 7.04658e9 | 0.872807 | 0.436403 | − | 0.899751i | \(-0.356252\pi\) | ||||
0.436403 | + | 0.899751i | \(0.356252\pi\) | |||||||
\(678\) | 1.14447e9 | 0.141026 | ||||||||
\(679\) | 2.00032e10 | 2.45220 | ||||||||
\(680\) | −6.15060e9 | −0.750130 | ||||||||
\(681\) | −4.58757e9 | −0.556631 | ||||||||
\(682\) | 5.71542e9 | 0.689926 | ||||||||
\(683\) | 8.62938e9 | 1.03635 | 0.518176 | − | 0.855274i | \(-0.326611\pi\) | ||||
0.518176 | + | 0.855274i | \(0.326611\pi\) | |||||||
\(684\) | −2.63346e10 | −3.14651 | ||||||||
\(685\) | 4.55863e8 | 0.0541897 | ||||||||
\(686\) | −1.76987e10 | −2.09318 | ||||||||
\(687\) | −2.92357e9 | −0.344005 | ||||||||
\(688\) | 1.71923e10 | 2.01267 | ||||||||
\(689\) | −1.47829e10 | −1.72184 | ||||||||
\(690\) | 1.09137e10 | 1.26474 | ||||||||
\(691\) | −6.42519e9 | −0.740820 | −0.370410 | − | 0.928868i | \(-0.620783\pi\) | ||||
−0.370410 | + | 0.928868i | \(0.620783\pi\) | |||||||
\(692\) | −2.45331e10 | −2.81437 | ||||||||
\(693\) | −1.58135e10 | −1.80494 | ||||||||
\(694\) | −1.37150e10 | −1.55753 | ||||||||
\(695\) | 4.01123e9 | 0.453243 | ||||||||
\(696\) | 1.15560e10 | 1.29920 | ||||||||
\(697\) | −1.25333e10 | −1.40201 | ||||||||
\(698\) | 1.92890e10 | 2.14692 | ||||||||
\(699\) | −2.20617e9 | −0.244325 | ||||||||
\(700\) | −3.26025e10 | −3.59259 | ||||||||
\(701\) | 6.47114e9 | 0.709525 | 0.354762 | − | 0.934957i | \(-0.384562\pi\) | ||||
0.354762 | + | 0.934957i | \(0.384562\pi\) | |||||||
\(702\) | 1.58151e10 | 1.72541 | ||||||||
\(703\) | −6.33414e9 | −0.687613 | ||||||||
\(704\) | −4.07787e9 | −0.440483 | ||||||||
\(705\) | 5.07844e8 | 0.0545843 | ||||||||
\(706\) | −1.56560e10 | −1.67442 | ||||||||
\(707\) | 1.16161e10 | 1.23621 | ||||||||
\(708\) | −5.90337e10 | −6.25149 | ||||||||
\(709\) | 7.25651e9 | 0.764656 | 0.382328 | − | 0.924027i | \(-0.375123\pi\) | ||||
0.382328 | + | 0.924027i | \(0.375123\pi\) | |||||||
\(710\) | 1.53723e9 | 0.161188 | ||||||||
\(711\) | −1.79531e10 | −1.87325 | ||||||||
\(712\) | 4.43619e10 | 4.60607 | ||||||||
\(713\) | −8.18738e9 | −0.845925 | ||||||||
\(714\) | −5.28795e10 | −5.43680 | ||||||||
\(715\) | 2.31997e9 | 0.237362 | ||||||||
\(716\) | −1.04901e10 | −1.06803 | ||||||||
\(717\) | −2.28814e10 | −2.31828 | ||||||||
\(718\) | −1.77286e10 | −1.78747 | ||||||||
\(719\) | −4.36593e9 | −0.438052 | −0.219026 | − | 0.975719i | \(-0.570288\pi\) | ||||
−0.219026 | + | 0.975719i | \(0.570288\pi\) | |||||||
\(720\) | 8.60820e9 | 0.859505 | ||||||||
\(721\) | −8.68555e9 | −0.863026 | ||||||||
\(722\) | 3.60387e9 | 0.356360 | ||||||||
\(723\) | −6.59071e9 | −0.648557 | ||||||||
\(724\) | 2.22981e10 | 2.18365 | ||||||||
\(725\) | 3.17313e9 | 0.309247 | ||||||||
\(726\) | 1.35888e10 | 1.31796 | ||||||||
\(727\) | 4.42118e9 | 0.426745 | 0.213372 | − | 0.976971i | \(-0.431555\pi\) | ||||
0.213372 | + | 0.976971i | \(0.431555\pi\) | |||||||
\(728\) | 5.15258e10 | 4.94954 | ||||||||
\(729\) | −1.69709e10 | −1.62240 | ||||||||
\(730\) | 3.68631e9 | 0.350721 | ||||||||
\(731\) | 1.11673e10 | 1.05740 | ||||||||
\(732\) | −3.30157e10 | −3.11123 | ||||||||
\(733\) | −3.24298e9 | −0.304144 | −0.152072 | − | 0.988369i | \(-0.548595\pi\) | ||||
−0.152072 | + | 0.988369i | \(0.548595\pi\) | |||||||
\(734\) | 1.63892e10 | 1.52975 | ||||||||
\(735\) | 7.61847e9 | 0.707721 | ||||||||
\(736\) | 2.71736e10 | 2.51232 | ||||||||
\(737\) | 8.43007e9 | 0.775703 | ||||||||
\(738\) | 3.64593e10 | 3.33896 | ||||||||
\(739\) | −1.50780e10 | −1.37432 | −0.687159 | − | 0.726507i | \(-0.741143\pi\) | ||||
−0.687159 | + | 0.726507i | \(0.741143\pi\) | |||||||
\(740\) | 5.25278e9 | 0.476516 | ||||||||
\(741\) | 1.90956e10 | 1.72413 | ||||||||
\(742\) | −4.73183e10 | −4.25222 | ||||||||
\(743\) | 5.06652e8 | 0.0453157 | 0.0226579 | − | 0.999743i | \(-0.492787\pi\) | ||||
0.0226579 | + | 0.999743i | \(0.492787\pi\) | |||||||
\(744\) | −2.24278e10 | −1.99655 | ||||||||
\(745\) | −4.05319e9 | −0.359129 | ||||||||
\(746\) | −2.86689e10 | −2.52828 | ||||||||
\(747\) | −4.96591e9 | −0.435889 | ||||||||
\(748\) | −2.27536e10 | −1.98790 | ||||||||
\(749\) | −1.66149e10 | −1.44481 | ||||||||
\(750\) | 1.70351e10 | 1.47445 | ||||||||
\(751\) | 1.32220e10 | 1.13908 | 0.569542 | − | 0.821962i | \(-0.307120\pi\) | ||||
0.569542 | + | 0.821962i | \(0.307120\pi\) | |||||||
\(752\) | 3.32764e9 | 0.285347 | ||||||||
\(753\) | −7.71248e9 | −0.658281 | ||||||||
\(754\) | −8.72323e9 | −0.741101 | ||||||||
\(755\) | 3.53946e9 | 0.299311 | ||||||||
\(756\) | 3.55216e10 | 2.98997 | ||||||||
\(757\) | −1.79649e10 | −1.50518 | −0.752591 | − | 0.658488i | \(-0.771196\pi\) | ||||
−0.752591 | + | 0.658488i | \(0.771196\pi\) | |||||||
\(758\) | 2.76968e9 | 0.230987 | ||||||||
\(759\) | 2.32109e10 | 1.92684 | ||||||||
\(760\) | 7.10941e9 | 0.587471 | ||||||||
\(761\) | 1.35129e10 | 1.11148 | 0.555741 | − | 0.831355i | \(-0.312434\pi\) | ||||
0.555741 | + | 0.831355i | \(0.312434\pi\) | |||||||
\(762\) | 1.62483e10 | 1.33035 | ||||||||
\(763\) | 2.92107e10 | 2.38071 | ||||||||
\(764\) | 5.63452e10 | 4.57120 | ||||||||
\(765\) | 5.59151e9 | 0.451558 | ||||||||
\(766\) | −3.94101e10 | −3.16816 | ||||||||
\(767\) | 2.56185e10 | 2.05008 | ||||||||
\(768\) | −2.72087e10 | −2.16742 | ||||||||
\(769\) | −1.21372e10 | −0.962449 | −0.481225 | − | 0.876597i | \(-0.659808\pi\) | ||||
−0.481225 | + | 0.876597i | \(0.659808\pi\) | |||||||
\(770\) | 7.42594e9 | 0.586184 | ||||||||
\(771\) | −2.69728e10 | −2.11951 | ||||||||
\(772\) | 1.01498e10 | 0.793956 | ||||||||
\(773\) | −7.91784e9 | −0.616564 | −0.308282 | − | 0.951295i | \(-0.599754\pi\) | ||||
−0.308282 | + | 0.951295i | \(0.599754\pi\) | |||||||
\(774\) | −3.24857e10 | −2.51825 | ||||||||
\(775\) | −6.15838e9 | −0.475237 | ||||||||
\(776\) | −4.81338e10 | −3.69772 | ||||||||
\(777\) | 2.59623e10 | 1.98550 | ||||||||
\(778\) | 7.76150e9 | 0.590905 | ||||||||
\(779\) | 1.44871e10 | 1.09799 | ||||||||
\(780\) | −1.58356e10 | −1.19482 | ||||||||
\(781\) | 3.26930e9 | 0.245571 | ||||||||
\(782\) | 4.64511e10 | 3.47354 | ||||||||
\(783\) | −3.45725e9 | −0.257374 | ||||||||
\(784\) | 4.99199e10 | 3.69971 | ||||||||
\(785\) | −5.88882e9 | −0.434495 | ||||||||
\(786\) | 5.85139e10 | 4.29813 | ||||||||
\(787\) | 1.30407e10 | 0.953649 | 0.476825 | − | 0.878998i | \(-0.341788\pi\) | ||||
0.476825 | + | 0.878998i | \(0.341788\pi\) | |||||||
\(788\) | 2.85853e10 | 2.08114 | ||||||||
\(789\) | 3.55121e10 | 2.57399 | ||||||||
\(790\) | 8.43067e9 | 0.608369 | ||||||||
\(791\) | −1.11552e9 | −0.0801421 | ||||||||
\(792\) | 3.80521e10 | 2.72170 | ||||||||
\(793\) | 1.43276e10 | 1.02028 | ||||||||
\(794\) | −3.85492e9 | −0.273303 | ||||||||
\(795\) | 8.36035e9 | 0.590119 | ||||||||
\(796\) | 3.06788e10 | 2.15597 | ||||||||
\(797\) | −1.26368e10 | −0.884168 | −0.442084 | − | 0.896974i | \(-0.645761\pi\) | ||||
−0.442084 | + | 0.896974i | \(0.645761\pi\) | |||||||
\(798\) | 6.11228e10 | 4.25788 | ||||||||
\(799\) | 2.16149e9 | 0.149913 | ||||||||
\(800\) | 2.04395e10 | 1.41141 | ||||||||
\(801\) | −4.03294e10 | −2.77273 | ||||||||
\(802\) | 2.65651e10 | 1.81845 | ||||||||
\(803\) | 7.83988e9 | 0.534324 | ||||||||
\(804\) | −5.75420e10 | −3.90471 | ||||||||
\(805\) | −1.06377e10 | −0.718725 | ||||||||
\(806\) | 1.69299e10 | 1.13889 | ||||||||
\(807\) | −4.14076e10 | −2.77347 | ||||||||
\(808\) | −2.79519e10 | −1.86411 | ||||||||
\(809\) | −8.89805e8 | −0.0590847 | −0.0295424 | − | 0.999564i | \(-0.509405\pi\) | ||||
−0.0295424 | + | 0.999564i | \(0.509405\pi\) | |||||||
\(810\) | 1.96873e9 | 0.130163 | ||||||||
\(811\) | −4.11626e9 | −0.270976 | −0.135488 | − | 0.990779i | \(-0.543260\pi\) | ||||
−0.135488 | + | 0.990779i | \(0.543260\pi\) | |||||||
\(812\) | −1.95929e10 | −1.28426 | ||||||||
\(813\) | −4.66336e9 | −0.304356 | ||||||||
\(814\) | 1.59204e10 | 1.03459 | ||||||||
\(815\) | 4.26023e9 | 0.275665 | ||||||||
\(816\) | 6.12194e10 | 3.94433 | ||||||||
\(817\) | −1.29082e10 | −0.828111 | ||||||||
\(818\) | 1.56788e9 | 0.100156 | ||||||||
\(819\) | −4.68420e10 | −2.97949 | ||||||||
\(820\) | −1.20139e10 | −0.760912 | ||||||||
\(821\) | 5.47547e9 | 0.345319 | 0.172659 | − | 0.984982i | \(-0.444764\pi\) | ||||
0.172659 | + | 0.984982i | \(0.444764\pi\) | |||||||
\(822\) | −9.43091e9 | −0.592246 | ||||||||
\(823\) | −5.61810e9 | −0.351310 | −0.175655 | − | 0.984452i | \(-0.556204\pi\) | ||||
−0.175655 | + | 0.984452i | \(0.556204\pi\) | |||||||
\(824\) | 2.09000e10 | 1.30137 | ||||||||
\(825\) | 1.74587e10 | 1.08249 | ||||||||
\(826\) | 8.20018e10 | 5.06283 | ||||||||
\(827\) | 8.60735e9 | 0.529176 | 0.264588 | − | 0.964362i | \(-0.414764\pi\) | ||||
0.264588 | + | 0.964362i | \(0.414764\pi\) | |||||||
\(828\) | −9.48180e10 | −5.80476 | ||||||||
\(829\) | −2.40091e10 | −1.46364 | −0.731822 | − | 0.681496i | \(-0.761330\pi\) | ||||
−0.731822 | + | 0.681496i | \(0.761330\pi\) | |||||||
\(830\) | 2.33196e9 | 0.141562 | ||||||||
\(831\) | 1.47074e10 | 0.889065 | ||||||||
\(832\) | −1.20793e10 | −0.727126 | ||||||||
\(833\) | 3.24258e10 | 1.94372 | ||||||||
\(834\) | −8.29845e10 | −4.95354 | ||||||||
\(835\) | 1.41554e8 | 0.00841435 | ||||||||
\(836\) | 2.63007e10 | 1.55684 | ||||||||
\(837\) | 6.70978e9 | 0.395521 | ||||||||
\(838\) | 2.40541e10 | 1.41200 | ||||||||
\(839\) | −1.02346e10 | −0.598282 | −0.299141 | − | 0.954209i | \(-0.596700\pi\) | ||||
−0.299141 | + | 0.954209i | \(0.596700\pi\) | |||||||
\(840\) | −2.91400e10 | −1.69634 | ||||||||
\(841\) | −1.53429e10 | −0.889452 | ||||||||
\(842\) | 1.79166e10 | 1.03434 | ||||||||
\(843\) | 2.46604e10 | 1.41776 | ||||||||
\(844\) | −3.28822e10 | −1.88262 | ||||||||
\(845\) | 2.23517e9 | 0.127442 | ||||||||
\(846\) | −6.28776e9 | −0.357026 | ||||||||
\(847\) | −1.32451e10 | −0.748968 | ||||||||
\(848\) | 5.47811e10 | 3.08493 | ||||||||
\(849\) | −2.52056e10 | −1.41358 | ||||||||
\(850\) | 3.49396e10 | 1.95142 | ||||||||
\(851\) | −2.28062e10 | −1.26852 | ||||||||
\(852\) | −2.23156e10 | −1.23615 | ||||||||
\(853\) | 2.74648e9 | 0.151514 | 0.0757572 | − | 0.997126i | \(-0.475863\pi\) | ||||
0.0757572 | + | 0.997126i | \(0.475863\pi\) | |||||||
\(854\) | 4.58610e10 | 2.51966 | ||||||||
\(855\) | −6.46316e9 | −0.353642 | ||||||||
\(856\) | 3.99804e10 | 2.17866 | ||||||||
\(857\) | −1.48574e9 | −0.0806324 | −0.0403162 | − | 0.999187i | \(-0.512837\pi\) | ||||
−0.0403162 | + | 0.999187i | \(0.512837\pi\) | |||||||
\(858\) | −4.79956e10 | −2.59415 | ||||||||
\(859\) | −2.53060e10 | −1.36222 | −0.681112 | − | 0.732180i | \(-0.738503\pi\) | ||||
−0.681112 | + | 0.732180i | \(0.738503\pi\) | |||||||
\(860\) | 1.07045e10 | 0.573882 | ||||||||
\(861\) | −5.93796e10 | −3.17049 | ||||||||
\(862\) | 2.67439e10 | 1.42217 | ||||||||
\(863\) | 2.71902e10 | 1.44004 | 0.720020 | − | 0.693953i | \(-0.244133\pi\) | ||||
0.720020 | + | 0.693953i | \(0.244133\pi\) | |||||||
\(864\) | −2.22695e10 | −1.17466 | ||||||||
\(865\) | −6.02103e9 | −0.316311 | ||||||||
\(866\) | −4.50481e9 | −0.235702 | ||||||||
\(867\) | 9.48157e9 | 0.494098 | ||||||||
\(868\) | 3.80256e10 | 1.97359 | ||||||||
\(869\) | 1.79300e10 | 0.926852 | ||||||||
\(870\) | 4.93335e9 | 0.253995 | ||||||||
\(871\) | 2.49712e10 | 1.28049 | ||||||||
\(872\) | −7.02897e10 | −3.58991 | ||||||||
\(873\) | 4.37584e10 | 2.22593 | ||||||||
\(874\) | −5.36923e10 | −2.72033 | ||||||||
\(875\) | −1.66043e10 | −0.837899 | ||||||||
\(876\) | −5.35134e10 | −2.68966 | ||||||||
\(877\) | 1.65208e10 | 0.827052 | 0.413526 | − | 0.910492i | \(-0.364297\pi\) | ||||
0.413526 | + | 0.910492i | \(0.364297\pi\) | |||||||
\(878\) | 1.94593e10 | 0.970278 | ||||||||
\(879\) | −3.83019e10 | −1.90221 | ||||||||
\(880\) | −8.59712e9 | −0.425269 | ||||||||
\(881\) | 2.13241e10 | 1.05064 | 0.525322 | − | 0.850904i | \(-0.323945\pi\) | ||||
0.525322 | + | 0.850904i | \(0.323945\pi\) | |||||||
\(882\) | −9.43264e10 | −4.62906 | ||||||||
\(883\) | −5.74320e9 | −0.280732 | −0.140366 | − | 0.990100i | \(-0.544828\pi\) | ||||
−0.140366 | + | 0.990100i | \(0.544828\pi\) | |||||||
\(884\) | −6.73997e10 | −3.28152 | ||||||||
\(885\) | −1.44883e10 | −0.702615 | ||||||||
\(886\) | −1.69281e10 | −0.817691 | ||||||||
\(887\) | −9.61464e9 | −0.462594 | −0.231297 | − | 0.972883i | \(-0.574297\pi\) | ||||
−0.231297 | + | 0.972883i | \(0.574297\pi\) | |||||||
\(888\) | −6.24731e10 | −2.99397 | ||||||||
\(889\) | −1.58374e10 | −0.756008 | ||||||||
\(890\) | 1.89385e10 | 0.900492 | ||||||||
\(891\) | 4.18701e9 | 0.198304 | ||||||||
\(892\) | 8.59271e10 | 4.05371 | ||||||||
\(893\) | −2.49844e9 | −0.117406 | ||||||||
\(894\) | 8.38526e10 | 3.92496 | ||||||||
\(895\) | −2.57452e9 | −0.120037 | ||||||||
\(896\) | 1.49870e10 | 0.696044 | ||||||||
\(897\) | 6.87541e10 | 3.18072 | ||||||||
\(898\) | −4.24034e9 | −0.195404 | ||||||||
\(899\) | −3.70095e9 | −0.169885 | ||||||||
\(900\) | −7.13201e10 | −3.26109 | ||||||||
\(901\) | 3.55834e10 | 1.62073 | ||||||||
\(902\) | −3.64124e10 | −1.65206 | ||||||||
\(903\) | 5.29080e10 | 2.39119 | ||||||||
\(904\) | 2.68428e9 | 0.120848 | ||||||||
\(905\) | 5.47252e9 | 0.245424 | ||||||||
\(906\) | −7.32245e10 | −3.27120 | ||||||||
\(907\) | 1.33667e10 | 0.594837 | 0.297419 | − | 0.954747i | \(-0.403874\pi\) | ||||
0.297419 | + | 0.954747i | \(0.403874\pi\) | |||||||
\(908\) | −1.87164e10 | −0.829702 | ||||||||
\(909\) | 2.54111e10 | 1.12215 | ||||||||
\(910\) | 2.19968e10 | 0.967640 | ||||||||
\(911\) | −2.32429e10 | −1.01853 | −0.509267 | − | 0.860609i | \(-0.670083\pi\) | ||||
−0.509267 | + | 0.860609i | \(0.670083\pi\) | |||||||
\(912\) | −7.07628e10 | −3.08904 | ||||||||
\(913\) | 4.95951e9 | 0.215671 | ||||||||
\(914\) | −3.01029e10 | −1.30406 | ||||||||
\(915\) | −8.10288e9 | −0.349676 | ||||||||
\(916\) | −1.19276e10 | −0.512767 | ||||||||
\(917\) | −5.70340e10 | −2.44254 | ||||||||
\(918\) | −3.80680e10 | −1.62409 | ||||||||
\(919\) | 4.33439e9 | 0.184214 | 0.0921072 | − | 0.995749i | \(-0.470640\pi\) | ||||
0.0921072 | + | 0.995749i | \(0.470640\pi\) | |||||||
\(920\) | 2.55975e10 | 1.08378 | ||||||||
\(921\) | 5.58305e10 | 2.35485 | ||||||||
\(922\) | 5.21412e10 | 2.19090 | ||||||||
\(923\) | 9.68418e9 | 0.405375 | ||||||||
\(924\) | −1.07801e11 | −4.49542 | ||||||||
\(925\) | −1.71543e10 | −0.712652 | ||||||||
\(926\) | 5.15785e10 | 2.13467 | ||||||||
\(927\) | −1.90002e10 | −0.783393 | ||||||||
\(928\) | 1.22833e10 | 0.504543 | ||||||||
\(929\) | 2.88880e10 | 1.18212 | 0.591062 | − | 0.806626i | \(-0.298709\pi\) | ||||
0.591062 | + | 0.806626i | \(0.298709\pi\) | |||||||
\(930\) | −9.57459e9 | −0.390328 | ||||||||
\(931\) | −3.74806e10 | −1.52224 | ||||||||
\(932\) | −9.00076e9 | −0.364186 | ||||||||
\(933\) | −5.69702e10 | −2.29648 | ||||||||
\(934\) | −2.87134e10 | −1.15311 | ||||||||
\(935\) | −5.58431e9 | −0.223424 | ||||||||
\(936\) | 1.12716e11 | 4.49283 | ||||||||
\(937\) | −6.06659e9 | −0.240911 | −0.120455 | − | 0.992719i | \(-0.538435\pi\) | ||||
−0.120455 | + | 0.992719i | \(0.538435\pi\) | |||||||
\(938\) | 7.99297e10 | 3.16227 | ||||||||
\(939\) | 1.16582e10 | 0.459517 | ||||||||
\(940\) | 2.07191e9 | 0.0813622 | ||||||||
\(941\) | 2.80351e9 | 0.109683 | 0.0548413 | − | 0.998495i | \(-0.482535\pi\) | ||||
0.0548413 | + | 0.998495i | \(0.482535\pi\) | |||||||
\(942\) | 1.21828e11 | 4.74864 | ||||||||
\(943\) | 5.21610e10 | 2.02561 | ||||||||
\(944\) | −9.49347e10 | −3.67302 | ||||||||
\(945\) | 8.71790e9 | 0.336047 | ||||||||
\(946\) | 3.24439e10 | 1.24599 | ||||||||
\(947\) | −4.39767e10 | −1.68266 | −0.841332 | − | 0.540519i | \(-0.818228\pi\) | ||||
−0.841332 | + | 0.540519i | \(0.818228\pi\) | |||||||
\(948\) | −1.22386e11 | −4.66556 | ||||||||
\(949\) | 2.32229e10 | 0.882033 | ||||||||
\(950\) | −4.03863e10 | −1.52827 | ||||||||
\(951\) | 4.09286e10 | 1.54310 | ||||||||
\(952\) | −1.24026e11 | −4.65889 | ||||||||
\(953\) | 3.44436e10 | 1.28909 | 0.644546 | − | 0.764565i | \(-0.277046\pi\) | ||||
0.644546 | + | 0.764565i | \(0.277046\pi\) | |||||||
\(954\) | −1.03512e11 | −3.85985 | ||||||||
\(955\) | 1.38285e10 | 0.513764 | ||||||||
\(956\) | −9.33518e10 | −3.45557 | ||||||||
\(957\) | 1.04920e10 | 0.386961 | ||||||||
\(958\) | 6.85947e10 | 2.52064 | ||||||||
\(959\) | 9.19239e9 | 0.336561 | ||||||||
\(960\) | 6.83134e9 | 0.249205 | ||||||||
\(961\) | −2.03298e10 | −0.738928 | ||||||||
\(962\) | 4.71588e10 | 1.70785 | ||||||||
\(963\) | −3.63461e10 | −1.31149 | ||||||||
\(964\) | −2.68889e10 | −0.966724 | ||||||||
\(965\) | 2.49101e9 | 0.0892340 | ||||||||
\(966\) | 2.20074e11 | 7.85503 | ||||||||
\(967\) | 1.37307e10 | 0.488315 | 0.244158 | − | 0.969736i | \(-0.421489\pi\) | ||||
0.244158 | + | 0.969736i | \(0.421489\pi\) | |||||||
\(968\) | 3.18717e10 | 1.12938 | ||||||||
\(969\) | −4.59644e10 | −1.62289 | ||||||||
\(970\) | −2.05487e10 | −0.722908 | ||||||||
\(971\) | −3.82566e10 | −1.34103 | −0.670515 | − | 0.741896i | \(-0.733927\pi\) | ||||
−0.670515 | + | 0.741896i | \(0.733927\pi\) | |||||||
\(972\) | −8.07135e10 | −2.81913 | ||||||||
\(973\) | 8.08857e10 | 2.81499 | ||||||||
\(974\) | −7.77821e10 | −2.69726 | ||||||||
\(975\) | 5.17154e10 | 1.78691 | ||||||||
\(976\) | −5.30940e10 | −1.82798 | ||||||||
\(977\) | 1.53271e10 | 0.525810 | 0.262905 | − | 0.964822i | \(-0.415319\pi\) | ||||
0.262905 | + | 0.964822i | \(0.415319\pi\) | |||||||
\(978\) | −8.81357e10 | −3.01277 | ||||||||
\(979\) | 4.02775e10 | 1.37190 | ||||||||
\(980\) | 3.10819e10 | 1.05491 | ||||||||
\(981\) | 6.39003e10 | 2.16103 | ||||||||
\(982\) | −6.34774e9 | −0.213909 | ||||||||
\(983\) | −2.05896e10 | −0.691369 | −0.345685 | − | 0.938351i | \(-0.612353\pi\) | ||||
−0.345685 | + | 0.938351i | \(0.612353\pi\) | |||||||
\(984\) | 1.42885e11 | 4.78084 | ||||||||
\(985\) | 7.01555e9 | 0.233902 | ||||||||
\(986\) | 2.09974e10 | 0.697582 | ||||||||
\(987\) | 1.02406e10 | 0.339012 | ||||||||
\(988\) | 7.79066e10 | 2.56995 | ||||||||
\(989\) | −4.64762e10 | −1.52772 | ||||||||
\(990\) | 1.62447e10 | 0.532095 | ||||||||
\(991\) | 3.22306e10 | 1.05199 | 0.525994 | − | 0.850488i | \(-0.323693\pi\) | ||||
0.525994 | + | 0.850488i | \(0.323693\pi\) | |||||||
\(992\) | −2.38394e10 | −0.775360 | ||||||||
\(993\) | 2.36126e10 | 0.765281 | ||||||||
\(994\) | 3.09979e10 | 1.00111 | ||||||||
\(995\) | 7.52934e9 | 0.242313 | ||||||||
\(996\) | −3.38526e10 | −1.08564 | ||||||||
\(997\) | −5.44583e10 | −1.74033 | −0.870164 | − | 0.492761i | \(-0.835988\pi\) | ||||
−0.870164 | + | 0.492761i | \(0.835988\pi\) | |||||||
\(998\) | 2.76302e10 | 0.879887 | ||||||||
\(999\) | 1.86903e10 | 0.593111 |
(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 | 547.8.a.a.1.8 | ✓ | 156 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.8.a.a.1.8 | ✓ | 156 | 1.1 | even | 1 | trivial |