Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(55.2921495107\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + 3375594921 x^{11} + 115310342333 x^{10} + \cdots + 51\!\cdots\!48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(15.9283\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.9283 | 1.49627 | 0.748133 | − | 0.663548i | \(-0.230950\pi\) | ||||
0.748133 | + | 0.663548i | \(0.230950\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 158.568 | 1.23881 | ||||||||
\(5\) | −421.077 | −1.50649 | −0.753245 | − | 0.657740i | \(-0.771513\pi\) | ||||
−0.753245 | + | 0.657740i | \(0.771513\pi\) | |||||||
\(6\) | 457.065 | 0.863870 | ||||||||
\(7\) | −62.1753 | −0.0685133 | −0.0342567 | − | 0.999413i | \(-0.510906\pi\) | ||||
−0.0342567 | + | 0.999413i | \(0.510906\pi\) | |||||||
\(8\) | 517.469 | 0.357330 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −7128.13 | −2.25411 | ||||||||
\(11\) | 8422.53 | 1.90795 | 0.953977 | − | 0.299878i | \(-0.0969461\pi\) | ||||
0.953977 | + | 0.299878i | \(0.0969461\pi\) | |||||||
\(12\) | 4281.34 | 0.715230 | ||||||||
\(13\) | 11389.2 | 1.43778 | 0.718889 | − | 0.695125i | \(-0.244651\pi\) | ||||
0.718889 | + | 0.695125i | \(0.244651\pi\) | |||||||
\(14\) | −1052.52 | −0.102514 | ||||||||
\(15\) | −11369.1 | −0.869773 | ||||||||
\(16\) | −11536.9 | −0.704154 | ||||||||
\(17\) | 1307.83 | 0.0645626 | 0.0322813 | − | 0.999479i | \(-0.489723\pi\) | ||||
0.0322813 | + | 0.999479i | \(0.489723\pi\) | |||||||
\(18\) | 12340.7 | 0.498756 | ||||||||
\(19\) | −7903.89 | −0.264365 | −0.132182 | − | 0.991225i | \(-0.542198\pi\) | ||||
−0.132182 | + | 0.991225i | \(0.542198\pi\) | |||||||
\(20\) | −66769.4 | −1.86626 | ||||||||
\(21\) | −1678.73 | −0.0395562 | ||||||||
\(22\) | 142579. | 2.85481 | ||||||||
\(23\) | −2032.53 | −0.0348329 | −0.0174164 | − | 0.999848i | \(-0.505544\pi\) | ||||
−0.0174164 | + | 0.999848i | \(0.505544\pi\) | |||||||
\(24\) | 13971.7 | 0.206304 | ||||||||
\(25\) | 99180.7 | 1.26951 | ||||||||
\(26\) | 192800. | 2.15130 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −9859.03 | −0.0848753 | ||||||||
\(29\) | 64202.2 | 0.488829 | 0.244414 | − | 0.969671i | \(-0.421404\pi\) | ||||
0.244414 | + | 0.969671i | \(0.421404\pi\) | |||||||
\(30\) | −192459. | −1.30141 | ||||||||
\(31\) | 320926. | 1.93481 | 0.967405 | − | 0.253233i | \(-0.0814939\pi\) | ||||
0.967405 | + | 0.253233i | \(0.0814939\pi\) | |||||||
\(32\) | −261536. | −1.41093 | ||||||||
\(33\) | 227408. | 1.10156 | ||||||||
\(34\) | 22139.4 | 0.0966029 | ||||||||
\(35\) | 26180.6 | 0.103215 | ||||||||
\(36\) | 115596. | 0.412938 | ||||||||
\(37\) | −143662. | −0.466269 | −0.233135 | − | 0.972444i | \(-0.574898\pi\) | ||||
−0.233135 | + | 0.972444i | \(0.574898\pi\) | |||||||
\(38\) | −133800. | −0.395560 | ||||||||
\(39\) | 307509. | 0.830102 | ||||||||
\(40\) | −217894. | −0.538314 | ||||||||
\(41\) | 577414. | 1.30841 | 0.654205 | − | 0.756318i | \(-0.273004\pi\) | ||||
0.654205 | + | 0.756318i | \(0.273004\pi\) | |||||||
\(42\) | −28418.2 | −0.0591866 | ||||||||
\(43\) | 817246. | 1.56752 | 0.783760 | − | 0.621064i | \(-0.213299\pi\) | ||||
0.783760 | + | 0.621064i | \(0.213299\pi\) | |||||||
\(44\) | 1.33555e6 | 2.36360 | ||||||||
\(45\) | −306965. | −0.502163 | ||||||||
\(46\) | −34407.3 | −0.0521193 | ||||||||
\(47\) | 264964. | 0.372259 | 0.186129 | − | 0.982525i | \(-0.440406\pi\) | ||||
0.186129 | + | 0.982525i | \(0.440406\pi\) | |||||||
\(48\) | −311495. | −0.406543 | ||||||||
\(49\) | −819677. | −0.995306 | ||||||||
\(50\) | 1.67896e6 | 1.89953 | ||||||||
\(51\) | 35311.5 | 0.0372752 | ||||||||
\(52\) | 1.80597e6 | 1.78114 | ||||||||
\(53\) | 1.60310e6 | 1.47909 | 0.739545 | − | 0.673107i | \(-0.235041\pi\) | ||||
0.739545 | + | 0.673107i | \(0.235041\pi\) | |||||||
\(54\) | 333200. | 0.287957 | ||||||||
\(55\) | −3.54653e6 | −2.87432 | ||||||||
\(56\) | −32173.8 | −0.0244818 | ||||||||
\(57\) | −213405. | −0.152631 | ||||||||
\(58\) | 1.08684e6 | 0.731418 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | −1.80277e6 | −1.07749 | ||||||||
\(61\) | −274208. | −0.154677 | −0.0773386 | − | 0.997005i | \(-0.524642\pi\) | ||||
−0.0773386 | + | 0.997005i | \(0.524642\pi\) | |||||||
\(62\) | 5.43273e6 | 2.89499 | ||||||||
\(63\) | −45325.8 | −0.0228378 | ||||||||
\(64\) | −2.95064e6 | −1.40698 | ||||||||
\(65\) | −4.79573e6 | −2.16600 | ||||||||
\(66\) | 3.84964e6 | 1.64823 | ||||||||
\(67\) | −1.66313e6 | −0.675562 | −0.337781 | − | 0.941225i | \(-0.609676\pi\) | ||||
−0.337781 | + | 0.941225i | \(0.609676\pi\) | |||||||
\(68\) | 207381. | 0.0799811 | ||||||||
\(69\) | −54878.3 | −0.0201108 | ||||||||
\(70\) | 443194. | 0.154437 | ||||||||
\(71\) | −2.97718e6 | −0.987190 | −0.493595 | − | 0.869692i | \(-0.664317\pi\) | ||||
−0.493595 | + | 0.869692i | \(0.664317\pi\) | |||||||
\(72\) | 377235. | 0.119110 | ||||||||
\(73\) | −2.72516e6 | −0.819904 | −0.409952 | − | 0.912107i | \(-0.634454\pi\) | ||||
−0.409952 | + | 0.912107i | \(0.634454\pi\) | |||||||
\(74\) | −2.43196e6 | −0.697663 | ||||||||
\(75\) | 2.67788e6 | 0.732954 | ||||||||
\(76\) | −1.25331e6 | −0.327499 | ||||||||
\(77\) | −523673. | −0.130720 | ||||||||
\(78\) | 5.20561e6 | 1.24205 | ||||||||
\(79\) | 1.33414e6 | 0.304442 | 0.152221 | − | 0.988346i | \(-0.451357\pi\) | ||||
0.152221 | + | 0.988346i | \(0.451357\pi\) | |||||||
\(80\) | 4.85790e6 | 1.06080 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 9.77465e6 | 1.95773 | ||||||||
\(83\) | 8.00004e6 | 1.53574 | 0.767872 | − | 0.640603i | \(-0.221316\pi\) | ||||
0.767872 | + | 0.640603i | \(0.221316\pi\) | |||||||
\(84\) | −266194. | −0.0490028 | ||||||||
\(85\) | −550698. | −0.0972629 | ||||||||
\(86\) | 1.38346e7 | 2.34543 | ||||||||
\(87\) | 1.73346e6 | 0.282225 | ||||||||
\(88\) | 4.35840e6 | 0.681769 | ||||||||
\(89\) | −1.07983e7 | −1.62365 | −0.811825 | − | 0.583901i | \(-0.801526\pi\) | ||||
−0.811825 | + | 0.583901i | \(0.801526\pi\) | |||||||
\(90\) | −5.19640e6 | −0.751370 | ||||||||
\(91\) | −708128. | −0.0985069 | ||||||||
\(92\) | −322295. | −0.0431515 | ||||||||
\(93\) | 8.66499e6 | 1.11706 | ||||||||
\(94\) | 4.48540e6 | 0.556998 | ||||||||
\(95\) | 3.32814e6 | 0.398263 | ||||||||
\(96\) | −7.06146e6 | −0.814602 | ||||||||
\(97\) | −1.36112e7 | −1.51425 | −0.757124 | − | 0.653272i | \(-0.773396\pi\) | ||||
−0.757124 | + | 0.653272i | \(0.773396\pi\) | |||||||
\(98\) | −1.38758e7 | −1.48924 | ||||||||
\(99\) | 6.14002e6 | 0.635985 | ||||||||
\(100\) | 1.57269e7 | 1.57269 | ||||||||
\(101\) | −8.15059e6 | −0.787162 | −0.393581 | − | 0.919290i | \(-0.628764\pi\) | ||||
−0.393581 | + | 0.919290i | \(0.628764\pi\) | |||||||
\(102\) | 597764. | 0.0557737 | ||||||||
\(103\) | −5.09641e6 | −0.459551 | −0.229776 | − | 0.973244i | \(-0.573799\pi\) | ||||
−0.229776 | + | 0.973244i | \(0.573799\pi\) | |||||||
\(104\) | 5.89356e6 | 0.513761 | ||||||||
\(105\) | 706876. | 0.0595910 | ||||||||
\(106\) | 2.71378e7 | 2.21311 | ||||||||
\(107\) | −2.19007e7 | −1.72828 | −0.864140 | − | 0.503251i | \(-0.832137\pi\) | ||||
−0.864140 | + | 0.503251i | \(0.832137\pi\) | |||||||
\(108\) | 3.12110e6 | 0.238410 | ||||||||
\(109\) | 19486.8 | 0.00144128 | 0.000720639 | − | 1.00000i | \(-0.499771\pi\) | ||||
0.000720639 | 1.00000i | \(0.499771\pi\) | ||||||||
\(110\) | −6.00368e7 | −4.30074 | ||||||||
\(111\) | −3.87888e6 | −0.269201 | ||||||||
\(112\) | 717307. | 0.0482439 | ||||||||
\(113\) | 7.14160e6 | 0.465608 | 0.232804 | − | 0.972524i | \(-0.425210\pi\) | ||||
0.232804 | + | 0.972524i | \(0.425210\pi\) | |||||||
\(114\) | −3.61259e6 | −0.228377 | ||||||||
\(115\) | 855851. | 0.0524754 | ||||||||
\(116\) | 1.01804e7 | 0.605568 | ||||||||
\(117\) | 8.30273e6 | 0.479259 | ||||||||
\(118\) | 3.47672e6 | 0.194797 | ||||||||
\(119\) | −81314.9 | −0.00442340 | ||||||||
\(120\) | −5.88314e6 | −0.310796 | ||||||||
\(121\) | 5.14518e7 | 2.64029 | ||||||||
\(122\) | −4.64189e6 | −0.231438 | ||||||||
\(123\) | 1.55902e7 | 0.755410 | ||||||||
\(124\) | 5.08886e7 | 2.39687 | ||||||||
\(125\) | −8.86607e6 | −0.406019 | ||||||||
\(126\) | −767290. | −0.0341714 | ||||||||
\(127\) | −3.64410e7 | −1.57862 | −0.789308 | − | 0.613997i | \(-0.789561\pi\) | ||||
−0.789308 | + | 0.613997i | \(0.789561\pi\) | |||||||
\(128\) | −1.64729e7 | −0.694280 | ||||||||
\(129\) | 2.20656e7 | 0.905008 | ||||||||
\(130\) | −8.11837e7 | −3.24091 | ||||||||
\(131\) | 1.30081e7 | 0.505549 | 0.252774 | − | 0.967525i | \(-0.418657\pi\) | ||||
0.252774 | + | 0.967525i | \(0.418657\pi\) | |||||||
\(132\) | 3.60597e7 | 1.36463 | ||||||||
\(133\) | 491427. | 0.0181125 | ||||||||
\(134\) | −2.81541e7 | −1.01082 | ||||||||
\(135\) | −8.28806e6 | −0.289924 | ||||||||
\(136\) | 676763. | 0.0230701 | ||||||||
\(137\) | −1.31043e7 | −0.435404 | −0.217702 | − | 0.976015i | \(-0.569856\pi\) | ||||
−0.217702 | + | 0.976015i | \(0.569856\pi\) | |||||||
\(138\) | −928998. | −0.0300911 | ||||||||
\(139\) | 8.55786e6 | 0.270280 | 0.135140 | − | 0.990827i | \(-0.456852\pi\) | ||||
0.135140 | + | 0.990827i | \(0.456852\pi\) | |||||||
\(140\) | 4.15141e6 | 0.127864 | ||||||||
\(141\) | 7.15403e6 | 0.214924 | ||||||||
\(142\) | −5.03986e7 | −1.47710 | ||||||||
\(143\) | 9.59260e7 | 2.74322 | ||||||||
\(144\) | −8.41036e6 | −0.234718 | ||||||||
\(145\) | −2.70340e7 | −0.736416 | ||||||||
\(146\) | −4.61325e7 | −1.22679 | ||||||||
\(147\) | −2.21313e7 | −0.574640 | ||||||||
\(148\) | −2.27803e7 | −0.577621 | ||||||||
\(149\) | 8.02680e7 | 1.98788 | 0.993941 | − | 0.109916i | \(-0.0350582\pi\) | ||||
0.993941 | + | 0.109916i | \(0.0350582\pi\) | |||||||
\(150\) | 4.53320e7 | 1.09669 | ||||||||
\(151\) | 606581. | 0.0143374 | 0.00716869 | − | 0.999974i | \(-0.497718\pi\) | ||||
0.00716869 | + | 0.999974i | \(0.497718\pi\) | |||||||
\(152\) | −4.09002e6 | −0.0944653 | ||||||||
\(153\) | 953410. | 0.0215209 | ||||||||
\(154\) | −8.86492e6 | −0.195592 | ||||||||
\(155\) | −1.35134e8 | −2.91477 | ||||||||
\(156\) | 4.87611e7 | 1.02834 | ||||||||
\(157\) | 6.17847e7 | 1.27418 | 0.637092 | − | 0.770788i | \(-0.280137\pi\) | ||||
0.637092 | + | 0.770788i | \(0.280137\pi\) | |||||||
\(158\) | 2.25847e7 | 0.455527 | ||||||||
\(159\) | 4.32837e7 | 0.853953 | ||||||||
\(160\) | 1.10127e8 | 2.12555 | ||||||||
\(161\) | 126373. | 0.00238652 | ||||||||
\(162\) | 8.99641e6 | 0.166252 | ||||||||
\(163\) | −1.21598e6 | −0.0219922 | −0.0109961 | − | 0.999940i | \(-0.503500\pi\) | ||||
−0.0109961 | + | 0.999940i | \(0.503500\pi\) | |||||||
\(164\) | 9.15595e7 | 1.62088 | ||||||||
\(165\) | −9.57564e7 | −1.65949 | ||||||||
\(166\) | 1.35427e8 | 2.29788 | ||||||||
\(167\) | 1.21038e7 | 0.201102 | 0.100551 | − | 0.994932i | \(-0.467940\pi\) | ||||
0.100551 | + | 0.994932i | \(0.467940\pi\) | |||||||
\(168\) | −868692. | −0.0141346 | ||||||||
\(169\) | 6.69656e7 | 1.06721 | ||||||||
\(170\) | −9.32240e6 | −0.145531 | ||||||||
\(171\) | −5.76194e6 | −0.0881215 | ||||||||
\(172\) | 1.29589e8 | 1.94187 | ||||||||
\(173\) | −1.01126e8 | −1.48492 | −0.742460 | − | 0.669890i | \(-0.766341\pi\) | ||||
−0.742460 | + | 0.669890i | \(0.766341\pi\) | |||||||
\(174\) | 2.93445e7 | 0.422284 | ||||||||
\(175\) | −6.16659e6 | −0.0869785 | ||||||||
\(176\) | −9.71695e7 | −1.34349 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | −1.82798e8 | −2.42941 | ||||||||
\(179\) | −7.67192e7 | −0.999813 | −0.499906 | − | 0.866079i | \(-0.666632\pi\) | ||||
−0.499906 | + | 0.866079i | \(0.666632\pi\) | |||||||
\(180\) | −4.86749e7 | −0.622087 | ||||||||
\(181\) | 4.41123e7 | 0.552949 | 0.276474 | − | 0.961021i | \(-0.410834\pi\) | ||||
0.276474 | + | 0.961021i | \(0.410834\pi\) | |||||||
\(182\) | −1.19874e7 | −0.147393 | ||||||||
\(183\) | −7.40363e6 | −0.0893030 | ||||||||
\(184\) | −1.05177e6 | −0.0124468 | ||||||||
\(185\) | 6.04929e7 | 0.702430 | ||||||||
\(186\) | 1.46684e8 | 1.67142 | ||||||||
\(187\) | 1.10153e7 | 0.123183 | ||||||||
\(188\) | 4.20149e7 | 0.461159 | ||||||||
\(189\) | −1.22380e6 | −0.0131854 | ||||||||
\(190\) | 5.63399e7 | 0.595907 | ||||||||
\(191\) | 3.96720e7 | 0.411972 | 0.205986 | − | 0.978555i | \(-0.433960\pi\) | ||||
0.205986 | + | 0.978555i | \(0.433960\pi\) | |||||||
\(192\) | −7.96674e7 | −0.812318 | ||||||||
\(193\) | −6.49743e7 | −0.650565 | −0.325283 | − | 0.945617i | \(-0.605459\pi\) | ||||
−0.325283 | + | 0.945617i | \(0.605459\pi\) | |||||||
\(194\) | −2.30416e8 | −2.26572 | ||||||||
\(195\) | −1.29485e8 | −1.25054 | ||||||||
\(196\) | −1.29975e8 | −1.23300 | ||||||||
\(197\) | 1.60147e8 | 1.49241 | 0.746204 | − | 0.665717i | \(-0.231874\pi\) | ||||
0.746204 | + | 0.665717i | \(0.231874\pi\) | |||||||
\(198\) | 1.03940e8 | 0.951603 | ||||||||
\(199\) | 3.62822e7 | 0.326368 | 0.163184 | − | 0.986596i | \(-0.447824\pi\) | ||||
0.163184 | + | 0.986596i | \(0.447824\pi\) | |||||||
\(200\) | 5.13229e7 | 0.453635 | ||||||||
\(201\) | −4.49046e7 | −0.390036 | ||||||||
\(202\) | −1.37976e8 | −1.17780 | ||||||||
\(203\) | −3.99179e6 | −0.0334913 | ||||||||
\(204\) | 5.59928e6 | 0.0461771 | ||||||||
\(205\) | −2.43136e8 | −1.97111 | ||||||||
\(206\) | −8.62737e7 | −0.687611 | ||||||||
\(207\) | −1.48171e6 | −0.0116110 | ||||||||
\(208\) | −1.31396e8 | −1.01242 | ||||||||
\(209\) | −6.65707e7 | −0.504396 | ||||||||
\(210\) | 1.19662e7 | 0.0891640 | ||||||||
\(211\) | −2.00331e8 | −1.46811 | −0.734056 | − | 0.679089i | \(-0.762375\pi\) | ||||
−0.734056 | + | 0.679089i | \(0.762375\pi\) | |||||||
\(212\) | 2.54200e8 | 1.83232 | ||||||||
\(213\) | −8.03838e7 | −0.569954 | ||||||||
\(214\) | −3.70742e8 | −2.58597 | ||||||||
\(215\) | −3.44123e8 | −2.36145 | ||||||||
\(216\) | 1.01853e7 | 0.0687682 | ||||||||
\(217\) | −1.99537e7 | −0.132560 | ||||||||
\(218\) | 329879. | 0.00215654 | ||||||||
\(219\) | −7.35795e7 | −0.473372 | ||||||||
\(220\) | −5.62367e8 | −3.56074 | ||||||||
\(221\) | 1.48952e7 | 0.0928267 | ||||||||
\(222\) | −6.56630e7 | −0.402796 | ||||||||
\(223\) | 1.92870e8 | 1.16465 | 0.582327 | − | 0.812955i | \(-0.302142\pi\) | ||||
0.582327 | + | 0.812955i | \(0.302142\pi\) | |||||||
\(224\) | 1.62611e7 | 0.0966676 | ||||||||
\(225\) | 7.23027e7 | 0.423171 | ||||||||
\(226\) | 1.20895e8 | 0.696674 | ||||||||
\(227\) | −3.48084e7 | −0.197512 | −0.0987560 | − | 0.995112i | \(-0.531486\pi\) | ||||
−0.0987560 | + | 0.995112i | \(0.531486\pi\) | |||||||
\(228\) | −3.38393e7 | −0.189081 | ||||||||
\(229\) | −2.38784e8 | −1.31396 | −0.656978 | − | 0.753910i | \(-0.728165\pi\) | ||||
−0.656978 | + | 0.753910i | \(0.728165\pi\) | |||||||
\(230\) | 1.44881e7 | 0.0785172 | ||||||||
\(231\) | −1.41392e7 | −0.0754714 | ||||||||
\(232\) | 3.32226e7 | 0.174673 | ||||||||
\(233\) | 3.17570e8 | 1.64473 | 0.822364 | − | 0.568962i | \(-0.192655\pi\) | ||||
0.822364 | + | 0.568962i | \(0.192655\pi\) | |||||||
\(234\) | 1.40551e8 | 0.717100 | ||||||||
\(235\) | −1.11570e8 | −0.560804 | ||||||||
\(236\) | 3.25666e7 | 0.161280 | ||||||||
\(237\) | 3.60217e7 | 0.175770 | ||||||||
\(238\) | −1.37653e6 | −0.00661858 | ||||||||
\(239\) | −1.63040e8 | −0.772505 | −0.386252 | − | 0.922393i | \(-0.626231\pi\) | ||||
−0.386252 | + | 0.922393i | \(0.626231\pi\) | |||||||
\(240\) | 1.31163e8 | 0.612453 | ||||||||
\(241\) | 9.18889e7 | 0.422867 | 0.211433 | − | 0.977392i | \(-0.432187\pi\) | ||||
0.211433 | + | 0.977392i | \(0.432187\pi\) | |||||||
\(242\) | 8.70993e8 | 3.95058 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −4.34808e7 | −0.191616 | ||||||||
\(245\) | 3.45147e8 | 1.49942 | ||||||||
\(246\) | 2.63915e8 | 1.13030 | ||||||||
\(247\) | −9.00191e7 | −0.380098 | ||||||||
\(248\) | 1.66069e8 | 0.691366 | ||||||||
\(249\) | 2.16001e8 | 0.886662 | ||||||||
\(250\) | −1.50088e8 | −0.607513 | ||||||||
\(251\) | −1.98730e7 | −0.0793242 | −0.0396621 | − | 0.999213i | \(-0.512628\pi\) | ||||
−0.0396621 | + | 0.999213i | \(0.512628\pi\) | |||||||
\(252\) | −7.18723e6 | −0.0282918 | ||||||||
\(253\) | −1.71190e7 | −0.0664596 | ||||||||
\(254\) | −6.16884e8 | −2.36203 | ||||||||
\(255\) | −1.48688e7 | −0.0561548 | ||||||||
\(256\) | 9.88239e7 | 0.368148 | ||||||||
\(257\) | 5.09658e8 | 1.87289 | 0.936447 | − | 0.350810i | \(-0.114094\pi\) | ||||
0.936447 | + | 0.350810i | \(0.114094\pi\) | |||||||
\(258\) | 3.73534e8 | 1.35413 | ||||||||
\(259\) | 8.93225e6 | 0.0319456 | ||||||||
\(260\) | −7.60451e8 | −2.68327 | ||||||||
\(261\) | 4.68034e7 | 0.162943 | ||||||||
\(262\) | 2.20205e8 | 0.756436 | ||||||||
\(263\) | −1.92628e8 | −0.652941 | −0.326471 | − | 0.945207i | \(-0.605859\pi\) | ||||
−0.326471 | + | 0.945207i | \(0.605859\pi\) | |||||||
\(264\) | 1.17677e8 | 0.393620 | ||||||||
\(265\) | −6.75028e8 | −2.22823 | ||||||||
\(266\) | 8.31903e6 | 0.0271011 | ||||||||
\(267\) | −2.91555e8 | −0.937415 | ||||||||
\(268\) | −2.63720e8 | −0.836896 | ||||||||
\(269\) | 4.06864e8 | 1.27443 | 0.637215 | − | 0.770686i | \(-0.280086\pi\) | ||||
0.637215 | + | 0.770686i | \(0.280086\pi\) | |||||||
\(270\) | −1.40303e8 | −0.433804 | ||||||||
\(271\) | −1.77838e8 | −0.542789 | −0.271395 | − | 0.962468i | \(-0.587485\pi\) | ||||
−0.271395 | + | 0.962468i | \(0.587485\pi\) | |||||||
\(272\) | −1.50883e7 | −0.0454620 | ||||||||
\(273\) | −1.91195e7 | −0.0568730 | ||||||||
\(274\) | −2.21834e8 | −0.651481 | ||||||||
\(275\) | 8.35352e8 | 2.42217 | ||||||||
\(276\) | −8.70195e6 | −0.0249135 | ||||||||
\(277\) | −5.24499e8 | −1.48274 | −0.741371 | − | 0.671095i | \(-0.765824\pi\) | ||||
−0.741371 | + | 0.671095i | \(0.765824\pi\) | |||||||
\(278\) | 1.44870e8 | 0.404411 | ||||||||
\(279\) | 2.33955e8 | 0.644937 | ||||||||
\(280\) | 1.35476e7 | 0.0368817 | ||||||||
\(281\) | −9.91059e7 | −0.266457 | −0.133229 | − | 0.991085i | \(-0.542534\pi\) | ||||
−0.133229 | + | 0.991085i | \(0.542534\pi\) | |||||||
\(282\) | 1.21106e8 | 0.321583 | ||||||||
\(283\) | 3.36868e8 | 0.883502 | 0.441751 | − | 0.897138i | \(-0.354357\pi\) | ||||
0.441751 | + | 0.897138i | \(0.354357\pi\) | |||||||
\(284\) | −4.72086e8 | −1.22294 | ||||||||
\(285\) | 8.98599e7 | 0.229937 | ||||||||
\(286\) | 1.62387e9 | 4.10458 | ||||||||
\(287\) | −3.59009e7 | −0.0896434 | ||||||||
\(288\) | −1.90659e8 | −0.470310 | ||||||||
\(289\) | −4.08628e8 | −0.995832 | ||||||||
\(290\) | −4.57641e8 | −1.10187 | ||||||||
\(291\) | −3.67504e8 | −0.874251 | ||||||||
\(292\) | −4.32125e8 | −1.01571 | ||||||||
\(293\) | 1.54762e8 | 0.359441 | 0.179720 | − | 0.983718i | \(-0.442481\pi\) | ||||
0.179720 | + | 0.983718i | \(0.442481\pi\) | |||||||
\(294\) | −3.74646e8 | −0.859815 | ||||||||
\(295\) | −8.64803e7 | −0.196128 | ||||||||
\(296\) | −7.43407e7 | −0.166612 | ||||||||
\(297\) | 1.65781e8 | 0.367186 | ||||||||
\(298\) | 1.35880e9 | 2.97440 | ||||||||
\(299\) | −2.31489e7 | −0.0500819 | ||||||||
\(300\) | 4.24627e8 | 0.907994 | ||||||||
\(301\) | −5.08125e7 | −0.107396 | ||||||||
\(302\) | 1.02684e7 | 0.0214525 | ||||||||
\(303\) | −2.20066e8 | −0.454468 | ||||||||
\(304\) | 9.11860e7 | 0.186153 | ||||||||
\(305\) | 1.15463e8 | 0.233020 | ||||||||
\(306\) | 1.61396e7 | 0.0322010 | ||||||||
\(307\) | 1.34130e8 | 0.264570 | 0.132285 | − | 0.991212i | \(-0.457769\pi\) | ||||
0.132285 | + | 0.991212i | \(0.457769\pi\) | |||||||
\(308\) | −8.30380e7 | −0.161938 | ||||||||
\(309\) | −1.37603e8 | −0.265322 | ||||||||
\(310\) | −2.28760e9 | −4.36128 | ||||||||
\(311\) | −1.66463e8 | −0.313802 | −0.156901 | − | 0.987614i | \(-0.550150\pi\) | ||||
−0.156901 | + | 0.987614i | \(0.550150\pi\) | |||||||
\(312\) | 1.59126e8 | 0.296620 | ||||||||
\(313\) | 4.01885e8 | 0.740793 | 0.370396 | − | 0.928874i | \(-0.379222\pi\) | ||||
0.370396 | + | 0.928874i | \(0.379222\pi\) | |||||||
\(314\) | 1.04591e9 | 1.90652 | ||||||||
\(315\) | 1.90857e7 | 0.0344049 | ||||||||
\(316\) | 2.11551e8 | 0.377147 | ||||||||
\(317\) | 1.50022e8 | 0.264513 | 0.132257 | − | 0.991216i | \(-0.457778\pi\) | ||||
0.132257 | + | 0.991216i | \(0.457778\pi\) | |||||||
\(318\) | 7.32720e8 | 1.27774 | ||||||||
\(319\) | 5.40745e8 | 0.932663 | ||||||||
\(320\) | 1.24245e9 | 2.11960 | ||||||||
\(321\) | −5.91318e8 | −0.997823 | ||||||||
\(322\) | 2.13929e6 | 0.00357086 | ||||||||
\(323\) | −1.03370e7 | −0.0170681 | ||||||||
\(324\) | 8.42697e7 | 0.137646 | ||||||||
\(325\) | 1.12959e9 | 1.82528 | ||||||||
\(326\) | −2.05845e7 | −0.0329062 | ||||||||
\(327\) | 526144. | 0.000832122 0 | ||||||||
\(328\) | 2.98794e8 | 0.467534 | ||||||||
\(329\) | −1.64742e7 | −0.0255047 | ||||||||
\(330\) | −1.62099e9 | −2.48304 | ||||||||
\(331\) | 2.12361e8 | 0.321867 | 0.160934 | − | 0.986965i | \(-0.448550\pi\) | ||||
0.160934 | + | 0.986965i | \(0.448550\pi\) | |||||||
\(332\) | 1.26855e9 | 1.90250 | ||||||||
\(333\) | −1.04730e8 | −0.155423 | ||||||||
\(334\) | 2.04898e8 | 0.300902 | ||||||||
\(335\) | 7.00307e8 | 1.01773 | ||||||||
\(336\) | 1.93673e7 | 0.0278536 | ||||||||
\(337\) | 3.59426e8 | 0.511570 | 0.255785 | − | 0.966734i | \(-0.417666\pi\) | ||||
0.255785 | + | 0.966734i | \(0.417666\pi\) | |||||||
\(338\) | 1.13362e9 | 1.59682 | ||||||||
\(339\) | 1.92823e8 | 0.268819 | ||||||||
\(340\) | −8.73232e7 | −0.120491 | ||||||||
\(341\) | 2.70301e9 | 3.69153 | ||||||||
\(342\) | −9.75399e7 | −0.131853 | ||||||||
\(343\) | 1.02168e8 | 0.136705 | ||||||||
\(344\) | 4.22899e8 | 0.560122 | ||||||||
\(345\) | 2.31080e7 | 0.0302967 | ||||||||
\(346\) | −1.71190e9 | −2.22184 | ||||||||
\(347\) | −1.80343e8 | −0.231711 | −0.115855 | − | 0.993266i | \(-0.536961\pi\) | ||||
−0.115855 | + | 0.993266i | \(0.536961\pi\) | |||||||
\(348\) | 2.74871e8 | 0.349625 | ||||||||
\(349\) | 1.08403e9 | 1.36506 | 0.682531 | − | 0.730856i | \(-0.260879\pi\) | ||||
0.682531 | + | 0.730856i | \(0.260879\pi\) | |||||||
\(350\) | −1.04390e8 | −0.130143 | ||||||||
\(351\) | 2.24174e8 | 0.276701 | ||||||||
\(352\) | −2.20279e9 | −2.69199 | ||||||||
\(353\) | −9.01373e8 | −1.09067 | −0.545335 | − | 0.838218i | \(-0.683597\pi\) | ||||
−0.545335 | + | 0.838218i | \(0.683597\pi\) | |||||||
\(354\) | 9.38715e7 | 0.112466 | ||||||||
\(355\) | 1.25362e9 | 1.48719 | ||||||||
\(356\) | −1.71227e9 | −2.01140 | ||||||||
\(357\) | −2.19550e6 | −0.00255385 | ||||||||
\(358\) | −1.29873e9 | −1.49599 | ||||||||
\(359\) | −4.12758e8 | −0.470830 | −0.235415 | − | 0.971895i | \(-0.575645\pi\) | ||||
−0.235415 | + | 0.971895i | \(0.575645\pi\) | |||||||
\(360\) | −1.58845e8 | −0.179438 | ||||||||
\(361\) | −8.31400e8 | −0.930111 | ||||||||
\(362\) | 7.46748e8 | 0.827359 | ||||||||
\(363\) | 1.38920e9 | 1.52437 | ||||||||
\(364\) | −1.12287e8 | −0.122032 | ||||||||
\(365\) | 1.14750e9 | 1.23518 | ||||||||
\(366\) | −1.25331e8 | −0.133621 | ||||||||
\(367\) | −5.59200e8 | −0.590521 | −0.295261 | − | 0.955417i | \(-0.595407\pi\) | ||||
−0.295261 | + | 0.955417i | \(0.595407\pi\) | |||||||
\(368\) | 2.34490e7 | 0.0245277 | ||||||||
\(369\) | 4.20935e8 | 0.436136 | ||||||||
\(370\) | 1.02404e9 | 1.05102 | ||||||||
\(371\) | −9.96732e7 | −0.101337 | ||||||||
\(372\) | 1.37399e9 | 1.38383 | ||||||||
\(373\) | 7.41533e8 | 0.739860 | 0.369930 | − | 0.929060i | \(-0.379382\pi\) | ||||
0.369930 | + | 0.929060i | \(0.379382\pi\) | |||||||
\(374\) | 1.86470e8 | 0.184314 | ||||||||
\(375\) | −2.39384e8 | −0.234415 | ||||||||
\(376\) | 1.37111e8 | 0.133019 | ||||||||
\(377\) | 7.31212e8 | 0.702827 | ||||||||
\(378\) | −2.07168e7 | −0.0197289 | ||||||||
\(379\) | −1.84508e9 | −1.74091 | −0.870457 | − | 0.492244i | \(-0.836177\pi\) | ||||
−0.870457 | + | 0.492244i | \(0.836177\pi\) | |||||||
\(380\) | 5.27738e8 | 0.493373 | ||||||||
\(381\) | −9.83906e8 | −0.911415 | ||||||||
\(382\) | 6.71581e8 | 0.616420 | ||||||||
\(383\) | 5.18339e8 | 0.471431 | 0.235716 | − | 0.971822i | \(-0.424257\pi\) | ||||
0.235716 | + | 0.971822i | \(0.424257\pi\) | |||||||
\(384\) | −4.44768e8 | −0.400843 | ||||||||
\(385\) | 2.20507e8 | 0.196929 | ||||||||
\(386\) | −1.09991e9 | −0.973419 | ||||||||
\(387\) | 5.95772e8 | 0.522507 | ||||||||
\(388\) | −2.15831e9 | −1.87587 | ||||||||
\(389\) | 1.36832e9 | 1.17860 | 0.589298 | − | 0.807916i | \(-0.299404\pi\) | ||||
0.589298 | + | 0.807916i | \(0.299404\pi\) | |||||||
\(390\) | −2.19196e9 | −1.87114 | ||||||||
\(391\) | −2.65821e6 | −0.00224890 | ||||||||
\(392\) | −4.24157e8 | −0.355652 | ||||||||
\(393\) | 3.51218e8 | 0.291879 | ||||||||
\(394\) | 2.71102e9 | 2.23304 | ||||||||
\(395\) | −5.61773e8 | −0.458639 | ||||||||
\(396\) | 9.73613e8 | 0.787867 | ||||||||
\(397\) | 3.13292e8 | 0.251294 | 0.125647 | − | 0.992075i | \(-0.459899\pi\) | ||||
0.125647 | + | 0.992075i | \(0.459899\pi\) | |||||||
\(398\) | 6.14196e8 | 0.488334 | ||||||||
\(399\) | 1.32685e7 | 0.0104573 | ||||||||
\(400\) | −1.14423e9 | −0.893932 | ||||||||
\(401\) | 7.32537e8 | 0.567315 | 0.283658 | − | 0.958926i | \(-0.408452\pi\) | ||||
0.283658 | + | 0.958926i | \(0.408452\pi\) | |||||||
\(402\) | −7.60160e8 | −0.583598 | ||||||||
\(403\) | 3.65509e9 | 2.78183 | ||||||||
\(404\) | −1.29242e9 | −0.975148 | ||||||||
\(405\) | −2.23778e8 | −0.167388 | ||||||||
\(406\) | −6.75743e7 | −0.0501119 | ||||||||
\(407\) | −1.21000e9 | −0.889620 | ||||||||
\(408\) | 1.82726e7 | 0.0133196 | ||||||||
\(409\) | −4.52805e8 | −0.327250 | −0.163625 | − | 0.986523i | \(-0.552319\pi\) | ||||
−0.163625 | + | 0.986523i | \(0.552319\pi\) | |||||||
\(410\) | −4.11588e9 | −2.94930 | ||||||||
\(411\) | −3.53817e8 | −0.251381 | ||||||||
\(412\) | −8.08129e8 | −0.569299 | ||||||||
\(413\) | −1.27695e7 | −0.00891967 | ||||||||
\(414\) | −2.50829e7 | −0.0173731 | ||||||||
\(415\) | −3.36863e9 | −2.31358 | ||||||||
\(416\) | −2.97868e9 | −2.02861 | ||||||||
\(417\) | 2.31062e8 | 0.156046 | ||||||||
\(418\) | −1.12693e9 | −0.754710 | ||||||||
\(419\) | 2.74019e8 | 0.181983 | 0.0909916 | − | 0.995852i | \(-0.470996\pi\) | ||||
0.0909916 | + | 0.995852i | \(0.470996\pi\) | |||||||
\(420\) | 1.12088e8 | 0.0738222 | ||||||||
\(421\) | −2.84288e9 | −1.85683 | −0.928414 | − | 0.371546i | \(-0.878828\pi\) | ||||
−0.928414 | + | 0.371546i | \(0.878828\pi\) | |||||||
\(422\) | −3.39127e9 | −2.19669 | ||||||||
\(423\) | 1.93159e8 | 0.124086 | ||||||||
\(424\) | 8.29553e8 | 0.528523 | ||||||||
\(425\) | 1.29712e8 | 0.0819631 | ||||||||
\(426\) | −1.36076e9 | −0.852803 | ||||||||
\(427\) | 1.70490e7 | 0.0105975 | ||||||||
\(428\) | −3.47275e9 | −2.14102 | ||||||||
\(429\) | 2.59000e9 | 1.58380 | ||||||||
\(430\) | −5.82543e9 | −3.53336 | ||||||||
\(431\) | 1.06285e9 | 0.639440 | 0.319720 | − | 0.947512i | \(-0.396411\pi\) | ||||
0.319720 | + | 0.947512i | \(0.396411\pi\) | |||||||
\(432\) | −2.27080e8 | −0.135514 | ||||||||
\(433\) | −1.53055e9 | −0.906022 | −0.453011 | − | 0.891505i | \(-0.649650\pi\) | ||||
−0.453011 | + | 0.891505i | \(0.649650\pi\) | |||||||
\(434\) | −3.37782e8 | −0.198346 | ||||||||
\(435\) | −7.29919e8 | −0.425170 | ||||||||
\(436\) | 3.08999e6 | 0.00178548 | ||||||||
\(437\) | 1.60649e7 | 0.00920858 | ||||||||
\(438\) | −1.24558e9 | −0.708290 | ||||||||
\(439\) | 5.70324e8 | 0.321733 | 0.160867 | − | 0.986976i | \(-0.448571\pi\) | ||||
0.160867 | + | 0.986976i | \(0.448571\pi\) | |||||||
\(440\) | −1.83522e9 | −1.02708 | ||||||||
\(441\) | −5.97545e8 | −0.331769 | ||||||||
\(442\) | 2.52151e8 | 0.138893 | ||||||||
\(443\) | −1.53721e9 | −0.840078 | −0.420039 | − | 0.907506i | \(-0.637984\pi\) | ||||
−0.420039 | + | 0.907506i | \(0.637984\pi\) | |||||||
\(444\) | −6.15067e8 | −0.333490 | ||||||||
\(445\) | 4.54693e9 | 2.44601 | ||||||||
\(446\) | 3.26496e9 | 1.74263 | ||||||||
\(447\) | 2.16724e9 | 1.14770 | ||||||||
\(448\) | 1.83457e8 | 0.0963966 | ||||||||
\(449\) | −3.53047e9 | −1.84065 | −0.920323 | − | 0.391160i | \(-0.872074\pi\) | ||||
−0.920323 | + | 0.391160i | \(0.872074\pi\) | |||||||
\(450\) | 1.22396e9 | 0.633177 | ||||||||
\(451\) | 4.86328e9 | 2.49639 | ||||||||
\(452\) | 1.13243e9 | 0.576802 | ||||||||
\(453\) | 1.63777e7 | 0.00827769 | ||||||||
\(454\) | −5.89248e8 | −0.295531 | ||||||||
\(455\) | 2.98176e8 | 0.148400 | ||||||||
\(456\) | −1.10430e8 | −0.0545396 | ||||||||
\(457\) | 2.13769e8 | 0.104770 | 0.0523850 | − | 0.998627i | \(-0.483318\pi\) | ||||
0.0523850 | + | 0.998627i | \(0.483318\pi\) | |||||||
\(458\) | −4.04221e9 | −1.96603 | ||||||||
\(459\) | 2.57421e7 | 0.0124251 | ||||||||
\(460\) | 1.35711e8 | 0.0650073 | ||||||||
\(461\) | −2.72011e9 | −1.29310 | −0.646551 | − | 0.762871i | \(-0.723789\pi\) | ||||
−0.646551 | + | 0.762871i | \(0.723789\pi\) | |||||||
\(462\) | −2.39353e8 | −0.112925 | ||||||||
\(463\) | −2.70333e9 | −1.26580 | −0.632901 | − | 0.774233i | \(-0.718136\pi\) | ||||
−0.632901 | + | 0.774233i | \(0.718136\pi\) | |||||||
\(464\) | −7.40691e8 | −0.344210 | ||||||||
\(465\) | −3.64863e9 | −1.68285 | ||||||||
\(466\) | 5.37593e9 | 2.46095 | ||||||||
\(467\) | 2.43270e9 | 1.10530 | 0.552650 | − | 0.833414i | \(-0.313617\pi\) | ||||
0.552650 | + | 0.833414i | \(0.313617\pi\) | |||||||
\(468\) | 1.31655e9 | 0.593713 | ||||||||
\(469\) | 1.03406e8 | 0.0462850 | ||||||||
\(470\) | −1.88870e9 | −0.839112 | ||||||||
\(471\) | 1.66819e9 | 0.735650 | ||||||||
\(472\) | 1.06277e8 | 0.0465204 | ||||||||
\(473\) | 6.88327e9 | 2.99076 | ||||||||
\(474\) | 6.09786e8 | 0.262999 | ||||||||
\(475\) | −7.83913e8 | −0.335614 | ||||||||
\(476\) | −1.28940e7 | −0.00547977 | ||||||||
\(477\) | 1.16866e9 | 0.493030 | ||||||||
\(478\) | −2.75999e9 | −1.15587 | ||||||||
\(479\) | 3.67141e8 | 0.152636 | 0.0763182 | − | 0.997084i | \(-0.475684\pi\) | ||||
0.0763182 | + | 0.997084i | \(0.475684\pi\) | |||||||
\(480\) | 2.97342e9 | 1.22719 | ||||||||
\(481\) | −1.63620e9 | −0.670392 | ||||||||
\(482\) | 1.55552e9 | 0.632721 | ||||||||
\(483\) | 3.41208e6 | 0.00137786 | ||||||||
\(484\) | 8.15862e9 | 3.27083 | ||||||||
\(485\) | 5.73138e9 | 2.28120 | ||||||||
\(486\) | 2.42903e8 | 0.0959856 | ||||||||
\(487\) | −3.04793e9 | −1.19579 | −0.597894 | − | 0.801575i | \(-0.703996\pi\) | ||||
−0.597894 | + | 0.801575i | \(0.703996\pi\) | |||||||
\(488\) | −1.41894e8 | −0.0552708 | ||||||||
\(489\) | −3.28314e7 | −0.0126972 | ||||||||
\(490\) | 5.84276e9 | 2.24353 | ||||||||
\(491\) | −4.09474e9 | −1.56114 | −0.780568 | − | 0.625071i | \(-0.785070\pi\) | ||||
−0.780568 | + | 0.625071i | \(0.785070\pi\) | |||||||
\(492\) | 2.47211e9 | 0.935813 | ||||||||
\(493\) | 8.39657e7 | 0.0315600 | ||||||||
\(494\) | −1.52387e9 | −0.568727 | ||||||||
\(495\) | −2.58542e9 | −0.958105 | ||||||||
\(496\) | −3.70247e9 | −1.36240 | ||||||||
\(497\) | 1.85107e8 | 0.0676356 | ||||||||
\(498\) | 3.65654e9 | 1.32668 | ||||||||
\(499\) | −3.30636e9 | −1.19124 | −0.595618 | − | 0.803268i | \(-0.703093\pi\) | ||||
−0.595618 | + | 0.803268i | \(0.703093\pi\) | |||||||
\(500\) | −1.40588e9 | −0.502982 | ||||||||
\(501\) | 3.26804e8 | 0.116106 | ||||||||
\(502\) | −3.36417e8 | −0.118690 | ||||||||
\(503\) | −4.42202e9 | −1.54929 | −0.774645 | − | 0.632397i | \(-0.782071\pi\) | ||||
−0.774645 | + | 0.632397i | \(0.782071\pi\) | |||||||
\(504\) | −2.34547e7 | −0.00816062 | ||||||||
\(505\) | 3.43202e9 | 1.18585 | ||||||||
\(506\) | −2.89797e8 | −0.0994412 | ||||||||
\(507\) | 1.80807e9 | 0.616152 | ||||||||
\(508\) | −5.77838e9 | −1.95561 | ||||||||
\(509\) | 3.77691e9 | 1.26947 | 0.634737 | − | 0.772728i | \(-0.281108\pi\) | ||||
0.634737 | + | 0.772728i | \(0.281108\pi\) | |||||||
\(510\) | −2.51705e8 | −0.0840225 | ||||||||
\(511\) | 1.69438e8 | 0.0561743 | ||||||||
\(512\) | 3.78145e9 | 1.24513 | ||||||||
\(513\) | −1.55572e8 | −0.0508770 | ||||||||
\(514\) | 8.62766e9 | 2.80235 | ||||||||
\(515\) | 2.14598e9 | 0.692310 | ||||||||
\(516\) | 3.49891e9 | 1.12114 | ||||||||
\(517\) | 2.23167e9 | 0.710252 | ||||||||
\(518\) | 1.51208e8 | 0.0477992 | ||||||||
\(519\) | −2.73041e9 | −0.857319 | ||||||||
\(520\) | −2.48164e9 | −0.773976 | ||||||||
\(521\) | −4.54529e9 | −1.40809 | −0.704044 | − | 0.710157i | \(-0.748624\pi\) | ||||
−0.704044 | + | 0.710157i | \(0.748624\pi\) | |||||||
\(522\) | 7.92303e8 | 0.243806 | ||||||||
\(523\) | −4.00555e9 | −1.22435 | −0.612176 | − | 0.790721i | \(-0.709706\pi\) | ||||
−0.612176 | + | 0.790721i | \(0.709706\pi\) | |||||||
\(524\) | 2.06267e9 | 0.626281 | ||||||||
\(525\) | −1.66498e8 | −0.0502171 | ||||||||
\(526\) | −3.26087e9 | −0.976974 | ||||||||
\(527\) | 4.19717e8 | 0.124916 | ||||||||
\(528\) | −2.62358e9 | −0.775666 | ||||||||
\(529\) | −3.40069e9 | −0.998787 | ||||||||
\(530\) | −1.14271e10 | −3.33403 | ||||||||
\(531\) | 1.49721e8 | 0.0433963 | ||||||||
\(532\) | 7.79247e7 | 0.0224380 | ||||||||
\(533\) | 6.57629e9 | 1.88120 | ||||||||
\(534\) | −4.93554e9 | −1.40262 | ||||||||
\(535\) | 9.22186e9 | 2.60364 | ||||||||
\(536\) | −8.60620e8 | −0.241399 | ||||||||
\(537\) | −2.07142e9 | −0.577242 | ||||||||
\(538\) | 6.88752e9 | 1.90689 | ||||||||
\(539\) | −6.90376e9 | −1.89900 | ||||||||
\(540\) | −1.31422e9 | −0.359162 | ||||||||
\(541\) | −1.98627e9 | −0.539320 | −0.269660 | − | 0.962956i | \(-0.586911\pi\) | ||||
−0.269660 | + | 0.962956i | \(0.586911\pi\) | |||||||
\(542\) | −3.01049e9 | −0.812157 | ||||||||
\(543\) | 1.19103e9 | 0.319245 | ||||||||
\(544\) | −3.42045e8 | −0.0910934 | ||||||||
\(545\) | −8.20544e6 | −0.00217127 | ||||||||
\(546\) | −3.23660e8 | −0.0850972 | ||||||||
\(547\) | −1.31698e9 | −0.344052 | −0.172026 | − | 0.985092i | \(-0.555031\pi\) | ||||
−0.172026 | + | 0.985092i | \(0.555031\pi\) | |||||||
\(548\) | −2.07793e9 | −0.539385 | ||||||||
\(549\) | −1.99898e8 | −0.0515591 | ||||||||
\(550\) | 1.41411e10 | 3.62422 | ||||||||
\(551\) | −5.07447e8 | −0.129229 | ||||||||
\(552\) | −2.83978e7 | −0.00718618 | ||||||||
\(553\) | −8.29503e7 | −0.0208584 | ||||||||
\(554\) | −8.87889e9 | −2.21858 | ||||||||
\(555\) | 1.63331e9 | 0.405548 | ||||||||
\(556\) | 1.35700e9 | 0.334826 | ||||||||
\(557\) | 3.87423e9 | 0.949931 | 0.474965 | − | 0.880004i | \(-0.342461\pi\) | ||||
0.474965 | + | 0.880004i | \(0.342461\pi\) | |||||||
\(558\) | 3.96046e9 | 0.964998 | ||||||||
\(559\) | 9.30778e9 | 2.25375 | ||||||||
\(560\) | −3.02042e8 | −0.0726789 | ||||||||
\(561\) | 2.97412e8 | 0.0711195 | ||||||||
\(562\) | −1.67770e9 | −0.398691 | ||||||||
\(563\) | −5.14028e9 | −1.21397 | −0.606984 | − | 0.794714i | \(-0.707621\pi\) | ||||
−0.606984 | + | 0.794714i | \(0.707621\pi\) | |||||||
\(564\) | 1.13440e9 | 0.266250 | ||||||||
\(565\) | −3.00716e9 | −0.701435 | ||||||||
\(566\) | 5.70262e9 | 1.32196 | ||||||||
\(567\) | −3.30425e7 | −0.00761259 | ||||||||
\(568\) | −1.54060e9 | −0.352752 | ||||||||
\(569\) | 5.94344e9 | 1.35252 | 0.676262 | − | 0.736661i | \(-0.263599\pi\) | ||||
0.676262 | + | 0.736661i | \(0.263599\pi\) | |||||||
\(570\) | 1.52118e9 | 0.344047 | ||||||||
\(571\) | −6.34028e9 | −1.42522 | −0.712611 | − | 0.701560i | \(-0.752487\pi\) | ||||
−0.712611 | + | 0.701560i | \(0.752487\pi\) | |||||||
\(572\) | 1.52108e10 | 3.39833 | ||||||||
\(573\) | 1.07114e9 | 0.237852 | ||||||||
\(574\) | −6.07742e8 | −0.134131 | ||||||||
\(575\) | −2.01588e8 | −0.0442208 | ||||||||
\(576\) | −2.15102e9 | −0.468992 | ||||||||
\(577\) | 2.74120e9 | 0.594052 | 0.297026 | − | 0.954869i | \(-0.404005\pi\) | ||||
0.297026 | + | 0.954869i | \(0.404005\pi\) | |||||||
\(578\) | −6.91739e9 | −1.49003 | ||||||||
\(579\) | −1.75431e9 | −0.375604 | ||||||||
\(580\) | −4.28674e9 | −0.912282 | ||||||||
\(581\) | −4.97405e8 | −0.105219 | ||||||||
\(582\) | −6.22122e9 | −1.30811 | ||||||||
\(583\) | 1.35021e10 | 2.82204 | ||||||||
\(584\) | −1.41019e9 | −0.292976 | ||||||||
\(585\) | −3.49609e9 | −0.722000 | ||||||||
\(586\) | 2.61986e9 | 0.537819 | ||||||||
\(587\) | −7.75794e8 | −0.158312 | −0.0791558 | − | 0.996862i | \(-0.525222\pi\) | ||||
−0.0791558 | + | 0.996862i | \(0.525222\pi\) | |||||||
\(588\) | −3.50932e9 | −0.711872 | ||||||||
\(589\) | −2.53656e9 | −0.511495 | ||||||||
\(590\) | −1.46397e9 | −0.293460 | ||||||||
\(591\) | 4.32398e9 | 0.861642 | ||||||||
\(592\) | 1.65741e9 | 0.328325 | ||||||||
\(593\) | 1.63585e9 | 0.322145 | 0.161072 | − | 0.986943i | \(-0.448505\pi\) | ||||
0.161072 | + | 0.986943i | \(0.448505\pi\) | |||||||
\(594\) | 2.80639e9 | 0.549408 | ||||||||
\(595\) | 3.42398e7 | 0.00666381 | ||||||||
\(596\) | 1.27280e10 | 2.46262 | ||||||||
\(597\) | 9.79619e8 | 0.188429 | ||||||||
\(598\) | −3.91872e8 | −0.0749360 | ||||||||
\(599\) | −4.17190e9 | −0.793121 | −0.396561 | − | 0.918009i | \(-0.629796\pi\) | ||||
−0.396561 | + | 0.918009i | \(0.629796\pi\) | |||||||
\(600\) | 1.38572e9 | 0.261906 | ||||||||
\(601\) | −4.54954e9 | −0.854883 | −0.427442 | − | 0.904043i | \(-0.640585\pi\) | ||||
−0.427442 | + | 0.904043i | \(0.640585\pi\) | |||||||
\(602\) | −8.60171e8 | −0.160693 | ||||||||
\(603\) | −1.21242e9 | −0.225187 | ||||||||
\(604\) | 9.61845e7 | 0.0177613 | ||||||||
\(605\) | −2.16652e10 | −3.97757 | ||||||||
\(606\) | −3.72535e9 | −0.680006 | ||||||||
\(607\) | −5.26426e9 | −0.955381 | −0.477691 | − | 0.878528i | \(-0.658526\pi\) | ||||
−0.477691 | + | 0.878528i | \(0.658526\pi\) | |||||||
\(608\) | 2.06715e9 | 0.373000 | ||||||||
\(609\) | −1.07778e8 | −0.0193362 | ||||||||
\(610\) | 1.95459e9 | 0.348660 | ||||||||
\(611\) | 3.01773e9 | 0.535225 | ||||||||
\(612\) | 1.51181e8 | 0.0266604 | ||||||||
\(613\) | −1.30761e9 | −0.229281 | −0.114641 | − | 0.993407i | \(-0.536572\pi\) | ||||
−0.114641 | + | 0.993407i | \(0.536572\pi\) | |||||||
\(614\) | 2.27059e9 | 0.395867 | ||||||||
\(615\) | −6.56466e9 | −1.13802 | ||||||||
\(616\) | −2.70985e8 | −0.0467103 | ||||||||
\(617\) | −5.09050e9 | −0.872493 | −0.436247 | − | 0.899827i | \(-0.643692\pi\) | ||||
−0.436247 | + | 0.899827i | \(0.643692\pi\) | |||||||
\(618\) | −2.32939e9 | −0.396993 | ||||||||
\(619\) | 8.73085e9 | 1.47958 | 0.739792 | − | 0.672836i | \(-0.234924\pi\) | ||||
0.739792 | + | 0.672836i | \(0.234924\pi\) | |||||||
\(620\) | −2.14280e10 | −3.61086 | ||||||||
\(621\) | −4.00063e7 | −0.00670359 | ||||||||
\(622\) | −2.81794e9 | −0.469532 | ||||||||
\(623\) | 6.71391e8 | 0.111242 | ||||||||
\(624\) | −3.54768e9 | −0.584519 | ||||||||
\(625\) | −4.01519e9 | −0.657850 | ||||||||
\(626\) | 6.80324e9 | 1.10842 | ||||||||
\(627\) | −1.79741e9 | −0.291213 | ||||||||
\(628\) | 9.79709e9 | 1.57848 | ||||||||
\(629\) | −1.87886e8 | −0.0301035 | ||||||||
\(630\) | 3.23088e8 | 0.0514789 | ||||||||
\(631\) | −7.67163e9 | −1.21558 | −0.607792 | − | 0.794096i | \(-0.707945\pi\) | ||||
−0.607792 | + | 0.794096i | \(0.707945\pi\) | |||||||
\(632\) | 6.90373e8 | 0.108786 | ||||||||
\(633\) | −5.40893e9 | −0.847615 | ||||||||
\(634\) | 2.53962e9 | 0.395782 | ||||||||
\(635\) | 1.53444e10 | 2.37817 | ||||||||
\(636\) | 6.86341e9 | 1.05789 | ||||||||
\(637\) | −9.33548e9 | −1.43103 | ||||||||
\(638\) | 9.15390e9 | 1.39551 | ||||||||
\(639\) | −2.17036e9 | −0.329063 | ||||||||
\(640\) | 6.93635e9 | 1.04593 | ||||||||
\(641\) | −3.46528e9 | −0.519679 | −0.259840 | − | 0.965652i | \(-0.583670\pi\) | ||||
−0.259840 | + | 0.965652i | \(0.583670\pi\) | |||||||
\(642\) | −1.00100e10 | −1.49301 | ||||||||
\(643\) | 5.49488e9 | 0.815117 | 0.407559 | − | 0.913179i | \(-0.366380\pi\) | ||||
0.407559 | + | 0.913179i | \(0.366380\pi\) | |||||||
\(644\) | 2.00388e7 | 0.00295645 | ||||||||
\(645\) | −9.29133e9 | −1.36339 | ||||||||
\(646\) | −1.74988e8 | −0.0255384 | ||||||||
\(647\) | 8.98807e9 | 1.30467 | 0.652336 | − | 0.757930i | \(-0.273789\pi\) | ||||
0.652336 | + | 0.757930i | \(0.273789\pi\) | |||||||
\(648\) | 2.75004e8 | 0.0397033 | ||||||||
\(649\) | 1.72981e9 | 0.248395 | ||||||||
\(650\) | 1.91221e10 | 2.73110 | ||||||||
\(651\) | −5.38749e8 | −0.0765337 | ||||||||
\(652\) | −1.92815e8 | −0.0272443 | ||||||||
\(653\) | −2.09537e9 | −0.294486 | −0.147243 | − | 0.989100i | \(-0.547040\pi\) | ||||
−0.147243 | + | 0.989100i | \(0.547040\pi\) | |||||||
\(654\) | 8.90673e6 | 0.00124508 | ||||||||
\(655\) | −5.47739e9 | −0.761604 | ||||||||
\(656\) | −6.66154e9 | −0.921321 | ||||||||
\(657\) | −1.98665e9 | −0.273301 | ||||||||
\(658\) | −2.78881e8 | −0.0381618 | ||||||||
\(659\) | 1.34881e10 | 1.83591 | 0.917953 | − | 0.396690i | \(-0.129841\pi\) | ||||
0.917953 | + | 0.396690i | \(0.129841\pi\) | |||||||
\(660\) | −1.51839e10 | −2.05580 | ||||||||
\(661\) | −2.15284e9 | −0.289939 | −0.144969 | − | 0.989436i | \(-0.546308\pi\) | ||||
−0.144969 | + | 0.989436i | \(0.546308\pi\) | |||||||
\(662\) | 3.59492e9 | 0.481599 | ||||||||
\(663\) | 4.02170e8 | 0.0535935 | ||||||||
\(664\) | 4.13977e9 | 0.548767 | ||||||||
\(665\) | −2.06928e8 | −0.0272863 | ||||||||
\(666\) | −1.77290e9 | −0.232554 | ||||||||
\(667\) | −1.30493e8 | −0.0170273 | ||||||||
\(668\) | 1.91928e9 | 0.249127 | ||||||||
\(669\) | 5.20748e9 | 0.672413 | ||||||||
\(670\) | 1.18550e10 | 1.52279 | ||||||||
\(671\) | −2.30953e9 | −0.295117 | ||||||||
\(672\) | 4.39049e8 | 0.0558110 | ||||||||
\(673\) | −1.17042e10 | −1.48010 | −0.740048 | − | 0.672554i | \(-0.765197\pi\) | ||||
−0.740048 | + | 0.672554i | \(0.765197\pi\) | |||||||
\(674\) | 6.08448e9 | 0.765445 | ||||||||
\(675\) | 1.95217e9 | 0.244318 | ||||||||
\(676\) | 1.06186e10 | 1.32207 | ||||||||
\(677\) | −6.54348e9 | −0.810491 | −0.405245 | − | 0.914208i | \(-0.632814\pi\) | ||||
−0.405245 | + | 0.914208i | \(0.632814\pi\) | |||||||
\(678\) | 3.26417e9 | 0.402225 | ||||||||
\(679\) | 8.46284e8 | 0.103746 | ||||||||
\(680\) | −2.84969e8 | −0.0347549 | ||||||||
\(681\) | −9.39827e8 | −0.114034 | ||||||||
\(682\) | 4.57574e10 | 5.52352 | ||||||||
\(683\) | 1.02317e10 | 1.22878 | 0.614390 | − | 0.789003i | \(-0.289402\pi\) | ||||
0.614390 | + | 0.789003i | \(0.289402\pi\) | |||||||
\(684\) | −9.13660e8 | −0.109166 | ||||||||
\(685\) | 5.51793e9 | 0.655932 | ||||||||
\(686\) | 1.72953e9 | 0.204547 | ||||||||
\(687\) | −6.44716e9 | −0.758612 | ||||||||
\(688\) | −9.42844e9 | −1.10377 | ||||||||
\(689\) | 1.82580e10 | 2.12660 | ||||||||
\(690\) | 3.91179e8 | 0.0453319 | ||||||||
\(691\) | −1.10128e10 | −1.26977 | −0.634887 | − | 0.772605i | \(-0.718953\pi\) | ||||
−0.634887 | + | 0.772605i | \(0.718953\pi\) | |||||||
\(692\) | −1.60354e10 | −1.83954 | ||||||||
\(693\) | −3.81758e8 | −0.0435734 | ||||||||
\(694\) | −3.05291e9 | −0.346701 | ||||||||
\(695\) | −3.60352e9 | −0.407174 | ||||||||
\(696\) | 8.97011e8 | 0.100848 | ||||||||
\(697\) | 7.55161e8 | 0.0844743 | ||||||||
\(698\) | 1.83508e10 | 2.04250 | ||||||||
\(699\) | 8.57439e9 | 0.949584 | ||||||||
\(700\) | −9.77826e8 | −0.107750 | ||||||||
\(701\) | 5.07374e9 | 0.556308 | 0.278154 | − | 0.960536i | \(-0.410277\pi\) | ||||
0.278154 | + | 0.960536i | \(0.410277\pi\) | |||||||
\(702\) | 3.79489e9 | 0.414018 | ||||||||
\(703\) | 1.13549e9 | 0.123265 | ||||||||
\(704\) | −2.48519e10 | −2.68445 | ||||||||
\(705\) | −3.01240e9 | −0.323780 | ||||||||
\(706\) | −1.52587e10 | −1.63193 | ||||||||
\(707\) | 5.06766e8 | 0.0539311 | ||||||||
\(708\) | 8.79298e8 | 0.0931150 | ||||||||
\(709\) | −9.55775e8 | −0.100715 | −0.0503575 | − | 0.998731i | \(-0.516036\pi\) | ||||
−0.0503575 | + | 0.998731i | \(0.516036\pi\) | |||||||
\(710\) | 2.12217e10 | 2.22524 | ||||||||
\(711\) | 9.72585e8 | 0.101481 | ||||||||
\(712\) | −5.58781e9 | −0.580178 | ||||||||
\(713\) | −6.52291e8 | −0.0673950 | ||||||||
\(714\) | −3.71662e7 | −0.00382124 | ||||||||
\(715\) | −4.03922e10 | −4.13263 | ||||||||
\(716\) | −1.21652e10 | −1.23858 | ||||||||
\(717\) | −4.40208e9 | −0.446006 | ||||||||
\(718\) | −6.98730e9 | −0.704488 | ||||||||
\(719\) | 9.39305e9 | 0.942444 | 0.471222 | − | 0.882015i | \(-0.343813\pi\) | ||||
0.471222 | + | 0.882015i | \(0.343813\pi\) | |||||||
\(720\) | 3.54141e9 | 0.353600 | ||||||||
\(721\) | 3.16871e8 | 0.0314854 | ||||||||
\(722\) | −1.40742e10 | −1.39169 | ||||||||
\(723\) | 2.48100e9 | 0.244142 | ||||||||
\(724\) | 6.99481e9 | 0.685001 | ||||||||
\(725\) | 6.36762e9 | 0.620574 | ||||||||
\(726\) | 2.35168e10 | 2.28087 | ||||||||
\(727\) | −1.28780e9 | −0.124302 | −0.0621508 | − | 0.998067i | \(-0.519796\pi\) | ||||
−0.0621508 | + | 0.998067i | \(0.519796\pi\) | |||||||
\(728\) | −3.66434e8 | −0.0351995 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 1.94253e10 | 1.84815 | ||||||||
\(731\) | 1.06882e9 | 0.101203 | ||||||||
\(732\) | −1.17398e9 | −0.110630 | ||||||||
\(733\) | 6.05304e8 | 0.0567687 | 0.0283844 | − | 0.999597i | \(-0.490964\pi\) | ||||
0.0283844 | + | 0.999597i | \(0.490964\pi\) | |||||||
\(734\) | −9.46631e9 | −0.883578 | ||||||||
\(735\) | 9.31897e9 | 0.865690 | ||||||||
\(736\) | 5.31579e8 | 0.0491468 | ||||||||
\(737\) | −1.40078e10 | −1.28894 | ||||||||
\(738\) | 7.12572e9 | 0.652576 | ||||||||
\(739\) | 6.67329e9 | 0.608253 | 0.304126 | − | 0.952632i | \(-0.401635\pi\) | ||||
0.304126 | + | 0.952632i | \(0.401635\pi\) | |||||||
\(740\) | 9.59224e9 | 0.870180 | ||||||||
\(741\) | −2.43051e9 | −0.219449 | ||||||||
\(742\) | −1.68730e9 | −0.151628 | ||||||||
\(743\) | −6.01656e9 | −0.538130 | −0.269065 | − | 0.963122i | \(-0.586715\pi\) | ||||
−0.269065 | + | 0.963122i | \(0.586715\pi\) | |||||||
\(744\) | 4.48386e9 | 0.399160 | ||||||||
\(745\) | −3.37990e10 | −2.99472 | ||||||||
\(746\) | 1.25529e10 | 1.10703 | ||||||||
\(747\) | 5.83203e9 | 0.511915 | ||||||||
\(748\) | 1.74667e9 | 0.152600 | ||||||||
\(749\) | 1.36168e9 | 0.118410 | ||||||||
\(750\) | −4.05237e9 | −0.350748 | ||||||||
\(751\) | 6.84419e9 | 0.589634 | 0.294817 | − | 0.955554i | \(-0.404741\pi\) | ||||
0.294817 | + | 0.955554i | \(0.404741\pi\) | |||||||
\(752\) | −3.05685e9 | −0.262127 | ||||||||
\(753\) | −5.36571e8 | −0.0457979 | ||||||||
\(754\) | 1.23782e10 | 1.05162 | ||||||||
\(755\) | −2.55417e8 | −0.0215991 | ||||||||
\(756\) | −1.94055e8 | −0.0163343 | ||||||||
\(757\) | 4.04396e8 | 0.0338822 | 0.0169411 | − | 0.999856i | \(-0.494607\pi\) | ||||
0.0169411 | + | 0.999856i | \(0.494607\pi\) | |||||||
\(758\) | −3.12341e10 | −2.60487 | ||||||||
\(759\) | −4.62214e8 | −0.0383704 | ||||||||
\(760\) | 1.72221e9 | 0.142311 | ||||||||
\(761\) | 3.58785e9 | 0.295112 | 0.147556 | − | 0.989054i | \(-0.452859\pi\) | ||||
0.147556 | + | 0.989054i | \(0.452859\pi\) | |||||||
\(762\) | −1.66559e10 | −1.36372 | ||||||||
\(763\) | −1.21160e6 | −9.87467e−5 0 | ||||||||
\(764\) | 6.29072e9 | 0.510356 | ||||||||
\(765\) | −4.01459e8 | −0.0324210 | ||||||||
\(766\) | 8.77461e9 | 0.705387 | ||||||||
\(767\) | 2.33910e9 | 0.187183 | ||||||||
\(768\) | 2.66824e9 | 0.212550 | ||||||||
\(769\) | −1.00703e10 | −0.798550 | −0.399275 | − | 0.916831i | \(-0.630738\pi\) | ||||
−0.399275 | + | 0.916831i | \(0.630738\pi\) | |||||||
\(770\) | 3.73281e9 | 0.294658 | ||||||||
\(771\) | 1.37608e10 | 1.08132 | ||||||||
\(772\) | −1.03029e10 | −0.805929 | ||||||||
\(773\) | 1.18136e10 | 0.919927 | 0.459964 | − | 0.887938i | \(-0.347862\pi\) | ||||
0.459964 | + | 0.887938i | \(0.347862\pi\) | |||||||
\(774\) | 1.00854e10 | 0.781809 | ||||||||
\(775\) | 3.18296e10 | 2.45627 | ||||||||
\(776\) | −7.04340e9 | −0.541086 | ||||||||
\(777\) | 2.41171e8 | 0.0184438 | ||||||||
\(778\) | 2.31634e10 | 1.76349 | ||||||||
\(779\) | −4.56381e9 | −0.345897 | ||||||||
\(780\) | −2.05322e10 | −1.54919 | ||||||||
\(781\) | −2.50754e10 | −1.88351 | ||||||||
\(782\) | −4.49990e7 | −0.00336496 | ||||||||
\(783\) | 1.26369e9 | 0.0940751 | ||||||||
\(784\) | 9.45649e9 | 0.700848 | ||||||||
\(785\) | −2.60161e10 | −1.91955 | ||||||||
\(786\) | 5.94553e9 | 0.436728 | ||||||||
\(787\) | −1.44585e10 | −1.05734 | −0.528668 | − | 0.848829i | \(-0.677308\pi\) | ||||
−0.528668 | + | 0.848829i | \(0.677308\pi\) | |||||||
\(788\) | 2.53943e10 | 1.84882 | ||||||||
\(789\) | −5.20095e9 | −0.376976 | ||||||||
\(790\) | −9.50988e9 | −0.686247 | ||||||||
\(791\) | −4.44031e8 | −0.0319004 | ||||||||
\(792\) | 3.17727e9 | 0.227256 | ||||||||
\(793\) | −3.12302e9 | −0.222392 | ||||||||
\(794\) | 5.30351e9 | 0.376003 | ||||||||
\(795\) | −1.82257e10 | −1.28647 | ||||||||
\(796\) | 5.75320e9 | 0.404309 | ||||||||
\(797\) | 2.14577e10 | 1.50134 | 0.750669 | − | 0.660678i | \(-0.229731\pi\) | ||||
0.750669 | + | 0.660678i | \(0.229731\pi\) | |||||||
\(798\) | 2.24614e8 | 0.0156468 | ||||||||
\(799\) | 3.46529e8 | 0.0240340 | ||||||||
\(800\) | −2.59393e10 | −1.79120 | ||||||||
\(801\) | −7.87200e9 | −0.541217 | ||||||||
\(802\) | 1.24006e10 | 0.848855 | ||||||||
\(803\) | −2.29528e10 | −1.56434 | ||||||||
\(804\) | −7.12044e9 | −0.483182 | ||||||||
\(805\) | −5.32128e7 | −0.00359526 | ||||||||
\(806\) | 6.18745e10 | 4.16236 | ||||||||
\(807\) | 1.09853e10 | 0.735792 | ||||||||
\(808\) | −4.21768e9 | −0.281277 | ||||||||
\(809\) | 1.76950e9 | 0.117498 | 0.0587491 | − | 0.998273i | \(-0.481289\pi\) | ||||
0.0587491 | + | 0.998273i | \(0.481289\pi\) | |||||||
\(810\) | −3.78818e9 | −0.250457 | ||||||||
\(811\) | −1.15307e10 | −0.759074 | −0.379537 | − | 0.925177i | \(-0.623917\pi\) | ||||
−0.379537 | + | 0.925177i | \(0.623917\pi\) | |||||||
\(812\) | −6.32971e8 | −0.0414895 | ||||||||
\(813\) | −4.80161e9 | −0.313379 | ||||||||
\(814\) | −2.04833e10 | −1.33111 | ||||||||
\(815\) | 5.12020e8 | 0.0331311 | ||||||||
\(816\) | −4.07383e8 | −0.0262475 | ||||||||
\(817\) | −6.45942e9 | −0.414397 | ||||||||
\(818\) | −7.66523e9 | −0.489653 | ||||||||
\(819\) | −5.16225e8 | −0.0328356 | ||||||||
\(820\) | −3.85536e10 | −2.44183 | ||||||||
\(821\) | 1.88474e10 | 1.18864 | 0.594321 | − | 0.804228i | \(-0.297421\pi\) | ||||
0.594321 | + | 0.804228i | \(0.297421\pi\) | |||||||
\(822\) | −5.98953e9 | −0.376133 | ||||||||
\(823\) | 2.70001e10 | 1.68836 | 0.844180 | − | 0.536059i | \(-0.180088\pi\) | ||||
0.844180 | + | 0.536059i | \(0.180088\pi\) | |||||||
\(824\) | −2.63723e9 | −0.164211 | ||||||||
\(825\) | 2.25545e10 | 1.39844 | ||||||||
\(826\) | −2.16166e8 | −0.0133462 | ||||||||
\(827\) | 2.57017e10 | 1.58013 | 0.790064 | − | 0.613024i | \(-0.210047\pi\) | ||||
0.790064 | + | 0.613024i | \(0.210047\pi\) | |||||||
\(828\) | −2.34953e8 | −0.0143838 | ||||||||
\(829\) | 1.20559e10 | 0.734952 | 0.367476 | − | 0.930033i | \(-0.380222\pi\) | ||||
0.367476 | + | 0.930033i | \(0.380222\pi\) | |||||||
\(830\) | −5.70253e10 | −3.46174 | ||||||||
\(831\) | −1.41615e10 | −0.856061 | ||||||||
\(832\) | −3.36055e10 | −2.02292 | ||||||||
\(833\) | −1.07200e9 | −0.0642595 | ||||||||
\(834\) | 3.91150e9 | 0.233487 | ||||||||
\(835\) | −5.09665e9 | −0.302958 | ||||||||
\(836\) | −1.05560e10 | −0.624853 | ||||||||
\(837\) | 6.31678e9 | 0.372354 | ||||||||
\(838\) | 4.63868e9 | 0.272295 | ||||||||
\(839\) | 1.49873e10 | 0.876106 | 0.438053 | − | 0.898949i | \(-0.355668\pi\) | ||||
0.438053 | + | 0.898949i | \(0.355668\pi\) | |||||||
\(840\) | 3.65786e8 | 0.0212936 | ||||||||
\(841\) | −1.31280e10 | −0.761047 | ||||||||
\(842\) | −4.81253e10 | −2.77831 | ||||||||
\(843\) | −2.67586e9 | −0.153839 | ||||||||
\(844\) | −3.17661e10 | −1.81872 | ||||||||
\(845\) | −2.81977e10 | −1.60774 | ||||||||
\(846\) | 3.26986e9 | 0.185666 | ||||||||
\(847\) | −3.19903e9 | −0.180895 | ||||||||
\(848\) | −1.84947e10 | −1.04151 | ||||||||
\(849\) | 9.09545e9 | 0.510090 | ||||||||
\(850\) | 2.19580e9 | 0.122639 | ||||||||
\(851\) | 2.91998e8 | 0.0162415 | ||||||||
\(852\) | −1.27463e10 | −0.706067 | ||||||||
\(853\) | 7.24550e9 | 0.399712 | 0.199856 | − | 0.979825i | \(-0.435953\pi\) | ||||
0.199856 | + | 0.979825i | \(0.435953\pi\) | |||||||
\(854\) | 2.88611e8 | 0.0158566 | ||||||||
\(855\) | 2.42622e9 | 0.132754 | ||||||||
\(856\) | −1.13329e10 | −0.617566 | ||||||||
\(857\) | 3.25083e10 | 1.76426 | 0.882128 | − | 0.471010i | \(-0.156110\pi\) | ||||
0.882128 | + | 0.471010i | \(0.156110\pi\) | |||||||
\(858\) | 4.38444e10 | 2.36978 | ||||||||
\(859\) | −1.44247e10 | −0.776480 | −0.388240 | − | 0.921558i | \(-0.626917\pi\) | ||||
−0.388240 | + | 0.921558i | \(0.626917\pi\) | |||||||
\(860\) | −5.45670e10 | −2.92540 | ||||||||
\(861\) | −9.69324e8 | −0.0517557 | ||||||||
\(862\) | 1.79922e10 | 0.956773 | ||||||||
\(863\) | −1.11462e10 | −0.590324 | −0.295162 | − | 0.955447i | \(-0.595374\pi\) | ||||
−0.295162 | + | 0.955447i | \(0.595374\pi\) | |||||||
\(864\) | −5.14781e9 | −0.271534 | ||||||||
\(865\) | 4.25820e10 | 2.23702 | ||||||||
\(866\) | −2.59096e10 | −1.35565 | ||||||||
\(867\) | −1.10330e10 | −0.574944 | ||||||||
\(868\) | −3.16402e9 | −0.164218 | ||||||||
\(869\) | 1.12368e10 | 0.580862 | ||||||||
\(870\) | −1.23563e10 | −0.636167 | ||||||||
\(871\) | −1.89418e10 | −0.971309 | ||||||||
\(872\) | 1.00838e7 | 0.000515012 0 | ||||||||
\(873\) | −9.92260e9 | −0.504749 | ||||||||
\(874\) | 2.71952e8 | 0.0137785 | ||||||||
\(875\) | 5.51251e8 | 0.0278177 | ||||||||
\(876\) | −1.16674e10 | −0.586419 | ||||||||
\(877\) | −2.20664e10 | −1.10467 | −0.552334 | − | 0.833623i | \(-0.686263\pi\) | ||||
−0.552334 | + | 0.833623i | \(0.686263\pi\) | |||||||
\(878\) | 9.65463e9 | 0.481399 | ||||||||
\(879\) | 4.17857e9 | 0.207523 | ||||||||
\(880\) | 4.09158e10 | 2.02396 | ||||||||
\(881\) | −5.78724e9 | −0.285138 | −0.142569 | − | 0.989785i | \(-0.545536\pi\) | ||||
−0.142569 | + | 0.989785i | \(0.545536\pi\) | |||||||
\(882\) | −1.01154e10 | −0.496414 | ||||||||
\(883\) | −3.69412e10 | −1.80571 | −0.902855 | − | 0.429944i | \(-0.858533\pi\) | ||||
−0.902855 | + | 0.429944i | \(0.858533\pi\) | |||||||
\(884\) | 2.36190e9 | 0.114995 | ||||||||
\(885\) | −2.33497e9 | −0.113235 | ||||||||
\(886\) | −2.60224e10 | −1.25698 | ||||||||
\(887\) | 8.57880e9 | 0.412756 | 0.206378 | − | 0.978472i | \(-0.433832\pi\) | ||||
0.206378 | + | 0.978472i | \(0.433832\pi\) | |||||||
\(888\) | −2.00720e9 | −0.0961934 | ||||||||
\(889\) | 2.26573e9 | 0.108156 | ||||||||
\(890\) | 7.69720e10 | 3.65989 | ||||||||
\(891\) | 4.47608e9 | 0.211995 | ||||||||
\(892\) | 3.05830e10 | 1.44279 | ||||||||
\(893\) | −2.09425e9 | −0.0984120 | ||||||||
\(894\) | 3.66877e10 | 1.71727 | ||||||||
\(895\) | 3.23047e10 | 1.50621 | ||||||||
\(896\) | 1.02421e9 | 0.0475674 | ||||||||
\(897\) | −6.25020e8 | −0.0289148 | ||||||||
\(898\) | −5.97649e10 | −2.75410 | ||||||||
\(899\) | 2.06041e10 | 0.945791 | ||||||||
\(900\) | 1.14649e10 | 0.524230 | ||||||||
\(901\) | 2.09658e9 | 0.0954939 | ||||||||
\(902\) | 8.23273e10 | 3.73526 | ||||||||
\(903\) | −1.37194e9 | −0.0620051 | ||||||||
\(904\) | 3.69555e9 | 0.166376 | ||||||||
\(905\) | −1.85747e10 | −0.833012 | ||||||||
\(906\) | 2.77247e8 | 0.0123856 | ||||||||
\(907\) | 4.99672e9 | 0.222362 | 0.111181 | − | 0.993800i | \(-0.464537\pi\) | ||||
0.111181 | + | 0.993800i | \(0.464537\pi\) | |||||||
\(908\) | −5.51951e9 | −0.244681 | ||||||||
\(909\) | −5.94178e9 | −0.262387 | ||||||||
\(910\) | 5.04762e9 | 0.222046 | ||||||||
\(911\) | −2.67519e10 | −1.17230 | −0.586151 | − | 0.810202i | \(-0.699358\pi\) | ||||
−0.586151 | + | 0.810202i | \(0.699358\pi\) | |||||||
\(912\) | 2.46202e9 | 0.107476 | ||||||||
\(913\) | 6.73806e10 | 2.93013 | ||||||||
\(914\) | 3.61875e9 | 0.156764 | ||||||||
\(915\) | 3.11750e9 | 0.134534 | ||||||||
\(916\) | −3.78635e10 | −1.62775 | ||||||||
\(917\) | −8.08780e8 | −0.0346368 | ||||||||
\(918\) | 4.35770e8 | 0.0185912 | ||||||||
\(919\) | −1.20296e10 | −0.511268 | −0.255634 | − | 0.966774i | \(-0.582284\pi\) | ||||
−0.255634 | + | 0.966774i | \(0.582284\pi\) | |||||||
\(920\) | 4.42876e8 | 0.0187510 | ||||||||
\(921\) | 3.62150e9 | 0.152749 | ||||||||
\(922\) | −4.60469e10 | −1.93483 | ||||||||
\(923\) | −3.39077e10 | −1.41936 | ||||||||
\(924\) | −2.24203e9 | −0.0934950 | ||||||||
\(925\) | −1.42485e10 | −0.591935 | ||||||||
\(926\) | −4.57629e10 | −1.89398 | ||||||||
\(927\) | −3.71528e9 | −0.153184 | ||||||||
\(928\) | −1.67911e10 | −0.689704 | ||||||||
\(929\) | 9.92866e9 | 0.406290 | 0.203145 | − | 0.979149i | \(-0.434884\pi\) | ||||
0.203145 | + | 0.979149i | \(0.434884\pi\) | |||||||
\(930\) | −6.17652e10 | −2.51799 | ||||||||
\(931\) | 6.47864e9 | 0.263124 | ||||||||
\(932\) | 5.03565e10 | 2.03751 | ||||||||
\(933\) | −4.49450e9 | −0.181174 | ||||||||
\(934\) | 4.11816e10 | 1.65382 | ||||||||
\(935\) | −4.63827e9 | −0.185573 | ||||||||
\(936\) | 4.29641e9 | 0.171254 | ||||||||
\(937\) | −4.20534e10 | −1.66998 | −0.834992 | − | 0.550262i | \(-0.814528\pi\) | ||||
−0.834992 | + | 0.550262i | \(0.814528\pi\) | |||||||
\(938\) | 1.75049e9 | 0.0692547 | ||||||||
\(939\) | 1.08509e10 | 0.427697 | ||||||||
\(940\) | −1.76915e10 | −0.694732 | ||||||||
\(941\) | −3.81848e9 | −0.149392 | −0.0746960 | − | 0.997206i | \(-0.523799\pi\) | ||||
−0.0746960 | + | 0.997206i | \(0.523799\pi\) | |||||||
\(942\) | 2.82396e10 | 1.10073 | ||||||||
\(943\) | −1.17361e9 | −0.0455757 | ||||||||
\(944\) | −2.36943e9 | −0.0916730 | ||||||||
\(945\) | 5.15313e8 | 0.0198637 | ||||||||
\(946\) | 1.16522e11 | 4.47497 | ||||||||
\(947\) | −1.89974e10 | −0.726892 | −0.363446 | − | 0.931615i | \(-0.618400\pi\) | ||||
−0.363446 | + | 0.931615i | \(0.618400\pi\) | |||||||
\(948\) | 5.71189e9 | 0.217746 | ||||||||
\(949\) | −3.10375e10 | −1.17884 | ||||||||
\(950\) | −1.32703e10 | −0.502169 | ||||||||
\(951\) | 4.05059e9 | 0.152717 | ||||||||
\(952\) | −4.20779e7 | −0.00158061 | ||||||||
\(953\) | −3.31060e10 | −1.23903 | −0.619514 | − | 0.784986i | \(-0.712670\pi\) | ||||
−0.619514 | + | 0.784986i | \(0.712670\pi\) | |||||||
\(954\) | 1.97834e10 | 0.737704 | ||||||||
\(955\) | −1.67050e10 | −0.620631 | ||||||||
\(956\) | −2.58529e10 | −0.956990 | ||||||||
\(957\) | 1.46001e10 | 0.538473 | ||||||||
\(958\) | 6.21507e9 | 0.228385 | ||||||||
\(959\) | 8.14766e8 | 0.0298310 | ||||||||
\(960\) | 3.35461e10 | 1.22375 | ||||||||
\(961\) | 7.54807e10 | 2.74349 | ||||||||
\(962\) | −2.76981e10 | −1.00308 | ||||||||
\(963\) | −1.59656e10 | −0.576093 | ||||||||
\(964\) | 1.45707e10 | 0.523853 | ||||||||
\(965\) | 2.73592e10 | 0.980070 | ||||||||
\(966\) | 5.77607e7 | 0.00206164 | ||||||||
\(967\) | 4.23227e9 | 0.150515 | 0.0752576 | − | 0.997164i | \(-0.476022\pi\) | ||||
0.0752576 | + | 0.997164i | \(0.476022\pi\) | |||||||
\(968\) | 2.66247e10 | 0.943455 | ||||||||
\(969\) | −2.79098e8 | −0.00985425 | ||||||||
\(970\) | 9.70227e10 | 3.41328 | ||||||||
\(971\) | 2.31036e10 | 0.809866 | 0.404933 | − | 0.914346i | \(-0.367295\pi\) | ||||
0.404933 | + | 0.914346i | \(0.367295\pi\) | |||||||
\(972\) | 2.27528e9 | 0.0794700 | ||||||||
\(973\) | −5.32088e8 | −0.0185178 | ||||||||
\(974\) | −5.15964e10 | −1.78922 | ||||||||
\(975\) | 3.04989e10 | 1.05382 | ||||||||
\(976\) | 3.16350e9 | 0.108917 | ||||||||
\(977\) | −5.89335e9 | −0.202177 | −0.101088 | − | 0.994877i | \(-0.532232\pi\) | ||||
−0.101088 | + | 0.994877i | \(0.532232\pi\) | |||||||
\(978\) | −5.55781e8 | −0.0189984 | ||||||||
\(979\) | −9.09494e10 | −3.09785 | ||||||||
\(980\) | 5.47294e10 | 1.85750 | ||||||||
\(981\) | 1.42059e7 | 0.000480426 0 | ||||||||
\(982\) | −6.93171e10 | −2.33588 | ||||||||
\(983\) | 4.17317e10 | 1.40129 | 0.700646 | − | 0.713509i | \(-0.252895\pi\) | ||||
0.700646 | + | 0.713509i | \(0.252895\pi\) | |||||||
\(984\) | 8.06743e9 | 0.269931 | ||||||||
\(985\) | −6.74343e10 | −2.24830 | ||||||||
\(986\) | 1.42140e9 | 0.0472222 | ||||||||
\(987\) | −4.44804e8 | −0.0147251 | ||||||||
\(988\) | −1.42742e10 | −0.470870 | ||||||||
\(989\) | −1.66108e9 | −0.0546012 | ||||||||
\(990\) | −4.37669e10 | −1.43358 | ||||||||
\(991\) | 2.97978e10 | 0.972583 | 0.486292 | − | 0.873797i | \(-0.338349\pi\) | ||||
0.486292 | + | 0.873797i | \(0.338349\pi\) | |||||||
\(992\) | −8.39335e10 | −2.72989 | ||||||||
\(993\) | 5.73375e9 | 0.185830 | ||||||||
\(994\) | 3.13355e9 | 0.101201 | ||||||||
\(995\) | −1.52776e10 | −0.491670 | ||||||||
\(996\) | 3.42509e10 | 1.09841 | ||||||||
\(997\) | 1.92441e10 | 0.614986 | 0.307493 | − | 0.951550i | \(-0.400510\pi\) | ||||
0.307493 | + | 0.951550i | \(0.400510\pi\) | |||||||
\(998\) | −5.59711e10 | −1.78241 | ||||||||
\(999\) | −2.82770e9 | −0.0897335 |
(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 | 177.8.a.d.1.15 | ✓ | 18 | |
3.2 | odd | 2 | 531.8.a.e.1.4 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.d.1.15 | ✓ | 18 | 1.1 | even | 1 | trivial | |
531.8.a.e.1.4 | 18 | 3.2 | odd | 2 |