Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,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, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
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: | \(135.996742959\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −58.2273 | −1.28665 | −0.643326 | − | 0.765592i | \(-0.722446\pi\) | ||||
−0.643326 | + | 0.765592i | \(0.722446\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | 1342.41 | 0.655475 | ||||||||
\(5\) | 11765.2 | 1.68369 | 0.841846 | − | 0.539717i | \(-0.181469\pi\) | ||||
0.841846 | + | 0.539717i | \(0.181469\pi\) | |||||||
\(6\) | 14149.2 | 0.742849 | ||||||||
\(7\) | 24587.2 | 0.552929 | 0.276465 | − | 0.961024i | \(-0.410837\pi\) | ||||
0.276465 | + | 0.961024i | \(0.410837\pi\) | |||||||
\(8\) | 41084.4 | 0.443284 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −685053. | −2.16633 | ||||||||
\(11\) | −938997. | −1.75794 | −0.878971 | − | 0.476875i | \(-0.841769\pi\) | ||||
−0.878971 | + | 0.476875i | \(0.841769\pi\) | |||||||
\(12\) | −326206. | −0.378439 | ||||||||
\(13\) | −1.32932e6 | −0.992984 | −0.496492 | − | 0.868041i | \(-0.665379\pi\) | ||||
−0.496492 | + | 0.868041i | \(0.665379\pi\) | |||||||
\(14\) | −1.43164e6 | −0.711428 | ||||||||
\(15\) | −2.85893e6 | −0.972081 | ||||||||
\(16\) | −5.14149e6 | −1.22583 | ||||||||
\(17\) | 500589. | 0.0855091 | 0.0427546 | − | 0.999086i | \(-0.486387\pi\) | ||||
0.0427546 | + | 0.999086i | \(0.486387\pi\) | |||||||
\(18\) | −3.43826e6 | −0.428884 | ||||||||
\(19\) | −1.82459e7 | −1.69052 | −0.845260 | − | 0.534355i | \(-0.820555\pi\) | ||||
−0.845260 | + | 0.534355i | \(0.820555\pi\) | |||||||
\(20\) | 1.57937e7 | 1.10362 | ||||||||
\(21\) | −5.97469e6 | −0.319234 | ||||||||
\(22\) | 5.46752e7 | 2.26186 | ||||||||
\(23\) | −3.11572e6 | −0.100938 | −0.0504691 | − | 0.998726i | \(-0.516072\pi\) | ||||
−0.0504691 | + | 0.998726i | \(0.516072\pi\) | |||||||
\(24\) | −9.98350e6 | −0.255930 | ||||||||
\(25\) | 8.95909e7 | 1.83482 | ||||||||
\(26\) | 7.74029e7 | 1.27763 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 3.30062e7 | 0.362432 | ||||||||
\(29\) | −1.34000e8 | −1.21316 | −0.606578 | − | 0.795024i | \(-0.707458\pi\) | ||||
−0.606578 | + | 0.795024i | \(0.707458\pi\) | |||||||
\(30\) | 1.66468e8 | 1.25073 | ||||||||
\(31\) | 1.46048e8 | 0.916232 | 0.458116 | − | 0.888892i | \(-0.348524\pi\) | ||||
0.458116 | + | 0.888892i | \(0.348524\pi\) | |||||||
\(32\) | 2.15234e8 | 1.13393 | ||||||||
\(33\) | 2.28176e8 | 1.01495 | ||||||||
\(34\) | −2.91479e7 | −0.110021 | ||||||||
\(35\) | 2.89272e8 | 0.930963 | ||||||||
\(36\) | 7.92682e7 | 0.218492 | ||||||||
\(37\) | −7.84276e8 | −1.85934 | −0.929672 | − | 0.368389i | \(-0.879909\pi\) | ||||
−0.929672 | + | 0.368389i | \(0.879909\pi\) | |||||||
\(38\) | 1.06241e9 | 2.17511 | ||||||||
\(39\) | 3.23026e8 | 0.573300 | ||||||||
\(40\) | 4.83364e8 | 0.746354 | ||||||||
\(41\) | 8.56325e8 | 1.15432 | 0.577162 | − | 0.816630i | \(-0.304160\pi\) | ||||
0.577162 | + | 0.816630i | \(0.304160\pi\) | |||||||
\(42\) | 3.47890e8 | 0.410743 | ||||||||
\(43\) | −1.12755e9 | −1.16966 | −0.584828 | − | 0.811157i | \(-0.698838\pi\) | ||||
−0.584828 | + | 0.811157i | \(0.698838\pi\) | |||||||
\(44\) | −1.26052e9 | −1.15229 | ||||||||
\(45\) | 6.94721e8 | 0.561231 | ||||||||
\(46\) | 1.81420e8 | 0.129872 | ||||||||
\(47\) | 1.67029e9 | 1.06231 | 0.531157 | − | 0.847274i | \(-0.321757\pi\) | ||||
0.531157 | + | 0.847274i | \(0.321757\pi\) | |||||||
\(48\) | 1.24938e9 | 0.707732 | ||||||||
\(49\) | −1.37280e9 | −0.694269 | ||||||||
\(50\) | −5.21663e9 | −2.36078 | ||||||||
\(51\) | −1.21643e8 | −0.0493687 | ||||||||
\(52\) | −1.78450e9 | −0.650876 | ||||||||
\(53\) | −1.57326e9 | −0.516753 | −0.258377 | − | 0.966044i | \(-0.583188\pi\) | ||||
−0.258377 | + | 0.966044i | \(0.583188\pi\) | |||||||
\(54\) | 8.35497e8 | 0.247616 | ||||||||
\(55\) | −1.10475e10 | −2.95983 | ||||||||
\(56\) | 1.01015e9 | 0.245105 | ||||||||
\(57\) | 4.43375e9 | 0.976023 | ||||||||
\(58\) | 7.80246e9 | 1.56091 | ||||||||
\(59\) | −7.14924e8 | −0.130189 | ||||||||
\(60\) | −3.83787e9 | −0.637175 | ||||||||
\(61\) | 1.01069e10 | 1.53216 | 0.766082 | − | 0.642742i | \(-0.222203\pi\) | ||||
0.766082 | + | 0.642742i | \(0.222203\pi\) | |||||||
\(62\) | −8.50396e9 | −1.17887 | ||||||||
\(63\) | 1.45185e9 | 0.184310 | ||||||||
\(64\) | −2.00272e9 | −0.233147 | ||||||||
\(65\) | −1.56397e10 | −1.67188 | ||||||||
\(66\) | −1.32861e10 | −1.30589 | ||||||||
\(67\) | 1.64187e10 | 1.48568 | 0.742842 | − | 0.669466i | \(-0.233477\pi\) | ||||
0.742842 | + | 0.669466i | \(0.233477\pi\) | |||||||
\(68\) | 6.71998e8 | 0.0560491 | ||||||||
\(69\) | 7.57121e8 | 0.0582767 | ||||||||
\(70\) | −1.68435e10 | −1.19783 | ||||||||
\(71\) | 1.39326e10 | 0.916454 | 0.458227 | − | 0.888835i | \(-0.348485\pi\) | ||||
0.458227 | + | 0.888835i | \(0.348485\pi\) | |||||||
\(72\) | 2.42599e9 | 0.147761 | ||||||||
\(73\) | −2.39204e10 | −1.35050 | −0.675248 | − | 0.737591i | \(-0.735963\pi\) | ||||
−0.675248 | + | 0.737591i | \(0.735963\pi\) | |||||||
\(74\) | 4.56663e10 | 2.39233 | ||||||||
\(75\) | −2.17706e10 | −1.05934 | ||||||||
\(76\) | −2.44935e10 | −1.10809 | ||||||||
\(77\) | −2.30873e10 | −0.972018 | ||||||||
\(78\) | −1.88089e10 | −0.737637 | ||||||||
\(79\) | −4.32713e9 | −0.158216 | −0.0791081 | − | 0.996866i | \(-0.525207\pi\) | ||||
−0.0791081 | + | 0.996866i | \(0.525207\pi\) | |||||||
\(80\) | −6.04905e10 | −2.06392 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −4.98615e10 | −1.48521 | ||||||||
\(83\) | 4.65457e10 | 1.29703 | 0.648515 | − | 0.761202i | \(-0.275391\pi\) | ||||
0.648515 | + | 0.761202i | \(0.275391\pi\) | |||||||
\(84\) | −8.02050e9 | −0.209250 | ||||||||
\(85\) | 5.88952e9 | 0.143971 | ||||||||
\(86\) | 6.56540e10 | 1.50494 | ||||||||
\(87\) | 3.25620e10 | 0.700416 | ||||||||
\(88\) | −3.85781e10 | −0.779267 | ||||||||
\(89\) | −3.36102e10 | −0.638007 | −0.319004 | − | 0.947754i | \(-0.603348\pi\) | ||||
−0.319004 | + | 0.947754i | \(0.603348\pi\) | |||||||
\(90\) | −4.04517e10 | −0.722109 | ||||||||
\(91\) | −3.26843e10 | −0.549050 | ||||||||
\(92\) | −4.18259e9 | −0.0661625 | ||||||||
\(93\) | −3.54896e10 | −0.528987 | ||||||||
\(94\) | −9.72562e10 | −1.36683 | ||||||||
\(95\) | −2.14666e11 | −2.84632 | ||||||||
\(96\) | −5.23019e10 | −0.654675 | ||||||||
\(97\) | 1.01084e11 | 1.19519 | 0.597596 | − | 0.801797i | \(-0.296123\pi\) | ||||
0.597596 | + | 0.801797i | \(0.296123\pi\) | |||||||
\(98\) | 7.99342e10 | 0.893283 | ||||||||
\(99\) | −5.54468e10 | −0.585981 | ||||||||
\(100\) | 1.20268e11 | 1.20268 | ||||||||
\(101\) | 9.86051e10 | 0.933538 | 0.466769 | − | 0.884379i | \(-0.345418\pi\) | ||||
0.466769 | + | 0.884379i | \(0.345418\pi\) | |||||||
\(102\) | 7.08295e9 | 0.0635204 | ||||||||
\(103\) | −2.67202e9 | −0.0227110 | −0.0113555 | − | 0.999936i | \(-0.503615\pi\) | ||||
−0.0113555 | + | 0.999936i | \(0.503615\pi\) | |||||||
\(104\) | −5.46144e10 | −0.440174 | ||||||||
\(105\) | −7.02932e10 | −0.537492 | ||||||||
\(106\) | 9.16066e10 | 0.664882 | ||||||||
\(107\) | 4.78542e10 | 0.329845 | 0.164922 | − | 0.986307i | \(-0.447263\pi\) | ||||
0.164922 | + | 0.986307i | \(0.447263\pi\) | |||||||
\(108\) | −1.92622e10 | −0.126146 | ||||||||
\(109\) | −1.86897e10 | −0.116347 | −0.0581735 | − | 0.998306i | \(-0.518528\pi\) | ||||
−0.0581735 | + | 0.998306i | \(0.518528\pi\) | |||||||
\(110\) | 6.43263e11 | 3.80828 | ||||||||
\(111\) | 1.90579e11 | 1.07349 | ||||||||
\(112\) | −1.26415e11 | −0.677796 | ||||||||
\(113\) | 4.59970e9 | 0.0234854 | 0.0117427 | − | 0.999931i | \(-0.496262\pi\) | ||||
0.0117427 | + | 0.999931i | \(0.496262\pi\) | |||||||
\(114\) | −2.58165e11 | −1.25580 | ||||||||
\(115\) | −3.66570e10 | −0.169949 | ||||||||
\(116\) | −1.79884e11 | −0.795193 | ||||||||
\(117\) | −7.84952e10 | −0.330995 | ||||||||
\(118\) | 4.16281e10 | 0.167508 | ||||||||
\(119\) | 1.23081e10 | 0.0472805 | ||||||||
\(120\) | −1.17458e11 | −0.430908 | ||||||||
\(121\) | 5.96404e11 | 2.09036 | ||||||||
\(122\) | −5.88499e11 | −1.97136 | ||||||||
\(123\) | −2.08087e11 | −0.666449 | ||||||||
\(124\) | 1.96056e11 | 0.600567 | ||||||||
\(125\) | 4.79581e11 | 1.40558 | ||||||||
\(126\) | −8.45372e10 | −0.237143 | ||||||||
\(127\) | 3.64958e10 | 0.0980217 | 0.0490109 | − | 0.998798i | \(-0.484393\pi\) | ||||
0.0490109 | + | 0.998798i | \(0.484393\pi\) | |||||||
\(128\) | −3.24187e11 | −0.833951 | ||||||||
\(129\) | 2.73994e11 | 0.675301 | ||||||||
\(130\) | 9.10657e11 | 2.15113 | ||||||||
\(131\) | 7.72535e11 | 1.74955 | 0.874774 | − | 0.484531i | \(-0.161010\pi\) | ||||
0.874774 | + | 0.484531i | \(0.161010\pi\) | |||||||
\(132\) | 3.06307e11 | 0.665273 | ||||||||
\(133\) | −4.48615e11 | −0.934739 | ||||||||
\(134\) | −9.56014e11 | −1.91156 | ||||||||
\(135\) | −1.68817e11 | −0.324027 | ||||||||
\(136\) | 2.05664e10 | 0.0379048 | ||||||||
\(137\) | −1.09549e12 | −1.93931 | −0.969653 | − | 0.244484i | \(-0.921381\pi\) | ||||
−0.969653 | + | 0.244484i | \(0.921381\pi\) | |||||||
\(138\) | −4.40851e10 | −0.0749819 | ||||||||
\(139\) | −1.12823e11 | −0.184423 | −0.0922114 | − | 0.995739i | \(-0.529394\pi\) | ||||
−0.0922114 | + | 0.995739i | \(0.529394\pi\) | |||||||
\(140\) | 3.88323e11 | 0.610223 | ||||||||
\(141\) | −4.05880e11 | −0.613327 | ||||||||
\(142\) | −8.11256e11 | −1.17916 | ||||||||
\(143\) | 1.24823e12 | 1.74561 | ||||||||
\(144\) | −3.03600e11 | −0.408609 | ||||||||
\(145\) | −1.57653e12 | −2.04258 | ||||||||
\(146\) | 1.39282e12 | 1.73762 | ||||||||
\(147\) | 3.33590e11 | 0.400836 | ||||||||
\(148\) | −1.05282e12 | −1.21875 | ||||||||
\(149\) | −9.06159e11 | −1.01083 | −0.505417 | − | 0.862875i | \(-0.668661\pi\) | ||||
−0.505417 | + | 0.862875i | \(0.668661\pi\) | |||||||
\(150\) | 1.26764e12 | 1.36300 | ||||||||
\(151\) | 3.34882e11 | 0.347151 | 0.173576 | − | 0.984821i | \(-0.444468\pi\) | ||||
0.173576 | + | 0.984821i | \(0.444468\pi\) | |||||||
\(152\) | −7.49621e11 | −0.749380 | ||||||||
\(153\) | 2.95593e10 | 0.0285030 | ||||||||
\(154\) | 1.34431e12 | 1.25065 | ||||||||
\(155\) | 1.71827e12 | 1.54265 | ||||||||
\(156\) | 4.33634e11 | 0.375784 | ||||||||
\(157\) | 1.23760e12 | 1.03545 | 0.517727 | − | 0.855546i | \(-0.326778\pi\) | ||||
0.517727 | + | 0.855546i | \(0.326778\pi\) | |||||||
\(158\) | 2.51957e11 | 0.203569 | ||||||||
\(159\) | 3.82302e11 | 0.298348 | ||||||||
\(160\) | 2.53227e12 | 1.90919 | ||||||||
\(161\) | −7.66069e10 | −0.0558117 | ||||||||
\(162\) | −2.03026e11 | −0.142961 | ||||||||
\(163\) | 1.54605e12 | 1.05243 | 0.526213 | − | 0.850353i | \(-0.323612\pi\) | ||||
0.526213 | + | 0.850353i | \(0.323612\pi\) | |||||||
\(164\) | 1.14954e12 | 0.756630 | ||||||||
\(165\) | 2.68453e12 | 1.70886 | ||||||||
\(166\) | −2.71023e12 | −1.66883 | ||||||||
\(167\) | 2.34543e12 | 1.39728 | 0.698638 | − | 0.715475i | \(-0.253790\pi\) | ||||
0.698638 | + | 0.715475i | \(0.253790\pi\) | |||||||
\(168\) | −2.45466e11 | −0.141511 | ||||||||
\(169\) | −2.50593e10 | −0.0139827 | ||||||||
\(170\) | −3.42930e11 | −0.185241 | ||||||||
\(171\) | −1.07740e12 | −0.563507 | ||||||||
\(172\) | −1.51363e12 | −0.766681 | ||||||||
\(173\) | −2.18244e12 | −1.07075 | −0.535376 | − | 0.844614i | \(-0.679830\pi\) | ||||
−0.535376 | + | 0.844614i | \(0.679830\pi\) | |||||||
\(174\) | −1.89600e12 | −0.901192 | ||||||||
\(175\) | 2.20279e12 | 1.01453 | ||||||||
\(176\) | 4.82785e12 | 2.15493 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | 1.95703e12 | 0.820894 | ||||||||
\(179\) | 1.31276e12 | 0.533940 | 0.266970 | − | 0.963705i | \(-0.413977\pi\) | ||||
0.266970 | + | 0.963705i | \(0.413977\pi\) | |||||||
\(180\) | 9.32603e11 | 0.367873 | ||||||||
\(181\) | −1.55261e11 | −0.0594058 | −0.0297029 | − | 0.999559i | \(-0.509456\pi\) | ||||
−0.0297029 | + | 0.999559i | \(0.509456\pi\) | |||||||
\(182\) | 1.90312e12 | 0.706437 | ||||||||
\(183\) | −2.45599e12 | −0.884596 | ||||||||
\(184\) | −1.28008e11 | −0.0447443 | ||||||||
\(185\) | −9.22714e12 | −3.13056 | ||||||||
\(186\) | 2.06646e12 | 0.680622 | ||||||||
\(187\) | −4.70052e11 | −0.150320 | ||||||||
\(188\) | 2.24221e12 | 0.696320 | ||||||||
\(189\) | −3.52799e11 | −0.106411 | ||||||||
\(190\) | 1.24994e13 | 3.66222 | ||||||||
\(191\) | 1.44276e12 | 0.410685 | 0.205343 | − | 0.978690i | \(-0.434169\pi\) | ||||
0.205343 | + | 0.978690i | \(0.434169\pi\) | |||||||
\(192\) | 4.86661e11 | 0.134608 | ||||||||
\(193\) | 4.97486e12 | 1.33726 | 0.668629 | − | 0.743596i | \(-0.266881\pi\) | ||||
0.668629 | + | 0.743596i | \(0.266881\pi\) | |||||||
\(194\) | −5.88584e12 | −1.53780 | ||||||||
\(195\) | 3.80045e12 | 0.965261 | ||||||||
\(196\) | −1.84286e12 | −0.455076 | ||||||||
\(197\) | −3.45348e12 | −0.829264 | −0.414632 | − | 0.909989i | \(-0.636090\pi\) | ||||
−0.414632 | + | 0.909989i | \(0.636090\pi\) | |||||||
\(198\) | 3.22852e12 | 0.753954 | ||||||||
\(199\) | 2.30272e12 | 0.523057 | 0.261529 | − | 0.965196i | \(-0.415773\pi\) | ||||
0.261529 | + | 0.965196i | \(0.415773\pi\) | |||||||
\(200\) | 3.68079e12 | 0.813347 | ||||||||
\(201\) | −3.98974e12 | −0.857760 | ||||||||
\(202\) | −5.74151e12 | −1.20114 | ||||||||
\(203\) | −3.29469e12 | −0.670789 | ||||||||
\(204\) | −1.63295e11 | −0.0323600 | ||||||||
\(205\) | 1.00748e13 | 1.94353 | ||||||||
\(206\) | 1.55585e11 | 0.0292211 | ||||||||
\(207\) | −1.83980e11 | −0.0336461 | ||||||||
\(208\) | 6.83471e12 | 1.21723 | ||||||||
\(209\) | 1.71329e13 | 2.97184 | ||||||||
\(210\) | 4.09298e12 | 0.691565 | ||||||||
\(211\) | 1.12022e13 | 1.84395 | 0.921976 | − | 0.387247i | \(-0.126574\pi\) | ||||
0.921976 | + | 0.387247i | \(0.126574\pi\) | |||||||
\(212\) | −2.11197e12 | −0.338719 | ||||||||
\(213\) | −3.38562e12 | −0.529115 | ||||||||
\(214\) | −2.78642e12 | −0.424396 | ||||||||
\(215\) | −1.32658e13 | −1.96934 | ||||||||
\(216\) | −5.89516e11 | −0.0853100 | ||||||||
\(217\) | 3.59090e12 | 0.506612 | ||||||||
\(218\) | 1.08825e12 | 0.149698 | ||||||||
\(219\) | 5.81266e12 | 0.779709 | ||||||||
\(220\) | −1.48303e13 | −1.94010 | ||||||||
\(221\) | −6.65445e11 | −0.0849092 | ||||||||
\(222\) | −1.10969e13 | −1.38121 | ||||||||
\(223\) | −5.12284e12 | −0.622063 | −0.311031 | − | 0.950400i | \(-0.600674\pi\) | ||||
−0.311031 | + | 0.950400i | \(0.600674\pi\) | |||||||
\(224\) | 5.29200e12 | 0.626983 | ||||||||
\(225\) | 5.29025e12 | 0.611607 | ||||||||
\(226\) | −2.67828e11 | −0.0302176 | ||||||||
\(227\) | −3.87426e12 | −0.426625 | −0.213313 | − | 0.976984i | \(-0.568425\pi\) | ||||
−0.213313 | + | 0.976984i | \(0.568425\pi\) | |||||||
\(228\) | 5.95193e12 | 0.639759 | ||||||||
\(229\) | 6.67895e12 | 0.700831 | 0.350415 | − | 0.936594i | \(-0.386040\pi\) | ||||
0.350415 | + | 0.936594i | \(0.386040\pi\) | |||||||
\(230\) | 2.13444e12 | 0.218665 | ||||||||
\(231\) | 5.61021e12 | 0.561195 | ||||||||
\(232\) | −5.50531e12 | −0.537772 | ||||||||
\(233\) | 1.77552e12 | 0.169383 | 0.0846913 | − | 0.996407i | \(-0.473010\pi\) | ||||
0.0846913 | + | 0.996407i | \(0.473010\pi\) | |||||||
\(234\) | 4.57056e12 | 0.425875 | ||||||||
\(235\) | 1.96512e13 | 1.78861 | ||||||||
\(236\) | −9.59724e11 | −0.0853356 | ||||||||
\(237\) | 1.05149e12 | 0.0913462 | ||||||||
\(238\) | −7.16666e11 | −0.0608336 | ||||||||
\(239\) | 7.31609e12 | 0.606863 | 0.303432 | − | 0.952853i | \(-0.401868\pi\) | ||||
0.303432 | + | 0.952853i | \(0.401868\pi\) | |||||||
\(240\) | 1.46992e13 | 1.19160 | ||||||||
\(241\) | 1.82714e13 | 1.44770 | 0.723848 | − | 0.689959i | \(-0.242372\pi\) | ||||
0.723848 | + | 0.689959i | \(0.242372\pi\) | |||||||
\(242\) | −3.47270e13 | −2.68957 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 1.35677e13 | 1.00430 | ||||||||
\(245\) | −1.61512e13 | −1.16894 | ||||||||
\(246\) | 1.21163e13 | 0.857488 | ||||||||
\(247\) | 2.42547e13 | 1.67866 | ||||||||
\(248\) | 6.00028e12 | 0.406151 | ||||||||
\(249\) | −1.13106e13 | −0.748840 | ||||||||
\(250\) | −2.79247e13 | −1.80850 | ||||||||
\(251\) | −9.76997e12 | −0.618996 | −0.309498 | − | 0.950900i | \(-0.600161\pi\) | ||||
−0.309498 | + | 0.950900i | \(0.600161\pi\) | |||||||
\(252\) | 1.94898e12 | 0.120811 | ||||||||
\(253\) | 2.92566e12 | 0.177444 | ||||||||
\(254\) | −2.12505e12 | −0.126120 | ||||||||
\(255\) | −1.43115e12 | −0.0831218 | ||||||||
\(256\) | 2.29781e13 | 1.30615 | ||||||||
\(257\) | −3.48937e13 | −1.94140 | −0.970699 | − | 0.240298i | \(-0.922755\pi\) | ||||
−0.970699 | + | 0.240298i | \(0.922755\pi\) | |||||||
\(258\) | −1.59539e13 | −0.868878 | ||||||||
\(259\) | −1.92831e13 | −1.02809 | ||||||||
\(260\) | −2.09950e13 | −1.09588 | ||||||||
\(261\) | −7.91258e12 | −0.404385 | ||||||||
\(262\) | −4.49826e13 | −2.25106 | ||||||||
\(263\) | 1.57851e13 | 0.773556 | 0.386778 | − | 0.922173i | \(-0.373588\pi\) | ||||
0.386778 | + | 0.922173i | \(0.373588\pi\) | |||||||
\(264\) | 9.37448e12 | 0.449910 | ||||||||
\(265\) | −1.85097e13 | −0.870054 | ||||||||
\(266\) | 2.61216e13 | 1.20268 | ||||||||
\(267\) | 8.16727e12 | 0.368354 | ||||||||
\(268\) | 2.20406e13 | 0.973829 | ||||||||
\(269\) | −2.10203e13 | −0.909916 | −0.454958 | − | 0.890513i | \(-0.650346\pi\) | ||||
−0.454958 | + | 0.890513i | \(0.650346\pi\) | |||||||
\(270\) | 9.82976e12 | 0.416910 | ||||||||
\(271\) | 9.01121e12 | 0.374500 | 0.187250 | − | 0.982312i | \(-0.440043\pi\) | ||||
0.187250 | + | 0.982312i | \(0.440043\pi\) | |||||||
\(272\) | −2.57378e12 | −0.104819 | ||||||||
\(273\) | 7.94229e12 | 0.316994 | ||||||||
\(274\) | 6.37875e13 | 2.49521 | ||||||||
\(275\) | −8.41256e13 | −3.22551 | ||||||||
\(276\) | 1.01637e12 | 0.0381989 | ||||||||
\(277\) | −1.25993e12 | −0.0464203 | −0.0232102 | − | 0.999731i | \(-0.507389\pi\) | ||||
−0.0232102 | + | 0.999731i | \(0.507389\pi\) | |||||||
\(278\) | 6.56935e12 | 0.237288 | ||||||||
\(279\) | 8.62397e12 | 0.305411 | ||||||||
\(280\) | 1.18846e13 | 0.412681 | ||||||||
\(281\) | −2.75168e13 | −0.936944 | −0.468472 | − | 0.883478i | \(-0.655195\pi\) | ||||
−0.468472 | + | 0.883478i | \(0.655195\pi\) | |||||||
\(282\) | 2.36333e13 | 0.789139 | ||||||||
\(283\) | −4.14144e13 | −1.35621 | −0.678104 | − | 0.734966i | \(-0.737198\pi\) | ||||
−0.678104 | + | 0.734966i | \(0.737198\pi\) | |||||||
\(284\) | 1.87033e13 | 0.600713 | ||||||||
\(285\) | 5.21638e13 | 1.64332 | ||||||||
\(286\) | −7.26811e13 | −2.24599 | ||||||||
\(287\) | 2.10546e13 | 0.638259 | ||||||||
\(288\) | 1.27094e13 | 0.377977 | ||||||||
\(289\) | −3.40213e13 | −0.992688 | ||||||||
\(290\) | 9.17972e13 | 2.62809 | ||||||||
\(291\) | −2.45634e13 | −0.690045 | ||||||||
\(292\) | −3.21111e13 | −0.885216 | ||||||||
\(293\) | 2.32467e12 | 0.0628912 | 0.0314456 | − | 0.999505i | \(-0.489989\pi\) | ||||
0.0314456 | + | 0.999505i | \(0.489989\pi\) | |||||||
\(294\) | −1.94240e13 | −0.515737 | ||||||||
\(295\) | −8.41120e12 | −0.219198 | ||||||||
\(296\) | −3.22215e13 | −0.824217 | ||||||||
\(297\) | 1.34736e13 | 0.338316 | ||||||||
\(298\) | 5.27632e13 | 1.30059 | ||||||||
\(299\) | 4.14180e12 | 0.100230 | ||||||||
\(300\) | −2.92251e13 | −0.694368 | ||||||||
\(301\) | −2.77232e13 | −0.646737 | ||||||||
\(302\) | −1.94993e13 | −0.446663 | ||||||||
\(303\) | −2.39610e13 | −0.538978 | ||||||||
\(304\) | 9.38112e13 | 2.07229 | ||||||||
\(305\) | 1.18910e14 | 2.57970 | ||||||||
\(306\) | −1.72116e12 | −0.0366735 | ||||||||
\(307\) | −6.10687e13 | −1.27808 | −0.639039 | − | 0.769174i | \(-0.720668\pi\) | ||||
−0.639039 | + | 0.769174i | \(0.720668\pi\) | |||||||
\(308\) | −3.09927e13 | −0.637134 | ||||||||
\(309\) | 6.49301e11 | 0.0131122 | ||||||||
\(310\) | −1.00050e14 | −1.98486 | ||||||||
\(311\) | −2.82075e13 | −0.549772 | −0.274886 | − | 0.961477i | \(-0.588640\pi\) | ||||
−0.274886 | + | 0.961477i | \(0.588640\pi\) | |||||||
\(312\) | 1.32713e13 | 0.254134 | ||||||||
\(313\) | −4.99330e13 | −0.939493 | −0.469746 | − | 0.882801i | \(-0.655655\pi\) | ||||
−0.469746 | + | 0.882801i | \(0.655655\pi\) | |||||||
\(314\) | −7.20618e13 | −1.33227 | ||||||||
\(315\) | 1.70812e13 | 0.310321 | ||||||||
\(316\) | −5.80880e12 | −0.103707 | ||||||||
\(317\) | −2.26238e13 | −0.396953 | −0.198476 | − | 0.980106i | \(-0.563599\pi\) | ||||
−0.198476 | + | 0.980106i | \(0.563599\pi\) | |||||||
\(318\) | −2.22604e13 | −0.383870 | ||||||||
\(319\) | 1.25826e14 | 2.13266 | ||||||||
\(320\) | −2.35623e13 | −0.392549 | ||||||||
\(321\) | −1.16286e13 | −0.190436 | ||||||||
\(322\) | 4.46061e12 | 0.0718103 | ||||||||
\(323\) | −9.13370e12 | −0.144555 | ||||||||
\(324\) | 4.68071e12 | 0.0728306 | ||||||||
\(325\) | −1.19095e14 | −1.82195 | ||||||||
\(326\) | −9.00222e13 | −1.35411 | ||||||||
\(327\) | 4.54159e12 | 0.0671730 | ||||||||
\(328\) | 3.51816e13 | 0.511693 | ||||||||
\(329\) | 4.10677e13 | 0.587384 | ||||||||
\(330\) | −1.56313e14 | −2.19871 | ||||||||
\(331\) | 2.60340e13 | 0.360153 | 0.180077 | − | 0.983653i | \(-0.442365\pi\) | ||||
0.180077 | + | 0.983653i | \(0.442365\pi\) | |||||||
\(332\) | 6.24835e13 | 0.850171 | ||||||||
\(333\) | −4.63107e13 | −0.619781 | ||||||||
\(334\) | −1.36568e14 | −1.79781 | ||||||||
\(335\) | 1.93168e14 | 2.50144 | ||||||||
\(336\) | 3.07188e13 | 0.391326 | ||||||||
\(337\) | 7.39619e13 | 0.926923 | 0.463462 | − | 0.886117i | \(-0.346607\pi\) | ||||
0.463462 | + | 0.886117i | \(0.346607\pi\) | |||||||
\(338\) | 1.45913e12 | 0.0179909 | ||||||||
\(339\) | −1.11773e12 | −0.0135593 | ||||||||
\(340\) | 7.90616e12 | 0.0943695 | ||||||||
\(341\) | −1.37138e14 | −1.61068 | ||||||||
\(342\) | 6.27342e13 | 0.725038 | ||||||||
\(343\) | −8.23701e13 | −0.936811 | ||||||||
\(344\) | −4.63246e13 | −0.518490 | ||||||||
\(345\) | 8.90765e12 | 0.0981201 | ||||||||
\(346\) | 1.27078e14 | 1.37769 | ||||||||
\(347\) | −5.03244e13 | −0.536991 | −0.268495 | − | 0.963281i | \(-0.586526\pi\) | ||||
−0.268495 | + | 0.963281i | \(0.586526\pi\) | |||||||
\(348\) | 4.37117e13 | 0.459105 | ||||||||
\(349\) | 1.23412e14 | 1.27591 | 0.637954 | − | 0.770075i | \(-0.279781\pi\) | ||||
0.637954 | + | 0.770075i | \(0.279781\pi\) | |||||||
\(350\) | −1.28262e14 | −1.30534 | ||||||||
\(351\) | 1.90743e13 | 0.191100 | ||||||||
\(352\) | −2.02104e14 | −1.99338 | ||||||||
\(353\) | −1.29551e14 | −1.25800 | −0.629000 | − | 0.777405i | \(-0.716536\pi\) | ||||
−0.629000 | + | 0.777405i | \(0.716536\pi\) | |||||||
\(354\) | −1.01156e13 | −0.0967107 | ||||||||
\(355\) | 1.63919e14 | 1.54303 | ||||||||
\(356\) | −4.51187e13 | −0.418198 | ||||||||
\(357\) | −2.99086e12 | −0.0272974 | ||||||||
\(358\) | −7.64382e13 | −0.686996 | ||||||||
\(359\) | 1.45803e14 | 1.29047 | 0.645235 | − | 0.763984i | \(-0.276760\pi\) | ||||
0.645235 | + | 0.763984i | \(0.276760\pi\) | |||||||
\(360\) | 2.85422e13 | 0.248785 | ||||||||
\(361\) | 2.16423e14 | 1.85786 | ||||||||
\(362\) | 9.04040e12 | 0.0764347 | ||||||||
\(363\) | −1.44926e14 | −1.20687 | ||||||||
\(364\) | −4.38759e13 | −0.359889 | ||||||||
\(365\) | −2.81428e14 | −2.27382 | ||||||||
\(366\) | 1.43005e14 | 1.13817 | ||||||||
\(367\) | 1.94975e14 | 1.52868 | 0.764338 | − | 0.644816i | \(-0.223066\pi\) | ||||
0.764338 | + | 0.644816i | \(0.223066\pi\) | |||||||
\(368\) | 1.60195e13 | 0.123733 | ||||||||
\(369\) | 5.05651e13 | 0.384774 | ||||||||
\(370\) | 5.37271e14 | 4.02795 | ||||||||
\(371\) | −3.86820e13 | −0.285728 | ||||||||
\(372\) | −4.76417e13 | −0.346738 | ||||||||
\(373\) | 1.89658e14 | 1.36011 | 0.680053 | − | 0.733163i | \(-0.261957\pi\) | ||||
0.680053 | + | 0.733163i | \(0.261957\pi\) | |||||||
\(374\) | 2.73698e13 | 0.193410 | ||||||||
\(375\) | −1.16538e14 | −0.811514 | ||||||||
\(376\) | 6.86227e13 | 0.470906 | ||||||||
\(377\) | 1.78130e14 | 1.20464 | ||||||||
\(378\) | 2.05425e13 | 0.136914 | ||||||||
\(379\) | −9.21260e13 | −0.605155 | −0.302578 | − | 0.953125i | \(-0.597847\pi\) | ||||
−0.302578 | + | 0.953125i | \(0.597847\pi\) | |||||||
\(380\) | −2.88170e14 | −1.86569 | ||||||||
\(381\) | −8.86848e12 | −0.0565929 | ||||||||
\(382\) | −8.40077e13 | −0.528409 | ||||||||
\(383\) | 3.06491e14 | 1.90031 | 0.950155 | − | 0.311779i | \(-0.100925\pi\) | ||||
0.950155 | + | 0.311779i | \(0.100925\pi\) | |||||||
\(384\) | 7.87774e13 | 0.481482 | ||||||||
\(385\) | −2.71626e14 | −1.63658 | ||||||||
\(386\) | −2.89672e14 | −1.72059 | ||||||||
\(387\) | −6.65806e13 | −0.389885 | ||||||||
\(388\) | 1.35697e14 | 0.783419 | ||||||||
\(389\) | 1.21080e14 | 0.689206 | 0.344603 | − | 0.938748i | \(-0.388014\pi\) | ||||
0.344603 | + | 0.938748i | \(0.388014\pi\) | |||||||
\(390\) | −2.21290e14 | −1.24196 | ||||||||
\(391\) | −1.55970e12 | −0.00863114 | ||||||||
\(392\) | −5.64005e13 | −0.307758 | ||||||||
\(393\) | −1.87726e14 | −1.01010 | ||||||||
\(394\) | 2.01087e14 | 1.06697 | ||||||||
\(395\) | −5.09094e13 | −0.266388 | ||||||||
\(396\) | −7.44326e13 | −0.384096 | ||||||||
\(397\) | 2.58359e14 | 1.31485 | 0.657424 | − | 0.753521i | \(-0.271646\pi\) | ||||
0.657424 | + | 0.753521i | \(0.271646\pi\) | |||||||
\(398\) | −1.34081e14 | −0.672993 | ||||||||
\(399\) | 1.09014e14 | 0.539672 | ||||||||
\(400\) | −4.60631e14 | −2.24918 | ||||||||
\(401\) | 1.57462e14 | 0.758372 | 0.379186 | − | 0.925321i | \(-0.376204\pi\) | ||||
0.379186 | + | 0.925321i | \(0.376204\pi\) | |||||||
\(402\) | 2.32311e14 | 1.10364 | ||||||||
\(403\) | −1.94145e14 | −0.909804 | ||||||||
\(404\) | 1.32369e14 | 0.611911 | ||||||||
\(405\) | 4.10226e13 | 0.187077 | ||||||||
\(406\) | 1.91841e14 | 0.863073 | ||||||||
\(407\) | 7.36433e14 | 3.26862 | ||||||||
\(408\) | −4.99764e12 | −0.0218844 | ||||||||
\(409\) | 8.32952e12 | 0.0359867 | 0.0179933 | − | 0.999838i | \(-0.494272\pi\) | ||||
0.0179933 | + | 0.999838i | \(0.494272\pi\) | |||||||
\(410\) | −5.86628e14 | −2.50064 | ||||||||
\(411\) | 2.66205e14 | 1.11966 | ||||||||
\(412\) | −3.58696e12 | −0.0148865 | ||||||||
\(413\) | −1.75780e13 | −0.0719853 | ||||||||
\(414\) | 1.07127e13 | 0.0432908 | ||||||||
\(415\) | 5.47617e14 | 2.18380 | ||||||||
\(416\) | −2.86116e14 | −1.12597 | ||||||||
\(417\) | 2.74159e13 | 0.106477 | ||||||||
\(418\) | −9.97599e14 | −3.82372 | ||||||||
\(419\) | −4.35102e14 | −1.64594 | −0.822970 | − | 0.568085i | \(-0.807684\pi\) | ||||
−0.822970 | + | 0.568085i | \(0.807684\pi\) | |||||||
\(420\) | −9.43625e13 | −0.352313 | ||||||||
\(421\) | −1.03075e14 | −0.379841 | −0.189921 | − | 0.981799i | \(-0.560823\pi\) | ||||
−0.189921 | + | 0.981799i | \(0.560823\pi\) | |||||||
\(422\) | −6.52273e14 | −2.37253 | ||||||||
\(423\) | 9.86288e13 | 0.354105 | ||||||||
\(424\) | −6.46364e13 | −0.229068 | ||||||||
\(425\) | 4.48483e13 | 0.156894 | ||||||||
\(426\) | 1.97135e14 | 0.680787 | ||||||||
\(427\) | 2.48501e14 | 0.847179 | ||||||||
\(428\) | 6.42401e13 | 0.216205 | ||||||||
\(429\) | −3.03320e14 | −1.00783 | ||||||||
\(430\) | 7.72430e14 | 2.53386 | ||||||||
\(431\) | −2.78201e14 | −0.901019 | −0.450509 | − | 0.892772i | \(-0.648758\pi\) | ||||
−0.450509 | + | 0.892772i | \(0.648758\pi\) | |||||||
\(432\) | 7.37748e13 | 0.235911 | ||||||||
\(433\) | 6.07379e14 | 1.91768 | 0.958841 | − | 0.283943i | \(-0.0916428\pi\) | ||||
0.958841 | + | 0.283943i | \(0.0916428\pi\) | |||||||
\(434\) | −2.09088e14 | −0.651833 | ||||||||
\(435\) | 3.83098e14 | 1.17928 | ||||||||
\(436\) | −2.50892e13 | −0.0762626 | ||||||||
\(437\) | 5.68492e13 | 0.170638 | ||||||||
\(438\) | −3.38455e14 | −1.00321 | ||||||||
\(439\) | −1.94149e14 | −0.568304 | −0.284152 | − | 0.958779i | \(-0.591712\pi\) | ||||
−0.284152 | + | 0.958779i | \(0.591712\pi\) | |||||||
\(440\) | −4.53878e14 | −1.31205 | ||||||||
\(441\) | −8.10623e13 | −0.231423 | ||||||||
\(442\) | 3.87471e13 | 0.109249 | ||||||||
\(443\) | 3.04022e14 | 0.846611 | 0.423305 | − | 0.905987i | \(-0.360870\pi\) | ||||
0.423305 | + | 0.905987i | \(0.360870\pi\) | |||||||
\(444\) | 2.55836e14 | 0.703648 | ||||||||
\(445\) | −3.95429e14 | −1.07421 | ||||||||
\(446\) | 2.98289e14 | 0.800378 | ||||||||
\(447\) | 2.20197e14 | 0.583605 | ||||||||
\(448\) | −4.92413e13 | −0.128914 | ||||||||
\(449\) | −3.59382e14 | −0.929399 | −0.464699 | − | 0.885469i | \(-0.653838\pi\) | ||||
−0.464699 | + | 0.885469i | \(0.653838\pi\) | |||||||
\(450\) | −3.08037e14 | −0.786926 | ||||||||
\(451\) | −8.04087e14 | −2.02923 | ||||||||
\(452\) | 6.17470e12 | 0.0153941 | ||||||||
\(453\) | −8.13763e13 | −0.200428 | ||||||||
\(454\) | 2.25587e14 | 0.548918 | ||||||||
\(455\) | −3.84536e14 | −0.924432 | ||||||||
\(456\) | 1.82158e14 | 0.432655 | ||||||||
\(457\) | 3.82052e13 | 0.0896569 | 0.0448284 | − | 0.998995i | \(-0.485726\pi\) | ||||
0.0448284 | + | 0.998995i | \(0.485726\pi\) | |||||||
\(458\) | −3.88897e14 | −0.901726 | ||||||||
\(459\) | −7.18291e12 | −0.0164562 | ||||||||
\(460\) | −4.92088e13 | −0.111397 | ||||||||
\(461\) | −2.71731e14 | −0.607833 | −0.303916 | − | 0.952699i | \(-0.598294\pi\) | ||||
−0.303916 | + | 0.952699i | \(0.598294\pi\) | |||||||
\(462\) | −3.26667e14 | −0.722063 | ||||||||
\(463\) | −2.18845e14 | −0.478016 | −0.239008 | − | 0.971018i | \(-0.576822\pi\) | ||||
−0.239008 | + | 0.971018i | \(0.576822\pi\) | |||||||
\(464\) | 6.88961e14 | 1.48712 | ||||||||
\(465\) | −4.17541e14 | −0.890651 | ||||||||
\(466\) | −1.03384e14 | −0.217937 | ||||||||
\(467\) | 2.84426e14 | 0.592551 | 0.296276 | − | 0.955103i | \(-0.404255\pi\) | ||||
0.296276 | + | 0.955103i | \(0.404255\pi\) | |||||||
\(468\) | −1.05373e14 | −0.216959 | ||||||||
\(469\) | 4.03689e14 | 0.821479 | ||||||||
\(470\) | −1.14424e15 | −2.30132 | ||||||||
\(471\) | −3.00736e14 | −0.597819 | ||||||||
\(472\) | −2.93722e13 | −0.0577106 | ||||||||
\(473\) | 1.05876e15 | 2.05619 | ||||||||
\(474\) | −6.12255e13 | −0.117531 | ||||||||
\(475\) | −1.63467e15 | −3.10180 | ||||||||
\(476\) | 1.65225e13 | 0.0309912 | ||||||||
\(477\) | −9.28994e13 | −0.172251 | ||||||||
\(478\) | −4.25996e14 | −0.780822 | ||||||||
\(479\) | 4.43363e14 | 0.803366 | 0.401683 | − | 0.915779i | \(-0.368425\pi\) | ||||
0.401683 | + | 0.915779i | \(0.368425\pi\) | |||||||
\(480\) | −6.15341e14 | −1.10227 | ||||||||
\(481\) | 1.04256e15 | 1.84630 | ||||||||
\(482\) | −1.06389e15 | −1.86268 | ||||||||
\(483\) | 1.86155e13 | 0.0322229 | ||||||||
\(484\) | 8.00621e14 | 1.37018 | ||||||||
\(485\) | 1.18927e15 | 2.01234 | ||||||||
\(486\) | 4.93353e13 | 0.0825388 | ||||||||
\(487\) | 9.07514e14 | 1.50122 | 0.750609 | − | 0.660746i | \(-0.229760\pi\) | ||||
0.750609 | + | 0.660746i | \(0.229760\pi\) | |||||||
\(488\) | 4.15237e14 | 0.679184 | ||||||||
\(489\) | −3.75690e14 | −0.607618 | ||||||||
\(490\) | 9.40439e14 | 1.50401 | ||||||||
\(491\) | 5.96037e14 | 0.942594 | 0.471297 | − | 0.881975i | \(-0.343786\pi\) | ||||
0.471297 | + | 0.881975i | \(0.343786\pi\) | |||||||
\(492\) | −2.79339e14 | −0.436841 | ||||||||
\(493\) | −6.70791e13 | −0.103736 | ||||||||
\(494\) | −1.41228e15 | −2.15985 | ||||||||
\(495\) | −6.52341e14 | −0.986612 | ||||||||
\(496\) | −7.50903e14 | −1.12314 | ||||||||
\(497\) | 3.42563e14 | 0.506735 | ||||||||
\(498\) | 6.58585e14 | 0.963497 | ||||||||
\(499\) | −6.54341e14 | −0.946785 | −0.473393 | − | 0.880852i | \(-0.656971\pi\) | ||||
−0.473393 | + | 0.880852i | \(0.656971\pi\) | |||||||
\(500\) | 6.43796e14 | 0.921326 | ||||||||
\(501\) | −5.69940e14 | −0.806718 | ||||||||
\(502\) | 5.68878e14 | 0.796432 | ||||||||
\(503\) | 1.33214e15 | 1.84470 | 0.922348 | − | 0.386360i | \(-0.126268\pi\) | ||||
0.922348 | + | 0.386360i | \(0.126268\pi\) | |||||||
\(504\) | 5.96483e13 | 0.0817015 | ||||||||
\(505\) | 1.16011e15 | 1.57179 | ||||||||
\(506\) | −1.70353e14 | −0.228308 | ||||||||
\(507\) | 6.08940e12 | 0.00807292 | ||||||||
\(508\) | 4.89924e13 | 0.0642508 | ||||||||
\(509\) | 1.04814e15 | 1.35979 | 0.679894 | − | 0.733311i | \(-0.262026\pi\) | ||||
0.679894 | + | 0.733311i | \(0.262026\pi\) | |||||||
\(510\) | 8.33321e13 | 0.106949 | ||||||||
\(511\) | −5.88136e14 | −0.746729 | ||||||||
\(512\) | −6.74016e14 | −0.846614 | ||||||||
\(513\) | 2.61809e14 | 0.325341 | ||||||||
\(514\) | 2.03176e15 | 2.49791 | ||||||||
\(515\) | −3.14368e13 | −0.0382383 | ||||||||
\(516\) | 3.67813e14 | 0.442643 | ||||||||
\(517\) | −1.56839e15 | −1.86749 | ||||||||
\(518\) | 1.12280e15 | 1.32279 | ||||||||
\(519\) | 5.30333e14 | 0.618199 | ||||||||
\(520\) | −6.42548e14 | −0.741117 | ||||||||
\(521\) | −8.97945e14 | −1.02481 | −0.512403 | − | 0.858745i | \(-0.671245\pi\) | ||||
−0.512403 | + | 0.858745i | \(0.671245\pi\) | |||||||
\(522\) | 4.60728e14 | 0.520303 | ||||||||
\(523\) | 5.23369e14 | 0.584855 | 0.292428 | − | 0.956288i | \(-0.405537\pi\) | ||||
0.292428 | + | 0.956288i | \(0.405537\pi\) | |||||||
\(524\) | 1.03706e15 | 1.14679 | ||||||||
\(525\) | −5.35278e14 | −0.585737 | ||||||||
\(526\) | −9.19125e14 | −0.995298 | ||||||||
\(527\) | 7.31099e13 | 0.0783462 | ||||||||
\(528\) | −1.17317e15 | −1.24415 | ||||||||
\(529\) | −9.43102e14 | −0.989811 | ||||||||
\(530\) | 1.07777e15 | 1.11946 | ||||||||
\(531\) | −4.22156e13 | −0.0433963 | ||||||||
\(532\) | −6.02227e14 | −0.612698 | ||||||||
\(533\) | −1.13833e15 | −1.14622 | ||||||||
\(534\) | −4.75558e14 | −0.473943 | ||||||||
\(535\) | 5.63013e14 | 0.555357 | ||||||||
\(536\) | 6.74551e14 | 0.658580 | ||||||||
\(537\) | −3.19000e14 | −0.308271 | ||||||||
\(538\) | 1.22395e15 | 1.17075 | ||||||||
\(539\) | 1.28905e15 | 1.22048 | ||||||||
\(540\) | −2.26622e14 | −0.212392 | ||||||||
\(541\) | 5.56840e14 | 0.516589 | 0.258295 | − | 0.966066i | \(-0.416839\pi\) | ||||
0.258295 | + | 0.966066i | \(0.416839\pi\) | |||||||
\(542\) | −5.24698e14 | −0.481852 | ||||||||
\(543\) | 3.77283e13 | 0.0342980 | ||||||||
\(544\) | 1.07744e14 | 0.0969614 | ||||||||
\(545\) | −2.19887e14 | −0.195893 | ||||||||
\(546\) | −4.62458e14 | −0.407861 | ||||||||
\(547\) | 6.40584e14 | 0.559301 | 0.279651 | − | 0.960102i | \(-0.409781\pi\) | ||||
0.279651 | + | 0.960102i | \(0.409781\pi\) | |||||||
\(548\) | −1.47060e15 | −1.27117 | ||||||||
\(549\) | 5.96805e14 | 0.510722 | ||||||||
\(550\) | 4.89840e15 | 4.15011 | ||||||||
\(551\) | 2.44495e15 | 2.05086 | ||||||||
\(552\) | 3.11058e13 | 0.0258331 | ||||||||
\(553\) | −1.06392e14 | −0.0874824 | ||||||||
\(554\) | 7.33623e13 | 0.0597268 | ||||||||
\(555\) | 2.24219e15 | 1.80743 | ||||||||
\(556\) | −1.51455e14 | −0.120885 | ||||||||
\(557\) | 4.05693e14 | 0.320623 | 0.160311 | − | 0.987067i | \(-0.448750\pi\) | ||||
0.160311 | + | 0.987067i | \(0.448750\pi\) | |||||||
\(558\) | −5.02150e14 | −0.392957 | ||||||||
\(559\) | 1.49888e15 | 1.16145 | ||||||||
\(560\) | −1.48729e15 | −1.14120 | ||||||||
\(561\) | 1.14223e14 | 0.0867874 | ||||||||
\(562\) | 1.60223e15 | 1.20552 | ||||||||
\(563\) | 2.20951e15 | 1.64627 | 0.823134 | − | 0.567847i | \(-0.192223\pi\) | ||||
0.823134 | + | 0.567847i | \(0.192223\pi\) | |||||||
\(564\) | −5.44858e14 | −0.402021 | ||||||||
\(565\) | 5.41162e13 | 0.0395422 | ||||||||
\(566\) | 2.41145e15 | 1.74497 | ||||||||
\(567\) | 8.57302e13 | 0.0614366 | ||||||||
\(568\) | 5.72412e14 | 0.406249 | ||||||||
\(569\) | 8.35343e14 | 0.587148 | 0.293574 | − | 0.955936i | \(-0.405155\pi\) | ||||
0.293574 | + | 0.955936i | \(0.405155\pi\) | |||||||
\(570\) | −3.03736e15 | −2.11439 | ||||||||
\(571\) | 6.77122e14 | 0.466840 | 0.233420 | − | 0.972376i | \(-0.425008\pi\) | ||||
0.233420 | + | 0.972376i | \(0.425008\pi\) | |||||||
\(572\) | 1.67564e15 | 1.14420 | ||||||||
\(573\) | −3.50589e14 | −0.237109 | ||||||||
\(574\) | −1.22595e15 | −0.821218 | ||||||||
\(575\) | −2.79141e14 | −0.185204 | ||||||||
\(576\) | −1.18259e14 | −0.0777158 | ||||||||
\(577\) | −1.07648e15 | −0.700711 | −0.350356 | − | 0.936617i | \(-0.613939\pi\) | ||||
−0.350356 | + | 0.936617i | \(0.613939\pi\) | |||||||
\(578\) | 1.98097e15 | 1.27724 | ||||||||
\(579\) | −1.20889e15 | −0.772066 | ||||||||
\(580\) | −2.11636e15 | −1.33886 | ||||||||
\(581\) | 1.14443e15 | 0.717166 | ||||||||
\(582\) | 1.43026e15 | 0.887848 | ||||||||
\(583\) | 1.47729e15 | 0.908422 | ||||||||
\(584\) | −9.82756e14 | −0.598653 | ||||||||
\(585\) | −9.23509e14 | −0.557293 | ||||||||
\(586\) | −1.35359e14 | −0.0809192 | ||||||||
\(587\) | −1.69997e15 | −1.00677 | −0.503385 | − | 0.864062i | \(-0.667912\pi\) | ||||
−0.503385 | + | 0.864062i | \(0.667912\pi\) | |||||||
\(588\) | 4.47815e14 | 0.262738 | ||||||||
\(589\) | −2.66477e15 | −1.54891 | ||||||||
\(590\) | 4.89761e14 | 0.282032 | ||||||||
\(591\) | 8.39196e14 | 0.478776 | ||||||||
\(592\) | 4.03235e15 | 2.27923 | ||||||||
\(593\) | −1.76484e15 | −0.988333 | −0.494167 | − | 0.869367i | \(-0.664527\pi\) | ||||
−0.494167 | + | 0.869367i | \(0.664527\pi\) | |||||||
\(594\) | −7.84530e14 | −0.435295 | ||||||||
\(595\) | 1.44807e14 | 0.0796059 | ||||||||
\(596\) | −1.21644e15 | −0.662577 | ||||||||
\(597\) | −5.59561e14 | −0.301987 | ||||||||
\(598\) | −2.41166e14 | −0.128961 | ||||||||
\(599\) | −3.07963e15 | −1.63174 | −0.815869 | − | 0.578237i | \(-0.803741\pi\) | ||||
−0.815869 | + | 0.578237i | \(0.803741\pi\) | |||||||
\(600\) | −8.94431e14 | −0.469586 | ||||||||
\(601\) | −8.80163e14 | −0.457882 | −0.228941 | − | 0.973440i | \(-0.573526\pi\) | ||||
−0.228941 | + | 0.973440i | \(0.573526\pi\) | |||||||
\(602\) | 1.61425e15 | 0.832126 | ||||||||
\(603\) | 9.69506e14 | 0.495228 | ||||||||
\(604\) | 4.49550e14 | 0.227549 | ||||||||
\(605\) | 7.01679e15 | 3.51952 | ||||||||
\(606\) | 1.39519e15 | 0.693478 | ||||||||
\(607\) | −7.46375e14 | −0.367637 | −0.183819 | − | 0.982960i | \(-0.558846\pi\) | ||||
−0.183819 | + | 0.982960i | \(0.558846\pi\) | |||||||
\(608\) | −3.92714e15 | −1.91693 | ||||||||
\(609\) | 8.00609e14 | 0.387280 | ||||||||
\(610\) | −6.92379e15 | −3.31917 | ||||||||
\(611\) | −2.22035e15 | −1.05486 | ||||||||
\(612\) | 3.96808e13 | 0.0186830 | ||||||||
\(613\) | 9.96720e14 | 0.465094 | 0.232547 | − | 0.972585i | \(-0.425294\pi\) | ||||
0.232547 | + | 0.972585i | \(0.425294\pi\) | |||||||
\(614\) | 3.55586e15 | 1.64444 | ||||||||
\(615\) | −2.44818e15 | −1.12210 | ||||||||
\(616\) | −9.48528e14 | −0.430880 | ||||||||
\(617\) | 1.97496e15 | 0.889180 | 0.444590 | − | 0.895734i | \(-0.353349\pi\) | ||||
0.444590 | + | 0.895734i | \(0.353349\pi\) | |||||||
\(618\) | −3.78070e13 | −0.0168708 | ||||||||
\(619\) | 1.46186e15 | 0.646556 | 0.323278 | − | 0.946304i | \(-0.395215\pi\) | ||||
0.323278 | + | 0.946304i | \(0.395215\pi\) | |||||||
\(620\) | 2.30663e15 | 1.01117 | ||||||||
\(621\) | 4.47072e13 | 0.0194256 | ||||||||
\(622\) | 1.64245e15 | 0.707365 | ||||||||
\(623\) | −8.26379e14 | −0.352773 | ||||||||
\(624\) | −1.66083e15 | −0.702766 | ||||||||
\(625\) | 1.26779e15 | 0.531750 | ||||||||
\(626\) | 2.90746e15 | 1.20880 | ||||||||
\(627\) | −4.16328e15 | −1.71579 | ||||||||
\(628\) | 1.66136e15 | 0.678714 | ||||||||
\(629\) | −3.92600e14 | −0.158991 | ||||||||
\(630\) | −9.94594e14 | −0.399276 | ||||||||
\(631\) | −1.71105e15 | −0.680929 | −0.340464 | − | 0.940257i | \(-0.610584\pi\) | ||||
−0.340464 | + | 0.940257i | \(0.610584\pi\) | |||||||
\(632\) | −1.77778e14 | −0.0701347 | ||||||||
\(633\) | −2.72213e15 | −1.06461 | ||||||||
\(634\) | 1.31732e15 | 0.510740 | ||||||||
\(635\) | 4.29379e14 | 0.165038 | ||||||||
\(636\) | 5.13208e14 | 0.195560 | ||||||||
\(637\) | 1.82489e15 | 0.689398 | ||||||||
\(638\) | −7.32649e15 | −2.74399 | ||||||||
\(639\) | 8.22705e14 | 0.305485 | ||||||||
\(640\) | −3.81411e15 | −1.40412 | ||||||||
\(641\) | 1.88928e15 | 0.689570 | 0.344785 | − | 0.938682i | \(-0.387952\pi\) | ||||
0.344785 | + | 0.938682i | \(0.387952\pi\) | |||||||
\(642\) | 6.77100e14 | 0.245025 | ||||||||
\(643\) | 7.12649e14 | 0.255691 | 0.127845 | − | 0.991794i | \(-0.459194\pi\) | ||||
0.127845 | + | 0.991794i | \(0.459194\pi\) | |||||||
\(644\) | −1.02838e14 | −0.0365832 | ||||||||
\(645\) | 3.22358e15 | 1.13700 | ||||||||
\(646\) | 5.31831e14 | 0.185992 | ||||||||
\(647\) | −4.01542e15 | −1.39238 | −0.696189 | − | 0.717858i | \(-0.745122\pi\) | ||||
−0.696189 | + | 0.717858i | \(0.745122\pi\) | |||||||
\(648\) | 1.43252e14 | 0.0492537 | ||||||||
\(649\) | 6.71312e14 | 0.228865 | ||||||||
\(650\) | 6.93459e15 | 2.34422 | ||||||||
\(651\) | −8.72589e14 | −0.292492 | ||||||||
\(652\) | 2.07544e15 | 0.689839 | ||||||||
\(653\) | −4.19924e15 | −1.38404 | −0.692019 | − | 0.721879i | \(-0.743279\pi\) | ||||
−0.692019 | + | 0.721879i | \(0.743279\pi\) | |||||||
\(654\) | −2.64444e14 | −0.0864284 | ||||||||
\(655\) | 9.08899e15 | 2.94570 | ||||||||
\(656\) | −4.40279e15 | −1.41500 | ||||||||
\(657\) | −1.41248e15 | −0.450165 | ||||||||
\(658\) | −2.39126e15 | −0.755760 | ||||||||
\(659\) | 2.44602e14 | 0.0766638 | 0.0383319 | − | 0.999265i | \(-0.487796\pi\) | ||||
0.0383319 | + | 0.999265i | \(0.487796\pi\) | |||||||
\(660\) | 3.60375e15 | 1.12012 | ||||||||
\(661\) | −5.05315e15 | −1.55759 | −0.778797 | − | 0.627276i | \(-0.784170\pi\) | ||||
−0.778797 | + | 0.627276i | \(0.784170\pi\) | |||||||
\(662\) | −1.51589e15 | −0.463392 | ||||||||
\(663\) | 1.61703e14 | 0.0490224 | ||||||||
\(664\) | 1.91230e15 | 0.574952 | ||||||||
\(665\) | −5.27803e15 | −1.57381 | ||||||||
\(666\) | 2.69655e15 | 0.797443 | ||||||||
\(667\) | 4.17507e14 | 0.122454 | ||||||||
\(668\) | 3.14854e15 | 0.915880 | ||||||||
\(669\) | 1.24485e15 | 0.359148 | ||||||||
\(670\) | −1.12477e16 | −3.21848 | ||||||||
\(671\) | −9.49039e15 | −2.69346 | ||||||||
\(672\) | −1.28596e15 | −0.361989 | ||||||||
\(673\) | 4.82571e15 | 1.34734 | 0.673672 | − | 0.739031i | \(-0.264716\pi\) | ||||
0.673672 | + | 0.739031i | \(0.264716\pi\) | |||||||
\(674\) | −4.30660e15 | −1.19263 | ||||||||
\(675\) | −1.28553e15 | −0.353112 | ||||||||
\(676\) | −3.36399e13 | −0.00916532 | ||||||||
\(677\) | 6.51006e14 | 0.175933 | 0.0879664 | − | 0.996123i | \(-0.471963\pi\) | ||||
0.0879664 | + | 0.996123i | \(0.471963\pi\) | |||||||
\(678\) | 6.50822e13 | 0.0174461 | ||||||||
\(679\) | 2.48537e15 | 0.660857 | ||||||||
\(680\) | 2.41967e14 | 0.0638201 | ||||||||
\(681\) | 9.41445e14 | 0.246312 | ||||||||
\(682\) | 7.98519e15 | 2.07239 | ||||||||
\(683\) | 1.40170e14 | 0.0360863 | 0.0180432 | − | 0.999837i | \(-0.494256\pi\) | ||||
0.0180432 | + | 0.999837i | \(0.494256\pi\) | |||||||
\(684\) | −1.44632e15 | −0.369365 | ||||||||
\(685\) | −1.28887e16 | −3.26520 | ||||||||
\(686\) | 4.79619e15 | 1.20535 | ||||||||
\(687\) | −1.62299e15 | −0.404625 | ||||||||
\(688\) | 5.79728e15 | 1.43380 | ||||||||
\(689\) | 2.09137e15 | 0.513128 | ||||||||
\(690\) | −5.18668e14 | −0.126247 | ||||||||
\(691\) | −3.29282e15 | −0.795131 | −0.397566 | − | 0.917574i | \(-0.630145\pi\) | ||||
−0.397566 | + | 0.917574i | \(0.630145\pi\) | |||||||
\(692\) | −2.92974e15 | −0.701852 | ||||||||
\(693\) | −1.36328e15 | −0.324006 | ||||||||
\(694\) | 2.93025e15 | 0.690920 | ||||||||
\(695\) | −1.32738e15 | −0.310511 | ||||||||
\(696\) | 1.33779e15 | 0.310483 | ||||||||
\(697\) | 4.28667e14 | 0.0987052 | ||||||||
\(698\) | −7.18597e15 | −1.64165 | ||||||||
\(699\) | −4.31452e14 | −0.0977931 | ||||||||
\(700\) | 2.95705e15 | 0.664997 | ||||||||
\(701\) | −1.08970e15 | −0.243140 | −0.121570 | − | 0.992583i | \(-0.538793\pi\) | ||||
−0.121570 | + | 0.992583i | \(0.538793\pi\) | |||||||
\(702\) | −1.11065e15 | −0.245879 | ||||||||
\(703\) | 1.43098e16 | 3.14326 | ||||||||
\(704\) | 1.88055e15 | 0.409859 | ||||||||
\(705\) | −4.77524e15 | −1.03265 | ||||||||
\(706\) | 7.54342e15 | 1.61861 | ||||||||
\(707\) | 2.42442e15 | 0.516181 | ||||||||
\(708\) | 2.33213e14 | 0.0492685 | ||||||||
\(709\) | 2.16098e15 | 0.452998 | 0.226499 | − | 0.974011i | \(-0.427272\pi\) | ||||
0.226499 | + | 0.974011i | \(0.427272\pi\) | |||||||
\(710\) | −9.54456e15 | −1.98534 | ||||||||
\(711\) | −2.55513e14 | −0.0527387 | ||||||||
\(712\) | −1.38085e15 | −0.282818 | ||||||||
\(713\) | −4.55044e14 | −0.0924828 | ||||||||
\(714\) | 1.74150e14 | 0.0351223 | ||||||||
\(715\) | 1.46856e16 | 2.93907 | ||||||||
\(716\) | 1.76226e15 | 0.349985 | ||||||||
\(717\) | −1.77781e15 | −0.350373 | ||||||||
\(718\) | −8.48972e15 | −1.66039 | ||||||||
\(719\) | 2.61328e15 | 0.507197 | 0.253598 | − | 0.967310i | \(-0.418386\pi\) | ||||
0.253598 | + | 0.967310i | \(0.418386\pi\) | |||||||
\(720\) | −3.57190e15 | −0.687972 | ||||||||
\(721\) | −6.56975e13 | −0.0125576 | ||||||||
\(722\) | −1.26017e16 | −2.39042 | ||||||||
\(723\) | −4.43994e15 | −0.835828 | ||||||||
\(724\) | −2.08424e14 | −0.0389390 | ||||||||
\(725\) | −1.20052e16 | −2.22592 | ||||||||
\(726\) | 8.43866e15 | 1.55282 | ||||||||
\(727\) | −2.19187e15 | −0.400291 | −0.200145 | − | 0.979766i | \(-0.564141\pi\) | ||||
−0.200145 | + | 0.979766i | \(0.564141\pi\) | |||||||
\(728\) | −1.34282e15 | −0.243385 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 1.63868e16 | 2.92562 | ||||||||
\(731\) | −5.64438e14 | −0.100016 | ||||||||
\(732\) | −3.29695e15 | −0.579831 | ||||||||
\(733\) | 4.76089e15 | 0.831029 | 0.415514 | − | 0.909587i | \(-0.363602\pi\) | ||||
0.415514 | + | 0.909587i | \(0.363602\pi\) | |||||||
\(734\) | −1.13529e16 | −1.96687 | ||||||||
\(735\) | 3.92474e15 | 0.674886 | ||||||||
\(736\) | −6.70610e14 | −0.114457 | ||||||||
\(737\) | −1.54171e16 | −2.61175 | ||||||||
\(738\) | −2.94427e15 | −0.495071 | ||||||||
\(739\) | −6.71737e15 | −1.12113 | −0.560563 | − | 0.828112i | \(-0.689415\pi\) | ||||
−0.560563 | + | 0.828112i | \(0.689415\pi\) | |||||||
\(740\) | −1.23866e16 | −2.05201 | ||||||||
\(741\) | −5.89389e15 | −0.969175 | ||||||||
\(742\) | 2.25235e15 | 0.367633 | ||||||||
\(743\) | −1.05977e16 | −1.71702 | −0.858508 | − | 0.512801i | \(-0.828608\pi\) | ||||
−0.858508 | + | 0.512801i | \(0.828608\pi\) | |||||||
\(744\) | −1.45807e15 | −0.234491 | ||||||||
\(745\) | −1.06611e16 | −1.70193 | ||||||||
\(746\) | −1.10433e16 | −1.74998 | ||||||||
\(747\) | 2.74848e15 | 0.432343 | ||||||||
\(748\) | −6.31004e14 | −0.0985311 | ||||||||
\(749\) | 1.17660e15 | 0.182381 | ||||||||
\(750\) | 6.78570e15 | 1.04414 | ||||||||
\(751\) | 6.75467e15 | 1.03177 | 0.515887 | − | 0.856657i | \(-0.327462\pi\) | ||||
0.515887 | + | 0.856657i | \(0.327462\pi\) | |||||||
\(752\) | −8.58777e15 | −1.30221 | ||||||||
\(753\) | 2.37410e15 | 0.357377 | ||||||||
\(754\) | −1.03720e16 | −1.54996 | ||||||||
\(755\) | 3.93994e15 | 0.584496 | ||||||||
\(756\) | −4.73602e14 | −0.0697500 | ||||||||
\(757\) | −1.32539e16 | −1.93783 | −0.968915 | − | 0.247395i | \(-0.920426\pi\) | ||||
−0.968915 | + | 0.247395i | \(0.920426\pi\) | |||||||
\(758\) | 5.36425e15 | 0.778625 | ||||||||
\(759\) | −7.10934e14 | −0.102447 | ||||||||
\(760\) | −8.81942e15 | −1.26173 | ||||||||
\(761\) | 9.80400e15 | 1.39248 | 0.696238 | − | 0.717811i | \(-0.254856\pi\) | ||||
0.696238 | + | 0.717811i | \(0.254856\pi\) | |||||||
\(762\) | 5.16387e14 | 0.0728154 | ||||||||
\(763\) | −4.59526e14 | −0.0643317 | ||||||||
\(764\) | 1.93677e15 | 0.269194 | ||||||||
\(765\) | 3.47770e14 | 0.0479904 | ||||||||
\(766\) | −1.78461e16 | −2.44504 | ||||||||
\(767\) | 9.50366e14 | 0.129276 | ||||||||
\(768\) | −5.58367e15 | −0.754107 | ||||||||
\(769\) | 4.16517e15 | 0.558519 | 0.279259 | − | 0.960216i | \(-0.409911\pi\) | ||||
0.279259 | + | 0.960216i | \(0.409911\pi\) | |||||||
\(770\) | 1.58160e16 | 2.10571 | ||||||||
\(771\) | 8.47917e15 | 1.12087 | ||||||||
\(772\) | 6.67831e15 | 0.876540 | ||||||||
\(773\) | 1.20746e16 | 1.57357 | 0.786784 | − | 0.617228i | \(-0.211745\pi\) | ||||
0.786784 | + | 0.617228i | \(0.211745\pi\) | |||||||
\(774\) | 3.87680e15 | 0.501647 | ||||||||
\(775\) | 1.30845e16 | 1.68112 | ||||||||
\(776\) | 4.15297e15 | 0.529809 | ||||||||
\(777\) | 4.68581e15 | 0.593565 | ||||||||
\(778\) | −7.05015e15 | −0.886769 | ||||||||
\(779\) | −1.56244e16 | −1.95141 | ||||||||
\(780\) | 5.10177e15 | 0.632704 | ||||||||
\(781\) | −1.30827e16 | −1.61107 | ||||||||
\(782\) | 9.08169e13 | 0.0111053 | ||||||||
\(783\) | 1.92276e15 | 0.233472 | ||||||||
\(784\) | 7.05823e15 | 0.851054 | ||||||||
\(785\) | 1.45605e16 | 1.74339 | ||||||||
\(786\) | 1.09308e16 | 1.29965 | ||||||||
\(787\) | −9.66403e15 | −1.14103 | −0.570515 | − | 0.821287i | \(-0.693257\pi\) | ||||
−0.570515 | + | 0.821287i | \(0.693257\pi\) | |||||||
\(788\) | −4.63600e15 | −0.543562 | ||||||||
\(789\) | −3.83579e15 | −0.446613 | ||||||||
\(790\) | 2.96431e15 | 0.342748 | ||||||||
\(791\) | 1.13094e14 | 0.0129858 | ||||||||
\(792\) | −2.27800e15 | −0.259756 | ||||||||
\(793\) | −1.34354e16 | −1.52142 | ||||||||
\(794\) | −1.50435e16 | −1.69175 | ||||||||
\(795\) | 4.49785e15 | 0.502326 | ||||||||
\(796\) | 3.09120e15 | 0.342851 | ||||||||
\(797\) | −5.54146e15 | −0.610385 | −0.305192 | − | 0.952291i | \(-0.598721\pi\) | ||||
−0.305192 | + | 0.952291i | \(0.598721\pi\) | |||||||
\(798\) | −6.34756e15 | −0.694370 | ||||||||
\(799\) | 8.36128e14 | 0.0908375 | ||||||||
\(800\) | 1.92830e16 | 2.08056 | ||||||||
\(801\) | −1.98465e15 | −0.212669 | ||||||||
\(802\) | −9.16859e15 | −0.975761 | ||||||||
\(803\) | 2.24612e16 | 2.37409 | ||||||||
\(804\) | −5.35588e15 | −0.562241 | ||||||||
\(805\) | −9.01292e14 | −0.0939698 | ||||||||
\(806\) | 1.13045e16 | 1.17060 | ||||||||
\(807\) | 5.10793e15 | 0.525340 | ||||||||
\(808\) | 4.05113e15 | 0.413822 | ||||||||
\(809\) | 1.54128e16 | 1.56374 | 0.781871 | − | 0.623440i | \(-0.214265\pi\) | ||||
0.781871 | + | 0.623440i | \(0.214265\pi\) | |||||||
\(810\) | −2.38863e15 | −0.240703 | ||||||||
\(811\) | 5.36186e15 | 0.536662 | 0.268331 | − | 0.963327i | \(-0.413528\pi\) | ||||
0.268331 | + | 0.963327i | \(0.413528\pi\) | |||||||
\(812\) | −4.42283e15 | −0.439686 | ||||||||
\(813\) | −2.18972e15 | −0.216218 | ||||||||
\(814\) | −4.28805e16 | −4.20558 | ||||||||
\(815\) | 1.81895e16 | 1.77196 | ||||||||
\(816\) | 6.25428e14 | 0.0605175 | ||||||||
\(817\) | 2.05731e16 | 1.97733 | ||||||||
\(818\) | −4.85005e14 | −0.0463023 | ||||||||
\(819\) | −1.92998e15 | −0.183017 | ||||||||
\(820\) | 1.35245e16 | 1.27393 | ||||||||
\(821\) | −6.85834e15 | −0.641699 | −0.320850 | − | 0.947130i | \(-0.603968\pi\) | ||||
−0.320850 | + | 0.947130i | \(0.603968\pi\) | |||||||
\(822\) | −1.55004e16 | −1.44061 | ||||||||
\(823\) | −1.33875e16 | −1.23595 | −0.617973 | − | 0.786200i | \(-0.712046\pi\) | ||||
−0.617973 | + | 0.786200i | \(0.712046\pi\) | |||||||
\(824\) | −1.09778e14 | −0.0100674 | ||||||||
\(825\) | 2.04425e16 | 1.86225 | ||||||||
\(826\) | 1.02352e15 | 0.0926200 | ||||||||
\(827\) | 1.11449e16 | 1.00183 | 0.500915 | − | 0.865496i | \(-0.332997\pi\) | ||||
0.500915 | + | 0.865496i | \(0.332997\pi\) | |||||||
\(828\) | −2.46978e14 | −0.0220542 | ||||||||
\(829\) | −4.45261e15 | −0.394971 | −0.197485 | − | 0.980306i | \(-0.563277\pi\) | ||||
−0.197485 | + | 0.980306i | \(0.563277\pi\) | |||||||
\(830\) | −3.18863e16 | −2.80979 | ||||||||
\(831\) | 3.06163e14 | 0.0268008 | ||||||||
\(832\) | 2.66226e15 | 0.231512 | ||||||||
\(833\) | −6.87208e14 | −0.0593664 | ||||||||
\(834\) | −1.59635e15 | −0.136998 | ||||||||
\(835\) | 2.75944e16 | 2.35258 | ||||||||
\(836\) | 2.29994e16 | 1.94797 | ||||||||
\(837\) | −2.09562e15 | −0.176329 | ||||||||
\(838\) | 2.53348e16 | 2.11775 | ||||||||
\(839\) | 9.72331e15 | 0.807465 | 0.403732 | − | 0.914877i | \(-0.367713\pi\) | ||||
0.403732 | + | 0.914877i | \(0.367713\pi\) | |||||||
\(840\) | −2.88795e15 | −0.238261 | ||||||||
\(841\) | 5.75554e15 | 0.471746 | ||||||||
\(842\) | 6.00178e15 | 0.488724 | ||||||||
\(843\) | 6.68659e15 | 0.540945 | ||||||||
\(844\) | 1.50380e16 | 1.20866 | ||||||||
\(845\) | −2.94826e14 | −0.0235426 | ||||||||
\(846\) | −5.74288e15 | −0.455610 | ||||||||
\(847\) | 1.46639e16 | 1.15582 | ||||||||
\(848\) | 8.08891e15 | 0.633450 | ||||||||
\(849\) | 1.00637e16 | 0.783007 | ||||||||
\(850\) | −2.61139e15 | −0.201868 | ||||||||
\(851\) | 2.44359e15 | 0.187679 | ||||||||
\(852\) | −4.54490e15 | −0.346822 | ||||||||
\(853\) | 1.55174e16 | 1.17652 | 0.588259 | − | 0.808672i | \(-0.299813\pi\) | ||||
0.588259 | + | 0.808672i | \(0.299813\pi\) | |||||||
\(854\) | −1.44695e16 | −1.09003 | ||||||||
\(855\) | −1.26758e16 | −0.948773 | ||||||||
\(856\) | 1.96606e15 | 0.146215 | ||||||||
\(857\) | −6.29204e15 | −0.464940 | −0.232470 | − | 0.972604i | \(-0.574681\pi\) | ||||
−0.232470 | + | 0.972604i | \(0.574681\pi\) | |||||||
\(858\) | 1.76615e16 | 1.29672 | ||||||||
\(859\) | −1.13138e16 | −0.825365 | −0.412683 | − | 0.910875i | \(-0.635408\pi\) | ||||
−0.412683 | + | 0.910875i | \(0.635408\pi\) | |||||||
\(860\) | −1.78082e16 | −1.29086 | ||||||||
\(861\) | −5.11627e15 | −0.368499 | ||||||||
\(862\) | 1.61989e16 | 1.15930 | ||||||||
\(863\) | 2.82180e15 | 0.200663 | 0.100331 | − | 0.994954i | \(-0.468010\pi\) | ||||
0.100331 | + | 0.994954i | \(0.468010\pi\) | |||||||
\(864\) | −3.08838e15 | −0.218225 | ||||||||
\(865\) | −2.56768e16 | −1.80282 | ||||||||
\(866\) | −3.53660e16 | −2.46739 | ||||||||
\(867\) | 8.26718e15 | 0.573129 | ||||||||
\(868\) | 4.82047e15 | 0.332071 | ||||||||
\(869\) | 4.06316e15 | 0.278135 | ||||||||
\(870\) | −2.23067e16 | −1.51733 | ||||||||
\(871\) | −2.18257e16 | −1.47526 | ||||||||
\(872\) | −7.67853e14 | −0.0515748 | ||||||||
\(873\) | 5.96891e15 | 0.398398 | ||||||||
\(874\) | −3.31017e15 | −0.219552 | ||||||||
\(875\) | 1.17915e16 | 0.777189 | ||||||||
\(876\) | 7.80300e15 | 0.511080 | ||||||||
\(877\) | 1.46198e16 | 0.951574 | 0.475787 | − | 0.879561i | \(-0.342163\pi\) | ||||
0.475787 | + | 0.879561i | \(0.342163\pi\) | |||||||
\(878\) | 1.13048e16 | 0.731211 | ||||||||
\(879\) | −5.64896e14 | −0.0363103 | ||||||||
\(880\) | 5.68004e16 | 3.62825 | ||||||||
\(881\) | 2.16330e16 | 1.37325 | 0.686624 | − | 0.727013i | \(-0.259092\pi\) | ||||
0.686624 | + | 0.727013i | \(0.259092\pi\) | |||||||
\(882\) | 4.72003e15 | 0.297761 | ||||||||
\(883\) | 2.11487e16 | 1.32587 | 0.662933 | − | 0.748679i | \(-0.269311\pi\) | ||||
0.662933 | + | 0.748679i | \(0.269311\pi\) | |||||||
\(884\) | −8.93303e14 | −0.0556559 | ||||||||
\(885\) | 2.04392e15 | 0.126554 | ||||||||
\(886\) | −1.77023e16 | −1.08929 | ||||||||
\(887\) | 1.97250e16 | 1.20625 | 0.603124 | − | 0.797648i | \(-0.293923\pi\) | ||||
0.603124 | + | 0.797648i | \(0.293923\pi\) | |||||||
\(888\) | 7.82982e15 | 0.475862 | ||||||||
\(889\) | 8.97329e14 | 0.0541991 | ||||||||
\(890\) | 2.30247e16 | 1.38213 | ||||||||
\(891\) | −3.27408e15 | −0.195327 | ||||||||
\(892\) | −6.87697e15 | −0.407747 | ||||||||
\(893\) | −3.04759e16 | −1.79586 | ||||||||
\(894\) | −1.28214e16 | −0.750898 | ||||||||
\(895\) | 1.54448e16 | 0.898992 | ||||||||
\(896\) | −7.97084e15 | −0.461116 | ||||||||
\(897\) | −1.00646e15 | −0.0578679 | ||||||||
\(898\) | 2.09259e16 | 1.19581 | ||||||||
\(899\) | −1.95704e16 | −1.11153 | ||||||||
\(900\) | 7.10171e15 | 0.400893 | ||||||||
\(901\) | −7.87557e14 | −0.0441871 | ||||||||
\(902\) | 4.68198e16 | 2.61092 | ||||||||
\(903\) | 6.73674e15 | 0.373394 | ||||||||
\(904\) | 1.88976e14 | 0.0104107 | ||||||||
\(905\) | −1.82667e15 | −0.100021 | ||||||||
\(906\) | 4.73832e15 | 0.257881 | ||||||||
\(907\) | 3.73802e15 | 0.202209 | 0.101105 | − | 0.994876i | \(-0.467762\pi\) | ||||
0.101105 | + | 0.994876i | \(0.467762\pi\) | |||||||
\(908\) | −5.20086e15 | −0.279642 | ||||||||
\(909\) | 5.82253e15 | 0.311179 | ||||||||
\(910\) | 2.23905e16 | 1.18942 | ||||||||
\(911\) | −1.90655e16 | −1.00669 | −0.503346 | − | 0.864085i | \(-0.667898\pi\) | ||||
−0.503346 | + | 0.864085i | \(0.667898\pi\) | |||||||
\(912\) | −2.27961e16 | −1.19644 | ||||||||
\(913\) | −4.37063e16 | −2.28010 | ||||||||
\(914\) | −2.22459e15 | −0.115357 | ||||||||
\(915\) | −2.88951e16 | −1.48939 | ||||||||
\(916\) | 8.96591e15 | 0.459377 | ||||||||
\(917\) | 1.89945e16 | 0.967376 | ||||||||
\(918\) | 4.18241e14 | 0.0211735 | ||||||||
\(919\) | 9.20979e15 | 0.463462 | 0.231731 | − | 0.972780i | \(-0.425561\pi\) | ||||
0.231731 | + | 0.972780i | \(0.425561\pi\) | |||||||
\(920\) | −1.50603e15 | −0.0753356 | ||||||||
\(921\) | 1.48397e16 | 0.737899 | ||||||||
\(922\) | 1.58222e16 | 0.782070 | ||||||||
\(923\) | −1.85209e16 | −0.910025 | ||||||||
\(924\) | 7.53123e15 | 0.367849 | ||||||||
\(925\) | −7.02640e16 | −3.41156 | ||||||||
\(926\) | 1.27428e16 | 0.615040 | ||||||||
\(927\) | −1.57780e14 | −0.00757032 | ||||||||
\(928\) | −2.88414e16 | −1.37563 | ||||||||
\(929\) | −3.45766e16 | −1.63944 | −0.819721 | − | 0.572762i | \(-0.805872\pi\) | ||||
−0.819721 | + | 0.572762i | \(0.805872\pi\) | |||||||
\(930\) | 2.43123e16 | 1.14596 | ||||||||
\(931\) | 2.50479e16 | 1.17368 | ||||||||
\(932\) | 2.38349e15 | 0.111026 | ||||||||
\(933\) | 6.85442e15 | 0.317411 | ||||||||
\(934\) | −1.65613e16 | −0.762407 | ||||||||
\(935\) | −5.53024e15 | −0.253093 | ||||||||
\(936\) | −3.22493e15 | −0.146725 | ||||||||
\(937\) | −1.44218e16 | −0.652309 | −0.326154 | − | 0.945317i | \(-0.605753\pi\) | ||||
−0.326154 | + | 0.945317i | \(0.605753\pi\) | |||||||
\(938\) | −2.35057e16 | −1.05696 | ||||||||
\(939\) | 1.21337e16 | 0.542416 | ||||||||
\(940\) | 2.63800e16 | 1.17239 | ||||||||
\(941\) | −2.61042e16 | −1.15337 | −0.576684 | − | 0.816967i | \(-0.695654\pi\) | ||||
−0.576684 | + | 0.816967i | \(0.695654\pi\) | |||||||
\(942\) | 1.75110e16 | 0.769186 | ||||||||
\(943\) | −2.66807e15 | −0.116515 | ||||||||
\(944\) | 3.67578e15 | 0.159589 | ||||||||
\(945\) | −4.15074e15 | −0.179164 | ||||||||
\(946\) | −6.16489e16 | −2.64560 | ||||||||
\(947\) | −6.66470e15 | −0.284352 | −0.142176 | − | 0.989841i | \(-0.545410\pi\) | ||||
−0.142176 | + | 0.989841i | \(0.545410\pi\) | |||||||
\(948\) | 1.41154e15 | 0.0598752 | ||||||||
\(949\) | 3.17980e16 | 1.34102 | ||||||||
\(950\) | 9.51822e16 | 3.99095 | ||||||||
\(951\) | 5.49757e15 | 0.229181 | ||||||||
\(952\) | 5.05670e14 | 0.0209587 | ||||||||
\(953\) | 9.43610e15 | 0.388849 | 0.194425 | − | 0.980917i | \(-0.437716\pi\) | ||||
0.194425 | + | 0.980917i | \(0.437716\pi\) | |||||||
\(954\) | 5.40928e15 | 0.221627 | ||||||||
\(955\) | 1.69742e16 | 0.691468 | ||||||||
\(956\) | 9.82122e15 | 0.397784 | ||||||||
\(957\) | −3.05757e16 | −1.23129 | ||||||||
\(958\) | −2.58158e16 | −1.03365 | ||||||||
\(959\) | −2.69351e16 | −1.07230 | ||||||||
\(960\) | 5.72565e15 | 0.226638 | ||||||||
\(961\) | −4.07855e15 | −0.160519 | ||||||||
\(962\) | −6.07052e16 | −2.37554 | ||||||||
\(963\) | 2.82574e15 | 0.109948 | ||||||||
\(964\) | 2.45277e16 | 0.948929 | ||||||||
\(965\) | 5.85300e16 | 2.25153 | ||||||||
\(966\) | −1.08393e15 | −0.0414597 | ||||||||
\(967\) | −1.99274e16 | −0.757889 | −0.378945 | − | 0.925419i | \(-0.623713\pi\) | ||||
−0.378945 | + | 0.925419i | \(0.623713\pi\) | |||||||
\(968\) | 2.45029e16 | 0.926623 | ||||||||
\(969\) | 2.21949e15 | 0.0834589 | ||||||||
\(970\) | −6.92479e16 | −2.58918 | ||||||||
\(971\) | −2.18003e16 | −0.810506 | −0.405253 | − | 0.914205i | \(-0.632817\pi\) | ||||
−0.405253 | + | 0.914205i | \(0.632817\pi\) | |||||||
\(972\) | −1.13741e15 | −0.0420488 | ||||||||
\(973\) | −2.77399e15 | −0.101973 | ||||||||
\(974\) | −5.28420e16 | −1.93155 | ||||||||
\(975\) | 2.89402e16 | 1.05190 | ||||||||
\(976\) | −5.19647e16 | −1.87817 | ||||||||
\(977\) | −1.26115e16 | −0.453259 | −0.226630 | − | 0.973981i | \(-0.572771\pi\) | ||||
−0.226630 | + | 0.973981i | \(0.572771\pi\) | |||||||
\(978\) | 2.18754e16 | 0.781794 | ||||||||
\(979\) | 3.15598e16 | 1.12158 | ||||||||
\(980\) | −2.16816e16 | −0.766209 | ||||||||
\(981\) | −1.10361e15 | −0.0387824 | ||||||||
\(982\) | −3.47056e16 | −1.21279 | ||||||||
\(983\) | 2.69450e16 | 0.936342 | 0.468171 | − | 0.883638i | \(-0.344913\pi\) | ||||
0.468171 | + | 0.883638i | \(0.344913\pi\) | |||||||
\(984\) | −8.54912e15 | −0.295426 | ||||||||
\(985\) | −4.06307e16 | −1.39623 | ||||||||
\(986\) | 3.90583e15 | 0.133472 | ||||||||
\(987\) | −9.97944e15 | −0.339127 | ||||||||
\(988\) | 3.25598e16 | 1.10032 | ||||||||
\(989\) | 3.51313e15 | 0.118063 | ||||||||
\(990\) | 3.79840e16 | 1.26943 | ||||||||
\(991\) | 3.48894e16 | 1.15955 | 0.579774 | − | 0.814777i | \(-0.303141\pi\) | ||||
0.579774 | + | 0.814777i | \(0.303141\pi\) | |||||||
\(992\) | 3.14345e16 | 1.03894 | ||||||||
\(993\) | −6.32626e15 | −0.207934 | ||||||||
\(994\) | −1.99465e16 | −0.651991 | ||||||||
\(995\) | 2.70919e16 | 0.880667 | ||||||||
\(996\) | −1.51835e16 | −0.490846 | ||||||||
\(997\) | −4.49354e15 | −0.144466 | −0.0722329 | − | 0.997388i | \(-0.523013\pi\) | ||||
−0.0722329 | + | 0.997388i | \(0.523013\pi\) | |||||||
\(998\) | 3.81005e16 | 1.21818 | ||||||||
\(999\) | 1.12535e16 | 0.357831 |
(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 | 177.12.a.c.1.7 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.c.1.7 | ✓ | 27 | 1.1 | even | 1 | trivial |