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 | 1.3 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −79.2286 | −1.75072 | −0.875360 | − | 0.483471i | \(-0.839376\pi\) | ||||
−0.875360 | + | 0.483471i | \(0.839376\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | 4229.17 | 2.06502 | ||||||||
\(5\) | 9672.04 | 1.38415 | 0.692075 | − | 0.721825i | \(-0.256697\pi\) | ||||
0.692075 | + | 0.721825i | \(0.256697\pi\) | |||||||
\(6\) | 19252.5 | 1.01078 | ||||||||
\(7\) | 84867.6 | 1.90855 | 0.954273 | − | 0.298935i | \(-0.0966314\pi\) | ||||
0.954273 | + | 0.298935i | \(0.0966314\pi\) | |||||||
\(8\) | −172811. | −1.86456 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −766302. | −2.42326 | ||||||||
\(11\) | 465513. | 0.871510 | 0.435755 | − | 0.900065i | \(-0.356481\pi\) | ||||
0.435755 | + | 0.900065i | \(0.356481\pi\) | |||||||
\(12\) | −1.02769e6 | −1.19224 | ||||||||
\(13\) | 1.10167e6 | 0.822927 | 0.411463 | − | 0.911426i | \(-0.365018\pi\) | ||||
0.411463 | + | 0.911426i | \(0.365018\pi\) | |||||||
\(14\) | −6.72394e6 | −3.34133 | ||||||||
\(15\) | −2.35031e6 | −0.799140 | ||||||||
\(16\) | 5.03021e6 | 1.19930 | ||||||||
\(17\) | −2.02733e6 | −0.346302 | −0.173151 | − | 0.984895i | \(-0.555395\pi\) | ||||
−0.173151 | + | 0.984895i | \(0.555395\pi\) | |||||||
\(18\) | −4.67837e6 | −0.583574 | ||||||||
\(19\) | −5.75353e6 | −0.533076 | −0.266538 | − | 0.963824i | \(-0.585880\pi\) | ||||
−0.266538 | + | 0.963824i | \(0.585880\pi\) | |||||||
\(20\) | 4.09047e7 | 2.85830 | ||||||||
\(21\) | −2.06228e7 | −1.10190 | ||||||||
\(22\) | −3.68820e7 | −1.52577 | ||||||||
\(23\) | 3.68952e6 | 0.119527 | 0.0597636 | − | 0.998213i | \(-0.480965\pi\) | ||||
0.0597636 | + | 0.998213i | \(0.480965\pi\) | |||||||
\(24\) | 4.19930e7 | 1.07650 | ||||||||
\(25\) | 4.47203e7 | 0.915872 | ||||||||
\(26\) | −8.72834e7 | −1.44071 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 3.58919e8 | 3.94119 | ||||||||
\(29\) | 2.53977e7 | 0.229935 | 0.114968 | − | 0.993369i | \(-0.463324\pi\) | ||||
0.114968 | + | 0.993369i | \(0.463324\pi\) | |||||||
\(30\) | 1.86211e8 | 1.39907 | ||||||||
\(31\) | 1.59360e8 | 0.999745 | 0.499873 | − | 0.866099i | \(-0.333380\pi\) | ||||
0.499873 | + | 0.866099i | \(0.333380\pi\) | |||||||
\(32\) | −4.46200e7 | −0.235074 | ||||||||
\(33\) | −1.13120e8 | −0.503167 | ||||||||
\(34\) | 1.60622e8 | 0.606278 | ||||||||
\(35\) | 8.20843e8 | 2.64172 | ||||||||
\(36\) | 2.49728e8 | 0.688341 | ||||||||
\(37\) | 6.00742e7 | 0.142422 | 0.0712112 | − | 0.997461i | \(-0.477314\pi\) | ||||
0.0712112 | + | 0.997461i | \(0.477314\pi\) | |||||||
\(38\) | 4.55844e8 | 0.933268 | ||||||||
\(39\) | −2.67705e8 | −0.475117 | ||||||||
\(40\) | −1.67143e9 | −2.58083 | ||||||||
\(41\) | 1.17324e8 | 0.158152 | 0.0790761 | − | 0.996869i | \(-0.474803\pi\) | ||||
0.0790761 | + | 0.996869i | \(0.474803\pi\) | |||||||
\(42\) | 1.63392e9 | 1.92912 | ||||||||
\(43\) | 1.58206e9 | 1.64114 | 0.820569 | − | 0.571547i | \(-0.193657\pi\) | ||||
0.820569 | + | 0.571547i | \(0.193657\pi\) | |||||||
\(44\) | 1.96873e9 | 1.79969 | ||||||||
\(45\) | 5.71125e8 | 0.461383 | ||||||||
\(46\) | −2.92316e8 | −0.209259 | ||||||||
\(47\) | −2.01137e9 | −1.27925 | −0.639624 | − | 0.768688i | \(-0.720910\pi\) | ||||
−0.639624 | + | 0.768688i | \(0.720910\pi\) | |||||||
\(48\) | −1.22234e9 | −0.692413 | ||||||||
\(49\) | 5.22519e9 | 2.64255 | ||||||||
\(50\) | −3.54313e9 | −1.60344 | ||||||||
\(51\) | 4.92640e8 | 0.199937 | ||||||||
\(52\) | 4.65913e9 | 1.69936 | ||||||||
\(53\) | 3.31605e8 | 0.108919 | 0.0544595 | − | 0.998516i | \(-0.482656\pi\) | ||||
0.0544595 | + | 0.998516i | \(0.482656\pi\) | |||||||
\(54\) | 1.13684e9 | 0.336926 | ||||||||
\(55\) | 4.50247e9 | 1.20630 | ||||||||
\(56\) | −1.46660e10 | −3.55859 | ||||||||
\(57\) | 1.39811e9 | 0.307772 | ||||||||
\(58\) | −2.01222e9 | −0.402552 | ||||||||
\(59\) | −7.14924e8 | −0.130189 | ||||||||
\(60\) | −9.93984e9 | −1.65024 | ||||||||
\(61\) | −8.69345e9 | −1.31789 | −0.658944 | − | 0.752192i | \(-0.728996\pi\) | ||||
−0.658944 | + | 0.752192i | \(0.728996\pi\) | |||||||
\(62\) | −1.26258e10 | −1.75027 | ||||||||
\(63\) | 5.01135e9 | 0.636182 | ||||||||
\(64\) | −6.76669e9 | −0.787746 | ||||||||
\(65\) | 1.06554e10 | 1.13905 | ||||||||
\(66\) | 8.96232e9 | 0.880904 | ||||||||
\(67\) | −3.59954e9 | −0.325714 | −0.162857 | − | 0.986650i | \(-0.552071\pi\) | ||||
−0.162857 | + | 0.986650i | \(0.552071\pi\) | |||||||
\(68\) | −8.57390e9 | −0.715121 | ||||||||
\(69\) | −8.96554e8 | −0.0690091 | ||||||||
\(70\) | −6.50343e10 | −4.62491 | ||||||||
\(71\) | 1.77404e10 | 1.16693 | 0.583463 | − | 0.812140i | \(-0.301697\pi\) | ||||
0.583463 | + | 0.812140i | \(0.301697\pi\) | |||||||
\(72\) | −1.02043e10 | −0.621519 | ||||||||
\(73\) | 9.43622e9 | 0.532749 | 0.266374 | − | 0.963870i | \(-0.414174\pi\) | ||||
0.266374 | + | 0.963870i | \(0.414174\pi\) | |||||||
\(74\) | −4.75959e9 | −0.249342 | ||||||||
\(75\) | −1.08670e10 | −0.528779 | ||||||||
\(76\) | −2.43326e10 | −1.10081 | ||||||||
\(77\) | 3.95070e10 | 1.66332 | ||||||||
\(78\) | 2.12099e10 | 0.831797 | ||||||||
\(79\) | 3.35436e10 | 1.22648 | 0.613240 | − | 0.789897i | \(-0.289866\pi\) | ||||
0.613240 | + | 0.789897i | \(0.289866\pi\) | |||||||
\(80\) | 4.86524e10 | 1.66000 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −9.29540e9 | −0.276880 | ||||||||
\(83\) | −5.21982e10 | −1.45454 | −0.727270 | − | 0.686351i | \(-0.759211\pi\) | ||||
−0.727270 | + | 0.686351i | \(0.759211\pi\) | |||||||
\(84\) | −8.72174e10 | −2.27545 | ||||||||
\(85\) | −1.96084e10 | −0.479334 | ||||||||
\(86\) | −1.25344e11 | −2.87317 | ||||||||
\(87\) | −6.17164e9 | −0.132753 | ||||||||
\(88\) | −8.04457e10 | −1.62498 | ||||||||
\(89\) | 6.06182e10 | 1.15069 | 0.575345 | − | 0.817911i | \(-0.304868\pi\) | ||||
0.575345 | + | 0.817911i | \(0.304868\pi\) | |||||||
\(90\) | −4.52494e10 | −0.807753 | ||||||||
\(91\) | 9.34957e10 | 1.57059 | ||||||||
\(92\) | 1.56036e10 | 0.246826 | ||||||||
\(93\) | −3.87244e10 | −0.577203 | ||||||||
\(94\) | 1.59358e11 | 2.23960 | ||||||||
\(95\) | −5.56484e10 | −0.737858 | ||||||||
\(96\) | 1.08427e10 | 0.135720 | ||||||||
\(97\) | 3.05431e10 | 0.361134 | 0.180567 | − | 0.983563i | \(-0.442207\pi\) | ||||
0.180567 | + | 0.983563i | \(0.442207\pi\) | |||||||
\(98\) | −4.13984e11 | −4.62637 | ||||||||
\(99\) | 2.74881e10 | 0.290503 | ||||||||
\(100\) | 1.89130e11 | 1.89130 | ||||||||
\(101\) | −4.43366e10 | −0.419754 | −0.209877 | − | 0.977728i | \(-0.567306\pi\) | ||||
−0.209877 | + | 0.977728i | \(0.567306\pi\) | |||||||
\(102\) | −3.90312e10 | −0.350034 | ||||||||
\(103\) | −1.25879e11 | −1.06991 | −0.534956 | − | 0.844880i | \(-0.679672\pi\) | ||||
−0.534956 | + | 0.844880i | \(0.679672\pi\) | |||||||
\(104\) | −1.90379e11 | −1.53439 | ||||||||
\(105\) | −1.99465e11 | −1.52520 | ||||||||
\(106\) | −2.62726e10 | −0.190687 | ||||||||
\(107\) | −2.47750e11 | −1.70766 | −0.853832 | − | 0.520549i | \(-0.825727\pi\) | ||||
−0.853832 | + | 0.520549i | \(0.825727\pi\) | |||||||
\(108\) | −6.06839e10 | −0.397414 | ||||||||
\(109\) | 1.58261e11 | 0.985210 | 0.492605 | − | 0.870253i | \(-0.336045\pi\) | ||||
0.492605 | + | 0.870253i | \(0.336045\pi\) | |||||||
\(110\) | −3.56724e11 | −2.11190 | ||||||||
\(111\) | −1.45980e10 | −0.0822276 | ||||||||
\(112\) | 4.26902e11 | 2.28891 | ||||||||
\(113\) | 3.15802e11 | 1.61244 | 0.806220 | − | 0.591616i | \(-0.201510\pi\) | ||||
0.806220 | + | 0.591616i | \(0.201510\pi\) | |||||||
\(114\) | −1.10770e11 | −0.538822 | ||||||||
\(115\) | 3.56852e10 | 0.165444 | ||||||||
\(116\) | 1.07411e11 | 0.474821 | ||||||||
\(117\) | 6.50522e10 | 0.274309 | ||||||||
\(118\) | 5.66424e10 | 0.227924 | ||||||||
\(119\) | −1.72054e11 | −0.660933 | ||||||||
\(120\) | 4.06158e11 | 1.49004 | ||||||||
\(121\) | −6.86090e10 | −0.240470 | ||||||||
\(122\) | 6.88770e11 | 2.30725 | ||||||||
\(123\) | −2.85097e10 | −0.0913092 | ||||||||
\(124\) | 6.73959e11 | 2.06450 | ||||||||
\(125\) | −3.97308e10 | −0.116445 | ||||||||
\(126\) | −3.97042e11 | −1.11378 | ||||||||
\(127\) | 1.92351e11 | 0.516623 | 0.258312 | − | 0.966062i | \(-0.416834\pi\) | ||||
0.258312 | + | 0.966062i | \(0.416834\pi\) | |||||||
\(128\) | 6.27497e11 | 1.61420 | ||||||||
\(129\) | −3.84439e11 | −0.947512 | ||||||||
\(130\) | −8.44209e11 | −1.99417 | ||||||||
\(131\) | −2.14235e11 | −0.485174 | −0.242587 | − | 0.970130i | \(-0.577996\pi\) | ||||
−0.242587 | + | 0.970130i | \(0.577996\pi\) | |||||||
\(132\) | −4.78402e11 | −1.03905 | ||||||||
\(133\) | −4.88288e11 | −1.01740 | ||||||||
\(134\) | 2.85187e11 | 0.570234 | ||||||||
\(135\) | −1.38783e11 | −0.266380 | ||||||||
\(136\) | 3.50344e11 | 0.645699 | ||||||||
\(137\) | 2.55783e11 | 0.452801 | 0.226401 | − | 0.974034i | \(-0.427304\pi\) | ||||
0.226401 | + | 0.974034i | \(0.427304\pi\) | |||||||
\(138\) | 7.10327e10 | 0.120816 | ||||||||
\(139\) | 7.46108e11 | 1.21961 | 0.609804 | − | 0.792552i | \(-0.291248\pi\) | ||||
0.609804 | + | 0.792552i | \(0.291248\pi\) | |||||||
\(140\) | 3.47148e12 | 5.45520 | ||||||||
\(141\) | 4.88764e11 | 0.738574 | ||||||||
\(142\) | −1.40555e12 | −2.04296 | ||||||||
\(143\) | 5.12840e11 | 0.717189 | ||||||||
\(144\) | 2.97029e11 | 0.399765 | ||||||||
\(145\) | 2.45648e11 | 0.318265 | ||||||||
\(146\) | −7.47618e11 | −0.932694 | ||||||||
\(147\) | −1.26972e12 | −1.52568 | ||||||||
\(148\) | 2.54064e11 | 0.294106 | ||||||||
\(149\) | −1.12183e11 | −0.125142 | −0.0625710 | − | 0.998041i | \(-0.519930\pi\) | ||||
−0.0625710 | + | 0.998041i | \(0.519930\pi\) | |||||||
\(150\) | 8.60980e11 | 0.925744 | ||||||||
\(151\) | 1.23881e12 | 1.28419 | 0.642097 | − | 0.766623i | \(-0.278065\pi\) | ||||
0.642097 | + | 0.766623i | \(0.278065\pi\) | |||||||
\(152\) | 9.94271e11 | 0.993951 | ||||||||
\(153\) | −1.19712e11 | −0.115434 | ||||||||
\(154\) | −3.13008e12 | −2.91200 | ||||||||
\(155\) | 1.54133e12 | 1.38380 | ||||||||
\(156\) | −1.13217e12 | −0.981127 | ||||||||
\(157\) | 2.33390e12 | 1.95270 | 0.976348 | − | 0.216206i | \(-0.0693684\pi\) | ||||
0.976348 | + | 0.216206i | \(0.0693684\pi\) | |||||||
\(158\) | −2.65761e12 | −2.14722 | ||||||||
\(159\) | −8.05799e10 | −0.0628844 | ||||||||
\(160\) | −4.31567e11 | −0.325378 | ||||||||
\(161\) | 3.13121e11 | 0.228123 | ||||||||
\(162\) | −2.76253e11 | −0.194525 | ||||||||
\(163\) | −1.13885e12 | −0.775238 | −0.387619 | − | 0.921820i | \(-0.626702\pi\) | ||||
−0.387619 | + | 0.921820i | \(0.626702\pi\) | |||||||
\(164\) | 4.96182e11 | 0.326588 | ||||||||
\(165\) | −1.09410e12 | −0.696458 | ||||||||
\(166\) | 4.13559e12 | 2.54649 | ||||||||
\(167\) | 2.48575e12 | 1.48087 | 0.740436 | − | 0.672127i | \(-0.234619\pi\) | ||||
0.740436 | + | 0.672127i | \(0.234619\pi\) | |||||||
\(168\) | 3.56385e12 | 2.05456 | ||||||||
\(169\) | −5.78494e11 | −0.322791 | ||||||||
\(170\) | 1.55354e12 | 0.839179 | ||||||||
\(171\) | −3.39740e11 | −0.177692 | ||||||||
\(172\) | 6.69077e12 | 3.38899 | ||||||||
\(173\) | −2.18667e12 | −1.07283 | −0.536414 | − | 0.843955i | \(-0.680221\pi\) | ||||
−0.536414 | + | 0.843955i | \(0.680221\pi\) | |||||||
\(174\) | 4.88970e11 | 0.232414 | ||||||||
\(175\) | 3.79531e12 | 1.74799 | ||||||||
\(176\) | 2.34163e12 | 1.04520 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | −4.80269e12 | −2.01454 | ||||||||
\(179\) | −1.47087e12 | −0.598249 | −0.299125 | − | 0.954214i | \(-0.596695\pi\) | ||||
−0.299125 | + | 0.954214i | \(0.596695\pi\) | |||||||
\(180\) | 2.41538e12 | 0.952767 | ||||||||
\(181\) | −4.92496e12 | −1.88439 | −0.942195 | − | 0.335064i | \(-0.891242\pi\) | ||||
−0.942195 | + | 0.335064i | \(0.891242\pi\) | |||||||
\(182\) | −7.40753e12 | −2.74967 | ||||||||
\(183\) | 2.11251e12 | 0.760883 | ||||||||
\(184\) | −6.37589e11 | −0.222865 | ||||||||
\(185\) | 5.81040e11 | 0.197134 | ||||||||
\(186\) | 3.06808e12 | 1.01052 | ||||||||
\(187\) | −9.43748e11 | −0.301805 | ||||||||
\(188\) | −8.50643e12 | −2.64167 | ||||||||
\(189\) | −1.21776e12 | −0.367300 | ||||||||
\(190\) | 4.40894e12 | 1.29178 | ||||||||
\(191\) | −3.46630e12 | −0.986695 | −0.493347 | − | 0.869832i | \(-0.664227\pi\) | ||||
−0.493347 | + | 0.869832i | \(0.664227\pi\) | |||||||
\(192\) | 1.64431e12 | 0.454805 | ||||||||
\(193\) | −9.90934e11 | −0.266366 | −0.133183 | − | 0.991091i | \(-0.542520\pi\) | ||||
−0.133183 | + | 0.991091i | \(0.542520\pi\) | |||||||
\(194\) | −2.41989e12 | −0.632245 | ||||||||
\(195\) | −2.58925e12 | −0.657633 | ||||||||
\(196\) | 2.20982e13 | 5.45693 | ||||||||
\(197\) | −1.24232e12 | −0.298311 | −0.149155 | − | 0.988814i | \(-0.547655\pi\) | ||||
−0.149155 | + | 0.988814i | \(0.547655\pi\) | |||||||
\(198\) | −2.17784e12 | −0.508590 | ||||||||
\(199\) | −2.76684e12 | −0.628481 | −0.314241 | − | 0.949343i | \(-0.601750\pi\) | ||||
−0.314241 | + | 0.949343i | \(0.601750\pi\) | |||||||
\(200\) | −7.72815e12 | −1.70770 | ||||||||
\(201\) | 8.74689e11 | 0.188051 | ||||||||
\(202\) | 3.51273e12 | 0.734872 | ||||||||
\(203\) | 2.15544e12 | 0.438842 | ||||||||
\(204\) | 2.08346e12 | 0.412875 | ||||||||
\(205\) | 1.13476e12 | 0.218906 | ||||||||
\(206\) | 9.97321e12 | 1.87312 | ||||||||
\(207\) | 2.17863e11 | 0.0398424 | ||||||||
\(208\) | 5.54161e12 | 0.986932 | ||||||||
\(209\) | −2.67834e12 | −0.464581 | ||||||||
\(210\) | 1.58033e13 | 2.67019 | ||||||||
\(211\) | 6.86381e12 | 1.12983 | 0.564914 | − | 0.825150i | \(-0.308910\pi\) | ||||
0.564914 | + | 0.825150i | \(0.308910\pi\) | |||||||
\(212\) | 1.40241e12 | 0.224920 | ||||||||
\(213\) | −4.31092e12 | −0.673725 | ||||||||
\(214\) | 1.96288e13 | 2.98964 | ||||||||
\(215\) | 1.53017e13 | 2.27158 | ||||||||
\(216\) | 2.47964e12 | 0.358834 | ||||||||
\(217\) | 1.35245e13 | 1.90806 | ||||||||
\(218\) | −1.25388e13 | −1.72483 | ||||||||
\(219\) | −2.29300e12 | −0.307583 | ||||||||
\(220\) | 1.90417e13 | 2.49104 | ||||||||
\(221\) | −2.23344e12 | −0.284981 | ||||||||
\(222\) | 1.15658e12 | 0.143958 | ||||||||
\(223\) | 1.20175e13 | 1.45928 | 0.729640 | − | 0.683831i | \(-0.239688\pi\) | ||||
0.729640 | + | 0.683831i | \(0.239688\pi\) | |||||||
\(224\) | −3.78679e12 | −0.448650 | ||||||||
\(225\) | 2.64069e12 | 0.305291 | ||||||||
\(226\) | −2.50205e13 | −2.82293 | ||||||||
\(227\) | −6.98874e11 | −0.0769585 | −0.0384792 | − | 0.999259i | \(-0.512251\pi\) | ||||
−0.0384792 | + | 0.999259i | \(0.512251\pi\) | |||||||
\(228\) | 5.91283e12 | 0.635556 | ||||||||
\(229\) | 1.89982e13 | 1.99351 | 0.996753 | − | 0.0805184i | \(-0.0256576\pi\) | ||||
0.996753 | + | 0.0805184i | \(0.0256576\pi\) | |||||||
\(230\) | −2.82729e12 | −0.289646 | ||||||||
\(231\) | −9.60020e12 | −0.960317 | ||||||||
\(232\) | −4.38899e12 | −0.428727 | ||||||||
\(233\) | −1.53061e13 | −1.46018 | −0.730090 | − | 0.683351i | \(-0.760522\pi\) | ||||
−0.730090 | + | 0.683351i | \(0.760522\pi\) | |||||||
\(234\) | −5.15400e12 | −0.480238 | ||||||||
\(235\) | −1.94541e13 | −1.77067 | ||||||||
\(236\) | −3.02353e12 | −0.268843 | ||||||||
\(237\) | −8.15109e12 | −0.708109 | ||||||||
\(238\) | 1.36316e13 | 1.15711 | ||||||||
\(239\) | −2.05455e13 | −1.70423 | −0.852114 | − | 0.523357i | \(-0.824680\pi\) | ||||
−0.852114 | + | 0.523357i | \(0.824680\pi\) | |||||||
\(240\) | −1.18225e13 | −0.958404 | ||||||||
\(241\) | 8.72286e12 | 0.691139 | 0.345570 | − | 0.938393i | \(-0.387686\pi\) | ||||
0.345570 | + | 0.938393i | \(0.387686\pi\) | |||||||
\(242\) | 5.43579e12 | 0.420996 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | −3.67661e13 | −2.72147 | ||||||||
\(245\) | 5.05382e13 | 3.65769 | ||||||||
\(246\) | 2.25878e12 | 0.159857 | ||||||||
\(247\) | −6.33846e12 | −0.438683 | ||||||||
\(248\) | −2.75391e13 | −1.86408 | ||||||||
\(249\) | 1.26842e13 | 0.839779 | ||||||||
\(250\) | 3.14782e12 | 0.203863 | ||||||||
\(251\) | −2.73350e13 | −1.73187 | −0.865933 | − | 0.500160i | \(-0.833275\pi\) | ||||
−0.865933 | + | 0.500160i | \(0.833275\pi\) | |||||||
\(252\) | 2.11938e13 | 1.31373 | ||||||||
\(253\) | 1.71752e12 | 0.104169 | ||||||||
\(254\) | −1.52397e13 | −0.904463 | ||||||||
\(255\) | 4.76484e12 | 0.276743 | ||||||||
\(256\) | −3.58575e13 | −2.03826 | ||||||||
\(257\) | −2.42947e12 | −0.135169 | −0.0675847 | − | 0.997714i | \(-0.521529\pi\) | ||||
−0.0675847 | + | 0.997714i | \(0.521529\pi\) | |||||||
\(258\) | 3.04586e13 | 1.65883 | ||||||||
\(259\) | 5.09835e12 | 0.271820 | ||||||||
\(260\) | 4.50633e13 | 2.35217 | ||||||||
\(261\) | 1.49971e12 | 0.0766451 | ||||||||
\(262\) | 1.69735e13 | 0.849405 | ||||||||
\(263\) | 4.85645e12 | 0.237992 | 0.118996 | − | 0.992895i | \(-0.462032\pi\) | ||||
0.118996 | + | 0.992895i | \(0.462032\pi\) | |||||||
\(264\) | 1.95483e13 | 0.938182 | ||||||||
\(265\) | 3.20730e12 | 0.150760 | ||||||||
\(266\) | 3.86864e13 | 1.78119 | ||||||||
\(267\) | −1.47302e13 | −0.664351 | ||||||||
\(268\) | −1.52231e13 | −0.672606 | ||||||||
\(269\) | −3.64117e13 | −1.57617 | −0.788085 | − | 0.615566i | \(-0.788927\pi\) | ||||
−0.788085 | + | 0.615566i | \(0.788927\pi\) | |||||||
\(270\) | 1.09956e13 | 0.466357 | ||||||||
\(271\) | −1.70716e12 | −0.0709486 | −0.0354743 | − | 0.999371i | \(-0.511294\pi\) | ||||
−0.0354743 | + | 0.999371i | \(0.511294\pi\) | |||||||
\(272\) | −1.01979e13 | −0.415318 | ||||||||
\(273\) | −2.27195e13 | −0.906783 | ||||||||
\(274\) | −2.02653e13 | −0.792729 | ||||||||
\(275\) | 2.08179e13 | 0.798192 | ||||||||
\(276\) | −3.79167e12 | −0.142505 | ||||||||
\(277\) | −3.21307e13 | −1.18381 | −0.591905 | − | 0.806008i | \(-0.701624\pi\) | ||||
−0.591905 | + | 0.806008i | \(0.701624\pi\) | |||||||
\(278\) | −5.91131e13 | −2.13519 | ||||||||
\(279\) | 9.41003e12 | 0.333248 | ||||||||
\(280\) | −1.41850e14 | −4.92563 | ||||||||
\(281\) | −3.49986e13 | −1.19170 | −0.595849 | − | 0.803096i | \(-0.703184\pi\) | ||||
−0.595849 | + | 0.803096i | \(0.703184\pi\) | |||||||
\(282\) | −3.87241e13 | −1.29304 | ||||||||
\(283\) | 3.29943e13 | 1.08047 | 0.540235 | − | 0.841514i | \(-0.318335\pi\) | ||||
0.540235 | + | 0.841514i | \(0.318335\pi\) | |||||||
\(284\) | 7.50272e13 | 2.40973 | ||||||||
\(285\) | 1.35226e13 | 0.426002 | ||||||||
\(286\) | −4.06316e13 | −1.25560 | ||||||||
\(287\) | 9.95700e12 | 0.301841 | ||||||||
\(288\) | −2.63477e12 | −0.0783580 | ||||||||
\(289\) | −3.01618e13 | −0.880075 | ||||||||
\(290\) | −1.94623e13 | −0.557193 | ||||||||
\(291\) | −7.42198e12 | −0.208501 | ||||||||
\(292\) | 3.99073e13 | 1.10014 | ||||||||
\(293\) | 1.27340e13 | 0.344503 | 0.172252 | − | 0.985053i | \(-0.444896\pi\) | ||||
0.172252 | + | 0.985053i | \(0.444896\pi\) | |||||||
\(294\) | 1.00598e14 | 2.67104 | ||||||||
\(295\) | −6.91478e12 | −0.180201 | ||||||||
\(296\) | −1.03815e13 | −0.265555 | ||||||||
\(297\) | −6.67961e12 | −0.167722 | ||||||||
\(298\) | 8.88811e12 | 0.219089 | ||||||||
\(299\) | 4.06462e12 | 0.0983622 | ||||||||
\(300\) | −4.59585e13 | −1.09194 | ||||||||
\(301\) | 1.34265e14 | 3.13219 | ||||||||
\(302\) | −9.81490e13 | −2.24826 | ||||||||
\(303\) | 1.07738e13 | 0.242345 | ||||||||
\(304\) | −2.89414e13 | −0.639316 | ||||||||
\(305\) | −8.40835e13 | −1.82415 | ||||||||
\(306\) | 9.48458e12 | 0.202093 | ||||||||
\(307\) | −4.39040e13 | −0.918847 | −0.459423 | − | 0.888217i | \(-0.651944\pi\) | ||||
−0.459423 | + | 0.888217i | \(0.651944\pi\) | |||||||
\(308\) | 1.67082e14 | 3.43479 | ||||||||
\(309\) | 3.05886e13 | 0.617714 | ||||||||
\(310\) | −1.22118e14 | −2.42264 | ||||||||
\(311\) | 3.76975e13 | 0.734735 | 0.367368 | − | 0.930076i | \(-0.380259\pi\) | ||||
0.367368 | + | 0.930076i | \(0.380259\pi\) | |||||||
\(312\) | 4.62622e13 | 0.885883 | ||||||||
\(313\) | −7.29934e13 | −1.37338 | −0.686688 | − | 0.726952i | \(-0.740936\pi\) | ||||
−0.686688 | + | 0.726952i | \(0.740936\pi\) | |||||||
\(314\) | −1.84912e14 | −3.41862 | ||||||||
\(315\) | 4.84700e13 | 0.880572 | ||||||||
\(316\) | 1.41861e14 | 2.53271 | ||||||||
\(317\) | 1.79108e13 | 0.314260 | 0.157130 | − | 0.987578i | \(-0.449776\pi\) | ||||
0.157130 | + | 0.987578i | \(0.449776\pi\) | |||||||
\(318\) | 6.38423e12 | 0.110093 | ||||||||
\(319\) | 1.18230e13 | 0.200391 | ||||||||
\(320\) | −6.54477e13 | −1.09036 | ||||||||
\(321\) | 6.02032e13 | 0.985920 | ||||||||
\(322\) | −2.48081e13 | −0.399380 | ||||||||
\(323\) | 1.16643e13 | 0.184605 | ||||||||
\(324\) | 1.47462e13 | 0.229447 | ||||||||
\(325\) | 4.92668e13 | 0.753696 | ||||||||
\(326\) | 9.02296e13 | 1.35723 | ||||||||
\(327\) | −3.84575e13 | −0.568811 | ||||||||
\(328\) | −2.02748e13 | −0.294884 | ||||||||
\(329\) | −1.70701e14 | −2.44150 | ||||||||
\(330\) | 8.66839e13 | 1.21930 | ||||||||
\(331\) | −2.70114e13 | −0.373674 | −0.186837 | − | 0.982391i | \(-0.559824\pi\) | ||||
−0.186837 | + | 0.982391i | \(0.559824\pi\) | |||||||
\(332\) | −2.20755e14 | −3.00366 | ||||||||
\(333\) | 3.54732e12 | 0.0474741 | ||||||||
\(334\) | −1.96943e14 | −2.59259 | ||||||||
\(335\) | −3.48149e13 | −0.450837 | ||||||||
\(336\) | −1.03737e14 | −1.32150 | ||||||||
\(337\) | 9.45958e13 | 1.18552 | 0.592758 | − | 0.805381i | \(-0.298039\pi\) | ||||
0.592758 | + | 0.805381i | \(0.298039\pi\) | |||||||
\(338\) | 4.58333e13 | 0.565118 | ||||||||
\(339\) | −7.67399e13 | −0.930942 | ||||||||
\(340\) | −8.29271e13 | −0.989835 | ||||||||
\(341\) | 7.41841e13 | 0.871288 | ||||||||
\(342\) | 2.69171e13 | 0.311089 | ||||||||
\(343\) | 2.75638e14 | 3.13489 | ||||||||
\(344\) | −2.73396e14 | −3.06000 | ||||||||
\(345\) | −8.67151e12 | −0.0955190 | ||||||||
\(346\) | 1.73247e14 | 1.87822 | ||||||||
\(347\) | −2.02122e13 | −0.215676 | −0.107838 | − | 0.994168i | \(-0.534393\pi\) | ||||
−0.107838 | + | 0.994168i | \(0.534393\pi\) | |||||||
\(348\) | −2.61009e13 | −0.274138 | ||||||||
\(349\) | −5.64261e13 | −0.583365 | −0.291682 | − | 0.956515i | \(-0.594215\pi\) | ||||
−0.291682 | + | 0.956515i | \(0.594215\pi\) | |||||||
\(350\) | −3.00697e14 | −3.06023 | ||||||||
\(351\) | −1.58077e13 | −0.158372 | ||||||||
\(352\) | −2.07712e13 | −0.204869 | ||||||||
\(353\) | 7.43872e13 | 0.722333 | 0.361166 | − | 0.932501i | \(-0.382379\pi\) | ||||
0.361166 | + | 0.932501i | \(0.382379\pi\) | |||||||
\(354\) | −1.37641e13 | −0.131592 | ||||||||
\(355\) | 1.71586e14 | 1.61520 | ||||||||
\(356\) | 2.56364e14 | 2.37620 | ||||||||
\(357\) | 4.18092e13 | 0.381590 | ||||||||
\(358\) | 1.16535e14 | 1.04737 | ||||||||
\(359\) | −1.13256e14 | −1.00240 | −0.501200 | − | 0.865331i | \(-0.667108\pi\) | ||||
−0.501200 | + | 0.865331i | \(0.667108\pi\) | |||||||
\(360\) | −9.86964e13 | −0.860276 | ||||||||
\(361\) | −8.33872e13 | −0.715830 | ||||||||
\(362\) | 3.90198e14 | 3.29904 | ||||||||
\(363\) | 1.66720e13 | 0.138836 | ||||||||
\(364\) | 3.95409e14 | 3.24331 | ||||||||
\(365\) | 9.12675e13 | 0.737404 | ||||||||
\(366\) | −1.67371e14 | −1.33209 | ||||||||
\(367\) | −1.91005e13 | −0.149755 | −0.0748774 | − | 0.997193i | \(-0.523857\pi\) | ||||
−0.0748774 | + | 0.997193i | \(0.523857\pi\) | |||||||
\(368\) | 1.85591e13 | 0.143348 | ||||||||
\(369\) | 6.92786e12 | 0.0527174 | ||||||||
\(370\) | −4.60350e13 | −0.345127 | ||||||||
\(371\) | 2.81425e13 | 0.207877 | ||||||||
\(372\) | −1.63772e14 | −1.19194 | ||||||||
\(373\) | 2.11166e14 | 1.51435 | 0.757174 | − | 0.653213i | \(-0.226579\pi\) | ||||
0.757174 | + | 0.653213i | \(0.226579\pi\) | |||||||
\(374\) | 7.47718e13 | 0.528377 | ||||||||
\(375\) | 9.65459e12 | 0.0672298 | ||||||||
\(376\) | 3.47587e14 | 2.38523 | ||||||||
\(377\) | 2.79798e13 | 0.189220 | ||||||||
\(378\) | 9.64812e13 | 0.643040 | ||||||||
\(379\) | −2.39226e14 | −1.57142 | −0.785710 | − | 0.618594i | \(-0.787702\pi\) | ||||
−0.785710 | + | 0.618594i | \(0.787702\pi\) | |||||||
\(380\) | −2.35346e14 | −1.52369 | ||||||||
\(381\) | −4.67413e13 | −0.298273 | ||||||||
\(382\) | 2.74630e14 | 1.72743 | ||||||||
\(383\) | −1.68715e14 | −1.04607 | −0.523034 | − | 0.852312i | \(-0.675200\pi\) | ||||
−0.523034 | + | 0.852312i | \(0.675200\pi\) | |||||||
\(384\) | −1.52482e14 | −0.931957 | ||||||||
\(385\) | 3.82114e14 | 2.30228 | ||||||||
\(386\) | 7.85102e13 | 0.466333 | ||||||||
\(387\) | 9.34188e13 | 0.547046 | ||||||||
\(388\) | 1.29172e14 | 0.745750 | ||||||||
\(389\) | 2.35191e14 | 1.33874 | 0.669372 | − | 0.742927i | \(-0.266563\pi\) | ||||
0.669372 | + | 0.742927i | \(0.266563\pi\) | |||||||
\(390\) | 2.05143e14 | 1.15133 | ||||||||
\(391\) | −7.47986e12 | −0.0413925 | ||||||||
\(392\) | −9.02968e14 | −4.92719 | ||||||||
\(393\) | 5.20591e13 | 0.280116 | ||||||||
\(394\) | 9.84272e13 | 0.522259 | ||||||||
\(395\) | 3.24435e14 | 1.69763 | ||||||||
\(396\) | 1.16252e14 | 0.599896 | ||||||||
\(397\) | 2.65418e14 | 1.35077 | 0.675387 | − | 0.737464i | \(-0.263977\pi\) | ||||
0.675387 | + | 0.737464i | \(0.263977\pi\) | |||||||
\(398\) | 2.19213e14 | 1.10029 | ||||||||
\(399\) | 1.18654e14 | 0.587397 | ||||||||
\(400\) | 2.24953e14 | 1.09840 | ||||||||
\(401\) | 2.13150e14 | 1.02658 | 0.513289 | − | 0.858216i | \(-0.328427\pi\) | ||||
0.513289 | + | 0.858216i | \(0.328427\pi\) | |||||||
\(402\) | −6.93004e13 | −0.329224 | ||||||||
\(403\) | 1.75561e14 | 0.822717 | ||||||||
\(404\) | −1.87507e14 | −0.866802 | ||||||||
\(405\) | 3.37243e13 | 0.153794 | ||||||||
\(406\) | −1.70773e14 | −0.768290 | ||||||||
\(407\) | 2.79653e13 | 0.124123 | ||||||||
\(408\) | −8.51335e13 | −0.372795 | ||||||||
\(409\) | −1.94878e14 | −0.841947 | −0.420974 | − | 0.907073i | \(-0.638312\pi\) | ||||
−0.420974 | + | 0.907073i | \(0.638312\pi\) | |||||||
\(410\) | −8.99056e13 | −0.383244 | ||||||||
\(411\) | −6.21552e13 | −0.261425 | ||||||||
\(412\) | −5.32363e14 | −2.20939 | ||||||||
\(413\) | −6.06739e13 | −0.248472 | ||||||||
\(414\) | −1.72609e13 | −0.0697529 | ||||||||
\(415\) | −5.04863e14 | −2.01330 | ||||||||
\(416\) | −4.91563e13 | −0.193449 | ||||||||
\(417\) | −1.81304e14 | −0.704141 | ||||||||
\(418\) | 2.12201e14 | 0.813352 | ||||||||
\(419\) | 4.34434e14 | 1.64341 | 0.821707 | − | 0.569910i | \(-0.193022\pi\) | ||||
0.821707 | + | 0.569910i | \(0.193022\pi\) | |||||||
\(420\) | −8.43570e14 | −3.14956 | ||||||||
\(421\) | 1.94537e14 | 0.716886 | 0.358443 | − | 0.933552i | \(-0.383308\pi\) | ||||
0.358443 | + | 0.933552i | \(0.383308\pi\) | |||||||
\(422\) | −5.43810e14 | −1.97801 | ||||||||
\(423\) | −1.18770e14 | −0.426416 | ||||||||
\(424\) | −5.73048e13 | −0.203086 | ||||||||
\(425\) | −9.06627e13 | −0.317168 | ||||||||
\(426\) | 3.41548e14 | 1.17950 | ||||||||
\(427\) | −7.37793e14 | −2.51525 | ||||||||
\(428\) | −1.04777e15 | −3.52636 | ||||||||
\(429\) | −1.24620e14 | −0.414069 | ||||||||
\(430\) | −1.21233e15 | −3.97691 | ||||||||
\(431\) | −2.48713e14 | −0.805515 | −0.402758 | − | 0.915307i | \(-0.631948\pi\) | ||||
−0.402758 | + | 0.915307i | \(0.631948\pi\) | |||||||
\(432\) | −7.21780e13 | −0.230804 | ||||||||
\(433\) | 3.64798e14 | 1.15178 | 0.575889 | − | 0.817528i | \(-0.304656\pi\) | ||||
0.575889 | + | 0.817528i | \(0.304656\pi\) | |||||||
\(434\) | −1.07153e15 | −3.34048 | ||||||||
\(435\) | −5.96924e13 | −0.183750 | ||||||||
\(436\) | 6.69313e14 | 2.03448 | ||||||||
\(437\) | −2.12278e13 | −0.0637172 | ||||||||
\(438\) | 1.81671e14 | 0.538491 | ||||||||
\(439\) | −2.03663e14 | −0.596153 | −0.298076 | − | 0.954542i | \(-0.596345\pi\) | ||||
−0.298076 | + | 0.954542i | \(0.596345\pi\) | |||||||
\(440\) | −7.78074e14 | −2.24922 | ||||||||
\(441\) | 3.08542e14 | 0.880850 | ||||||||
\(442\) | 1.76952e14 | 0.498922 | ||||||||
\(443\) | −1.65338e14 | −0.460418 | −0.230209 | − | 0.973141i | \(-0.573941\pi\) | ||||
−0.230209 | + | 0.973141i | \(0.573941\pi\) | |||||||
\(444\) | −6.17375e13 | −0.169802 | ||||||||
\(445\) | 5.86302e14 | 1.59273 | ||||||||
\(446\) | −9.52132e14 | −2.55479 | ||||||||
\(447\) | 2.72605e13 | 0.0722508 | ||||||||
\(448\) | −5.74273e14 | −1.50345 | ||||||||
\(449\) | 5.98301e14 | 1.54727 | 0.773633 | − | 0.633634i | \(-0.218437\pi\) | ||||
0.773633 | + | 0.633634i | \(0.218437\pi\) | |||||||
\(450\) | −2.09218e14 | −0.534479 | ||||||||
\(451\) | 5.46158e13 | 0.137831 | ||||||||
\(452\) | 1.33558e15 | 3.32972 | ||||||||
\(453\) | −3.01030e14 | −0.741430 | ||||||||
\(454\) | 5.53708e13 | 0.134733 | ||||||||
\(455\) | 9.04295e14 | 2.17394 | ||||||||
\(456\) | −2.41608e14 | −0.573858 | ||||||||
\(457\) | −4.00303e14 | −0.939397 | −0.469699 | − | 0.882827i | \(-0.655637\pi\) | ||||
−0.469699 | + | 0.882827i | \(0.655637\pi\) | |||||||
\(458\) | −1.50520e15 | −3.49007 | ||||||||
\(459\) | 2.90899e13 | 0.0666458 | ||||||||
\(460\) | 1.50919e14 | 0.341645 | ||||||||
\(461\) | −1.68156e14 | −0.376146 | −0.188073 | − | 0.982155i | \(-0.560224\pi\) | ||||
−0.188073 | + | 0.982155i | \(0.560224\pi\) | |||||||
\(462\) | 7.60610e14 | 1.68125 | ||||||||
\(463\) | 4.82686e14 | 1.05431 | 0.527156 | − | 0.849769i | \(-0.323258\pi\) | ||||
0.527156 | + | 0.849769i | \(0.323258\pi\) | |||||||
\(464\) | 1.27756e14 | 0.275760 | ||||||||
\(465\) | −3.74544e14 | −0.798936 | ||||||||
\(466\) | 1.21268e15 | 2.55637 | ||||||||
\(467\) | 3.98412e14 | 0.830021 | 0.415011 | − | 0.909817i | \(-0.363778\pi\) | ||||
0.415011 | + | 0.909817i | \(0.363778\pi\) | |||||||
\(468\) | 2.75117e14 | 0.566454 | ||||||||
\(469\) | −3.05485e14 | −0.621640 | ||||||||
\(470\) | 1.54132e15 | 3.09995 | ||||||||
\(471\) | −5.67138e14 | −1.12739 | ||||||||
\(472\) | 1.23547e14 | 0.242745 | ||||||||
\(473\) | 7.36468e14 | 1.43027 | ||||||||
\(474\) | 6.45799e14 | 1.23970 | ||||||||
\(475\) | −2.57300e14 | −0.488230 | ||||||||
\(476\) | −7.27647e14 | −1.36484 | ||||||||
\(477\) | 1.95809e13 | 0.0363063 | ||||||||
\(478\) | 1.62779e15 | 2.98363 | ||||||||
\(479\) | 3.18807e14 | 0.577674 | 0.288837 | − | 0.957378i | \(-0.406731\pi\) | ||||
0.288837 | + | 0.957378i | \(0.406731\pi\) | |||||||
\(480\) | 1.04871e14 | 0.187857 | ||||||||
\(481\) | 6.61816e13 | 0.117203 | ||||||||
\(482\) | −6.91100e14 | −1.20999 | ||||||||
\(483\) | −7.60884e13 | −0.131707 | ||||||||
\(484\) | −2.90159e14 | −0.496577 | ||||||||
\(485\) | 2.95414e14 | 0.499864 | ||||||||
\(486\) | 6.71295e13 | 0.112309 | ||||||||
\(487\) | −5.27807e13 | −0.0873103 | −0.0436552 | − | 0.999047i | \(-0.513900\pi\) | ||||
−0.0436552 | + | 0.999047i | \(0.513900\pi\) | |||||||
\(488\) | 1.50232e15 | 2.45728 | ||||||||
\(489\) | 2.76741e14 | 0.447584 | ||||||||
\(490\) | −4.00407e15 | −6.40359 | ||||||||
\(491\) | 1.54389e13 | 0.0244157 | 0.0122078 | − | 0.999925i | \(-0.496114\pi\) | ||||
0.0122078 | + | 0.999925i | \(0.496114\pi\) | |||||||
\(492\) | −1.20572e14 | −0.188556 | ||||||||
\(493\) | −5.14894e13 | −0.0796270 | ||||||||
\(494\) | 5.02187e14 | 0.768011 | ||||||||
\(495\) | 2.65866e14 | 0.402100 | ||||||||
\(496\) | 8.01613e14 | 1.19899 | ||||||||
\(497\) | 1.50559e15 | 2.22713 | ||||||||
\(498\) | −1.00495e15 | −1.47022 | ||||||||
\(499\) | 9.35812e14 | 1.35405 | 0.677026 | − | 0.735959i | \(-0.263268\pi\) | ||||
0.677026 | + | 0.735959i | \(0.263268\pi\) | |||||||
\(500\) | −1.68028e14 | −0.240462 | ||||||||
\(501\) | −6.04038e14 | −0.854982 | ||||||||
\(502\) | 2.16572e15 | 3.03201 | ||||||||
\(503\) | 7.11605e14 | 0.985406 | 0.492703 | − | 0.870198i | \(-0.336009\pi\) | ||||
0.492703 | + | 0.870198i | \(0.336009\pi\) | |||||||
\(504\) | −8.66014e14 | −1.18620 | ||||||||
\(505\) | −4.28826e14 | −0.581003 | ||||||||
\(506\) | −1.36077e14 | −0.182371 | ||||||||
\(507\) | 1.40574e14 | 0.186364 | ||||||||
\(508\) | 8.13484e14 | 1.06684 | ||||||||
\(509\) | −5.49290e14 | −0.712613 | −0.356306 | − | 0.934369i | \(-0.615964\pi\) | ||||
−0.356306 | + | 0.934369i | \(0.615964\pi\) | |||||||
\(510\) | −3.77511e14 | −0.484500 | ||||||||
\(511\) | 8.00830e14 | 1.01678 | ||||||||
\(512\) | 1.55582e15 | 1.95423 | ||||||||
\(513\) | 8.25568e13 | 0.102591 | ||||||||
\(514\) | 1.92483e14 | 0.236644 | ||||||||
\(515\) | −1.21751e15 | −1.48092 | ||||||||
\(516\) | −1.62586e15 | −1.95663 | ||||||||
\(517\) | −9.36321e14 | −1.11488 | ||||||||
\(518\) | −4.03935e14 | −0.475881 | ||||||||
\(519\) | 5.31361e14 | 0.619398 | ||||||||
\(520\) | −1.84136e15 | −2.12383 | ||||||||
\(521\) | 1.52469e14 | 0.174010 | 0.0870050 | − | 0.996208i | \(-0.472270\pi\) | ||||
0.0870050 | + | 0.996208i | \(0.472270\pi\) | |||||||
\(522\) | −1.18820e14 | −0.134184 | ||||||||
\(523\) | −5.46877e13 | −0.0611126 | −0.0305563 | − | 0.999533i | \(-0.509728\pi\) | ||||
−0.0305563 | + | 0.999533i | \(0.509728\pi\) | |||||||
\(524\) | −9.06034e14 | −1.00190 | ||||||||
\(525\) | −9.22260e14 | −1.00920 | ||||||||
\(526\) | −3.84770e14 | −0.416658 | ||||||||
\(527\) | −3.23074e14 | −0.346214 | ||||||||
\(528\) | −5.69016e14 | −0.603445 | ||||||||
\(529\) | −9.39197e14 | −0.985713 | ||||||||
\(530\) | −2.54109e14 | −0.263939 | ||||||||
\(531\) | −4.22156e13 | −0.0433963 | ||||||||
\(532\) | −2.06505e15 | −2.10096 | ||||||||
\(533\) | 1.29252e14 | 0.130148 | ||||||||
\(534\) | 1.16705e15 | 1.16309 | ||||||||
\(535\) | −2.39625e15 | −2.36366 | ||||||||
\(536\) | 6.22039e14 | 0.607312 | ||||||||
\(537\) | 3.57421e14 | 0.345399 | ||||||||
\(538\) | 2.88485e15 | 2.75943 | ||||||||
\(539\) | 2.43239e15 | 2.30301 | ||||||||
\(540\) | −5.86937e14 | −0.550080 | ||||||||
\(541\) | −1.22752e15 | −1.13879 | −0.569396 | − | 0.822063i | \(-0.692823\pi\) | ||||
−0.569396 | + | 0.822063i | \(0.692823\pi\) | |||||||
\(542\) | 1.35256e14 | 0.124211 | ||||||||
\(543\) | 1.19677e15 | 1.08795 | ||||||||
\(544\) | 9.04593e13 | 0.0814066 | ||||||||
\(545\) | 1.53071e15 | 1.36368 | ||||||||
\(546\) | 1.80003e15 | 1.58752 | ||||||||
\(547\) | −6.27744e13 | −0.0548090 | −0.0274045 | − | 0.999624i | \(-0.508724\pi\) | ||||
−0.0274045 | + | 0.999624i | \(0.508724\pi\) | |||||||
\(548\) | 1.08175e15 | 0.935045 | ||||||||
\(549\) | −5.13340e14 | −0.439296 | ||||||||
\(550\) | −1.64937e15 | −1.39741 | ||||||||
\(551\) | −1.46126e14 | −0.122573 | ||||||||
\(552\) | 1.54934e14 | 0.128671 | ||||||||
\(553\) | 2.84676e15 | 2.34079 | ||||||||
\(554\) | 2.54567e15 | 2.07252 | ||||||||
\(555\) | −1.41193e14 | −0.113815 | ||||||||
\(556\) | 3.15541e15 | 2.51852 | ||||||||
\(557\) | 1.41405e15 | 1.11754 | 0.558768 | − | 0.829324i | \(-0.311274\pi\) | ||||
0.558768 | + | 0.829324i | \(0.311274\pi\) | |||||||
\(558\) | −7.45544e14 | −0.583425 | ||||||||
\(559\) | 1.74290e15 | 1.35054 | ||||||||
\(560\) | 4.12901e15 | 3.16820 | ||||||||
\(561\) | 2.29331e14 | 0.174247 | ||||||||
\(562\) | 2.77289e15 | 2.08633 | ||||||||
\(563\) | −7.52424e13 | −0.0560617 | −0.0280309 | − | 0.999607i | \(-0.508924\pi\) | ||||
−0.0280309 | + | 0.999607i | \(0.508924\pi\) | |||||||
\(564\) | 2.06706e15 | 1.52517 | ||||||||
\(565\) | 3.05445e15 | 2.23186 | ||||||||
\(566\) | −2.61409e15 | −1.89160 | ||||||||
\(567\) | 2.95915e14 | 0.212061 | ||||||||
\(568\) | −3.06574e15 | −2.17580 | ||||||||
\(569\) | −3.78781e14 | −0.266238 | −0.133119 | − | 0.991100i | \(-0.542499\pi\) | ||||
−0.133119 | + | 0.991100i | \(0.542499\pi\) | |||||||
\(570\) | −1.07137e15 | −0.745811 | ||||||||
\(571\) | 2.32982e15 | 1.60629 | 0.803145 | − | 0.595783i | \(-0.203158\pi\) | ||||
0.803145 | + | 0.595783i | \(0.203158\pi\) | |||||||
\(572\) | 2.16888e15 | 1.48101 | ||||||||
\(573\) | 8.42311e14 | 0.569668 | ||||||||
\(574\) | −7.88879e14 | −0.528439 | ||||||||
\(575\) | 1.64997e14 | 0.109472 | ||||||||
\(576\) | −3.99566e14 | −0.262582 | ||||||||
\(577\) | −1.28910e15 | −0.839110 | −0.419555 | − | 0.907730i | \(-0.637814\pi\) | ||||
−0.419555 | + | 0.907730i | \(0.637814\pi\) | |||||||
\(578\) | 2.38968e15 | 1.54077 | ||||||||
\(579\) | 2.40797e14 | 0.153787 | ||||||||
\(580\) | 1.03888e15 | 0.657224 | ||||||||
\(581\) | −4.42993e15 | −2.77606 | ||||||||
\(582\) | 5.88033e14 | 0.365027 | ||||||||
\(583\) | 1.54366e14 | 0.0949239 | ||||||||
\(584\) | −1.63068e15 | −0.993340 | ||||||||
\(585\) | 6.29188e14 | 0.379685 | ||||||||
\(586\) | −1.00890e15 | −0.603129 | ||||||||
\(587\) | 1.71101e15 | 1.01331 | 0.506655 | − | 0.862149i | \(-0.330882\pi\) | ||||
0.506655 | + | 0.862149i | \(0.330882\pi\) | |||||||
\(588\) | −5.36986e15 | −3.15056 | ||||||||
\(589\) | −9.16881e14 | −0.532941 | ||||||||
\(590\) | 5.47848e14 | 0.315482 | ||||||||
\(591\) | 3.01884e14 | 0.172230 | ||||||||
\(592\) | 3.02186e14 | 0.170807 | ||||||||
\(593\) | −4.88833e14 | −0.273754 | −0.136877 | − | 0.990588i | \(-0.543706\pi\) | ||||
−0.136877 | + | 0.990588i | \(0.543706\pi\) | |||||||
\(594\) | 5.29216e14 | 0.293635 | ||||||||
\(595\) | −1.66412e15 | −0.914831 | ||||||||
\(596\) | −4.74441e14 | −0.258421 | ||||||||
\(597\) | 6.72342e14 | 0.362854 | ||||||||
\(598\) | −3.22034e14 | −0.172205 | ||||||||
\(599\) | 3.48930e15 | 1.84881 | 0.924403 | − | 0.381418i | \(-0.124564\pi\) | ||||
0.924403 | + | 0.381418i | \(0.124564\pi\) | |||||||
\(600\) | 1.87794e15 | 0.985939 | ||||||||
\(601\) | −1.28836e15 | −0.670236 | −0.335118 | − | 0.942176i | \(-0.608776\pi\) | ||||
−0.335118 | + | 0.942176i | \(0.608776\pi\) | |||||||
\(602\) | −1.06376e16 | −5.48359 | ||||||||
\(603\) | −2.12549e14 | −0.108571 | ||||||||
\(604\) | 5.23912e15 | 2.65189 | ||||||||
\(605\) | −6.63589e14 | −0.332847 | ||||||||
\(606\) | −8.53593e14 | −0.424279 | ||||||||
\(607\) | 1.47555e15 | 0.726803 | 0.363402 | − | 0.931633i | \(-0.381615\pi\) | ||||
0.363402 | + | 0.931633i | \(0.381615\pi\) | |||||||
\(608\) | 2.56722e14 | 0.125312 | ||||||||
\(609\) | −5.23773e14 | −0.253366 | ||||||||
\(610\) | 6.66181e15 | 3.19358 | ||||||||
\(611\) | −2.21586e15 | −1.05273 | ||||||||
\(612\) | −5.06280e14 | −0.238374 | ||||||||
\(613\) | −3.36346e15 | −1.56947 | −0.784736 | − | 0.619830i | \(-0.787202\pi\) | ||||
−0.784736 | + | 0.619830i | \(0.787202\pi\) | |||||||
\(614\) | 3.47845e15 | 1.60864 | ||||||||
\(615\) | −2.75747e14 | −0.126386 | ||||||||
\(616\) | −6.82723e15 | −3.10135 | ||||||||
\(617\) | −6.14389e14 | −0.276615 | −0.138307 | − | 0.990389i | \(-0.544166\pi\) | ||||
−0.138307 | + | 0.990389i | \(0.544166\pi\) | |||||||
\(618\) | −2.42349e15 | −1.08145 | ||||||||
\(619\) | −4.30442e15 | −1.90378 | −0.951888 | − | 0.306448i | \(-0.900860\pi\) | ||||
−0.951888 | + | 0.306448i | \(0.900860\pi\) | |||||||
\(620\) | 6.51856e15 | 2.85757 | ||||||||
\(621\) | −5.29406e13 | −0.0230030 | ||||||||
\(622\) | −2.98672e15 | −1.28632 | ||||||||
\(623\) | 5.14452e15 | 2.19614 | ||||||||
\(624\) | −1.34661e15 | −0.569806 | ||||||||
\(625\) | −2.56789e15 | −1.07705 | ||||||||
\(626\) | 5.78316e15 | 2.40440 | ||||||||
\(627\) | 6.50838e14 | 0.268226 | ||||||||
\(628\) | 9.87046e15 | 4.03236 | ||||||||
\(629\) | −1.21790e14 | −0.0493211 | ||||||||
\(630\) | −3.84021e15 | −1.54164 | ||||||||
\(631\) | −3.85187e15 | −1.53289 | −0.766444 | − | 0.642311i | \(-0.777976\pi\) | ||||
−0.766444 | + | 0.642311i | \(0.777976\pi\) | |||||||
\(632\) | −5.79669e15 | −2.28684 | ||||||||
\(633\) | −1.66791e15 | −0.652306 | ||||||||
\(634\) | −1.41905e15 | −0.550181 | ||||||||
\(635\) | 1.86043e15 | 0.715084 | ||||||||
\(636\) | −3.40786e14 | −0.129858 | ||||||||
\(637\) | 5.75641e15 | 2.17463 | ||||||||
\(638\) | −9.36717e14 | −0.350828 | ||||||||
\(639\) | 1.04755e15 | 0.388975 | ||||||||
\(640\) | 6.06918e15 | 2.23429 | ||||||||
\(641\) | −1.86345e15 | −0.680140 | −0.340070 | − | 0.940400i | \(-0.610451\pi\) | ||||
−0.340070 | + | 0.940400i | \(0.610451\pi\) | |||||||
\(642\) | −4.76981e15 | −1.72607 | ||||||||
\(643\) | −8.75431e14 | −0.314095 | −0.157048 | − | 0.987591i | \(-0.550198\pi\) | ||||
−0.157048 | + | 0.987591i | \(0.550198\pi\) | |||||||
\(644\) | 1.32424e15 | 0.471080 | ||||||||
\(645\) | −3.71832e15 | −1.31150 | ||||||||
\(646\) | −9.24144e14 | −0.323192 | ||||||||
\(647\) | 3.41312e15 | 1.18353 | 0.591764 | − | 0.806111i | \(-0.298432\pi\) | ||||
0.591764 | + | 0.806111i | \(0.298432\pi\) | |||||||
\(648\) | −6.02553e14 | −0.207173 | ||||||||
\(649\) | −3.32807e14 | −0.113461 | ||||||||
\(650\) | −3.90334e15 | −1.31951 | ||||||||
\(651\) | −3.28645e15 | −1.10162 | ||||||||
\(652\) | −4.81639e15 | −1.60088 | ||||||||
\(653\) | 2.79838e14 | 0.0922325 | 0.0461163 | − | 0.998936i | \(-0.485316\pi\) | ||||
0.0461163 | + | 0.998936i | \(0.485316\pi\) | |||||||
\(654\) | 3.04693e15 | 0.995829 | ||||||||
\(655\) | −2.07209e15 | −0.671554 | ||||||||
\(656\) | 5.90164e14 | 0.189671 | ||||||||
\(657\) | 5.57199e14 | 0.177583 | ||||||||
\(658\) | 1.35244e16 | 4.27439 | ||||||||
\(659\) | −2.21300e15 | −0.693605 | −0.346803 | − | 0.937938i | \(-0.612733\pi\) | ||||
−0.346803 | + | 0.937938i | \(0.612733\pi\) | |||||||
\(660\) | −4.62713e15 | −1.43820 | ||||||||
\(661\) | −4.73366e15 | −1.45911 | −0.729557 | − | 0.683920i | \(-0.760274\pi\) | ||||
−0.729557 | + | 0.683920i | \(0.760274\pi\) | |||||||
\(662\) | 2.14007e15 | 0.654199 | ||||||||
\(663\) | 5.42725e14 | 0.164534 | ||||||||
\(664\) | 9.02040e15 | 2.71207 | ||||||||
\(665\) | −4.72275e15 | −1.40824 | ||||||||
\(666\) | −2.81049e14 | −0.0831140 | ||||||||
\(667\) | 9.37054e13 | 0.0274835 | ||||||||
\(668\) | 1.05127e16 | 3.05803 | ||||||||
\(669\) | −2.92026e15 | −0.842516 | ||||||||
\(670\) | 2.75834e15 | 0.789289 | ||||||||
\(671\) | −4.04692e15 | −1.14855 | ||||||||
\(672\) | 9.20191e14 | 0.259028 | ||||||||
\(673\) | −2.45606e15 | −0.685736 | −0.342868 | − | 0.939384i | \(-0.611398\pi\) | ||||
−0.342868 | + | 0.939384i | \(0.611398\pi\) | |||||||
\(674\) | −7.49469e15 | −2.07551 | ||||||||
\(675\) | −6.41688e14 | −0.176260 | ||||||||
\(676\) | −2.44655e15 | −0.666572 | ||||||||
\(677\) | 1.22414e15 | 0.330821 | 0.165411 | − | 0.986225i | \(-0.447105\pi\) | ||||
0.165411 | + | 0.986225i | \(0.447105\pi\) | |||||||
\(678\) | 6.07999e15 | 1.62982 | ||||||||
\(679\) | 2.59212e15 | 0.689242 | ||||||||
\(680\) | 3.38854e15 | 0.893745 | ||||||||
\(681\) | 1.69826e14 | 0.0444320 | ||||||||
\(682\) | −5.87750e15 | −1.52538 | ||||||||
\(683\) | −6.97032e15 | −1.79448 | −0.897240 | − | 0.441543i | \(-0.854431\pi\) | ||||
−0.897240 | + | 0.441543i | \(0.854431\pi\) | |||||||
\(684\) | −1.43682e15 | −0.366938 | ||||||||
\(685\) | 2.47394e15 | 0.626745 | ||||||||
\(686\) | −2.18384e16 | −5.48831 | ||||||||
\(687\) | −4.61657e15 | −1.15095 | ||||||||
\(688\) | 7.95807e15 | 1.96821 | ||||||||
\(689\) | 3.65317e14 | 0.0896323 | ||||||||
\(690\) | 6.87031e14 | 0.167227 | ||||||||
\(691\) | 7.05580e15 | 1.70379 | 0.851897 | − | 0.523709i | \(-0.175452\pi\) | ||||
0.851897 | + | 0.523709i | \(0.175452\pi\) | |||||||
\(692\) | −9.24780e15 | −2.21541 | ||||||||
\(693\) | 2.33285e15 | 0.554439 | ||||||||
\(694\) | 1.60139e15 | 0.377589 | ||||||||
\(695\) | 7.21639e15 | 1.68812 | ||||||||
\(696\) | 1.06653e15 | 0.247526 | ||||||||
\(697\) | −2.37854e14 | −0.0547684 | ||||||||
\(698\) | 4.47056e15 | 1.02131 | ||||||||
\(699\) | 3.71938e15 | 0.843035 | ||||||||
\(700\) | 1.60510e16 | 3.60963 | ||||||||
\(701\) | −7.19727e15 | −1.60590 | −0.802950 | − | 0.596046i | \(-0.796738\pi\) | ||||
−0.802950 | + | 0.596046i | \(0.796738\pi\) | |||||||
\(702\) | 1.25242e15 | 0.277266 | ||||||||
\(703\) | −3.45639e14 | −0.0759220 | ||||||||
\(704\) | −3.14998e15 | −0.686529 | ||||||||
\(705\) | 4.72735e15 | 1.02230 | ||||||||
\(706\) | −5.89359e15 | −1.26460 | ||||||||
\(707\) | −3.76274e15 | −0.801121 | ||||||||
\(708\) | 7.34719e14 | 0.155217 | ||||||||
\(709\) | 2.97413e14 | 0.0623456 | 0.0311728 | − | 0.999514i | \(-0.490076\pi\) | ||||
0.0311728 | + | 0.999514i | \(0.490076\pi\) | |||||||
\(710\) | −1.35945e16 | −2.82776 | ||||||||
\(711\) | 1.98072e15 | 0.408827 | ||||||||
\(712\) | −1.04755e16 | −2.14553 | ||||||||
\(713\) | 5.87961e14 | 0.119497 | ||||||||
\(714\) | −3.31248e15 | −0.668057 | ||||||||
\(715\) | 4.96021e15 | 0.992697 | ||||||||
\(716\) | −6.22055e15 | −1.23540 | ||||||||
\(717\) | 4.99255e15 | 0.983936 | ||||||||
\(718\) | 8.97310e15 | 1.75492 | ||||||||
\(719\) | 4.12277e15 | 0.800166 | 0.400083 | − | 0.916479i | \(-0.368981\pi\) | ||||
0.400083 | + | 0.916479i | \(0.368981\pi\) | |||||||
\(720\) | 2.87288e15 | 0.553335 | ||||||||
\(721\) | −1.06830e16 | −2.04198 | ||||||||
\(722\) | 6.60665e15 | 1.25322 | ||||||||
\(723\) | −2.11966e15 | −0.399029 | ||||||||
\(724\) | −2.08285e16 | −3.89131 | ||||||||
\(725\) | 1.13579e15 | 0.210591 | ||||||||
\(726\) | −1.32090e15 | −0.243062 | ||||||||
\(727\) | −2.20204e15 | −0.402148 | −0.201074 | − | 0.979576i | \(-0.564443\pi\) | ||||
−0.201074 | + | 0.979576i | \(0.564443\pi\) | |||||||
\(728\) | −1.61571e16 | −2.92846 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −7.23100e15 | −1.29099 | ||||||||
\(731\) | −3.20734e15 | −0.568329 | ||||||||
\(732\) | 8.93415e15 | 1.57124 | ||||||||
\(733\) | 7.67019e15 | 1.33886 | 0.669428 | − | 0.742877i | \(-0.266539\pi\) | ||||
0.669428 | + | 0.742877i | \(0.266539\pi\) | |||||||
\(734\) | 1.51330e15 | 0.262179 | ||||||||
\(735\) | −1.22808e16 | −2.11177 | ||||||||
\(736\) | −1.64626e14 | −0.0280978 | ||||||||
\(737\) | −1.67564e15 | −0.283863 | ||||||||
\(738\) | −5.48884e14 | −0.0922934 | ||||||||
\(739\) | −4.60255e15 | −0.768164 | −0.384082 | − | 0.923299i | \(-0.625482\pi\) | ||||
−0.384082 | + | 0.923299i | \(0.625482\pi\) | |||||||
\(740\) | 2.45732e15 | 0.407086 | ||||||||
\(741\) | 1.54025e15 | 0.253274 | ||||||||
\(742\) | −2.22969e15 | −0.363934 | ||||||||
\(743\) | −7.62174e15 | −1.23485 | −0.617427 | − | 0.786628i | \(-0.711825\pi\) | ||||
−0.617427 | + | 0.786628i | \(0.711825\pi\) | |||||||
\(744\) | 6.69199e15 | 1.07623 | ||||||||
\(745\) | −1.08504e15 | −0.173215 | ||||||||
\(746\) | −1.67304e16 | −2.65120 | ||||||||
\(747\) | −3.08225e15 | −0.484847 | ||||||||
\(748\) | −3.99127e15 | −0.623235 | ||||||||
\(749\) | −2.10259e16 | −3.25916 | ||||||||
\(750\) | −7.64919e14 | −0.117701 | ||||||||
\(751\) | 3.56762e15 | 0.544953 | 0.272476 | − | 0.962162i | \(-0.412157\pi\) | ||||
0.272476 | + | 0.962162i | \(0.412157\pi\) | |||||||
\(752\) | −1.01176e16 | −1.53420 | ||||||||
\(753\) | 6.64242e15 | 0.999893 | ||||||||
\(754\) | −2.21680e15 | −0.331271 | ||||||||
\(755\) | 1.19818e16 | 1.77752 | ||||||||
\(756\) | −5.15010e15 | −0.758483 | ||||||||
\(757\) | 2.86324e15 | 0.418631 | 0.209315 | − | 0.977848i | \(-0.432876\pi\) | ||||
0.209315 | + | 0.977848i | \(0.432876\pi\) | |||||||
\(758\) | 1.89535e16 | 2.75112 | ||||||||
\(759\) | −4.17358e14 | −0.0601421 | ||||||||
\(760\) | 9.61663e15 | 1.37578 | ||||||||
\(761\) | 1.63278e14 | 0.0231906 | 0.0115953 | − | 0.999933i | \(-0.496309\pi\) | ||||
0.0115953 | + | 0.999933i | \(0.496309\pi\) | |||||||
\(762\) | 3.70325e15 | 0.522192 | ||||||||
\(763\) | 1.34313e16 | 1.88032 | ||||||||
\(764\) | −1.46596e16 | −2.03755 | ||||||||
\(765\) | −1.15786e15 | −0.159778 | ||||||||
\(766\) | 1.33670e16 | 1.83137 | ||||||||
\(767\) | −7.87607e14 | −0.107136 | ||||||||
\(768\) | 8.71337e15 | 1.17679 | ||||||||
\(769\) | 8.05214e15 | 1.07973 | 0.539867 | − | 0.841750i | \(-0.318475\pi\) | ||||
0.539867 | + | 0.841750i | \(0.318475\pi\) | |||||||
\(770\) | −3.02743e16 | −4.03065 | ||||||||
\(771\) | 5.90360e14 | 0.0780401 | ||||||||
\(772\) | −4.19082e15 | −0.550052 | ||||||||
\(773\) | 7.43296e15 | 0.968667 | 0.484334 | − | 0.874883i | \(-0.339062\pi\) | ||||
0.484334 | + | 0.874883i | \(0.339062\pi\) | |||||||
\(774\) | −7.40144e15 | −0.957725 | ||||||||
\(775\) | 7.12662e15 | 0.915639 | ||||||||
\(776\) | −5.27817e15 | −0.673355 | ||||||||
\(777\) | −1.23890e15 | −0.156935 | ||||||||
\(778\) | −1.86338e16 | −2.34377 | ||||||||
\(779\) | −6.75026e14 | −0.0843072 | ||||||||
\(780\) | −1.09504e16 | −1.35803 | ||||||||
\(781\) | 8.25841e15 | 1.01699 | ||||||||
\(782\) | 5.92619e14 | 0.0724667 | ||||||||
\(783\) | −3.64429e14 | −0.0442510 | ||||||||
\(784\) | 2.62838e16 | 3.16920 | ||||||||
\(785\) | 2.25736e16 | 2.70282 | ||||||||
\(786\) | −4.12456e15 | −0.490404 | ||||||||
\(787\) | −7.39938e14 | −0.0873643 | −0.0436822 | − | 0.999045i | \(-0.513909\pi\) | ||||
−0.0436822 | + | 0.999045i | \(0.513909\pi\) | |||||||
\(788\) | −5.25398e15 | −0.616019 | ||||||||
\(789\) | −1.18012e15 | −0.137405 | ||||||||
\(790\) | −2.57045e16 | −2.97208 | ||||||||
\(791\) | 2.68014e16 | 3.07742 | ||||||||
\(792\) | −4.75024e15 | −0.541660 | ||||||||
\(793\) | −9.57728e15 | −1.08452 | ||||||||
\(794\) | −2.10287e16 | −2.36483 | ||||||||
\(795\) | −7.79373e14 | −0.0870414 | ||||||||
\(796\) | −1.17014e16 | −1.29783 | ||||||||
\(797\) | −1.21756e15 | −0.134112 | −0.0670560 | − | 0.997749i | \(-0.521361\pi\) | ||||
−0.0670560 | + | 0.997749i | \(0.521361\pi\) | |||||||
\(798\) | −9.40079e15 | −1.02837 | ||||||||
\(799\) | 4.07771e15 | 0.443006 | ||||||||
\(800\) | −1.99542e15 | −0.215298 | ||||||||
\(801\) | 3.57944e15 | 0.383563 | ||||||||
\(802\) | −1.68876e16 | −1.79725 | ||||||||
\(803\) | 4.39269e15 | 0.464296 | ||||||||
\(804\) | 3.69920e15 | 0.388329 | ||||||||
\(805\) | 3.02852e15 | 0.315757 | ||||||||
\(806\) | −1.39095e16 | −1.44035 | ||||||||
\(807\) | 8.84804e15 | 0.910002 | ||||||||
\(808\) | 7.66184e15 | 0.782656 | ||||||||
\(809\) | −1.28451e16 | −1.30322 | −0.651612 | − | 0.758552i | \(-0.725907\pi\) | ||||
−0.651612 | + | 0.758552i | \(0.725907\pi\) | |||||||
\(810\) | −2.67193e15 | −0.269251 | ||||||||
\(811\) | 5.68684e15 | 0.569189 | 0.284594 | − | 0.958648i | \(-0.408141\pi\) | ||||
0.284594 | + | 0.958648i | \(0.408141\pi\) | |||||||
\(812\) | 9.11573e15 | 0.906219 | ||||||||
\(813\) | 4.14841e14 | 0.0409622 | ||||||||
\(814\) | −2.21565e15 | −0.217304 | ||||||||
\(815\) | −1.10150e16 | −1.07305 | ||||||||
\(816\) | 2.47808e15 | 0.239784 | ||||||||
\(817\) | −9.10240e15 | −0.874852 | ||||||||
\(818\) | 1.54399e16 | 1.47401 | ||||||||
\(819\) | 5.52083e15 | 0.523531 | ||||||||
\(820\) | 4.79910e15 | 0.452047 | ||||||||
\(821\) | 1.88909e16 | 1.76753 | 0.883763 | − | 0.467934i | \(-0.155002\pi\) | ||||
0.883763 | + | 0.467934i | \(0.155002\pi\) | |||||||
\(822\) | 4.92446e15 | 0.457682 | ||||||||
\(823\) | −1.30076e16 | −1.20087 | −0.600437 | − | 0.799672i | \(-0.705007\pi\) | ||||
−0.600437 | + | 0.799672i | \(0.705007\pi\) | |||||||
\(824\) | 2.17532e16 | 1.99491 | ||||||||
\(825\) | −5.05875e15 | −0.460836 | ||||||||
\(826\) | 4.80711e15 | 0.435004 | ||||||||
\(827\) | 1.61858e16 | 1.45497 | 0.727485 | − | 0.686124i | \(-0.240689\pi\) | ||||
0.727485 | + | 0.686124i | \(0.240689\pi\) | |||||||
\(828\) | 9.21377e14 | 0.0822755 | ||||||||
\(829\) | −1.82837e15 | −0.162186 | −0.0810932 | − | 0.996707i | \(-0.525841\pi\) | ||||
−0.0810932 | + | 0.996707i | \(0.525841\pi\) | |||||||
\(830\) | 3.99996e16 | 3.52473 | ||||||||
\(831\) | 7.80777e15 | 0.683473 | ||||||||
\(832\) | −7.45462e15 | −0.648257 | ||||||||
\(833\) | −1.05932e16 | −0.915120 | ||||||||
\(834\) | 1.43645e16 | 1.23275 | ||||||||
\(835\) | 2.40423e16 | 2.04975 | ||||||||
\(836\) | −1.13272e16 | −0.959371 | ||||||||
\(837\) | −2.28664e15 | −0.192401 | ||||||||
\(838\) | −3.44196e16 | −2.87716 | ||||||||
\(839\) | 6.27284e15 | 0.520923 | 0.260462 | − | 0.965484i | \(-0.416125\pi\) | ||||
0.260462 | + | 0.965484i | \(0.416125\pi\) | |||||||
\(840\) | 3.44697e16 | 2.84381 | ||||||||
\(841\) | −1.15555e16 | −0.947130 | ||||||||
\(842\) | −1.54129e16 | −1.25507 | ||||||||
\(843\) | 8.50467e15 | 0.688027 | ||||||||
\(844\) | 2.90282e16 | 2.33312 | ||||||||
\(845\) | −5.59522e15 | −0.446792 | ||||||||
\(846\) | 9.40995e15 | 0.746535 | ||||||||
\(847\) | −5.82268e15 | −0.458949 | ||||||||
\(848\) | 1.66804e15 | 0.130626 | ||||||||
\(849\) | −8.01761e15 | −0.623810 | ||||||||
\(850\) | 7.18308e15 | 0.555273 | ||||||||
\(851\) | 2.21645e14 | 0.0170234 | ||||||||
\(852\) | −1.82316e16 | −1.39126 | ||||||||
\(853\) | −1.56569e16 | −1.18709 | −0.593546 | − | 0.804800i | \(-0.702273\pi\) | ||||
−0.593546 | + | 0.804800i | \(0.702273\pi\) | |||||||
\(854\) | 5.84543e16 | 4.40350 | ||||||||
\(855\) | −3.28598e15 | −0.245953 | ||||||||
\(856\) | 4.28138e16 | 3.18403 | ||||||||
\(857\) | −8.16164e15 | −0.603091 | −0.301546 | − | 0.953452i | \(-0.597503\pi\) | ||||
−0.301546 | + | 0.953452i | \(0.597503\pi\) | |||||||
\(858\) | 9.87347e15 | 0.724919 | ||||||||
\(859\) | 9.60173e15 | 0.700466 | 0.350233 | − | 0.936663i | \(-0.386102\pi\) | ||||
0.350233 | + | 0.936663i | \(0.386102\pi\) | |||||||
\(860\) | 6.47135e16 | 4.69087 | ||||||||
\(861\) | −2.41955e15 | −0.174268 | ||||||||
\(862\) | 1.97052e16 | 1.41023 | ||||||||
\(863\) | −2.59016e15 | −0.184191 | −0.0920954 | − | 0.995750i | \(-0.529356\pi\) | ||||
−0.0920954 | + | 0.995750i | \(0.529356\pi\) | |||||||
\(864\) | 6.40248e14 | 0.0452400 | ||||||||
\(865\) | −2.11496e16 | −1.48496 | ||||||||
\(866\) | −2.89024e16 | −2.01644 | ||||||||
\(867\) | 7.32933e15 | 0.508112 | ||||||||
\(868\) | 5.71973e16 | 3.94019 | ||||||||
\(869\) | 1.56150e16 | 1.06889 | ||||||||
\(870\) | 4.72934e15 | 0.321695 | ||||||||
\(871\) | −3.96549e15 | −0.268038 | ||||||||
\(872\) | −2.73492e16 | −1.83698 | ||||||||
\(873\) | 1.80354e15 | 0.120378 | ||||||||
\(874\) | 1.68185e15 | 0.111551 | ||||||||
\(875\) | −3.37186e15 | −0.222242 | ||||||||
\(876\) | −9.69748e15 | −0.635165 | ||||||||
\(877\) | −2.83381e15 | −0.184448 | −0.0922238 | − | 0.995738i | \(-0.529398\pi\) | ||||
−0.0922238 | + | 0.995738i | \(0.529398\pi\) | |||||||
\(878\) | 1.61359e16 | 1.04370 | ||||||||
\(879\) | −3.09437e15 | −0.198899 | ||||||||
\(880\) | 2.26483e16 | 1.44671 | ||||||||
\(881\) | 1.78252e16 | 1.13153 | 0.565765 | − | 0.824567i | \(-0.308581\pi\) | ||||
0.565765 | + | 0.824567i | \(0.308581\pi\) | |||||||
\(882\) | −2.44453e16 | −1.54212 | ||||||||
\(883\) | 2.31060e16 | 1.44857 | 0.724286 | − | 0.689499i | \(-0.242169\pi\) | ||||
0.724286 | + | 0.689499i | \(0.242169\pi\) | |||||||
\(884\) | −9.44557e15 | −0.588492 | ||||||||
\(885\) | 1.68029e15 | 0.104039 | ||||||||
\(886\) | 1.30995e16 | 0.806063 | ||||||||
\(887\) | 2.48053e16 | 1.51693 | 0.758465 | − | 0.651714i | \(-0.225950\pi\) | ||||
0.758465 | + | 0.651714i | \(0.225950\pi\) | |||||||
\(888\) | 2.52269e15 | 0.153318 | ||||||||
\(889\) | 1.63244e16 | 0.986000 | ||||||||
\(890\) | −4.64519e16 | −2.78842 | ||||||||
\(891\) | 1.62314e15 | 0.0968344 | ||||||||
\(892\) | 5.08242e16 | 3.01345 | ||||||||
\(893\) | 1.15725e16 | 0.681937 | ||||||||
\(894\) | −2.15981e15 | −0.126491 | ||||||||
\(895\) | −1.42263e16 | −0.828067 | ||||||||
\(896\) | 5.32542e16 | 3.08077 | ||||||||
\(897\) | −9.87702e14 | −0.0567894 | ||||||||
\(898\) | −4.74026e16 | −2.70883 | ||||||||
\(899\) | 4.04737e15 | 0.229877 | ||||||||
\(900\) | 1.11679e16 | 0.630432 | ||||||||
\(901\) | −6.72271e14 | −0.0377188 | ||||||||
\(902\) | −4.32713e15 | −0.241304 | ||||||||
\(903\) | −3.26265e16 | −1.80837 | ||||||||
\(904\) | −5.45739e16 | −3.00648 | ||||||||
\(905\) | −4.76345e16 | −2.60828 | ||||||||
\(906\) | 2.38502e16 | 1.29804 | ||||||||
\(907\) | −1.40277e16 | −0.758835 | −0.379417 | − | 0.925226i | \(-0.623876\pi\) | ||||
−0.379417 | + | 0.925226i | \(0.623876\pi\) | |||||||
\(908\) | −2.95565e15 | −0.158921 | ||||||||
\(909\) | −2.61803e15 | −0.139918 | ||||||||
\(910\) | −7.16460e16 | −3.80596 | ||||||||
\(911\) | −1.31685e16 | −0.695321 | −0.347660 | − | 0.937621i | \(-0.613024\pi\) | ||||
−0.347660 | + | 0.937621i | \(0.613024\pi\) | |||||||
\(912\) | 7.03277e15 | 0.369109 | ||||||||
\(913\) | −2.42989e16 | −1.26765 | ||||||||
\(914\) | 3.17154e16 | 1.64462 | ||||||||
\(915\) | 2.04323e16 | 1.05318 | ||||||||
\(916\) | 8.03466e16 | 4.11664 | ||||||||
\(917\) | −1.81816e16 | −0.925978 | ||||||||
\(918\) | −2.30475e15 | −0.116678 | ||||||||
\(919\) | 2.07390e16 | 1.04365 | 0.521823 | − | 0.853054i | \(-0.325252\pi\) | ||||
0.521823 | + | 0.853054i | \(0.325252\pi\) | |||||||
\(920\) | −6.16679e15 | −0.308479 | ||||||||
\(921\) | 1.06687e16 | 0.530497 | ||||||||
\(922\) | 1.33227e16 | 0.658526 | ||||||||
\(923\) | 1.95440e16 | 0.960294 | ||||||||
\(924\) | −4.06009e16 | −1.98308 | ||||||||
\(925\) | 2.68654e15 | 0.130441 | ||||||||
\(926\) | −3.82425e16 | −1.84581 | ||||||||
\(927\) | −7.43303e15 | −0.356638 | ||||||||
\(928\) | −1.13325e15 | −0.0540518 | ||||||||
\(929\) | −3.76027e16 | −1.78292 | −0.891462 | − | 0.453095i | \(-0.850320\pi\) | ||||
−0.891462 | + | 0.453095i | \(0.850320\pi\) | |||||||
\(930\) | 2.96746e16 | 1.39871 | ||||||||
\(931\) | −3.00633e16 | −1.40868 | ||||||||
\(932\) | −6.47319e16 | −3.01530 | ||||||||
\(933\) | −9.16050e15 | −0.424200 | ||||||||
\(934\) | −3.15656e16 | −1.45314 | ||||||||
\(935\) | −9.12797e15 | −0.417744 | ||||||||
\(936\) | −1.12417e16 | −0.511465 | ||||||||
\(937\) | 6.38433e15 | 0.288767 | 0.144383 | − | 0.989522i | \(-0.453880\pi\) | ||||
0.144383 | + | 0.989522i | \(0.453880\pi\) | |||||||
\(938\) | 2.42031e16 | 1.08832 | ||||||||
\(939\) | 1.77374e16 | 0.792919 | ||||||||
\(940\) | −8.22746e16 | −3.65648 | ||||||||
\(941\) | 3.29317e16 | 1.45503 | 0.727514 | − | 0.686093i | \(-0.240676\pi\) | ||||
0.727514 | + | 0.686093i | \(0.240676\pi\) | |||||||
\(942\) | 4.49335e16 | 1.97374 | ||||||||
\(943\) | 4.32869e14 | 0.0189035 | ||||||||
\(944\) | −3.59622e15 | −0.156135 | ||||||||
\(945\) | −1.17782e16 | −0.508398 | ||||||||
\(946\) | −5.83493e16 | −2.50400 | ||||||||
\(947\) | −3.81365e16 | −1.62711 | −0.813553 | − | 0.581491i | \(-0.802470\pi\) | ||||
−0.813553 | + | 0.581491i | \(0.802470\pi\) | |||||||
\(948\) | −3.44723e16 | −1.46226 | ||||||||
\(949\) | 1.03956e16 | 0.438413 | ||||||||
\(950\) | 2.03855e16 | 0.854754 | ||||||||
\(951\) | −4.35232e15 | −0.181438 | ||||||||
\(952\) | 2.97328e16 | 1.23235 | ||||||||
\(953\) | 3.05216e16 | 1.25776 | 0.628878 | − | 0.777504i | \(-0.283515\pi\) | ||||
0.628878 | + | 0.777504i | \(0.283515\pi\) | |||||||
\(954\) | −1.55137e15 | −0.0635622 | ||||||||
\(955\) | −3.35262e16 | −1.36573 | ||||||||
\(956\) | −8.68902e16 | −3.51927 | ||||||||
\(957\) | −2.87298e15 | −0.115696 | ||||||||
\(958\) | −2.52586e16 | −1.01135 | ||||||||
\(959\) | 2.17077e16 | 0.864193 | ||||||||
\(960\) | 1.59038e16 | 0.629519 | ||||||||
\(961\) | −1.29429e13 | −0.000509394 0 | ||||||||
\(962\) | −5.24348e15 | −0.205190 | ||||||||
\(963\) | −1.46294e16 | −0.569221 | ||||||||
\(964\) | 3.68904e16 | 1.42722 | ||||||||
\(965\) | −9.58435e15 | −0.368691 | ||||||||
\(966\) | 6.02837e15 | 0.230582 | ||||||||
\(967\) | −2.94657e15 | −0.112065 | −0.0560327 | − | 0.998429i | \(-0.517845\pi\) | ||||
−0.0560327 | + | 0.998429i | \(0.517845\pi\) | |||||||
\(968\) | 1.18564e16 | 0.448371 | ||||||||
\(969\) | −2.83442e15 | −0.106582 | ||||||||
\(970\) | −2.34053e16 | −0.875122 | ||||||||
\(971\) | 1.54015e16 | 0.572607 | 0.286304 | − | 0.958139i | \(-0.407573\pi\) | ||||
0.286304 | + | 0.958139i | \(0.407573\pi\) | |||||||
\(972\) | −3.58332e15 | −0.132471 | ||||||||
\(973\) | 6.33204e16 | 2.32768 | ||||||||
\(974\) | 4.18174e15 | 0.152856 | ||||||||
\(975\) | −1.19718e16 | −0.435146 | ||||||||
\(976\) | −4.37299e16 | −1.58054 | ||||||||
\(977\) | −6.06880e14 | −0.0218114 | −0.0109057 | − | 0.999941i | \(-0.503471\pi\) | ||||
−0.0109057 | + | 0.999941i | \(0.503471\pi\) | |||||||
\(978\) | −2.19258e16 | −0.783595 | ||||||||
\(979\) | 2.82186e16 | 1.00284 | ||||||||
\(980\) | 2.13735e17 | 7.55321 | ||||||||
\(981\) | 9.34516e15 | 0.328403 | ||||||||
\(982\) | −1.22320e15 | −0.0427450 | ||||||||
\(983\) | 9.73684e15 | 0.338356 | 0.169178 | − | 0.985586i | \(-0.445889\pi\) | ||||
0.169178 | + | 0.985586i | \(0.445889\pi\) | |||||||
\(984\) | 4.92678e15 | 0.170251 | ||||||||
\(985\) | −1.20158e16 | −0.412907 | ||||||||
\(986\) | 4.07943e15 | 0.139405 | ||||||||
\(987\) | 4.14802e16 | 1.40960 | ||||||||
\(988\) | −2.68064e16 | −0.905890 | ||||||||
\(989\) | 5.83703e15 | 0.196161 | ||||||||
\(990\) | −2.10642e16 | −0.703965 | ||||||||
\(991\) | 2.00885e16 | 0.667640 | 0.333820 | − | 0.942637i | \(-0.391662\pi\) | ||||
0.333820 | + | 0.942637i | \(0.391662\pi\) | |||||||
\(992\) | −7.11063e15 | −0.235014 | ||||||||
\(993\) | 6.56377e15 | 0.215741 | ||||||||
\(994\) | −1.19286e17 | −3.89909 | ||||||||
\(995\) | −2.67610e16 | −0.869912 | ||||||||
\(996\) | 5.36434e16 | 1.73416 | ||||||||
\(997\) | −3.71564e16 | −1.19457 | −0.597283 | − | 0.802030i | \(-0.703753\pi\) | ||||
−0.597283 | + | 0.802030i | \(0.703753\pi\) | |||||||
\(998\) | −7.41430e16 | −2.37057 | ||||||||
\(999\) | −8.61999e14 | −0.0274092 |
(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.1.3 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.c.1.3 | ✓ | 27 | 1.1 | even | 1 | trivial |